NASASpaceFlight.com Forum
General Discussion => New Physics for Space Technology => Topic started by: Chris Bergin on 12/12/2014 11:40 AM

Thread 1:
http://forum.nasaspaceflight.com/index.php?topic=29276.0
Problems with Thread 1 explained (note the things to avoid in the new thread):
http://forum.nasaspaceflight.com/index.php?topic=29276.msg1301657#msg1301657
Thus Thread 2, with more focus on space flight applications to ensure this can have a healthy home here. Remember, this is a space flight site.

I really do hope they EM drive theorists are onto something; if it works, and depending on how well it works, the space flight applications range from replacing maneuvering thrusters to decreasing the cruising times of missions. If, by some miracle of physics, EM drives work spectacularly well, they could replace chemical rocketry for orbital insertion completely and make space access trivial.
If EM drives offer any degree of thrust, telecommunications and science missions will benefit considerably. If it's possible to supply a lot of thrust, they'll literally change the destiny of humanity. But first, we need to know if they work or not. The theories are certainly intriguing, and there are a fair few anecdotal hints that there is something there, but as the several hundred pages of the previous thread show, figuring out what's going on is a real bear.

Chris, thanks for cleaning up the old thread. There is a lot of good discussion and information in there.
EM drives would have to push or pull against something. The favorite explanation seems to be the Mach Effect, but is there any experimental evidence that points to the Mach Effect being real? Since the origin of inertia seems to be the key, what about the Higgs field? Local gravitational field?
Although I have my doubts, the potential payoff for spaceflight is so large, this should be looked into, but the experiments need to be rigorously done and repeatable.

Thanks, Chris.
I really do want to follow this, on the chance that it bears out. There was some good stuff on that thread, but a low s/n ratio combined with a high post count, at the longago point I stopped following.
Hoping this will do better. (Might even suggest you leave the old thread open to allow this one to stay cleaner, but know that wouldn't work!)
Cheers, Martin

Has there been the least indication yet when we are too get some more results in relation to those who are experimenting in this area?

Has there been the least indication yet when we are too get some more results in relation to those who are experimenting in this area?
This paper, presented at the Joint Propulsion Conference this past summer in Cleveland, should address your question.

Wow, great paper, Gary! Thanks for pointing it out. I see SSI's efforts got a mention as well.
Interesting this seems to be picking up steam just as Hollywood put out a SciFi movie that takes Spacetime, wormholes, and gravity seriously.

Well, looking at the thermistor data with the PZT stack mach effect thruster, whatever it's doing doesn't look like a transient thermal effect...

That is a very interesting paper. Very clean results compared to previous presentations and the Hoyl and Narliker approach to theory looks promising. It needs to be emphasised that this is an ME device, not EM, and that the paper reports that the theory is a work in progress.

Only had a quick look at the paper. I would like to know the positioning of the accelerometer. If this is a displacement or zero set type balance the acceleration during the constant thrust segment should be zero. Possibly the mounting accounts for this ??
Edit: OK. The "accelerometer" is between the PZT. It is not the system accelerating, just an indication that the transducers are receiving power.

Well, looking at the thermistor data with the PZT stack mach effect thruster, whatever it's doing doesn't look like a transient thermal effect...
I can attest that it is not thermal. It works in a vacuum. It works in a Faraday cage and it works when you reverse the device (the thrust reverses).

That is a very interesting paper. Very clean results compared to previous presentations and the Hoyl and Narliker approach to theory looks promising. It needs to be emphasised that this is an ME device, not EM, and that the paper reports that the theory is a work in progress.
Quite so. Perhaps the thread needs to be called "Space Drive" (a la Arthur C. Clarke), or "Propellantless Propulsion."

"With more focus on space flight applications " (as per http://forum.nasaspaceflight.com/index.php?topic=36313.msg1301658#msg1301658) the metric chosen by the NASA's "Anomalous" report was the thrust force per power input.
EDIT: Dimensions for Shawyer's and Brady et.al.'s cavities updated as per latest estimates on 05/20/15
Here is a comparison of reported measurements for EM Drives and for the latest report by Fearn, Zachar, Woodward & Wanser.
Notice that the force per power input reported by Fearn, Zachar, Woodward & Wanser is several orders of magnitude lower than the "EM drives". Actually it is barely (3.5 times higher) more than the force per power input of a photon rocket:
reported measurement ForcePerPowerInput (milliNewtons/kW)
(* Cannae Superconducting *) 761.9 to 952.4
(* Shawyer Demo *) 80 to 243
(* Shawyer Experimental *) 18.82
(* Brady c TE mode *) 21.31
(* Brady a TM mode*) 5.396
(* Brady b TM mode*) 3.000
(*Fearn, Zachar, Woodward & Wanser*) 0.01176
lengths in meter
rfFrequency in 1/second (microwave frequency during test)
power in watts
force in milliNewtons
force per PowerInput in milliNewtons/kW
c= 299705000 m/s (speed of light in air)
c= 299792458 m/s (speed of light in vacuum) (for Cannae Superconducting)
(the difference between c in air compared to c in vacuum is negligible)
Note: SmallDiameter for Shawyer's EM Drives obtained from his reported ShawyerDesignFactor .
Force/PowerInput of a Photon Rocket = 1 / c
(* Cannae Superconducting *)
rfFrequency = 1.047*10^9;
cavityLength = 0.01+0.004+0.006+0.01 = 0.03;
bigDiameter =(22.862*(0.00430)) = 0.220;
smallDiameter = bigDiameter2*0.01=0.200;
power = 10.5
Q = 1.1*(10^7)
measured force = 8 to 10
measured ForcePerPowerInput = 761.9 to 952.4
Force/PowerInput of a Photon Rocket =0.003337
measured ForcePerPowerInput to the one of a photon rocket = 228,400 to 285,500
(* Shawyer Experimental *)
rfFrequency=2.45*10^9;
cavityLength=0.156;(estimated from photographs)
bigDiameter=0.16; (given by Shawyer)
smallDiameter=0.1025; (obtained from the Design Factor, bigDiameter and frequency provided by Shawyer)
Design Factor = 0.497;
power = 850;
Q = 5900 ;
measured force = 16
measured ForcePerPowerInput = 18.82
Force/PowerInput of a Photon Rocket =0.003337
measured ForcePerPowerInput to the one of a photon rocket =5,640
(* Shawyer Demo *)
rfFrequency=2.45*10^9;
cavityLength=0.345;(estimated from photographs)
bigDiameter=0.28;(given by Shawyer)
smallDiameter= 0.09613; (from the Design Factor, bigDiameter and frequency provided by Shawyer)
Design Factor = 0.844;
power = 421 to 1200;
Q = 45000;
(measured force = 102.30 milliNewtons only reported for 421 watts, 243 milliNewtons/kW )
measured ForcePerPowerInput = 80 to 243
Force/PowerInput of a Photon Rocket =0.003337
measured ForcePerPowerInput to the one of a photon rocket =23,980 to 72,830
All Brady cases have the following dimensions:
cavityLength=0.2286; (provided by Paul March)
bigDiameter=0.2794; (provided by Paul March)
smallDiameter=0.15875; (provided by Paul March)
(* Brady a TM mode*)
rfFrequency=1.9326*10^9;
power = 16.9
Q = 7320
measured force = 0.0912
measured ForcePerPowerInput = 5.396
Force/PowerInput of a Photon Rocket =0.003337
measured ForcePerPowerInput to the one of a photon rocket =1,617.2
(* Brady b TM mode*)
rfFrequency=1.9367*10^9;
power = 16.7
Q = 18100
measured force = 0.0501
measured ForcePerPowerInput = 3.000
Force/PowerInput of a Photon Rocket =0.003337
measured ForcePerPowerInput to the one of a photon rocket =899.12
(* Brady c TE mode *)
rfFrequency = 1.8804*10^9;
power = 2.6
Q = 22000
measured force = 0.05541
measured ForcePerPowerInput = 21.31
Force/PowerInput of a Photon Rocket =0.003337
measured ForcePerPowerInput to the one of a photon rocket =6,386.7
(* Fearn, Zachar, Woodward & Wanser*)
rfFrequency = 39,300;
power = 170
measured force = 0.002
measured ForcePerPowerInput = 0.01176
Force/PowerInput of a Photon Rocket =0.003337
measured ForcePerPowerInput to the one of a photon rocket = 3.526

"With more focus on space flight applications " (as per http://forum.nasaspaceflight.com/index.php?topic=36313.msg1301658#msg1301658) the metric chosen by the NASA's "Anomalous" report was the thrust force per power input.
Here is a comparison of reported measurements for EM Drives and for the latest report by Fearn, Zachar, Woodward & Wanser.
Notice that the force per power input reported by Fearn, Zachar, Woodward & Wanser is several orders of magnitude lower than the "EM drives". Actually it is barely (3.5 times higher) more than the force per power input of a photon rocket:
reported measurement ForcePerPowerInput (milliNewtons/kW)
(* Cannae Superconducting *) 761.9 to 952.4
(* Shawyer Demo *) 80 to 243
(* Shawyer Experimental *) 18.82
(* Brady c TE mode *) 21.31
(* Brady a TM mode*) 5.396
(* Brady b TM mode*) 3.000
(*Fearn, Zachar, Woodward & Wanser*) 0.01176
lengths in meter
rfFrequency in 1/second (microwave frequency during test)
power in watts
force in milliNewtons
force per PowerInput in milliNewtons/kW
c= 299705000 m/s (speed of light in air)
c= 299792458 m/s (speed of light in vacuum) (for Cannae Superconducting)
(the difference between c in air compared to c in vacuum is negligible)
Note: SmallDiameter for Shawyer's EM Drives obtained from his reported ShawyerDesignFactor .
Force/PowerInput of a Photon Rocket = 1 / c
(* Cannae Superconducting *)
rfFrequency = 1.047*10^9;
cavityLength = 0.01+0.004+0.006+0.01 = 0.03;
bigDiameter =(22.862*(0.00430)) = 0.220;
smallDiameter = bigDiameter2*0.01=0.200;
power = 10.5
Q = 1.1*(10^7)
measured force = 8 to 10
measured ForcePerPowerInput = 761.9 to 952.4
Force/PowerInput of a Photon Rocket =0.003336
measured ForcePerPowerInput to the one of a photon rocket = 228,400 to 285,500
(* Shawyer Experimental *)
rfFrequency=2.45*10^9;
cavityLength=0.156;
bigDiameter=0.16;
smallDiameter=0.127546;
power = 850
Q = 5900
measured force = 16
measured ForcePerPowerInput = 18.82
Force/PowerInput of a Photon Rocket =0.003337
measured ForcePerPowerInput to the one of a photon rocket =5,640
(* Shawyer Demo *)
rfFrequency=2.45*10^9;
cavityLength=0.345;
bigDiameter=0.28;
smallDiameter= 0.128853
power = 421 to 1200
Q = 45000
(measured force = 102.30 milliNewtons only reported for 421 watts, 243 milliNewtons/kW )
measured ForcePerPowerInput = 80 to 243
Force/PowerInput of a Photon Rocket =0.003337
measured ForcePerPowerInput to the one of a photon rocket =23,980 to 72,830
All Brady cases have the following dimensions:
cavityLength=0.332;
bigDiameter=0.397;
smallDiameter=0.244;
(* Brady a TM mode*)
rfFrequency=1.9326*10^9;
power = 16.9
Q = 7320
measured force = 0.0912
measured ForcePerPowerInput = 5.396
Force/PowerInput of a Photon Rocket =0.003337
measured ForcePerPowerInput to the one of a photon rocket =1,617.2
(* Brady b TM mode*)
rfFrequency=1.9367*10^9;
power = 16.7
Q = 18100
measured force = 0.0501
measured ForcePerPowerInput = 3.000
Force/PowerInput of a Photon Rocket =0.003337
measured ForcePerPowerInput to the one of a photon rocket =899.12
(* Brady c TE mode *)
rfFrequency = 1.8804*10^9;
power = 2.6
Q = 22000
measured force = 0.05541
measured ForcePerPowerInput = 21.31
Force/PowerInput of a Photon Rocket =0.003337
measured ForcePerPowerInput to the one of a photon rocket =6,386.7
(* Fearn, Zachar, Woodward & Wanser*)
rfFrequency = 39,300;
power = 170
measured force = 0.002
measured ForcePerPowerInput = 0.01176
Force/PowerInput of a Photon Rocket =0.003337
measured ForcePerPowerInput to the one of a photon rocket = 3.526
While the force per power input is smaller, at least the ME work seems to be much furhter along. After skimming the newest paper I also noticed that there is an additional paper that was published this year focusing on the experimental results.
http://www.researchgate.net/profile/Heidi_Fearn/publication/264040874_EXPtests13/links/00b4953c9a2675bcc0000000?ev=pub_ext_doc_dl&origin=publication_list&inViewer=true (http://www.researchgate.net/profile/Heidi_Fearn/publication/264040874_EXPtests13/links/00b4953c9a2675bcc0000000?ev=pub_ext_doc_dl&origin=publication_list&inViewer=true)
Only half way through reading this paper but it seems like more more effort was given to potential spurious forces, compared to the published information we have available for the EM Drives.

I'm glad to see the discussion continued in this thread. I must admit, I felt disappointed at the prospect of losing this resource and the small band of interested theorists and experimentalists exploring what may appear to be the impossible, but which may ultimately result in profound space flight applications.
Might I suggest, that if this forum turns out not to be the right place in the future (e.g., if the thread is removed again), that all those who maintain an interest in the topic to congregate in the http://www.reddit.com/r/emdrive forum. In fact, I suggest that you bookmark that page now for future reference.
I too do not appreciate personal attacks, which have no place in this kind of discussion, and so I understand the desire to keep the thread clean. On the other hand, this topic is too important not to keep alive.
Can I just thank you for providing that link as it appears to be a good source of information on this topic.

"With more focus on space flight applications " (as per http://forum.nasaspaceflight.com/index.php?topic=36313.msg1301658#msg1301658) the metric chosen by the NASA's "Anomalous" report was the thrust force per power input.
Here is a comparison of reported measurements for EM Drives and for the latest report by Fearn, Zachar, Woodward & Wanser.
Notice that the force per power input reported by Fearn, Zachar, Woodward & Wanser is several orders of magnitude lower than the "EM drives". Actually it is barely (3.5 times higher) more than the force per power input of a photon rocket:
reported measurement ForcePerPowerInput (milliNewtons/kW)
(* Cannae Superconducting *) 761.9 to 952.4
(* Shawyer Demo *) 80 to 243
(* Shawyer Experimental *) 18.82
(* Brady c TE mode *) 21.31
(* Brady a TM mode*) 5.396
(* Brady b TM mode*) 3.000
(*Fearn, Zachar, Woodward & Wanser*) 0.01176
...
Quite true. "And yet, it moves." :)

....
While I was sceptic and still am, I learned a lot of interesting things from the previous thread, and enjoyed it even with its defaults.
It's great to have you posting again here, Frobnicat, as your always thoughtfully scientific and frobnicating posts have been one of the main attractions of this thread.
Welcome back, frobnicat !
I hope that Mulletron & all the others return to post here again as well, and sooner rather than later !

Excellent stuff indeed, I will be perusing the previous thread in an attempt to better understand the logic. Easy enough for me to ignore the nonsense. Hoping we see more evidence from the many experiments underway to fuel the discussion. Many thanks to all the contributing members, truly a thought provoking thread.

What is the latest news on the EM Drive? What are they planning to do next? If the EM Drive does work, this will be amazing, space exploration will change.

May I suggest that people interested in "Mach effect" (reality of which having obvious consequences on directions advanced spaceflight can take) contribute on a thread with a more appropriate explicit topic (and historical content) : Propellantless Field Propulsion and application. The risk in splitting the somewhat frozen propellantless discussion of late would be to make it even harder to revive some activity, but EM and ME approaches are two very different kind of theories and devices, interwining of both topic discussion in a single thread was one of the reason of the chaos that plagued the 1st EM drive thread.
Anyhow, for those interested in Mach effect, here are two versions of results from attempt of Woodward (2008...) at "proof of effect" exhumed from Propellantless thread:
http://forum.nasaspaceflight.com/index.php?action=dlattach;topic=13020.0;attach=260412
http://forum.nasaspaceflight.com/index.php?action=dlattach;topic=13020.0;attach=260481
Haven't read in detail yet.
I won't crosspost here my posts about that (if I have the courage to address some of it deeper)
http://forum.nasaspaceflight.com/index.php?topic=13020.msg1304798#msg1304798

May I suggest that people interested in "Mach effect" (reality of which having obvious consequences on directions advanced spaceflight can take) contribute on a thread with a more appropriate explicit topic (and historical content) : Propellantless Field Propulsion and application. The risk in splitting the somewhat frozen propellantless discussion of late would be to make it even harder to revive some activity, but EM and ME approaches are two very different kind of theories and devices, interwining of both topic discussion in a single thread was one of the reason of the chaos that plagued the 1st EM drive thread.
Anyhow, for those interested in Mach effect, here are two versions of results from attempt of Woodward (2008...) at "proof of effect" exhumed from Propellantless thread:
http://forum.nasaspaceflight.com/index.php?action=dlattach;topic=13020.0;attach=260412
http://forum.nasaspaceflight.com/index.php?action=dlattach;topic=13020.0;attach=260481
Haven't read in detail yet.
I won't crosspost here my posts about that (if I have the courage to address some of it deeper)
http://forum.nasaspaceflight.com/index.php?topic=13020.msg1304798#msg1304798
Good points, frobnicat, besides the PropellantLess thread:
http://forum.nasaspaceflight.com/index.php?topic=13020.0
the Woodward effect fans have had their own threads @ NASASpaceFlight, for example this one, completely dedicated to the Woodward effect:
http://forum.nasaspaceflight.com/index.php?topic=31037.0
The reported "thrust" force/(power input) of the latest Woodward experiments (Fearn, Zachar, Woodward & Wanser) is about 2000 times less than the NASA Brady et.al TE mode and about 20,000 times less than the Shawyer Demo
In other words, it takes (for the latest Woodward experiments) 3 to 4 orders of magnitude greater input power to produce the same level of what is reported as "thrust" force

May I suggest that people interested in "Mach effect" (reality of which having obvious consequences on directions advanced spaceflight can take) contribute on a thread with a more appropriate explicit topic (and historical content) : Propellantless Field Propulsion and application. The risk in splitting the somewhat frozen propellantless discussion of late would be to make it even harder to revive some activity, but EM and ME approaches are two very different kind of theories and devices, interwining of both topic discussion in a single thread was one of the reason of the chaos that plagued the 1st EM drive thread.
Anyhow, for those interested in Mach effect, here are two versions of results from attempt of Woodward (2008...) at "proof of effect" exhumed from Propellantless thread:
http://forum.nasaspaceflight.com/index.php?action=dlattach;topic=13020.0;attach=260412
http://forum.nasaspaceflight.com/index.php?action=dlattach;topic=13020.0;attach=260481
Haven't read in detail yet.
I won't crosspost here my posts about that (if I have the courage to address some of it deeper)
http://forum.nasaspaceflight.com/index.php?topic=13020.msg1304798#msg1304798
Good points, frobnicat, besides the PropellantLess thread:
http://forum.nasaspaceflight.com/index.php?topic=13020.0
the Woodward effect fans have had their own threads @ NASASpaceFlight, for example this one, completely dedicated to the Woodward effect:
http://forum.nasaspaceflight.com/index.php?topic=31037.0
The reported "thrust" force/(power input) of the latest Woodward experiments (Fearn, Zachar, Woodward & Wanser) is about 2000 times less than the NASA Brady et.al TE mode and about 20,000 times less than the Shawyer Demo
In other words, it takes (for the latest Woodward experiments) 3 to 4 orders of magnitude greater input power to produce the same level of what is reported as "thrust" force
Why does this matter? I was under the impression that while both lines of inquiry hold incredible promise. They still require more research and testing to get to the point where a wider audience would be willing to accept them.

The reported "thrust" force/(power input) of the latest Woodward experiments (Fearn, Zachar, Woodward & Wanser) is about 2000 times less than the NASA Brady et.al TE mode and about 20,000 times less than the Shawyer Demo
In other words, it takes (for the latest Woodward experiments) 3 to 4 orders of magnitude greater input power to produce the same level of what is reported as "thrust" force
Why does this matter? I was under the impression that while both lines of inquiry hold incredible promise. They still require more research and testing to get to the point where a wider audience would be willing to accept them.
As Chris Bergin made clear, the purpose of this forum is to deal with SPACEFLIGHT APPLICATIONS (of EM Drives: those propellantless drives comprised of a microwave cavity as the devices tested by Shawyer in the UK, Prof. Juan Yang in China and Brady, March, White, et.al. at NASA):
focus on space flight applications to ensure this can have a healthy home here.
It matters because the amount of power required to produce a given level of thrust is of vital importance for spaceflight applications.
The fact that the latest Woodward experiments (Fearn, Zachar, Woodward & Wanser) show that it takes 20,000 times more power to produce a given level of thrust than the power required to produce the same thrust for the EM Drive (Shawyer demo) is extremely important for spaceflight applications.

The reported "thrust" force/(power input) of the latest Woodward experiments (Fearn, Zachar, Woodward & Wanser) is about 2000 times less than the NASA Brady et.al TE mode and about 20,000 times less than the Shawyer Demo
In other words, it takes (for the latest Woodward experiments) 3 to 4 orders of magnitude greater input power to produce the same level of what is reported as "thrust" force
Why does this matter? I was under the impression that while both lines of inquiry hold incredible promise. They still require more research and testing to get to the point where a wider audience would be willing to accept them.
As Chris Bergin made clear, the purpose of this forum is to deal with SPACEFLIGHT APPLICATIONS (of EM Drives: those propellantless drives comprised of a microwave cavity as the devices tested by Shawyer in the UK, Prof. Juan Yang in China and Brady, March, White, et.al. at NASA):
focus on space flight applications to ensure this can have a healthy home here.
It matters because the amount of power required to produce a given level of thrust is of vital importance for spaceflight applications.
The fact that the latest Woodward experiments (Fearn, Zachar, Woodward & Wanser) show that it takes 20,000 times more power to produce a given level of thrust than the power required to produce the same thrust for the EM Drive (Shawyer demo) is extremely important for spaceflight applications.
I get that efficiency matters. What ever propulsion device yields the highest thrust for the least amount of input energy is a superior device. That said since you also wrote a critique of the Eagle Works test showing that the results could be thermal effects I would think the Thrust figures of either EM Drives or MET thrusters would be consider as simply a measure of how far both approaches have to go to be useful. It could be that a large part of the EM Drive thrust numbers are thermal and will be reduced when tested in vacuum. It could also be that the MET results are small only because of the materials in use. It could also be that neither of these things will ever work. My point being, I do not see how the thrust figures as they exist today can be used as a useful indicator of which area of research should get preferential treatment. They are simply mile markers that cannot be easily compared between the two types of propulsion ideas.

The reported "thrust" force/(power input) of the latest Woodward experiments (Fearn, Zachar, Woodward & Wanser) is about 2000 times less than the NASA Brady et.al TE mode and about 20,000 times less than the Shawyer Demo
In other words, it takes (for the latest Woodward experiments) 3 to 4 orders of magnitude greater input power to produce the same level of what is reported as "thrust" force
Why does this matter? I was under the impression that while both lines of inquiry hold incredible promise. They still require more research and testing to get to the point where a wider audience would be willing to accept them.
As Chris Bergin made clear, the purpose of this forum is to deal with SPACEFLIGHT APPLICATIONS (of EM Drives: those propellantless drives comprised of a microwave cavity as the devices tested by Shawyer in the UK, Prof. Juan Yang in China and Brady, March, White, et.al. at NASA):
focus on space flight applications to ensure this can have a healthy home here.
It matters because the amount of power required to produce a given level of thrust is of vital importance for spaceflight applications.
The fact that the latest Woodward experiments (Fearn, Zachar, Woodward & Wanser) show that it takes 20,000 times more power to produce a given level of thrust than the power required to produce the same thrust for the EM Drive (Shawyer demo) is extremely important for spaceflight applications.
question is: are those thrust to power rations result of the physics itself?
if they find a better material than PZT stacks to test Mach Effects, suddenly, the efficiency may be much higher.
to what part the thrust to power ratio of each system is an engineering or a physics problem?

As Chris Bergin made clear, the purpose of this forum is to deal with SPACEFLIGHT APPLICATIONS (of EM Drives: those propellantless drives comprised of a microwave cavity as the devices tested by Shawyer in the UK, Prof. Juan Yang in China and Brady, March, White, et.al. at NASA):
focus on space flight applications to ensure this can have a healthy home here.
Why is this prescription by Chris Bergin being ignored?
Although the latest Woodward experiments (Fearn, Zachar, Woodward & Wanser) show that it takes 20,000 times more power to produce a given level of thrust than the power required to produce the same thrust for the EM Drive (Shawyer demo), and therefore these experiments do not constitute "EM Drive Spaceflight Applications" (as instructed by Chris Bergin) Woodward fans persist on carrying a debate on this thread rather than their own Woodward thread.
Frankly, I don't understand what is the goal being pursued here by Woodwardeffect fans to insist to carry arguments concerning Woodward's theory and experiments in this thread.
The curtailment of the previous EM Drive thread by this forum's moderator was due to disruptive discussions regarding the validity of the Woodward effect, including a negative review of Woodward's book by a physicist.
As remarked by Frobnicat,
May I suggest that people interested in "Mach effect" (reality of which having obvious consequences on directions advanced spaceflight can take) contribute on a thread with a more appropriate explicit topic (and historical content) :>> << As reminded by managing editor, NSF is about space flight. Given the turn taken by the thread, the admin intervention is quite understandable, and most of the content wasn't thrashed, thanks. While the "space drives" in general are on topic here if proven, the reality of any effect at all (and with what possible backing theories) is still controversial, and this open question is more a matter of fundamental science and has interest in and by itself beyond space flight. Since discussing those theoretical and experimental aspects are only marginally appropriate on this forum then that could proceed "preemptively" at other more appropriate place. Otherwise some talks will be rather contrived ( how make comment sound "space flight relevant" while it's not directly )
As previously remarked, there is a thread in this forum exclusively dedicated to the Woodward effect:
http://forum.nasaspaceflight.com/index.php?topic=31037.0
If the Woodward fans are looking for subjects to debate in the Woodward thread, here are a few suggestions you can add to such a discussion:
1) Extremely small reported thrust force/power input of the latest Woodward experiments (20.000 times less than Shawyer's demo and only barely more than the thrust of military search light acting as a photon rocket)
2) Recall Woodward's own words on his methodology:
http://forum.nasaspaceflight.com/index.php?action=dlattach;topic=13020.0;attach=260412
After carrying out a variety of experiments designed to exploit the presumed existence of Mach effects to produce small thrusts that yielded varying results, the decision was taken to carry out an experiment to test for the existence of such effects in the simplest of all possible circumstances. The aim was to settle the question of the existence the effects. Underlying physics suggests that these effects should exist; but in some experiments the effects expected were either not present, or much smaller than predicted. Without experimental evidence that the predicted Mach effects in fact do exist, situations in which they are small or not present may be taken as evidence that Mach effects do not exist.
Due to the extremely small level of thrust/power input (20,000 times less than Shawyer's demo) I am personally not interested in pursuing this Woodward debate, because these experiments show a level of thrust/power input that is so small that it does not constitute "Spaceflight Applications"
If there would be Woodward effect experiments with a similar or higher thrust/powerinput as the Shawyer demo, I would be interested in pursuing this. My approach then would be to model the thermomechanical and piezoelectric stresses in the Woodward experiment (for example with finiteelement analysis) which to my knowledge has not been presented for the Woodward experiments.

...That said since you also wrote a critique of the Eagle Works test showing that the results could be thermal effects I would think the Thrust figures of either EM Drives or MET thrusters would be consider as simply a measure of how far both approaches have to go to be useful. It could be that a large part of the EM Drive thrust numbers are thermal and will be reduced when tested in vacuum. ...
The technical paper I wrote concerned a thermomechanical effect that can explain the NASA Eagleworks truncated cone experimental results for the TE (transverse electric) mode both quantitatively and the initial impulsive rise timewise response. I showed that it is incorrect to posit (as some have done) that a thermal effect cannot produce an impulsivelike rise in the same timeframe as the NASA Eagleworks experiments.
Please also notice that it is incorrect to posit the following (if this was written in reference to my paper)
It could be that a large part of the EM Drive thrust numbers are thermal and will be reduced when tested in vacuum.
Because the thermomechanical effect I addressed in my technical paper does not at all need an atmosphere to take place. As remarked in my paper, the same results would be expected in a vacuum.
Besides the effect discussed in my technical paper regarding the NASA Eagleworks truncated cone TE experiments, the following paper by Oak Ridge Lab:
http://web.ornl.gov/~webworks/cppr/y2001/pres/111404.pdf
addresses yet another thermal effect, specifically discussing the Woodward/Mahood experiments, which also can take place in a vacuum and does not need an atmosphere to take place.
A thermal effect that can take place in a vacuum that (as far as I know) has not been adequately explored (through numerical analysis) to explain the extremely small thrust/powerinput results of the latest Fearn et.al experiments is the type of thermal recoil due to thermal radiation effect that has explained the Pioneer anomaly:
http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.108.241101

@Rodal,
Thank you for the clarification. That said I must say I am very cloudy on how anyone can have any interesting "Space Flight Applications" discussions about either of these technologies. Mainly because I am assuming that when someone uses the term "Space Flight Applications" they are talking about how these technologies can be used in different mission profiles. If that is the case then it doesnt matter what the technology is, the only thing that matters is the performance of the technology. Which would lead me to ask why even bother discussing any technology. Why not only have each thread in this forum focusing on a specific performance profile?
I have no objections to moving discussions about Mach Effect propulsion to another thread that is focused on just Mach Effects. The only reason I inquired about your comment regarding thrust comparisons is because given what we know, neither of them are ready for application today or even in the short term.
Anyway, I shall return to my lurker's seat while I await more EmDrive results.

Some things don't scale  Woodward is one. Another with a much better chance is the Sagnac effect, the only challenge is getting anything useful out of them. At a larger scale it would be awesome if Stirling engines would scale.
EmDrive will stay in the lab

Some things don't scale  Woodward is one. Another with a much better chance is the Sagnac effect, the only challenge is getting anything useful out of them. At a larger scale it would be awesome if Stirling engines would scale.
EmDrive will stay in the lab
I will avoid the obvious joke about the fact that your insight doesn't scale...
Woodward effect... And yet it moves! (HMXHMX I think)
Sagnac effect... hmmm
By Stirling engines I presume you mean ASRG. It will never provide multiKWMW power. It doesn't scale.
You claim to have knowledge of scaling of systems. It is quite apparent you do not.

@Birchoff
Thank you for your comments. If this was my forum, I would also prefer to discuss all these propellantless drives together, including their R&D and theoretical foundations; I miss Mulletron & others' discussions. However, this is not our house; we are just guests. Things got very rowdy, after which the host closed the door for a few days and warned us that we are welcome here only under these conditions. Otherwise the host will close the door again.

First, thanks to Chris for opening this new thread.
That said, some definitions might be in order to avoid confusion.
Stirling Engine: The version I am familiar with is proven old line technology, essentially a temperature difference engine. I have seen DIY versions on YouTube and elsewhere, and read of others that can act as low power solar generators, but have no idea how this might pertain to spaceflight. What is 'ASRG?'
Sagnac effect. I have not heard of this before.

First, thanks to Chris for opening this new thread.
That said, some definitions might be in order to avoid confusion.
Stirling Engine: The version I am familiar with is proven old line technology, essentially a temperature difference engine. I have seen DIY versions on YouTube and elsewhere, and read of others that can act as low power solar generators, but have no idea how this might pertain to spaceflight. What is 'ASRG?'
Sagnac effect. I have not heard of this before.
ASRG is advanced Stirling radioisotope generator. It is purposed to generate more power than the traditional RTG at the cost of having moving parts.
The MSL rover has an RTG capable of 100W. This is the current stateoftheart wrt RTG's.
Sagnac effect wrt to space flight is bunkum, IMHO...

Ok, did some googling.
First, to clarify things: I live in Alaska, right at the edge of the wilderness. I own property in the wilderness. Some years ago, I was contemplating putting a cabin on that property  until my back told the rest of me in no uncertain terms that wasn't going to work. Prior to that, though, I did some research on power generation, which is how I came to be aware of Stirling Engines. The ones I was looking at were small  about the size of a larger bicycle pump, and not much more complex. Given a heat source, they could generate electricity, but not much  but then again, they didn't need much of a heat source. I figured just one wasn't going to do the trick. Then I thought about it, and realized as small as they were, I could use the same heat source (wood stove) to power maybe six or eight of the things, hence generating six or eight times the power.
That said, to me ASRG looks both doable and noncontroversial. I don't grasp how it could be used for spaceflight propulsion, but it should be adequate for a Martian rover, automated station, or even a small manned installation.
The Sagnac effect also looks like proven technology, useful for determining terrestrial location. To my mind, its essentially a way of 'tricking light via rotation.' This gives me half an idea relevant to the EM drive:
Suppose the whole copper frustum was rotating very, very, fast on its axis, AND you had the exterior (?) wrapped in about a quarter mile worth of wire (two wires)? Seems to me that might be enough to produce an asymmetry in this system  though I have no idea whether that would be a useful asymmetry.

So, curious about this mention of Sagnac effect by Avron and relation to Emdrives, there is a short sentence at end of http://emdrive.com/principle.html :
...the system of EM wave and waveguide can be regarded as an open system, with the EM wave and the waveguide having separate frames of reference.
A similar approach is necessary to explain the principle of the laser gyroscope, where open system attitude information is obtained from an apparently closed system device.
For what it's worth, a comment on Slashdot (http://science.slashdot.org/story/13/02/08/0030240/chinasradicalnewspacedrive) (search Sagnac) about Wired article (http://www.wired.co.uk/news/archive/201302/06/emdriveandcoldfusion) about 2012 publication of Yang Juan (http://www.emdrive.com/yangjuanpaper2012.pdf) states :
There is a description of the Sagnac effect on wikipedia, this is the basis of a laser gyroscope. Interestingly Newtonian physics and relativity give the same answer for this. I isn't related to the microwave drive. I think they mention it because laser gyroscopes are conceptually complicated and they hope that the reader won't understand them, and therefor not understand that if anything they are yet more evidence that this trick doesn't work.
Uncorrected for spelling. The comment is about another post musing about the last sentence of emdrive.com principle page about laser gyroscope.
So, is there anything published with some level of detail explaining how a hypothetical "space drive effect", and with "good scaling" at that, could be derived or elucidated from the proven physics of Sagnac effect ?

http://www.mehtapress.com/mehtapress/Journals/JournalofSpaceExploration/Volume3Issue1/vol_3_issue_1_file_2.pdf
I'm not qualified to judge the space flight applicability of the above article by Dr. Woodward as it pertains to this forum. A brief history, theory and recent experiments are detailed. It also contains a critique of quantum vacuum explanations for emdrive propulsion. Just thought I should bring it to this groups attention and I'll return to lurking. I've passively appreciated this discussion for a long time. Some of the most contentious moments have been the most educational. I'll miss the perspectives of Ron Stahl and Mullertron assuming they don't return. Thanks to everyone who has contributed. Truly fascinating.

There is some similarity of the EMDrive to the Sagnac oscillator if the optical fiber has a linear variation in the index of refraction. The frames of reference are stationary and accelerating rather than constant velocity. But, I havn't seen any reference or calculation giving rotary forces as yet. At the moment I'm chasing old photon to graviton papers.

There is some similarity of the EMDrive to the Sagnac oscillator if the optical fiber has a linear variation in the index of refraction. The frames of reference are stationary and accelerating rather than constant velocity. But, I havn't seen any reference or calculation giving rotary forces as yet. At the moment I'm chasing old photon to graviton papers.
The Sagnac effect compares the (rotating) velocity frame of reference in which the opposing photons show the same frequency w/ the (stationary) frame in which the doppler photons are observed.
The Shawyer cavity photons can be compared in the (stationary) dispersion frame w/ the same frequency and in an (accelerated) frame which balances out the dispersion and expresses the doppler shifts.

There is some similarity of the EMDrive to the Sagnac oscillator if the optical fiber has a linear variation in the index of refraction. The frames of reference are stationary and accelerating rather than constant velocity. But, I havn't seen any reference or calculation giving rotary forces as yet. At the moment I'm chasing old photon to graviton papers.
The Sagnac effect compares the (rotating) velocity frame of reference in which the opposing photons show the same frequency w/ the (stationary) frame in which the doppler photons are observed.
The Shawyer cavity photons can be compared in the (stationary) dispersion frame w/ the same frequency and in an (accelerated) frame which balances out the dispersion and expresses the doppler shifts.
A classic (1967, Air Force Cambridge Research Lab , Massachusetts) article on the Sagnac effect, by Post:
http://www.orgonelab.org/EtherDrift/Post1967.pdf
Post admits in his great review article: “The search for a physically meaningful transformation for rotation
is not aided in any way whatever by the principle of general spacetime covariance (relativity), nor is it true that the spacetime theory of gravitation (general relativity) plays any role in establishing physically correct transformations (relevant to the Sagnac effect).”
(parenthesis and bold added for explanatory purposes)
For a contentious viewpoint, here is a paper claiming interferometric measurements validate the classical approach and invalidate the relativistic approach (W. Engelhardt, Division Head, Wissenschatlicher Angestellter JET, MaxPlanckInstitut für Physik)
http://www.kritikrelativitaetstheorie.de/Anhaenge/WolfgangEngelhardtSagnac.pdf
In 1925 Michelson and Gale built a huge earthfixed Sagnac Interferometer in Illinois demonstrating that the light velocity is anisotropic on the rotating earth. For Sagnac this result did not come as a surprise having explained the underlying effect on the basis of the ether theory in 1913. The Special Relativity Theory (SRT), however, had predicted on the basis of the Lorentz Transformation (LT) that the velocity of light is isotropic in all inertial systems

http://www.mehtapress.com/mehtapress/Journals/JournalofSpaceExploration/Volume3Issue1/vol_3_issue_1_file_2.pdf
I'm not qualified to judge the space flight applicability of the above article by Dr. Woodward as it pertains to this forum. A brief history, theory and recent experiments are detailed. It also contains a critique of quantum vacuum explanations for emdrive propulsion. Just thought I should bring it to this groups attention and I'll return to lurking. I've passively appreciated this discussion for a long time. Some of the most contentious moments have been the most educational. I'll miss the perspectives of Ron Stahl and Mullertron assuming they don't return. Thanks to everyone who has contributed. Truly fascinating.
thanks Econocritic, but Rodal just chastised us for posting about Woodward's Mach Effect theory in this thread, at post #32
the purpose of this forum is to deal with SPACEFLIGHT APPLICATIONS (of EM Drives: those propellantless drives comprised of a microwave cavity as the devices tested by Shawyer in the UK, Prof. Juan Yang in China and Brady, March, White, et.al. at NASA)
...
and therefore these experiments do not constitute "EM Drive Spaceflight Applications" (as instructed by Chris Bergin) Woodward fans persist on carrying a debate on this thread rather than their own Woodward thread.
Frankly, I don't understand what is the goal being pursued here by Woodwardeffect fans to insist to carry arguments concerning Woodward's theory and experiments in this thread.
He is right about that. This is the EM Drive thread. And my guess is that what he wrote was valid for everyone of us, including new members like you.
So I think you should post your link in another topic, probably the Propellantless Field Propulsion and Applications thread...
http://forum.nasaspaceflight.com/index.php?topic=13020.1830

Woodward discussion thread here;
http://forum.nasaspaceflight.com/index.php?topic=31037.465
Somewhat highjacked but may be returned to the original topic.

There is some similarity of the EMDrive to the Sagnac oscillator if the optical fiber has a linear variation in the index of refraction. The frames of reference are stationary and accelerating rather than constant velocity. But, I havn't seen any reference or calculation giving rotary forces as yet. At the moment I'm chasing old photon to graviton papers.
The Sagnac effect compares the (rotating) velocity frame of reference in which the opposing photons show the same frequency w/ the (stationary) frame in which the doppler photons are observed.
The Shawyer cavity photons can be compared in the (stationary) dispersion frame w/ the same frequency and in an (accelerated) frame which balances out the dispersion and expresses the doppler shifts.
A classic (1967, Air Force Cambridge Research Lab , Massachusetts) article on the Sagnac effect, by Post:
http://www.orgonelab.org/EtherDrift/Post1967.pdf
Post admits in his great review article: “The search for a physically meaningful transformation for rotation
is not aided in any way whatever by the principle of general spacetime covariance (relativity), nor is it true that the spacetime theory of gravitation (general relativity) plays any role in establishing physically correct transformations (relevant to the Sagnac effect).”
(parenthesis and bold added for explanatory purposes)
For a contentious viewpoint, here is a paper claiming interferometric measurements validate the classical approach and invalidate the relativistic approach (W. Engelhardt, Division Head, Wissenschatlicher Angestellter JET, MaxPlanckInstitut für Physik)
http://www.kritikrelativitaetstheorie.de/Anhaenge/WolfgangEngelhardtSagnac.pdf
In 1925 Michelson and Gale built a huge earthfixed Sagnac Interferometer in Illinois demonstrating that the light velocity is anisotropic on the rotating earth. For Sagnac this result did not come as a surprise having explained the underlying effect on the basis of the ether theory in 1913. The Special Relativity Theory (SRT), however, had predicted on the basis of the Lorentz Transformation (LT) that the velocity of light is isotropic in all inertial systems
After reading these papers my conclusions are that you can dismiss the second one as looking to disprove relativity. The 1967 paper is exhaustive and it shows decisively (I could see no errors in the math) that the closed path of the Sagnac effect is an example of a "closed system" even in the case of a dispersive medium.
Edit: I suppose I should add that the EMDrive can be treated the same way(s) with the radius and area = to infinity (or the cosmological size ?) but the implications are not immediately obvious.
Edit2: Went back to check a few thoughts. Nothing was considered that could give any relevant calculation to the EMDrive, unfortunately. The only dispersion considered here would just cancel out.
Edit3: (the last ? for now)
By way of clarification, I've been following the proposition that the existance of photon dispersion in a (gravitational, for instance) accelerated frame of reference (AFR) can imply the generation of an acceleration in a stationary frame by the presence of a dispersed photon field and it's possible application to the EMDrive.
In practice, the dispersion relation is translated to an AFR in which the wavenumber dispersion disappears and the doppler shifted frequency dispersion can be used to calculate the force exerted per photon.
The required conditions for a cavity resonator would seem, so far, to be the assymetry of the cavity dispersion relation and the existance of higher order modes which exhibit "cutoff frequencies".
The 1967 paper above, and other papers I've looked at so far do not include calculations that meet those criteria.
The conservation of momentum is still to be rationalised. So far, none of the electrogravitational papers I've seen have had the interaction arise "naturally" out of General Relativity. (that may be my own predudice, so I'm still looking)
Thanks for your patience.

.....
After reading these papers my conclusions are that you can dismiss the second one as looking to disprove relativity. The 1967 paper is exhaustive and it shows decisively (I could see no errors in the math) that the closed path of the Sagnac effect is an example of a "closed system" even in the case of a dispersive medium.
Edit: I suppose I should add that the EMDrive can be treated the same way(s) with the radius and area = to infinity (or the cosmological size ?) but the implications are not immediately obvious.
Edit2: Went back to check a few thoughts. Nothing was considered that could give any relevant calculation to the EMDrive, unfortunately. The only dispersion considered here would just cancel out.
Edit3: (the last ? for now)
By way of clarification, I've been following the proposition that the existance of photon dispersion in a (gravitational, for instance) accelerated frame of reference (AFR) can imply the generation of an acceleration in a stationary frame by the presence of a dispersed photon field and it's possible application to the EMDrive.
In practice, the dispersion relation is translated to an AFR in which the wavenumber dispersion disappears and the doppler shifted frequency dispersion can be used to calculate the force exerted per photon.
The required conditions for a cavity resonator would seem, so far, to be the assymetry of the cavity dispersion relation and the existance of higher order modes which exhibit "cutoff frequencies".
The 1967 paper above, and other papers I've looked at so far do not include calculations that meet those criteria.
The conservation of momentum is still to be rationalised. So far, none of the electrogravitational papers I've seen have had the interaction arise "naturally" out of General Relativity. (that may be my own predudice, so I'm still looking)
Thanks for your patience.
Thanks for the great comment and explanation !
It is known that an electric charge emits radiation if there is a relative acceleration between the charge and its electric field. And that emission of radiation produces a force. Unequal radiation produced in opposite directions should result in a net force in one direction. (In order to satisfy energy and momentum conservation, the charged particle must experience a recoil at the time of emission. The radiation must exert an additional force on the charged particle: the Abraham–Lorentz force)
This should exist both for a charge accelerated in a free space, as well for a charge supported at rest in an accelerated field, for example, a gravitational field. In both situations, the charges radiate.
But, if this is due to the acceleration of gravity, at first glance it seems like the charge would radiate in a dipolar power pattern that looks like an asymmetric radiallypolarized doughnut (a dougnhut with a larger crosssection in one direction and a smaller crosssection in the opposite direction). A doughnut whose axis is parallel to the direction of the gravity force, hence one should be able to discriminate this by orienting the EM Drive with the central axis of the truncated cone oriented like the force of gravity, and orienting it perpendicular to that direction. NASA Eagleworks unfortunately did not orient the truncated cone with its longitudinal axis oriented in the vertical direction, parallel to the direction of the acceleration of gravity. Dr. White said in the NASA Ames 2014 August Conference that he was planning to do this in the next series of trials. However, Shawyer did orient his EM Drive in the vertical direction and did obtain similar results as in the horizontal direction, which would seem to preclude this explanation?
(http://www.mpl.mpg.de/fileadmin/leuchs/img/4pipac/doughnut.png)

For any closed cavity the gravitational component is just the "weight" of the RF energy
W=PQahf/c^2
The Shawer effect seems to be something else which requires the dispersion relation to have a specific form.
(just had a minute to quip...more later)
Maxwell's equations are just the tautological relationship between the field and particle representations.
Yes, so much easy info to wait for. My (Xmas) wish is that they looked for any new frequencies in the spectra. (probably not there but cavity modes are bound states and it would be good to look for transitions anyway)
Correction: W = Nahf/c^2 = (PQ/hf)*(ahf/c^2) = PQa/c^2
(I gotta find a way to get more than a minute free at a time !)

Another blog post from Professor McCulloch. He links to a paper he just published describing how he believes the EM drive is a manifestation of his theory:
http://physicsfromtheedge.blogspot.com/

Another blog post from Professor McCulloch. He links to a paper he just published describing how he believes the EM drive is a manifestation of his theory:
http://physicsfromtheedge.blogspot.com/
Certainly close enough to be interesting. I would have liked to see simplified Eq. 6 filled out to include the effect of the cavity modes.

Awoke to memories of the '60s, ie. the SachsSchwebel version of GR using quaternions having an addl. coupling. Found at least one ref. this AM.
mendelsachsfromspecialtogeneralrelativitymacrotoquantumdomains28p120114095137phpapp02.pdf
"This expression predicts a coupling of the ‘gravitational field’ (in terms of qk) with the matter field components Tρ to define a gravitational current contribution. The latter is not foreseen in the conventional theories that neglect the gravitational coupling to matter fields."
That expression has a form that is at least "similar" in outline to that from the cavity dispersion relation. The "gravitational current" might provide the missing momentum.
I need to find a way to get copies of the original papers which were in Il Nuovo Cimento as I recall.
Edit: Looking for,
Sachs, M. (1964).Nuovo cimento,31, 98.
Sachs, M. (1968a).International Journal of Theoretical Physics, Vol. 1, No. 4, p. 387.
Sachs, M. (1968b).Nuovo cimento,53A, 561.
Sachs, M. and Schwebel, S. L. (1961).Nuovo cimento, Supplement21, 197.
Sachs, M. and Schwebel, S. L. (1962).Journal of Mathematics and Physics,3, 843.
Sachs, M. and Schwebel, S. L. (1963).Nuclear Physics,43, 204.
Also: Schwebel, S. L. INT J THEOR PHYS , vol. 6, no. 1, pp. 6174, 1972, "Interaction theory of the electromagnetic field"

If you wanted to build a vehicle using this technology would there be a preferred shape to use?

Awoke to memories of the '60s, ie. the SachsSchwebel version of GR using quaternions having an addl. coupling. Found at least one ref. this AM.
mendelsachsfromspecialtogeneralrelativitymacrotoquantumdomains28p120114095137phpapp02.pdf
"This expression predicts a coupling of the ‘gravitational field’ (in terms of qk) with the matter field components Tρ to define a gravitational current contribution. The latter is not foreseen in the conventional theories that neglect the gravitational coupling to matter fields."
That expression has a form that is at least "similar" in outline to that from the cavity dispersion relation. The "gravitational current" might provide the missing momentum.
I need to find a way to get copies of the original papers which were in Il Nuovo Cimento as I recall.
Edit: Looking for,
Sachs, M. (1964).Nuovo cimento,31, 98.
Sachs, M. (1968a).International Journal of Theoretical Physics, Vol. 1, No. 4, p. 387.
Sachs, M. (1968b).Nuovo cimento,53A, 561.
Sachs, M. and Schwebel, S. L. (1961).Nuovo cimento, Supplement21, 197.
Sachs, M. and Schwebel, S. L. (1962).Journal of Mathematics and Physics,3, 843.
Sachs, M. and Schwebel, S. L. (1963).Nuclear Physics,43, 204.
I found this this paper that Sachs wrote under sponsorship from the Air Force Cambridge Research Lab in Trieste in July 1966 while on leave from B.U., "To be submitted to Nuovo Cimento"
"ON FACTORIZATION OF EINSTEIN'S FORMALISM INTO A PAIR OF QUATERNION FIELD EQUATIONS"
http://streaming.ictp.trieste.it/preprints/P/66/081.pdf
it might be remarked that the quaternion form of the metrical field equations lends itself in a natural way to a unification between the inertial and gravitational manifestations of interacting matter. This is because of the basic expression of the matter fields themselves in terms of the same spinor and quaternion variables.
Mendel Sachs has a website:
http://mendelsachs.com/
In his website he has posted several of his articles. For example this relatively recent one on the Mach principle and origin of inertia:
http://mendelsachs.com/wpcontent/uploads/articles/themachprinciple.pdf
In that reference, Sachs convincingly argues against the approach to Mach's Principle followed by Woodward (of course he does not mention Woodward), he considers the particleantiparticle pairs of the quantum vacuum having a most important effect, while the effect of distant stars is negligible:
I have found in my research program in general relativity, that the primary contribution to the inertial mass of any local elementary matter, such as an ‘electron’, are the nearby particleantiparticle pairs that constitute what we call the ‘physical vacuum’. [The main developments of this research are demonstrated in my two monographs: General Relativity and Matter, and Quantum Mechanics from General Relativity]. A prediction of this research program is that the main influence of these pairs on the mass of, say, an electron comes from a domain of the ‘physical vacuum’ in its vicinity, whose volume has a radius that is the order of 10^(15) cm. Of course, the distant stars, billions of lightyears away, also contribute to the electron’s mass, though negligibly, just as the Sun’s mass contribution to the weight of a person on Earth is negligible compared with the Earth’s influence on this person’s weight! Nevertheless, it was Mach’s contention that in principle all of the matter of the closed system – the nearby as well as far away constituents – determines the inertial mass of any local matter.
(Bold added for emphasis) ==> this is the antithesis of Woodward's approach to Mach's principle!
There are many other interesting references, for example this one on Dirac's Quantum Negative Energy Problem:
http://mendelsachs.com/publication/view/thequantumnegativeenergyproblemrevisited/

Yes, thanks. This is great stuff and will require a lot of reading. (not to mention the brainbusting)
But do look back at that expression in the AM reference, it looks (to me w/o justification) like it could be the "doppler frame" expression.
Edit: Found the AM paper online, (on the Beardon site, of all places! I have NO idea what this would have to do w/ free energy.)
http://www.cheniere.org/references/Symmetry_in_Electrodynamics.pdf
See p.24, the threecurrent density

So what TRL would you guys say the devices presented in the "Anomalous Thrust Production...." papers are at right now? I'd say probably a TRL 2. Possibly on the way to a TRL 3, hopefully. :) I base this partly on Dr. White's comments at the 29:55 mark in the NASA Ames Research Director’s Colloquium, August 12, 2014 video posted here recently. He remarks that the Qthruster concept is potentially higher TRL than the Warp concepts at least.
http://www.nasa.gov/content/technologyreadinesslevel/
http://en.wikipedia.org/wiki/Technology_readiness_level#NASA_definitions
The reason I'm asking is, what kind of actual real "space flight applications" can we discuss given what we know right now? What can we actually do right now in space with the numbers quoted below?
"With more focus on space flight applications " (as per http://forum.nasaspaceflight.com/index.php?topic=36313.msg1301658#msg1301658) the metric chosen by the NASA's "Anomalous" report was the thrust force per power input.
Here is a comparison of reported measurements for EM Drives.........
reported measurement ForcePerPowerInput (milliNewtons/kW)
(* Brady c TE mode *) 21.31
(* Brady a TM mode*) 5.396
(* Brady b TM mode*) 3.000
A quick online conversion of the 21 milliNewton figure gives me a 0.0755 ozf figure. That has to be worth something given that solar panels essentially supply electrical power for free (besides building/getting the space vehicle in orbit to begin with). So would this be useful for at least station keeping even now? Or could it power a small probe somewhere interesting, faster than the usual burn and coast method?
According to the oracle: http://en.wikipedia.org/wiki/Hall_effect_thruster
"Devices operating at 1.35 kW produce about 83 mN of thrust" "...hall effect thrusters have input power 1.35–10 kilowatts, exhaust velocity 10–50 kilometers per second, thrust 40–600 millinewtons and efficiency 45–60 percent."
That 21 milliNewton/KW figure is creeping up on what a Hall thruster can do, but with NO propellant.

So what TRL would you guys say the devices presented in the "Anomalous Thrust Production...." papers are at right now?....
Hey Mulletron, a very warm WELCOME BACK !
We really missed you !
Glad that you are back

Yes, thanks. This is great stuff and will require a lot of reading. (not to mention the brainbusting)
But do look back at that expression in the AM reference, it looks (to me w/o justification) like it could be the "doppler frame" expression.
Edit: Found the AM paper online, (on the Beardon site, of all places! I have NO idea what this would have to do w/ free energy.)
http://www.cheniere.org/references/Symmetry_in_Electrodynamics.pdf
See p.24, the threecurrent density
Very interesting. Also p. 21:
The role of the Mach principle is revealed at this stage of the analysis. Since Fρλ depends on the spin curvature tensor Kρλ, which automatically vanishes in a vacuum (i.e. a flat spacetime), the electromagnetic field, and therefore the previously considered electric charge of any quantity of matter in a vacuum must vanish. Thus, not only the inertial mass but also the electric charge of a ‘particle’ of matter does not exist when there is no coupling to other matter. I have generalized this idea in the field theory based on General Relativity, to the case where all previously considered intrinsic properties of discrete matter, in addition to inertial mass and electric charge, vanish identically in a vacuum. This view exorcises all of the remaining features of the discrete, separable ‘elementary particle’ of matter. It is replaced with a view of matter in terms of a closed, continuous field theory, according to the theory of general relativity. I have called this view of matter, whereby all of its previously considered intrinsic properties are explained in terms of coupling within the closed system, ‘the generalized Mach principle’.
Sachs formally answered (in the 1960's !) the criticism that the matter in Quantum Vacuum "does not gravitate": intrinsic properties are explained in terms of coupling within the closed system, they don't really exist (thus they are "virtual") in the vacuum per se, they only become into existence when there is coupling.

...
Sachs formally answered (in the 1960's !) the criticism that the matter in Quantum Vacuum "does not gravitate": intrinsic properties are explained in terms of coupling within the closed system, they don't really exist (thus they are "virtual") in the vacuum per se, they only become into existence when there is coupling.
Not sure I understand what your saying here. do you mind breaking that down?

Hmmm, Schwebel had mentioned, at the time, that because of that, there was no need for renormalization, but because it had already been done, no one cared.

...
In his website he has posted several of his articles. For example this relatively recent one on the Mach principle and origin of inertia:
http://mendelsachs.com/wpcontent/uploads/articles/themachprinciple.pdf
In that reference, Sachs convincingly argues against the approach to Mach's Principle followed by Woodward (of course he does not mention Woodward), he considers the particleantiparticle pairs of the quantum vacuum having a most important effect, while the effect of distant stars is negligible:
I have found in my research program in general relativity, that the primary contribution to the inertial mass of any local elementary matter, such as an ‘electron’, are the nearby particleantiparticle pairs that constitute what we call the ‘physical vacuum’. [The main developments of this research are demonstrated in my two monographs: General Relativity and Matter, and Quantum Mechanics from General Relativity]. A prediction of this research program is that the main influence of these pairs on the mass of, say, an electron comes from a domain of the ‘physical vacuum’ in its vicinity, whose volume has a radius that is the order of 10^(15) cm. Of course, the distant stars, billions of lightyears away, also contribute to the electron’s mass, though negligibly, just as the Sun’s mass contribution to the weight of a person on Earth is negligible compared with the Earth’s influence on this person’s weight! Nevertheless, it was Mach’s contention that in principle all of the matter of the closed system – the nearby as well as far away constituents – determines the inertial mass of any local matter.
(Bold added for emphasis) ==> this is the antithesis of Woodward's approach to Mach's principle!
So I read the paper expecting the supporting arguments for why Sach's claims that it is the matter closest that has the most important effect. Unfortunately I realized by the end that those arguments actually lie in his books. I read the descriptions of them on amazon and the reviews and I do not believe this is a show stopper for woodward. For the following reasons
* If Sach's is right then Mach's Principle is apart of Einsteins General Relativity theory. Which Woodward is also claiming.
* From my perspective (NOT A PHYSICIST) I get the impression that for the Mach Effects being claimed by woodward it isn't so much that we start with the farthest matter to determine the effects on local matter. Instead it is more important that the inertial mass of any local matter depends on all the matter in the universe.
* In the Quantum Mechanics from General Relativity (http://www.amazon.com/QuantumMechanicsGeneralRelativityApproximation/dp/9027722471/ref=sr_1_4?s=books&ie=UTF8&qid=1419822072&sr=14) book. It looks like from the reviews that Sachs also proves the Feynman & Wheeler Absorber theory (http://en.wikipedia.org/wiki/Wheeler%E2%80%93Feynman_absorber_theory) (which is the "delayed action at a distance" being referenced by the customer review). This is important because it is also being used by Woodward to explain how inertial actions are instantaenous.
...
The "delayed action at a distance"of Feynman and Wheeler is restored to currency. The "advanced" solutions take their place beside the "retarded" solutions in a single, complete spacetime.
...
From my limited perspective I see two men looking at the same thing from different perspectives. And while I believe this will end up affecting the details. The question really is whose version is a more accurate representation of reality?
P.S. Yes I know this may sound like a ME fan boy defending his sacred cow,but I can guarantee you that I am just as much a fan boy of NASA's EmDrive research and eagerly awaiting more results to digest. That said without a thorough understanding of both Sach's and Woodwards theories the only way I can compare the two is to look at just how similar or different their line of reasoning is. And from where I stand the detail being pointed to seems small enough to not matter. Especially given the extensive experimental work Woodward and Paul March has done. The only questions I have for them in my mind is can they scale it up? What material science issue need to be resolved? And what is their timeline to get to a performance level applicable to micro gravity applications?

...
Sachs formally answered (in the 1960's !) the criticism that the matter in Quantum Vacuum "does not gravitate": intrinsic properties are explained in terms of coupling within the closed system, they don't really exist (thus they are "virtual") in the vacuum per se, they only become into existence when there is coupling.
so how does one create this coupling?

...
Sachs formally answered (in the 1960's !) the criticism that the matter in Quantum Vacuum "does not gravitate": intrinsic properties are explained in terms of coupling within the closed system, they don't really exist (thus they are "virtual") in the vacuum per se, they only become into existence when there is coupling.
so how does one create this coupling?
See: http://link.springer.com/staticcontent/lookinside/986/art%253A10.1007%252FBF02755823/000.png

...
Sachs formally answered (in the 1960's !) the criticism that the matter in Quantum Vacuum "does not gravitate": intrinsic properties are explained in terms of coupling within the closed system, they don't really exist (thus they are "virtual") in the vacuum per se, they only become into existence when there is coupling.
so how does one create this coupling?
See: http://link.springer.com/staticcontent/lookinside/986/art%253A10.1007%252FBF02755823/000.png
Since I am not a physicist, and I didnt sleep at a holiday in express last night. I will not even begin to pretend I understood most of what that reply was attempting to show. All I could get out of it was Sachs provided a point of clarification on why the complaint of his theory lacking internal consistency was not correct. other than that didnt see an argument for how one could physically force the virtual particles to experience coupling and gain their intrinsic properties. Though I suspect this experiment may light the path towards doing something of the sort
http://www.bibliotecapleyades.net/ciencia/secret_projects/project077.htm (http://www.bibliotecapleyades.net/ciencia/secret_projects/project077.htm)

...
Sachs formally answered (in the 1960's !) the criticism that the matter in Quantum Vacuum "does not gravitate": intrinsic properties are explained in terms of coupling within the closed system, they don't really exist (thus they are "virtual") in the vacuum per se, they only become into existence when there is coupling.
so how does one create this coupling?
See: http://link.springer.com/staticcontent/lookinside/986/art%253A10.1007%252FBF02755823/000.png
Since I am not a physicist, and I didnt sleep at a holiday in express last night. I will not even begin to pretend I understood most of what that reply was attempting to show. All I could get out of it was Sachs provided a point of clarification on why the complaint of his theory lacking internal consistency was not correct. other than that didnt see an argument for how one could physically force the virtual particles to experience coupling and gain their intrinsic properties. Though I suspect this experiment may light the path towards doing something of the sort
http://www.bibliotecapleyades.net/ciencia/secret_projects/project077.htm (http://www.bibliotecapleyades.net/ciencia/secret_projects/project077.htm)
Instead of photons colliding with electrons "whizzing down the twomilelong Stanford accelerator" as in the above paper (".. The paths of colliding electrons and photons in the experiment ")
it's better to think of low energy two photon physics ( http://en.wikipedia.org/wiki/Twophoton_physics ). See this article for example on such experiments:
Probing the quantum vacuum with polarized light: a low energy photonphoton collider
http://indico.cern.ch/event/1743/contribution/8/material/slides/0.pdf
Theme
– Vacuum as a “target”: low energy photonphoton collider
• QED interactions
• other interactions?
Aim
– Measure the magnetically induced linear birefringence and linear dichroism (optical rotation) of the Vacuum element (in practice a gas in the zeropressure limit)
– Possible contributions to macroscopic properties
• photonphoton scattering
• photon splitting
• production of:
– neutral bosons
Main parameters of the apparatus
– magnet
• dipole, 6 T, temp. 4.2 K, 1 m field zone
– cryostat
• rotation frequency ~300 mHz, sliding contacts, warm bore to allow light propagation in the interaction zone
– laser
• 1064 nm, 100 mW, frequencylocked to the F.P. cavity
– FabryPerot optical cavity
• 6.4 m length, finesse ~100000, optical path in the interaction region ~ 60 km
– heterodyne ellipsometer
• ellipticity modulator (SOM) and high extinction (~107) crossed polarisers + Quarter Wave Plate (QWP)
• timemodulation of the effect
– detection chain
• photodiode with lownoise amplifier
– DAQ
• Slow: demodulated at low frequency and phaselocked to the magnetic field instantaneous direction
• Fast: high sampling frequency direct acquisition

OT: I found a thing and put it over in the "New Hope For Warp Drive" thread. it does have some interesting details that can be examined in a very loose sort of way. not a technical paper by any means but it does describe the set up and effects. i found it interesting the weight of his test object and magnitude of effect on it.

Curious that there has been no coverage of this in the mainstream science press for the end of year, not a mention in anyone that I've seen roundups of 2014.
For comparison the detection of primordial gravity waves has been well covered even though this discovery has been heavily disputed since.

Curious that there has been no coverage of this in the mainstream science press for the end of year, not a mention in anyone that I've seen roundups of 2014.
For comparison the detection of primordial gravity waves has been well covered even though this discovery has been heavily disputed since.
The reason is well explained by xkcd, see: http://www.explainxkcd.com/wiki/index.php/1404:_Quantum_Vacuum_Virtual_Plasma
(http://www.explainxkcd.com/wiki/images/3/32/quantum_vacuum_virtual_plasma.png)
[Note however that the comic is wildly exaggerated regarding NASA's tests: NASA only "pumped" 2.6 to 17 watts of power into the truncated cone cavity, about 1,000 to 8,000 times less inputpower than what the comic shows]
None of these experiments have demonstrated a linear acceleration: all of them have measured rotational accelerations. None of the EM Drives have been tested in a vacuum. None of the measured forces are high enough to levitate the drive.
Some of Woodward's experiments have been conducted in a vacuum, however, from a practicalapplications viewpoint or proofofconcept viewpoint, they are even more disappointing: The reported "thrust" force/(power input) of the latest Woodward experiments (Fearn, Zachar, Woodward & Wanser) is about 2000 times less than the NASA Brady et.al TE mode and about 20,000 times less than the Shawyer Demo In other words, it takes (for the latest Woodward experiments) 3 to 4 orders of magnitude greater input power to produce the same level of what is reported as "thrust" force as for the EM Drives.
(http://angryflower.com/experi.gif)
For comparison, the Wright Brothers experimented with real flying machines, Goddard with real chemical propulsion rockets that although small had enough thrust to lift the rockets, and worldrenowned physicists like Freeman Dyson (based on ideas by the worldknown mathematician Ulam) successfully conducted explosively loaded experiments to thrust up payloads for Project Orion's explosiveloaded propulsion.
If any of these experimenters ever gets any payload to get thrusted upwards, levitated or at least propelled in outer space, you may then see this covered in the mainstream science press. Until then, there is really no experimental breakthrough to report in the mainstream science press. Even NASA's Dr. White titled his experimental paper with the weakly tentative title "Anomalous..." and it was given at an AIAA conference and not published in a peerreviewed journal.

OT: I found a thing and put it over in the "New Hope For Warp Drive" thread. it does have some interesting details that can be examined in a very loose sort of way. not a technical paper by any means but it does describe the set up and effects. i found it interesting the weight of his test object and magnitude of effect on it.
Not much to go by, it seems to be a 2 meter (146 MHz) asymmetric resonant antenna, so it could meet the requirement for a "SachsSchwebel" gravitational current generator instead of a warp drive. It could also be seeing electromagnetic forces between the antenna and the faraday cage walls which are in the near field. The interferometer tests are interesting, but again, not much data.
There is a paper of sorts: http://swdllc.paresspacewarpresearch.org/PressRelease/Press.htm

Has anyone discussed testing spin using a Woodward effect device, like a pendulum, using a cheap very high altitude balloon of the sort JP Aerospace launch? It's not perfect vacuum, but its cheaper than launching a cubesat. It just seems like navel gazing to me unless the effect does anything practical.

Not much to go by, it seems to be a 2 meter (146 MHz) asymmetric resonant antenna, so it could meet the requirement for a "SachsSchwebel" gravitational current generator instead of a warp drive. It could also be seeing electromagnetic forces between the antenna and the faraday cage walls which are in the near field. The interferometer tests are interesting, but again, not much data.
There is a paper of sorts: http://swdllc.paresspacewarpresearch.org/PressRelease/Press.htm
When you say that it means it really was topical for this thread after all.
I am slightly optimistic about it now; but i have seen this guy's web page before. I kind of dismissed it as true fringe, but then I saw the article and the video with video demonstration footage. That moved it up a step or two in my estimation. The guy is not completely nuts but his idea has a giggle factor that has ensured he has been interviewed on tons of fringe kook venues; pod casts and such.

On another forum they were discussing how such drives could accelerate the end of the universe, I looked at some of the explanations on there as too what was meant but they completely lost me I'm afraid to admit?

On another forum they were discussing how such drives could accelerate the end of the universe, I looked at some of the explanations on there as too what was meant but they completely lost me I'm afraid to admit?
well...that's a step ahead of what is already a shaky concept or two. but I think anything that is a linear drive like the thing i was just talking about would be an infinitesimal perturbation in the scheme of the whole cosmos. but i have heard arguments about collapsing the vacuum state of the universe. but i think that that was in reference to collider experiments and not warp drives or em drives.

On another forum they were discussing how such drives could accelerate the end of the universe, I looked at some of the explanations on there as too what was meant but they completely lost me I'm afraid to admit?
well...that's a step ahead of what is already a shaky concept or two. but I think anything that is a linear drive like the thing i was just talking about would be an infinitesimal perturbation in the scheme of the whole cosmos. but i have heard arguments about collapsing the vacuum state of the universe. but i think that that was in reference to collider experiments and not warp drives or em drives.
God help us if the media ever get hold of this, you can imagine the headlines now!

On another forum they were discussing how such drives could accelerate the end of the universe, I looked at some of the explanations on there as too what was meant but they completely lost me I'm afraid to admit?
well...that's a step ahead of what is already a shaky concept or two. but I think anything that is a linear drive like the thing i was just talking about would be an infinitesimal perturbation in the scheme of the whole cosmos. but i have heard arguments about collapsing the vacuum state of the universe. but i think that that was in reference to collider experiments and not warp drives or em drives.
God help us if the media ever get hold of this, you can imagine the headlines now!
oh they already did. it's just that after the LHC black hole media hype no one paid attention to the "collapse of the vacuum state" scare. i remember seeing articles about it in new scientist if i recall right.

ok. this is interesting... neutrinos that collide with nuclei at an oblique angle create particles out of the vacuum. evidently said new particles don't annihilate with a virtual twin? is that right?
http://phys.org/news/201412neutrinosfullonglancing.html
so here is a real interaction with the vacuum. that was being argued a few pages back WRT Dr White's Theory of how QVPTs work i think.

ok. this is interesting... neutrinos that collide with nuclei at an oblique angle create particles out of the vacuum. evidently said new particles don't annihilate with a virtual twin? is that right?
http://phys.org/news/201412neutrinosfullonglancing.html
so here is a real interaction with the vacuum. that was being argued a few pages back WRT Dr White's Theory of how QVPTs work i think.
Ok, let's try this : there is no question that there can be real interaction with the vacuum (vacuum polarization, pair production from strong electric field or gamma photon bouncing on nucleus or photon/photon...) the question is at what energetic cost ? If there is conservation of momentum_energy in those interactions then you are no better of than with the photon rocket (again) or shooting the supposedly available neutrinos backward (almost the same).

So what TRL would you guys say the devices presented in the "Anomalous Thrust Production...." papers are at right now? I'd say probably a TRL 2. Possibly on the way to a TRL 3, hopefully.
Well, Cannae were talking about flying theirs in a nanosatellite about a year ago, and I suspect that is still ongoing. The Chinese appear to be more cautious but are somewhere around 4+. Shawyer certainly claimed to be at 4 some time ago. And if rumour is to be believed, an aerospace company has pushed Shawyer's work on some from there.

Has there been the least indication yet when we are too get some more results in relation to those who are experimenting in this area?
There is essentially a news blackout on the experimental side from NASA.
The problem is, if this drive really works, the defence implications are huge. Those in charge might feel it would not necessarily be a good idea to go public with it  especially from the US perspective. Remember that 'Sputnik moment'?

Curious that there has been no coverage of this in the mainstream science press for the end of year, not a mention in anyone that I've seen roundups of 2014.
For comparison the detection of primordial gravity waves has been well covered even though this discovery has been heavily disputed since.
The primordial gravity wave research was peer reviewed and done by scientists who are respected by the rest of the scientific community. The debate over it was from within the scientific community. That's why the mainstream media covered it.
The reactionless drive work is entirely outside the scientific mainstream, and every mainstream scientist who has examined it has found it to be without sufficient evidence to claim a discovery. That's why the mainstream media has not covered it much.

So what TRL would you guys say the devices presented in the "Anomalous Thrust Production...." papers are at right now? I'd say probably a TRL 2. Possibly on the way to a TRL 3, hopefully.
Well, Cannae were talking about flying theirs in a nanosatellite about a year ago, and I suspect that is still ongoing. The Chinese appear to be more cautious but are somewhere around 4+. Shawyer certainly claimed to be at 4 some time ago. And if rumour is to be believed, an aerospace company has pushed Shawyer's work on some from there.
No, it's TRL1. Basic research has not even established sufficient evidence of anything anomalous to convince even a small part of the mainstream physics community.

ok. this is interesting... neutrinos that collide with nuclei at an oblique angle create particles out of the vacuum. evidently said new particles don't annihilate with a virtual twin? is that right?
http://phys.org/news/201412neutrinosfullonglancing.html
so here is a real interaction with the vacuum. that was being argued a few pages back WRT Dr White's Theory of how QVPTs work i think.
Ok, let's try this : there is no question that there can be real interaction with the vacuum (vacuum polarization, pair production from strong electric field or gamma photon bouncing on nucleus or photon/photon...) the question is at what energetic cost ? If there is conservation of momentum_energy in those interactions then you are no better of than with the photon rocket (again) or shooting the supposedly available neutrinos backward (almost the same).
But neutrinos are "free" so there is no real cost or at least not a commensurate cost similar to banging high energy gamma photons together. Further I know no way of increasing the amount ambient neutrinos. Since only an occasional neutrino collides with anything and of those only a few do the glancing blow trick I was not shooting for using them for a drive of any sort. What i was pointing at was the vacuum interaction itself; which you covered nicely in the first line of your reply. :)

None of these experiments have demonstrated a linear acceleration: all of them have measured rotational accelerations. None of the EM Drives have been tested in a vacuum. None of the measured forces are high enough to levitate the drive.
Forget about levitation. I havent read much or anything about it, but are the forces even in the same ballpark as existing magnetic torquer rods for cubesats ? If yes, in theory this could assist with attitude control in deep space, at least for desaturation.

Curious that there has been no coverage of this in the mainstream science press for the end of year, not a mention in anyone that I've seen roundups of 2014.
For comparison the detection of primordial gravity waves has been well covered even though this discovery has been heavily disputed since.
The primordial gravity wave research was peer reviewed and done by scientists who are respected by the rest of the scientific community. The debate over it was from within the scientific community. That's why the mainstream media covered it.
The reactionless drive work is entirely outside the scientific mainstream, and every mainstream scientist who has examined it has found it to be without sufficient evidence to claim a discovery. That's why the mainstream media has not covered it much.
I suspect there are people who may disagree with you with that statement, but that's not my debate to have.:)

So what TRL would you guys say the devices presented in the "Anomalous Thrust Production...." papers are at right now? I'd say probably a TRL 2. Possibly on the way to a TRL 3, hopefully.
Well, Cannae were talking about flying theirs in a nanosatellite about a year ago, and I suspect that is still ongoing. The Chinese appear to be more cautious but are somewhere around 4+. Shawyer certainly claimed to be at 4 some time ago. And if rumour is to be believed, an aerospace company has pushed Shawyer's work on some from there.
No, it's TRL1. Basic research has not even established sufficient evidence of anything anomalous to convince even a small part of the mainstream physics community.
Writing to his friend, Joseph Priestley, Benjamin Franklin said, “We may perhaps learn to deprive large Masses of their Gravity & give them absolute Levity, for the sake of easy Transport.
Another researcher believes he can build a small craft with much levity.
http://www.omaha.com/news/metro/workingtowardawarpdrive
inhisgaragelabomahan/article_b6489acf56225419ac180c44474da9c9.html

In his website he has posted several of his articles. For example this
relatively recent one on the Mach principle and origin of inertia:
http://mendelsachs.com/wpcontent/uploads/articles/themachprinciple.pdf
In that reference, Sachs convincingly argues against the approach to Mach's
Principle followed by Woodward (of course he does not mention Woodward),
he considers the particleantiparticle pairs of the quantum vacuum having
a most important effect, while the effect of distant stars is
negligible:
I have found in my research program in general relativity, that the primary
contribution to the inertial mass of any local elementary matter, such as an
'electron', are the nearby particleantiparticle pairs that constitute what
we call the 'physical vacuum'. [The main developments of this research are
demonstrated in my two monographs: General Relativity and Matter, and
Quantum Mechanics from General Relativity]. A prediction of this research
program is that the main influence of these pairs on the mass of, say, an
electron comes from a domain of the 'physical vacuum' in its vicinity, whose
volume has a radius that is the order of 10^(15) cm. Of course, the distant
stars, billions of lightyears away, also contribute to the electron's mass,
though negligibly, just as the Sun's mass contribution to the weight of a
person on Earth is negligible compared with the Earth's influence on this
person's weight! Nevertheless, it was Mach's contention that in principle
all of the matter of the closed system  the nearby as well as far away
constituents  determines the inertial mass of any local matter.
(Bold added for emphasis) ==> this is the antithesis of Woodward's
approach to Mach's principle!
This is quite an interesting find and it is refreshing to see that it supports our conclusions (not sure who all agreed with me on this) from the previous thread and forward
(http://forum.nasaspaceflight.com/index.php?topic=29276.msg1266237#msg1266237) during the origin of inertia days; that all the competing theories on the origin of inertia are correct, none are exclusively correct; they they all share a component to inertia. The evidence tells me that inertia is the aggregate effect caused by many different types of interactions happening at once. It also falls in line with the Feynman quote, "All mass is interaction." Even inertial mass? Why not I say.
It is incorrect to state (in my humble view at least) that inertia is
Machian (distant matter) or arises only from vacuum interaction or is
intrinsic to matter itself, gravitational, electromagnetic, whatever.
I saw evidence recently that Mach didn't mean JUST the distant stars/matter when he
envisioned inertia......I didn't know this until now! Is this true?!? Did Woodward acknowledge this?
From page 3 here:
http://mendelsachs.com/wpcontent/uploads/articles/themachprinciple.pdf
"In contrast to this, in his Science of Mechanics Mach said that all of the
matter of the universe, not only the distant stars, determines the inertial
mass of any localized matter."
Break:
I've noticed a delve back into theory recently, which I have been avoiding because of the call for a greater focus on spaceflight applications. Of course I support this because I want to keep our moderator happy and this is his home, we're the guests. I don't want our thread (and work) to go poof again either :(
Is theory off the table?
I assure those who are reading, that this theory we're slinging around here occasionally has the potential to eventually support spaceflight applications. But as I eluded to in my first post in this thread, there
simply aren't spaceflight applications for this emerging technology, YET.
The TRL of this is potential technology is at the concept stage. I tried to stretch a potential application out what's known and didn't do too well. There isn't much space flight application to talk about yet; mostly theory. This may be debunked tomorrow. The space flight application of this post is simply, we better figure out this inertia thing if we want to improve upon and build new and exciting means of space flight.
Those of us who continually plug away on this problem are doing it for good reason. It certainly isn't fun at times reading scientific papers for hours until my eyes go cross. My wife certainly isn't happy with the time I devote to this now. So it is a labor of love. I think many of us really care about solving this problem. I can't stand not knowing how something works for one and the potential payoff for others is enormous if it works. So it is very exciting. Even if it is debunked, we still learn something new in the end, which could be rolled into a new impossible thruster. The potential space flight applications of this post and others like it might (humbly think mine won't) apply to real missions at some point. I do feel that these issues concerning the science behind these potential thrusters needs to be discussed and it seems people are reading, as the the view count of the old thread continues to climb.
Break:
I don't like to double post so I'll add one more subject here.
Turning light into matter:
http://phys.org/news/201405scientistsyearquest.html
I remembered this article this morning. I can see a potential space flight application of this in the future. That is if you take the matter that was created and shoot it out the back end, like an ion drive. Instead of carrying around propellant like xenon, you create it on the fly.

Trying to put numbers to the SachsSchwebel gravitational current, I have not been able to get copies of the Dyatlov (in Russian) papers below but did find a reference to his gravitational polarization density.
This paper is from the old balllightning arguments.
http://www.math.nsc.ru/directions/tornadoeng.htm
"The presence of positive and negative gravitational charges gives the vacuum a polarization property in a gravitational field, that, apart from everything else, permits an explanation of the nature of a gravitational current of displacement, arising in gravitational waves.
In his work [11] V. L. Dyatlov gives a high assessment of gravitational polarization of a physical vacuum in the gravitational field of the Earth. By this account, 10^8 kg of negative mass is concentrated onto the upper surface of a cubic volume which is 1 decimeter in size and subjected to a gravitational field, whereas the same amount positive mass is concentrated onto the lower surface of the cubic volume."
[11] Dyatlov V. L.Polarization model of nonhomogeneous physical vacuum. Novosibirsk, Publishing of Institute of Mathematics of Siberian branch of Russian Academy of Sciences, 1998, 183 p. (in Russian)
Dyatlov V.L. Linear equations of macroscopic electrogravidynamics. Moscow, Inst.Teor.Appl.Phys. Acad. Nat.Sci., Preprint No.11, 1995 (in Russian)
Which led to:
http://www.sinor.ru/~che/Vdyatlov1.htm
which references:
52.Terletskiy, Y. P. Paradoxes of the Theory of Relativity. Moscow: Nauka, 1966. 120 pp.
58.Terletskiy, Ya. P., and Yu. P. Rybakov. Electrodynamics. Moscow: Vyssh. shk., 1990. 352 pp.
Which "sounds like" a Russian invention of the SachsSchwebel ( quadrigues vs quarternions )
In any event, all I can gather from scanning the equations (so far) is that it looks like they are concerned w/ "gravity currents" as opposed to "gravitational currents". That makes sense if they are looking at balllightning and tornadoes, etc.
I don't know if the polarization density they claim (10^5kg/m^3 @ g) is useful or relevant at this point.

...
52.Terletskiy, Y. P. Paradoxes of the Theory of Relativity. Moscow: Nauka, 1966. 120 pp.
58.Terletskiy, Ya. P., and Yu. P. Rybakov. Electrodynamics. Moscow: Vyssh. shk., 1990. 352 pp.
Which "sounds like" a Russian invention of the SachsSchwebel ( quadrigues vs quarternions )
...
"The
Sonobioelectronic and Sonobioelectrogravitic Nature of Life on Earth And Why Pilotwave Subquantum
Mechanics and Information Is Not Enough" (http://www.researchgate.net/profile/Frank_Maye/publication/242650713_
The_Sonobioelectronic_and_Sonobioelectrogravitic_Nature_of_Life_on_Earth_And_Why_Pilotwave_Subquantum_Mechanics_and_Information_Is_
Not_Enough/links/00b7d51ce056c06be3000000)
A. R. BORDON
D. H. HASLER
J.A. SANCHEZ
F.M. MAYE
R. B. SOLINGEN
describes the quadrigue (group of four) of particles of Terletskiy as follows (quadrigue, from the Latin: "A Roman racing chariot drawn by four horses abreast"):
In accepting negative mass, one must therefore accept the quadrigue (group of four) of particles
of Terletskiy (88), which is neatly buttressed by Dirac’s quadrupling of states in his quantum theory. It
is also a remarkable turn of events in the modeling of the physical vacuum as a polarizing medium.
Terletskiy’s quadrigue is actually four particles (or, actually, four electrical charges, masses, magnetic
moments and spin moments), the sum of which equal zero – from which, interestingly enough, one can
derive any two pairs of particles in which their electrical charges, masses, magnetic and spin moments
equal zero! This allows theorists to build a basic model of cella (or distinguishable compartments) of
the physical vacuum as a wholecloth neutral polarizing medium, from which then three kinds of
physical vacuums can manifest: (a) an absolute physical vacuum, represented by the quadrigues; (b) a
physical vacuum of matter, which is made up of particles, one of which is an ordinary one; and (c) a
physical vacuum of antimatter, which is made up of particle pairs, one of which is an antiparticle.
What is most remarkable is that the absolute physical vacuum is described quite well by Maxwell and
Heaviside equations, and thus in the absolute physical vacuum, the polarization model breaks down
into two independent models: the Maxwell theory of electromagnetism, and the Heaviside theory of
gravitational spin. But in physical reality, the relationships of electrical and gravitational polarizations
and of magnetic and spin polarization in the absolute as well as in the physical matter vacuums come
out as quite a unified system of equations that become the basis of a combined electrogravitodynamic
model of matter electrogravitogeneration (via electrical charges and magnetic polarizations) and
continuum dynamics (via masses and moments of the quantity of movement set by way of the
Heaviside equations).
Apparently a different concept than (Hamilton's) quaternion algebra:
i^2 = j^2 = k^2 = ijk = −1
which is noncommutative.
(http://www.euclideanspace.com/maths/algebra/realNormedAlgebra/quaternions/transforms/derivations/vectors/quaternionRotation.png)
One motivation for quaternions is that rotations in 3 dimensions ("3D") are not a 3D vector space (we can't combine rotations in 3D space using vector addition). Representations of 3D rotations using 3 scalar values are non linear, they have singularities and they are difficult to combine. To get around these issues one can embed the representation of 3D rotations into a higher dimensional space, in this case the 4D quaternion space.
http://upload.wikimedia.org/wikipedia/commons/thumb/8/85/Euler2a.gif/170pxEuler2a.gif
http://www.toymaker.info/Games/assets/images/yawpitchroll.jpg

http://www.researchgate.net/publication/242544190_GravityLike_Fields_and_Space_Propulsion_Concepts
Interesting experimental results. Found just by accident.
Edit: They are still at it, so ?

http://www.researchgate.net/profile/Arbab_Arbab/publication/
51916988_The_unified_quantum_wave_equation/links/0912f50de92ef30406000000.pdf
We have investigated in this work the quaternionic momentum eigen value problem in quantum mechanics. We have written the wave function, energy and momentum of the particle as quaternionic quantities. The momentum eigen value equation reveals that the scalar and vector parts of the wavefunction are governed by a new wave equation. This is a new equation that we wish it will describe bosons and fermions. When the interaction of the particle with an electromagnetic field is introduced a spin term appeared in the equation of motion. The scalar equation doesn't change due to the interaction of the electromagnetic field with the particle. However, the vector equations are altered. We generalized the ordinary uncertainty relation to quaternionic one. This generalization provides us with the energy momentum relation of Einstein and the remaining uncertainty relations. Hence, by adopting the quaternionic quantum mechanics, namely, Dirac equation, we arrived at a dissipative or generalized
KleinGordon equation with a particle spin. This formalism gives rise to the generation of spin angular momentum of the particle when a photon field is introduced in the equation of motion. Further investigation is going on to explore the physics of these two waves

So what TRL would you guys say the devices presented in the "Anomalous Thrust Production...." papers are at right now? I'd say probably a TRL 2. Possibly on the way to a TRL 3, hopefully.
Well, Cannae were talking about flying theirs in a nanosatellite about a year ago, and I suspect that is still ongoing. The Chinese appear to be more cautious but are somewhere around 4+. Shawyer certainly claimed to be at 4 some time ago. And if rumour is to be believed, an aerospace company has pushed Shawyer's work on some from there.
No, it's TRL1. Basic research has not even established sufficient evidence of anything anomalous to convince even a small part of the mainstream physics community.
Being believed by the mainstream community has nothing to do with TRL. If it works, it works. And if the Chinese fly their Emdrive (possibly this year?) and get acceleration, I doubt they'll care what anyone else thinks however loudly they say it can't be true.
I suspect these things really will be operational before a lot of the mainstream starts accepting them, the will to disbelieve is that strong.

http://www.researchgate.net/profile/Arbab_Arbab/publication/51916988
_The_unified_quantum_wave_equation/links/0912f50de92ef30406000000.pdf
We have investigated in this work the quaternionic momentum eigen value problem in quantum mechanics. We have written the wave function, energy and momentum of the particle as quaternionic quantities. The momentum eigen value equation reveals that the scalar and vector parts of the wavefunction are governed by a new wave equation. This is a new equation that we wish it will describe bosons and fermions. When the interaction of the particle with an electromagnetic field is introduced a spin term appeared in the equation of motion. The scalar equation doesn't change due to the interaction of the electromagnetic field with the particle. However, the vector equations are altered. We generalized the ordinary uncertainty relation to quaternionic one. This generalization provides us with the energy momentum relation of Einstein and the remaining uncertainty relations. Hence, by adopting the quaternionic quantum mechanics, namely, Dirac equation, we arrived at a dissipative or generalized
KleinGordon equation with a particle spin. This formalism gives rise to the generation of spin angular momentum of the particle when a photon field is introduced in the equation of motion. Further investigation is going on to explore the physics of these two waves
Very nice, if I'm reading it right, there may be the implication that the spins of the counterpropagating cavity photons could add to 2 in an interaction. But, at the moment, I don't see that generating enough force. (who knows at this point, .... it would need a very high vacuum energy density ?)
Added: (18) to (24) is the argument for translating the cavity dispersion to the "doppler plane" to calculate the accelerated frame of reference. (in a different context)
Insight ??: It seems here that work must be done to install the cavity photons within the limiting boundary conditions of the cavity and that produces a potential energy component which does not appear in the AFR which eliminates the dispersion and doppler shifts the photons. Since we are holding the cavity static we do not see the energy expenditure, only the static initial force on the unbalanced cavity. The work done is a good starting number. Someone must have done that calculation. (he says w/ a straight face ... been there !)
And that force could drop off dramatically under acceleration w/o knowing the energy. In fact it must as a function of the cavity Q.
But that brings up a further question. Unless the work done is a scalar function, maintaining the acceleration in an isolated system may introduce that compensating momentum which would render the whole point mute.
So the place to start is probably the radiation pressure integrated over the boundary of the cavity compared to the free photon case. (not quite the Shawyer case)

So what TRL would you guys say the devices presented in the "Anomalous Thrust Production...." papers are at right now? I'd say probably a TRL 2. Possibly on the way to a TRL 3, hopefully.
Well, Cannae were talking about flying theirs in a nanosatellite about a year ago, and I suspect that is still ongoing. The Chinese appear to be more cautious but are somewhere around 4+. Shawyer certainly claimed to be at 4 some time ago. And if rumour is to be believed, an aerospace company has pushed Shawyer's work on some from there.
No, it's TRL1. Basic research has not even established sufficient evidence of anything anomalous to convince even a small part of the mainstream physics community.
Being believed by the mainstream community has nothing to do with TRL. If it works, it works. And if the Chinese fly their Emdrive (possibly this year?) and get acceleration, I doubt they'll care what anyone else thinks however loudly they say it can't be true.
I suspect these things really will be operational before a lot of the mainstream starts accepting them, the will to disbelieve is that strong.
You could end up getting a situation with people still throwing cold water on this just as someone flies past their window in a flying car. :)

I agree. Even now, without full assurance of these phenomena's existence (without playing favorites, any single one of them being true would be disruptive), the philosophical rejection it causes seems to be way above the expected from new scientific fields or incipient domains.
Yes, I also think it is very possible engineers could earn the merit of using this first, making the applications come before science at large even accepts its existence.
And this could happen in China before the West. Their own existing results, if confirmed and proven to exist to their own authorities, would be worth of a practical test in the short term.

Ok, paging Doctor Rodal for a translation here (from Not so sure of its' link);
Source
Article: Physics of Extreme Gravitomagnetic and GravityLike Fields for Novel Space Propulsion and Energy Generation
Jochem Hauser, Walter Dröscher
[Hide abstract]
ABSTRACT: In 2006 Tajmar et al. reported on the measurements of extreme gravitomagnetic fields from small Nb rings at cryogenic temperatures that are about 18 orders of magnitude larger than gravitomagnetic fields obtained from GR (general relativity). Cifuolini in 2004 and the NASAStanford Gravity ProbeB experiment in 2007 confirmed the LenseThirring effect as predicted by GR (gravitomagnetic fields generated by a rotating massive body, i.e. Earth) within some 10%. In 2007 gravitomagnetic fields generated by a rotating cryogenic lead disk were measured by Graham et al. Though these measurements were not conclusive (the accuracy of the laser gyrometer was not sufficient to produce a standard deviation small enough) their experiment seems to have seen the same phenomenon reported earlier by Tajmar et al., termed parity violation. This means that gravitomagnetic fields produced by the cryogenic rotating ring or disk vary substantially and change sign for clockwise and counterclockwise directions of rotation. The experimental situation therefore occurs to be contradictory. On the one hand GR has been confirmed while at the same time, there seems to be experimental evidence for the existence of extreme gravitomagnetic fields that cannot be generated by the movement of large masses. If these experiments can be confirmed, they give a clear indication for the existence of additional gravitational fields of nonNewtonian nature. As was shown by the GPB experiment, measuring gravitomagnetic fields from GR poses extreme difficulties. Therefore a novel physical mechanism should exist for the generation of gravitylike fields, which might also provide the key to gravitational engineering similar to electromagnetic technology
: Emerging Physics for Novel Field Propulsion Science
Jochem Hauser, Walter Dröscher
[Hide abstract]
ABSTRACT: All space vehicles in use today need some kind of fuel for operation. The basic physics underlying this propulsion principle severely limits the specific impulse and/or available thrust. Launch capabilities from the surface of the Earth require huge amounts of fuel. Hence, space flight, as envisaged by von Braun in the early 50s of the last century, will not be possible using this concept. Only if novel physical principles are found can these limits be overcome. Gravitational field propulsion is based on the generation of gravitational (gravitylike) fields by manmade devices. In other words, gravitylike fields should be experimentally controllable. Present physics believes that there are four fundamental interactions: strong (nuclei), weak (radioactive decay), electromagnetism and Newtonian gravitation. As experience has shown for the last six decades, none of these physical interactions is suitable as a basis for novel space propulsion. None of the advanced physical theories like string theory or quantum gravity, go beyond these four known interactions. On the contrary, recent results from causal dynamical triangulation simulations indicate that wormholes in spacetime do not seem to exist, and thus even this type of exotic space travel may well be impossible. Recently, novel physical concepts were published that might lead to advanced space propulsion technology, represented by two additional long range gravitationallike force fields that would be both attractive and repulsive, resulting from interaction of gravity with electromagnetism. A propulsion technology, based on these novel long range fields, would be working without propellant

Ok, paging Doctor Rodal for a translation here (from Not so sure of its' link);
Links to the papers:
Arxiv: Physics of Extreme Gravitomagnetic and GravityLike Fields for Novel Space Propulsion and Energy Generation
(http://arxiv.org/abs/1104.3247)
PDF link: Emerging Physics for Novel Field Propulsion Science (http://www.hpccspace.com/publications/documents/AIP2010Hauser.pdf)

if it is the initial martin Tajmar discovery he later recanted due to discovering the flow of his cryogenic coolant was the source of his interesting phenomenon. Unfortunate. However that explanation does not illuminate whether he think there is a nonspurious effect lurking after his error is factored out or not. After all he is definitely not the only researcher who thinks his kind of setup affects gravity. Podkletnov for example. There must be some reason this is so.

http://www.emdrive.com/EmDriveForceMeasurement.pdf
New info:
Some clarification from Shawyer. Helps to clear up some of the arguments we had about how Shawyer uses thrust and reaction, and which way it moves.

Very nice, if I'm reading it right, there may be the implication that the spins of the counterpropagating cavity photons could add to 2 in an interaction. But, at the moment, I don't see that generating enough force. (who knows at this point, .... it would need a very high vacuum energy density ?)
I bolded spin 2 above. It immediately caught my eye because gravitons are spin 2 massless particles (if they exist). Don't know what to make of it yet, but it jumped right off of the page when I saw it. Very interesting work you're doing. I really think you were on to something with dispersion too. It makes way more sense to approach radiation pressure differences leading to thrust using your ideas than how Shawyer explains it with his group velocity model.

http://www.preposterousuniverse.com/blog/2013/10/03/guestpostlancedixononcalculatingamplitudes/
Along the way, Zvi, John Joseph and Henrik, thanks to the timehonored method of “just staring at” the loop integrand provided by unitarity, also stumbled on a new property of gauge theory amplitudes, which tightly couples them to gravity. They found that gauge theory amplitudes can be written in such a way that their kinematic part obeys relations that are structurally identical to the Jacobi identities known to fans of Lie algebras. This socalled colorkinematics duality, when achieved, leads to a simple “double copy” prescription for computing amplitudes in suitable theories of gravity: Take the gauge theory amplitude, remove the color factors and square the kinematic numerator factors. Crudely, a graviton looks very much like two gluons laid on top of each other. If you’ve ever looked at the Feynman rules for gravity, you’d be shocked that such a simple prescription could ever work, but it does. Although these relations could in principle have been discovered without unitaritybased methods, the power of the methods to provide very simple expressions, led people to find initial patterns, and then easily test the patterns in many other examples to gain confidence.
These guys won the Sakurai Prize for Physics.

All I can say so far is, that I think that if the cavity dispersion relation has an asymmetric variation in at least one spatial dimension, then there exists an accelerated frame of reference such that the dispersion is eliminated [and the cavity acts as an open system ?] (ie. the boundary condition is nullified, the photons act as free photon wavefunctions, the impedance matches that of the vacuum [?]) The SachsSchwebel anomalous current "looks like" it might contain this relation. Conservation of 4momentum is still open to question.

http://www.emdrive.com/EmDriveForceMeasurement.pdf
New info:
Some clarification from Shawyer. Helps to clear up some of the arguments we had about how Shawyer uses thrust and reaction, and which way it moves.
Hold the phone... am I reading this right. You can only ever measure thrust if the cavity is accelerating? So just sitting on a flat floating stationary table top should yield no force, the same with when the cavity is moving at constant velocity. Did I mis interpret that pdf?

if so that pushes it into Dr Woodward and vis inert or "fictitious" fields such as inertia, and gravity. (I'm currently reading Woodward's book )

http://www.emdrive.com/EmDriveForceMeasurement.pdf
New info:
Some clarification from Shawyer. Helps to clear up some of the arguments we had about how Shawyer uses thrust and reaction, and which way it moves.
Hold the phone... am I reading this right. You can only ever measure thrust if the cavity is accelerating? So just sitting on a flat floating stationary table top should yield no force, the same with when the cavity is moving at constant velocity. Did I mis interpret that pdf?
if so that pushes it into Dr Woodward and vis inert or "fictitious" fields such as inertia, and gravity. (I'm currently reading Woodward's book )
Unlike the concepts of displacement, (and its time rates: velocity, acceleration) and strain (which can be mathematically defined in terms of geometry), the concept of "force" is intuitive and has been impossible to mathematically define intrinsically except in terms of other variables. (Although Cauchy and most recently Truesdell made valiant attempts).
Forces can never be measured directly. Forces are always measured indirectly: for example measuring the resulting acceleration (and calculating the inertial force as F=m*a) or measuring a strain (and calculating an average Force=(crosssectional Area)*(modulus of Elasticity)*strain ) or measuring a displacement (and calculating Force=(spring stiffness)*displacement).
It is not practical to use a "balance scale" to measure unknown, timevaryingforces
(http://upload.wikimedia.org/wikipedia/commons/thumb/d/d0/Balance_scale_IMGP9755.jpg/220pxBalance_scale_IMGP9755.jpg)
EDIT: Notwithstanding the above (true) statements I find Shawyer's writing to be confusing and easily lead to confusion. NASA Eagleworks used a torsional pendulum to figure out the force produced by an initially static (truncated cone) EM Drive. NASA reported to have figured out the EM Drive forces from the EM Drive measured displacement , using a calibration Force=stiffness*displacement. Unfortunately NASA did not clearly specify whether the displacement (for the truncated cone) was in the direction of the small end or the direction of the large end of the truncated cone.

This "clarification" by Shawyer can hardly be interpreted at all. It states that a reaction force equal and opposite to the thrust is to be expected when not accelerating (reaction from a support) "so is Newtonian" but then plays with orientation conventions and decides that "This situation is unique to a propellantless thruster such as EmDrive and analogies with conventional devices are pointless." Ha !
So we are left wondering what makes "propellantless Newtons" special compared to "usual Newtons". I agree (with Rodal) that, as far as conventional Newtons are concerned, measurement of force needs some kind of displacement, but for constant force such displacement reaches a stable equilibrium (static situation) where R=T and both can then be determined by said dispacement. Shawyer's paper clearly states that this shouldn't be expected from "propellantless Newtons".
Clearly, in a static situation, where T and R both exist as forces, they will cancel out. Thus any attempt to measure them by simply placing the thruster vertically on a set of scales will fail. If however the thrust is sufficient such that a=g,then the thruster could be made to hover above the scales.
So if we have a thruster with a ever so slightly below g the balance records no change (full weight of thruster) and then an infinitesimally small increase of a above g makes the thruster hover above the balance that all of a sudden will record a weight of 0. How strange transition ! Moreover the same argument of experiment "at rest" => no measured force is made in horizontal setting (Fig 3).
It therefore appears that a force measurement can only be made in a dynamic environment, ideally by allowing the thruster to accelerate, ...
But isn't a vertical thruster in a dynamic environment thanks to g ? It's like the "propellantless Newtons" can tell the difference between being "restrained" or "unleashed". Not only equivalence principle is broken by such special Newtons, but paradoxes directly relevant to space flight are obvious :
assume such a thruster is mounted at the back of a spacecraft, but between the thruster and this big inertial mass there is a spring (no matter how stiff) and a displacement/stress sensor that tells the Newtons communicated by the thruster to the spacecraft. Take a body small enough (asteroid...) that the thruster is supposed to be able to hover the craft above at constant altitude. In this "static situation" the "propellantless Newtons" can't be measured (by a displacement related to stress of the link between thruster and craft). So I guess a spacecraft expects "conventional Newtons" to hover around: the "propellantless Newtons" can't be communicated from the thruster to useful push on a craft through a conventional link that would allow stress deformation (and therefore conventional measurement)...
Same argument would forbid thrusting at constant speed and constant thrust against a medium (horizontal flight in atmosphere). Worse : if equivalence principle is to hold, can't accelerate a spacecraft in free space as it's the same as hovering at constant altitude in a given gravity field.
Basically, saying a thruster is not stressing a scale's spring is saying that running the thing aboard a ship is useless : the thrust is 0 for all practical purpose. Unless we are speaking of an extending inertia modifying field that goes beyond the inner skin of walls of the thruster and accelerating directly the bulk of the rest of spacecraft (that would then need clarification for the range of such field.)
We could also discuss the orientation conventions : fig1 in the usual sense a reaction pseudoforce like R is opposite to a (italic for vectors) : the usual M a = T would go T  M a = 0 and to T + R = 0 (as common sense would tell) that is
R =  Ma and not the opposite.
Now we understand why Shawyer's design of LEO launcher puts pointy end of thruster up, because the thrust is toward the ground (but this is unconventional Newtons...).
This latest paper is moving the goalpost, ideally by allowing the goalpost to accelerate...

So, before I trundle off to bed...(be'in old an' all)
When we are in the AFR that removes the cavity dispersion at the expense of splitting the frequency into doppler components, and giving us a flat metric tensor, what tensor quantities can we generate which will give zero force in this frame (despite the difference in frequency) and allow us to find the force in the rest frame of the cavity. Then the question is: can this be done in GR or does it need extensions (such as SachsSchwebel, etc)

Dear Mr. Shawyer, it is very simple. Put your device PLUS power supply on a balance scale, switch it on. If the scale moves (or most preferably in ~vacuum in LEO, kindly ask your chinese friends to arrange for that  they reported almost a Newton "thrust", didn't they), you become an eternally famous person. If it however does not move, stop deluding yourself and others. Deal?

Considering that NASA will fly just about anything of scientific note into space for the cost of the paperwork (and the Ukrainians will fly anything for you for less than $100k) most of these gadgets could be demonstrated in LEO.. if they worked.

ISTM like they may be able to get a clear signal without going all the way into LEO. Couldn't they send an appropriately sensitive test rig up on a vomit comet or a balloon(then drop it), vacuum chamber included if need be? 1 Newton sounds like a lot with respect to sensitivity/margins/etc in microgravity, so the test rig probably shouldn't need to be terribly complicated or expensive in either case. At least not when compared to something that's going to LEO and the associated launch/operation costs.

Considering that NASA will fly just about anything of scientific note into space for the cost of the paperwork (and the Ukrainians will fly anything for you for less than $100k) most of these gadgets could be demonstrated in LEO.. if they worked.
Is this something that could be tested on the outside of ISS?

So, before I trundle off to bed...(be'in old an' all)
When we are in the AFR that removes the cavity dispersion at the expense of splitting the frequency into doppler components, and giving us a flat metric tensor, what tensor quantities can we generate which will give zero force in this frame (despite the difference in frequency) and allow us to find the force in the rest frame of the cavity. Then the question is: can this be done in GR or does it need extensions (such as SachsSchwebel, etc)
It would a big surprise if this would be possible within General Relativity: it would certainly go against what Sean M. Carroll and John Baez have stated (particularly concerning frames of reference). The implication is that extra coupling terms and/or nonlinearities would be needed, such as SachsSchwebel.

Things are coming together slowly. I have the connectors and pigtails. Got the Ntype female bulkhead threaded solder cup connectors and Ntype male to SMA male connectors. Also got the panel type bulkhead connectors which I'm familiar with but don't really like, as a backup. I purchased instead of borrowed and shipping costs more than the actual product. The horn antennas in which to couple the rf across the gap will be homebrew (have to make these myself because standard gain horns are way too expensive; this could make it or break it). Copper sheeting is expensive so I didn't just order a bunch of it yet. Mostly because I don't want to waste material, and honestly I'm being lazy (and am still unsure on wasting expendable cash on a failed experiment), and I spent most of my extra cash on Christmas for the kids. Today I finally got around to planning out the frustum configuration and dims. Attached is a screen shot of the cut sheet utilizing a 2x4' sheet. The full CAD is in the google drive link. I can do a light cone (by the base) and a 45 degree (by the apex) with one sheet and have room for cutouts to make the flat ends. The design intent is to provide a cone in which I can quickly change resonant modes by inserting discs of varying diameter. With this setup I can support 2.4ghz ISM band at the narrow end and support 2 full wavelengths plus more in length. 5ghz is also supported.
Tools used:
https://www.google.com/?gws_rd=ssl#q=right%20circular%20cone%20calc%3A%20find%20A_L&skip=s
http://www.analyzemath.com/Geometry_calculators/surface_volume_frustum.html
http://www.calculatorsoup.com/calculators/geometrysolids/conicalfrustum.php
http://www.cleavebooks.co.uk/scol/calsect.htm
http://en.wikipedia.org/wiki/IEEE_802.11#Channels_and_frequencies
http://www.wavelengthcalculator.com/
CAD drawing with cut sheet:
https://drive.google.com/folderview?id=0B4PCfHCM1KYoTXhSUTd5ZDN2WnM&usp=sharing#list
Copper:
http://basiccopper.com/10milcoppersheet24x41.html (not cheap)
http://basiccopper.com/24x416milcos.html (might go with thicker, more expensive 16mil.
I think 10 mil is the way to go (I'm going for strength enough to support its own weight, but still be lightweight) but before I drop a hunski on it I'm going to get a sampler http://basiccopper.com/samplerpacks.html. I might go with 16 mil http://basiccopper.com/24x416milcos.html. It depends. Here's why I think 10mil or alternate 16mil is the right choice: http://basiccopper.com/thicknessguide.html

By the way, John Baez (in his blog https://plus.google.com/117663015413546257905/posts/C7vx2G85kr4 , answering correspondence) had some nonflattering things to say about Woodward's approach as well.
which however is not the subject of this thread, as you pointed out at page 2 and 3 of this thread
As Chris Bergin made clear, the purpose of this forum is to deal with SPACEFLIGHT APPLICATIONS (of EM Drives: those propellantless drives comprised of a microwave cavity as the devices tested by Shawyer in the UK, Prof. Juan Yang in China and Brady, March, White, et.al. at NASA):
Why is this prescription by Chris Bergin being ignored?
Although the latest Woodward experiments (Fearn, Zachar, Woodward & Wanser) show that it takes 20,000 times more power to produce a given level of thrust than the power required to produce the same thrust for the EM Drive (Shawyer demo), and therefore these experiments do not constitute "EM Drive Spaceflight Applications" (as instructed by Chris Bergin) Woodward fans persist on carrying a debate on this thread rather than their own Woodward thread.
Frankly, I don't understand what is the goal being pursued here by Woodwardeffect fans to insist to carry arguments concerning Woodward's theory and experiments in this thread.
The curtailment of the previous EM Drive thread by this forum's moderator was due to disruptive discussions regarding the validity of the Woodward effect, including a negative review of Woodward's book by a physicist.
seriously Rodal, you chastised us and now posts about Woodward here? Looks like a bait for someone to come defend Woodward theory here... ::)
if you want to post about Woodward Theory, be it questions, praise, analysis, ARTICLES or CRITICISM, the place is this thread
http://forum.nasaspaceflight.com/index.php?topic=13020.1845
and yes, the article was about EM Drive, but you specifically called out in your comment the criticism by John Baez regarding Woodward Theory, and THAT criticism should be pointed out and discussed in the appropriate thread, as pointed out by yourself in the 2nd and 3rd pages.

Good that Shawyer has clarified the force measurement. Referring to his Fig. 1 from the paper
http://www.emdrive.com/EmDriveForceMeasurement.pdf
and reproduced below, I conclude he is saying the force that is acting on the EMdrive is in the same direction as the vector labeled T. The only difficulty I have with this is from looking at the videos of the EM=drive. When it is operating it moves with the small end forward.
https://www.youtube.com/watch?v=57q3_aRiUXs
In the earlier thread I stated that maybe the thrust was due to heat convection from the sloped sides. This was dismissed because the EMdrive moves in the opposite direction as seen in the video.

I think it is about time for us to get on Eagleworks for an update:
https://www.facebook.com/eagleworksnasa

@AcesHigh
I think it was because i mentioned Woodward while trying to explain the difference between Vis Vivo forces like electromagnetism, the strong force, weak force and forces that are only apparent when a force or acceleration is applied to a mass such as inertia. such forces are labelled "fictitious" in physics without any negative meaning. everyone realizes there is a such thing as inertia and gravity.
So anyway; i invoked Woodward before Dr Rodal made his reply containing comments on Woodward.

Good that Shawyer has clarified the force measurement. Referring to his Fig. 1 from the paper
http://www.emdrive.com/EmDriveForceMeasurement.pdf
and reproduced below, I conclude he is saying the force that is acting on the EMdrive is in the same direction as the vector labeled T. The only difficulty I have with this is from looking at the videos of the EM=drive. When it is operating it moves with the small end forward.
https://www.youtube.com/watch?v=57q3_aRiUXs
In the earlier thread I stated that maybe the thrust was due to heat convection from the sloped sides. This was dismissed because the EMdrive moves in the opposite direction as seen in the video.
Look at Fig. 2 in http://www.emdrive.com/EmDriveForceMeasurement.pdf:
the acceleration according to Shawyer is directed towards the small end, which is entirely consistent with the movement in the video.
Furthermore, Shawyer himself writes that the experiment in the video with the rotary airbearing with the SPR Demonstrator calculated the force based on measurement of the acceleration (directed towards the small end):
It therefore appears that a force measurement can only be made in a dynamic environment, ideally by allowing the thruster to accelerate, measuring that acceleration, and then calculating the thrust from T =  Ma. This is not a very easy method, although the SPR Demonstrator Thruster was successfully tested in this way on a rotary air bearing
As discussed by Frobnicat and me in posts above, the definition of the thrust force by Shawyer ( Shawyer defines the thrust force in the opposite direction as to the movement) is highly unorthodox and Shawyer's force arguments are inconsistent, but anyway, as I discuss above, forces can never be measured directly: what can be measured are displacements, strains or accelerations. The acceleration as defined by Shawyer in Fig. 2 is entirely consistent with the movement in the video.

at the risk of raising the ire or EM thruster purists; this is the time to ask:
only apparent in a dynamic environment, only apparent in excelleration and so forth...
and i noticed that thing i posted in the warp thread thrusts in the opposite direction it should by Newtonian physics. The direction of the induced motion is in the same direction the radiated energy travels. (If I understood it right.)
don't these things kind of resemble "vis inert" or "fictitious" forces?
If not; forgive me, I apparently have that book passage on my mind now, perhaps to uncalled for extremes.

...and your point is?

Had a couple minutes. Just thought I'd check the consistency of the dispersion idea against the Greg Egan cavity. No problem. It's not a general expression, he has the numeric results for a few modes, but that's enough.

...and your point is?
who me? You trying to get me in trouble? ;)
well... I guess it would mean that the EM bit is somewhat misleading. The real mechanism would be from some ordinarily inert and undetectable source that might be nonlocal or global in nature. He who shall not be named in this thread would suggest the gravitational influence of mostly distant matter. But that is probably far from the only candidate among so called fictitious fields. The EM details, asymmetric capacitors or wobbly cams or whatever was used to create a dynamic environment would only be acting like the small voltage that biases a transistor or the current that pull the contact arm down in a relay. Once you have an *appropriate* dynamic system the "fictitious" fields would stop pretending to not exist and make themselves known. It would be the aroused dead energy/vis inert that creates the motive force and not necessarily the EM put through the device.

Thank you SB. That makes it all as clear as mud.

Oh great; then we're both at about the same level of understanding on my ramblings then :)
The references to the effect only being evident when the system was in a dynamic state and others led me to think that that is how inert or dead energies or fictitious energies are described and to speculate that if they sound the same they might be the same. I think it would explain how you can have half a hundred different design approaches that somehow get comparable results. I could go on but I doubt it would be appreciated.

ME thrusters are exploring quite a different range of "bulk acceleration" magnitudes (more than 1000s of Gs if I recall, back and forth around the piezos) compared to a freely moving EM drive, horizontally (a few milli Gs ?) or vertically on a scale (1G)... And the "thrusts" (equivalently M times measured a, to deal with recently introduced "special Newtons") should be roughly impacted by a few order of magnitudes less for EM devices than ME devices. That is, if the same "dynamic setting effect" is at play...
Beyond unorthodox pseudoforces orientation conventions, this "dynamic environment" condition seems quite problematic and ill defined. Ignoring theoretical musings, Shawyer makes 3 phenomenological predictions :
 That a vertical EM thruster on a scale will record no thrust (unless the thruster is efficient enough to fly against 1G) page 2 "Thus any attempt to measure them by simply placing the thruster vertically on a set of scales will fail"
 That a horizontal EM thruster restrained from accelerating horizontally (through an opposing spring) will record no thrust, page 3 figure 3 "Because the thruster is at rest, no force will be measured on the load cell"
 That a horizontal EM thruster free to move will accelerate horizontally, page 2 figure 2 "In free space, the thruster will simply accelerate at a m/s/s" In this case we are not in free space but on the horizontal axis this is all the same (and claimed results by Shawyer of accelerations on horizontally rotating arms confirm this view from the author)
So if one thing is clear it is that, for him, the definition of "being at rest" is the same whether not moving on a 0G axis (sorry for the ugly wording) as in restrained horizontal situation or not moving in altitude at fixed G pulling, as in vertical situation. Well, maybe that is the common sense most non physicists give to the intuitive concept of "being at rest", but the 2 situations are very different from what equivalence principle would tell : on a horizontal axis a "static object" shows no departure from an inertial rest frame, while on a vertical axis a "static object" (constant altitude) shows an accelerating departure from an inertial rest frame (free falling). Telling the two situations have the same consequence (no differential stressing of springs between device on and off) is either saying that the "effect" does not depend on acceleration relative to inertial rest frames (that is : it is always 0, there is no effect !) or that it breaks equivalence principle.
All right then, equivalence principle is strong but this is not a sacred cow, we can sacrifice it if it's worth. But then there are problems... how can we define "at rest" vs "dynamic environment" in a scientifically sane and quantitatively predictive way as far as measurable quantities are concerned ? Taking the 3 experimental predictions of Shawyer together, certainly not relative to distant matter (ŕ la Machian) since it would depend on local gravity.
Now Shawyer can claim that measuring a 0 net difference on a scale's spring is actually a confirmation of the theory... But if EM drives like to be free, why not just mount the thruster freely in a box, let it accelerate, bump into one end of the box (on a spring) so that the box recoils, and the thruster is free again to accelerate and so on. This cycle would convert "freely accelerating thingy" into net linear momentum, averaged. This box, as seen from outside, could either be itself freely accelerating, or having a net pushing on a spring of a restraining scale as any well behaved thruster is expected to be able to do. Call that a pulsed EM drive.

Looking over the last several posts, I see absolutely nothing related to space flight applications. All I see is more of exactly what got the previous version of this thread to disappear for a while.

Looking over the last several posts, I see absolutely nothing related to space flight applications. All I see is more of exactly what got the previous version of this thread to disappear for a while.
I would respectfully disagree. I find the discussion both highly pertinent to possible space flight applications and quite thought provoking. We must not lose the forest for the trees, but at the same time, it is difficult to comprehend the forest without the trees.

None of these experiments have demonstrated a linear acceleration: all of them have measured rotational accelerations. None of the EM Drives have been tested in a vacuum. None of the measured forces are high enough to levitate the drive.
Forget about levitation. I havent read much or anything about it, but are the forces even in the same ballpark as existing magnetic torquer rods for cubesats ? If yes, in theory this could assist with attitude control in deep space, at least for desaturation.
Anyone ? Anyone ?
I mean, actual spaceflight application. Desaturation spends fuel. Can we get a propellantless desaturation device, with main attitude control provided by reaction wheels ?
Again, from the claimed experimental setups, are the reported angular momentums even on a scale where they could turn a cubesat  even if it takes a long time to do so ? Its not like torquer rods are fast or anything, but they only work within earths magnetic field.
And if it cannot turn a cubesat, the entire thing is no better than Steorn Orbo, is it ?

....
Beyond unorthodox pseudoforces orientation conventions, this "dynamic environment" condition seems quite problematic and ill defined. Ignoring theoretical musings, Shawyer makes 3 phenomenological predictions :
....
 That a horizontal EM thruster restrained from accelerating horizontally (through an opposing spring) will record no thrust, page 3 figure 3 "Because the thruster is at rest, no force will be measured on the load cell"
....
A spring (with finite stiffness) attached to a wall NEVER prevents an object attached to it from accelerating, thus Shawyer's statement is not well stated or it is incorrect. Only an infinitely stiff (rigid) spring would prevent an object from accelerating. Otherwise (for finite spring constant) the system will just obey a solution of the second order differential equation: m d^2x/dt^2 +c dx/dt + k x = F.
If the displacement is a function of time, such that the second order derivative of the displacement with respect to time is not zero, there is an acceleration a = d^2x/dt^2 =( F  c dx/dt  k x )/m . In words: the acceleration equals the applied force minus the viscous force, minus the spring force, all divided by the mass.
If the displacement is not a function of time, we have simply (the "steadystate" solution) F=k*x (force=springConstant*displacement)
In the NASA Eagleworks tests of the truncated cone:
1) The truncated cone EM thruster was restrained by the torsional spring constant of the torsional pendulum used for measurement. The torsional spring constant effectively acts like a spring attached to a wall (the difference being that in the NASA Eagleworks test we have a torsional pendulum where the EM Drive performs a rotation instead of a rectilinear motion)
2) The truncated cone EM thruster was initially at rest (prior to power input).
3) A timevarying displacement (effectively due to a rotation around the torsional axis) was recorded and thus a force was calculated by NASA Eagleworks using the known constants of the system.
4) We have verified this: we modeled NASA Eagleworks torsional pendulum, and furthermore analyzed the data using Fourier Transforms to obtain the Power Spectral Density and the Autocorrelation of the response.
Thus:
Shawyer's statement "That a horizontal EM thruster restrained from accelerating horizontally (through an opposing spring) will record no thrust" in http://www.emdrive.com/EmDriveForceMeasurement.pdf is not well stated or it is incorrect, as shown, for example, by the experiments carried out at NASA Eagleworks.

None of these experiments have demonstrated a linear acceleration: all of them have measured rotational accelerations. None of the EM Drives have been tested in a vacuum. None of the measured forces are high enough to levitate the drive.
Forget about levitation. I havent read much or anything about it, but are the forces even in the same ballpark as existing magnetic torquer rods for cubesats ? If yes, in theory this could assist with attitude control in deep space, at least for desaturation.
Anyone ? Anyone ?
I mean, actual spaceflight application. Desaturation spends fuel. Can we get a propellantless desaturation device, with main attitude control provided by reaction wheels ?
...
As an example you can use for calculations, Shawyer reported (for his "Shawyer Demo") a measured force = 0.1023 Newtons (1/10th of a Newton) for a power input of 421 watts.
NASA Eagleworks (Brady et.al) reported (for the TE mode of the truncated cone) a measured force = 0.00005541 Newtons (55.41 MicroNewtons) for a power input of 2.6 watts.

I thought I would make up a summary of the dispersion relation approach, as I keep
doing this in bits and pieces.
1. The initial question was:
In General Relativity (GR), if an RF cavity subject to an accelerating frame of
reference (AFR) displays asymmetric frequency dispersion, will an asymmetric RF
cavity which exhibits wavelength dispersion generate an accelerating frame of
reference.
2. It turned out that the asymmetric cavity dispersion relation is easily solved
for an AFR in which the wavelength dispersion dissapears, being replaced by a
frequency dispersed Doppler pair. Energy is conserved.
g = (X[subm,n])^2*(c/4*pi^2)*lambda^2*((1/a^2)(1/b^2))
where a anb b are the end plate radii and the X are the Bessel function zeros.
X[subm,n] = mth root of dJ[subn](x)/dx = 0
[1,0]=3.83, [1,1]=1.84, [1,2]=3.05, [2,0]=7.02, [2,1]=5.33, [2,2]=8.54, [3,0]
=10.17, etc.
Lambda < cutoff wavelength.
Lambda is the free space wavelength c/f.
giving thrust per photon:
T = (X[subm,n])^2*(h/4*pi^2)*lambda*((1/a^2)(1/b^2))
3. The surprise was that the force "on the photons" T, which would be required to
maintain that acceleration closely matched the experimental forces reported for
these cavities. The difference from other calculations is that there is a term
dependent on the particular mode of the cavity, (X[subm,n])^2, not just the area
of the end plates.
T = P*Q*(X[subm,n])^2*(1/c*4*pi^2)*lambda^2*((1/a^2)(1/b^2))
TM211 T=9.84e5 vs 9.12e5 P=16.9 Q=7320
TM211 T=2.39e4 vs 5.01e5 P=16.7 Q=18100
TE012 T=1.32e4 vs 5.54e5 P=2.6 Q=22000
4. So where do things stand?
If the experimental forces are real and repeatable then since the acceleration of
the "Doppler" frame is considered the "Gravitational Potential" in GR. The
corresponding term in the rest frame could only be an "Electromagnetic Potential",
calculated from the dispersion relation of the cavity.
That is to say, in GR, there is no valid equation here without introducing a cross
term between gravity and electromagnetism. So, new physics would be required.
The SachsSchwebel "quaternion" formulation of GR has a cross term which "looks
like" it might fit, but it's hard for me to evaluate. There is no shortage of
other theoretical attempts.
5. Momentum:
Conservation of momentum would have to be satisfied with the cross term. The
suggestion from the experimental results (assuming they are real), that the
required momentum transfer is the same (or nearly the same) as that available from
the rest frame photons, implies that the cross term contains a field of very high
energy density compared to that of the photons. (to "push off" ?)

I thought I would make up a summary of the dispersion relation approach, as I keep doing this in bits and pieces.
....
Thanks for the summary, much appreciated.
The difference from other calculations is that there is a term dependent on the particular mode of the cavity, (X[subm,n])^2, not just the area of the end plates.
Indeed! It is very impressive that not only your calculations are not that far from actual results but that your theory correctly predicts mode dependence and that the magnitude of the mode dependence corresponds with experimental results: the Transverse Electric TE012 mode produces much more [thrust force/input power] than the Transverse Magnetic TM211 mode , which was confirmed by the NASA Eagleworks experiments! Neither the Shawyer nor the simplified McCulloch equations show this modedependence.

I got some help making those equations look pretty with LaTeX, but I'm not sure it's rendered correctly. Are these accurate?
EDIT: Formulas were rendered inaccurately, and have been unlinked.
Thrust per photon:
http://i.imgur.com/V24BnsY.png
\mathrm T = \left( \mathrm X _{m,n} \right) ^2 \left( \frac{\hslash}{4} \pi ^2 \right) \lambda \left( \frac{1}{a^2}  \frac{1}{b^2} \right)
Force on the photons:
http://i.imgur.com/YvP9Zj9.png
\mathrm{T = P} \mathbb Q \left( \mathrm X_{m,n} \right) ^2 \left( \frac{1}{\mathrm{c}} 4 \pi ^2 \right) \lambda^2 \left( \frac{1}{a^2}  \frac{1}{b^2} \right)

I got some help making those equations look pretty with LaTeX, but I'm not sure it's rendered correctly. Are these accurate?
Thrust per photon:
(http://i.imgur.com/V24BnsY.png)
\mathrm T = \left( \mathrm X _{m,n} \right) ^2 \left( \frac{\hslash}{4} \pi ^2 \right) \lambda \left( \frac{1}{a^2}  \frac{1}{b^2} \right)
Force on the photons:
(http://i.imgur.com/YvP9Zj9.png)
\mathrm{T = P} \mathbb Q \left( \mathrm X_{m,n} \right) ^2 \left( \frac{1}{\mathrm{c}} 4 \pi ^2 \right) \lambda^2 \left( \frac{1}{a^2}  \frac{1}{b^2} \right)
@RotoSequence: thank you for putting this in Latex.
@Notsosureofit: did you mean to use the "reduced Planck constant", also called "Dirac constant" hbar as in the Latex equations above or did you mean to use the Planck constant h as per your post ?
where
h = hbar * 2 * Pi
Given the de Broglie wavelength λ of a photon and the speed of light c, the energy E of the photon is
E = h c / λ = hbar * 2 * Pi * c / λ
It seems to me that you meant
1) to use h (instead of hbar in the Latex equation)
2) the factors of (Pi^2) in the first Latex equation and 4 Pi^2 in the 2nd Latex equation are in an incorrect position: the factors should be (h/(4 Pi^2)) in the first equation and (1/(c 4 Pi^2)) in the second equation
Please check, thanks

g = (X[subm,n])^2*(c/(4*pi^2))*lambda^2*((1/a^2)(1/b^2))
T = (X[subm,n])^2*(h/(4*pi^2))*lambda*((1/a^2)(1/b^2))
T = P*Q*(X[subm,n])^2*(1/(c*4*pi^2))*lambda^2*((1/a^2)(1/b^2))
I'm not where I can double check, but I usually use h and "My Dear Aunt Sally".
Probably should call the last one NT...

Thrust per photon, with Planck's constant instead of the reduced constant: http://i.imgur.com/Lm9OVYD.png
EDIT: The original image has been unlinked because the formula is rendered inaccurately.

Thrust per photon, with Planck's constant instead of the reduced constant:
(http://i.imgur.com/Lm9OVYD.png)
I think that the factors of (Pi^2) in the first Latex equation and 4 Pi^2 in the 2nd Latex equation are in an incorrect position (they should be in the denominator instead of the numerator): the factors should be (h/(4 Pi^2)) in the first equation and (1/(c 4 Pi^2)) in the second equation.

I think that the factors of (Pi^2) in the first Latex equation and 4 Pi^2 in the 2nd Latex equation are in an incorrect position (they should be in the denominator instead of the numerator): the factors should be (h/(4 Pi^2)) in the first equation and (1/(c 4 Pi^2)) in the second equation.
Hmm. Are you sure? Oh well, here they are just the same:
EDIT: Added NotSoSureOfIt's third equation to the list:
(http://i.imgur.com/CigE4HR.png)
(http://i.imgur.com/0AT8Jep.png)
(http://i.imgur.com/DmV4xbE.png)
Old versions:
Changed T to NT http://i.imgur.com/kBUnXiA.png
http://i.imgur.com/NjgzBtl.png

I think that the factors of (Pi^2) in the first Latex equation and 4 Pi^2 in the 2nd Latex equation are in an incorrect position (they should be in the denominator instead of the numerator): the factors should be (h/(4 Pi^2)) in the first equation and (1/(c 4 Pi^2)) in the second equation.
Hmm. Are you sure? Oh well, here they are just the same:
(http://i.imgur.com/0AT8Jep.png)
(http://i.imgur.com/NjgzBtl.png)
Yes, thanks. That's what I think. But these are @Notsosureofit equations, hopefully he can double check them and see whether he agrees :)
PS: I agree with Notsosureofit, the second equation would better read NT, where "N" stands for the thrust of all the photons, instead of the thrust of a single photon "T".

PS: I agree with Notsosureofit, the second equation would better read NT, where "N" stands for the thrust of all the photons, instead of the thrust of a single photon "T".
Edited :)
EDIT: And because my friend who showed me LaTeX insists, c4 is becoming 4c ;)
Also added Notsosureofit's third equation, hopefully without error!
(http://i.imgur.com/CigE4HR.png)

Guys, Guys......I stopped reading some time ago.....now we are into the 2nd thread.
Time to "let it go"........prove it one way or another. The energy spent back and forth could have been put into a cad file, exported into STEP or IGES format by now....(someone please do it)
Then maybe if time permits i'll print out a test model.
Someone then talk maybe to Nanoracks, and lets get it tested. :)

Guys, Guys......I stopped reading some time ago.....now we are into the 2nd thread.
Time to "let it go"........prove it one way or another. The energy spent back and forth could have been put into a cad file, exported into STEP or IGES format by now....(someone please do it)
Then maybe if time permits i'll print out a test model.
Someone then talk maybe to Nanoracks, and lets get it tested. :)
What are STEP and IGES ?

Guys, Guys......I stopped reading some time ago.....now we are into the 2nd thread.
Time to "let it go"........prove it one way or another. The energy spent back and forth could have been put into a cad file, exported into STEP or IGES format by now....(someone please do it)
Then maybe if time permits i'll print out a test model.
Someone then talk maybe to Nanoracks, and lets get it tested. :)
What are STEP and IGES ?
They are graphics file data formats for supposedly "vendor neutral" purposes for digital exchange of CAD (Computer Aided Design) drawings. (As opposed to, for example vendorspecific AutoCad data files, for which you need vendorprovided software like AutoCad to be able to read them).
Imagine if somebody told airplane or rocket developers [if NASA Eagleworks or Shawyer can be compared [?] to the Wright Brothers or Goddard] :"I stopped reading some time ago, it has now been [months (?) for us] since you guys have been writing about this in this forum. Time to "let it go": give me detailed engineeringquality drawings showing how to make this so that I can fabricate it to test whether this flying machine or rocket does indeed fly" :)
For Nanoracks vision, see: http://nanoracks.com/aboutus/ourvision/ or this video:
https://www.youtube.com/watch?v=AdtiVFwlXdw

Hmmm...
http://www.nature.com/nphys/journal/vaop/ncurrent/full/nphys3226.html
"A selfaccelerating electronic wave packet can acquire a phase akin to the Aharonov–Bohm effect, but in the absence of a magnetic field."
"The vector potential in question is a gaugedependent quantity, namely a mathematical construct whose form is not uniquely defined."
http://www.nature.com/nphys/journal/vaop/ncurrent/full/nphys3196.html
"The Aharonov–Bohm effect predicts that two parts of the electron wavefunction can accumulate a phase difference even when they are confined to a region in space with zero electromagnetic field. Here we show that engineering the wavefunction of electrons, as accelerating shapeinvariant solutions of the potentialfree Dirac equation, fundamentally acts as a force and the electrons accumulate an Aharonov–Bohmtype phase—which is equivalent to a change in the proper time and is related to the twinparadox gedanken experiment. This implies that fundamental relativistic effects such as length contraction and time dilation can be engineered by properly tailoring the initial conditions. As an example, we suggest the possibility of extending the lifetime of decaying particles, such as an unstable hydrogen isotope, or altering other decay processes. We find these shapepreserving Dirac wavefunctions to be part of a family of accelerating quantum particles, which includes massive/massless fermions/bosons of any spin."
See:
http://www.nature.com/nphys/journal/vaop/ncurrent/extref/nphys3196s1.pdf

The main criticism against propellantless EM Drives has been conservation of momentum.
It is discussed here that conservation of momentum for certain effects (like the AharonovBohm Effect) is neither trivial nor has it been satisfactorily derived
Feynman's conservation of momentum paradox and the AharonovBohm Effect
http://digitalcommons.unl.edu/cgi/viewcontent.cgi?article=1129&context=physicsfacpub
what is the correct force expression for the force on the solenoid and
second, the assumption that Newton’s third law holds in the sense that the
change of the solenoid’s momentum is compensated by the change of the
electron’s momentum. The discussion of “Feynman’s paradox” shows that
the latter is not always the case. It is possible that a change in field momentum
is an essential part of the AharonovBohm discussion, which is exactly
what Aharonov and Casher claim in 1984 [45]. Many theoretical papers have
discussed this issue [16, 17, 36, 37]. These discussions involve imbalanced
forces, field momentum and relativistic terms, all of which are present in our
above discussion. However, none of the discussions gives an explicit and exact
derivation of the delicate balance of all the momentum terms, but often
resort to a treatment of simplified systems. For example, Aharonov and D.
Rohrlich [16] discuss a flux tube with a radially moving charge, instead of a
charge passing by the flux tube. While the issue of whether the charge distribution
of the solenoid is perturbed has been addressed [17, 36, 46], none of
the discussions mention the relativistic electric field imbalance.
As it is possible to describe a solenoid as a collection of moving charged
particles, the above treatment of the Feynman paradox provides hope to settle
the theoretical discussion on forces. Integration over a solenoidal current
distribution would provide an exact derivation of momentum conservation
for the AharonovBohm case.

Guys, Guys......I stopped reading some time ago.....now we are into the 2nd thread.
Not being read or heard. There is absolutely nothing related to spaceflight here.
Again, NASA tested what, a 20 watt setup ? That is within power budget of a 3U cubesat. Flight model ? Demonstrate torque, if not directional thrust ?

Agreed, this thread will end up like the last one unless it stays within the realm of spaceflight. which is odd, because space is a great place to test this.

Guys, Guys......I stopped reading some time ago.....now we are into the 2nd thread.
Not being read or heard. There is absolutely nothing related to spaceflight here.
Again, NASA tested what, a 20 watt setup ? That is within power budget of a 3U cubesat. Flight model ? Demonstrate torque, if not directional thrust ?
I suggest those of you concerned that NASA is not testing this yet in space make your representations to them.:)

"With more focus on space flight applications " (as per http://forum.nasaspaceflight.com/index.php?topic=36313.msg1301658#msg1301658) the metric chosen by the NASA's "Anomalous" report was the thrust force per power input.
Here is a comparison of reported measurements for EM Drives and for the latest report by Fearn, Zachar, Woodward & Wanser.
Notice that the force per power input reported by Fearn, Zachar, Woodward & Wanser is several orders of magnitude lower than the "EM drives". Actually it is barely (3.5 times higher) more than the force per power input of a photon rocket:
reported measurement ForcePerPowerInput (milliNewtons/kW)
(* Cannae Superconducting *) 761.9 to 952.4
(* Shawyer Demo *) 80 to 243
(* Shawyer Experimental *) 18.82
(* Brady c TE mode *) 21.31
(* Brady a TM mode*) 5.396
(* Brady b TM mode*) 3.000
(*Fearn, Zachar, Woodward & Wanser*) 0.01176
lengths in meter
rfFrequency in 1/second (microwave frequency during test)
power in watts
force in milliNewtons
force per PowerInput in milliNewtons/kW
c= 299705000 m/s (speed of light in air)
c= 299792458 m/s (speed of light in vacuum) (for Cannae Superconducting)
(the difference between c in air compared to c in vacuum is negligible)
Note: SmallDiameter for Shawyer's EM Drives obtained from his reported ShawyerDesignFactor .
Force/PowerInput of a Photon Rocket = 1 / c
(* Cannae Superconducting *)
rfFrequency = 1.047*10^9;
cavityLength = 0.01+0.004+0.006+0.01 = 0.03;
bigDiameter =(22.862*(0.00430)) = 0.220;
smallDiameter = bigDiameter2*0.01=0.200;
power = 10.5
Q = 1.1*(10^7)
measured force = 8 to 10
measured ForcePerPowerInput = 761.9 to 952.4
Force/PowerInput of a Photon Rocket =0.003336
measured ForcePerPowerInput to the one of a photon rocket = 228,400 to 285,500
(* Shawyer Experimental *)
rfFrequency=2.45*10^9;
cavityLength=0.156;
bigDiameter=0.16;
smallDiameter=0.127546;
power = 850
Q = 5900
measured force = 16
measured ForcePerPowerInput = 18.82
Force/PowerInput of a Photon Rocket =0.003337
measured ForcePerPowerInput to the one of a photon rocket =5,640
(* Shawyer Demo *)
rfFrequency=2.45*10^9;
cavityLength=0.345;
bigDiameter=0.28;
smallDiameter= 0.128853
power = 421 to 1200
Q = 45000
(measured force = 102.30 milliNewtons only reported for 421 watts, 243 milliNewtons/kW )
measured ForcePerPowerInput = 80 to 243
Force/PowerInput of a Photon Rocket =0.003337
measured ForcePerPowerInput to the one of a photon rocket =23,980 to 72,830
All Brady cases have the following dimensions:
cavityLength=0.332;
bigDiameter=0.397;
smallDiameter=0.244;
(* Brady a TM mode*)
rfFrequency=1.9326*10^9;
power = 16.9
Q = 7320
measured force = 0.0912
measured ForcePerPowerInput = 5.396
Force/PowerInput of a Photon Rocket =0.003337
measured ForcePerPowerInput to the one of a photon rocket =1,617.2
(* Brady b TM mode*)
rfFrequency=1.9367*10^9;
power = 16.7
Q = 18100
measured force = 0.0501
measured ForcePerPowerInput = 3.000
Force/PowerInput of a Photon Rocket =0.003337
measured ForcePerPowerInput to the one of a photon rocket =899.12
(* Brady c TE mode *)
rfFrequency = 1.8804*10^9;
power = 2.6
Q = 22000
measured force = 0.05541
measured ForcePerPowerInput = 21.31
Force/PowerInput of a Photon Rocket =0.003337
measured ForcePerPowerInput to the one of a photon rocket =6,386.7
(* Fearn, Zachar, Woodward & Wanser*)
rfFrequency = 39,300;
power = 170
measured force = 0.002
measured ForcePerPowerInput = 0.01176
Force/PowerInput of a Photon Rocket =0.003337
measured ForcePerPowerInput to the one of a photon rocket = 3.526
Ok, let's break it down a bit simpler.
How many units of energy are being used to produce how many units of thrust? Newtons as the unit of measure could work.

None of these experiments have demonstrated a linear acceleration: all of them have measured rotational accelerations. None of the EM Drives have been tested in a vacuum. None of the measured forces are high enough to levitate the drive.
Forget about levitation. I havent read much or anything about it, but are the forces even in the same ballpark as existing magnetic torquer rods for cubesats ? If yes, in theory this could assist with attitude control in deep space, at least for desaturation.
Anyone ? Anyone ?
I mean, actual spaceflight application. Desaturation spends fuel. Can we get a propellantless desaturation device, with main attitude control provided by reaction wheels ?
Again, from the claimed experimental setups, are the reported angular momentums even on a scale where they could turn a cubesat  even if it takes a long time to do so ? Its not like torquer rods are fast or anything, but they only work within earths magnetic field.
And if it cannot turn a cubesat, the entire thing is no better than Steorn Orbo, is it ?
Trying to elaborate on desaturation which savuporo brought up as a possible application. Here's more info concerning the problem:
http://space.stackexchange.com/questions/323/howoftenmusttheissdesaturateitscontrolmomentgyros
http://en.wikipedia.org/wiki/Control_moment_gyroscope#International_Space_Station
http://spacestationlive.jsc.nasa.gov/displays/adcoDisplay3.html
http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/20100024204.pdf slide 2123 especially.
I remember reading about VASIMR the other day and found that NASA spends $210 million annually in fuel costs just to reboost the ISS. So there's the above potential application, and the cost savings which are potential (if it works) space flight applications.
Guys, Guys......I stopped reading some time ago.....now we are into the 2nd thread.
Not being read or heard. There is absolutely nothing related to spaceflight here.
Again, NASA tested what, a 20 watt setup ? That is within power budget of a 3U cubesat. Flight model ? Demonstrate torque, if not directional thrust ?
I read your post and you are being heard. Please give this unproven technology some time to fail or fly. I don't know what it can do yet. For all we know EMdrives could all be a mistake.

....
Ok, let's break it down a bit simpler.
How many units of energy are being used to produce how many units of thrust? Newtons as the unit of measure could work.
Energy can be expressed in units of Force*displacement (for example, Joule=Newton*meter), and Thrust is a Force of course. Whether one uses Newtons, KilogramForce, PoundForce, or any other (arbitrary but consistent) unit to measure Force, the unit of Energy/Thrust is the unit of length, because Energy/Thrust = Force*displacement/Force = displacement, and displacement has units of length.
Regarding the experiments, it took a given amount of input power to produce a constant EM Drive force.
For example,Shawyer reported (for his "Shawyer Demo") a measured force = 0.1023 Newtons (1/10th of a Newton) for a power input of 421 watts. NASA Eagleworks (Brady et.al) reported (for the TE mode of the truncated cone) a measured force = 0.00005541 Newtons (55.41 MicroNewtons) for a power input of 2.6 watts.
Since Energy is the integral of Power with respect to time, the amount of input Energy required to produce the (approximately constant) thrust force, at (effectively) constant power, was (effectively) a linearly increasing function of time.
So, it is Power/Thrust which has units of velocity (or inversely, Thrust/Power) rather than Energy/Thrust that NASA Eagleworks (Brady, March, White et.al.) used (at its own peril) to scaleup for their proposed EM Drive missions to Mars, Enceladus, etc.
EDIT: Notice that NASA Eagleworks assumed a 2 MegaWatt Power Input for the crewed Mars and Enceladus missions. A 2 MegaWatt Power Input seems to require a Nuclear Power Input in the spacecraft.
For the Mars and Enceladus crewed missions they assumed 0.4 N/kW Thrust/PowerInput, which is certainly feasible for a Superconducting EM Drive (the Canae Superconducting experiment reported almost 1 N/kW). Certainly much more conservative than Shawyer's 30000 N/kW assumption used in his projection for a superconducting Shawyer flying car (which assumes a Q of 5 billion).
(http://4.bp.blogspot.com/i8ERUjGAbzw/UF3jAwLrRI/AAAAAAAAxLo/4savWVpmFIM/s1600/nasatestemdrive7.png)

Throwing around ideas/stuff to think about here:
Since the thrust/power ratio of these devices is pretty bad, they are severely limited by the amount of electrical power you can put on orbit.
Here's what I found about the ISS:
" The complete power system, consisting of U.S. and Russian hardware, generates 110 kilowatts (kW) total power, about as much as 55 houses would typically use. Approximately 30 kW are available for research activities."
Source: http://www.nasa.gov/centers/glenn/about/fs06grc.html
Probes:
Cassini launched with 3 RTGs providing ~300W electrical power each. http://spacemath.gsfc.nasa.gov/Modules/8Mod7Prob2.pdf http://saturn.jpl.nasa.gov/spacecraft/safety/solar.pdf
New Horizons launched with a spare Cassini RTG providing ~250W electrical power, 200 at encounter with Pluto. http://en.wikipedia.org/wiki/New_Horizons or 290W/230W at arrival after 9.5 years according to here: http://www.boulder.swri.edu/~tcase/OttmanHersman_IECEC_paper.pdf
The newer RTGs, MMRTGs like the on in Curiosity provide ~125W/100W energy after 14 years: http://en.wikipedia.org/wiki/MultiMission_Radioisotope_Thermoelectric_Generator
http://en.wikipedia.org/wiki/Curiosity_%28rover%29#Specifications
http://mars.jpl.nasa.gov/files/mep/MMRTG_Jan2008.pdf
So we really don't have very much electrical power to play with in space.
Factoring in efficiencies such as what SLAC (most powerful klystrons I could find, while thinking about manned missions) reports on their Klystrons; http://www.slac.stanford.edu/cgiwrap/getdoc/slacpub10620.pdf the best I see is around 70%.
Another efficient amplifier capable of very high rf power output, a CFA:
http://www.radartutorial.eu/08.transmitters/CrossedField%20Amplifier%20%28Amplitron%29.en.html
The future? More power.
Two interesting things I found about high power space flight projects at none other than JSC. What is also interesting is that both of these mention Qthrusters.
http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/20140004802.pdf
http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/20140004416.pdf

Let's better hope that compact (preferably pB11 directconversion) fusion generators will be implemented soon. Lockheed Martin et al. are working on these things and LM have announced a prototype reactor (100MW class) for around 2019/20. 100MW should be enough for a little spaceship. I wonder when new experimental results will be published by NASA.

Throwing around ideas/stuff to think about here:
Since the thrust/power ratio of these devices is pretty bad, they are severely limited by the amount of electrical power you can put on orbit.
If it works as Shawyer claims, the superconducting version will be producing far more thrust:
http://emdrive.com/faq.html
"The second generation engines will be capable of producing a specific thrust of 30kN/kW. Thus for 1 kilowatt (typical of the power in a microwave oven) a static thrust of 3 tonnes can be obtained, which is enough to support a large car. This is clearly adequate for terrestrial transport applications.
The static thrust/power ratio is calculated assuming a superconducting EmDrive with a Q of 5 x 109. This Q value is routinely achieved in superconducting cavities."

Throwing around ideas/stuff to think about here:
Since the thrust/power ratio of these devices is pretty bad, they are severely limited by the amount of electrical power you can put on orbit.
If it works as Shawyer claims, the superconducting version will be producing far more thrust:
http://emdrive.com/faq.html
"The second generation engines will be capable of producing a specific thrust of 30kN/kW. Thus for 1 kilowatt (typical of the power in a microwave oven) a static thrust of 3 tonnes can be obtained, which is enough to support a large car. This is clearly adequate for terrestrial transport applications.
The static thrust/power ratio is calculated assuming a superconducting EmDrive with a Q of 5 x 109. This Q value is routinely achieved in superconducting cavities."
(http://4.bp.blogspot.com/IOhb45CEI9I/URSurOhJNPI/AAAAAAAAh5M/c5oSLgis9qE/s640/emdrivespaceplane3.png)
You meant to write "assuming a superconducting EmDrive with a Q of 5 * 10^9" = 5,000,000,000 (five billion) (rather than Q = 5 x 109 =545).
In his IAC 2014 October 2014 presentation Shawyer (in his slide #3 in http://www.emdrive.com/iac2014presentation.pdf ) instead uses a projected Q = 5*(10^7), which is 100 times less than the value assumed by Shawyer for the above 30kN/kW projection.
Reviewing actual published data, the maximum Q measurement for a superconducting EM Drive I have seen reported is for the Canae superconducting drive experiment which gave a Q = 1.1*(10^7), this is 500 times less than the value assumed by Shawyer for the above 30kN/kW projection.
Also comparing with actual experimental data, Canae's measured ForcePerPowerInput for the superconducting Canae experiment was only 0.7619 to 0.9524 N/kW, which is 31500 times less than the 30kN/kW projection, therefore besides the decrease in thrust by a factor of 500 due to the lower actual Q, there was another factor decreasing thrust (by a factor of 63 times) in the actual experimental reported results (500*63=31500) as compared to Shawyer's optimistic 30kN/kW projection..

You meant to write "assuming a superconducting EmDrive with a Q of 5 * 10^9" = 5,000,000,000 (five billion) (rather than Q = 5 x 109 =545).
In his IAC 2014 October 2014 presentation Shawyer (in his slide #3 in http://www.emdrive.com/iac2014presentation.pdf ) instead uses a projected Q = 5*(10^7), which is 100 times less than the value assumed by Shawyer for the above 30kN/kW projection.
Reviewing actual published data, the maximum Q actually measured for a superconducting EM Drive I have seen reported is for the Canae superconducting drive experiment which gave a Q = 1.1*(10^7), this is 500 times less than the value assumed by Shawyer for the above 30kN/kW projection.
Also comparing with actual experimental data, Canae's measured ForcePerPowerInput for the superconducting Canae experiment was only 0.7619 to 0.9524 N/kW, which is 31500 times less than the 30kN/kW projection, therefore besides the decrease in thrust by a factor of 500 due to the lower actual Q, there was another factor of decrease in thrust (by a factor of 63 times) in the actual performance of the experiment (500*63=31500).
On the plus side, with the right power source, 0.7619 Newtons from a kilowatt of electricity is still, probably, enough thrust to displace rockets for orbital insertion. It's not competing with airplanes, but it is an exciting number. :)

You meant to write "assuming a superconducting EmDrive with a Q of 5 * 10^9" = 5,000,000,000 (five billion) (rather than Q = 5 x 109 =545).
In his IAC 2014 October 2014 presentation Shawyer (in his slide #3 in http://www.emdrive.com/iac2014presentation.pdf ) instead uses a projected Q = 5*(10^7), which is 100 times less than the value assumed by Shawyer for the above 30kN/kW projection.
Reviewing actual published data, the maximum Q actually measured for a superconducting EM Drive I have seen reported is for the Canae superconducting drive experiment which gave a Q = 1.1*(10^7), this is 500 times less than the value assumed by Shawyer for the above 30kN/kW projection.
Also comparing with actual experimental data, Canae's measured ForcePerPowerInput for the superconducting Canae experiment was only 0.7619 to 0.9524 N/kW, which is 31500 times less than the 30kN/kW projection, therefore besides the decrease in thrust by a factor of 500 due to the lower actual Q, there was another factor of decrease in thrust (by a factor of 63 times) in the actual performance of the experiment (500*63=31500).
On the plus side, with the right power source, 0.7619 Newtons from a kilowatt of electricity is still, probably, enough thrust to displace rockets for orbital insertion. It's not competing with airplanes, but it is an exciting number. :)
Agreed.
For the Mars and Titan/Enceladus crewed missions NASA Eagleworks assumed 0.4 N/kW Thrust/PowerInput, which is certainly feasible for a Superconducting EM Drive (the Canae Superconducting experiment reported almost 1 N/kW). Certainly much more conservative than Shawyer's 30000 N/kW assumption used in his projection for a superconducting Shawyer flying car (which assumes a Q of 5 billion).
(NASA Eagleworks also assumed a 2 MegaWatt Power Input for the crewed Mars and Titan/Enceladus missions, which implies Nuclear Power generation available in the spacecraft.)
(http://i.guim.co.uk/static/w620/h/q95/sysimages/Guardian/Pix/pictures/2012/4/25/1335371334433/Artistsimpressionofpro009.jpg)
(http://www.esa.int/var/esa/storage/images/esa_multimedia/images/2014/04/inside_enceladus/143620291engGB/Inside_Enceladus_node_full_image_2.jpg)
EDIT: and the Chinese (Prof. Juan Yang) have reported (for their ambienttemperature nonsuperconducting EM Drive) experimental measurements of 0.29 N/kW Thrust/PowerInput, which is not too far off (28% difference) from the 0.4 N/kW Thrust/PowerInput assumed by NASA Eagleworks for the Mars and Enceladus crewed missions.

Guys, Guys......I stopped reading some time ago.....now we are into the 2nd thread.
Not being read or heard. There is absolutely nothing related to spaceflight here.
Again, NASA tested what, a 20 watt setup ? That is within power budget of a 3U cubesat. Flight model ? Demonstrate torque, if not directional thrust ?
I suggest those of you concerned that NASA is not testing this yet in space make your representations to them.:)
Nah, just point out the opportunities out there.
:o

So when in a reasonable setup with a 20 watts of input power, you are hoping to generate zero point zero zero zero zero zero and then some point oh millinewtons of linear thrust, or torque, doesn't really matter ( again, see xkcd #1404 ) .. any mentions of levitating cars and interstellar travel is just eroding the credibility of the whole thing.
Cubesat , even a whopping 3U one is not that difficult to get to orbit, and is demonstrably well within the capabilities of crowdfunding even. Getting a NIAC grant also works, although SBIR might be a stretch, at this point.

The future? More power.
Two interesting things I found about high power space flight projects at none other than JSC. What is also interesting is that both of these mention Qthrusters.
http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/20140004802.pdf
http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/20140004416.pdf
it may be that i have an outdated reader but those pdfs fail to load for me. the first gets 2/3s of the way loaded according to the progress bar and then hangs. the second gets 1/4 of the way loaded and then hangs.
:(

it may be that i have an outdated reader but those pdfs fail to load for me. the first gets 2/3s of the way loaded according to the progress bar and then hangs. the second gets 1/4 of the way loaded and then hangs.
:(
NTRS does that a lot with firefox, try chrome or curl/wget

it may be that i have an outdated reader but those pdfs fail to load for me. the first gets 2/3s of the way loaded according to the progress bar and then hangs. the second gets 1/4 of the way loaded and then hangs.
:(
NTRS does that a lot with firefox, try chrome or curl/wget
Thanks. :)

In this report http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/20110023492.pdf NASA's Dr. White wrote of his continuing "dialogue with the (International Space Station) ISS national labs office for an on orbit DTO (On Orbit Detailed Test Objectives)" of the EM Drive (which he calls "QThruster"):
The near term focus of the laboratory work is focused on gathering performance data to support development of a Qthruster engineering prototype targeting Reaction Control System (RCS) applications with force range of 0.11 N with corresponding input power range of 0.33 kW. Up first will be testing of a refurbished test article to duplicate historical performance on the high fidelity torsion pendulum (14 mN at 1040 W). The team is maintaining a dialogue with the ISS national labs office for an on orbit DTO.
How would Qthrusters revolutionize human exploration of the outer planets? Making minimal extrapolation of performance, assessments show that delivery of a 50 mT payload to Jovian orbit can be accomplished in 35 days with a 2 MW power source [specific force of thruster (N/kW) is based on potential measured thrust performance in lab, propulsion mass (Qthrusters) would be additional 20 mT (10 kg/kW), and associate power system would be 20 mT (10 kg/kW)]. Qthruster performance allows the use of nuclear reactor technology that would not require MHD conversion or other more complicated schemes to accomplish single digit specific mass performance usually required for standard electric propulsion systems to the outer solar system. In 70 days, the same system could reach the orbit of Saturn.
(http://www.delhidailynews.com/news_image/1415199916ISS.jpg)

In this report http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/20110023492.pdf NASA's Dr. White wrote of his continuing "dialogue with the (International Space Station) ISS national labs office for an on orbit DTO (On Orbit Detailed Test Objectives)" of the EM Drive (which he calls "QThruster"):
The "QThruster" in this case appears to be a Woodward/ME device.

The "QThruster" in this case appears to be a Woodward/ME device.
Yes. No. Sort of.
Despite claimed differing operating principles, the 'QThruster' and Woodward/ME device appear to differ in minor detail, in terms of construction and results. At least that is my (possibly badly flawed) understanding.
Heated debates about this in the old thread contributed to its demise. We attempt to keep Woodward/Mach out of this thread, but the equations and thoughts keep heading that way.

In this report http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/20110023492.pdf NASA's Dr. White wrote of his continuing "dialogue with the (International Space Station) ISS national labs office for an on orbit DTO (On Orbit Detailed Test Objectives)" of the EM Drive (which he calls "QThruster"):
The "QThruster" in this case appears to be a Woodward/ME device.
The "QThruster" in this case appears to be a Woodward/ME device.
Yes. No. Sort of.
Despite claimed differing operating principles, the 'QThruster' and Woodward/ME device appear to differ in minor detail, in terms of construction and results. At least that is my (possibly badly flawed) understanding.
Heated debates about this in the old thread contributed to its demise. We attempt to keep Woodward/Mach out of this thread, but the equations and thoughts keep heading that way.
Yeah it's a MLT. You can tell by the pixels caps. Essentially when these devices get through the door over at Eagleworks, it seems the favored theory of operation for all these devices becomes the White model. It is his house after all. And I believe this is for good reason.
Paul March seems to believe these devices are related, yet their theories diverge.
His actual words, "Dr. Woodward maintains that the ME's mass fluctuations occur in the "squishy" intermolecular chemical bonds of the dielectric and not in the rest mass of the ions in question. Next question is what are these squishy intermolecular chemical bonds made of? They are typically called covalent sharing of molecular electrons and/or an imbalance of ionic electric charges between the charged ions. Ok then what is in between the electrons and ions in these dielectric molecules that is affected by the ME equation's transient gravity waves, or in other words what do the ME's pressure transients in the cosmological gravitational field affect in between the molecules that for all practical purposes is a pure vacuum state. A vacuum state filled only with virtual photons of the electric fields and perhaps the virtual e/p pairs of the quantum vacuum. That is why I continue to say that Dr. White in only trying to answer what Woodward's ME "gravity" pressure waves are effecting at the molecular and subatomic scales. A place that Dr. Woodward refuses to go to this date except perhaps in his musings on the ADM electron structure where the gravitational field is used to counter balance the electrostatic field forces, but once again ignoring the basic question of what either of these fields are composed of. That is supposed to be the realm of quantum gravity, but since no one has come up with an accepted answer for same, Dr. White is free to suggest his own."
The issue is discussed here: http://www.talkpolywell.org/bb/viewtopic.php?t=2949&p=115985 He goes on to mention that Woodward doesn't address some issues relating to ME and how it effects covalent bonds and because of that, Dr. White is free to make his own conclusions to fill in the gaps. Further on in the thread, it becomes clear that the supposed ME/EM dichotomy really boils down to what the origin of inertia is.
Now enter EMdrive developments thread 1 and 2, and a thorough research of the inertia issue using all available evidence, it was concluded by myself and others that these devices do in fact share the same mechanism of operation and that the theories supporting both types (Woodward, White, Shawyer, Fetta) had their own unique issues, but no dichotomy was required.
The same effect was happening with varying success (http://forum.nasaspaceflight.com/index.php?topic=36313.msg1302455#msg1302455) in each of these devices and this success was directly informed by design, further informed by theory held by the inventors. As very recently supported by Dr. Rodal's research, here: http://forum.nasaspaceflight.com/index.php?topic=36313.msg1307817#msg1307817, inertia isn't simply caused by one single thing. Evidence keeps piling up which supports we need to cast off old theories and think differently about things.
All this didn't sit well with some of the Woodward fans, who were very much welcome to participate in the discussion in thread 1. Given the emotional attachment to the theories, which lead to bad behavior by some and then more bad behavior in response from myself included; I support the attempt to keep Woodward/Mach out of this thread. Besides they have their own happy home here on NSF too here: http://forum.nasaspaceflight.com/index.php?topic=13020.1830 and here http://forum.nasaspaceflight.com/index.php?topic=31037.465
Ok, so how does all of this I just banged out relate to space flight applications I ask myself? It is the same as trying to build a better mouse trap. If a lab or inventor is hell bent on building a device that interacts with theoretical X in Y fashion, trying to achieve thrust, to the exclusion of all other ideas, and it continues to not work so well for them...., we're going to go nowhere fast. I think the attachment sums this up nicely. The truth is buried within the noise. Find it? Then we'll have some all electric space flight action.
From what I'm seeing coming out of Eagleworks, they are using sound scientific methods to test/develop these (still not completely vetted) theories and more importantly they are using lessons learned and applying them to the future. For example, in the Eagleworks Newsletter 2013 (https://xa.yimg.com/kq/groups/86787010/513081407/name/Eagleworks+Newsletter+2013.pdf), they concluded the "magnitude of the thrust is dependent on the AC content of the turnon and turnoff pulse" in the first device and further concluded "...confirms that the RF approach will be a quicker path to longlife flight thrusters" with the Cannae. This shows that an AC signal is important, a key insight.
Next came the Anomalous thrust production...(http://www.libertariannews.org/wpcontent/uploads/2014/07/AnomalousThrustProductionFromanRFTestDeviceBradyEtAl.pdf) paper, which continued using the RF approach.
Most importantly what they didn't do was the same thing over and over and over again.

In this report http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/20110023492.pdf NASA's Dr. White wrote of his continuing "dialogue with the (International Space Station) ISS national labs office for an on orbit DTO (On Orbit Detailed Test Objectives)" of the EM Drive (which he calls "QThruster"):
The "QThruster" in this case appears to be a Woodward/ME device.
The "QThruster" in this case appears to be a Woodward/ME device.
Yes. No. Sort of.
....
1) The example of "QThruster" pictured in the report is what's called by Woodward followers a "MachLorentz thruster (MLT)". As such, it is not a Woodward Mach Effect (Piezoelectric) device. The MachLorentz thruster (MLT) uses a charging capacitor embedded in a magnetic field created by a magnetic coil. It is claimed that a Lorentz force, cross product between the electric field and the magnetic field, appears and acts upon the ions inside the capacitor dielectric. In such electromagnetic experiments, the power can be applied at frequencies of several megahertz, unlike piezoelectric PZT stack actuators where frequency is presently limited to tens of kilohertz. This kind of Mach Lorentz thruster (MLT) was nullified by the experiments of Brito, Marini and Galian (who used a classic Cavendish type pendulum where all the power supply was selfcontained with the MLT device). The nullifying experiments of Brito Marini and Galian (http://enu.kz/repository/2009/AIAA20095070.pdf) where repeated and published in a peerreviewed AIAA journal (Journal of Propulsion and Power) (http://arc.aiaa.org/doi/abs/10.2514/1.46541?journalCode=jpp). Woodward has instead concentrated on the Mach Effect (Piezoelectric) thruster.
2) To concentrate on spaceflight applications (the subject of this thread) it is of paramount importance the amount of power required to produce a given level of thrust. Notice that the force per power input reported by Woodward's Mach Effect thruster in their latest reported experiments (Fearn, Zachar, Woodward & Wanser) is several orders of magnitude lower than the "EM drives". Actually it is barely (3.5 times higher) more than the force per power input of a photon rocket (using a military searchlight as a means of propulsion ! ):
reported measurement ForcePerPowerInput (milliNewtons/kW)
MICROWAVE (* Cannae Superconducting *) 761.9 to 952.4
MICROWAVE (* Prof. Juan Yang et.al. China*) 290
MICROWAVE (* Shawyer Demo *) 80 to 243
MICROWAVE (* Shawyer Experimental *) 18.82
MICROWAVE (* Brady c TE mode *) 21.31
MICROWAVE (* Brady a TM mode*) 5.396
MICROWAVE (* Brady b TM mode*) 3.000
PIEZOELECTRIC (*Fearn, Zachar, Woodward & Wanser*) 0.01176
3) To understand what is important for spaceflight applications: how small is the force (for a given power input) produced by Woodward's (Fearn, Zachar, Woodward & Wanser) latest Mach Effect experiments: it takes 80000 times greater power to produce the same level of force with the Woodward's (Fearn, Zachar, Woodward & Wanser) device as the superconducting EM Drive. Also for spaceflight applications comparison, notice that while Dr. White calculated that it would take 2 MW power input (nuclear power generation) for the microwave EM Drive at 0.4 N/kW missions to Mars and Titan/Enceladus, it would take 68 *(10 ^9) watts (68 Gigawatts) for Woodward's (Fearn, Zachar, Woodward & Wanser) device to produce the same thrust, given its tiny 0.00001176 N/kW thrust/PowerInput. (Fearn, Zachar, Woodward & Wanser device gives just 3.5 times the thrust/powerInput of a very inefficient classicalphysics means of propellantless propulsion: using a military searchlight as a photonrocket ) .
4) Thus, it is evident, that for spaceflight applications (the subject of this thread) we should concentrate on the devices that require orders of magnitude (up to 80000 times) less power to produce a given level of thrust: the microwave EM Drives.
5) Dr. White used the term "Qthruster" in general for all of these devices (including the MLT Thruster, Boeing's Serrano Effect Device and the microwave EM drives). See the slide by Dr. White enclosed below. For the abovepointed (and other) reasons, Dr. White at NASA Eagleworks has moved on and is presently concentrating on MicrowaveCavity Drives, as the reported experimental data shows that they are much more promising for spaceflight applications. This makes sense.
6) The point is that Dr. White wrote that he has a dialogue with the (International Space Station) ISS national labs office for an on orbit DTO (On Orbit Detailed Test Objectives)" of the EM Drive (which he calls "QThruster") and therefore his plan is to eventually test the EM Drive in the ISS: which would obviously constitute a spaceflight demonstration.

Great posts by Rodal and Mulletron.
And I concur: the next step is to firmly cement the scientific nature of the mentioned thrusters (them being falsifiable), by providing additional replications and tests. Theories can come later, if empiric evidence is there.
It doesn't matter if H. White's theory is right or wrong, the same as Woodward's (or Shawyer's, which is most likely wrong). What matters is that the phenomena related to those theories would have evidence of being real.
Humanity has used real phenomena nobody can explain for millenia, and this way before even having complete formal descriptions/theories for them. We still do, as we don't know the provenance and nature of inertia and gravity, and they are part of our everyday lives and expected to work for a lot of technology to function as well.

Great posts by Rodal and Mulletron.
And I concur: the next step is to firmly cement the scientific nature of the mentioned thrusters (them being falsifiable), by providing additional replications and tests. Theories can come later, if empiric evidence is there.
It doesn't matter if H. White's theory is right or wrong, the same as Woodward's (or Shawyer's, which is most likely wrong). What matters is that the phenomena related to those theories would have evidence of being real.
Humanity has used real phenomena nobody can explain for millenia, and this way before even having complete formal descriptions/theories for them. We still do, as we don't know the provenance and nature of inertia and gravity, and they are part of our everyday lives and expected to work for a lot of technology to function as well.
All well & good unless it proves through theory they are doing some fundamental damage. Something raised in fiction by a Star Trek: The Next Generation & the use of warp drive damaging the universe.

All well & good unless it proves through theory they are doing some fundamental damage. Something raised in fiction by a Star Trek: The Next Generation & the use of warp drive damaging the universe.
Well, it has happened in the past. For example, that's what happened with those first researching radioactive and nuclear phenomena in general. They first knew they had some new phenomena in their hands and they knew how to produce some of the effects, but they didn't know how bad it was to have it near you. Several people died of radiation poisoning, and some cases even documented by the victim, in a moving display of dedication to science.
These are not precisely universedestroying dangers per se, but equally lifewrecking stuff.
And we also learned.

:D There is (however tenuously) a potential real world equivalent. collapse of the vacuum potential of the universe from mucking about with high energy collisions, quantum vacuums and warping space. the odds are about 2/3'rds in an infinity1 gabbillion chance of it. but it could theoretically happen. :)
EDIT: But then I think the *vacuum* potential is measured in microHoover (TM) units.

Big difference between figure 5 here: http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/20110023492.pdf (same old Qthruster paper we've been reading)
and figures 2/3 here: http://www.jhuapl.edu/techdigest/TD/td2804/McNutt.pdf (MPD thrusters/Nuclear power)
The difference between Jupiter transit times is astonishing. Not to mention you don't have to carry aloft ~75 percent of your mass as propellant. Disclaimer though, the empty mass of Jupiter mission spacecraft (fig. 2 McNutt) is ~4081 metric tons (why so massive? anybody know*? This is about half as much as of one of these metal monstrosities http://en.wikipedia.org/wiki/Ticonderogaclass_cruiser), compared to the 90 metric tons (fig. 5 White) (50mT payload, propulsion mass 20 mT, 2MW power system 20 mT. I'm not sure what the author intended here. I'm assuming a spacecraft with a mass of at least 90 metric tons total though.)
Anybody have any idea how massive this is? http://en.wikipedia.org/wiki/High_beta_fusion_reactor
It would be interesting to put together an imaginary ship using say....a cluster of the Brady c TE mode articles @21.31 milliNewtons/kW + a Lockheed Martin 100MW miracle reactor reasonable electrical power and RF efficiency losses, to see if anything interesting can be done. Is there even enough information for this to be doable yet?
Edit: * Found the mass, (McNutt pg. 385) "For the types of systems envisioned in the calculations of Fig. 5, ~1700 t of mass is sufficient to cross from Earth to Neptune in ~2 years (assuming 0.1 kg/kWe and an exhaust speed of 200 km·s−1). The mass of ~420 t is intended to carry food for a crew of six for 5 years, little more shielding than that provided by the structural mass of the ship, and a Boreasstyle station that could be used as a science staging base on Triton and left there for any future expeditions."
Seems like the Dr. White example from figure 5 might be a little light.

Big difference between figure 5 here: http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/20110023492.pdf (same old Qthruster paper we've been reading)
and figures 2/3 here: http://www.jhuapl.edu/techdigest/TD/td2804/McNutt.pdf (MPD thrusters/Nuclear power)
The difference between Jupiter transit times is astonishing. Not to mention you don't have to carry aloft ~75 percent of your mass as propellant. Disclaimer though, the empty mass of Jupiter mission spacecraft (fig. 2 McNutt) is ~4081 metric tons (why so massive? anybody know? This is about half as much as of one of these metal monstrosities http://en.wikipedia.org/wiki/Ticonderogaclass_cruiser), compared to the 90 metric tons (fig. 5 White) (50mT payload, propulsion mass 20 mT, 2MW power system 20 mT. I'm not sure what the author intended here. I'm assuming a spacecraft with a mass of at least 90 metric tons total though.)
Anybody have any idea how massive this is? http://en.wikipedia.org/wiki/High_beta_fusion_reactor
It would be interesting to put together an imaginary ship using say....a cluster of the Brady c TE mode articles @21.31 milliNewtons/kW + a Lockheed Martin 100MW miracle reactor reasonable electrical power and RF efficiency losses, to see if anything interesting can be done. Is there even enough information for this to be doable yet?
As the Lockheed Martin reactor will supposedly fit onto a truck, my guesstimate is 5..10mt with shielding, superconducting magnets and whatnot. If it is a thermal conversion model, then LM will need to use heat exchangers with gas turbines to get the electrical power out (makes it heavier again). My favorite, the direct conversion model with pB11 fuel, would obviously be more compact. I'm worrying a bit about how to get rid of that immense waste heat in a vacuum, though. The radiators would glow redhot, I guess. They could also use the photon pressure from the waste heat to accelerate.. .

Big difference between figure 5 here: http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/20110023492.pdf (same old Qthruster paper we've been reading)
and figures 2/3 here: http://www.jhuapl.edu/techdigest/TD/td2804/McNutt.pdf (MPD thrusters/Nuclear power)
The difference between Jupiter transit times is astonishing. Not to mention you don't have to carry aloft ~75 percent of your mass as propellant. Disclaimer though, the empty mass of Jupiter mission spacecraft (fig. 2 McNutt) is ~4081 metric tons (why so massive? anybody know? This is about half as much as of one of these metal monstrosities http://en.wikipedia.org/wiki/Ticonderogaclass_cruiser), compared to the 90 metric tons (fig. 5 White) (50mT payload, propulsion mass 20 mT, 2MW power system 20 mT. I'm not sure what the author intended here. I'm assuming a spacecraft with a mass of at least 90 metric tons total though.)
Anybody have any idea how massive this is? http://en.wikipedia.org/wiki/High_beta_fusion_reactor
It would be interesting to put together an imaginary ship using say....a cluster of the Brady c TE mode articles @21.31 milliNewtons/kW + a Lockheed Martin 100MW miracle reactor reasonable electrical power and RF efficiency losses, to see if anything interesting can be done. Is there even enough information for this to be doable yet?
As the Lockheed Martin reactor will supposedly fit onto a truck, my guesstimate is 5..10mt with shielding, superconducting magnets and whatnot. If it is a thermal conversion model, then LM will need to use heat exchangers with gas turbines to get the electrical power out (makes it heavier again). My favorite, the direct conversion model with pB11 fuel, would obviously be more compact. I'm worrying a bit about how to get rid of that immense waste heat in a vacuum, though. The radiators would glow redhot, I guess. They could also use the photon pressure from the waste heat to accelerate.. .
Lockheed Martin keeps throwing around that it will fit onto a truck. http://www.lockheedmartin.com/us/products/compactfusion.html As I suspected, that can be a very wide range of weight.
First depending on where you look, an empty 18 wheeler with trailer weights ~15mT.
I did some digging and I found that the max gross weight of every conex box size is ~30mT. http://en.wikipedia.org/wiki/Intermodal_container#Specifications
If I use the federal interstate gross vehicle weight limits, they are ~36mT. Subtract that ~15mT empty truck weight plus another ton to keep things super simple, you get ~20mT.
So to me, "it fits on a truck" sounds like 2030mT.
If we want to get ridiculous here though, with a permit, using Florida and Texas as examples, you can haul as much as 78mT and 90mT respectively. http://www.fhwa.dot.gov/reports/tswstudy/Vol2Chapter2.pdf
Now for perspective, the ISS weights in at 924,739 pounds or ~420mT.
http://www.nasa.gov/mission_pages/station/main/onthestation/facts_and_figures.html#.VLG_FnupjSh
http://www.arianespace.com/newspressrelease/2014/7292014VA219launchsuccess.asp
Also Skylab, http://en.wikipedia.org/wiki/Skylab ~77mT.
So that kind of tonnage on orbit isn't out of our reach by any means already. Just launched in stages.
Since I know, and I'm sure many of you have seen as well, reality hardly lives up to expectations, so I'm inclined to, for the purpose of this exercise, make the reactor twice as massive and deliver half the power. So double the Dr. White/"it fits on a truck" 20mT figure and factoring in ~50% DEC, http://en.wikipedia.org/wiki/Direct_energy_conversion, 50MW power. A 40mT/50 MWe power system.
@Rodal, care to throw some math at combining this 40mT/50 MWe power system with one of those thrusters you got the calcs on? Honestly the only numbers I trust are the Brady et al ones, not the inventor's numbers. How much RF can you pump into just one of those Shawyer designs before it starts to melt down? >9000 Watts? What about a hundred of them at once? I estimate they weigh ~10lbs each. It seems ~70% RF amp efficiency is a good round number (http://forum.nasaspaceflight.com/index.php?topic=36313.msg1311433#msg1311433).
Edit:
Um I feel like I screwed this up? The final velocity seems kinda um, large. :o I didn't subtract the Sun pulling on it, but I think something else is wrong.
So throwing around numbers using the ISS as an example (just converted it to an interplanetary spaceship) with a mass of 500mT (420mT original + 40mT 50MWe reactor module add on + 20mT propulsion/aux systems add on + 20mT logistics module add on.
Total mass: 500mT
40MWe available to propulsion, 10MWe left in reserve/used/rest lost to heat
Assuming 70% propulsion system efficiency
28MW RF available for drive
Brady c TE mode @21.31 milliNewtons/kW performance propulsion system
Thrust at 28MW RF @0.02131N/kw=596N
Acceleration=0.00119200m/s^2
Velocity after 1 year=37.59km/s, 135327km/h, 84088.5mph
Displacement 3.96AU

Since my some months ago post interchange with Mullerton in which we more or less agreed that I should pursue the possibility of evanescent waves being the source of the EM Drive effect, I have been doing that with some results.
Using FDTD software I found the following salient points. First though, my computer is not powerful enough to perform FDTD calculations in high resolution, so I'm stuck with moderate resolution at best. That rules out resolving the thin copper sheets on the circuit board ends of the cavity. Second, there isn't any data that I can discover describing copper at this frequency and the power level experienced by the cavity ends. Sure, lots of data on copper for shielding, but ...
Consider that operating at Q = 22,000 and drive power of 2.6 watts with the cavity end diameter giving an area of 0.058 m^2 the radiation intensity approaches a kW/cm^2, or almost a MW/m^2. That is a lot of power and it seems no one has researched the behavior of copper under those intense conditions.
With those two points understood, I did calibrate the FDTD model to a photon rocket, giving thrust of very nearly 1/c as it should. This is with the detector plane about two cavity lengths behind the source antenna.
For the reasons given above, I used a perfect metal or ideal conductor as the material for the cavity model. Not surprisingly, when I ran the model totally enclosing the source with perfect metal, there was zero force detected. That result has been calculated analytically and discussed here on NSF.
I went further, considering that the end is bolted onto the cavity, what if it leaks RF? I modelled a narrow slice around the circumference of the cavity cone in the end plate, a variable sized opening but at the smallest resolution my computer will allow, 0.2% of the cavity large end radius.
The simulation detected Force/Power ranging from 2/c to 3/c.
That is two to three times the thrust of an ideal photon rocket. I think the cause of the force is evanescent waves escaping through the very narrow gap in the cavity base.
My data does not answer the question, "What causes the thrust of the EM drive?" It does point in a direction.
I can run more cases with low to moderate resolution and perfect metal, but as I wrote at the top, I need a bigger computer and better knowledge of copper behavior under intense radiation in order to calculate definitive results.
I'm sure someone will ask, so, Yes, I did look at forces generated by similar gaps in the small end of the cavity. Forces exist but only about one forth as great as at the large end. That may be directly due to the gap area, the small end circumference being about half that of the large end, and the dielectric does interfere. I should probably remove the dielectric and run some small end test cases.

Welcome back!

Welcome back!
Thanks.

Total mass: 500mT
40MWe available to propulsion, 10MWe left in reserve/used/rest lost to heat
Assuming 70% propulsion system efficiency
28MW RF available for drive
Brady c TE mode @21.31 milliNewtons/kW performance propulsion system
Thrust at 28MW RF @0.02131N/kw=596N
Acceleration=0.00119200m/s^2
Velocity after 1 year=37.59km/s, 135327km/h, 84088.5mph
Displacement 3.96AU
So...if I am following this correctly, allowing for deceleration, a 3 year trip to Saturn, give or take a month? Versus a bit over 9 months for the Eagleworks proposal.

Welcome back Aero!
I went further, considering that the end is bolted onto the cavity, what if it leaks RF? I modelled a narrow slice around the circumference of the cavity cone in the end plate, a variable sized opening but at the smallest resolution my computer will allow, 0.2% of the cavity large end radius.
The simulation detected Force/Power ranging from 2/c to 3/c.
That is two to three times the thrust of an ideal photon rocket. I think the cause of the force is evanescent waves escaping through the very narrow gap in the cavity base
Isn't that about on a par with Woodward's device? The worst performer of the bunch?

Welcome back Aero!
I went further, considering that the end is bolted onto the cavity, what if it leaks RF? I modelled a narrow slice around the circumference of the cavity cone in the end plate, a variable sized opening but at the smallest resolution my computer will allow, 0.2% of the cavity large end radius.
The simulation detected Force/Power ranging from 2/c to 3/c.
That is two to three times the thrust of an ideal photon rocket. I think the cause of the force is evanescent waves escaping through the very narrow gap in the cavity base
Isn't that about on a par with Woodward's device? The worst performer of the bunch?
I think 2x to 3x photon thrust is pretty much exactly the same number as the Woodward device, actually.

... the radiation intensity approaches a kW/cm^2, or almost a MW/m^2.
10,000 sq cm in one sq metre, not 1,000.
Cheers, Martin

Total mass: 500mT
40MWe available to propulsion, 10MWe left in reserve/used/rest lost to heat
Assuming 70% propulsion system efficiency
28MW RF available for drive
Brady c TE mode @21.31 milliNewtons/kW performance propulsion system
Thrust at 28MW RF @0.02131N/kw=596N
Acceleration=0.00119200m/s^2
Velocity after 1 year=37.59km/s, 135327km/h, 84088.5mph
Displacement 3.96AU
So...if I am following this correctly, allowing for deceleration, a 3 year trip to Saturn, give or take a month? Versus a bit over 9 months for the Eagleworks proposal.
Not sure because I didn't factor in any orbital mechanics. That was just straight line constant acceleration. I'm surprised it could even move at all within a reasonable amount of time. I'm downloading something called Orbiter right now, slowly to see if I can simulate this kind of stuff. http://orbit.medphys.ucl.ac.uk/zipinstall.html Found a CPA for Saturn/Earth of 8.052au. This was in the past. Next one I don't know. Plugged that into Celestia. See screenshot.

... the radiation intensity approaches a kW/cm^2, or almost a MW/m^2.
10,000 sq cm in one sq metre, not 1,000.
Cheers, Martin
Yes I know. That's why I weasel worded it. If we don't look at the higher power devices from Shawyer or China, just the three Brady devices, the stored power comes out as: 2.12E+006, 9.81E+005, and 5.18E+006 Watts/m^2. All shy of 1 kW/cm^2. On the other hand, other devices operate an 100 times the power level of the Brady device, even 1000 times in one particular case. ( 2.6 watts .cf. 2.5 kW)
My point is that the characteristic behavior of copper in this regime is not easy to find. (Make that impossible to find) It seems that high power radar wave guides should operate in this regime. Does anyone have a Drude model or test data with which to create one? Or even a known material that in thick sheets, behaves like copper in thin sheets under high power radiation?

Welcome back Aero!
I went further, considering that the end is bolted onto the cavity, what if it leaks RF? I modelled a narrow slice around the circumference of the cavity cone in the end plate, a variable sized opening but at the smallest resolution my computer will allow, 0.2% of the cavity large end radius.
The simulation detected Force/Power ranging from 2/c to 3/c.
That is two to three times the thrust of an ideal photon rocket. I think the cause of the force is evanescent waves escaping through the very narrow gap in the cavity base
Isn't that about on a par with Woodward's device? The worst performer of the bunch?
I think 2x to 3x photon thrust is pretty much exactly the same number as the Woodward device, actually.
And I think that producing thrust by making a resonant cavity and putting the end on losely is a lot easier than making a Woodward device. But that is not my point.
My point is that EM drive thrust may be produced by evanescent waves. If only I knew the behavior of copper and had a more powerful computer to run the calculations over thin sheets I could find out for sure. (I think)

.....
Total mass: 500mT
40MWe available to propulsion, 10MWe left in reserve/used/rest lost to heat
Assuming 70% propulsion system efficiency
28MW RF available for drive
Brady c TE mode @21.31 milliNewtons/kW performance propulsion system
Thrust at 28MW RF @0.02131N/kw=596N
Acceleration=0.00119200m/s^2
Velocity after 1 year=37.59km/s, 135327km/h, 84088.5mph
Displacement 3.96AU
Using the following parameters from @Mulletron:
TotalMass 500000 kgm
Power Input: 28000000 Watts
ThrustForce/power: 0.00002131 Newton/Watt
we indeed immediately obtain:
ThrustForce: 596.7 Newtons
Acceleration: 0.001193 m/s^2
From, "Human Outer Solar System Exploration via QThruster Technology" by B. Kent Joosten and Harold G. “Sonny” White, http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/20140013174.pdf, their equation (4):
minimum flight time = 2 * Sqrt[(radiusTargetradiusEarth)/Acceleration]
and the following heliocentric radii:
radiusEarth 1.496E+11 m
radiusMats 2.2794E+11 m
radiusJupiter 7.7833E+11 m
radiusSaturn 1.4246E+12 m
The following flight times for @Mulletron parameters vs the flight times (for the different parameters considered by) "Human Outer Solar System Exploration via QThruster Technology" by B. Kent Joosten and Harold G. “Sonny” White, http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/20140013174.pdf follow:
From Earth to: time @Mulletron (days/months) time Joosten/White (days/months)
Mars 188/6.3 76/2.5
Jupiter 531/17.7 194/6.5
Saturn 757/25.2 277/9.2
The main reason for the ~3x longer flight times for Mulletron is because of the lower thrust/PowerInput considered (Mulletron=0.02131 N/kW vs. White=0.4 N/kW, hence Sqrt[0.4/0.02131]=4 times)
NOTE: The parameters considered by @Mulletron, under all cases considered (including Earth to Saturn in 757 days or 25.2 months) are safely under the "paradox condition" of Joosten/White. There is no paradox for these Mulletron Missions: the change in kinetic energy is less than the energy consumed
The "paradox condition" of Joosten/White for the parameters considered by @Mulletron occurs at 910 days (30.3 months of continuous acceleration).
The "paradox condition" is defined as the condition for which the change in kinetic energy of the spacecraft exceeds the input energy.
Change of KineticEnergy of Spacecraft >= EnergyInput
Assuming constant thrust force (and hence constant acceleration for a constant spacecraft mass) under constant input power, the energy consumed is simply:
EnergyConsumed=Power*time
And the change in kinetic energy of the spacecraft can be expressed as:
Change of KineticEnergy of Spacecraft = mass*((change in velocity)^2)/2
= (mass/2)*((ThrustForce/mass)*time)^2)
= (mass/2)*(((ThrustForce/Power)*Power/mass)*time)^2)
Therefore
ParadoxTime = 2 * mass / (power*((thrustForce/power)^2))
see Appendix A of "Human Outer Solar System Exploration via QThruster Technology" by B. Kent Joosten and Harold G. “Sonny” White, http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/20140013174.pdf and the post by Frobnicat http://forum.nasaspaceflight.com/index.php?topic=29276.msg1281724#msg1281724 and by Mulletron http://forum.nasaspaceflight.com/index.php?topic=29276.msg1281736#msg1281736
Also, of course
should examine specific earth departure and return techniques. Unconstrained QShip spiral trajectories
could expose crewmembers to undesirable levels of radiation exposure due to the Van Allen radiation belts.
(http://www.solpass.org/5s/images/planetss.jpg)

What is the evanescent wave effect? Is this a false positive (IE wouldn't work in space)?

Since under constant acceleration (where "velocity" stands for "delta velocity"=vfinalvinitial and "time" stands for "delta time"=tfinal  tinitial)
time=velocity/acceleration
and acceleration=thrustForce/mass
time= velocity*mass/thrustForce
Substituting this into the paradox equation:
time = 2 * mass / (power*((thrustForce/power)^2))
velocity*mass/thrustForce = 2 * mass / (power*((thrustForce/power)^2))
and simplifying:
Paradox velocity = 2*(thrustForce/ power) /(thrustForce/power)^2)
= 2/(thrustForce/ power)
=2*power/thrustForce
Hence the paradox occurs when the (change in) velocity exceeds 2 times the PowerInput divided by the thrust force
This makes sense of course, since
for any vehicle power P, the thrust that may be provided is:
ThrustForce = 2*Power/velocity
EXAMPLES
For
(Brady TE mode) ThrustForce/power: 0.00002131 Newton/Watt
ParadoxVelocity = 2/0.00002131 m/s = 93853 m/s = 93.85 km/s
For
(Prof. Juan Yang et.al. China) ThrustForce/power: 0.000290 Newton/Watt
ParadoxVelocity = 2/0.000290 m/s = 6897 m/s = 6.90 km/s
For
(Cannae Superconducting) ThrustForce/power: 0.0009524 Newton/Watt
ParadoxVelocity = 2/0.0009524 m/s = 2100 m/s = 2.10 km/s

NOTE: The parameters considered by @Mulletron, under all cases considered (including Earth to Saturn in 757 days or 25.2 months) are safely under the "paradox condition" of Joosten/White. There is no paradox for these Mulletron Missions: the change in kinetic energy is less than the energy consumed
The "paradox condition" of Joosten/White for the parameters considered by @Mulletron occurs at 910 days (30.3 months of continuous acceleration).
The "paradox condition" is defined as the condition for which the change in kinetic energy of the spacecraft exceeds the input energy.
Maybe not the brightest of questions, but could Doctor McCulloch's theory possibly resolve the paradox issue? Accelerate long enough, and inertial radiation becomes significant?

What is the evanescent wave effect? Is this a false positive (IE wouldn't work in space)?
Evanescent waves are a solution to Maxwell's equation, commonly named the "near field." So no, it is not a false positive and yes, it should work in space.

Home w/ a cold so puttering around, looking to add the 3rd mode number into consideration. (cavity length)
Found out that the Wikipedia formulas for the cylindrical cavity resonance frequency is in error. It has an extra c term. Edit: Whoops, nope those are relative numbers. They are OK.
So redoing everything w/ m,n,p.

NOTE: The parameters considered by @Mulletron, under all cases considered (including Earth to Saturn in 757 days or 25.2 months) are safely under the "paradox condition" of Joosten/White. There is no paradox for these Mulletron Missions: the change in kinetic energy is less than the energy consumed
The "paradox condition" of Joosten/White for the parameters considered by @Mulletron occurs at 910 days (30.3 months of continuous acceleration).
The "paradox condition" is defined as the condition for which the change in kinetic energy of the spacecraft exceeds the input energy.
Maybe not the brightest of questions, but could Doctor McCulloch's theory possibly resolve the paradox issue? Accelerate long enough, and inertial radiation becomes significant?
I don't think so. The paradox occurs under conditions of constant acceleration. Under constant acceleration, the Unruh radiation stays the same in McCulloch's theory. (Ditto for Hawking radiation under constant acceleration).
The paradox occurs under constant acceleration when the velocity exceeds 2 times the PowerInput divided by the thrust force, since that implies a change in kinetic energy greater than the energy provided.

I don't think so. The paradox occurs under conditions of constant acceleration. Under constant acceleration, the Unruh radiation stays the same in McCulloch's theory.
The paradox occurs when the velocity equals or exceeds 2 times the Power Input divided by the thrust force.
So...How much of the physics textbooks will need rewritten if this device ignores the paradox? (continues to accelerate with the velocity exceeding twice the power input divided by the thrust force).
Would that be Free Energy?

I don't think so. The paradox occurs under conditions of constant acceleration. Under constant acceleration, the Unruh radiation stays the same in McCulloch's theory.
The paradox occurs when the velocity equals or exceeds 2 times the Power Input divided by the thrust force.
So...How much of the physics textbooks will need rewritten if this device ignores the paradox? (continues to accelerate with the velocity exceeding twice the power input divided by the thrust force).
Would that be Free Energy?
No, Dr. White does not propose that the EM Drive ignores this energy constraint.
Effectively, White proposes that the maximum velocity possibly achievable for these EM Drives is 2*PowerInput/ThrustForce.
When this situation occurs, in order to ensure that the input energy is equal to the change in kinetic energy, the thrust to power performance will have to decrease
At constant input power, the thrust, and therefore the acceleration, must decrease with time, to ensure that the spacecraft's (change in) velocity never exceeds 2*Power/Thrust
(This energy constraint is known even from Sutton's textbook on Elements of Rocket Propulsion (equation
191 Rocket propulsion elements 7th edition Sutton)).
The higher the ThrustForce/InputPower, the lower the maximum velocity of an EM Drive:
MAXIMUM VELOCITY OF EM DRIVE = 2 /(thrustForce/PowerInput)
(Brady TE mode) ThrustForce/power: 0.00002131 Newton/Watt
MaximumVelocity = 2/0.00002131 m/s = 93853 m/s = 93.85 km/s
(Prof. Juan Yang et.al. China) ThrustForce/power: 0.000290 Newton/Watt
MaximumVelocity = 2/0.000290 m/s = 6897 m/s = 6.90 km/s
(Cannae Superconducting) ThrustForce/power: 0.0009524 Newton/Watt
MaximumVelocity = 2/0.0009524 m/s = 2100 m/s = 2.10 km/s

Just a thought, but the higher the Q, the narrower the bandwidth, and the Doppler shift due to actual acceleration (or velocity in the rest frame) would probably limit that amount by exceeding the bandwidth.

Just a thought, but the higher the Q, the narrower the bandwidth, and the Doppler shift due to actual acceleration (or velocity in the rest frame) would probably limit that amount by exceeding the bandwidth.
To all, let's recall that
ThrustForce/PowerInput ~ Q*otherParameters
in all the formulas (Shawyer's, McCulloch's and NotSoSureOfIt's). (NotSoSureOfIt's formula also depends explicitly on the microwave's cavity mode of operation).
Therefore the maximum velocity of the EM Drive is inversely proportional to Q:
MAXIMUM VELOCITY OF EM DRIVE = 2 /(thrustForce/PowerInput)
MAXIMUM VELOCITY OF EM DRIVE ~ (2 /(Q*otherParameters))
The higher the Q, the lower the maximum velocity

At constant input power, the thrust, and therefore the acceleration, must decrease with time, to ensure that the spacecraft's velocity never exceeds 2*Power/Thrust
I was going to start a thread, but there is a photon rocket variant idea I have been batting around for a few months now:
take a long hollow cylinder, closed at one end, open on the other. Probably several hundred meters long, by three or four meters in diameter. Running the length of this cylinder, spaced at even intervals are low beams  probably no more than ten or twenty centimeters high. So the inner edge of the cylinder has...call it a dozen shallow troughs. At regular intervals  maybe a meter  these beams have specially designed reflective points. Open end of the cylinder, you have a powerful high frequency laser (or something emitting a focused photon beam) aimed at a 45 degree angle into each trough. One laser per trough, call it twelve total.
Now, a laser, like a military searchlight, is also a photon rocket.
Photons, as pointed out in the previous thread are durable little critters, and can bounce around a good 50,000+ times before going wherever it is expired photons go. And photons can transfer momentum with each bounce.
So, turn the lasers on. The initial 'thrust' is backward. Actually, 'backward and sideways' because of the angle.
That thrust gets negated at the first bounce point. Photons hit that (reflective) point, transfer momentum, and head over to the next bounce point, set at a 45 degree angle to the first.
At the second bounce point, the whole thing is moving forward. Repeat for the length of the cylinder. Because the photons are hitting at an angle, the cylinder might start rotating as well as moving forward, but I don't see that as a major issue. At the end of the cylinder, the photons hit a shaped surface and bounce back along the tubes center and out into space.
Did a bit of reading on laser propulsion systems. A Doctor Bae ran some laboratory tests on this: bouncing laser beams multiplied the 'thrust' by a factor of 3000+  into EM Drive territory without the physics headache. He proposed two linked spacecraft, with laser beams between them, something NASA is supposed to be looking into for near earth applications. My idea is one spacecraft (the cylinder) and a multiplier of about 1500, if the cylinder is long enough. Not sure, but that's should be on a par with the Brady EM drive model.
Alter the angles a bit, test different lasers/emitters, might get a lot more work out of the photons, increasing thrust further.
Would this violate the paradox?

What is the evanescent wave effect? Is this a false positive (IE wouldn't work in space)?
Evanescent waves are a solution to Maxwell's equation, commonly named the "near field." So no, it is not a false positive and yes, it should work in space.
OK, so how does this handle the conservation of momentum issue if it's more efficient than a photon rocket? What's the "reaction"?
At constant input power, the thrust, and therefore the acceleration, must decrease with time, to ensure that the spacecraft's velocity never exceeds 2*Power/Thrust
Velocity measured relative to what?

At constant input power, the thrust, and therefore the acceleration, must decrease with time, to ensure that the spacecraft's velocity never exceeds 2*Power/Thrust
I was going to start a thread, but there is a photon rocket variant idea I have been batting around for a few months now:
take a long hollow cylinder, closed at one end, open on the other. Probably several hundred meters long, by three or four meters in diameter. Running the length of this cylinder, spaced at even intervals are low beams  probably no more than ten or twenty centimeters high. So the inner edge of the cylinder has...call it a dozen shallow troughs. At regular intervals  maybe a meter  these beams have specially designed reflective points. Open end of the cylinder, you have a powerful high frequency laser (or something emitting a focused photon beam) aimed at a 45 degree angle into each trough. One laser per trough, call it twelve total.
Now, a laser, like a military searchlight, is also a photon rocket.
Photons, as pointed out in the previous thread are durable little critters, and can bounce around a good 50,000+ times before going wherever it is expired photons go. And photons can transfer momentum with each bounce.
So, turn the lasers on. The initial 'thrust' is backward. Actually, 'backward and sideways' because of the angle.
That thrust gets negated at the first bounce point. Photons hit that (reflective) point, transfer momentum, and head over to the next bounce point, set at a 45 degree angle to the first.
At the second bounce point, the whole thing is moving forward. Repeat for the length of the cylinder. Because the photons are hitting at an angle, the cylinder might start rotating as well as moving forward, but I don't see that as a major issue. At the end of the cylinder, the photons hit a shaped surface and bounce back along the tubes center and out into space.
Did a bit of reading on laser propulsion systems. A Doctor Bae ran some laboratory tests on this: bouncing laser beams multiplied the 'thrust' by a factor of 3000+  into EM Drive territory without the physics headache. He proposed two linked spacecraft, with laser beams between them, something NASA is supposed to be looking into for near earth applications. My idea is one spacecraft (the cylinder) and a multiplier of about 1500, if the cylinder is long enough. Not sure, but that's should be on a par with the Brady EM drive model.
Alter the angles a bit, test different lasers/emitters, might get a lot more work out of the photons, increasing thrust further.
Would this violate the paradox?
You seem to misunderstand the fundamentals of mechanics.
If a photon hits a mirror at a 45 degree angle and reflects off it, the mirror will receive an impulse perpendicular to the plane of the mirror only. It will not be pushed in the direction of the other component of the photon at all.
It's not just with photons. If you have a billiard ball and you bounce it off another billiard ball that was stationary so that the original ball end up leaving at a 90 degree angle to its initial direction of travel, the other ball will end up traveling at a 45 degree angle to the path of the original ball.
It's nonintuitive because our intuition is shaped by friction tending to pull things along, but such friction is not a part of purely elastic collisions, and photons bouncing off mirrors are purely elastic.
So, every time your photon bounces off the wall, the momentum it imparts will only be to push outward perpendicular to the axis of the tube. And it will be cancelled by the next bounce off the opposite wall.
The only effect of the net momentum of the tube is the opposite of whatever momentum the photo has when it finally leaves the tube. Whatever it does as it bounces around in the tube will have no net effect.

What is the evanescent wave effect? Is this a false positive (IE wouldn't work in space)?
Evanescent waves are a solution to Maxwell's equation, commonly named the "near field." So no, it is not a false positive and yes, it should work in space.
OK, so how does this handle the conservation of momentum issue if it's more efficient than a photon rocket? What's the "reaction"?
... snip ...
See this paper  Extraordinary momentum and spin in evanescent waves Middle of page 5.
http://arxiv.org/pdf/1308.0547.pdf (http://arxiv.org/pdf/1308.0547.pdf)
First, note that the evanescent wave (7) possesses longitudinal canonical momentum p^{O}_{z}∝k_{z}>k, which exceeds the momentum of a plane wave with the same local intensity.
That's what led me to look in this direction. Evanescent waves exhibit unusual behavior. The answer to your question then is that the photon rocket is not the ultimate in efficiency. Make a photon rocket using evanescent wave photons and the efficiency will be higher.
... Maybe ... that is what we're all here to find out.

What is the evanescent wave effect? Is this a false positive (IE wouldn't work in space)?
Evanescent waves are a solution to Maxwell's equation, commonly named the "near field." So no, it is not a false positive and yes, it should work in space.
OK, so how does this handle the conservation of momentum issue if it's more efficient than a photon rocket? What's the "reaction"?
... snip ...
See this paper  Extraordinary momentum and spin in evanescent waves Middle of page 5.
http://arxiv.org/pdf/1308.0547.pdf (http://arxiv.org/pdf/1308.0547.pdf)
First, note that the evanescent wave (7) possesses longitudinal canonical momentum p^{O}_{z}∝k_{z}>k, which exceeds the momentum of a plane wave with the same local intensity.
That's what led me to look in this direction. Evanescent waves exhibit unusual behavior. The answer to your question then is that the photon rocket is not the ultimate in efficiency. Make a photon rocket using evanescent wave photons and the efficiency will be higher.
... Maybe ... that is what we're all here to find out.
The linked paper ( http://arxiv.org/pdf/1308.0547.pdf] ) addresses canonicalmomentum and angular/spinmomentum of evanescent waves in general. The studied effect (spin Hall effect of light http://en.wikipedia.org/wiki/Spin_Hall_effect) can be used for example for rotating nanoparticles using an external (to the particles) plasmonic opticalnanotweezer.
(http://webwib.com/wpcontent/uploads/2014/03/manipulasitweezer.jpg)
What remains unclear is how the linked paper by itself addresses the issue of conservation of momentum of an EM Drive: I do not recall the linked paper specifically addressing conservation of momentum of an EM Drive cavity where all the microwave photons remain inside the cavity. If it is claimed that the evanescent waves (resulting from exponentiallydecaying solutions to the electromagnetic field inside cavity) cause the EM Drive (and spacecraft) to accelerate, what balances the change in the EM Drive (and the spacecraft’s) momentum?.
By contrast,
* in Dr. McCulloch's theory momentum of the EM Drive cavity is balanced by emitted Unruh radiation,
* in Dr. White's theory and in other theories investigated by @Mulletron, it is balanced by interaction with the Quantum Vacuum,
* in @NotSoSureOfIt's formulation it may be balanced by terms coupling electromagnetism with gravitational forces.
* people in this forum also investigated (in the earlier thread) momentum balancing of the EM Drive by photon interaction coupling with Dark Matter (specifically: Axions). [For a far out idea, a "Through the wormhole" episode (minute 11 of the episode, see the video http://www.sciencechannel.com/tvshows/throughthewormhole/videos/throughthewormhole2darkmatter/ ) Tim Tate , of UC Irvine, tells us dark matter may be "massless photons spinning in the 4th dimension that appear to us as having mass because they are rapidly spinning in the 4th dimension" see: http://wwwconf.slac.stanford.edu/ssi/2011/Tait_072911.pdf]
So the question remains: what balances the momentum change of an EM Drive accelerated by evanescent waves? Are you proposing an interaction with the Quantum Vacuum? or terms coupling electromagnetism with gravitational forces? or something else?

In relativity; coupling of gravity and electromagnetism is infinitesimal though. That's what got Martin Tajmar's experiment so much attention at first. It suggested gravityEM coupling billions of times stronger than predicted by RT. and what he got was still extremely tiny too.
Of course later he attributed his results to air currents caused by his cryocoolant sublimating and retracted his paper.
Parenthetically, Tajmar's general design was also used by Ning Li and Podkletnov but probably differed in the details of cooling and method of obtaining rotation and materials for the disks.
That branch (family?) of gravityEM drive designs has had bad luck even though there may be something there. Tajmar retracted, Ning Li allegedly absconded with research funds, Podkletnov got the kook treatment and retreated to Russia where he continues to claim results.
EDIT: in other news a recent experiment designed to test spin gravity failed to detect any difference in gravitation effects on a particle with a zero spin value and a non zero spin value. fermion and bosons were used...
http://phys.org/news/201407equivalenceprincipleeffectsspingravitycoupling.html

In relativity; coupling of gravity and electromagnetism is infinitesimal though. That's what got Martin Tajmar's experiment so much attention at first. It suggested gravityEM coupling billions of times stronger than predicted by RT. and what he got was still extremely tiny too.
Of course later he attributed his results to air currents caused by his cryocoolant sublimating and retracted his paper.
Parenthetically, Tajmar's general design was also used by Ning Li and Podkletnov but probably differed in the details of cooling and method of obtaining rotation and materials for the disks.
That branch (family?) of gravityEM drive designs has had bad luck even though there may be something there. Tajmar retracted, Ning Li allegedly absconded with research funds, Podkletnov got the kook treatment and retreated to Russia where he continues to claim results.
EDIT: in other news a recent experiment designed to test spin gravity failed to detect any difference in gravitation effects on a particle with a zero spin value and a non zero spin value. fermion and bosons were used...
http://phys.org/news/201407equivalenceprincipleeffectsspingravitycoupling.html
Classically, you need a gravitational gradient for the interaction. Maybe they can combine w/
http://phys.org/news/201501gravitycurvature.html#nRlv

So the question remains: what balances the momentum change of an EM Drive accelerated by evanescent waves? Are you proposing an interaction with the Quantum Vacuum? or terms coupling electromagnetism with gravitational forces? or something else?
No  I am proposing that electromagnetic wave momentum depends on group velocity, and that evanescent waves in these circumstances exhibit superluminal group velocity. Nothing is violated  wave momentum reacts against the base plate and energy is inductively drawn from the cavity.
I'll challange you, Dr. Rodel, and Mathematica to demonstrate why/how the energy resolves from the subluminal velocity solution of wave equations. I can help you formulate the problem but we need independent confirmation and you have shown great capability with Mathematica. Do that and you will have solved the EM drive paradox.

So the question remains: what balances the momentum change of an EM Drive accelerated by evanescent waves? Are you proposing an interaction with the Quantum Vacuum? or terms coupling electromagnetism with gravitational forces? or something else?
No  I am proposing that electromagnetic wave momentum depends on group velocity, and that evanescent waves in these circumstances exhibit superluminal group velocity. Nothing is violated  wave momentum reacts against the base plate and energy is inductively drawn from the cavity.
I'll challange you, Dr. Rodel, and Mathematica to demonstrate why/how the energy resolves from the subluminal velocity solution of wave equations. I can help you formulate the problem but we need independent confirmation and you have shown great capability with Mathematica. Do that and you will have solved the EM drive paradox.
But evanescent waves decay exponentially. If you enclose the whole device in a large (imaginary) box, everything coming out will be just regular plane waves with wellknown momentum. So where's the extra momentum coming from?

So the question remains: what balances the momentum change of an EM Drive accelerated by evanescent waves? Are you proposing an interaction with the Quantum Vacuum? or terms coupling electromagnetism with gravitational forces? or something else?
No  I am proposing that electromagnetic wave momentum depends on group velocity, and that evanescent waves in these circumstances exhibit superluminal group velocity. Nothing is violated  wave momentum reacts against the base plate and energy is inductively drawn from the cavity.
I'll challange you, Dr. Rodel, and Mathematica to demonstrate why/how the energy resolves from the subluminal velocity solution of wave equations. I can help you formulate the problem but we need independent confirmation and you have shown great capability with Mathematica. Do that and you will have solved the EM drive paradox.
But evanescent waves decay exponentially. If you enclose the whole device in a large (imaginary) box, everything coming out will be just regular plane waves with wellknown momentum. So where's the extra momentum coming from?
I don't think it matters what happens to the photons after they depart the thruster interface. An analogy would be the classic photon rocket, or a chemical rocket engine.
A chemical rocket leaves the launch pad but the momentum of the exhaust gas is immediately diverted. The rocket still works. Same thing for a photon rocket, it doesn't matter if the expelled photon beam strikes a planetary body, a mirror or is adsorbed by a dust cloud, the rocket still works. The same rule should hold for evanescent waves.

Meanwhile, I gather there are at least two other labs (besides NASA, Yang Juan and Shawyer) working with cavitytype EmDrives. Anyone heard anything? Do we know what Boeing did after testing the one Shawyer sent them? They say they are not working with him, but that doesn't rule out developing his technology.

... Anyone heard anything? Do we know what Boeing did after testing the one Shawyer sent them? They say they are not working with him, but that doesn't rule out developing his technology.
David Hambling http://www.theguardian.com/profile/davidhambling
http://www.wired.co.uk/search/author/David+Hambling
wrote in Aviation Week and Space Technology Nov 5, 2012 (http://aviationweek.com/awin/propellentlessspacepropulsionresearchcontinues):
Such work has evidently ceased. “Phantom Works is not working with Mr. Shawyer,” a Boeing representative says, adding that the company is no longer pursuing this avenue.
Notice that Hambling disclosed not only that “Phantom Works is not working with Mr. Shawyer” but even more final , they added that "the company (Boeing) is no longer pursuing this avenue." From what Hambling wrote, it reads to me that Boeing Phantom Works is no longer pursuing this (EM Drive) avenue. Furthermore, given a previous arrangement between Boeing and Shawyer, it would be highly nonstandard for Boeing to continue working on Shawyer's technology without an Intellectual Property arrangement with Shawyer that would allow this. And, if Boeing would have conducted their own independent microwave cavity EM Drive R&D work prior to the arrangement with Shawyer, it would not make Intellectual Property sense that Boeing would have entered into an arrangement with Shawyer, as large companies usually refuse to discuss inventions with outside inventors because such discussions and arrangements create Intellectual Property issues (Ford Motor Company has an old classic legal case on such IP questions, involving windshield wipers). Since Boeing is a very large public company with an extensive IP department, this implies that indeed "they are no longer pursuing this (EM Drive) avenue" at all, and if, hypothetically, Boeing were to conduct such development in the future, it would have to be a very different (for Intellectual Property purposes) engineering design than Shawyer's EM Drive.
In other words, Boeing would not be developing "his (Shawyer's) technology" but Boeing's separate, unique, very different (for IP purposes) technology.

At constant input power, the thrust, and therefore the acceleration, must decrease with time, to ensure that the spacecraft's velocity never exceeds 2*Power/Thrust
Velocity measured relative to what?
It should read "At constant input power, the thrust, and therefore the acceleration, must decrease with time, to ensure that the spacecraft's (change in) velocity never exceeds 2*Power/Thrust"(I have accordingly added "change in" in the original entry).
It is the change in Kinetic Energy (between the final time under consideration and the initial time) under constant acceleration produced directly by the propulsion engine that matters and therefore it is the change in velocity that matters. Since only the change in velocity matters, any arbitrary additive constant for defining the initial and final velocities disappears from consideration. Ultimately, the definition of "change in velocity" in this context really follows from the definition of constant acceleration as acceleration=(delta velocity)/(delta time) so that (delta velocity)=acceleration*(delta time). Given acceleration=ThrustForce/Mass, the change in velocity is uniquely defined in terms of: ThrustForce, total Mass of the spacecraft and DeltaTime (regardless of velocityframe of observance) directly as
(delta velocity)=(ThrustForce/Mass)*(delta time).
Of course, changes in velocity produced by external forces (for example by gravitational slingshot) are not part of this consideration, only the ThrustForce is under consideration.

Sounds to me the answer to the question by Vultur would then be "relative to initial velocity". Which poses the problem (already mentioned) of what records/holds the initial velocity ?
Say we have 1N/kW, 1kg spacecraft, 4MJ energy onboard to spend at a flow of 1kW (yielding 1N thrust), for a duration of 2000s (we will spend only 2MJ). a=F/m=1/1=1m/s˛ Final velocity at 2000s vf=a*2000=2000m/s. DeltaV is 2km/s.
Kinetic energy Ek=.5*1*2000˛=2MJ exactly what was spent. Now any more use of the thruster with the remaining 2MJ should yield less than 1N/kW efficiency if we are to be shy of the "energetic paradox".
At this point, first spacecraft meets another spacecraft that was put there (at same velocity) by conventional means. Otherwise, second spacecraft has same design (EM thruster...) and batteries loaded at 2MJ. The two spacecrafts are undistinguishable, same design, same onboard energy of 2MJ, except that one has already used his "EM drive credit" and can't anymore use power at 1N/kW efficiency, while the other is "fresh", and can have 1N/kW for 2000s. There would be a kind of "memory effect" to differentiate those two spacecrafts.
BTW, "added kinetic energy" seems a poor metric, there is always an inertial reference frame in which it is 0 (for instance relative to the mean velocity between Vinitial and Vfinal). To me it is hopeless to save propellantless schemes at thrust/power > 1/c from both energetic "paradoxes" and special rest frame (aether) : if this kind of ratio is possible one of those must be abandoned, either a problem of diminishing returns appears relative to some absolute velocity rest frame (local vector to be determined) or power is pumped from somewhere (with tachyons involved, if relativity is to be respected). Taking together apparent respect of energy conservation and relativity (change in velocity) gives worse paradox than (apparently) breaking energy conservation alone. Equating "change of velocity" with "change of kinetic energy" is ill defined : 2/m*DeltaEk = (VfVr)˛(ViVr)˛ = Vf˛Vi˛+2Vr(ViVf) with Vr the arbitrary velocity of a change in inertial reference frame, how could deltaEk have any meaning as soon as Vi != Vf ?
If I may quote myself from this post (http://forum.nasaspaceflight.com/index.php?topic=29276.msg1275281#msg1275281), believe this is the proper relativistic derivation (not being challenged so far) :
3/ We are not using a bath or aether, the EMdrive just comes by on its own in nothingness and emits something that is forever lost (can't be closed, closed solutions can't see their centre of energy depart from an inertial trajectory). So if I consider a device in its own rest frame, it is spending a infinitesimal energy E, with this Energy it "creates" and gives velocity to a "thing" of mass m that is leaving and never to come back again. With Gamma the Lorentz factor 1/sqrt(1v˛/c˛), v in the rest frame where the device is not (yet) moving.
E = gamma m c˛ Energy spent by device to give thing of mass m a velocity of v
p = gamma m v Momentum of the thing of mass m and velocity leaving the device forever
We agree that conservation of energy and conservation of momentum are the two most fundamental rules to apply. So for the later, the device gets a reaction kick of p momentum, at the price of spent energy E.
Thrust is momentum kicks per second, Power is spent Energy per second. Hence :
thrust/power = p/E = v/c˛
The consequences are
thrust/power < 1/c => v/c˛ < 1/c => v<c classical rocket, reaction on usual mass
thrust/power = 1/c => v/c˛ = 1/c => v=c photon rocket, reaction on particles of 0 rest mass
thrust/power > 1/c => v/c˛ > 1/c => v>c tachyon rocket, reaction on particles of imaginary rest mass
Note that in the above inequalities, the thrust/power is understood in the very particular way (in the case of the classical rocket) that the energy equivalent content of ejected mass is counted in "spent power" (otherwise a classical rocket obviously does much better than 1/c, but it spits quite a lot of valuable energy as mass, never to be recovered...)
Insisting on both relativistic (difference, not absolute velocities) and spent/gained energy balance hypothesis should invariably have tachyons as consequence.

1) Ron Maimon answers the question "Is the change in kinetic energy of a particle frame independent?" with a resounding: NO: "energy isn't conserved the same way in every frame because the energy is not separate from the momentum. This is clearest in relativity, where the energy is the timecomponent of the energymomentum vector. Then if you change frames, what you called energy partly becomes momentum, and it is the conservation law of the total energymomentum vector which is frame independent."
I would have written this instead as "the total energymomentum vector is covariant, not invariant".
See:
http://physics.stackexchange.com/questions/23323/isthechangeinkineticenergyofaparticleframeindependent
and
http://www.quora.com/DoesthekineticenergyofanobjectdependonthereferenceframeoftheobserverWhyorwhynot
and
http://physics.stackexchange.com/questions/23734/istheenergyconservedinamovingframeofreference
and
http://www.loreto.unican.es/Carpeta2012/TPT%28Tefft%29RelativityGalilean2007.pdf
2) The frameofreference kinetic energy issues (for nonrelativistic spacecraft speeds) are eliminated by the definition of constant acceleration as acceleration=(delta velocity)/(delta time) so that (delta velocity)=acceleration*(delta time). Since from Newton's 2nd law, acceleration=ThrustForce/Mass, the change in velocity is uniquely defined in terms of: ThrustForce, total Mass of the spacecraft and DeltaTime (regardless of velocityframeofreference) directly as
(delta velocity)=(ThrustForce/Mass)*(delta time).
and the intrinsic definition of the change in KineticEnergy of the spacecraft under constant acceleration:
deltaKineticEnergy = (1/2)*Mass*((delta velocity)^2)
= (1/2)*Mass*([(ThrustForce/Mass)*(delta time) ]^2)
where thrustForce, mass and deltaTime have frameindependent unique meanings. This follows directly from A) the definition of constant acceleration and B) Newton's second law.
EDIT: This relationship for the deltaKineticEnergy follows by arbitrarily defining the end velocity to be equal to the deltaVelocity and arbitrarily defining the initial velocity to be zero:
end velocity = delta velocity
initial velocity = 0
effectively setting the initial kinetic energy KEinitial=0
( which we are free to do since the definition of velocity is arbitrary to within an arbitrary additive constant since the absolute value of velocity is relative)
3) You are correct, for the EM Drive to make any sense as a closed system it implies having memory of its timehistory in order to never exceed the critical velocity at which (for constant InputPower throughout the time period (delta time))
(1/2)*Mass*[(ThrustForce/Mass)*(delta time) ]^2 = InputPower*(delta time) .
This equation relating thrust force to change in velocity of the spacecraft is consistent with textbooks on Rocket Propulsion, for example: Sutton's textbook on Elements of Rocket Propulsion (equation 191 Rocket propulsion elements 7th edition Sutton)).
for any vehicle power P, the thrust that may be provided is: ThrustForce = 2*Power/velocity
As to how such a memory can arise in a seemingly simple system of microwave photons in a cavity, let's add this to the enigma of conservation of momentum of the EM Drive. We know of materials that have memory of their time history (of stress, strain, stress rate and strain rate) but they are macroscopic materials much more complex than the apparently much simpler microwave cavity EM Drive.
Maimon's last words maybe particularly pertinent:
the transformation law shows that if energy is conserved in any one frame for a system which also conserves momentum, then the energy is conserved in another frame. This means that the total energy change is only meaningful for a system where no momentum flows in or out
If the EM drive conserves momentum by interacting with the QuantumVacuum for example, we have an open system where momentum will be flowing in or out of the cavity, and therefore the open system should be taken into account in the conservation of kinetic energy (which we have not done) in order to arrive at a satisfactory answer.

3) You are correct, for the EM Drive to make any sense it implies having memory of its timehistory in order to never exceed the critical velocity at which (for constant InputPower throughout the time period (delta time))
Strangely enough, Doctor McCulloch's latest blog post deals with this issue or its first cousin.

....
Note that in the above inequalities, the thrust/power is understood in the very particular way (in the case of the classical rocket) that the energy equivalent content of ejected mass is counted in "spent power" (otherwise a classical rocket obviously does much better than 1/c, ...)
....
Just like you take into account the energy of ejected mass from a classical rocket, also for an EM Drive the energy and momentum of the total open system has to be taken into account to reach any conclusions on velocity limitations:
*for Dr.McCulloch's theory, the energy/momentum of the radiated Unruh radiation has to be taken into account
*for theories advocating interaction with the Quantum Vacuum (Dr. White's or the theories considered by @Mulletron) the energy/momentum of the involved Quantum Vacuum has to be taken into account. An example would be given by Dr.White's analogy of the propeller in a submarine: the energy/momentum of the water propelled by the propeller has to be taken into account.
*ditto for theories advocating coupling between electromagnetism and gravitational forces, or theories advocating coupling with Dark Matter, or any other theories explaining conservation of momentum of the EM Drive: the energy/momentum of the coupled field also needs to be taken into account
Thus my conclusion is that Joosten and White's "paradox" analysis for the EM Drive (Appendix A of "Human Outer Solar System Exploration via QThruster Technology" by B. Kent Joosten and Harold G. “Sonny” White, http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/20140013174.pdf ) is incorrect/incomplete because they failed to take into account the energy/momentum of the involved Quantum Vacuum (which they advocate as the reason for conservation of momentum yet they fail to take into account when they perform the kinetic energy constraint).
If the EM drive conserves momentum by interacting with the QuantumVacuum, we have an open system where momentum will be flowing in or out of the cavity, and therefore the open system should be taken into account in the conservation of energy in order to arrive at a satisfactory answer concerning any velocity limitation.
(http://history.nasa.gov/SP4404/p275.jpg)
(http://upload.wikimedia.org/wikipedia/commons/6/66/Cavitatingprop.jpg)

http://www.technologyreview.com/view/426281/giantcasimireffectpredictedinsidemetamaterials/
http://arxiv.org/abs/1110.1919
With this type of set up could you determine if the casimir effect is a suitable stunt double for exotic energy or mass for purposes of White's warp drive idea? :\

http://www.technologyreview.com/view/426281/giantcasimireffectpredictedinsidemetamaterials/
http://arxiv.org/abs/1110.1919
With this type of set up could you determine if the casimir effect is a suitable stunt double for exotic energy or mass for purposes of White's warp drive idea? :\
The article was published in 2011. The authors claim that
Since the parameters of metamaterials we proposed are quite simple, this experiment would be easily implemented in laboratory
We are now in 2015. If the experiments to confirm their theoretical expectation are so easy to implement in a laboratory as the authors claimed in their 2011 paper, has anyone heard anything regarding their experimental confirmation or nullification? :\

http://www.mouser.com/new/teampconnectors/teconnectivityariso/?utm_medium=email&utm_source=january2015&utm_campaign=cmenewstech2015&utm_content=p2lm
Just an FYI on contactless connector for garage builds.
Update:
OK! I can get all 3 quantum numbers to agree w/ the Brady results. The mode numbers they give have to be erroneous as they don't fit w/ the cavity frequency calculations. That limits the fit. I'll try to get time to send the whole ballawax by this weekend.

This is the latest exposition on the proposition that dispersion caused by an accelerating frame of reference implied an accelerating frame of reference caused by a dispersive cavity resonator. (to 1st order using massless, perfectly conducting cavity)
Unlike the previous waveguide attempt, this wasn't done on a series of scribbled postit notes.
Here I've tried to incorporate all 3 subscripts into the expression and eliminate some of my own confusion about the reported modes. This should allow for some comparison w/ the Dynamical Casimir Effect which also shows Doppler type behavior.
I had a lot of trouble trying to figure out the X's from the "given" modes until I remembered they were in the cavity frequency formulas. That eliminated most of the possible modes.
Starting with the expressions for the frequency of an RF cavity:
f = (c/(2*Pi))*((X[sub m,n]/R)^2+((p*Pi)/L)^2)^.5
Where I use: R = ((1/2)*(a^2+b^2))^0.5
a and b are the end plate radii and L is the cavity length.
For TM modes, X[sub m,n] = the nth zero of the mth Bessel function.
[1,1]=3.83, [0,1]=2.40, [0,2]=5.52 [1,2]=7.02, [2,1]=5.14, [2,2]=8.42, [1,3]=10.17, etc.
and for TE modes, X'[subm,n] = the nth zero of the derivative of the mth Bessel function.
[0,1]=3.83, [1,1]=1.84, [2,1]=3.05, [0,2]=7.02, [1,2]=5.33, [1,3]=8.54, [0,3]=10.17, [2,2]=6.71, etc.
So, using these to identify the frequencies, I chose:
Bradya => TM122 or TE022 X[sub m,n] = 7.02 p = 2
Bradyb => TE213 X'[sub m,n] = 3.05 p = 3
Bradyc => TE222 X'[sub m,n] = 6.71 p = 2
Rotate the dispersion relation of the cavity into doppler frame to get the Doppler shifts, that is to say, look at the dispersion curve intersections of constant wave number instead of constant frequency.
df = (1/(2*f))*(c/(2*Pi))^2*(X[sub m,n])^2*((1/a^2)(1/b^2))
and from there the expression for the acceleration g from:
g = (c^2/L)*(df/f) such that:
g = (c^2/(2*L*f^2))*(c/(2*Pi))^2*(X[sub m,n])^2*((1/a^2)(1/b^2))
Using the "weight" of the photon in the accelerated frame from:
"W" = (h*f/c^2)*g => "W" = T = (h/L)*df
gives thrust per photon:
T = (h/(2*L*f))*(c/(2*pi))^2*(X[sub m,n])^2*((1/a^2)(1/b^2))
If the number of photons is ((P/f)*Q)/hf then:
NT = P*Q*(1/(2*L*f^3))(c/(2*pi))^2*(X[sub m,n])^2*((1/a^2)(1/b^2))
Plugging the numbers in we get:
Bradya NT= 1.04e4 vs 9.12e5 Pwr= 16.9 Q=7320 TM122 or TE022
Bradyb NT= 4.80e5 vs 5.01e5 Pwr= 16.7 Q=18100 TE213
Bradyc NT= 4.78e5 vs 5.54e5 Pwr= 2.6 Q=22000 TE222
I kept everything in terms of frequency this time to minimize my own confusion. Hopefully, I didn't screw it up and can get on to momentum conservation.
Thanks for your patience.

Keeping my eyes on the conference scene, nothing out of this one: http://www.aiaascitech.org/ http://www.aiaa.org/EventsCalendar.aspx?id=79 I scanned the program and didn't spot anything.
I suspect the next two potential ones will be STAIF II http://www.staif2.org/about.html and this one: http://www.aiaapropulsionenergy.org/default.aspx
Things have been pretty quiet for a few months now. What's going on here? The follow up news after "anomalous thrust..." hasn't been coming. Anyone have any new gouge?
Has there been the least indication yet when we are too get some more results in relation to those who are experimenting in this area?
There is essentially a news blackout on the experimental side from NASA.
The problem is, if this drive really works, the defence implications are huge. Those in charge might feel it would not necessarily be a good idea to go public with it  especially from the US perspective. Remember that 'Sputnik moment'?
@wembley, do you have any specific info about why you think there is a news blackout?
Also, do you have any further verifiable information from this post: http://forum.nasaspaceflight.com/index.php?topic=29276.msg1265607#msg1265607 stating Shawyer stopped using a dielectric section?

With my tinfoil hat on;) it's gone into the black and no more will be heard about it. Mind you surely the genie is out of the box now for it as an experiment able to be replicated including by other countries.
With my serious hat on perhaps you should ask on TalkPolywell as there's probably people on there who might have an answer for you?

Poking around the internet, I ended up at this paper on Arxiv: http://arxiv.org/abs/1411.3987
Photons that travel in free space slower than the speed of light
That the speed of light in free space is constant is a cornerstone of modern physics. However, light beams have finite transverse size, which leads to a modification of their wavevectors resulting in a change to their phase and group velocities. We study the group velocity of single photons by measuring a change in their arrival time that results from changing the beam's transverse spatial structure. Using timecorrelated photon pairs we show a reduction of the group velocity of photons in both a Bessel beam and photons in a focused Gaussian beam. In both cases, the delay is several microns over a propagation distance of the order of 1 m. Our work highlights that, even in free space, the invariance of the speed of light only applies to plane waves. Introducing spatial structure to an optical beam, even for a single photon, reduces the group velocity of the light by a readily measurable amount.
What effect does reduced group velocity in free space have on the momentum of photons?

With my tinfoil hat on;) it's gone into the black and no more will be heard about it. Mind you surely the genie is out of the box now for it as an experiment able to be replicated including by other countries.
With my serious hat on perhaps you should ask on TalkPolywell as there's probably people on there who might have an answer for you?
Since the genie is out of the bottle there is no way to put it in the black. They already went public with it. But as @Wembley stated, there are huge defense uses for this....why DARPA is involved. The military applications of it will be black, for certain, as they should be.
There is essentially a news blackout on the experimental side from NASA.
The problem is, if this drive really works, the defence implications are huge. Those in charge might feel it would not necessarily be a good idea to go public with it  especially from the US perspective. Remember that 'Sputnik moment'?
It would be an interesting exercise to see what emdrives could do for say a boomer http://en.wikipedia.org/wiki/Ohioclass_submarine with its S8G reactor onboard http://www.ewp.rpi.edu/hartford/~ernesto/F2010/EP2/Materials4Students/Misiaszek/NuclearMarinePropulsion.pdf http://en.wikipedia.org/wiki/S8G_reactor
So if these emdrives work, they'll likely find their way into applications such as this before they are helping us explore the solar system.
On the flip side, this will flood the arena with dollars and expertise, especially if the Chinese have already one upped us.
Break:
So as far as space flight applications, the other day when, for the purpose of exercise, I converted the ISS to an interplanetary spaceship, would such a thing in the real world make sense? Or is it just plain ridiculous? I was thinking that from an economic standpoint, converting it to that use, and boosting it out of LEO and beyond, would be far cheaper than building a whole new space craft. And since it is modular already, it has to be a pretty straightforward adaptation for an exploration mission.
Found this: http://www.universetoday.com/15561/thespacestationasaninterplanetarytransportvehicle/

....
the Brady results. The mode numbers they give have to be erroneous as they don't fit w/ the cavity frequency calculations. ...
...
Here I've tried to incorporate all 3 subscripts into the expression and eliminate some of my own confusion about the reported modes. ...I had a lot of trouble trying to figure out the X's from the "given" modes until I remembered they were in the cavity frequency formulas. That eliminated most of the possible modes...
So, using these to identify the frequencies, I chose:
Bradya => TM122 or TE022 X[sub m,n] = 7.02 p = 2
Bradyb => TE213 X[sub m,n] = 3.05 p = 3
Bradyc => TE222 X[sub m,n] = 6.71 p = 2
...
Bradya NT= 1.04e4 vs 9.12e5 Pwr= 16.9 Q=7320 TM122 or TE022
Bradyb NT= 4.80e5 vs 5.01e5 Pwr= 16.7 Q=18100 TE213
Bradyc NT= 4.78e5 vs 5.54e5 Pwr= 2.6 Q=22000 TE222
...
First of all congratulations on the extremely impressive further development of your theoretical prediction. Your formulas now are superior to the ones of Shawyer and McCulloch in these important considerations:
1) the only ones that show mode shape dependence
2) closest to NASA's Brady et.al. experimental results.
There is a lot to discuss, but I would like to start with your finding that the Brady mode shape quantum numbers (m, n, p) must be erroneous.
Concerning Brady, White, March, Lawrence and Davies "Anomalous Thrust Production from an RF Test Device Measured on a LowThrust Torsion Pendulum", Propulsion and Energy Forum, Cleveland, OH
AIAA 20144029, (http://www.libertariannews.org/wpcontent/uploads/2014/07/AnomalousThrustProductionFromanRFTestDeviceBradyEtAl.pdf ) I note, that:
A) The NASA authors report that they used the commercial finite element software COMSOL Multiphysics® to calculate the frequencies and mode shapes. COMSOL Multiphysics® software can indeed calculate the frequencies and it can be used to plot the mode shapes, but COMSOL Multiphysics® does not define the mode shape quantum numbers. Such mode shape quantum numbers can only be defined by convention.
B) The truncated cone (tapered frustum) is asymptotically closest to a cylindrical waveguide, the two becoming identical at a tapered cone angle of zero. However we must admit that a truncated cone mode shapes cannot be identical to the mode shapes of a cylindrical cavity. However, as an engineering approximation, for the tapered cone angle being small it should be acceptable to describe the tapered cone mode shapes with the same terminology as the one used for a cylindrical waveguide.
C) The presence of the dielectric is very important in discussing mode shapes, as the presence of a dielectric necessarily makes the cavity mode shape different from an empty cavity. Hence the description of the cavity mode shapes entails both:
C1) Idealizing the tapered cavity as a cylindrical cavity and
C2) Ignoring the presence of the dielectric: assuming an empty cavity.
D) the standard convention to name electromagnetic modes of a cylindrical cavity in terms of the three quantum numbers m, n and p that I am familiar with is:
The first subscript (m) is the azimuthal mode number: it indicates the number of fullwave patterns around the circumference of the cavity. It is zero for modes in which there is no variation in the circumferential direction.
The second subscript (n) is the radial mode number: it indicates the number of halfwave patterns across the diameter. The radial mode number (n) plus one indicates the number of nodes across the diameter (counting as nodes the end nodes).
The third subscript (p) is the longitudinal mode number. It indicates the number of full halfwave patterns along the longitudinal length of the cavity. It is zero for modes in which there is no variation in the longitudinal direction.
E) The following file (http://www.engr.sjsu.edu/rkwok/EE172/circular_WG.JPG, created by Dr. Ray Kwok at San Jose State University) shows the contour plots for the first Transverse Electric (TE) and Transverse Magnetic (TM) modes of a cylindrical cavity
F) Comparing the mode shapes determined by @NotSoSureOfIt with the mode shapes reported by NASA's Brady et.al., we show the corresponding mode number contour plot from Dr. Ray Kwok at San Jose State University (where we drop the longitudinal mode number "p" for simplification):
NASATest NASAmodereported Kwok# @NotSoSureOfItmode Kwok#
Brady a TM21 7 TM12 15
Brady a TM21 7 TE02 14
Brady b TM21 7 TE21 3
Brady c TE01 5 TE22 13
http://www.engr.sjsu.edu/rkwok/EE172/circular_WG.JPG

@RODAL
A. I'm still having conceptual difficulties w/ the mode numbers trying to resolve the waveguide vs cavity versions of this thing.
B. Don't have access to COMSOL anyway
C. Used square avg to get close to an equivalent vol cylinder
D. Didn't use included dielectric, but assumed it might change the res freq somewhat. Prob the biggest errors. (enough to change mode numbers?)
E. Sounds like what I wound up using
F. Nice !
G. Those still might not be the correct modes given that the dielectric is not taken into account along w/ the dimensional approximations. i didn't try all matches.
@RotoSequence
http://arxiv.org/abs/1411.3987
This is a very interesting paper !

Poking around the internet, I ended up at this paper on Arxiv: http://arxiv.org/abs/1411.3987
Photons that travel in free space slower than the speed of light
That the speed of light in free space is constant is a cornerstone of modern physics. However, light beams have finite transverse size, which leads to a modification of their wavevectors resulting in a change to their phase and group velocities. We study the group velocity of single photons by measuring a change in their arrival time that results from changing the beam's transverse spatial structure. Using timecorrelated photon pairs we show a reduction of the group velocity of photons in both a Bessel beam and photons in a focused Gaussian beam. In both cases, the delay is several microns over a propagation distance of the order of 1 m. Our work highlights that, even in free space, the invariance of the speed of light only applies to plane waves. Introducing spatial structure to an optical beam, even for a single photon, reduces the group velocity of the light by a readily measurable amount.
What effect does reduced group velocity in free space have on the momentum of photons?
I agree with @NotSoSureOfIt, very interesting post. The ending paragraph is also worthy of note:
The speed of light in free space propagation is a fundamental quantity. It holds a pivotal
role in the foundations of relativity and field theory....
It has previously been experimentally established that single photons travel at the group
velocity. We have now shown that transverse structuring of the photon results in a
decrease in the group velocity along the axis of propagation. The effect can be derived
from a simple geometric argument, which is also supported by a rigorous calculation of
the harmonic average of the group velocity. Beyond light, the effect observed will have
applications to any wave theory, including sound waves and, potentially, gravitational
waves.

wait. going from "that" book again: the speed of light is constant in local frames of reference only. If you are way over there and i am way over here we measure light where we happen to be the same (locally invariant.) But if am over here and i measure the speed of light over there (where you are) i may get a different value for the speed of light (where you are) than you do.
E.G; if you are near the event horizon of a black hole and i am way over here; you still experience light and other things as you would expect but i see light and other things as frozen where you are at.
I have encountered dozens of people who argue for pages and pages that relativistic time dilation causes a stationary observer on earth to experience 1000's of years when a relativistic rocket (at 99% C) travels 4 light years to Alpha Centauri. They get it completely wrong and argue the wrong reference frame for pages as if their lives depended on it. These are people that have at least read books on relativity written at the popular level.
In short thinking about reference frames can warp your mind and your calculations. I recommend laying down and avoiding them.

Oh well, time for me to make a spectacle of myself again...
if I am following Notsosureofits and Rodal correctly, then...
1) the experimenters are proceeding from badly flawed assumptions about mode, among other things; and
2) their positive results come about through chance or design accident.

Oh well, time for me to make a spectacle of myself again...
if I am following Notsosureofits and Rodal correctly, then...
1) the experimenters are proceeding from badly flawed assumptions about mode, among other things; and
2) their positive results come about through chance or design accident.
The fact that they do not sufficiently explore the complete mode shapes in the cavity does not mean that they proceeded from "badly flawed assumptions". That is too severe an assessment.
Brady' a and b experiments (which they labeled with the TM211 mode for reasons that are unclear and they do not explain) had significantly lower thrust/InputPower than Brady's c experiment (which they labeled TE012). Therefore Brady's c is most important to deal with. My contention is that Brady c "looks" like a TE01 mode strictly because of the field in the dielectric. If you look at the contour plot shown by Brady, the only part of the cavity experiencing significant (yellow and red) field contours is the dielectric. The rest of the cavity has extremely small (dark blue) levels in comparison. See:
(http://forum.nasaspaceflight.com/index.php?action=dlattach;topic=36313.0;attach=631726;image)
Therefore (just looking at the above picture, based solely on the field within the dielectric and ignoring the field in the rest of the cavity as being negligible) it makes some sense for Brady to label the c mode as TE01.
EDIT: On the other hand, the presence of the dielectric may not be that relevant to what matters: the thrust, because NotSoSureOfIt predicts the reported experimentally measured thrust based on an empty cavity with no dielectric (and hence a very different mode shape: TE22 instead of TE01).
What is really most impressive is that NotSoSureOfIt has come up with an analytical solution (which Brady et.al. did not do) that models the experimental results accurately in terms of mode shape quantum numbers, and that NotSoSureOfIt has done this with a minimum of data compared with the data available to Brady et.al.

For c: TE01 doesn't compute but TE022 is a good fit, maybe better than TE222. (w/o dielectric that is)
Edit: Nope, frequency is too high (dielectric might bring it down ?)
For b: TE213 seems the only good fit
For a: Can't tell the difference between TE022 andTM122
Probably as good as this model is gonna get w/o the dielectric (and the COMSOL)

Quick question:
Did someone mention in the past that the equations at the Oracle are no good? Or were they good?
http://en.wikipedia.org/wiki/Microwave_cavity#Cylindrical_cavity
or are these good
Am I better off going with the Kwok slide 13?
http://www.engr.sjsu.edu/rkwok/EE172/Cavity_Resonator.pdf
or this guy's method?
http://www.chrislmueller.com/studies/Jackson86.pdf
Playing catch up here. This page is nifty. http://mathworld.wolfram.com/BesselFunctionZeros.html

Quick question:
Did someone mention in the past that the equations at the Oracle are no good? Or were they good?
http://en.wikipedia.org/wiki/Microwave_cavity#Cylindrical_cavity
or are these good
Am I better off going with the Kwok slide 13?
http://www.engr.sjsu.edu/rkwok/EE172/Cavity_Resonator.pdf
or this guy's method?
http://www.chrislmueller.com/studies/Jackson86.pdf
Playing catch up here. This page is nifty. http://mathworld.wolfram.com/BesselFunctionZeros.html
Quick glance: I took a quick gander at them and they all look identical, insofar as being related to X'm,n and Xm,n (the zeros of the derivative of the Bessel function or the zeros of the Bessel function respectively) for TE and TM respectively. What difference do you see between them?
For example, notice (from http://wwwal.kuicr.kyotou.ac.jp/www/accelerator/a4/besselroot.htmlx )
that X'_{1},_{1} = 1.84118378134065
And therefore in Kwok slide 13 (http://www.engr.sjsu.edu/rkwok/EE172/Cavity_Resonator.pdf ) with radius of the Coke can a = 1.25
kc = X'_{1},_{1} / a = 1.8412 / 1.25 = 1.473
f111=(c/(2*Pi))*Sqrt[(kc)^2+(p*Pi/d)^2]
The expressions for ChrisMueller and Wikipedia look identical except for the factor of 2*Pi due to the fact that ChrisMueller calculates the angular frequency (omega) while Wikipedia calculates the frequency (f). Since omega = 2 *Pi*f, the expressions in Wikipedia and in ChrisMueller are both identical and both are correct. Kwok's expression is missing the factor of the squareRoot of the relative permeability and relative permittivity of the cavity filling because Kwok explicitly wrote that he is calculating the example for air inside the cavity. (For a vacuum they are exactly unity, for air they are approximately unity).
(http://upload.wikimedia.org/wikipedia/commons/c/c9/AngularFrequency.gif)

I get the air thing which means I can just drop that part. The part that screwed with me was
f = (c/(2*Pi))*((X[sub m,n]/R)^2+((p*Pi)/L)^2)^.5
silly enough the ^.5 part because I'm used to seeing sqrt typed out, but that works too. Thanks for clearing all that up.
This is all looking pretty good, so far as I've gotten. I think it might be time for @Notsosureofit to put some polish on it, add some prose, and make it a packaged deal.
I think it might be time for a spaceflight application minute. Theory is getting pretty heavy once again.

...
I think it might be time for a spaceflight application minute...
Good idea, I'm ready :)

...
For TM modes, X[sub m,n] = the nth zero of the mth Bessel function.
[1,1]=3.83, [0,1]=2.40, [0,2]=5.52 [1,2]=7.02, [2,1]=5.14, [2,2]=8.42, [1,3]=10.17, etc.
and for TE modes, X[subm,n] = the nth zero of the derivative of the mth Bessel function.
[0,1]=3.83, [1,1]=1.84, [2,1]=3.05, [0,2]=7.02, [1,2]=5.33, [1,3]=8.54, [0,3]=10.17, [2,2]=6.71, etc.
...
A minor point. For further clarity you may want to include a prime symbol (or an apostrophe) on X
"for TE modes, X'[subm,n] = the nth zero of the derivative of the mth Bessel function"
instead of
"for TE modes, X[subm,n] = the nth zero of the derivative of the mth Bessel function"
to differentiate X' (as used for the TE modes) from X (as used for the TM modes). :)

...
For TM modes, X[sub m,n] = the nth zero of the mth Bessel function.
[1,1]=3.83, [0,1]=2.40, [0,2]=5.52 [1,2]=7.02, [2,1]=5.14, [2,2]=8.42, [1,3]=10.17, etc.
and for TE modes, X[subm,n] = the nth zero of the derivative of the mth Bessel function.
[0,1]=3.83, [1,1]=1.84, [2,1]=3.05, [0,2]=7.02, [1,2]=5.33, [1,3]=8.54, [0,3]=10.17, [2,2]=6.71, etc.
...
A minor point. For further clarity you may want to include a prime symbol (or an apostrophe) on X
"for TE modes, X'[subm,n] = the nth zero of the derivative of the mth Bessel function"
instead of
"for TE modes, X[subm,n] = the nth zero of the derivative of the mth Bessel function"
to differentiate X' (as used for the TE modes) from X (as used for the TM modes). :)
Perfect timing, in the RF & Microwave Toolbox app I've been using, I found they messed up exactly what you are saying. Emailed developer. See screenshot.
Still trying to think of another spaceflight application. We need more power Scotty!
(http://www.quickmeme.com/img/e6/e61f7f0012fb504e3292ba7068f661f9e67231b46e415e5b569847b2a8d9bcdf.jpg)

For applications, I would imagine a key figure is practical thrust/weight and thrust/power. It probably isn't enough for a very low orbit PROFAC atmosphere collector, but a high orbit PROFAC might work. Tether/rotovator reboost is another application.

Space travel applications...
If applied, would 'Notsosureofits's' mode calculations significantly help or hinder the 'Mulletron Mission to Saturn'?

Space travel applications...
If applied, would 'Notsosureofit's mode calculations significantly help or hinder the 'Mulletron Mission to Saturn'?
Might help if it could calculate an "optimum" cavity shape. Such has been done for acoustic cavity refrigerators, etc. What is the maximum asymmetric dispersion you can get ? What is the optimum frequency ? (and the highest Q, of course)
Then too, it's not yet apparent why this calculation works at all.
Maybe that's what the Cannae was about, short cavity w/ high mode numbers ? I could see where they might have been trying to stabilize some mode w/ the fins, sorta like some magnetrons.

Space travel applications...
If applied, would 'Notsosureofit's mode calculations significantly help or hinder the 'Mulletron Mission to Saturn'?
Might help if it could calculate an "optimum" cavity shape. Such has been done for acoustic cavity refrigerators, etc. What is the maximum asymmetric dispersion you can get ? What is the optimum frequency ? (and the highest Q, of course)
Then too, it's not yet apparent why this calculation works at all.
I think the other half of the calculation remains to be completed, which is the part concerning how to, and may provide a way to, conserve momentum. The other side of the momentum vector diagram concerns vacuum radiation pressure; well I think it is anyway. At the bottom of page 91 is a nice mashup. We've discussed this in depth in thread one, yet the math remains elusive, but I don't think it is out of our reach.
Google book link to: The Quantum Vacuum: A Scientific and Philosophical Concept, from Electrodynamics to String Theory and the Geometry of the Microscopic World. Luciano Boi
http://bit.ly/1CKmGWX

@RODAL
A. I'm still having conceptual difficulties w/ the mode numbers trying to resolve the waveguide vs cavity versions of this thing.
B. Don't have access to COMSOL anyway
C. Used square avg to get close to an equivalent vol cylinder
D. Didn't use included dielectric, but assumed it might change the res freq somewhat. Prob the biggest errors. (enough to change mode numbers?)
E. Sounds like what I wound up using
F. Nice !
G. Those still might not be the correct modes given that the dielectric is not taken into account along w/ the dimensional approximations. i didn't try all matches.
...snip...
@Notsosureofit
I encountered similar problems with the mode numbers. I note here http://mathworld.wolfram.com/BesselFunctionZeros.html (http://mathworld.wolfram.com/BesselFunctionZeros.html) that the first J'_{0}(x) value is given as nonzero in the table but the curve of J_{0}(x) clearly shows a zero for the derivative at x=0. This is explained in the text, but the text does not resolve the question of which value to use for cavity resonance. That of course will change the TE mode numbers.
There is also the remark that I found (somewhere) while reading up on Bessel functions or resonance cavitys. In communicating mode numbers it is important to specify the order of the subscripts. Some people communicate TE_{0,1} as TE_{1,0} and so forth.
Regarding your concern W.R.T. frequency changing with dielectric. The dielectric constant for the Brady cavity dielectric is about 1.76, I think. I obtained this value by iteratively running meep for different values of the dielectric constant and using Harminv to calculate the resonant frequency. The cavity resonated at 1880.5 MHz using a dielectric value of 1.76. I called that close enough. Note that is about 50% density of P.E.
I will check using meep again to see how strong an effect the dielectric constant has on the resonance frequency. I have conflicting recall on that subject at the moment.

...
For TM modes, X[sub m,n] = the nth zero of the mth Bessel function.
[1,1]=3.83, [0,1]=2.40, [0,2]=5.52 [1,2]=7.02, [2,1]=5.14, [2,2]=8.42, [1,3]=10.17, etc.
and for TE modes, X'[subm,n] = the nth zero of the derivative of the mth Bessel function.
[0,1]=3.83, [1,1]=1.84, [2,1]=3.05, [0,2]=7.02, [1,2]=5.33, [1,3]=8.54, [0,3]=10.17, [2,2]=6.71, etc.
So, using these to identify the frequencies, I chose:
Bradya => TM122 or TE022 X[sub m,n] = 7.02 p = 2
Bradyb => TE213 X'[sub m,n] = 3.05 p = 3
Bradyc => TE222 X'[sub m,n] = 6.71 p = 2
....
1) I have checked your abovegiven definitions for X_{m},_{n} and X'_{m},_{n} vs. the ones obtained from Mathematica and vs. the ones given by University of Kyoto, Japan in http://wwwal.kuicr.kyotou.ac.jp/www/accelerator/a4/besselroot.htmlx . They are all identical, therefore the discrepancies in mode shape definitions that I will discuss below have nothing to do with the definitions of X_{m},_{n} and X'_{m},_{n} . You and I are using identical definitions. (For anybody interested in the reason why Mathematica, the University of Kyoto and others has the J'0(x)@x=0 value as nonzero (as opposed to the old reference: Abramowitz) , see for example Theorem 3.1 in http://www.irjabs.com/files_site/paperlist/r_1259_130901233803.pdf : the value of the derivative at the origin (x=0) is mathematically undefined as the closedform solution has zero/zero at the origin.)
2) It appears that the exact geometrical dimensions play a paramount role concerning the actual mode shape for a given frequency, particularly for higher modes, where different mode shapes are more likely to give frequencies close to each other. This makes sense.
3) Let's define as "Aero geometry" the following definition for the NASA Brady et. al. cavity:
Aero Best estimate as of 11/9/2014 http://forum.nasaspaceflight.com/index.php?topic=29276.msg1285896#msg1285896
cavityLength = 0.24173 m
bigDiameter = 0.27246 m
smallDiameter = 0.15875 m
4) Let's define as "Fornaro geometry" the following definition for the NASA Brady et. al. cavity:
Fornaro estimate http://forum.nasaspaceflight.com/index.php?topic=36313.msg1302455#msg1302455
cavityLength = 0.332 m
bigDiameter = 0.397 m
smallDiameter = 0.244 m
5) Let's use the GeometricalMeanDiameter=Sqrt[bigDiameter*smallDiameter] as the equivalent diameter of the equivalent cylindrical cavity
6) Given the experimentally reported frequencies, the geometrical dimensions and the value of speed of light in air, one can invert the frequency equation (see: http://en.wikipedia.org/wiki/Microwave_cavity#Cylindrical_cavity ) to obtain X_{m},_{n} and X'_{m} values as a function of constants and the longitudinal mode shape number "p". Let's define the error difference between these X_{m},_{n} and X'_{m},_{n} values and actual X_{m},_{n} and X'_{m} values as:
error= (value of X_{m},_{n} or X'_{m},_{n} obtained from frequency eqn.)/ (correct value of X_{m},_{n} or X'_{m},_{n} ) 1
where X_{m},_{n} is used for TM modes and X'_{m},_{n} is used for TE modes.
7) Then I obtain the following mode shapes:
BRADY "A"
Fornaro Geometry
Best result: TM022 error=+0.956%
2nd best: TM310 error=  1.206%
Aero Geometry
Best result: TE310 error=+0.255%
2nd best: TM111 or TE011 error= + 4.11%
BRADY "B"
Fornaro Geometry
Best result: TM310 error=  0.997%
2nd best: TM022 error= + 1.230%
Aero Geometry
Best result: TE310 error=+0.468%
2nd best: TM111 or TE011 error= + 4.36%
BRADY "C"
Fornaro Geometry
Best result: TE412 error= + 1.166%
2nd best: TE313 error= + 1.259%
Aero Geometry
Best result: TE212 error=+0.859%
2nd best: TE011 or TM111 ; error= + 0.971%
CONCLUSIONS
1) The modeshape to frequency relation is very sensitive to the exact geometrical dimensions of the cavity. The abovegiven Fornaro and Aero guesses of the dimensions of the Brady et.al cavity give very different mode shapes (all other parameters being the same).
2) Before these calculations the consensus was that Aero's latest estimates of the geometry were superior (for a number of reasons). These calculations give further confirmation that Brady et.al. actual geometry may be closer to Aero's estimates:
2a) In all cases examined above, the errors are smaller using the Aero estimate of geometry.
2b) Aero's estimate of geometry (predicting a smaller Brady et.al. cavity than Fornaro) lead to more stable values of mode shape with frequency: Aero's estimate gives the same mode shape (TE310 for both Brady "A" and Brady"B", which differ very little in frequency). Fornaro's geometry gives different mode shapes for Brady "A" and "B".
2c) Aero's estimate of geometry gives more discrimination between mode shapes for Brady cases "A" and "B": the mode shape (TE310) with the smallest error has an error off less than 1% while the next closest mode shapes have errors exceeding 4%. Fornaro's geometry has errors much closer together which do not provide as much power to discriminate between the actual mode shape.
3) It is interesting that I obtained for Brady case "C" (NASA's experiment which gave the largest by far thrust/PowerInput) mode TE01 as the second best mode shape, with an error of less than 1%: just 0.971%. This coincides with NASA's Brady et.al. mode shape first two quantum numbers (circumferential and radial). I propose that TE01 may indeed be the actual mode shape for Brady "C" (the difference in errors between TE01 and TE21 is insignificant) because of the effect of the dielectric polymer in the cavity (which we do not take into account). The dielectric polymer is a circumferential doughnutshape polymer that must have a TE01 mode shape  obviously (see this picture)
(http://forum.nasaspaceflight.com/index.php?action=dlattach;topic=36313.0;attach=631726;image). This dielectric polymer must force the cavity into the TE01 mode shape. As to why I calculate TE011 while NASA Brady et.al give TE012 that also can be readily explained by the polymer dielectric as the dielectric will produce an extra longitudinal full wave in the dielectric polymer, resulting in two full waves in the longitudinal direction of the whole cavity: 1) one full wave within the doughnutshaped polymer dielectric itself, along the thickness of the doughnut and 2) the other full wave within the longitudinal direction of the rest of the empty cavity that has no dielectric polymer.
4) The Aero geometry estimate of the Brady et.al. cavity (that appear to be the best geometrical estimate) gives TE (transverse electric) mode shapes as the best mode shape estimates for all frequencies tested by NASA Brady et.al. Actually, the TE01 mode is a close mode shape for all the Brady experiments. It just happens that the frequency that best excites TE01 happens to be Brady C, that provided the highest thrust/PowerInput. This is critical, because TE01 is also the mode excited by the dielectric polymer. This is important also if indeed the thrust force is mainly a result of the internal, centrally located magnetic field (contained within the Transverse Electric (TE) circumferential field) being responsible for the experimental results (as previously argued either as thermal buckling artifact or whether as a result of the central longitudinal magnetic field interacting with the Quantum Vacuum providing quantum vacuum radiation pressure, for example).
5) I have to doublecheck my Mathematica program for any errors and my above transcription for any errors. Thank you for your patience :)

At constant input power, the thrust, and therefore the acceleration, must decrease with time, to ensure that the spacecraft's velocity never exceeds 2*Power/Thrust
I was going to start a thread, but there is a photon rocket variant idea I have been batting around for a few months now:
take a long hollow cylinder, closed at one end, open on the other. Probably several hundred meters long, by three or four meters in diameter. Running the length of this cylinder, spaced at even intervals are low beams  probably no more than ten or twenty centimeters high. So the inner edge of the cylinder has...call it a dozen shallow troughs. At regular intervals  maybe a meter  these beams have specially designed reflective points. Open end of the cylinder, you have a powerful high frequency laser (or something emitting a focused photon beam) aimed at a 45 degree angle into each trough. One laser per trough, call it twelve total.
Now, a laser, like a military searchlight, is also a photon rocket.
Photons, as pointed out in the previous thread are durable little critters, and can bounce around a good 50,000+ times before going wherever it is expired photons go. And photons can transfer momentum with each bounce.
So, turn the lasers on. The initial 'thrust' is backward. Actually, 'backward and sideways' because of the angle.
That thrust gets negated at the first bounce point. Photons hit that (reflective) point, transfer momentum, and head over to the next bounce point, set at a 45 degree angle to the first.
At the second bounce point, the whole thing is moving forward. Repeat for the length of the cylinder. Because the photons are hitting at an angle, the cylinder might start rotating as well as moving forward, but I don't see that as a major issue. At the end of the cylinder, the photons hit a shaped surface and bounce back along the tubes center and out into space.
Did a bit of reading on laser propulsion systems. A Doctor Bae ran some laboratory tests on this: bouncing laser beams multiplied the 'thrust' by a factor of 3000+  into EM Drive territory without the physics headache. He proposed two linked spacecraft, with laser beams between them, something NASA is supposed to be looking into for near earth applications. My idea is one spacecraft (the cylinder) and a multiplier of about 1500, if the cylinder is long enough. Not sure, but that's should be on a par with the Brady EM drive model.
Alter the angles a bit, test different lasers/emitters, might get a lot more work out of the photons, increasing thrust further.
Would this violate the paradox?
You seem to misunderstand the fundamentals of mechanics.
If a photon hits a mirror at a 45 degree angle and reflects off it, the mirror will receive an impulse perpendicular to the plane of the mirror only. It will not be pushed in the direction of the other component of the photon at all.
It's not just with photons. If you have a billiard ball and you bounce it off another billiard ball that was stationary so that the original ball end up leaving at a 90 degree angle to its initial direction of travel, the other ball will end up traveling at a 45 degree angle to the path of the original ball.
It's nonintuitive because our intuition is shaped by friction tending to pull things along, but such friction is not a part of purely elastic collisions, and photons bouncing off mirrors are purely elastic.
So, every time your photon bounces off the wall, the momentum it imparts will only be to push outward perpendicular to the axis of the tube. And it will be cancelled by the next bounce off the opposite wall.
The only effect of the net momentum of the tube is the opposite of whatever momentum the photo has when it finally leaves the tube. Whatever it does as it bounces around in the tube will have no net effect.
What about a severe conewith a 5 degree opening? Lasers shot up into th mirrorwould glance off at an approximate 7 degerr angle, still proceeding upwards to the conical apex, where they would then be relected directly outwards. Obviously the photons would loose energy with each bounceand you'd have to cool the conical mirror, as at best, you MIGHT get a 97% reflectivity from it, but could THAT work as a propulsive system? (BTW the 7 degree is an approximation of the angle. Your milage may vary).

...
For TM modes, X[sub m,n] = the nth zero of the mth Bessel function.
[1,1]=3.83, [0,1]=2.40, [0,2]=5.52 [1,2]=7.02, [2,1]=5.14, [2,2]=8.42, [1,3]=10.17, etc.
and for TE modes, X'[subm,n] = the nth zero of the derivative of the mth Bessel function.
[0,1]=3.83, [1,1]=1.84, [2,1]=3.05, [0,2]=7.02, [1,2]=5.33, [1,3]=8.54, [0,3]=10.17, [2,2]=6.71, etc.
So, using these to identify the frequencies, I chose:
Bradya => TM122 or TE022 X[sub m,n] = 7.02 p = 2
Bradyb => TE213 X'[sub m,n] = 3.05 p = 3
Bradyc => TE222 X'[sub m,n] = 6.71 p = 2
....
OK, let's use your terminology to check the labeling of the modes.
The lowest modes that have exactly the same numerical values, according to your definition above are:
For TM modes, X[sub m,n] = the nth zero of the mth Bessel function.
[1,1]=3.83 Therefore m=1,n=1 and TM11 corresponds to X_{1},_{1}=3.83
and for TE modes, X'[subm,n] = the nth zero of the derivative of the mth Bessel function.
[0,1]=3.83 Therefore m=0,n=1 and TE01 corresponds to X'_{0},_{1}=3.83
* Actually, in general X_{1,n} = X'_{0,n} for any n *
*
EDIT:
therefore
frequency of TM_{1}_{n}_{p} = frequency of TE_{0}_{n}_{p} for given radius and cavity length, for any value of n and any value of p
*
Therefore the modes that have the same numerical value are TM11 and TE01 (and not TM12 or TE02).
Conclusion: it appears that the radial quantum number "n" in your mode number is higher than the correct value by one. (For some reason it also appears that your longitudinal "p" is also inflated by one: it should be TM111 instead of TM122 and it should be TE011 instead of TE022).

X[sub 1,a] = X'[sub 0,a]
These are the columns that correspond.
http://mathworld.wolfram.com/BesselFunctionZeros.html
TM111 gives me 1.03 GHz ditto for TE011
I couldn't find a formula for a tapered cavity.
I'm thinking the volumetric radius might be the best choice as radius
R^2 = (a^2+a*b+b^2)/3
Havn't had time to try recalculations, but if you have Mathematica you can try lots

...
TM111 gives me 1.03 GHz ditto for TE011
From http://en.wikipedia.org/wiki/Microwave_cavity#Cylindrical_cavity, the frequency equation gives:
frequencyTM111 =( cAir/(2*Pi))*Sqrt[((X_{1},_{1} /(aeroGeometricMeanDiameter/2))^2) +(1*Pi/aeroLength)^2]
= 1.8643 GHz instead of 1.03 GHz
ditto for frequencyTE011
using
m=1
n=1
p=1
X_{1},_{1} = 3.83170597020751
cair = 299705000 m/s = (299792458 m/s) / (Sqrt[mur*epsilonr] = c / (Sqrt[mur*epsilonr])
aeroGeometricMeanDiameter = 0.207974 m = Sqrt[ (0.27246 m) * (0.15875 m)]
aeroLength = 0.24173 m

...
TM111 gives me 1.03 GHz ditto for TE011
If, were one to use the diameter instead of the radius in the frequency equation one would obain:
frequencyTM111 =( cAir/(2*Pi))*Sqrt[((X_{1},_{1} /(aeroGeometricMeanDiameter))^2) +(1*Pi/aeroLength)^2]
= 1.07 GHz which is very close to your calculated 1.03 GHz
==> Please consider whether your mode shape calculations may be incorrect perhaps because you inadvertently may have used the diameter instead of the radius in the expression for frequency <===
Remember:
Aero Best estimate as of 11/9/2014 http://forum.nasaspaceflight.com/index.php?topic=29276.msg1285896#msg1285896
cavityLength = 0.24173 m
bigDiameter = 0.27246 m
smallDiameter = 0.15875 m

We are using different radii. I'm thinking of going to the volumetric, might be closest, still looking for an actual f solution.

...
I'm thinking the volumetric radius might be the best choice as radius
R^2 = (a^2+a*b+b^2)/3
Havn't had time to try recalculations, but if you have Mathematica you can try lots
Are you thinking this way?
Defining these symbols for the radii of the truncated cone (frustum of a cone):
r=smallRadius=smallDiameter/2
R=bigRadius=bigDiameter/2
The volume of a truncated cone and the volume of a cylinder are:
Volume of the frustum of a cone =Height*Pi*(r^2+r*R+R^2)/3
Volume of a cylinder= Pi*(EquivalentR^2)*Height
Equating these volumes one arrives at an expression for the Equivalent Radius of a cylinder having the same volume as the volume of the frustum of a cone:
Volume of a cylinder = Volume of the frustum of a cone
Pi*(EquivalentR^2)*Height = Height*Pi*(r^2+r*R+R^2)/3
hence
EquivalentCylindricalRadius = Sqrt[(r^2+r*R+R^2)/3]
= Sqrt[(smallDiameter^2+smallDiameter*bigDiameter+bigDiameter^2)/12]
See this example: it makes very little difference what mean to use:
aeroLength=0.24173 meter;aeroBigDiameter=0.27246 meter;aeroSmallDiameter=0.15875 meter;
aeroGeometricMeanDiameter=Sqrt[aeroBigDiameter*aeroSmallDiameter]
= 0.207974 meter
aeroMeanDiameter =(aeroBigDiameter+aeroSmallDiameter)/2
= 0.215605 meter
aeroVolumetricDiameter=Sqrt[(aeroSmallDiameter^2+aeroSmallDiameter*aeroBigDiameter+aeroBigDiameter^2)/3]
= 0.218089 meter
The differences between these different means (just a few % between them) is less than the level of uncertainty we have for the geometry. The difference between these means is much less than the difference between Aero and Fornaro's estimates of the geometry. It would be useful to know what dimensions did you use.

We are using different radii. ,,,
I used Aero's and also Fornaro's dimensions. For example,
Aero Best estimate as of 11/9/2014 http://forum.nasaspaceflight.com/index.php?topic=29276.msg1285896#msg1285896
cavityLength = 0.24173 m
bigDiameter = 0.27246 m
smallDiameter = 0.15875 m
What dimensions did you use for the tapered cone (frustum) ?
I don't recall you stating the dimensions in this post: http://forum.nasaspaceflight.com/index.php?topic=36313.msg1317866#msg1317866 . Sorry if it is in some of your other posts and I missed it.

Ok...so if I am following the latest exchange correctly, then these devices dimensions MUST be in complete sync with the given frequency in order for them to work at all? Or do they just function very poorly if the match is not exact?
I also recollect long posts in the other thread about how difficult it was to attain and maintain the correct frequency  something about it shifting?

Ok...so if I am following the latest exchange correctly, then these devices dimensions MUST be in complete sync with the given frequency in order for them to work at all? Or do they just function very poorly if the match is not exact?
I also recollect long posts in the other thread about how difficult it was to attain and maintain the correct frequency  something about it shifting?
These are cavity resonators that use the Quality Factor Q to achieve greater response. So, definitely you have to be at a peak resonant frequency to achieve highest Q.
But what we have been discussing as of late, besides Q and frequency is the mode shape: the shape of the electric and magnetic fields inside the cavity at a given frequency. There are an infinite number of possible mode shapes inside a cavity (considering all frequencies). Even in the MHz and GHz frequency ranges there are several natural frequencies and associated mode shapes to consider.
Take a gander at the attached picture for a few mode shapes
The question is what mode shape may be most effective for thrust generation. This is the emphasis of our discussion: how to achieve the greatest level of thrust of an EM Drive for a given level of inputpower.

On seeing the cavity geometry revisited, I will just mention that my measurements were of necessity of the outside of the cavity. The inside dimensions would be smaller by the amount of copper thickness. As I recall, we estimated the copper cone to be most likely 1/32" copper and the end copper ground plane on the circuit board to be ~ 2 thousandths of an inch.
I did a Google search for circuit boards, and found that they are rated in ounces of metal per square ? something 1, 2 and 3 oz. plating being common. Translated to thickness it came to 3040 microns, 6575 microns and just over 100 microns. I dropped that line of investigation an went with the 2/1000 estimate.
As for the cone thickness of 1/32 inch, I think I gave the pixel count for the 1 1/2 inch square beam end which I believe it puts 1/32 inch on the order of 1 pixel. But my measurements of the outer dimension are also at best, on that order so I don't know what kind of wizardry it would take to pull up a better estimate of the inner dimensions of the cone.
There it is, if anyone wants to take a shot at further correction to the big and small diameters.
Add: Of course one could just subtract the thickness from the radius. And I note that the small end diameter is the diameter of the dielectric, so it is already the inside diameter.

There is essentially a news blackout on the experimental side from NASA.
The problem is, if this drive really works, the defence implications are huge. Those in charge might feel it would not necessarily be a good idea to go public with it  especially from the US perspective. Remember that 'Sputnik moment'?
[/quote]
@wembley, do you have any specific info about why you think there is a news blackout?
Also, do you have any further verifiable information from this post: http://forum.nasaspaceflight.com/index.php?topic=29276.msg1265607#msg1265607 stating Shawyer stopped using a dielectric section?
[/quote]
I been in contact with NASA on this and the lack of direct response has been marked. They will talk about the warp drive and other work, but will not even mention the EmDrive in their replies. It's as though they cannot speak its name...I also have it from other sources that NASA have requested that they do not discuss NASA's work in this area. If you can find any official NASA public comment on anything related to their EmDrive work I will be impressed! It does look like a blackout to me.
The info about Shawyer not using dielectric section was in an email from the man himself.

I have no way of telling if this would work, and it seems to me that the forces involved are rather high for the device to deal with, but potentially it could produce much more thrust for the same input
"Here, we review the derivation of the equation of thrust of Shawyer’s thruster, by obtaining a new expression, which includes the indexes of refraction of the two parallel plates in the tapered waveguide. This new expression shows that, by strongly increasing the index of refraction of the plate with the largest area, the value of the thrust can be strongly increased. "
http://www.frandeaquino.org/Shawyer%20Thruster.pdf

There is essentially a news blackout on the experimental side from NASA.
The problem is, if this drive really works, the defence implications are huge. Those in charge might feel it would not necessarily be a good idea to go public with it  especially from the US perspective. Remember that 'Sputnik moment'?
@wembley, do you have any specific info about why you think there is a news blackout?
Also, do you have any further verifiable information from this post: http://forum.nasaspaceflight.com/index.php?topic=29276.msg1265607#msg1265607 stating Shawyer stopped using a dielectric section?
[/quote]
I been in contact with NASA on this and the lack of direct response has been marked. They will talk about the warp drive and other work, but will not even mention the EmDrive in their replies. It's as though they cannot speak its name...I also have it from other sources that NASA have requested that they do not discuss NASA's work in this area. If you can find any official NASA public comment on anything related to their EmDrive work I will be impressed! It does look like a blackout to me.
The info about Shawyer not using dielectric section was in an email from the man himself.
[/quote]
Interesting to hear.
What happens if another country wheels a drive out, haven't others been working in this area?

...
TM111 gives me 1.03 GHz ditto for TE011
If, were one to use the diameter instead of the radius in the frequency equation one would obain:
You are exactly right, I've been (inadvertantly) calculating w/ DIAMETERS !
I've got to stop using Postit notes !

...
TM111 gives me 1.03 GHz ditto for TE011
If, were one to use the diameter instead of the radius in the frequency equation one would obain:
You are exactly right, I've been (inadvertantly) calculating w/ DIAMETERS !
I've got to stop using Postit notes !
"The man with insight enough to admit his mistakes comes nearest to perfection."
Johann Wolfgang von Goethe
Keep doing what you have been doing, as it is only thanks to you that we have a thrust equation incorporating the mode shape, and thus thanks to you that we are (only now) able to investigate optimum mode shapes and therefore have greater insight into what is going on ! :)
I plan today to run the calculations again using the volumetric mean instead of the geometric mean (I expect little difference, but just to confirm). Next I plan to calculate mode shapes for the Shawyer experiments (as nobody has ever discussed the mode shapes involved in Shawyer's experiments).

Great ! In my 2 minutes at a time I'm off to figure out why df/c = the momentum, but in the accelerated frame of reference.
Added: http://scitechdaily.com/wayselfpropelsubatomicparticleswithoutexternalforces/
"We find these shapepreserving Dirac wavefunctions to be part of a family of accelerating quantum particles, which includes massive/massless fermions/bosons of any spin."

...
Added: http://scitechdaily.com/wayselfpropelsubatomicparticleswithoutexternalforces/
Interesting work by MIT PostDoc !
It turns out that this selfacceleration does not actually violate any physical laws — such as the conservation of momentum — because at the same time the particle is accelerating, it is also spreading out spatially in the opposite direction.
“The electron’s wave packet is not just accelerating, it’s also expanding,” Kaminer says, “so there is some part of it that compensates. It’s referred to as the tail of the wave packet, and it will go backward, so the total momentum will be conserved. There is another part of the wave packet that is paying the price for the main part’s acceleration.”
It turns out, according to further analysis, that this selfacceleration produces effects that are associated with relativity theory: It is a variation on the dilation of time and contraction of space, effects predicted by Albert Einstein to take place when objects move close to the speed of light. An example of this is Einstein’s famous twin paradox, in which a twin who travels at high speed in a rocket ages more slowly than another twin who remains on Earth.

I been in contact with NASA on this and the lack of direct response has been marked. They will talk about the warp drive and other work, but will not even mention the EmDrive in their replies. It's as though they cannot speak its name...I also have it from other sources that NASA have requested that they do not discuss NASA's work in this area. If you can find any official NASA public comment on anything related to their EmDrive work I will be impressed! It does look like a blackout to me.
If NASA really decides to go silent on this, that would be a strong indication that the effect is not only real, but imminently useful. For those in the administration that might feel going silent is the optimal approach, I would suggest to them otherwise. Attempting to impede and to cover such information in the age of the Internet is futile. Though it may slow the efforts within the U.S. to reproduce and harness the effect, this is a multinational effort, and the advancement and evolution of our species will continue in its progression despite such efforts. To any and all leaders within NASA or other governmental organizations whose first reaction is to suppress, please consider that such an approach is very 20th century.

1) I have rerun the calculations using the Volumetric Mean instead of the Geometric Mean. Please compare the results shown below using the Volumetric Mean with the GeometricMean results previously shown in post http://forum.nasaspaceflight.com/index.php?topic=36313.msg1319117#msg1319117 .
2) We define the Volumetric Mean as follows:
VolumetricMeanDiameter=Sqrt[(aeroSmallDiameter^2+aeroSmallDiameter*aeroBigDiameter+aeroBigDiameter^2)/3]
DERIVATION OF VOLUMETRIC MEAN
Defining the following symbols for the radii of the truncated cone (frustum of a cone):
r=smallRadius=smallDiameter/2
R=bigRadius=bigDiameter/2
The volume of a truncated cone and the volume of a cylinder are:
Volume of the frustum of a cone =Height*Pi*(r^2+r*R+R^2)/3
Volume of a cylinder= Pi*(EquivalentR^2)*Height
Equating these volumes one arrives at an expression for the Equivalent Radius of a cylinder having the same volume as the volume of the frustum of a cone:
Volume of a cylinder = Volume of the frustum of a cone
Pi*(EquivalentR^2)*Height = Height*Pi*(r^2+r*R+R^2)/3
hence
VolumetricMeanRadius = EquivalentR
= Sqrt[(r^2+r*R+R^2)/3]
= Sqrt[(smallDiameter^2+smallDiameter*bigDiameter+bigDiameter^2)/12]
or,
VolumetricMeanDiameter=Sqrt[(aeroSmallDiameter^2+aeroSmallDiameter*aeroBigDiameter+aeroBigDiameter^2)/3]
3) Let's define as "Aero geometry" the following definition for the NASA Brady et. al. cavity:
Aero Best estimate as of 11/9/2014 http://forum.nasaspaceflight.com/index.php?topic=29276.msg1285896#msg1285896
cavityLength = 0.24173 m
bigDiameter = 0.27246 m
smallDiameter = 0.15875 m
then
aeroGeometricMeanDiameter=Sqrt[aeroBigDiameter*aeroSmallDiameter]
= 0.207974 meter
aeroMeanDiameter =(aeroBigDiameter+aeroSmallDiameter)/2
= 0.215605 meter
aeroVolumetricMeanDiameter=Sqrt[(aeroSmallDiameter^2+aeroSmallDiameter*aeroBigDiameter+aeroBigDiameter^2)/3]
= 0.218089 meter
4) Let's define as "Fornaro geometry" the following definition for the NASA Brady et. al. cavity:
Fornaro estimate http://forum.nasaspaceflight.com/index.php?topic=36313.msg1302455#msg1302455
cavityLength = 0.332 m
bigDiameter = 0.397 m
smallDiameter = 0.244 m
then
fornaroGeometricMeanDiameter=Sqrt[fornaroBigDiameter*fornaroSmallDiameter]
= 0.311236 meter
fornaroMeanDiameter =(fornaroBigDiameter+fornaroSmallDiameter)/2
= 0.3205 meter
fornaroVolumetricMeanDiameter=Sqrt[(fornaroSmallDiameter^2+fornaroSmallDiameter*fornaroBigDiameter+fornaroBigDiameter^2)/3]
= 0.323529 meter
5) Given the experimentally reported frequencies, the geometrical dimensions and the value of speed of light in air, one can invert the frequency equation (see: http://en.wikipedia.org/wiki/Microwave_cavity#Cylindrical_cavity ) to obtain X_{m},_{n} and X'_{m} values as a function of constants and the longitudinal mode shape number "p". Let's define the error difference between these X_{m},_{n} and X'_{m},_{n} values and actual X_{m},_{n} and X'_{m} values as:
error= (value of X_{m},_{n} or X'_{m},_{n} obtained from frequency eqn.)/ (correct value of X_{m},_{n} or X'_{m},_{n} ) 1
where X_{m},_{n} is used for TM modes and X'_{m},_{n} is used for TE modes.
6) Then I obtain the following mode shapes and associated errors:
BRADY "A"
Fornaro Geometry
Best result: TM311 error=  0.146%
2nd best: TM014 error=  3.00%
Aero Geometry
Best result: TE311 error=  0.427%
2nd best: TE212 error= + 3.05%
BRADY "B"
Fornaro Geometry
Best result: TM311 error= + 0.0780%
2nd best: TM014 error=  1.389%
Aero Geometry
Best result: TE311 error=  0.192%
2nd best: TE310 error= + 5.35%
BRADY "C"
Fornaro Geometry
Best result: TM310 error=  0.0781%
2nd best: TM012 error= + 1.303%
Aero Geometry
Best result: TE310 error= + 2.292%
2nd best: TE311 error=  3.43%
TE011 or TM111 error= + 5.88%
CONCLUSIONS
1) At the frequencies tested by Brady et.al. , what modeshape corresponds to a given frequency is very sensitive to the exact geometrical dimensions of the cavity. The reason for this is that there are many natural frequencies very close to each other, each of these frequencies having different mode shapes. Therefore, the abovegiven Fornaro and Aero guesses of the dimensions of the Brady et.al cavity give very different mode shapes for a given frequency.
2) Using the Volumetric Mean, all cases run by Brady et.al, for the Fornaro dimensions correspond to transverse magnetic (TM) mode shapes, all cases run by Brady et.al, for the Aero dimensions correspond to transverse electric (TE) mode shapes:
Fornaro dimensions > Transverse Magnetic mode shapes : the magnetic field is in the circumferential direction
Aero dimensions > Transverse Electric mode shapes: the electric field is in the circumferential direction
EDIT: Actually, using the Aero dimensions, all cases run by Brady et.al, correspond to transverse electric (TE) mode shapes, using either the Geometric Mean or the Volumetric Mean to estimate the equivalent cylindrical diameter. I think that the TE mode shapes are the one that should provide thrust because it is only the TE mode shapes that have the magnetic field directed along the longitudinal direction of the EM Drive. Physically, an axial magnetic field may result in a measured thrust either 1) as an artifact, because the magnetic field can heat the flat ends of the truncated cone and hence produce thermal buckling or 2) as a real means of propulsion, by the magnetic field coupling with the Quantum Vacuum, for example.
3) Using the Volumetric Mean, the field mode shapes for the Fornaro dimensions are similar to the field for the Aero dimensions: mode 311 for Brady cases "a" and "b"" and mode 310 for Brady case "c". The difference between them is that for the Fornaro dimensions the circumferential field is magnetic while for the Aero dimensions the circumferential field is electric. Furthermore, one can state that the field mode shapes in the circumferential cross section for the Fornaro dimensions are similar to the field for the Aero dimensions for ALL Brady cases: they are all 31. The difference between them is
Brady cases "a" and "b'' > one halfwave in the longitudinal direction
Mode 311 > 3 fullwave patterns around the circumference
1 halfwave pattern across the diameter
1 halfwave pattern along the longitudinal length
______________________________________________
Brady case "c'' > constant in the longitudinal direction
Mode 310 > 3 fullwave patterns around the circumference
1 halfwave pattern across the diameter
constant along the longitudinal length
4) Using the volumetric mean in all cases, the errors are smaller using the Fornaro estimate of geometry, while using the geometric mean in all cases, the errors are smaller using the Aero estimate of geometry. Conclusion: this may be fortuitous and it may not be something to discriminate between the two estimates of geometry.
5) Using the volumetric mean leads to more stable values of mode shape with variation in frequency than when using the geometric mean: it gives mode shape 31 for all Brady cases.
6) The most important conclusion: this exercise has made me appreciate the true role and value of the dielectric polymer, and why NASA reported it was so important. It is evident that at these frequencies there are so many mode shapes bunched next to each other that:
it would be extremely difficult to predict what mode shape one will get with a given geometry at these frequencies, because small variations in geometry lead to large changes in mode shape. Certainly it would be impossible to predict the mode shape of an empty cavity with the coarse finite element model used by NASA Brady et.al.
(There are no Bessel functions in a finite element model: the solution is approximated with low power piecewise polynomials in each finite element. The finite element solution is a Galerkin solution "in an integral sense" and not an exact partial differential solution "point to point through the domain".)
Hence the function of the dielectric polymer is to force the cavity to function into a preferred mode shape.
For NASA Brady et.al. they used a doughnutshaped dielectric polymer to try to force the cavity to operate in TE01 mode shape (constant electric field in the circumferential direction). The calculations show that Brady experiment"c" was the closest to be such a mode shape while experiments "a" and "c" were much further apart. Hence experiment "c" resulted in a much larger thrust per PowerInput with the dielectric polymer having a constant electric field in the circumferential direction and the rest of the cavity having a constant electric field in the circumferential direction with a half wave amplitude in the longitudinal direction, resulting in a mode TE012. The polymer dielectric will produce an extra longitudinal half wave in the dielectric polymer, resulting in two half waves in the longitudinal direction of the whole cavity: 1) one half wave within the doughnutshaped polymer dielectric itself, along the thickness of the doughnut and 2) the other half wave within the longitudinal direction of the rest of the empty cavity that has no dielectric polymer.
7) So, an optimal design of an EM Drive would proceed as follows: first decide what mode shape provides the largest thrust per power Input. Then design a dielectric polymer shape that would best force this mode shape. Then model the geometry of the cavity such that the rest of the cavity is also in the same crosssectional mode shape (to amplify the resonance) and accurately model at what frequency this occurs.

If NASA really decides to go silent on this, that would be a strong indication that the effect is not only real, but imminently useful. For those in the administration that might feel going silent is the optimal approach, I would suggest to them otherwise. Attempting to impede and to cover such information in the age of the Internet is futile. Though it may slow the efforts within the U.S. to reproduce and harness the effect, this is a multinational effort, and the advancement and evolution of our species will continue in its progression despite such efforts. To any and all leaders within NASA or other governmental organizations whose first reaction is to suppress, please consider that such an approach is very 20th century.
Thinking about potential historic parallels, they ought to be seriously considering to avoid another Sputnik moment.
It is possible they would want to use it in military projects in the short term (endless autonomy/repositioning satellites would revolutionize spy sats and antisat warfare).
But there is the Chinese interest in it too. If they verified it works, they could be already working in military applications, and probably on a few civil ones. Unlimited range space probes would be a very good publicity stunt for them, for proving their technical superiority.

If NASA really decides to go silent on this, that would be a strong indication that the effect is not only real, but imminently useful. For those in the administration that might feel going silent is the optimal approach, I would suggest to them otherwise. Attempting to impede and to cover such information in the age of the Internet is futile. Though it may slow the efforts within the U.S. to reproduce and harness the effect, this is a multinational effort, and the advancement and evolution of our species will continue in its progression despite such efforts. To any and all leaders within NASA or other governmental organizations whose first reaction is to suppress, please consider that such an approach is very 20th century.
Thinking about potential historic parallels, they ought to be seriously considering to avoid another Sputnik moment.
It is possible they would want to use it in military projects in the short term (endless autonomy/repositioning satellites would revolutionize spy sats and antisat warfare).
But there is the Chinese interest in it too. If they verified it works, they could be already working in military applications, and probably on a few civil ones. Unlimited range space probes would be a very good publicity stunt for them, for proving their technical superiority.
A case perhaps of shutting the stable door after the horse has bolted.

Would you say it's a case of shutting the stable door after the horse has bolted?
It probably is, but I don't think it would be an attempt at censorship by making all information about this a secret. That horse already left the stable, as you say.
In all probability (if they already know this exists and works outside of the public peer review process) they are trying to prevent the spread of sensitive "next step" information, allowing potential enemy powers to quickly develop the same technology, just by reading the same public reports we on the Internet do.
It's not the first time I have read people pleading for keeping the reports about Qthruster technology a secret, because in case of being true, they would certainly be matters of national security.

Would you say it's a case of shutting the stable door after the horse has bolted?
It probably is, but I don't think it would be an attempt at censorship by making all information about this a secret. That horse already left the stable, as you say.
In all probability (if they already know this exists and works outside of the public peer review process) they are trying to prevent the spread of sensitive "next step" information, allowing potential enemy powers to quickly develop the same technology, just by reading the same public reports we on the Internet do.
It's not the first time I have read people pleading for keeping the reports about Qthruster technology a secret, because in case of being true, they would certainly be matters of national security.
So does that mean we shouldn't except to hear anything more from the US on this & if that's the case what does that mean for civil applications?

Great ! In my 2 minutes at a time I'm off to figure out why df/c = the momentum, but in the accelerated frame of reference.
Added: http://scitechdaily.com/wayselfpropelsubatomicparticleswithoutexternalforces/
"We find these shapepreserving Dirac wavefunctions to be part of a family of accelerating quantum particles, which includes massive/massless fermions/bosons of any spin."
Yeah that article on Physorg http://phys.org/news/201501analysisselfpropelsubatomicparticles.html made me do this (see below), because it is relevant to what we're exploring here and what a surprising result! Also Marin Soljačić is the professor cited in the evanescent wave explorations from thread 1.
This thread is exploding! once again thanks especially to @Notsosureofit and @Rodal. I really think a milestone happened here over the last couple of days. I wish I could bring the bacon like those two have but I'm kinda stuck in a rutt on figuring out this QV deal.
It turns out that this selfacceleration does not actually violate any physical laws — such as the conservation of momentum — because at the same time the particle is accelerating, it is also spreading out spatially in the opposite direction.
“The electron’s wave packet is not just accelerating, it’s also expanding,” Kaminer says, “so there is some part of it that compensates. It’s referred to as the tail of the wave packet, and it will go backward, so the total momentum will be conserved. There is another part of the wave packet that is paying the price for the main part’s acceleration.”
It turns out, according to further analysis, that this selfacceleration produces effects that are associated with relativity theory: It is a variation on the dilation of time and contraction of space, effects predicted by Albert Einstein to take place when objects move close to the speed of light. An example of this is Einstein’s famous twin paradox, in which a twin who travels at high speed in a rocket ages more slowly than another twin who remains on Earth.
The above quote (it popped out to me too) and what it means, could actually drop the QV model by changing the way we think about how to conserve momentum. It also sounds eerily like dispersion too.
(https://artgalleryfor.us/music/wpcontent/uploads/2014/06/throwpapersmeme150x150.jpg)
Break: I've seen anecdotal evidence that using the math for a resonant cylinder is "close enough" for a conical frustum. I can find references again if you wish where I found this. But I'm not so sure if this is a good approximation. Anyone know anything about cylindrical coordinate systems? I just started trying to figure this out.
zenin? http://forum.nasaspaceflight.com/index.php?topic=29276.msg1275592#msg1275592

So does that mean we shouldn't except to hear anything more from the US on this & if that's the case what does that mean for civil applications?
I don't believe they can prevent any public disclosure of undeniably working prototypes by the Chinese, in a few years (or months). So they probably are just buying some time for having a working version on our side by then.
That or someone on NASA became aware of the potential huge embarrassment this represents, and told all the guys off and ordered them to pretend it never happened.
But as H. White et al seem to be still working at NASA, I somewhat doubt it's a case of disowning a blunder. Or at least, I hope so.

if you talking about a electron's self energy...
isn't it infinite? So science has sort of looked the other way and declared it a SEP (Hitchhiker's Guide reference meaning someone else's problem) while they got on with the bits of the math that doesn't make them uncomfortable?
http://en.wikipedia.org/wiki/Somebody_Else%27s_Problem
Speaking of physorg... you know there is doozy of an article in there today... :D (the galaxy may be a wormhole)

There is essentially a news blackout on the experimental side from NASA.
The problem is, if this drive really works, the defence implications are huge. Those in charge might feel it would not necessarily be a good idea to go public with it  especially from the US perspective. Remember that 'Sputnik moment'?
@wembley, do you have any specific info about why you think there is a news blackout?
Also, do you have any further verifiable information from this post: http://forum.nasaspaceflight.com/index.php?topic=29276.msg1265607#msg1265607 stating Shawyer stopped using a dielectric section?
I been in contact with NASA on this and the lack of direct response has been marked. They will talk about the warp drive and other work, but will not even mention the EmDrive in their replies. It's as though they cannot speak its name...I also have it from other sources that NASA have requested that they do not discuss NASA's work in this area. If you can find any official NASA public comment on anything related to their EmDrive work I will be impressed! It does look like a blackout to me.
The info about Shawyer not using dielectric section was in an email from the man himself.
Interesting to hear.
What happens if another country wheels a drive out, haven't others been working in this area?
It means an arms race, with the benefit being new tech making its way into the private sector eventually, as it usually does. I think our academic institutions and Nasa are being careful, either confirming a breakthrough or squashing a blunder.
....fixing all those quotes was a mess, did I screw them up?

So does that mean we shouldn't except to hear anything more from the US on this & if that's the case what does that mean for civil applications?
I don't believe they can prevent any public disclosure of undeniably working prototypes by the Chinese, in a few years (or months). So they probably are just buying some time for having a working version on our side by then.
That or someone on NASA became aware of the potential huge embarrassment this represents, and told all the guys off and ordered them to pretend it never happened.
But as H. White et al seem to be still working at NASA, I somewhat doubt it's a case of disowning a blunder. Or at least, I hope so.
It could be that the decision, assuming it does work, on what to say and what not to say has gone right the way up the chain of command literally to the very top and in the meantime the blackout is put in place.
This might sound odd but perhaps it's for the best that for now this stays outside of the mainstream of public awareness.

So does that mean we shouldn't except to hear anything more from the US on this & if that's the case what does that mean for civil applications?
I don't believe they can prevent any public disclosure of undeniably working prototypes by the Chinese, in a few years (or months). So they probably are just buying some time for having a working version on our side by then.
That or someone on NASA became aware of the potential huge embarrassment this represents, and told all the guys off and ordered them to pretend it never happened.
But as H. White et al seem to be still working at NASA, I somewhat doubt it's a case of disowning a blunder. Or at least, I hope so.
Yep you nailed it....... This is TOO public so the truth will have to come and come soon. This isn't your typical flash in the pan news story. The potential worth of this kind of discovery is priceless, on the order of Newton and Einstein. Or just a big series of unfortunate mistakes.

So does that mean we shouldn't except to hear anything more from the US on this & if that's the case what does that mean for civil applications?
I don't believe they can prevent any public disclosure of undeniably working prototypes by the Chinese, in a few years (or months). So they probably are just buying some time for having a working version on our side by then.
That or someone on NASA became aware of the potential huge embarrassment this represents, and told all the guys off and ordered them to pretend it never happened.
But as H. White et al seem to be still working at NASA, I somewhat doubt it's a case of disowning a blunder. Or at least, I hope so.
It could be that the decision, assuming it does work, on what to say and what not to say has gone right the way up the chain of command literally to the very top and in the meantime the blackout is put in place.
This might sound odd but perhaps it's for the best that for now this stays outside of the mainstream of public awareness.
only if this thing can go hyper velocity or relativistic velocity in a flight profile that makes it useful as a weapon of mass destruction. so far the most optimistic projection by Dr White would make it have to fly for over twelve days and then turn around and come back to make it into a WMD. that's not really a realistic flight profile for a sneak attack weapon.

It could be that the decision, assuming it does work, on what to say and what not to say has gone right the way up the chain of command literally to the very top and in the meantime the blackout is put in place.
This might sound odd but perhaps it's for the best that for now this stays outside of the mainstream of public awareness.
Assuming there really is a blackout from NASA (not convinced of that yet), your scenario seems plausible. The problem is, opaque governments are becoming a thing of the past. The Internet, and its communities, are pressuring governments to be more open and transparent. Secrecy, even in the name of national security, can sometimes backfire, particularly when certain technologies have the capability of lifting people of the world out of poverty. In other words, withholding technological progress in the civilian space can result in a moral failure.

So does that mean we shouldn't except to hear anything more from the US on this & if that's the case what does that mean for civil applications?
I don't believe they can prevent any public disclosure of undeniably working prototypes by the Chinese, in a few years (or months). So they probably are just buying some time for having a working version on our side by then.
That or someone on NASA became aware of the potential huge embarrassment this represents, and told all the guys off and ordered them to pretend it never happened.
But as H. White et al seem to be still working at NASA, I somewhat doubt it's a case of disowning a blunder. Or at least, I hope so.
It could be that the decision, assuming it does work, on what to say and what not to say has gone right the way up the chain of command literally to the very top and in the meantime the blackout is put in place.
This might sound odd but perhaps it's for the best that for now this stays outside of the mainstream of public awareness.
only if this thing can go hyper velocity or relativistic velocity in a flight profile that makes it useful as a weapon of mass destruction. so far the most optimistic projection by Dr White would make it have to fly for over twelve days and then turn around and come back to make it into a WMD. that's not really a realistic flight profile for a sneak attack weapon.
Well, if it works, then parking a second strike kinetic weapon package at earthsun L4/L5 is feasible (hell, earthmoon L2 would make the package immune from terrestrial laser attack). This IS the US military we're talking about, who dreamed up Project Horizon to bomb the earth from a moonbase, and that was with a 3 day lag using chemical propulsion. Added fun is using an expendable electrodynamic tether as a power source as you approach earth, since you only need high relative speed at impact (drop into a counterorbit).
Actually, I wonder how applicable that would be, using an ED tether as a power source for orbital capture ops, as a possible alternative to aerocapture...

Well, if it works, then parking a second strike kinetic weapon package at earthsun L4/L5 is feasible (hell, earthmoon L2 would make the package immune from terrestrial laser attack). This IS the US military we're talking about, who dreamed up Project Horizon to bomb the earth from a moonbase, and that was with a 3 day lag using chemical propulsion. Added fun is using an expendable electrodynamic tether as a power source as you approach earth, since you only need high relative speed at impact (drop into a counterorbit).
Actually, I wonder how applicable that would be, using an ED tether as a power source for orbital capture ops, as a possible alternative to aerocapture...
You know, despite the well meaning attempts to place this within the known laws of physics, and telling us this works and respects conservation of momentum (and energy), I'm still not convinced how that could be. Rockets respect conservation of momentum and energy by losing mass (and thus energy) in greater amounts than they gain by expelling that mass. These things don't have any clear way to remember how much energy they have spent, and what relative maximum velocity they can reach in order to not be "overunity". No wonder they face very strong skepticism.
But leaving that part out. Even assuming they are limited in speed, they still seem capable of gathering a fair bit of kinetic energy (tens of kms per second as per a previous post).
Thus the geopolitical impact of this technology being real is evident if you think about it a little.
In the short term, endless autonomy in terms of thrust and repositioning would completely change the rules of engagement for spy satellites and antisatellite weapons. You can have limitless observation capabilities and limitless loitering, following, attacking (and dodging) capabilities too. War bots in orbit could finally fulfill Ronald Reagan's dreams for war in space. And not just that.
Even very slight accelerations (as reported by Brady, White et al) with preposterously limited top speeds, they can serve for pushing and placing dormant kinetic bombs far away from Earth, beyond the reach of any feasible enemy's detection or attack; and they would also serve for bringing them back to Earth at their maker's command, for landing at any desired spot, producing nearly any desired amount of damage.
While all of us sit here on Earth, sharing the same biosphere and the same rock under our feet, the development and availability of that weaponry would result in an aggravated and somewhat madder version of MAD. Because even if you could be attacked in secret from any direction, you can very well threaten to respond by attacking all your potential enemies with nuclear or kinetic nastiness, ruining the game and the fun for all your potential attackers.
But if you have parties/adversaries living in space, could you threaten to crack all the planets in the Solar System?, or all the artificial habitats floating in the space between?
Removing the speed limitations (thus conservation of energy) only makes things worse, making it feasible to have interstellar adversaries sending relativistic missiles to you. Those have no way to be stopped and even less, any way to provide adequate or proportionate response (you and all around you sharing the same planet would simply be dead).

Thus the geopolitical impact of this technology being real is evident if you think about it a little.
In the short term, endless autonomy in terms of thrust and repositioning would completely change the rules of engagement for spy satellites and antisatellite weapons. You can have limitless observation capabilities and limitless loitering, following, attacking (and dodging) capabilities too. War bots in orbit could finally fulfill Ronald Reagan's dreams for war in space. And not just that.
Even very slight accelerations (as reported by Brady, White et al) with preposterously limited top speeds, they can serve for pushing and placing dormant kinetic bombs far away from Earth, beyond the reach of any feasible enemy's detection or attack; and they would also serve for bringing them back to Earth at their maker's command, for landing at any desired spot, producing nearly any desired amount of damage.
While all of us sit here on Earth, sharing the same biosphere and the same rock under our feet, the development and availability of that weaponry would result in an aggravated and somewhat madder version of MAD. Because even if you could be attacked in secret from any direction, you can very well threaten to respond by attacking all your potential enemies with nuclear or kinetic nastiness, ruining the game and the fun for all your potential attackers.
But if you have parties/adversaries living in space, could you threaten to crack all the planets in the Solar System?, or all the artificial habitats floating in the space between?
Removing the speed limitations (thus conservation of energy) only makes things worse, making it feasible to have interstellar adversaries sending relativistic missiles to you. Those have no way to be stopped and even less, any way to provide adequate or proportionate response (you and all around you sharing the same planet would simply be dead).
I agree that the geopolitical impact of this technology being real is evident. Consider, however, that the geopolitical impact might be far more positive than supposed. If asteroids can be mined economically using this technology, can you imagine the impact? Mining on Earth could therefore be reduced, thereby reducing negative impacts on Earth's ecosystem.
If sufficient lift can be achieved, freights and shipping become far more economical such that providing goods to the poorest of the world to meet the basic necessities of life all of the sudden becomes quite feasible.
Wars and poverty often go handinhand. If you can uplift and help a society become more selfsufficient and civilized, the trajectory toward war diminishes. Even if this technology (assuming it works) is used for defense or purposes of war, the mutually assured destruction principal would apply equally well here as it would with other dual purpose technologies.

So does that mean we shouldn't except to hear anything more from the US on this & if that's the case what does that mean for civil applications?
I don't believe they can prevent any public disclosure of undeniably working prototypes by the Chinese, in a few years (or months). So they probably are just buying some time for having a working version on our side by then.
The Chinese will not go public. They have had a fairly tight clampdown for a couple of years now, with the only evidence being odd scientific papers. They don't want anyone else getting a lead on them either.

...Rockets respect conservation of momentum and energy by losing mass (and thus energy) in greater amounts than they gain by expelling that mass. These things don't have any clear way to remember how much energy they have spent, and what relative maximum velocity they can reach in order to not be "overunity"....
Just like one needs to take into account the energy/momentum of ejected mass from a classical rocket (or injected into and ejected from a turbojet), also for an EM Drive the energy and momentum of the total open system has to be taken into account to reach any conclusions on velocity limitations:
*for Dr.McCulloch's EM Drive theory, the energy/momentum of the radiated Unruh radiation has to be taken into account. According to Dr. McCulloch's theory, there is Unruh radiation being emitted from the EM Drive, that Unruh radiation has energy/momentum, and it is responsible for conservation of momentum.
*for EM Drive theories advocating interaction with the Quantum Vacuum (Dr. White's or the theories considered by @Mulletron) the energy/momentum of the involved Quantum Vacuum has to be taken into account. An example would be given by Dr.White's analogy of the propeller in a submarine: the energy/momentum of the water propelled by the propeller has to be taken into account.
*ditto for EM Drive theories advocating coupling between electromagnetism and gravitational forces, or theories advocating coupling with Dark Matter, or any other theories explaining conservation of momentum of the EM Drive: the energy/momentum of the coupled field also needs to be taken into account
Thus my conclusion is that Joosten and White's "paradox" analysis for the EM Drive (Appendix A of "Human Outer Solar System Exploration via QThruster Technology" by B. Kent Joosten and Harold G. “Sonny” White, http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/20140013174.pdf ) is incorrect/incomplete because they failed to take into account the energy/momentum of the involved Quantum Vacuum (which they advocate as the reason for conservation of momentum yet they fail to take into account when they perform the kinetic energy constraint). Actually Dr. White in the same article shows how a classical ion rocket suffers the same "paradox" if one fails to take into account the energy/momentum of the ejected propellant.
No, the EM Drives do NOT need to remember how much energy they have spent, and what relative maximum velocity they can reach in order to not be "overunity", that "memory" would be a requirement only if one disregards conservation of momentum, which none of us is prepared to do, because it violates a basic law of physics.
If the EM drive conserves momentum, for example, by interacting with the QuantumVacuum, we have an open system where momentum will be flowing in or out of the cavity, and therefore the open system should be taken into account in the conservation of energy in order to arrive at a satisfactory answer concerning any velocity limitation.
(http://history.nasa.gov/SP4404/p275.jpg)
(http://upload.wikimedia.org/wikipedia/commons/6/66/Cavitatingprop.jpg)

So does that mean we shouldn't except to hear anything more from the US on this & if that's the case what does that mean for civil applications?
I don't believe they can prevent any public disclosure of undeniably working prototypes by the Chinese, in a few years (or months). So they probably are just buying some time for having a working version on our side by then.
The Chinese will not go public. They have had a fairly tight clampdown for a couple of years now, with the only evidence being odd scientific papers. They don't want anyone else getting a lead on them either.
Sounding like a game of Texas Hold' em between them and the U.S. Wonder if there are any other players of substance in this game?

Really hoping that discussing such subjective political prospects and other implications of an as yet very theoretical space propulsion technology, is not going to get this thread locked for good..

Really hoping that discussing such subjective political prospects and other implications of an as yet very theoretical space propulsion technology, is not going to get this thread locked for good..
1) As explained here http://forum.nasaspaceflight.com/index.php?topic=29276.msg1301657#msg1301657, the previous long thread (which due to its extreme length would have been eventually locked to start a new thread anyway) was locked because of personal attacks and "stupid" and "pointless" posts "that did not feel like this site's subject matter." Specifically, posts (sometimes involving ad hominem attacks) dealing with MachEffect Piezoelectric experiments and theory (which already had dedicated threads to deal specifically with that topic) instead of the thread's subject: (Microwave ) EM Drive developments.
2) Political ramifications of space flight applications (for example NASA's rocket developments, SpaceX developments, or Advanced Concepts like Vasimir development or Fusion Power technology) are routinely discussed in many threads of NASA's SpaceFlight Forum, why shouldn't political ramifications of (Microwave) EM Drive space flight applications be discussed as well? (as long of course as they do not contain ad hominem attacks).
3) This EM Drive technology has now been repeatedly tested (experimentally ) at NASA in the USA, in the UK and in China. The experimental results of these measurements reportedly produce thrust/PowerInput that are within practical SpaceFlight Applications. Such spaceflight applications have been discussed in several reports by NASA and in this thread. So, assuming that the experimental results at NASA, UK and China are not all artifacts, the subject being discussed here is not just a theory (unlike some threads in the "Advanced Concepts" section of the NASA SpaceFlight Forum that discuss topics that are much further away from SpaceFlight applications).

@Rodal tested in the UK, never knew that?
Who was carrying out those experiments?

@Rodal tested in the UK, never knew that?
Who was carrying out those experiments?
Isn't Shawyer a UK native?

@Rodal tested in the UK, never knew that?
Who was carrying out those experiments?
Satellite Propulsion Research Ltd (SPR Ltd), a UK based company, with partial funding from the UK government for some of their tests. See http://www.emdrive.com/

why shouldn't political ramifications of (Microwave) EM Drive space flight applications be discussed as well?
I don't mind them myself. But I got the possibly mistaken impression (e.g. people actually asking for this to be locked even after thread v.2) that they put the discussion thread too close to or beyond this website's tolerances. My bad.
Seeing such a thorough crunching thru the uncertainties of such an advanced and frankly just plain cool potential technology, IMHO is too excellent to lose. Even if EM Drives all turn out to be nothing, the process of making sense of it as detailed in these two threads is exemplary.

why shouldn't political ramifications of (Microwave) EM Drive space flight applications be discussed as well?
I don't mind them myself. But I got the possibly mistaken impression (e.g. people actually asking for this to be locked even after thread v.2) that they put the discussion thread too close to or beyond this website's tolerances. My bad.
Seeing such a thorough crunching thru the uncertainties of such an advanced and frankly just plain cool potential technology, IMHO is too excellent to lose. Even if EM Drives all turn out to be nothing, the process of making sense of it as detailed in these two threads is exemplary.
Happy to hear that you share our excitement of the potential of propellantless spacepropulsion technology :)

The way you guys systematically work every scenario to its end, leaving no stone unturned is really awesome. Ok, I'll let signal/noise go back to normal now.

@Notsosureofit
This is a little information regarding the effect of the dielectric on resonance frequency in a cylindrical cavity.
Using the Wikipedia equations for resonance of a cylindrical cavity, J'_{1}(1) = 1.8412, and L = c/2.45E9/s, with p = 1, I calculated frequency to be 2.45 GHz when R = 0.0377449 m. I think this is the TE_{1,1,1} mode.
I then modelled this cylindrical cavity in meep, the FDTD software, with a drive frequency of 2.45E9 Hz, electrical. On running the software with the cavity model empty (containing vacuum, no dielectric), Harminv calculated resonance to be 1.85058E+009 GHz. Qfactor was 484476.647518797. I don't know why frequency is not 2.45 GHz but it isn't.
I then inserted a PE dielectric with a constant of 1.76, length of 20% of the cavity length, radius = cavity radius. The dielectric was against one end of the cavity. I ran this in meep and Harminv calculated a resonance frequency of 1.70036E+009 and 3.67196E+009 Hz. Qfactors of 342650.708941864 and 280142.928092836.
Pardon all of the digits. Result is,
Resonate frequency = 1850. MHz, Q = 4.8 E+05 with no dielectric
Resonate frequency = 1700. MHz, Q = 3.4 E+05 with 20 % cavity filled with dielectric, constant 1.76.
And another resonant mode at 3671 MHz, Q = 2.8 E+05.
A corresponding second mode may have existed for the empty cavity. I don't know as I had to extend the frequency band search to find the 1.7 GHz frequency which extended the band upward as well as downward.
In any case, these numbers are one way to look at the effect of the dielectric within the cavity. I did make an effort to change the cavity parameters in order to hold the resonant frequency constant. That's to hard.
I would be curious to know if anyone can explain why the difference between the Wikipedia formula calculation of resonant frequency and the resonant frequency obtained by integrating Maxwell's equations in the time domain then doing Fourier analysis to calculate the resonant frequencies. In a nutshell, meep excites the cavity with Gaussian noise across the search band, waits for the noise to die down, then extracts the 100 strongest frequencies, dropping those for which Q is less than 50. It reports those that remain.

....
I would be curious to know if anyone can explain why the difference between the Wikipedia formula calculation of resonant frequency and the resonant frequency obtained by integrating Maxwell's equations in the time domain then doing Fourier analysis to calculate the resonant frequencies. In a nutshell, meep ...
Meep (an acronym for MIT Electromagnetic Equation Propagation) solves the Maxwell partial differential equations with the old Finite Difference numerical technique (developed decades before the Finite Element Method or the Boundary Element Method and other numerical techniques), albeit with an interesting implementation (and it is free, of course).
Before embarking on a solution of a more complicated geometry (truncated cone) and materials (dielectric inside the cavity) it is always advisable to compare your numerical solution for a problem having an exact solution to see whether your finite difference spatial and time discretization have converged, to examine possible illconditioning of the matrices and to make sure that there are no human errors of input or bugs or theoretical problems with the software. Any numerical solution is always inferior to an exact solution, the only point of a numerical solution is to solve problems for which an exact solution is not possible. Thus you are doing the right thing by testing the solution vs the exact solution for a cylindrical empty (no dielectric) cavity. Your present numerical results are so far from the exact solution for an empty cylindrical cavity that it is not meaningful yet to discuss your solution for a dielectric included until you can show good convergence between your numerical result towards the exact solution for the empty cylindrical cavity (of course, besides discretization convergence problems there is always the possibility that you have made a human error somewhere or that the software has a bug or a theoretical problem).
The starting point of any finite difference solution is the discretization of space and time into a grid. Meep uses the standard Yee grid discretization (see http://abinitio.mit.edu/wiki/index.php/Yee_grid ) (http://abinitio.mit.edu/wiki/images/thumb/6/6f/Yeecube.png/250pxYeecube.png) which staggers the electric and magnetic fields in time and in space, with each field component sampled at different spatial locations, allowing the time and space derivatives to be formulated as centerdifference approximations. Meep further divides the grid into chunks that are joined together into an arbitrary topology via boundary conditions.
To examine the convergence of your solution you should do a convergence study: run different cases with finer spatial grids and smaller time increments (output the frequencies for each spatial and time discretization). The time discretization is very important as it has been known for a long time that the central finite difference time discretization has a stability problem (the time increment needs to be small enough for a good result). This is assuming that one uses the time stepping technique (that I would start with). For a frequencydomain solver you will have to examine convergence of the frequencydomain solver. Also, I assume of course that you are using at least double precision. Examining the convergence should give you an idea of how much finer spatial and time discretization you need in order to arrive to results that match the exact solution. Only once you have been able to accurately match your numerical discretization output with the exact solution for the empty cylindrical cavity you should pursue more complicated geometries containing dielectric materials, problems for which there is no closedform solution.
Godspeed and carry on :)
NOTE: The frequencydomain solver assumes a time dependence of e^(−iωt) for all currents and fields, and solves the resulting linear equations for the steadystate response or eigenmodes. Thus if you eventually want to solve problems with nonlinear dielectric materials or active systems, be forewarned that the frequency domain solver is inadequate for nonlinear materials and for active systems in which frequency is not conserved.
To obtain the frequencydomain response of a cavity with multiple longlived resonant modes, in the time domain, is very challenging for numerical techniques, like Meep. These modes require a long simulation to reach steady state, whereas in the frequency domain the resonances correspond to poles that increase the condition number ( http://en.wikipedia.org/wiki/Condition_number ) and hence slow convergence due to illconditioning of the matrix. (R. Barrett, M. Berry, T. Chan, J. Demmel, J. Donato, J. Dongarra, V. Eijkhout, R. Pozo, C. Romine, H. V. der Vorst, Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods, SIAM, Philadelphia, PA, 1994, http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.83.867&rep=rep1&type=pdf )

Lightly following this thread but you folks are veering into territory I DO actually understand and I felt the need to correct some misconceptions.
Why is there the "assumption" that no matter how much (or little) an operational EMDrive would generate it would be of military/geopolitical value beyond, say, extending the service life of spy, communications, etc satellites? That it provides for greatly enhanced (or even practical) kinetic bombardment weapons? That it has some sort of huge military purpose that will ignite an arms race?
Really? No. Only if it has enough thrust to power an aircraft with a reasonable (turbinegenerator) amount of power and is more efficent AND more powerful than current jet or rocket engines. Otherwise its simply a lowthrust station keeping and manuever system with a long service life :)
A thrust of 0.09lb to 0.9lb per KW as noted in the cited paper isn't that great really. Again the main advantge is you don't have to carry propellant/reaction mass. The main "geopolitical" ramification of the EMDrive would be that satellite servicing is going to look a lot LESS attractive since with it you'd (supposedly) never have to fill up maneuvering system every again which was the major driver for that concept. :)
Hidden "RodsFromGods" in deep space ready to rain down on anyone, anywhere and "undetectable" due to the EMDrive? Uh, NO just no.
First of all: There is no "stealth" in space. Period.
http://www.projectrho.com/public_html/rocket/spacewardetect.php
Your rod carrier is going to be spotted and tracked. The EMDrive requires power, which is going to have heat that is going to have to be rejected, which is going to be "visible" to anyone looking in the right direction. The EMDrive itself (according to one post above) "emits" radiation which can be detected with the right sensor set up. And lastly you CAN see objects in space if you look carefully enough. Even if you used solar panels to provide the power for the EMDrive they are going to "reflect" some of the energy they recieve AND they are going to be sources of waste heat for the energy they absorb but do not use.
I wonder if anyone has pointed out that IF this "works" the way it would seem to what they've invented is basically the "Space:1889" Ether Propeller :)
Randy

http://en.wikipedia.org/wiki/Space:_1889
(http://upload.wikimedia.org/wikipedia/en/thumb/a/af/Space1889rpg.jpg/250pxSpace1889rpg.jpg)

Lightly following this thread but you folks are veering into territory I DO actually understand and I felt the need to correct some misconceptions.
Why is there the "assumption" that no matter how much (or little) an operational EMDrive would generate it would be of military/geopolitical value beyond, say, extending the service life of spy, communications, etc satellites? That it provides for greatly enhanced (or even practical) kinetic bombardment weapons? That it has some sort of huge military purpose that will ignite an arms race?
Really? No. Only if it has enough thrust to power an aircraft with a reasonable (turbinegenerator) amount of power and is more efficent AND more powerful than current jet or rocket engines. Otherwise its simply a lowthrust station keeping and manuever system with a long service life :)
A thrust of 0.09lb to 0.9lb per KW as noted in the cited paper isn't that great really. Again the main advantge is you don't have to carry propellant/reaction mass. The main "geopolitical" ramification of the EMDrive would be that satellite servicing is going to look a lot LESS attractive since with it you'd (supposedly) never have to fill up maneuvering system every again which was the major driver for that concept. :)
Hidden "RodsFromGods" in deep space ready to rain down on anyone, anywhere and "undetectable" due to the EMDrive? Uh, NO just no.
First of all: There is no "stealth" in space. Period.
http://www.projectrho.com/public_html/rocket/spacewardetect.php
Your rod carrier is going to be spotted and tracked. The EMDrive requires power, which is going to have heat that is going to have to be rejected, which is going to be "visible" to anyone looking in the right direction. The EMDrive itself (according to one post above) "emits" radiation which can be detected with the right sensor set up. And lastly you CAN see objects in space if you look carefully enough. Even if you used solar panels to provide the power for the EMDrive they are going to "reflect" some of the energy they recieve AND they are going to be sources of waste heat for the energy they absorb but do not use.
I wonder if anyone has pointed out that IF this "works" the way it would seem to what they've invented is basically the "Space:1889" Ether Propeller :)
Randy
I don't know Randy. All the talk about Dark Energy, Dark Matter and Quantum Vacume are starting to sound a lot like the Aether concept!
I guess everything old is new again.

http://en.wikipedia.org/wiki/Space:_1889
(http://upload.wikimedia.org/wikipedia/en/thumb/a/af/Space1889rpg.jpg/250pxSpace1889rpg.jpg)
But is it the Edison, Zepplin, or Armstrong type? :)
I don't know Randy. All the talk about Dark Energy, Dark Matter and Quantum Vacume are starting to sound a lot like the Aether concept!
I guess everything old is new again.
As I recall SEVERAL people working in quantum mechanics have pointed out that its FAR to easy to "slip" into that description when talking to us "laymen," however it has the dangers of being taken TOO far way to fast as is a problem with most analogies :)
It probably does not help though that I've noted many of those same people tend to have "steampunk" leanings :)
Randy

But is it the Edison, Zepplin, or Armstrong type? :)
(http://ourworlds.topcities.com/space1889/ships/enterpriseside.gif)
(http://ourworlds.topcities.com/space1889/ships/tempestside.gif)
(http://ourworlds.topcities.com/space1889/ships/yorkold.gif)

@Rodel
The first subscript (m) is the azimuthal mode number: it indicates the number of fullwave patterns around the circumference of the waveguide. It is zero for modes in which there is no variation in the circumferential direction.
The second subscript (n) is the radial mode number: it indicates the number of halfwave patterns across the diameter. The radial mode number (n) plus one indicates the number of nodes across the diameter (counting as nodes the end nodes).
The third subscript (p) is the longitudinal mode number. It indicates the number of fullwave patterns along the longitudinal length of the waveguide. It is zero for modes in which there is no variation in the longitudinal direction.
I did double check everything as you advised and there does not seem to be anything wrong with my meep simulation. Neither could I find any questions related to my problem on the Internet. That leads me to think that my problem is still my understanding of mode shapes and cavity dimensions. I thought I had TE1,1, but from the above, for the mode to be TE 1,1, the cavity radius needs to be 1/4 wavelength and the circumference should support 1 full wave pattern. The wavelength for 2.45 GHz is 0.1223642686 in vacuum. So, for the vacuum filled cavity to resonate at 2.45 GHz in the TE 1,1 mode the radius needs to be 0.0305910671 meters. But simply plugging that radius into the formula calculates a resonance frequency of ~2.92GHz in air. So it seems evident that I am still confused about modes and use of the formula to calculate resonance frequencies. Would you lead me through the example of a resonant cavity dimensions for 2.45 GHz resonance?
I also note that driving the cavity from my previous post at 2.45 GHz, R = 0.0377449, there is no sign of resonance in the field images. So the cavity does not resonate at 2.45 GHz and therefore my dimensions must be wrong.

....
I did double check everything as you advised and there does not seem to be anything wrong with my meep simulation.....
Please provide the convergence study you have done, to analyze the convergence rate of your Meep calculation. I can't help you without seeing, and thus being able to analyze, the convergence study data.
....
So the cavity does not resonate at 2.45 GHz and therefore my dimensions must be wrong.
Incorrect dimensioning is one of several kinds of numerical simulation errors possible.

@Rodel 
I am going to explain my understanding of meep in excruciating detail. If you detect a misunderstanding, PLEASE tell me. First, I am setting my simulation in 2D, running in 64bit single precision. To run in double precision would require a recompilation of meep from source code and I am not prepared to do that.
Here is what I have:
Drive frequency 2.45 E+9 Hz, so wavelength = 0.1223642686 meters.
Geometry actual inside dimensions L= 0.1223642686, Dia = 0.0754898000 meters air filled cylindrical cavity with no dielectric. I am ignoring the difference between speed of light in air and vacuum.
Scale factor, 0.01, but is a parameter to adjust
The above gives geometry simulation dimensions in scaled units = 012.23642686, 007.54898000
There is a boundary layer, PML layer around the inside of the computational lattice.
The PML layer thickness is set to 1.
Through an abundance of caution I have set my computational lattice (cell) to twice the geometry dimensions plus twice the PML layer thickness.
Twice the PML layer is correct because there is a layer within on all 4 sides.
Twice the geometry dimensions separates the geometry by onehalf its width/height from the PML layer.
This results in 
Computational cell is 26.8729 x 17.498 x 0 (it is a 2D model)
The geometry model is in the center of the computational cell.
The antenna is located at x = 0. and y offset to the radius of the cylinder, and inward  the length is 0.007 meters, or 0.7 scaled units.
The other significant parameter is Resolution, that is, the density of the pixel grid within each distance unit of the computational cell. If resolution = 1, then there would be about 12 pixels lengthwise and 7.5 pixels crosswise in space within the geometry. That is not actually enough density to resolve the wave pattern across the search bandwidth. The tutorial indicates that meep likes a minimum of 10 pixels per wavelength of the frequency, or the frequency to be detected. It happens that the minimum frequency to be searched for is the drive frequency minus half the search band width. In other words, to detect resonance frequency as low as 1.75 GHz, (wavelength = 0.171309976 meters, 17.13 units). The corresponding highest frequency in the bandwidth is 3.15 GHz. The wavelength at 3.15 GHz ~ .095 meters or 9.5 simulation units. This constrains resolution to be no less than 2. Time descretization is the significant constraint.
Time in meep is normalized to the speed of light, that is, c =1. The meep literature is very confusing on time scaling, but by setting the resolution and simply running the simulation for 1 time unit, meep displays the number of time steps. In this way, I find the the number of time steps = 2 times resolution.
Now, running the simulation, using cylindrical coordinates (effectively a 1D simulation) and setting resolution sequentially to 1, 2, 3, 4 meep gives no results. With resolution = 5, meep does give a result. I made these low resolution runs for the purpose of this convergence study, in reality, I rarely use resolution less than 40. And from the meep tutorial document, " Note: this error is only the uncertainty in the signal
processing"
Here are my results.
Resolution number of time steps resonant frequency Q error
1 2 none detected
2 4 none detected
3 6 none detected
4 8 none detected
5 10 1.84921E+009 negative 2 e4
10 20 1.85128E+009 negative 2 e4
20 40 1.86441E+009 ~ 500 6 e4
40 80 1.87262E+009 ~ 1200 3 e4
80 160 1.86992E+009 ~ 300 13 e4
160 320 1.87042E+009 ~ 80 47 e4
The detected frequency bounces around consistently with the error which can be taken as estimating the number of significant digits of the frequency detected.
The quality is very low. I take that to be a result of the cavity dimensions being incorrect for the resonant frequency detected as they are also incorrect for the drive frequency.
I would seriously like to know how to properly design a resonant cavity for a selected resonant mode. I can tinker with the dimensions in meep and get higher quality factors, but that is not very efficient and forces me to guess the mode by looking at images of the wave pattern.

....
Here are my results.
Resolution number of time steps resonant frequency Q error
1 2 none detected
2 4 none detected
3 6 none detected
4 8 none detected
5 10 1.84921E+009 negative 2 e4
10 20 1.85128E+009 negative 2 e4
20 40 1.86441E+009 ~ 500 6 e4
40 80 1.87262E+009 ~ 1200 3 e4
80 160 1.86992E+009 ~ 300 13 e4
160 320 1.87042E+009 ~ 80 47 e4
The detected frequency bounces around consistently with the error which can be taken as estimating the number of significant digits of the frequency detected.
The quality is very low. I take that to be a result of the cavity dimensions being incorrect for the resonant frequency detected as they are also incorrect for the drive frequency.
....
Well, there is a lot of stuff here for me to digest, I will need some time to read your post very carefully, and consider what to do, but my first impression is that there is a convergence problem that is most evident from the Q:
Resolution number of time steps resonant frequency Q error
1 2 none detected
2 4 none detected
3 6 none detected
4 8 none detected
5 10 1.84921E+009 negative 2 e4
10 20 1.85128E+009 negative 2 e4
20 40 1.86441E+009 ~ 500 6 e4
40 80 1.87262E+009 ~ 1200 3 e4
80 160 1.86992E+009 ~ 300 13 e4
160 320 1.87042E+009 ~ 80 47 e4
Notice how the Q is completely wrong ("negative") even for
10 20 1.85128E+009 negative 2 e4
then reaches a maximum for:
40 80 1.87262E+009 ~ 1200 3 e4
which, as you wrote, it is still a very low value for Q, and then as you increase the time step discretization, the Q gets worse rather than better:
80 160 1.86992E+009 ~ 300 13 e4
160 320 1.87042E+009 ~ 80 47 e4
And notice that the error also increased, as you increased the time step for those two cases.
I don't see how the convergence problem can be due to the geometry. By "geometry" I mean the dimensions of the cavity (in meters or whatever consistent unit of length). The geometry stayed constant (I presume) for the different discretizations. Therefore the wrong geometry can lead to a wrong solution but not to a solution that gets worse (increasing error and decreasing Q) with increased discretization.
I'll be back.

.. I am setting my simulation in 2D, running in 64bit single precision....
Just to be speaking the same language, are you really using 64bit: Double Precision as defined by the IEEE 754 standard ?
64bit: Double Precision see http://en.wikipedia.org/wiki/Doubleprecision_floatingpoint_format
32bit Double Precision: Computers with 32bit storage locations use two memory locations to store a 64bit doubleprecision number (a single storage location can hold a singleprecision number).
32bit: Single Precision see http://en.wikipedia.org/wiki/Singleprecision_floatingpoint_format

.....
The quality is very low. I take that to be a result of the cavity dimensions being incorrect for the resonant frequency detected as they are also incorrect for the drive frequency.
I would seriously like to know how to properly design a resonant cavity for a selected resonant mode. I can tinker with the dimensions in meep and get higher quality factors, but that is not very efficient and forces me to guess the mode by looking at images of the wave pattern.
What did you use for the bandwidth (df) source around the frequency of interest (Drive frequency 2.45 E+9 Hz)?
Could you try running all these cases again, everything the same as before except with a significantly narrower bandwidth (df) source around the frequency of interest ? . Reportedly harminv does a better job the narrower the source is around the frequency of interest .

.....
The quality is very low. I take that to be a result of the cavity dimensions being incorrect for the resonant frequency detected as they are also incorrect for the drive frequency.
I would seriously like to know how to properly design a resonant cavity for a selected resonant mode. I can tinker with the dimensions in meep and get higher quality factors, but that is not very efficient and forces me to guess the mode by looking at images of the wave pattern.
What did you use for the bandwidth source around the frequency of interest (Drive frequency 2.45 E+9 Hz)?
Could you try running all these cases again, everything the same as before except with a significantly narrower bandwidth source around the frequency of interest ? . Reportedly harminv does a better job the narrower the source is around the frequency of interest .
Ok, I did run it again with bandwidth = 0.2 * Drive frequency, for cases up to resolution of 80, but I didn't get anything. Once I narrow the bandwidth to exclude the resonant frequency at 1.87 GHz, there are no resonances within the bandwidth.
Harminv does work better at identifying the resonant frequency with narrower bandwidth, when the frequency is within the bandwidth. I set the drive frequency to 1.873 GHz, narrowed the bandwidth to 0.07 * frequency and got this:
frequency Quality factor error
1,873,339,229.3075 Hz 18,325,307.0778158 1.673972608680621e7+0.0i
As you can see the quality factor is much higher and the processing error is much lower. The only problem is that it is not the frequency I had hoped for.
I did some further searching and found two things.
1  The value of the J'_{0}(1) Bessel function = 1.8411837813 which agrees with the number we have.
2  Meep doesn't actually excite the cavity with Gaussian noise, rather it uses the derivative of a Gaussian signal, whatever that means.
I really don't think this particular problem is in the meep software. As I wrote before, I searched the discussion list, which goes back at least 8 years, and there is no mention of this particular problem. If it were in meep, some user would have encountered it long ago. A 25% discrepancy is hard to overlook. There is a chance that it is in my general understanding of how to model using meep, but my knowledge of meep is far superior to my knowledge of resonant cavity design so using Occam's razor, it is most likely that my cavity design is the problem.
Dr. Rodal, I really appreciate your efforts on my behalf. I will continue to look into the details of resonant cavity design. Maybe it has something to do with the cavity length. But actually, that doesn't seem very likely at all. What do you know about Gaussian noise derivatives and could that be a simple frequency correction? But, when generated with a continuous wave at 2.45 GHz, the field images don't show any resonance.

.....
The quality is very low. I take that to be a result of the cavity dimensions being incorrect for the resonant frequency detected as they are also incorrect for the drive frequency.
I would seriously like to know how to properly design a resonant cavity for a selected resonant mode. I can tinker with the dimensions in meep and get higher quality factors, but that is not very efficient and forces me to guess the mode by looking at images of the wave pattern.
What did you use for the bandwidth source around the frequency of interest (Drive frequency 2.45 E+9 Hz)?
Could you try running all these cases again, everything the same as before except with a significantly narrower bandwidth source around the frequency of interest ? . Reportedly harminv does a better job the narrower the source is around the frequency of interest .
Ok, I did run it again with bandwidth = 0.2 * Drive frequency, for cases up to resolution of 80, but I didn't get anything. Once I narrow the bandwidth to exclude the resonant frequency at 1.87 GHz, there are no resonances within the bandwidth.
Harminv does work better at identifying the resonant frequency with narrower bandwidth, when the frequency is within the bandwidth. I set the drive frequency to 1.873 GHz, narrowed the bandwidth to 0.07 * frequency and got this:
frequency Quality factor error
1,873,339,229.3075 Hz 18,325,307.0778158 1.673972608680621e7+0.0i
As you can see the quality factor is much higher and the processing error is much lower. The only problem is that it is not the frequency I had hoped for.
I did some further searching and found two things.
1  The value of the J'_{0}(1) Bessel function = 1.8411837813 which agrees with the number we have.
2  Meep doesn't actually excite the cavity with Gaussian noise, rather it uses the derivative of a Gaussian signal, whatever that means.
I really don't think this particular problem is in the meep software. As I wrote before, I searched the discussion list, which goes back at least 8 years, and there is no mention of this particular problem. If it were in meep, some user would have encountered it long ago. A 25% discrepancy is hard to overlook. There is a chance that it is in my general understanding of how to model using meep, but my knowledge of meep is far superior to my knowledge of resonant cavity design so using Occam's razor, it is most likely that my cavity design is the problem.
Dr. Rodal, I really appreciate your efforts on my behalf. I will continue to look into the details of resonant cavity design. Maybe it has something to do with the cavity length. But actually, that doesn't seem very likely at all. What do you know about Gaussian noise derivatives and could that be a simple frequency correction? But, when generated with a continuous wave at 2.45 GHz, the field images don't show any resonance.
Ok, that (drive frequency to 1.873 GHz, bandwidth to 0.07 * frequency) takes care of the Q and error problems :
frequency Quality factor error
1,873,339,229.3075 Hz 18,325,307.0778158 1.673972608680621e7+0.0i
I hope that tomorrow I have some time to go over the equations and the dimensions (which I did not have the time to go over yet) to check if I find any reason why you calculate it should be 2.45 GHz and Meep resonates at1.873 GHz instead.

It was partly due to a misunderstand of the formula. I changed modes, to T??,?,0 and found that with p=0, while the cylinder length has no effect on frequency from the formula, it has a strong effect in meep. It is understandable that changing length should effect the resonance. In fact the effect of changing length is stronger than the effect of changing radius but that is likely due to having a radius not associated with any given mode. The nearest frequency mode is TM0,1,0
I didn't notice that I was looking at the wrong table of frequencies until after I iterated meep to the 2.45 GHz frequency. I'll look at it again tomorrow, but it's getting tired here now.

Went back to investigate what I reported in post #233 http://forum.nasaspaceflight.com/index.php?topic=36313.msg1318683#msg1318683 about the RF and Microwave Toolbox app. I found that the app is reporting the correct solutions for TE and TM. The help file just had a typo. I verified it against the KWOK lectures http://www.engr.sjsu.edu/rkwok/EE172/Cavity_Resonator.pdf slide 16. KWOK and the APP match. So this works as a quick and easy way to find resonant modes! There really is an app for everything.
I remain unconvinced that calculating resonant modes for cylinders is a good approximation for conical frustums though.

people have mentioned Dr Dr. Michael McCulloch a few times. i though i would drop a link to one of his papers. though actual discussion should be taken up elsewhere. it is related to the present topic because he has alternate views of how these EM devices (Shawyer, Cannae, White, the Chinese, etc) work.
http://www.pteponline.com/index_files/2015/PP4015.PDF

@Rodel
The first subscript (m) is the azimuthal mode number: it indicates the number of fullwave patterns around the circumference of the waveguide. It is zero for modes in which there is no variation in the circumferential direction.
The second subscript (n) is the radial mode number: it indicates the number of halfwave patterns across the diameter. The radial mode number (n) plus one indicates the number of nodes across the diameter (counting as nodes the end nodes).
The third subscript (p) is the longitudinal mode number. It indicates the number of fullwave patterns along the longitudinal length of the waveguide. It is zero for modes in which there is no variation in the longitudinal direction.
I did double check everything as you advised and there does not seem to be anything wrong with my meep simulation. Neither could I find any questions related to my problem on the Internet. That leads me to think that my problem is still my understanding of mode shapes and cavity dimensions. I thought I had TE1,1, but from the above, for the mode to be TE 1,1, the cavity radius needs to be 1/4 wavelength and the circumference should support 1 full wave pattern. The wavelength for 2.45 GHz is 0.1223642686 in vacuum. So, for the vacuum filled cavity to resonate at 2.45 GHz in the TE 1,1 mode the radius needs to be 0.0305910671 meters. But simply plugging that radius into the formula calculates a resonance frequency of ~2.92GHz in air. So it seems evident that I am still confused about modes and use of the formula to calculate resonance frequencies. Would you lead me through the example of a resonant cavity dimensions for 2.45 GHz resonance?
I also note that driving the cavity from my previous post at 2.45 GHz, R = 0.0377449, there is no sign of resonance in the field images. So the cavity does not resonate at 2.45 GHz and therefore my dimensions must be wrong.
I want to point out a discrepancy I found. Perhaps I'm the discrepancy, because I don't agree with my old post or any of the other sources, which is highly unlikely.
First here's what I have about mode numbering from various sources:
ME from thread 1: T(MorE)mnp. m is the # of 1/2 wavelengths around a half circumference, n is the # of 1/2 wavelengths across a radius, p is the # of 1/2 wavelengths of length of the cavity.
Navy Neets mod 11 (screenshot below): The first subscript indicates the number of fullwave patterns around the circumference of the waveguide. The second subscript indicates the number of halfwave patterns across the diameter.........(p left out).
Oracle: http://en.wikipedia.org/wiki/Transverse_mode In circular waveguides, circular modes exist and here m is the number of halfwavelengths along a halfcircumference and n is the number of halfwavelengths along a radius.......(p left out).
Rodal: The first subscript (m) is the azimuthal mode number: it indicates the number of fullwave patterns around the circumference of the waveguide.
The second subscript (n) is the radial mode number: it indicates the number of halfwave patterns across the diameter. The third subscript (p) is the longitudinal mode number. It indicates the number of fullwave patterns along the longitudinal length of the waveguide.
So there is conflicting information. Rodal and the Navy agree, the oracle and me are different. I'll see if I can clear it up.....and find deal here.
Using the coke can example from http://www.engr.sjsu.edu/rkwok/EE172/Cavity_Resonator.pdf slide 17, for a radius of 1.25"(or diameter of 2.5"), depth of 5". This comes out to a TE111 f,res of 3.01ghz, which gives me a wavelength of 3.923". So first, to test the first subscript m, the circumference of a circle with r 1.25" is 7.85". 7.85"inch is 2 wavelengths @3.01ghz.
So it appears that m should be the # of full wavelengths around half a circumference.
or
If you don't do any rounding with the coke can example, @3.01ghz you get 3.923928113636958 inches, multiply that by 2 you get 7.847856227273916 inches, which is just shy of the calculated circumference of 7.85, which technically is not a FULL cycle of 2 wavelengths. Which means this example sits on the edge of TE111 and TE211. Technically that 0 wasn't crossed yet.
So is that the answer? FULL wavelengths must be counted, the rest is dropped? Meaning if you go around 2.6 times for example, you just get an m of 2?
###Resolution:
http://forum.nasaspaceflight.com/index.php?topic=36313.msg1321080#msg1321080
http://forum.nasaspaceflight.com/index.php?topic=36313.msg1321196#msg1321196
This is important because soon I'm going to be cutting copper shapes and making stupid mistakes can be very expensive.
I've found fault with the Navy references before on other things, and we all know that everything on the Oracle needs to be verified, and I'm frequently wrong, but Rodal is usually right. So what's going on there?
As far as n or p go, I'm not even going to look at them until I get some feedback about the m discrepancies. I just want to clear this up. I don't mind getting egg on my face.
Break:
You know, I think this got overlooked: "We performed some very early evaluations without the dielectric resonator (TE012 mode at 2168 MHz, with power levels up to ~30 watts) and measured no significant net thrust."
I got a lot of grief before for my approach to deriving the cavity dimensions (starting with the 6.25 inch small end, using the dimensions of the PE discs from 14 of Brady et al Anomalous thust...., but I think those dimensions, (see screenshot below) are exactly spot on and here's empirical proof. So my calculated cavity length in Autocad after scaling based on 6.25inch small ends size, was 10.88". If you look at the frequency of 2168mhz, you'll find the wavelength is 5.4479". Take two wavelengths of this, you'll arrive at 10.8958, my cavity length was 10.88". Converted to meters, it is:
Dsmall=0.15875m (0.159m)
Dlarge=0.30098m (0.3m) amazingly round number
Length=0.27637m (.276m)
###Edit: Added link to resolution with current and correct info.

The Rational Wiki has an interesting page on these EM drives.
http://rationalwiki.org/wiki/EmDrive
NASA plans to upgrade their equipment to higher power levels, use vacuumcapable RF amplifiers with power ranges of up to 125 W, and design a new tapered cavity analytically expected to produce thrust in the 0.1 N/kW range. Then, the test article will be shipped to other laboratories for independent verification and continued evaluations of the technology, at Glenn Research Center, the Jet Propulsion Laboratory and the Johns Hopkins University Applied Physics Laboratory.
I know that has been discussed here but thought there might be additional info in it that may have not been noticed before.

....
First here's what I have about mode numbering from various sources:
ME from thread 1: T(MorE)mnp. m is the # of 1/2 wavelengths around a half circumference...
Navy Neets mod 11 (screenshot below): The first subscript indicates the number of fullwave patterns around the circumference of the waveguide....
Oracle: http://en.wikipedia.org/wiki/Transverse_mode In circular waveguides, circular modes exist and here m is the number of halfwavelengths along a halfcircumference....
Rodal: The first subscript (m) is the azimuthal mode number: it indicates the number of fullwave patterns around the circumference of the waveguide.
....
So there is conflicting information. Rodal and the Navy agree, the oracle and me are different....
As far as n or p go, I'm not even going to look at them until I get some feedback about the m discrepancies....
As far as "m" goes, I don't see any discrepancy whatsoever. They all agree:
Mulletron (from thread 1) "the # of 1/2 wavelengths around a half circumference"
Wikipedia " the number of halfwavelengths along a halfcircumference"
US NAVY: the number of fullwave patterns around the full circumference
Rodal: the number of fullwave patterns around the full circumference
" the number of halfwavelengths around a halfcircumference" is exactly the same as the number of fullwave patterns around the full circumference of the waveguide because a full wave around the full circumference is exactly one halfwave around the halfcircumference, or 1/3 wave around 1/3 the circumference, or 1/nr wave around 1/nr circumference where nr is an arbitrary integer.
And the definition of wavelength is exactly the same length as the definition of "full wave pattern".

We differ in the full mnp description. Look at n. M is the same between us, but the coke can example has me wondering.

We differ in the full mnp description. Look at n. M is the same between us, but the coke can example has me wondering.
Well, I wanted to clear that up, because you had previously written:
As far as n or p go, I'm not even going to look at them until I get some feedback about the m discrepancies....
and I don't see any "m discrepancies"

I'm mixed up on the m after studying the KWOK example mostly.

....
Here are my results.
Resolution number of time steps resonant frequency Q error
1 2 none detected
2 4 none detected
3 6 none detected
4 8 none detected
5 10 1.84921E+009 negative 2 e4
10 20 1.85128E+009 negative 2 e4
20 40 1.86441E+009 ~ 500 6 e4
40 80 1.87262E+009 ~ 1200 3 e4
80 160 1.86992E+009 ~ 300 13 e4
160 320 1.87042E+009 ~ 80 47 e4
The detected frequency bounces around consistently with the error which can be taken as estimating the number of significant digits of the frequency detected.
The quality is very low. I take that to be a result of the cavity dimensions being incorrect for the resonant frequency detected as they are also incorrect for the drive frequency.
....
Aero, please tell me again exactly what is the actual numerical value that you actually inputed into MEEP for the drive frequency for the above calculations. What is the number that you inputed into MEEP.

So is the m resolved because the KWOK modes were so close but no cigar together? That's my hunch, but I want verify before I let it go. Lesson learned.....don't round off when it comes to mode shapes then?

So is the m resolved because the KWOK modes were so close but no cigar together? That's my hunch, but I want verify before I let it go. Lesson learned.....don't round off when it comes to mode shapes then?
I need to take care of $ paying work first :). As I get time, my first priority is to deal with aero's problem (it came first :) ) and after that I'll take a thorough look at the numbers in KWOK and the "n" and "p" issue you brought up. Sorry I don't want to give you an answer as an immediate reflex. I want to give you a thoughtful answer. I need some time to go carefully over these issues :).

FWIW for TE111(mnp) 2.45ghz, cavity dimensions for a cylinder are Length=0.122448m Diameter=0.0827888m in air. Or 4.8208"x 3.2594". Much more precision than necessary or attainable. The exact frequency I could get is 2.450019ghz.
Anyway what you do if you build something like this is build it to the ball park dimensions, then tune it the rest of the way with tuning screws to bring it into resonance and maximize Q. You can't build something easily with those kind of tolerances above.
Edit:
Okay to get a perfect 2.45ghz, TE111 with way too high precision:
L=0.1224489m
D=0.08278945m

....
Here are my results.
Resolution number of time steps resonant frequency Q error
1 2 none detected
2 4 none detected
3 6 none detected
4 8 none detected
5 10 1.84921E+009 negative 2 e4
10 20 1.85128E+009 negative 2 e4
20 40 1.86441E+009 ~ 500 6 e4
40 80 1.87262E+009 ~ 1200 3 e4
80 160 1.86992E+009 ~ 300 13 e4
160 320 1.87042E+009 ~ 80 47 e4
The detected frequency bounces around consistently with the error which can be taken as estimating the number of significant digits of the frequency detected.
The quality is very low. I take that to be a result of the cavity dimensions being incorrect for the resonant frequency detected as they are also incorrect for the drive frequency.
....
Aero, please tell me again exactly what is the actual numerical value that you actually inputed into MEEP for the drive frequency for the above calculations. What is the number that you inputed into MEEP.
Drive frequency 2.45 E+9 Hz, so wavelength = 0.1223642686 meters.
Geometry actual inside dimensions L= 0.1223642686, Dia = 0.0754898000 meters air filled cylindrical cavity with no dielectric. I am ignoring the difference between speed of light in air and vacuum.
I copied those numbers straight from the control file. This is what I used.

Drive frequency 2.45 E+9 Hz, so wavelength = 0.1223642686 meters.
Geometry actual inside dimensions L= 0.1223642686, Dia = 0.0754898000 meters air filled cylindrical cavity with no dielectric. I am ignoring the difference between speed of light in air and vacuum.
I copied those numbers straight from the control file. This is what I used.
I get TE111, 2.63018ghz from that.

....
Here are my results.
Resolution number of time steps resonant frequency Q error
1 2 none detected
2 4 none detected
3 6 none detected
4 8 none detected
5 10 1.84921E+009 negative 2 e4
10 20 1.85128E+009 negative 2 e4
20 40 1.86441E+009 ~ 500 6 e4
40 80 1.87262E+009 ~ 1200 3 e4
80 160 1.86992E+009 ~ 300 13 e4
160 320 1.87042E+009 ~ 80 47 e4
The detected frequency bounces around consistently with the error which can be taken as estimating the number of significant digits of the frequency detected.
The quality is very low. I take that to be a result of the cavity dimensions being incorrect for the resonant frequency detected as they are also incorrect for the drive frequency.
....
Aero, please tell me again exactly what is the actual numerical value that you actually inputed into MEEP for the drive frequency for the above calculations. What is the number that you inputed into MEEP.
Drive frequency 2.45 E+9 Hz, so wavelength = 0.1223642686 meters.
Geometry actual inside dimensions L= 0.1223642686, Dia = 0.0754898000 meters air filled cylindrical cavity with no dielectric. I am ignoring the difference between speed of light in air and vacuum.
I copied those numbers straight from the control file. This is what I used.
Sorry to be insistent, but just to make clear, could you please confirm that the numerical value that you actually typed as an input for MEEP was 2.45 E+9 ?
I am not asking what the frequency in Hz should be. I am asking what number you typed as an input to MEEP.

....
Here are my results.
Resolution number of time steps resonant frequency Q error
1 2 none detected
2 4 none detected
3 6 none detected
4 8 none detected
5 10 1.84921E+009 negative 2 e4
10 20 1.85128E+009 negative 2 e4
20 40 1.86441E+009 ~ 500 6 e4
40 80 1.87262E+009 ~ 1200 3 e4
80 160 1.86992E+009 ~ 300 13 e4
160 320 1.87042E+009 ~ 80 47 e4
The detected frequency bounces around consistently with the error which can be taken as estimating the number of significant digits of the frequency detected.
The quality is very low. I take that to be a result of the cavity dimensions being incorrect for the resonant frequency detected as they are also incorrect for the drive frequency.
....
Aero, please tell me again exactly what is the actual numerical value that you actually inputed into MEEP for the drive frequency for the above calculations. What is the number that you inputed into MEEP.
Drive frequency 2.45 E+9 Hz, so wavelength = 0.1223642686 meters.
Geometry actual inside dimensions L= 0.1223642686, Dia = 0.0754898000 meters air filled cylindrical cavity with no dielectric. I am ignoring the difference between speed of light in air and vacuum.
I copied those numbers straight from the control file. This is what I used.
Sorry to be insistent, but just to make clear, could you please confirm that the numerical value that you actually typed as an input for MEEP was 2.45 E+9 ?
I am not asking what the frequency in Hz should be. I am asking what number you typed as an input to MEEP.
Moreover, since c = 1 in Meep units, a (or a / c) is our unit of time as well. In particular, the frequency f in Meep (corresponding to a time dependence e − i2πft) is always specified in units of c / a
Note: if you use meters as the unit of length in MEEP, then it must follow that the MEEP unit of time is meters and the MEEP unit of frequency is 1/meter.
If you used meters as the unit of length such that your input was
aeroMeepLength = 0.1223642686
aeroMeepDiameter = 0.0754898000
[Showing only 6 signficant digits for calculations from now on, but I am using full Mathematica precision]
aeroMeepRadius = 0.0377449
In meters/second the speeds of light:
cVacuum = c
= 299792458;
cAir = c / (Sqrt[mur*epsilonr])
= 299705000
Then your input for frequency to MEEP, in MEEP units, for mode TE111, (m=1,n=1,p=1) should have been:
p = 1;
X'_{1},_{1}=1.84118378134065;
frequencyTEMeep
= (cAir/cVacuum) (1/(2*Pi))*Sqrt[(X'_{1},_{1}/aeroMeepRadius)^2 +((p*Pi/aeroMeepLength)^2)]
= (cAir/cVacuum) (1/(2*Pi))*Sqrt[(1.84118378134065/0.0377449)^2 +((1*Pi/0.122364)^2)]
= 8.77064
In MEEP units of frequency (1/meter) which is almost 9 orders of magnitude smaller than 2.45 E+9
In other words, as an input to MEEP you must divide the expression for frequency (for example as it appears in Wikipedia) by cVacuum in order to input frequency in MEEP frequency units of 1/length.
Once you have done this, you consequently have to interpret the MEEP output for frequency in MEEP frequency units (which are not Hz, they are 1/length).
For example: Meep frequency of 8.77064 (1/meter) corresponds to 8.77064*c = 8.77064*cVacuum = 2.62937 GHz

...
Geometry actual inside dimensions L= 0.1223642686, Dia = 0.0754898000 meters air filled cylindrical cavity with no dielectric. I am ignoring the difference between speed of light in air and vacuum.
Scale factor, 0.01, but is a parameter to adjust
The above gives geometry simulation dimensions in scaled units = 012.23642686, 007.54898000
...
I don't follow the need for this "scale factor" (Scale factor, 0.01) you are using. It may unnecessarily complicate things  I would not use it until you have exactly matched the exact solution.
The mention of "scale factor" in MEEP I found was in http://abinitio.mit.edu/wiki/index.php/Meep_Reference as:
susceptibility
Parent class for various dispersive susceptibility terms, parameterized by an anisotropic amplitude σ (see Material dispersion in Meep):
sigma [number]
The scale factor σ.
But the exact solution (of an empty cylindrical cavity) we are considering does not consider any anisotropic materials consideration.
You have to be careful as to what MEEP will interpret as inputs ("garbage in" = "garbage out" :) ). If you input to MEEP L= 0.1223642686 (meters), Dia = 0.0754898000 (meters), then the MEEP frequency should be as per my previous post in 8.77064 1/meters units. (And you should interpret the output in 1/meters frequency units as well)
If instead you input L = 12.23642686, D= 7.54898000 you are effectively using centimeters as your input unit, and therefore your MEEP frequency should be input in 1/cm units, giving 0.0877064 1/centimeter , but again, what is the need to use a Scale Factor?

The scale factor, also known as characteristic length  "we pick some characteristic lengthscale in the system, a, and use that as our unit of distance." Or, more detailed, from "Units in Meep" here; http://abinitio.mit.edu/wiki/index.php/Meep_Introduction (http://abinitio.mit.edu/wiki/index.php/Meep_Introduction)
In particular, because Maxwell's equations are scale invariant (multiplying the sizes of everything by 10 just divides the corresponding solution frequencies by 10), it is convenient in electromagnetic problems to choose scaleinvariant units (see our online textbook, ch. 2). That means that we pick some characteristic lengthscale in the system, a, and use that as our unit of distance.

The scale factor, also known as characteristic length  "we pick some characteristic lengthscale in the system, a, and use that as our unit of distance." Or, more detailed, from "Units in Meep" here; http://abinitio.mit.edu/wiki/index.php/Meep_Introduction (http://abinitio.mit.edu/wiki/index.php/Meep_Introduction)
In particular, because Maxwell's equations are scale invariant (multiplying the sizes of everything by 10 just divides the corresponding solution frequencies by 10), it is convenient in electromagnetic problems to choose scaleinvariant units (see our online textbook, ch. 2). That means that we pick some characteristic lengthscale in the system, a, and use that as our unit of distance.
It unnecessarily complicates things at this point, it presents extra problems of interpretation  I would not use it until you have exactly matched the exact solution. If you must, use Scale Factor =1, for the time being: if you input to MEEP L= 0.1223642686 (meters), Dia = 0.0754898000 (meters), then the MEEP frequency should be as per my previous post in 8.77064 1/meters units. (And you should interpret the output in 1/meters frequency units as well)
If instead you input L = 12.23642686, D= 7.54898000 you are effectively using centimeters as your input unit of length, and therefore your MEEP frequency should be input in 1/cm units, giving MEEP Frequency = 0.0877064 1/centimeter, and you would have to multiply the output frequencies by cVacuum = 29979245800 centimeter/second to express the output in Hz. Unnecessarily messy at this point.

The scale factor, also known as characteristic length  "we pick some characteristic lengthscale in the system, a, and use that as our unit of distance." Or, more detailed, from "Units in Meep" here; http://abinitio.mit.edu/wiki/index.php/Meep_Introduction (http://abinitio.mit.edu/wiki/index.php/Meep_Introduction)
In particular, because Maxwell's equations are scale invariant (multiplying the sizes of everything by 10 just divides the corresponding solution frequencies by 10), it is convenient in electromagnetic problems to choose scaleinvariant units (see our online textbook, ch. 2). That means that we pick some characteristic lengthscale in the system, a, and use that as our unit of distance.
It unnecessarily complicates things at this point, it presents extra problems of interpretation  I would not use it until you have exactly matched the exact solution. If you must, use Scale Factor =1, for the time being: if you input to MEEP L= 0.1223642686 (meters), Dia = 0.0754898000 (meters), then the MEEP frequency should be as per my previous post in 8.77064 1/meters units. (And you should interpret the output in 1/meters frequency units as well)
If instead you input L = 12.23642686, D= 7.54898000 you are effectively using centimeters as your input unit of length, and therefore your MEEP frequency should be input in 1/cm units, giving MEEP Frequency = 0.0877064 1/centimeter, and you would have to multiply the output frequencies by cVacuum = 29979245800 centimeter/second to express the output in Hz. Unnecessarily messy at this point.
It doesn't work that way. I input units in meters, and the scale factor. The input is scaled, then the output that I gave you is "unscaled" to be in SI units. But yes, I can run meep with a scale factor of 1. It gives the same answers but takes more CPU so the runs are longer. Not to bad for this simple 1D calibration problem though.
Here is an example using resolution = 1200, which is quite low resolution.
frequency quality factor error
1.86060E+009 37934.0653626318 7.872026063658947e6+0.0i
Had I used this scale factor and geometry to generate 2D images of the developing fields, it would take about 12 hours computer run time, per meep estimate. Generating those images using a scale factor of 0.01 takes about 45 minutes as I recall.
I think the solution is in p, the cavity length. If I understand it at all, the cavity with length less than 1/2 wavelength resonates in the p=0 mode, with cavity length between 1/2 and 3/2 wavelength it can resonate in a p=1 mode, with cavity length between 3/2 and 5/2 wavelength it can resonate in p=2 mode and so forth.
But when I calculate a radius using cavity length = wave length, that radius gives a resonant frequency of about 2.28 GHz. Then I adjust the cavity length to obtain a resonant frequency of 2.45 GHz, the formula (inverted to calculate R) gives a new R. Plugging that new R back into the frequency formula with the adjusted cavity length, the frequency formula gives back the same 2.28 GHz. I don't understand it yet but I'm working on it.

The scale factor, also known as characteristic length  "we pick some characteristic lengthscale in the system, a, and use that as our unit of distance." Or, more detailed, from "Units in Meep" here; http://abinitio.mit.edu/wiki/index.php/Meep_Introduction (http://abinitio.mit.edu/wiki/index.php/Meep_Introduction)
In particular, because Maxwell's equations are scale invariant (multiplying the sizes of everything by 10 just divides the corresponding solution frequencies by 10), it is convenient in electromagnetic problems to choose scaleinvariant units (see our online textbook, ch. 2). That means that we pick some characteristic lengthscale in the system, a, and use that as our unit of distance.
It unnecessarily complicates things at this point, it presents extra problems of interpretation  I would not use it until you have exactly matched the exact solution. If you must, use Scale Factor =1, for the time being: if you input to MEEP L= 0.1223642686 (meters), Dia = 0.0754898000 (meters), then the MEEP frequency should be as per my previous post in 8.77064 1/meters units. (And you should interpret the output in 1/meters frequency units as well)
If instead you input L = 12.23642686, D= 7.54898000 you are effectively using centimeters as your input unit of length, and therefore your MEEP frequency should be input in 1/cm units, giving MEEP Frequency = 0.0877064 1/centimeter, and you would have to multiply the output frequencies by cVacuum = 29979245800 centimeter/second to express the output in Hz. Unnecessarily messy at this point.
It doesn't work that way. I input units in meters, and the scale factor. The input is scaled, then the output that I gave you is "unscaled" to be in SI units. But yes, I can run meep with a scale factor of 1. It gives the same answers but takes more CPU so the runs are longer. Not to bad for this simple 1D calibration problem though.
Here is an example using resolution = 1200, which is quite low resolution.
frequency quality factor error
1.86060E+009 37934.0653626318 7.872026063658947e6+0.0i
Had I used this scale factor and geometry to generate 2D images of the developing fields, it would take about 12 hours computer run time, per meep estimate. Generating those images using a scale factor of 0.01 takes about 45 minutes as I recall.
Wait a minute, this is the first time that I see:
frequency quality factor error
1.86060E+009 37934.0653626318 7.872026063658947e6+0.0i
from you.
do you agree or not, that your input frequency should have been frequencyTEMeep = 8.77064 (1/meters) if your length input is in meters? ???
and that the problem you had was that you were inputting frequency into Meep in Hertz instead of using consistent MEEP units ? ???

No it's not, that resolution is likely somewhere between these lines.
10 20 1.85128E+009 negative 2 e4
20 40 1.86441E+009 ~ 500 6 e4
40 80 1.87262E+009 ~ 1200 3 e4
that I posted 2 pages back.
And no I don't. The meep input frequency must be in the same dimensional units as the geometry, I use SI units.
I have made progress though. Using the frequency formula to adjust cavity length so that the formula gave 2.45GHz, required a cavity length about 0.0965 meters. Iteratively running meep and adjusting the cavity length to force resonance at 2.45 GHZ independently produced a cavity length of 0.0936 meters.
I emphasize that I worked those problems independently of each other so the fact that they are in near agreement is telling. I would like to find a combination length and radius that would give the frequency without the length being so close to 3/4 wavelength. In fact, I would like for the length to be exactly one wavelength and for which I knew the mode. TE 1,1,1 would be good, but TE 1,4,1 might also work. Maybe now that I have found one solution, I can find more solutions.

No it's not, that resolution is likely somewhere between these lines.
10 20 1.85128E+009 negative 2 e4
20 40 1.86441E+009 ~ 500 6 e4
40 80 1.87262E+009 ~ 1200 3 e4
that I posted 2 pages back.
And no I don't. The meep input frequency must be in the same dimensional units as the geometry, I use SI units.
I have made progress though. Using the frequency formula to adjust cavity length so that the formula gave 2.45GHz, required a cavity length about 0.0965 meters. Iteratively running meep and adjusting the cavity length to force resonance at 2.45 GHZ independently produced a cavity length of 0.0936 meters.
I emphasize that I worked those problems independently of each other so the fact that they are in near agreement is telling. I would like to find a combination length and radius that would give the frequency without the length being so close to 3/4 wavelength. In fact, I would like for the length to be exactly one wavelength and for which I knew the mode. TE 1,1,1 would be good, but TE 1,4,1 might also work. Maybe now that I have found one solution, I can find more solutions.
Well, we disagree. The correct solution for the geometry you input
aeroMeepLength = 0.1223642686 meters
aeroMeepDiameter = 0.0754898000 meters
at TE111 is 2.63 Ghz, I agree with Mulletron. (Mulletron 2.63018 Ghz, Rodal 2.62937 GHz) Also, you should have quite a lot of frequencies bunched up nearby TE111 at 2.63 Ghz. It is incorrect to get only one frequency and very far away at 1.87 GHz instead of 2.63 Ghz.
Also, unless you input a finite tan delta (which I did not find in your writing), your Q should be extremely large (for tan delta=0, Q goes to infinity). The Q's you report are very low.
____
At my next break :) I will look into the m,n,p issue brought by Mulletron.

My input frequency is converted to meep units in the control file, meep frequency = 0.08172320332354725. That is scaled by the 0.01 factor. But that is not an input. The input is frequency in SI units. The conversion is scale factor/c so I guess the units would be 1/meter internally.
It's difficult for me to come up with 8.77064 1/meters though. That is your 2.63 GHz number and I've not seen it in any of my meep runs that I recall.

My input frequency is converted to meep units in the control file, meep frequency = 0.08172320332354725. That is scaled by the 0.01 factor. But that is not an input. The input is frequency in SI units. The conversion is scale factor/c so I guess the units would be 1/meter internally.
It's difficult for me to come up with 8.77064 1/meters though. That is your 2.63 GHz number and I've not seen it in any of my meep runs that I recall.
1) It should be 0.0877064 1/centimeter Meep frequency units instead of 0.0817232. For
aeroMeepLength = 0.1223642686 meters
aeroMeepDiameter = 0.0754898000 meters
at TE111, since the frequency is 2.63 Ghz as Mulletron and I get.
2) You should run with your "scale factor" of 1 instead, for as long as that takes, and see what results you get. If the scale factor of 1 results in a longer run, it means that your scale factor is getting mixed with the finite difference mesh discretization.

....
I want to point out a discrepancy I found. Perhaps I'm the discrepancy, because I don't agree with my old post or any of the other sources, which is highly unlikely.
First here's what I have about mode numbering from various sources:
ME from thread 1: T(MorE)mnp. m is the # of 1/2 wavelengths around a half circumference, n is the # of 1/2 wavelengths across a radius, p is the # of 1/2 wavelengths of length of the cavity.
Navy Neets mod 11 (screenshot below): The first subscript indicates the number of fullwave patterns around the circumference of the waveguide. The second subscript indicates the number of halfwave patterns across the diameter.........(p left out).
Oracle: http://en.wikipedia.org/wiki/Transverse_mode In circular waveguides, circular modes exist and here m is the number of halfwavelengths along a halfcircumference and n is the number of halfwavelengths along a radius.......(p left out).
Rodal: The first subscript (m) is the azimuthal mode number: it indicates the number of fullwave patterns around the circumference of the waveguide.
The second subscript (n) is the radial mode number: it indicates the number of halfwave patterns across the diameter. The third subscript (p) is the longitudinal mode number. It indicates the number of fullwave patterns along the longitudinal length of the waveguide.
So there is conflicting information. Rodal and the Navy agree, the oracle and me are different. I'll see if I can clear it up.....and find deal here.
Using the coke can example from http://www.engr.sjsu.edu/rkwok/EE172/Cavity_Resonator.pdf slide 17, for a radius of 1.25"(or diameter of 2.5"), depth of 5". This comes out to a TE111 f,res of 3.01ghz, which gives me a wavelength of 3.923". So first, to test the first subscript m, the circumference of a circle with r 1.25" is 7.85". 7.85"inch is 2 wavelengths @3.01ghz.
So it appears that m should be the # of full wavelengths around half a circumference.
or
If you don't do any rounding with the coke can example, @3.01ghz you get 3.923928113636958 inches, multiply that by 2 you get 7.847856227273916 inches, which is just shy of the calculated circumference of 7.85, which technically is not a FULL cycle of 2 wavelengths. Which means this example sits on the edge of TE111 and TE211. Technically that 0 wasn't crossed yet.
So is that the answer? FULL wavelengths must be counted, the rest is dropped? Meaning if you go around 2.6 times for example, you just get an m of 2?
This is important because soon I'm going to be cutting copper shapes and making stupid mistakes can be very expensive.
I've found fault with the Navy references before on other things, and we all know that everything on the Oracle needs to be verified, and I'm frequently wrong, but Rodal is usually right. So what's going on there?
As far as n or p go, I'm not even going to look at them until I get some feedback about the m discrepancies. I just want to clear this up. I don't mind getting egg on my face.
Break:
You know, I think this got overlooked: "We performed some very early evaluations without the dielectric resonator (TE012 mode at 2168 MHz, with power levels up to ~30 watts) and measured no significant net thrust."
I got a lot of grief before for my approach to deriving the cavity dimensions (starting with the 6.25 inch small end, using the dimensions of the PE discs from 14 of Brady et al Anomalous thust...., but I think those dimensions, (see screenshot below) are exactly spot on and here's empirical proof. So my calculated cavity length in Autocad after scaling based on 6.25inch small ends size, was 10.88". If you look at the frequency of 2168mhz, you'll find the wavelength is 5.4479". Take two wavelengths of this, you'll arrive at 10.8958, my cavity length was 10.88". Converted to meters, it is:
Dsmall=0.15875m (0.159m)
Dlarge=0.30098m (0.3m) amazingly round number
Length=0.27637m (.276m)
Thank you @Mulletron for looking at this discrepancy, which enables me to correct this mistake: :)
My description of the quantum mode number "p" for the longitudinal direction of a cylindrical cavity in http://forum.nasaspaceflight.com/index.php?topic=36313.msg1318217#msg1318217 should be corrected from "number of fullwave patterns along the longitudinal length " to "number of halfwave patterns along the longitudinal length "
The first subscript (m) is the azimuthal mode number: it indicates the number of fullwave patterns around the circumference of the cylindrical cavity. It is zero for modes in which there is no variation in the circumferential direction.
The second subscript (n) is the radial mode number: it indicates the number of halfwave patterns across the diameter. The radial mode number (n) plus one indicates the number of nodes across the diameter (counting as nodes the end nodes).
The third subscript (p) is the longitudinal mode number. It indicates the number of fullwave patterns along the longitudinal length of the waveguide. It is zero for modes in which there is no variation in the longitudinal direction.
to:
The first subscript (m) is the azimuthal mode number: it indicates the number of fullwave patterns around the circumference of the cavity. It is zero for modes in which there is no variation in the circumferential direction.
The second subscript (n) is the radial mode number: it indicates the number of halfwave patterns across the diameter. The radial mode number (n) plus one indicates the number of nodes across the diameter (counting as nodes the end nodes). The radial mode number (n) minus one indicates the number of middle nodes across the diameter (not counting as nodes the end nodes). The radial mode number (n) cannot be zero.
The third subscript (p) is the longitudinal mode number. It indicates the number of halfwave patterns along the longitudinal length of the cavity. It is zero for modes in which there is no variation in the longitudinal direction.
I doublechecked the others (m and n) and I am sure that they are correct.
The US Navy reference is correct. GO NAVY !
(http://orangehoodie.com/photo/lifeliberty800.jpg)
Concerning, "m" "the azimuthal mode number: it indicates the number of fullwave patterns around the circumference of the cavity, all the descriptive references you brought up agree (as we previously discussed in this thread).
Concerning "n" (the radial mode number that "indicates the number of halfwave patterns across the diameter"), the Wikipedia link is incorrect I didn't have the time to check the history of that Wiki entry to see what is the history of that Wikipedia error. When I have the time I will examine that and I will correct the entry in Wikipedia.
To make the long story short, the quantum mode numbers have to respect the boundary conditions:
1) In the circumferential direction there is really no boundary, the condition is one of periodicity, hence m must be the number of full waves in the circumferential direction. All references agree
2) In the radial and longitudinal directions, the boundary conditions (electrical conductivity at the surfaces) are at each end of the diametral direction or at each end of the longitudinal direction. There is no boundary condition at the center of the circular crosssection other than symmetry or antisymmetry (unless it would be a doubleconcentric cylinder having an inner conductive cylinder in addition to the outer conductive cylindrical surface) hence a halfwave can be supported within the diameter direction and a halfwave can be supported within the longitudinal direction. Hence the radial and longitudinal directions n and p are the number of halfwaves in both directions, just like a rectangular cavity.

I have not had a chance to look at your Coke can for the numbers in KWOK yet.

I found this very interesting (expired) 1969 patent by Wolf, owned by JOHNSON CONTROLS INTERNATIONAL, that deals with conical cavities !
http://www.google.com/patents/US3425006
It has a lot of interesting practical stuff, for example dealing with spherical ends (like in Greg Egan's solution http://gregegan.customer.netspace.net.au/SCIENCE/Cavity/Cavity.html ) instead of flat end plates (NASA Brady et.al., Shawyer(Experimental and Demo) and Prof. Juan Yang in China's EM Drives all have flat ends):
The naturally conforming reflecting end for a conical Waveguide is such a sphere, just as the conforming end for a cylindrical waveguide is a flat plate. It is believed that the reason that the spherical end is superior is that fewer higher order modes need be excited in reflection from such an end than from a fiat end, or that the degree of such excitation is less. It is further believed that higher order modes can be excited in the large end of the resonator which are undetectable through the input and output structures located at the small end, where these modes are below cutoff. They are however, detectable in that such coupling between modes may cause a reduction in the Q factor of the desired mode.
Since the curvature of the end plate cannot be altered as the resonator is tuned, the curvature of this end plate is also a factor which does not scale during the tuning of the cavity. It thus will cause slight perturbation of the modes. It appears to be possible to employ this perturbation to offset the effects of the perturbation due to the gap around the plunger, which also varies during tuning. This generally requires empirical adjustment of the plunger radius of curvature until the Q factor remains good over the tuning range.
As a feature of the third concept, an absorber is provided in the back cavity, behind the plunger or base plate and around the rim of the base plate. Successful use has also been made in experiment of grooves made in the face of the plate and partially filled with absorbing material.
This looks like the earlier Shawyer designs (with the adjustable end):
http://patentimages.storage.googleapis.com/pages/US34250060.png
EDIT: it is interesting that the only EM Drive with spherical end sections is the 2014 superconducting design by Shawyer, who after his experience with the more traditional designs has now: 1) replaced the flat ends with spherical ends, 2) discarded the adjustable end, 3) adopted piezoelectric compensation for Doppler shift, 4) uses superconductive inner surfaces to get much higher Q, 5) reportedly (according to @Wembley) discarded the dielectric and 6) it has a length smaller than both the small and big diameters.

I find myself wondering: Shawyer has been at this for a long while, and seems pretty bright.
So...did he discard the dielectric for good, or is he just doing 'prep work' of some sort that doesn't require a dielectric at the moment.
Also, my memory is a bit hazy at the moment, but when you allow for the tortured grammar, it seemed almost like Shawyer was talking about something similar to Doctor McCulloch's theory when it came to operating principle. (That was more pages back than I care to think about.)

Thank you @Mulletron for looking at this discrepancy, which enables me to correct this mistake: :)
My description of the quantum mode number "p" for the longitudinal direction of a cylindrical cavity in http://forum.nasaspaceflight.com/index.php?topic=36313.msg1318217#msg1318217 should be corrected from "number of fullwave patterns along the longitudinal length " to "number of halfwave patterns along the longitudinal length "
The first subscript (m) is the azimuthal mode number: it indicates the number of fullwave patterns around the circumference of the cylindrical cavity. It is zero for modes in which there is no variation in the circumferential direction.
The second subscript (n) is the radial mode number: it indicates the number of halfwave patterns across the diameter. The radial mode number (n) plus one indicates the number of nodes across the diameter (counting as nodes the end nodes).
The third subscript (p) is the longitudinal mode number. It indicates the number of fullwave patterns along the longitudinal length of the waveguide. It is zero for modes in which there is no variation in the longitudinal direction.
to:
The first subscript (m) is the azimuthal mode number: it indicates the number of fullwave patterns around the circumference of the cavity. It is zero for modes in which there is no variation in the circumferential direction.
The second subscript (n) is the radial mode number: it indicates the number of halfwave patterns across the diameter. The radial mode number (n) plus one indicates the number of nodes across the diameter (counting as nodes the end nodes). The radial mode number (n) minus one indicates the number of middle nodes across the diameter (not counting as nodes the end nodes). The radial mode number (n) cannot be zero.
The third subscript (p) is the longitudinal mode number. It indicates the number of halfwave patterns along the longitudinal length of the cavity. It is zero for modes in which there is no variation in the longitudinal direction.
I doublechecked the others (m and n) and I am sure that they are correct.
The US Navy reference is correct. GO NAVY !
(http://orangehoodie.com/photo/lifeliberty800.jpg)
Concerning, "m" "the azimuthal mode number: it indicates the number of fullwave patterns around the circumference of the cavity, all the descriptive references you brought up agree (as we previously discussed in this thread).
Concerning "n" (the radial mode number that "indicates the number of halfwave patterns across the diameter"), the Wikipedia link is incorrect I didn't have the time to check the history of that Wiki entry to see what is the history of that Wikipedia error. When I have the time I will examine that and I will correct the entry in Wikipedia.
To make the long story short, the quantum mode numbers have to respect the boundary conditions:
1) In the circumferential direction there is really no boundary, the condition is one of periodicity, hence m must be the number of full waves in the circumferential direction. All references agree
2) In the radial and longitudinal directions, the boundary conditions (electrical conductivity at the surfaces) are at each end of the diametral direction or at each end of the longitudinal direction. There is no boundary condition at the center of the circular crosssection other than symmetry or antisymmetry (unless it would be a doubleconcentric cylinder having an inner conductive cylinder in addition to the outer conductive cylindrical surface) hence a halfwave can be supported within the diameter direction and a halfwave can be supported within the longitudinal direction. Hence the radial and longitudinal directions n and p are the number of halfwaves in both directions, just like a rectangular cavity.
I figured out the confusion I had over the m subscript after studying the KWOK 3.01ghz coke can, and the 2.45ghz example. The issue is, wavelengths is NOT the same as wave pattern. For both the frequency examples, you get pretty much exactly 2 wavelengths around the circumference, which breaks TE111. So wavelengths is where I got it wrong. My old n subscript was jacked up too. As the Navy example states, and @Rodal did too. It is wave PATTERN. Glad I got that sorted out. So the Navy example is correct, and then add the p subscript from my old post, and it all falls in to place, as Rodal typed it out above the Navy logo, which is perfect.
So around a circumference there is of course no E field boundary condition, so trying to quantify it in wavelengths makes no sense. Pattern variation does. On the other hand, across a diameter or along the length, standard E field boundary conditions apply, so pattern or half wavelengths works equally well. I'm being super cautious before I sink cash on a large copper sheet, so I'm testing everything.

..
I figured out the confusion I had over the m subscript after studying the KWOK 3.01ghz coke can, and the 2.45ghz example. The issue is, wavelengths is NOT the same as wave pattern. For both the frequency examples, you get pretty much exactly 2 wavelengths around the circumference, which breaks TE111. So wavelengths is where I got it wrong. My old n subscript was jacked up too. As the Navy example states, and @Rodal did too. It is wave PATTERN. Glad I got that sorted out. So the Navy example is correct, and then add the p subscript from my old post, and it all falls in to place, as Rodal typed it out above the Navy logo, which is perfect.
So around a circumference there is of course no E field boundary condition, so trying to quantify it in wavelengths makes no sense. Pattern variation does. On the other hand, across a diameter or along the length, standard E field boundary conditions apply, so pattern or half wavelengths works equally well. I'm being super cautious before I sink cash on a large copper sheet, so I'm testing everything.
Thanks again @Mulletron for bringing up this issue and the joint effort. This was a great collaboration. :)
Here are my planned next steps:
1) discuss the issue of modes in a cylindrical cavity (using the Volumetric Mean) in comparison with the actual modes of a tapered cone (frustum). I would like to post some information on this. I need time to post it. Hopefully we can discuss it during the next few days.
2) Calculate the cyindrical cavity mode shapes for the Shawyer Experimental and Demo based on the Volumetric Mean. Then post the mode shapes for all the cases: NASA Brady and Shawyer, to compare.
3) Calculate the @NotSoSureOfIt expression for NASA Brady and Shawyer Experimental and Demo and compare it with McCulloch's and Shawyer's calculations.
4) I plan to eventually write a program in Mathematica to analyze the tapered cone, but I'm not going to have time for that until weeks from now at the earliest, depending on how much extra time I get.

I was wondering if this phenomena might have an effect on this system?
http://gizmodo.com/subatomicparticlescouldacceleratethemselves1681765188 (http://gizmodo.com/subatomicparticlescouldacceleratethemselves1681765188)

...
Concerning "n" (the radial mode number that "indicates the number of halfwave patterns across the diameter"), the Wikipedia link is incorrect I didn't have the time to check the history of that Wiki entry to see what is the history of that Wikipedia error. When I have the time I will examine that and I will correct the entry in Wikipedia.
...
I made the changes in the Wikipedia page https://en.wikipedia.org/wiki/Transverse_mode#Types_of_modes , to correct "wavelength" to "wave pattern" and the expressions for m and n for the circular waveguide. I also added the US NAVY reference. Let's see how long these corrections last in the Wikipedia world where anybody gets to be an Oracle :)

I've attached a video that Tom Ligon made for me some time ago. Can anyone tell me what mode this is, in particular, what is "p" . As for the operating frequency  it is consistent within meep and Harminv but these last few pages of discussion have shaken my confidence that it is consistent with the real world for those cavity dimensions.
The cavity is similar to the Brady cavity in perfect metal, but the dielectric constant is to high.
I don't expect to make a new video until I get the frequencies and modes sorted out.
Edit: add cite to the trailer of video.

I've attached a video that Tom Ligon made for me some time ago. Can anyone tell me what mode this is, in particular, what is "p" . As for the operating frequency  it is consistent within meep and Harminv but these last few pages of discussion have shaken my confidence that it is consistent with the real world for those cavity dimensions.
The cavity is similar to the Brady cavity in perfect metal, but the dielectric constant is to high.
I don't expect to make a new video until I get the frequencies and modes sorted out.
1) Only the longitudinalradial (z, r) crosssectional area (perpendicular to the circumferential direction) is shown (at a fixed azimuthal angle), and it indicates that p=3 since there are three halfwave patterns along the longitudinal axis.
The third subscript (p) is the longitudinal mode number. It indicates the number of halfwave patterns along the longitudinal length of the cavity. It is zero for modes in which there is no variation in the longitudinal direction.
2) The circular crosssection is not shown in the video and therefore there is no way to tell what the circumferential "m" quantum number of the mode shape is. One needs a circularcross section contour plot (the crosssectional area perpendicular to the longitudinal direction) in order to ascertain what m is, and to make sure what is n. It would be interesting to supply at least 2 crosssectional circumferential plots: one located at the longitudinaldirectionmiddle section of the dielectric and the other one in the empty section of the cavity to compare the field in the dielectric and the rest of the cavity.
3) Based on the limited information given by the sole longitudinalradial (z, r) crosssection shown, it appears that the radial quantum number n =1 since there is one halfwave pattern along the diameter
The second subscript (n) is the radial mode number: it indicates the number of halfwave patterns across the diameter. The radial mode number (n) plus one indicates the number of nodes across the diameter (counting as nodes the end nodes). The radial mode number (n) minus one indicates the number of middle nodes across the diameter (not counting as nodes the end nodes). The radial mode number (n) cannot be zero.
4) It is interesting that the two interior nodal lines separating the longitudinal halfwave patterns are spherical even though the ends are flat. It really shows that the cone mode shapes naturally prefer spherical ends, as in Greg Egan's solution, and as discussed in the 1969 Patent by Grant I posted previously. The flat ends of the EM Drive degenerate the natural mode shapes of the cone cavity.
5) It would be informative to also see plots of the magnetic field

I was wondering if this phenomena might have an effect on this system?
http://gizmodo.com/subatomicparticlescouldacceleratethemselves1681765188 (http://gizmodo.com/subatomicparticlescouldacceleratethemselves1681765188)
I've had a chance to go through these papers over the weekend. I didn't see anything that would rule it out.
The most encouraging aspect is the inclusion of Rindlerlike coordinates ie. accelerating frame of reference.
The shapemaintaining requirement is met by the physical cavity.
Still a long way from obvious.

******EDIT: This study does not take into account the cutoff frequency condition that eliminates several of these mode shapes. A new study incorporating the cutoff frequency will be posted *****
MODE SHAPE CALCULATION FOR SHAWYER EXPERIMENTAL AND SHAWYER DEMO
1) We define the Volumetric Mean as follows:
VolumetricMeanDiameter=Sqrt[(SmallDiameter^2+SmallDiameter*BigDiameter+BigDiameter^2)/3]
For a derivation of the Volumetric Mean (equating the volume of an equivalent cylinder to the volume of a truncated cone): See http://forum.nasaspaceflight.com/index.php?topic=36313.msg1319655#msg1319655
2) Let's define as "Shawyer EXPERIMENTAL geometry" the following estimate of the Shawyer Experimental cavity:
shawyerExpLength = 0.156 meter;
shawyerExpBigDiameter = 0.16 meter
shawyerExpSmallDiameter = 0.127546 meter;
then
shawyerExpGeometricMeanDiameter =Sqrt[shawyerExpBigDiameter * shawyerExpSmallDiameter]
= 0.142854 meter
shawyerExpMeanDiameter =( shawyerExpBigDiameter + shawyerExpSmallDiameter)/2
= 0.143773 meter
shawyerExpVolumetricDiameter =Sqrt[(shawyerExpSmallDiameter^2+shawyerExpSmallDiameter*shawyerExpBigDiameter+shawyerExpBigDiameter^2)/3]
= 0.144078 meter
Observe that shawyerExpVolumetricDiameter is just 0.21 % greater than shawyerExpMeanDiameter, and 0.86 % greater than shawyerExpGeometricMeanDiameter.
3) Let's define as " Shawyer DEMO geometry" the following definition for the Shawyer Demo cavity:
shawyerDemoLength = 0.345 meter;
shawyerDemoBigDiameter = 0.28 meter;
shawyerDemoSmallDiameter = 0.128853 meter;
then
shawyerDemoGeometricMeanDiameter=Sqrt[shawyerDemoBigDiameter*shawyerDemoSmallDiameter]
= 0.189944 meter
shawyerDemoMeanDiameter=(shawyerDemoBigDiameter+shawyerDemoSmallDiameter)/2
= 0.204427 meter
shawyerDemoVolumetricDiameter=Sqrt[(shawyerDemoSmallDiameter^2+shawyerDemoSmallDiameter* shawyerDemoBigDiameter+ shawyerDemoBigDiameter^2)/3]
= 0.209031 meter
Observe that shawyerDemoVolumetricDiameter is 2.25 % greater than shawyerDemoMeanDiameter, and 10.05 % greater than shawyerDemoGeometricMeanDiameter. The difference between the mean diameter measures is much greater for Shawyer's Demo than for Shawyer's Experimental because Shawyer's Demo has a greater difference between the small and big diameters.
4) The experimentally reported frequency was
rfFrequency = 2.45*10^9 Hz;
for both Shawyer Demo and for Shawyer Experimental.
5) Given the experimentally reported frequency, the geometrical dimensions and the value of speed of light in air, one can invert the frequency equation (see: http://en.wikipedia.org/wiki/Microwave_cavity#Cylindrical_cavity ) to obtain X_{m},_{n} and X'_{m} values as a function of constants and the longitudinal mode shape number "p". Let's define the error difference between these X_{m},_{n} and X'_{m},_{n} values and actual X_{m},_{n} and X'_{m} values as:
error= (value of X_{m},_{n} or X'_{m},_{n} obtained from frequency eqn.)/ (correct value of X_{m},_{n} or X'_{m},_{n} ) 1
where X_{m},_{n} is used for TM modes and X'_{m},_{n} is used for TE modes.
6) Then I obtain the following mode shapes and associated errors:
Shawyer EXPERIMENTAL
Geometric Mean
Best result: TE010 or TM110 error=  4.253%
2nd best: TM012 error=  5.329%
Volumetric Mean
Best result: TE010 or TM110 error=  3.433%
2nd best: TM012 error=  4.518%
Mode 010 > constant around the circumference
1 halfwave pattern across the diameter
constant along the longitudinal length
Shawyer DEMO
Geometric Mean
Best result: TE313 error=  1.673%
2nd best: TM210 error=  5.015%
Volumetric Mean
Best result: TE411 error=  0.6458%
2nd best: TE410 error= + 0.9534%
Mode 411 > 4 fullwave patterns around the circumference
1 halfwave pattern across the diameter
1 halfwave pattern along the longitudinal length
CONCLUSIONS
1) At the frequencies tested by Shawyer, what modeshape corresponds to a given frequency is very sensitive to the exact geometrical dimensions of the cavity. The reason for this is that there are many natural frequencies very close to each other, each of these frequencies having different mode shapes. It would be difficult to predict what mode shape one will get with a given geometry at these frequencies, because small variations in geometry lead to large changes in mode shape. Therefore a dielectric is needed to force a circumferentialcrosssectionmodeshape or movingend to adjust the length of the cavity. Certainly it would be very difficult to predict the mode shape of an empty cavity with the coarse finite element model used by NASA Brady et.al. or with a Finite Difference code like MEEP (There are no Bessel functions in a finite element or finite difference model: the solution is approximated with low power piecewise polynomials in each finite element. The finite element solution is a Galerkin solution "in an integral sense" and not an exact partial differential solution "point to point through the domain".) Finite Difference solutions (like MEEP) have even more discretization and convergence problems than Finite Element models.
2) Both with the Geometric Mean and with the Volumetric Mean, all Shawyer cases: the Shawyer Experimental and the Shawyer Demo experiments, correspond to transverse electric (TE) mode shapes: the electric field is in the circumferential direction and the magnetic field is perpendicular to it. I think that the TE mode shapes are the ones that should provide thrust because it is only the TE mode shapes that have the magnetic field directed along the longitudinal direction of the EM Drive. Physically, an axial magnetic field may result in a measured thrust either 1) as an artifact, because the magnetic field can heat the flat ends of the truncated cone by induction heating and hence produce thermal buckling and other heat effects or/and 2) as a real means of propulsion, by the magnetic field coupling with the Quantum Vacuum, among several possible physical mechanisms.
3) Using the volumetric mean leads to lower errors than the geometric mean.
4) No dielectric was considered, and it is unknown whether Shawyer used a dielectric and if so what material and geometry of dielectric, for these experiments. The dielectric will produce an extra longitudinal half wave in the dielectric region of the cavity, and it should reduce the number of fullwave patterns around the circumference, probably making the electric field constant in the circumferential direction for a TE mode, essentially forcing TE41 into TE01. For the DEMO, Shawyer used an adjustable end, that allowed him (unlike NASA, that did not use adjustable ends) to finetune the natural frequency of the cavity.

@Rodel
I believe that your answer is that the mode is
TX a,1,3
where X = (E or M)
it could be that a = 1, 2, ... or more.
There must be an upper limit on the value of a, but ...
I agree that more video views would be interesting, but as I wrote, I don't plan to make more until I get the frequency question ironed out. I'm still working that problem but have determined that it is either an issue with Harminv or with my use of Harminv. But it's not geometry or frequency input values, rather it is signal amplitude, run time and wait time issues. Most likely all of them. In the video I posted, it is clear that the cavity is resonating strongly at the drive frequency. The drive frequency is only moderately near the Brady experimental drive frequency. I took that to be a result of the relatively higher dielectric constant used, 2.3 compared to the 1.76 value that gives the Brady experimental value of 1.8804 GHz. But now I'm not confident of that assumption either.
I am looking into ParaView, an open source data visualization tool. With it, I might be able to generate some 3D views of interest but movies are to hard. Making of that movie took 12 hours of CPU, another 8 hours to upload the PNG files to Box, and I don't know how long to download and make the movie, then send it back. To hard just for simple exploration of the data.

@Rodel
I believe that your answer is that the mode is
TX a,1,3
where X = (E or M)
it could be that a = 1, 2, ... or more.
There must be an upper limit on the value of a, but ...
...
Yes, except:
TX m,1,3
with m=0,1, ... (the lowest possible m value is 0 meaning constant field in the circumferential direction)
I think that X is most likely to be E (because you have a dielectric in the cavity) and that m is low (because you have a dielectric in the cavity).
So I would bet that it is most likely TE013 (but we would need to see the circular crosssection contour plot to be sure what is "m")
Thank you for the excellent update on your progress :)
Godspeed :)

.....
I am looking into ParaView, an open source data visualization tool. With it, I might be able to generate some 3D views of interest but movies are to hard. Making of that movie took 12 hours of CPU, another 8 hours to upload the PNG files to Box, and I don't know how long to download and make the movie, then send it back. To hard just for simple exploration of the data.
Absolutely, we do NOT need a movie, we only need the very last still picture, since we are only interested in the steadystate standingwave.
(http://staticp2.photoxpress.com/jpg/00/05/25/40/400_F_5254097_d5Zs7X8V9fTEduGJtCKJk31PZVejXWP0_PXP.jpg)
But it was fun, enjoyable to see the movie of how MEEP proceeds from the transient waves in both directions to finally achieve a standing wave  very educational (it could be used to teach students how standing waves get formed) :)

...'m still working that problem but have determined that it is either an issue with Harminv or with my use of Harminv. But it's not geometry or frequency input values, rather it is signal amplitude, run time and wait time issues. Most likely all of them. In the video I posted, it is clear that the cavity is resonating strongly at the drive frequency. The drive frequency is only moderately near the Brady experimental drive frequency. I took that to be a result of the relatively higher dielectric constant used, 2.3 compared to the 1.76 value that gives the Brady experimental value of 1.8804 GHz. ...
I wonder about the reason why you get much better results for the truncated cone case with the dielectric (compared to experimental frequency) than with the cylindrical cavity with no dielectric (compared to exact solution). I wonder whether the reason for this is that the matrix that needs to be inverted in MEEP is numerically illconditioned (because there are many mode shapes very close together, actually the frequencies for mode shapes TE01p and TM11p are identical ! ) and that placing the dielectric makes the matrix much better numerically conditioned (the dielectric forces the mode into TE and low values for m and n ). So, for different reasons (numerical conditioning of the matrix to be inverted in the case of MEEP and finetuning frequency and modeshape in the case of the real experiments) the dielectric may be beneficial both for the numerical solution and for the experiment.
Example of an illconditioned matrix:
(http://www.phy.ornl.gov/csep/CSEP/BF/IMG245.GIF)

This discovery for cavity cooling of quantum oscillators looks interesting. Could it be relative to the subject of EM drives?
http://physics.aps.org/articles/v8/8
Cavity optomechanics studies the interaction between light and mechanical systems, most often mediated by radiation pressure—the force exerted by photons hitting on a mirror. In a typical optomechanics setup, microwave or optical photons travel in a cavity formed by two or more mirrors, one of which is free to move and acts like a mechanical oscillator whose position changes because of radiation pressure and thermal fluctuations. A recent milestone in the field was the cavity cooling of mechanical oscillators to a regime in which they have less than one quantum of motion [1]. This could have important applications, ranging from the observation of quantum behavior in macroscopic systems to the development of ultrasensitive detectors that could reveal the tiny vibrations caused by the stillelusive gravitational waves. However, todatedemonstrated schemes require that the frequency of the cooling light be lower than the cavity resonant frequency by an amount corresponding to the frequency of the mechanical oscillator. These two frequencies can be measurably different only if the oscillator’s frequency is sufficiently large. This poses an important limitation, as low frequency, heavy oscillators cannot be cooled by this method.
Now a team led by Roman Schnabel at the Albert Einstein Institute in Hannover, Germany has reported an optomechanical cooling scheme that gets rid of this frequencydetuning requirement [2]. The key to their achievement is a novel form of optomechanical coupling. Optomechanics has been mainly investigated using “dispersive coupling,” in which displacements of the oscillating mirror change the resonant frequency of the cavity [3]. Here, the authors rely instead on “dissipative coupling,” in which the mirror oscillations modify the coupling between the cavity and its environment, for instance by modulating the speed at which cavity photons are lost (i.e., the cavity bandwidth).
In the dispersive coupling regime, the most widely used cooling approach is “cavity cooling” [3]. In this method, light cools a mechanical mode via a “parametric” process: quanta of mechanical excitations are upconverted into cavity photons, which are then dissipated through the cavity. The light frequency must be detuned from the cavity resonant frequency: the mechanical oscillator produces lowerfrequency (red) and higherfrequency (blue) sidebands, which are shifted from the cavity resonance by multiples of the mechanical frequency ωM. When the driving frequency is tuned to the first red sideband, photons entering the cavity take away phonons with energy ħωM from the mechanical system, cooling the oscillator. In a number of previous studies, this method allowed researchers to bring mechanical oscillators to their quantum ground state (i.e., states in which the average number of mechanical excitations is reduced below unity) [1] and to realize the coherent conversion of photons to mechanical motion and of microwave photons to optical photons [4]. But these realizations required the system to be in the “resolved sideband regime”: for the red sideband to be distinguishable from the cavity frequency, the frequency of the mechanical oscillator (determining the shift of the sidebands) has to be larger than the cavity bandwidth. Groundstate cooling has been achieved for frequencies down to hundreds of megahertz, but reaching lower frequencies (such as the ∼100kilohertz frequency of the mechanical resonator used by Schnabel’s team) would require cavities with extremely narrow bandwidths, which are currently not available.
However, a recent theory shows that cavity cooling could be possible without the requirement to resolve the mechanicaloscillator sidebands [5] if the optomechanical coupling is dissipative [6]. In dissipatively coupled systems, two types of fluctuating forces act on the mechanical resonator: the noise in the light injected into the cavity and the quantum fluctuation of the cavity field. These two types of noise, which have different spectra, can interfere destructively. With proper parameter choice, such interference can reduce the spectral density of the noise at the frequency (ωM) of the oscillator, effectively cooling it. This mechanism, which does not require to resolve the sidebands, can work with a low oscillator frequency.

...
I have made progress though. Using the frequency formula to adjust cavity length so that the formula gave 2.45GHz, required a cavity length about 0.0965 meters. Iteratively running meep and adjusting the cavity length to force resonance at 2.45 GHZ independently produced a cavity length of 0.0936 meters.
I emphasize that I worked those problems independently of each other so the fact that they are in near agreement is telling. I would like to find a combination length and radius that would give the frequency without the length being so close to 3/4 wavelength. In fact, I would like for the length to be exactly one wavelength and for which I knew the mode. TE 1,1,1 would be good, but TE 1,4,1 might also work. Maybe now that I have found one solution, I can find more solutions.
For:
MeepDiameter = 7.54898 centimeter
MeepLength = 12.2364 centimeter
cAir= (29970500000 centimeter)/second
The exact solution first few modeshapes and frequencies are:
{{"TE", 1, 1, 0}, 2.32677*10^9},
{{"TE", 1, 1, 1}, 2.62937*10^9},
{{"TM", 0, 1, 0}, 3.03906*10^9},
So that TE111 has a frequency of 2.63 GHz, as @Mulletron and I compute. Therefore I don't understand why you are inputing an excitation frequency of 2.45 GHz, which does not correspond to any natural frequency, and moreover sits between two natural frequencies: TE110 (2.33 GHz) and TE111 (2.63 GHz).
Your excitation frequency of 2.45 GHz is closer to TE110 than to the mode you said you wanted to excite: TE111.
For:
MeepDiameter = 7.54898 centimeter
MeepLength = 9.65 centimeter
cAir= (29970500000 centimeter)/second
The exact solution first few modeshapes and frequencies are:
{{"TE", 1, 1, 0}, 2.32677*10^9},
{{"TE", 1, 1, 1}, 2.79737*10^9},
{{"TM", 0, 1, 0}, 3.03906*10^9},
By decreasing the cavity length, you made your excitation frequency of 2.45 GHz further away from the mode you said you wanted to excite (TE111).
For:
MeepDiameter = 7.54898 centimeter
MeepLength = 9.36 centimeter
cAir= (29970500000 centimeter)/second
The exact solution first few modeshapes and frequencies are:
{{"TE", 1, 1, 0}, 2.32677*10^9},
{{"TE", 1, 1, 1}, 2.82436*10^9},
{{"TM", 0, 1, 0}, 3.03906*10^9},
By decreasing the cavity length even further, you made your excitation frequency of 2.45 GHz even further away from the mode you said you wanted to excite (TE111).
As you decrease the length , the frequency of mode shapes TE110 and TM010 remain exactly the same (2.33 GHz and 3.04 GHz respectively) while the frequency of TE111 increases from 2.63 GHz to 2.82 GHz, so that your excitation frequency of 2.45 GHz remains at the same distance from TE110 but is further and further away from TE111 as you decrease the length.
I'm puzzled as to why you are using an excitation frequency of 2.45 GHz which does not correspond to any natural frequency of the cavity. If you want to excite TE110 you should use an excitation frequency of 2.32677 GHz (using the speed of light in air, while if you use the speed of light in vacuum it would be 2.32745 GHz). The natural frequency of mode shape TE110, 2.33 GHz, is independent of the length of the cavity.
If you want to excite mode TE111, which does depend on the cavity length, you should use an excitation frequency significantly higher, as shown above, and as indicated by @Mulletron and me. Furthermore, if you decrease the cavity length, the TE111 natural frequency increases, so you have to increase the excitation frequency to correspond to it, if you want to excite TE111, otherwise, decreasing the cavity length keeping the excitation frequency constant 2.45GHz should make it more difficult to excite TE111 (rather than easier, which is the opposite of what you wrote you were looking for).

I found this very interesting (expired) 1969 patent by Grant, owned by JOHNSON CONTROLS INTERNATIONAL, that deals with conical cavities !
http://www.google.com/patents/US3425006
It has a lot of interesting practical stuff, for example dealing with spherical ends (like in Greg Egan's solution http://gregegan.customer.netspace.net.au/SCIENCE/Cavity/Cavity.html ) instead of flat end plates (NASA Brady et.al., Shawyer(Experimental and Demo) and Prof. Juan Yang in China's EM Drives all have flat ends):
Found some time to read over this patent. It is a gold mine of good info. Great find. A couple takeaways I found is that it confirms that TE modes are highly desirable compared to TM. Also this caught my eye:
It has been found possible to predict the resonances approximately by defining a phase shift per unit length as 21r/ \g, where Ag is given by the usual formula for circular waveguides of diameter D, but where D and hence Ag vary along the cone. If this phase shift is integrated from the location of the cutoff diameter to the position of the plunger or movable end wall, resonances will be found when the integral has values of 11 pi."
Looks like math for predicting resonant modes for cones. It looks like some of the text got messed up in the character translation over to Google patents, see the bold part.

I found this very interesting (expired) 1969 patent by Grant Wolf, owned by JOHNSON CONTROLS INTERNATIONAL, that deals with conical cavities !
http://www.google.com/patents/US3425006
It has a lot of interesting practical stuff, for example dealing with spherical ends (like in Greg Egan's solution http://gregegan.customer.netspace.net.au/SCIENCE/Cavity/Cavity.html ) instead of flat end plates (NASA Brady et.al., Shawyer(Experimental and Demo) and Prof. Juan Yang in China's EM Drives all have flat ends):
Found some time to read over this patent. It is a gold mine of good info. Great find. A couple takeaways I found is that it confirms that TE modes are highly desirable compared to TM. Also this caught my eye:
It has been found possible to predict the resonances approximately by defining a phase shift per unit length as 21r/ \g, where Ag is given by the usual formula for circular waveguides of diameter D, but where D and hence Ag vary along the cone. If this phase shift is integrated from the location of the cutoff diameter to the position of the plunger or movable end wall, resonances will be found when the integral has values of 11 pi."
Looks like math for predicting resonant modes for cones. It looks like some of the text got messed up in the character translation over to Google patents, see the bold part.
Glad you agree that this 1969 patent is a gold mine for people interested in EM Drives.
Please see the attached Adobe Acrobat .pdf file of page 3 of the original patent, top of column 4, for the actual formulas and symbols
The patent states
"n * Pi" instead of "11 * Pi"
"2 * Pi / Lambda_{g} " instead of b]21r/ \g[/b]
"Lambda_{g}" instead of "Ag " where Lambda_{g} must mean the waveguide's wavelength

....
Found some time to read over this patent. It is a gold mine of good info. Great find. A couple takeaways I found is that it confirms that TE modes are highly desirable compared to TM. Also this caught my eye:
It has been found possible to predict the resonances approximately by defining a phase shift per unit length as 21r/ \g, where Ag is given by the usual formula for circular waveguides of diameter D, but where D and hence Ag vary along the cone. If this phase shift is integrated from the location of the cutoff diameter to the position of the plunger or movable end wall, resonances will be found when the integral has values of 11 pi."
Looks like math for predicting resonant modes for cones. It looks like some of the text got messed up in the character translation over to Google patents, see the bold part.
Glad you agree that this 1969 patent is a gold mine for people interested in EM Drives.
Please see the attached Adobe Acrobat .pdf file of page 3 of the original patent, top of column 4, for the actual formulas and symbols
The patent states
"n * Pi" instead of "11 * Pi"
"2 * Pi / Lambda_{g} " instead of b]21r/ \g[/b]
"Lambda_{g}" instead of "Ag " where Lambda_{g} must mean the waveguide's wavelength
I attach the Adobe Acrobat .pdf file for the whole patent
Publication number US3425006 A
Publication date Jan 28, 1969
Filing date Feb 1, 1967
Priority date Feb 1, 1967
Inventors Wolf James M
Original Assignee Johnson Service Co

I'm puzzled as to why you are using an excitation frequency of 2.45 GHz which does not correspond to any natural frequency of the cavity. If you want to excite TE110 you should use an excitation frequency of 2.32677 GHz (using the speed of light in air, while if you use the speed of light in vacuum it would be 2.32745 GHz). The natural frequency of mode shape TE110, 2.33 GHz, is independent of the length of the cavity.
It's very simple. 2.45 GHz is a given.
Cavity length and radius are the independent variables to be adjusted to establish resonance at 2.45 GHz.
And yes, I'm quite sure I want TE 1,1,1 mode.

I'm puzzled as to why you are using an excitation frequency of 2.45 GHz which does not correspond to any natural frequency of the cavity. If you want to excite TE110 you should use an excitation frequency of 2.32677 GHz (using the speed of light in air, while if you use the speed of light in vacuum it would be 2.32745 GHz). The natural frequency of mode shape TE110, 2.33 GHz, is independent of the length of the cavity.
It's very simple. 2.45 GHz is a given.
Cavity length and radius are the independent variables to be adjusted to establish resonance at 2.45 GHz.
And yes, I'm quite sure I want TE 1,1,1 mode.
If you insist in specifying the exciting frequency as 2.45GHz and the diameter of the cylindrical cavity, and having the length as the variable to be adjusted, then you are going the wrong way in reducing the length !
The inverted formula for length in terms of the other variables is simply:
length = pNr/(2 Sqrt[( fr/cMediumNr)^2  ( xbesselNr/([Pi]*diameterNr))^2])
If you specify:
diameterNr = 7.54898 centimeter
cMediumNr = cAir = (29970500000 centimeter)/second
fr = 2.45*10^9/second
and for TE111 you must have:
xbesselNr = X'_{1}_{1} = 1.84118378134065
pNr = p = 1
Then, this results in a length of
length = pNr/(2 Sqrt[( fr/cMediumNr)^2  ( xbesselNr/(\[Pi]*diameterNr))^2])
= 1 /(2 Sqrt[(2.45*10^9/second/ (29970500000 centimeter)/second)^2  (1.84118378134065/([Pi]* 7.54898 centimeter))^2])
= 19.531439054546873` centimeters
instead of 12.2364 centimeter.
Conversely, the following inputs
diameter = 7.54898 centimeter
length=19.531439054546873` centimeters
cMedium = cAir = (29970500000 centimeter)/second
give the following lowest modes and frequencies
{{"TE", 1, 1, 0}, 2.32677*10^9},
{{"TE", 1, 1, 1}, 2.45*10^9},
{{"TE", 1, 1, 2}, 2.7872*10^9},
{{"TM", 0, 1, 0}, 3.03906*10^9},
which fully verifies that length= 19.531439054546873` centimeters gives a frequency of 2.45 GHz and mode shape TE111, for a diameter = 7.54898 centimeter, in air.
But instead of inputing the correct length (for TE111) that is length=19.5314 centimeters, first you inputed the incorrect length of 12.2364 centimeter, which was much smaller than the correct length, but then proceeded to make it worse by reducing it even further to 9.36 centimeter which does not make sense. You should have input length=19.5314 centimeters to get TE111 :)
But in general, it is inadvisable to pose the problem by specifying the frequency, diameter and mode shape to calculate the length, because you are then illposing the problem. If the frequency you specify is low enough, there will be no real length solution.
The lowest frequency you can specify is
fr= (cMediumNr* xbesselNr/([Pi]*diameterNr))
which will result in an infinite length !

Isn't it possible to increase radius while leaving length at or around 12 cm? I would prefer that but can't find a radius that works with 2.45 GHz.

Isn't it possible to increase radius while leaving length at or around 12 cm? I would prefer that but can't find a radius that works with 2.45 GHz.
Yes, it's possible.
If you insist in specifying the exciting frequency as 2.45GHz and the length of the cylindrical cavity, and having the diameter as the variable to be adjusted, then
The inverted formula for diameter in terms of the other variables is, trivially:
diameter= (2 xbesselNr)/([Pi] Sqrt[4 (fr/cMediumNr)^2  (pNr/lengthNr)^2])
If you specify:
lengthNr = 12 centimeter (Please notice you asked 12 cm instead of the previous 12.2364 cm)
cMediumNr = cAir = (29970500000 centimeter)/second
fr = 2.45*10^9/second
and for TE111 you must have:
xbesselNr = X'_{1}_{1} = 1.84118378134065
pNr = p = 1
Then, this results in a diameter of
length =(2 xbesselNr)/([Pi] Sqrt[4 (fr/cMediumNr)^2  (pNr/lengthNr)^2])
= (2 1.84118378134065)/([Pi] Sqrt[4 (2.45*10^9/second/29970500000 centimeter)/second)^2  (1/(12 centimeter))^2])
= 8.332965999678832` centimeters
instead of the diameter=7.54898 centimeter you used.
Conversely, the following inputs
diameter = 8.332965999678832` centimeter
length=12 centimeters
cMedium = cAir = (29970500000 centimeter)/second
give the following lowest modes and frequencies
{{"TE", 1, 1, 0}, 2.10786*10^9},
{{"TE", 1, 1, 1}, 2.45*10^9},
{{"TM", 0, 1, 0}, 2.75314*10^9},
{{"TM", 0, 1, 1}, 3.02311*10^9},
which fully verifies that diameter = 8.332965999678832` centimeter gives a frequency of 2.45 GHz and mode shape TE111, for a length=12 centimeters, in air.
quod erat demonstrandum :)
But in general, it is inadvisable to pose the problem by specifying the frequency, length and mode shape to calculate the diameter, because you are then illposing the problem. If the frequency you specify is low enough, there will be no real diameter solution.
The lowest frequency (for a specified length) you can specify is
fr= cMediumNr*(pNr/lengthNr) /2
which will result in an infinite diameter!
We have now looked at this three different ways, and all these ways show that you inputed the incorrect parameters to best excite a TE111 natural frequency.

If you specify:
lengthNr = 12.23642686` centimeter
cMediumNr = cAir = (29970500000 centimeter)/second
fr = 2.45*10^9/second
and for TE111 you must have:
xbesselNr = X'11 = 1.84118378134065
pNr = p = 1
Then, this results in a diameter of 8.277559638179381` centimeter;
Conversely, the following inputs
diameter = 8.277559638179381` centimeter
length=12.23642686` centimeters
cMedium = cAir = (29970500000 centimeter)/second
give the following lowest modes and frequencies
{{"TE", 1, 1, 0}, 2.12197*10^9},
{{"TE", 1, 1, 1}, 2.45*10^9},
{{"TM", 0, 1, 0}, 2.77157*10^9},
{{"TM", 0, 1, 1}, 3.03007*10^9},
quod erat demonstrandum :)

Well according the above posts and others, http://forum.nasaspaceflight.com/index.php?topic=36313.msg1320981#msg1320981 we're all getting pretty adept at using our skills/resources for calculating resonant modes of cylinders, which is a good first step. Well I'm learning new skills as I go along. So I can do cylinders all day, cones...not so much..yet. I certainly didn't come to the table knowing how to calculate resonant modes of anything 56 months ago.
I'm trying to figure out how to use the (2 * Pi ) / (Lambda * g) expression from the patent or the Volumetric Mean approach (which is better?) toward calculating resonant modes of conical frustums. I think the holy grail would be a quick and easy correction to convert from cylinder solutions to conical frustums.
So the (2 * Pi ) / (Lambda * g) above, does that mean what when I take 6.28 and divide that by x wavelength, and get a multiple of pi, that diameter or can support a resonant mode?
Trying to figure out how to convert this cylinder to a cone, by keeping the diameter as the small diameter, adjusting the length to arrive at the new large diameter along a 45 or 90 degree cone, and still maintain resonance @ 2.45ghz TE111:
2.45ghz, TE111
L=0.1224489m
D=0.08278945m

Well according the above posts and others, http://forum.nasaspaceflight.com/index.php?topic=36313.msg1320981#msg1320981 we're all getting pretty adept at using our skills/resources for calculating resonant modes of cylinders, which is a good first step. Well I'm learning new skills as I go along. So I can do cylinders all day, cones...not so much..yet. I certainly didn't come to the table knowing how to calculate resonant modes of anything 56 months ago.
I'm trying to figure out how to use the (2 * Pi ) / (Lambda_{g} ) expression from the patent or the Volumetric Mean approach (which is better?) toward calculating resonant modes of conical frustums. I think the holy grail would be a quick and easy correction to convert from cylinder solutions to conical frustums.
So the (2 * Pi ) / (Lambda_{g} ) above, does that mean what when I take 6.28 and divide that by x wavelength, and get a multiple of pi, that diameter or can support a resonant mode?
Trying to figure out how to convert this cylinder to a cone, by keeping the diameter as the small diameter, adjusting the length to arrive at the new large diameter along a 45 or 90 degree cone, and still maintain resonance @ 2.45ghz TE111:
2.45ghz, TE111
L=0.1224489m
D=0.08278945m
Regarding the Edit of http://forum.nasaspaceflight.com/index.php?topic=36313.msg1320981#msg1320981, glad :) that we also agree that the diameter should be 8.28 centimeters for that length and TE111 frequency.
As to the comparison between the longitudinal integration (of D and lambda_{g} expressed as a function of the lengthwise coordinate of the cone) as suggested by Wolf's 1969 patent in comparison with the Volumetric Mean approach I have to run the calculations when I get a chance. But I first observe that the patent's author (Wolf) admits that the suggested approach is unable to obtain any TM mode that is constant in the length direction: TMmn0 , (notice that he uses indices lmn instead of mnp). I have some reservations that this integration approach offers any benefit over the Volumetric Mean approach but I will keep an open mind until I get a chance to compare. [Note: I corrected my nomenclature to lambda_{g} to better show that lambda_{g} means the cylindricalwaveguide's wavelength]
Meanwhile, I would particularly appreciate @NotSoSureOfIt 's comments regarding Wolf's suggestion on how to calculate the resonances of a truncated cone cavity (lines 60 to 75 of column 3 and lines 1 to 11 of column 4) of the US patent #3,425,006 (which I attach below as an Adobe Acrobat .pdf document).
Publication number US3425006 A
Publication date Jan 28, 1969
Filing date Feb 1, 1967
Priority date Feb 1, 1967
Inventors Wolf James M
Original Assignee Johnson Service Co

..
So the (2 * Pi ) / (Lambda_{g}) above, does that mean what when I take 6.28 and divide that by x wavelength, and get a multiple of pi, that diameter or can support a resonant mode?
...
Not precisely. Instead the patent's author (Wolf) means that resonance occurs when the definite Integral of (2 Pi / lambda_{g}) taken along the lengthwise coordinate of the cone is an integer multiple of Pi (where the cylindricalwaveguide's wavelength lambda_{g} and diameter D are expressed as functions of the lengthwise cone coordinate, under the integral sign).
Since Pi is a constant under the integral, it seems to me that it is simpler to express this as follows: resonance occurs when the definite Integral of (2 / lambda_{g}) taken along the lengthwise coordinate of the cone is an integer multiple of unity: 1, 2, 3, 4, 5, ....(where the cylindricalwaveguide's wavelength lambda_{g} and diameter D are expressed as functions of the lengthwise cone coordinate, under the integral sign).

Isn't it possible to increase radius while leaving length at or around 12 cm? I would prefer that but can't find a radius that works...
That's another reason why to compare a numerical solution (by Finite Difference, Finite Element or any other numerical method that relies on a mesh to obtain results) to an exact solution, you should first pick dimensions, discretize the problem to a fine mesh to ensure convergence (this is what takes most of the person's time in a numerical solution) and if necessary, explore different exciting frequencies (keeping dimensions constant, instead of keeping the same excitation frequency and changing dimensions, which means changing the mesh). For example using the exciting frequency of 2.63GHz for TE111 (for MeepDiameter = 7.54898 centimeter, MeepLength = 12.2364 centimeter) as obtained by @Mulletron and me.
To insist on a fixed excitation frequency for a given mode (like TE111) means that you will have to change dimensions (and hence discretize with a mesh again with the correct dimension that is associated with a natural frequency) if there are no natural frequencies for the frequency you are insisting on, and this only if there is a finite dimension for the frequency you are insisting to get (see previous posts for minimum natural frequency for a given diameter or a given length).

...
What did you use for the bandwidth source around the frequency of interest (Drive frequency 2.45 E+9 Hz)?
Could you try running all these cases again, everything the same as before except with a significantly narrower bandwidth source around the frequency of interest ? . Reportedly harminv does a better job the narrower the source is around the frequency of interest .
Ok, I did run it again with bandwidth = 0.2 * Drive frequency, for cases up to resolution of 80, but I didn't get anything. Once I narrow the bandwidth to exclude the resonant frequency at 1.87 GHz, there are no resonances within the bandwidth.
Harminv does work better at identifying the resonant frequency with narrower bandwidth, when the frequency is within the bandwidth. I set the drive frequency to 1.873 GHz, narrowed the bandwidth to 0.07 * frequency and got this:
frequency Quality factor error
1,873,339,229.3075 Hz 18,325,307.0778158 1.673972608680621e7+0.0i
....
A bandwidth of 0.2 * Drive frequency is way too large for the cases you are trying to match. Look at my message http://forum.nasaspaceflight.com/index.php?topic=36313.msg1322181#msg1322181 for example.
The exact solutions for the lowest modes with those cavity dimensions are:
{{"TE", 1, 1, 0}, 2.12197*10^9},
{{"TE", 1, 1, 1}, 2.45*10^9},
{{"TM", 0, 1, 0}, 2.77157*10^9},
{{"TM", 0, 1, 1}, 3.03007*10^9},
Therefore the bandwidth between {{"TE", 1, 1, 1}, 2.45*10^9} and {{"TM", 0, 1, 0}, 2.77157*10^9} is
( 2.77157*10^9  2.45*10^9) / 2.45*10^9 = 0.13
hence the bandwidth separating those modes is 0.13 * Drive frequency which is much smaller than the bandwith of 0.2 * Drive frequency you first used (with Drive frequency = 2.45*10^9).
This means that you should first calculate the exact natural frequencies around the frequency you are interested in, and therefore the bandwidth between them. After that input in Meep an even smaller bandwidth for the excitation frequency (as shown in the above example) :). In this case it means that you should input in Meep a bandwidth smaller than 0.13 * Drive frequency

Ok, I'll try that.
I did correct my analytical formula spread sheet while verifying your formula, and now my analytical formula calculations agree with yours in all respects.
Still need agreement from meep/Harminv however.

Meanwhile, I would particularly appreciate @NotSoSureOfIt 's comments regarding Wolf's suggestion on how to calculate the resonances of a truncated cone cavity (lines 60 to 75 of column 3 and lines 1 to 11 of column 4) of the US patent #3,425,006 (which I attach below as an Adobe Acrobat .pdf document).
Publication number US3425006 A
Publication date Jan 28, 1969
Filing date Feb 1, 1967
Priority date Feb 1, 1967
Inventors Wolf James M
Original Assignee Johnson Service Co
Mmmm.. That's the argument that I used to come up w/ "volumetric". Been otherwise occupied, but I'll take a look at it as time permits.
Edit: Lessee, that's the "guide" wavelength, for equal phase planes.
Basically, you want to solve for the k[sub z] w/ R as a function of z.
like k[sub z]^2 = (omega/c)^2 (X[sub m,n]/R[fn z])^2 or X'

Meanwhile, I would particularly appreciate @NotSoSureOfIt 's comments regarding Wolf's suggestion on how to calculate the resonances of a truncated cone cavity (lines 60 to 75 of column 3 and lines 1 to 11 of column 4) of the US patent #3,425,006 (which I attach below as an Adobe Acrobat .pdf document).
Publication number US3425006 A
Publication date Jan 28, 1969
Filing date Feb 1, 1967
Priority date Feb 1, 1967
Inventors Wolf James M
Original Assignee Johnson Service Co
Mmmm.. That's the argument that I used to come up w/ "volumetric". Been otherwise occupied, but I'll take a look at it as time permits.
Edit: Lessee, that's the "guide" wavelength, for equal phase planes.
Basically, you want to solve for the k[sub z] w/ R as a function of z.
like k[sub z]^2 = (omega/c)^2 (X[sub m,n]/R[fn z])^2 or X'
Yes, thank you for looking at it, and formulating the eigenvalue problem :).
I get an interesting closedform expression containing an ArcTan term for that integration, so, it looks like it should give different results than the cylindrical cavity formula based on any mean diameter measure like the Mean, Geometric Mean or the Volumetric Mean. I will double check my closedform integration and run some numbers when I have time available, to see what difference it makes.
It is interesting that the patent's author (Wolf) did not actually give the resulting closedform integral but he just hinted at how to solve the eigenvalue problem for the cone :).

;D
Well inventors often try to deliberately hide stuff in their schematics. Even Leonardo Da Vinchi did (His tank and Orinthopter thing for example) And of course the alchemists and later chemists did. There is an ancient time honored tradition of trying to screw your would be successors and possible competitors over by booby trapping your paper records.

https://en.wikipedia.org/wiki/Ornithopter
(http://media.web.britannica.com/ebmedia/40/96240004A9CAD60A.jpg)
(https://upload.wikimedia.org/wikipedia/commons/4/41/Skybird.gif)

******EDIT: This study does not take into account the cutoff frequency condition that eliminates several of these mode shapes. A new study incorporating the cutoff frequency will be posted *****
MODE SHAPE STUDY of NASA Brady et.al.'s EXPERIMENTS according to different assumed GEOMETRIES
1) We conduct a thorough study of the modeshapes of the experiments in NASA Brady et.al.'s " Anomalous Thrust Production ..." report (http://www.libertariannews.org/wpcontent/uploads/2014/07/AnomalousThrustProductionFromanRFTestDeviceBradyEtAl.pdf) , taking into account @Mulletron's assumed geometry as well as the extra experiment conducted at 2168 Mhz.
2) The experimental data can be found in p .18, Table 2. Tapered Cavity Testing : Summary of Results and in the section on p .18, F.Tapered Cavity RF Evaluation, General Findings and Lessons Learned; of (http://www.libertariannews.org/wpcontent/uploads/2014/07/AnomalousThrustProductionFromanRFTestDeviceBradyEtAl.pdf )
3) We define the Volumetric Mean as follows:
VolumetricMeanDiameter=Sqrt[(SmallDiameter^2+SmallDiameter*BigDiameter+BigDiameter^2)/3]
For a derivation of the Volumetric Mean (equating the volume of an equivalent cylinder to the volume of a truncated cone): See http://forum.nasaspaceflight.com/index.php?topic=36313.msg1319655#msg1319655
4) Let's define as "Mulletron geometry" the following definition for the NASA Brady et. al. cavity:
Mulletron Best estimate as of 11/9/2014
http://forum.nasaspaceflight.com/index.php?topic=36313.msg1320903#msg1320903
cavityLength = 0.27637 m
bigDiameter = 0.30098 m
smallDiameter = 0.15875 m
then
VolumetricMeanDiameter=Sqrt[(SmallDiameter^2+SmallDiameter*BigDiameter+BigDiameter^2)/3]
= 0.2335031034055008` meter
5) Let's define as "Aero geometry" the following definition for the NASA Brady et. al. cavity:
Aero Best estimate as of 11/9/2014 http://forum.nasaspaceflight.com/index.php?topic=29276.msg1285896#msg1285896
cavityLength = 0.24173 m
bigDiameter = 0.27246 m
smallDiameter = 0.15875 m
then
VolumetricMeanDiameter=Sqrt[(SmallDiameter^2+SmallDiameter*BigDiameter+BigDiameter^2)/3]
= 0.21808946107809366` meter
6) Let's define as "Fornaro geometry" the following definition for the NASA Brady et. al. cavity:
Fornaro estimate http://forum.nasaspaceflight.com/index.php?topic=36313.msg1302455#msg1302455
cavityLength = 0.332 m
bigDiameter = 0.397 m
smallDiameter = 0.244 m
then
VolumetricMeanDiameter= Sqrt[(SmallDiameter^2+SmallDiameter*BigDiameter+BigDiameter^2)/3]
= 0.32352897860933574` centimeter
7) These are the experimentally reported frequencies and the COMSOLcalculated mode shapes:
frequencyBradyA = 1.9326*10^9 1/second; TM211
frequencyBradyB = 1.9367*10^9 1/second; TM211
frequencyBradyC = 1.8804*10^9 1/second; TE012
frequencyBradyD = 2.168*10^9 1/second; TE012
Notice the contradiction in NASA's report: mode shape TE012 at 1.88GHz, mode shape TM211 at a higher frequency 1.93 GHz and mode shape TE012 again at an even higher frequency 2.17 GHz (? ). This is impossible. Our interpretation is that NASA Brady et.al.'s made a typo and they meant to write TM211 (or another mode) for frequencyBradyD = 2.168*10^9 .
8) Given the the geometrical dimensions (using the previously defined Volumetric Mean Diameter), and the value of speed of light in air, we use the frequency equation (see: http://en.wikipedia.org/wiki/Microwave_cavity#Cylindrical_cavity ) to calculate frequencies as a function of the mode shape quantum numbers: circumferential (m), radial (n), and longitudinal (p). Mode shapes are reported as TXmnp where "X" can stand for E= electric transverse mode or M= magnetic transverse mode.
9) Then I obtain the following mode for the three different assumed geometries:
Mulletron Geometry
{{"TE", 1, 1, 0}, 7.52226*10^8},
{{"TE", 1, 1, 1}, 9.27278*10^8},
{{"TM", 0, 1, 0}, 9.82506*10^8},
{{"TM", 0, 1, 1}, 1.12219*10^9},
{{"TE", 2, 1, 0}, 1.24783*10^9},
{{"TE", 1, 1, 2}, 1.31979*10^9},
{{"TE", 2, 1, 1}, 1.36054*10^9},
{{"TM", 0, 1, 2}, 1.46332*10^9},
{{"TM", 1, 1, 0}, 1.56547*10^9},
{{"TE", 0, 1, 0}, 1.56547*10^9},
{{"TE", 2, 1, 2}, 1.6532*10^9},
{{"TM", 1, 1, 1}, 1.65671*10^9},
{{"TE", 0, 1, 1}, 1.65671*10^9},
{{"TE", 3, 1, 0}, 1.71642*10^9},
{{"TE", 1, 1, 3}, 1.79216*10^9},
{{"TE", 3, 1, 1}, 1.80003*10^9},
{{"TM", 0, 1, 3}, 1.90034*10^9},
{{"TM", 1, 1, 2}, 1.90438*10^9},
{{"TE", 0, 1, 2}, 1.90438*10^9},
{{"TE", 3, 1, 2}, 2.03029*10^9},
{{"TE", 2, 1, 3}, 2.05014*10^9},
{{"TM", 2, 1, 0},2.09819*10^9},
{{"TM", 2, 1, 1}, 2.16712*10^9},
{{"TE", 4, 1, 0}, 2.17252*10^9},
Mode shapes bracketing NASAreported frequencies:
frequencyBradyA = 1.9326*10^9 1/second;
{{"TE", 0, 1, 2}, 1.9043845840829124`*^9}; {{"TM", 1, 1, 2}, 1.9043845840829124`*^9};
{{"TE", 3, 1, 2}, 2.0302945503765867`*^9};
frequencyBradyB = 1.9367*10^9 1/second;
{{"TE", 0, 1, 2}, 1.9043845840829124`*^9}; {{"TM", 1, 1, 2}, 1.9043845840829124`*^9};
{{"TE", 3, 1, 2}, 2.0302945503765867`*^9};
frequencyBradyC = 1.8804*10^9 1/second;
{{"TE", 3, 1, 1}, 1.8000272999857957`*^9};
{{"TM", 0, 1, 3}, 1.9003447870125527`*^9};
frequencyBradyD = 2.168*10^9 1/second;
{{"TM", 2, 1, 1}, 2.167116717351836`*^9};
{{"TE", 4, 1, 0}, 2.17251756371995`*^9};
Frequencies of NASAreported mode shapes:
{{"TE", 0, 1, 2}, 1.9043845840829124`*^9}
{{"TM", 2, 1, 1}, 2.167116717351836`*^9}
Aero geometry
{{"TE", 1, 1, 0}, 8.05391*10^8},
{{"TE", 1, 1, 1}, 1.01634*10^9},
{{"TM", 0, 1, 0}, 1.05194*10^9},
{{"TM", 0, 1, 1}, 1.22102*10^9},
{{"TE", 2, 1, 0}, 1.33602*10^9},
{{"TE", 2, 1, 1}, 1.47283*10^9},
{{"TE", 1, 1, 2}, 1.47846*10^9},
{{"TM", 0, 1, 2}, 1.62597*10^9},
{{"TM", 1, 1, 0}, 1.67611*10^9},
{{"TE", 0, 1, 0}, 1.67611*10^9},
{{"TM", 1, 1, 1}, 1.78707*10^9},
{{"TE", 0, 1, 1}, 1.78707*10^9},
{{"TE", 2, 1, 2}, 1.82267*10^9},
{{"TE", 3, 1, 0}, 1.83773*10^9},
{{"TE", 3, 1, 1}, 1.93947*10^9},
{{"TE", 1, 1, 3}, 2.02665*10^9},
{{"TM", 1, 1, 2}, 2.08483*10^9},
{{"TE", 0, 1, 2}, 2.08483*10^9},
{{"TM", 0, 1, 3}, 2.13665*10^9},
{{"TE", 3, 1, 2}, 2.21685*10^9}
Mode shapes bracketing NASAreported frequencies:
frequencyBradyA = 1.9326*10^9 1/second;
{{"TE", 3, 1, 0}, 1.8377297671354957`*^9};
{{"TE", 3, 1, 1}, 1.9394709580599272`*^9};
frequencyBradyB = 1.9367*10^9 1/second;
{{"TE", 3, 1, 0}, 1.8377297671354957`*^9};
{{"TE", 3, 1, 1}, 1.9394709580599272`*^9};
frequencyBradyC = 1.8804*10^9 1/second;
{{"TE", 3, 1, 0}, 1.8377297671354957`*^9};
{{"TE", 3, 1, 1}, 1.9394709580599272`*^9};
frequencyBradyD = 2.168*10^9 1/second;
{{"TM", 0, 1, 3}, 2.136646973612425`*^9};
{{"TE", 3, 1, 2}, 2.216853242229605`*^9};
Frequencies of NASAreported mode shapes:
{{"TE", 0, 1, 2}, 2.0848310776817226`*^9};
{{"TM", 2, 1, 1}, 2.330443792149791`*^9}
Fornaro geometry
{{"TE", 1, 1, 0}, 5.4291*10^8},
{{"TE", 1, 1, 1}, 7.06031*10^8},
{{"TM", 0, 1, 0}, 7.09111*10^8},
{{"TM", 0, 1, 1}, 8.40576*10^8},
{{"TE", 2, 1, 0}, 9.00604*10^8},
{{"TE", 2, 1, 1}, 1.00738*10^9},
{{"TE", 1, 1, 2}, 1.05341*10^9},
{{"TM", 1, 1, 0}, 1.12986*10^9},
{{"TE", 0, 1, 0}, 1.12986*10^9},
{{"TM", 0, 1, 2}, 1.14793*10^9},
{{"TM", 1, 1, 1}, 1.21668*10^9},
{{"TE", 0, 1, 1}, 1.21668*10^9},
{{"TE", 3, 1, 0}, 1.23881*10^9},
{{"TE", 2, 1, 2}, 1.27515*10^9},
{{"TE", 3, 1, 1}, 1.31847*10^9},
{{"TM", 1, 1, 2}, 1.4462*10^9},
{{"TE", 0, 1, 2}, 1.4462*10^9},
{{"TE", 1, 1, 3}, 1.45887*10^9},
{{"TM", 2, 1, 0}, 1.51434*10^9},
{{"TM", 0, 1, 3}, 1.52853*10^9},
{{"TE", 3, 1, 2}, 1.53283*10^9},
{{"TE", 4, 1, 0}, 1.56799*10^9},
{{"TE", 1, 2, 0}, 1.57208*10^9},
{{"TM", 2, 1, 1}, 1.58018*10^9},
{{"TE", 2, 1, 3}, 1.62624*10^9},
{{"TM", 0, 2, 0}, 1.62771*10^9},
{{"TE", 4, 1, 1}, 1.63166*10^9},
{{"TE", 1, 2, 1}, 1.6356*10^9},
{{"TM", 0, 2, 1}, 1.68913*10^9},
{{"TM", 2, 1, 2}, 1.76299*10^9},
{{"TM", 1, 1, 3}, 1.76356*10^9},
{{"TE", 0, 1, 3}, 1.76356*10^9},
{{"TE", 4, 1, 2}, 1.80928*10^9},
{{"TE", 1, 2, 2}, 1.81283*10^9},
{{"TE", 3, 1, 3}, 1.83526*10^9},
{{"TM", 0, 2, 2}, 1.86127*10^9},
{{"TM", 3, 1, 0}, 1.88132*10^9},
{{"TE", 1, 1, 4}, 1.88531*10^9},
{{"TE", 5, 1, 0}, 1.89177*10^9},
{{"TM", 3, 1, 1}, 1.93471*10^9},
{{"TM", 0, 1, 4}, 1.93972*10^9},
{{"TE", 5, 1, 1}, 1.94487*10^9},
{{"TE", 2, 2, 0}, 1.97744*10^9},
{{"TE", 2, 1, 4}, 2.01761*10^9},
{{"TE", 2, 2, 1}, 2.0283*10^9},
{{"TM", 2, 1, 3}, 2.03145*10^9},
{{"TM", 1, 2, 0}, 2.06869*10^9},
{{"TE", 0, 2, 0}, 2.06869*10^9},
{{"TE", 4, 1, 3}, 2.07175*10^9},
{{"TE", 1, 2, 3}, 2.07485*10^9},
{{"TM", 3, 1, 2}, 2.08669*10^9},
{{"TE", 5, 1, 2}, 2.09612*10^9},
{{"TM", 0, 2, 3}, 2.11731*10^9},
{{"TM", 1, 2, 1}, 2.11736*10^9},
{{"TE", 0, 2, 1}, 2.11736*10^9},
{{"TM", 1, 1, 4}, 2.12984*10^9},
{{"TE", 0, 1, 4}, 2.12984*10^9},
{{"TE", 2, 2, 2}, 2.17375*10^9},
Mode shapes bracketing NASAreported frequencies:
frequencyBradyA = 1.9326*10^9 1/second;
{{"TE", 5, 1, 0}, 1.891774278367002`*^9};
{{"TM", 3, 1, 1}, 1.9347074025015635`*^9};
frequencyBradyB = 1.9367*10^9 1/second;
{{"TM", 3, 1, 1}, 1.9347074025015635`*^9};
{{"TM", 0, 1, 4}, 1.9397152624956703`*^9};
frequencyBradyC = 1.8804*10^9 1/second;
{{"TM", 0, 2, 2}, 1.8612746091297557`*^9};
{{"TM", 3, 1, 0}, 1.8813198077493927`*^9};
frequencyBradyD = 2.168*10^9 1/second;
{{"TE", 0, 1, 4}, 2.129842918761221`*^9};
{{"TE", 2, 2, 2}, 2.173747734247802`*^9};
Frequencies of NASAreported mode shapes:
{{"TE", 0, 1, 2}, 1.4461980111408324`*^9}
{{"TM", 2, 1, 1}, 1.5801773963619902`*^9}
CONCLUSIONS
1)The "Fornaro Assumed Geometry" gives:
1a) frequencies of NASAreported mode shapes:
{{"TE", 0, 1, 2}, 1.4461980111408324`*^9}
{{"TM", 2, 1, 1}, 1.5801773963619902`*^9}
that are much lower (25%) than the tested frequencies. If one takes into account that the NASA's experiments were conducted with a dielectric, whose inclusion will lower the natural frequency, it is clear that NASA's truncated cone cavity must have had dimensions significantly smaller than assumed by Fornaro.
1b) The mode shapes obtained under the Fornaro geometrical assumptions have the incorrect transverse field: Transverse Magnetic modes for the experiments that resulted in measured thrust (Brady a, b and c) and Transverse Electric mode for the experiment that resulted in no measured thrust (Brady d). A correct geometry should result in the opposite: TE modes for Brady a, b and c and TM mode for Brady d. It is clear then that NASA's truncated cone could not have Fornaro's assumed geometry.
1c) The Fornaro geometry has so many natural frequencies in the experimental range, so close to each other, that it would have been extremely difficult to tune the EM Drive to a particular frequency. What we learn from this is that if one wants to drive EM Drives with these natural frequencies and mode shapes, EM Drives should be small enough (smaller than Fornaro's dimensions) so that natural frequencies are apart enough from each other that the EM Drive can be tuned if one wants to excite some of these frequencies. To achieve the thrust required for crewed space missions would then require a large number of small EM Drives, rather than a large single EM Drive as pictured in some of Shawyer's concepts or in Aether Drives in steampunk.
One could aim to excite the lowest natural frequency: TE110 with a large EM Drive, which for Fornaro's geometry means 0.54291 GHz (less than 1/3 the frequencies tested at NASA by Brady et.al.), but I don't think that this mode TE110 (see picture below) is likely to produce significant thrust according to any theories that claim coupling with external fields (like the Quantum Vacuum, etc.)
2) The "Mulletron assumed geometry":
2a) achieves an outstanding fit by very closely predicting the frequency of 2.168 GHz for Brady's experiment "d", mentioned in the section on p .18, F.Tapered Cavity RF Evaluation, General Findings and Lessons Learned; of (http://www.libertariannews.org/wpcontent/uploads/2014/07/AnomalousThrustProductionFromanRFTestDeviceBradyEtAl.pdf ). This is a very important fit, since it is the only experiment that which we are sure was conducted without a dielectric, and hence it should be best modeled by the exact solution:
frequencyBradyD = 2.168*10^9 1/second;
{{"TM", 2, 1, 1}, 2.167116717351836`*^9};
2b) it predicts that the mode shape should be TM211, which is a Transverse Magnetic mode. Brady et.al reported no thrust measurement at this frequency. Our explanation is that this may have been due to the fact that Transverse Electric modes are required for thrust measurements (either as an artifact due to heating of the ends by heat induction or as a legitimate propulsion for example by coupling with the Quantum Vacuum). Hence Transverse Magnetic modes should result in no thrust, which agrees with the experimental results.
Brady et.al. write:
We performed some very early evaluations without the dielectric resonator (TE012 mode at 2168 MHz, with power levels up to ~30 watts) and measured no significant net thrust.
Brady et.al. report mode shape TE012 for this frequeny. The assumption that the mode shape was TE012 may be an error in the report, because their Table 2. Tapered Cavity Testing: Summary of Results, clearly shows the mode shape TE012 occurring at a lower frequency than TM211, so it doesn't make any sense for Brady et.al. to write that the mode shape TE012 can occur both below and above TM211. We think that they may have intended to write "TM211 mode at 2168 MHz" which would be in agreement with Mulletron's geometry.
2c) it predicts mode shape TE012 for the frequencies of NASA Brady et.al.'s experiments a and b:
frequencyBradyA = 1.9326*10^9 1/second;
{{"TE", 0, 1, 2}, 1.9043845840829124`*^9};
frequencyBradyB = 1.9367*10^9 1/second;
{{"TE", 0, 1, 2}, 1.9043845840829124`*^9};
Brady et.al. report mode shape TM211 for these frequencies, based on their numerical calculations using the Finite Element code COMSOL. However the data on their Figure 16. "Predicted and Actual S21 plots" shows that their COMSOL numerical calculations are substantially in error (probably due to an unconverged, insufficiently fine finiteelement mesh), particularly at this frequency range in question: 1.9 GHz. It makes most sense that the actual mode shape was TE012, rather than a magnetic mode (TM211) for the previously discussed reasons.
2d) it has a problem for Brady et.al.'s experiment c, where it predicts mode shape TM013, with mode shape TE311 giving a lower frequency:
frequencyBradyC = 1.8804*10^9 1/second;
{{"TE", 3, 1, 1}, 1.8000272999857957`*^9};
{{"TM", 0, 1, 3}, 1.9003447870125527`*^9};
NASA's Brady et.al. reported mode shape TE012 for this frequency, which makes more sense because this is NASA's experiment that resulted in the highest thrust/PowerInput. It is possible that the discrepancy is that the exact solution we are using does not include the effect of the dielectric. Mulletron's geometry predicts a frequency of 1.90 GHz for mode shape TE012 without the dielectric:
{{"TE", 0, 1, 2}, 1.9043845840829124`*^9}
It is very possible that the dielectric lowers the frequency and that the actual mode shape for Brady et.al.'s experiment c at 1.8804 GHz was TE012 (or actually TE013: two halfwave patterns in the empty section of the cavity in the longitudinal direction, like TE012, and another extra halfwave in the dielectric).
3) The "Aero assumed geometry":
3a) The strength of Aero's assumed geometry is that it is the only assumed geometry that very consistently predicts mode shape TE (transverse electric) modes for the Brady et.al. experiments that measured thrust: (experiments a, b and c), while predicting mode shape TM (transverse magnetic) for the Brady experiment that measured no thrust: Brady et.al. experiment d:
Mode shapes bracketing NASAreported frequencies:
frequencyBradyA = 1.9326*10^9 1/second;
{{"TE", 3, 1, 1}, 1.9394709580599272`*^9};
frequencyBradyB = 1.9367*10^9 1/second;
{{"TE", 3, 1, 1}, 1.9394709580599272`*^9};
frequencyBradyC = 1.8804*10^9 1/second;
{{"TE", 3, 1, 0}, 1.8377297671354957`*^9};
frequencyBradyD = 2.168*10^9 1/second;
{{"TM", 0, 1, 3}, 2.136646973612425`*^9};
3b) The presence of a dielectric inside the cavity may have resulted lowering the frequency predicted for mode shape TE012 from 2.08GHz to 1.88 GHz:
Frequencies of NASAreported mode shapes:
{{"TE", 0, 1, 2}, 2.0848310776817226`*^9};
{{"TM", 2, 1, 1}, 2.330443792149791`*^9}
4) It is clear that the actual geometry of NASA's Brady et.al. experiments was smaller than as predicted by Fornaro's assumptions. Based on the evidence discussed above, the geometry was close to Mulletron's and Aero's assumed geometry, with Mulletron's geometry having an edge for the abovediscussed reasons.
Images of modes TE01p, TM21p, and TE11p (where p can be any p=0,1,2,3,...):
electric field ________________ solid lines
magnetic field              dashed lines

Very interesting.
Here's another little wrinkle you can play with.
Define x = r/R where
r is the small diameter of the cone,
and R is the big diameter of the cone.
Then let Rcy equal the diameter of the cylindrical cavity. I get
f(x) = (x^2+x+1)
R = sqrt(Rcy^2 /f(x)/3)
Of course the formula can be inverted to solve for Rcy.
For my geometry, (aero geometry) I get x = 0.5826543346
For Mulletron geometry, x = 0.527443684
and for Fornaro geometry, x = 0.6146095718
This is not quite the formula that we need (check it before using), we need something that relates L / Rcy, I think, because I read somewhere that cylindrical cavities won't resonate when L/Rcy < ~ 2.02. It has to do with cutoff frequency as I recall.

Isn't it possible to increase radius while leaving length at or around 12 cm? I would prefer that but can't find a radius that works with 2.45 GHz.
Yes, it's possible.
If you insist in specifying the exciting frequency as 2.45GHz and the length (12 cm) of the cylindrical cavity, and having the diameter as the variable to be adjusted, then
....
= 8.332965999678832` centimeters
instead of the diameter=7.54898 centimeter you used.
@Aero, is the reason why you insist in keeping a frequency of 2.45GHz in your modeling because you are looking at making a small EM Drive using a kitchen's microwave's magnetron as the source (which are nominally rated to operate at ~ 2.45 GHz) ?
(http://jlnlabs.online.fr/plasma/images/2M253A.gif)

@Aero, is the reason why you insist in keeping a frequency of 2.45GHz in your modeling because you are looking at making a small EM Drive using a kitchen's microwave's magnetron as the source (which are nominally ~ 2.45 GHz) ?
I certainly won't, but look around. Magnetron technology advances but there are orders of magnitude more magnetrons made for the kitchen microwave than for anything else. That means research and technology advance will and does focus on the 2.45 GHz operating point. Even now there exists all digital 1000W, 2.45 GHz microwave power generators on the market. A little pricy at $39.95 each in lots of 10,000 but price/lot size will come down. The web link, which I don't have available at the moment, indicated that they are pretty slick little devices, digitally tunable, sized for microwave application and long lived.
We are researching EM thruster theory. Its not to early to think about the price point for the manufacture of these devices. Yes, after a few 100 or few 1000 are made and work, then research money will start to flow into the development of the microwave generators at whatever frequency. Until then, as the Chinese experiments illustrate, 2.45 GHz is the most convenient frequency to use for research.

IRT the last couple posts, the unlicensed ISM band is more approachable for enthusiasts. I want folks like us to explore this proposition that we can achieve all electric thrust in the vacuum of space without propellant. I'm awaiting word from our academic institutions and NASA about what is really going on here, but that word may not come. Part of my mission on here, besides hopefully bringing attention to the underlying research which could support this (Tiggelen et al), and trying to figure this out myself with the help of my fellow posters, is also to inspire builders to take up experimentation by providing as much research and backup as possible. At the end, I want this thread (or the derivative of) to mature from "advanced concepts" to proven flight ready in my lifetime. There is NO way humanity is going to be stuck on this planet forever.
I in particular am trying fervently to find a solution for an unloaded conical frustum geometry resonant at 2437mhz at TE111 to start with. 2450mhz is a good start. From there you can perturb the cavity down to 2437mhz at will (mostly trial and error). I am still unsure if angle by the apex is truly important for resonance, but according to Egan, it is: http://www.gregegan.net/SCIENCE/Cavity/Cavity.html But if my hunch about the importance of the QV to spacetime is correct (pretty much has to be), 45 and 90 degrees by the apex is important. Since there appears to not be a ready made solution for this available to me in the world (short of simulating it like buying COMSOL and learning it, or hints from that patent), I(we) have to figure it out, somehow.
So in short. I want to crowdsource this problem. We need help! We all sink or swim together, as they say.

....
I in particular am trying fervently to find a solution for an unloaded conical frustum geometry resonant at 2437mhz at TE111 to start with. 2450mhz is a good start. From there you can perturb the cavity down to 2437mhz at will (mostly trial and error)...
I think one has a greater chance of achieving thrust (it that is indeed possible) with mode shape TE01p than with mode TE11p, for any p. The images below illustrate the difference between them.
Also, NASA reported mode TE012 for their experiment that gave greatest thrust/PowerInput.
More discussion of this here: http://forum.nasaspaceflight.com/index.php?topic=36313.msg1322952#msg1322952
As to calculations for a cone geometry, there is Greg Egan's http://gregegan.customer.netspace.net.au/SCIENCE/Cavity/Cavity.html . We will be reporting on a comparison as well.
Images of modes TE01p, and TE11p (where p can be any p=0,1,2,3,...):
electric field ________________ solid lines
magnetic field              dashed lines

...I am still unsure if angle by the apex is truly important for resonance, but according to Egan, it is: http://www.gregegan.net/SCIENCE/Cavity/Cavity.html But if my hunch about the importance of the QV to spacetime is correct (pretty much has to be), 45 and 90 degrees by the apex is important. ..
@Mulletron, why do you think that the cone angle (theta_{w} in Egan's nomenclature), of an EM Drive, should (ideally) be 45 degrees ? (I don't recall the reasons(s), please refresh my mind).
(http://gregegan.customer.netspace.net.au/SCIENCE/Cavity/CavityShape.gif)
In Egan's geometry, the cone angle (theta_{w}) is measured from the longitudinal axis of the cone, "z", therefore this picture should show a negative cone angle (  theta_{w}) on the left, and a positive ( + theta_{w}) on the right.
For reference. the tangent of theta_{w} and the angle theta_{w}, for the following cases are:
Example (and geometry) { Tan[theta_{w}],theta_{w} (degrees) }
NASA Brady et.al. (Fornaro) {0.230422, 12.9757}
NASA Brady et.al. (Aero) {0.2352, 13.2354}
NASA Brady et.al. (Mulletron) {0.257318, 14.4302}
Shawyer Experimental {0.104019, 5.93851}
Shawyer Demo {0.219054, 12.3557}
Shawyer Superconducting 2014 {0.7002, 35}
Egan's example {0.36397 , 20}
We see that the cone angle theta_{w} for NASA's Brady et.al. truncated cone was about 14 degrees, Shawyer's Experimental was only 6 degrees, Shawyer's Demo was 12 degrees, and Egan's only example is 20 degrees (Egan's example has a cone angle much larger than the cone angle of experiments). The "cone angle theta_{w}" for a cylinder is zero, Shawyer's Experimental was closest to a cylinder, and NASA's Brady et.al. was the experiment with the largest cone angle.
Shawyer's latest (2014) superconducting design (see image, presented at the IAC 2014 conference in Toronto), for which there are no experimental results reported yet, appears to have a significantly larger cone angle than his previous experimental and demo geometries, and significantly larger than NASA's Brady et.al.'s.
EDIT: Shawyer's (2014) superconducting EM Drive design has a cone angle theta_{w} of about 35 degrees.
(http://1.bp.blogspot.com/IUOMkncS1sM/VFLSUw2HeoI/AAAAAAAA3yE/Zl3iaKJyrX0/s1600/emdrivedata2.png)
(*
Fornaro estimate \
http://forum.nasaspaceflight.com/index.php?topic=36313.msg1302455#msg1302455;
fornaroLength=0.332 m
fornaroBigDiameter=0.397 m
fornaroSmallDiameter=0.244 m
*)
(*
Aero Best estimate as of 11/9/2014 \
http://forum.nasaspaceflight.com/index.php?topic=29276.msg1285896#msg1285896 ;
aeroLength=0.24173 m
aeroBigDiameter=0.27246 m
aeroSmallDiameter=0.15875 m
*)
(*
Mulletron Best estimate as of 11/9/2014
http://forum.nasaspaceflight.com/index.php?topic=36313.msg1320903#msg1320903;
mulletronLength=0.27637 m
mulletronBigDiameter=0.30098 m
mulletronSmallDiameter=0.15875 m
*)
(*
"Shawyer EXPERIMENTAL geometry"
shawyerExpLength=0.156 meter;
shawyerExpBigDiameter=0.16 meter
shawyerExpSmallDiameter=0.127546 meter;
*)
(*
" Shawyer DEMO geometry"
shawyerDemoLength=0.345 meter;
shawyerDemoBigDiameter=0.28 meter;
shawyerDemoSmallDiameter=0.128853 meter;
*)

Also, the larger the cone angle theta_{w}, the more important is to have EM Drive spherical ends rather than flat ends. The curvature of the spherical ends is more pronounced for larger cone angle theta_{w}. Shawyer realized this: he has spherical ends in his 2014 superconducting design shown in the above image.

I learned a new trick. :) Here are some images of the ez field along the x coordinate.
The imaginary and real parts are shown at x=194, because that showed a powerful signal.
The imaginary and real parts are shown at x=216, because that is the big end of the cavity.
The imaginary and real parts are shown at x=39, because that is the just inside the dielectric at the small end.
I'll see if I can get some magnetic field images.

I learned a new trick. :) Here are some images of the ez field along the x coordinate.
The imaginary and real parts are shown at x=194, because that showed a powerful signal.
The imaginary and real parts are shown at x=216, because that is the big end of the cavity.
The imaginary and real parts are shown at x=39, because that is the just inside the dielectric at the small end.
I'll see if I can get some magnetic field images.
The real parts of the electric field shape at the location of highest intensity (x=194) and at the small end dielectric ( x=39) look like mode shape TE12 (see image attached). Looking forward to seeing the magnetic field, to be sure what mode it is.
electric field ________________ solid lines
magnetic field              dashed lines

I learned a new trick. :) Here are some images of the ez field along the x coordinate.
The imaginary and real parts are shown at x=194, because that showed a powerful signal.
The imaginary and real parts are shown at x=216, because that is the big end of the cavity.
The imaginary and real parts are shown at x=39, because that is the just inside the dielectric at the small end.
I'll see if I can get some magnetic field images.
Are you running the same dielectric properties, overall geometry and source frequency as in your message http://forum.nasaspaceflight.com/index.php?topic=36313.msg1321460#msg1321460 ?
It the answer is yes, then it looks like the mode shape was TE123 , that is m=1, n=2, p =3.
Based just on the limited information from the movie's image of the z,r plane I previously thought ( http://forum.nasaspaceflight.com/index.php?action=post;msg=1321476;topic=36313.320 ) the mode shape could be TE013: m=0, n=1, p=3. Based on the z,r plane previously shown one could not tell what m was. The field does not look constant in the circumferential direction (which would be needed for m=0). It seems to have a full wave, which means m=1. I previously thought that n=1 , but n =2 can look like n=1 on the z,r plane at the right circumferential (azimuthal ) angle.
To be 100% sure one would need an image of the plane z , r, showing a still picture of the electric field in the longitudinal direction, like you did in the movie (where z is the longitudinal axis of the cone and r is the radial axis) rotated (around the longitudinal axis z) at an angle 90 degrees from the previous circumferential angle.
(Or even better, get two new still images showing the electric field in the longitudinal direction:
1) of a plane z , r located at a circumferential angle theta1 and
2) of another plane z, r located at a different circumferential angle theta2
such that theta2 is rotated (around the longitudinal axis z) by 90 degrees from theta1 so that theta2= theta1 + 90 degrees)
(http://mathworld.wolfram.com/images/epsgif/CylindricalCoordinates_1001.gif)
(http://www.ibiblio.org/links/devmodules/shared/graphics/cylindrical.jpg)
The magnetic field images will also be helpful to understand what mode shape it is.

I will try to get additional views as time and health permits. My boy brought something home from school and we've all contracted it. Unfortunately for me, I didn't throw it off like the wife and boy did.
This image is in 3D, which means very low resolution, so no its not like the other one. It's the same cavity and same drive frequency though so it should be generally very similar.

I will try to get additional views as time and health permits. My boy brought something home from school and we've all contracted it. Unfortunately for me, I didn't throw it off like the wife and boy did.
This image is in 3D, which means very low resolution, so no its not like the other one. It's the same cavity and same drive frequency though so it should be generally very similar.
Thanks for updating us on your great progress. Hope you feel better soon :)

I learned a new trick. :) Here are some images of the ez field along the x coordinate.
The imaginary and real parts are shown at x=194, because that showed a powerful signal.
The imaginary and real parts are shown at x=216, because that is the big end of the cavity.
The imaginary and real parts are shown at x=39, because that is the just inside the dielectric at the small end.
I'll see if I can get some magnetic field images.
For these truncated cone calculations, you reported (in the movie attachment to http://forum.nasaspaceflight.com/index.php?topic=36313.msg1321460#msg1321460 ) that the value of the relative permittivity (dielectric constant) you used was 2.3.
I did not find the value of relative permeability ( the degree of magnetization of the material ) you used for your truncated cone (NASA Brady et.al.) calculations.
Just to be sure, could you please confirm that you used a value of 1 (one) for the relative permeability in the above calculations ?

I learned a new trick. :) Here are some images of the ez field along the x coordinate.
The imaginary and real parts are shown at x=194, because that showed a powerful signal.
The imaginary and real parts are shown at x=216, because that is the big end of the cavity.
The imaginary and real parts are shown at x=39, because that is the just inside the dielectric at the small end.
I'll see if I can get some magnetic field images.
For these truncated cone calculations, you reported (in the movie attachment to http://forum.nasaspaceflight.com/index.php?topic=36313.msg1321460#msg1321460 ) that the value of the relative permittivity (dielectric constant) you used was 2.3.
I did not find the value of relative permeability ( the degree of magnetization of the material ) you used for your truncated cone (NASA Brady et.al.) calculations.
Just to be sure, could you please confirm that you used a value of 1 (one) for the relative permeability in the above calculations ?
I used the dielectric constant of 1.76 for the dielectric disk. That number was 2.3 in the movie but I only use 1.76 now that I've decided that 1.76 is the correct value. To investigate resonance of an empty cavity I can replace the dielectric material with "air." The value is 1.76 for the above runs.
In all cases the cone material, which should be copper, is a material defined by meep as a "Perfect Metal." The content of the cavity is another material defined by meep as "air." The material outside the cavity, the environment, defaults to "vacuum." I do move the antenna location around and often forget to put it back to the most representative location for the run type. I move it because when I run Harminv using Cylindrical coordinates, the antenna must be on the central axis of rotation of the cone. If it is not, then in Cylindrical coordinates, nothing excites the cavity.
You can most likely tell by looking at the images, where the antenna was located for a particular run.

I learned a new trick. :) Here are some images of the ez field along the x coordinate.
The imaginary and real parts are shown at x=194, because that showed a powerful signal.
The imaginary and real parts are shown at x=216, because that is the big end of the cavity.
The imaginary and real parts are shown at x=39, because that is the just inside the dielectric at the small end.
I'll see if I can get some magnetic field images.
For these truncated cone calculations, you reported (in the movie attachment to http://forum.nasaspaceflight.com/index.php?topic=36313.msg1321460#msg1321460 ) that the value of the relative permittivity (dielectric constant) you used was 2.3.
I did not find the value of relative permeability ( the degree of magnetization of the material ) you used for your truncated cone (NASA Brady et.al.) calculations.
Just to be sure, could you please confirm that you used a value of 1 (one) for the relative permeability in the above calculations ?
I used the dielectric constant of 1.76 for the dielectric disk. That number was 2.3 in the movie but I only use 1.76 now that I've decided that 1.76 is the correct value. To investigate resonance of an empty cavity I can replace the dielectric material with "air." The value is 1.76 for the above runs.
..
As I understand, the z,r (axial,radial) plane image in the movie was based on a relative permittivity of 2.3, while the theta, r (circumferential, radial) plane images of your above message are based on the different value of relative permittivity of 1.76.
Therefore it is possible that the mode shape in the z,r (axial,radial) plane image in the movie is different than the mode shape of the theta, r (circumferential, radial) plane images of your above message, the different mode shapes being due to the different values of relative permittivity that were used in each calculation.

I learned a new trick. :) Here are some images of the ez field along the x coordinate.
The imaginary and real parts are shown at x=194, because that showed a powerful signal.
The imaginary and real parts are shown at x=216, because that is the big end of the cavity.
The imaginary and real parts are shown at x=39, because that is the just inside the dielectric at the small end.
I'll see if I can get some magnetic field images.
For these truncated cone calculations, you reported (in the movie attachment to http://forum.nasaspaceflight.com/index.php?topic=36313.msg1321460#msg1321460 ) that the value of the relative permittivity (dielectric constant) you used was 2.3.
I did not find the value of relative permeability ( the degree of magnetization of the material ) you used for your truncated cone (NASA Brady et.al.) calculations.
Just to be sure, could you please confirm that you used a value of 1 (one) for the relative permeability in the above calculations ?
..." I do move the antenna location around and often forget to put it back to the most representative location for the run type. I move it because when I run Harminv using Cylindrical coordinates, the antenna must be on the central axis of rotation of the cone. If it is not, then in Cylindrical coordinates, nothing excites the cavity.
For the calculations for the movie (with relative permittivity of 2.3) you used an excitation frequency of 1.76365 GHz.
What excitation frequency did you use for the calculations in your above message (with relative permittivity of 1.76) ?

...I am still unsure if angle by the apex is truly important for resonance, but according to Egan, it is: http://www.gregegan.net/SCIENCE/Cavity/Cavity.html But if my hunch about the importance of the QV to spacetime is correct (pretty much has to be), 45 and 90 degrees by the apex is important. ..
@Mulletron, why do you think that the cone angle (theta_{w} in Egan's nomenclature), of an EM Drive, should (ideally) be 45 degrees ? (I don't recall the reasons(s), please refresh my mind).
Keeping first principles in mind concerning the QV model for how these thrusters may work. If they do interact with the QV somehow, their design should obviously be complimentary to the geometry of spacetime (there are crazy folks out there http://www.onlyspacetime.com/, I'm one of them, who believe spacetime emerges from the quantum world.) I wanted to test whether opening angle had any significance. When faced with choosing an opening angle amongst seemingly arbitrary angles I've found amongst Shawyer's prototypes, I wondered if a light cone opening angle of 45 degrees (measured from the longitudinal axis for a total of 90 as measured from outside) would be of any benefit or not. http://en.wikipedia.org/wiki/Minkowski_diagram After seeing that a light cone setup would be a ginormous cone after factoring in the necessary conical sections for front and end walls, I further halved it to 22.5 degrees (total of 45). That's why I have 2 drawn up in CAD. So it really came down to a question of what angle to pick out of so many choices. Those two I want to try.
Trying to reconcile the above ideas with simultaneously hunting a viable rf solution is proving daunting. Mostly due to the lack of resources. I may not be afforded the option to choose an opening angle and stay on freq and within reasonable size limits. As I'm researching this it is becoming clear that opening angle will be dominated by chosen frequency and practical considerations.
After following up on Aero's post: http://forum.nasaspaceflight.com/index.php?topic=29276.msg1274400#msg1274400 about this: http://www.emdrive.com/NWPU2010translation.pdf trying to see if I can find a good solution for calculating exact solutions for conical frustums, I learned that no such method exists to find closed form solutions to that problem. The Egan method is similar to what we need but it doesn't address the problem. None of what we're dealing here has spherical end caps. And honestly, the Egan way is way too high speed for me.
"Currently have two ways to find the electromagnetic field of the rectangular and circular waveguides, the eigenvalue equation which is an analytical method and numerical solution, when finding solution for the resonator, Maxwell equation in is need to be created in a spherical coordinate system, because the complexity of the spherical coordinate fielder equation, has not found anyone using eigenvalue method to calculated the distribution of the resonant field. Only find in Paper [4] using asymptotic method for conical waveguide. That method assume a equivalent radius ae, believes field of wavefront sphere of cone waveguide Eo,EФ,Ho,HФ can use its wavefront position radius ae equivalent circular waveguide field Er,EФ,Hr,HФ, this method of finding the field distribution within the conical resonator can be used as reference, but the accuracy reduced as the cone half opening angle increases. Using finite element to numerically simulate the Maxwell electromagnetic equation for the idealised conical resonator, the distribution of electromagnetic can be obtained directly, this method is not limited by the cavity structure and microwave mode."
By keep the diameter of the Small End constant, increase the large end of the cavity, in order to have the same resonant frequency, cavity height must be reduced, quality factor also reduce.
They're basically saying: (1) That I'm hosed trying to calculate such things. Simulating the conical frustum using FEM software is the way to go. Which I simply don't have access to. (2) Also they're saying that as the opening angle opens up, approximating the resonant modes becomes more and more difficult. (3) You have to shorten the cavity height as opening angle increases to maintain resonance at desired frequency, but it lowers Q. So I should probably (for now) rethink using such wide opening angles.
So I'm switching gears a bit using what I've learned from the above reporting.
(1) Keeping Cannae in mind, who says we need a cone anyway? We've discussed the commonality between Shawyer and Cannae in thread 1. http://forum.nasaspaceflight.com/index.php?topic=29276.msg1298712#msg1298712 So I'm thinking it would be smart to use what we've learned about cylinders and try a cylinder experiment.
(2) Instead of trying to optimize right out of the gate by throwing around light cones. It would be smarter to use the dims we already have for Shawyer experimental and demo, which you provided on the previous page.
(3) If I ever get this build going, I'm going to have to easter egg it anyway using a siggen and a power meter to find the resonant frequency (treat it like a filter, tune it until I get get an output from sample port), so I don't need to have exact calculations. I just need to be close enough to be within tunable limits.

(*
"Shawyer EXPERIMENTAL geometry"
shawyerExpLength=0.156 meter;
shawyerExpBigDiameter=0.16 meter
shawyerExpSmallDiameter=0.127546 meter;
*)
(*
" Shawyer DEMO geometry"
shawyerDemoLength=0.345 meter;
shawyerDemoBigDiameter=0.28 meter;
shawyerDemoSmallDiameter=0.128853 meter;
*)
These were both 2450mhz experiments. Where did the small diameters and lengths come from? I see the Large diameters here: http://www.emdrive.com/yangjuanpaper2012.pdf.

(*
"Shawyer EXPERIMENTAL geometry"
shawyerExpLength=0.156 meter;
shawyerExpBigDiameter=0.16 meter
shawyerExpSmallDiameter=0.127546 meter;
*)
(*
" Shawyer DEMO geometry"
shawyerDemoLength=0.345 meter;
shawyerDemoBigDiameter=0.28 meter;
shawyerDemoSmallDiameter=0.128853 meter;
*)
These were both 2450mhz experiments. Where did the small diameters and lengths come from? I see the Large diameters here: http://www.emdrive.com/yangjuanpaper2012.pdf.
If I my memory is correct, we worked this out in Thread 1, the major contribution by far being from aero (aero deserves all the praise, if there are any mistakes in the above figures, they are mine). I recall feeling very confident about the rationale that aero used to estimate these numbers, which I remember had a very solid foundation.

Well if they are correct, they are a ready made solution for ISM band experimentation.
Break:
So I swore off the theory bug a few weeks ago but I've got a bug I need swatting concerning the behavior of confined photons vs the usual free range variety. Here's a quote and a video, both of which have bells ringing and light bulbs floating over my head.
Quoting John A. Macken, from http://www.onlyspacetime.com/HiggsBoson
Suppose that there was a box with hypothetical 100% reflecting internal walls. It would be possible to trap some light energy in such a box. A freely propagating photon is a massless particle, but what about a “confined photon” trapped in the box. That photon is forced to have the box’s specific frame of reference. A calculation at the end of chapter 1 shows that the photon pressure exerted on the walls of the box is uniform if the box is not accelerating, but the pressure becomes unequal if the box is accelerated. This difference in pressure results in a net force which resists acceleration. This is the inertia of the confined photon energy and it exactly equals the inertia of an equal amount of energy in the form of matter particles. This is not a coincidence.
That scenario sure sounds familiar......like within magic resonant cavity thrusters. I read that a few days ago and really didn't believe any of it, but I filed it away for later.
Now I'm going to re arrange a portion of the above quote and put out a RFC on it:
.......the photon pressure exerted on the walls of the box is uniform if the box is not accelerating, but the pressure becomes unequal if the box is accelerated. This difference in pressure results in a net force which resists acceleration.
Let's assume that if the author were correct, is it logical to say the flipside is also correct?
.......if the photon pressure exerted on the walls of the box is non uniform if the box is not accelerating accelerates, but the pressure becomes unequal if when the box is accelerated. This difference in pressure results in a net force which resists enables acceleration.
Perhaps it is better to find his calculation at the end of chapter 1 and rearrange it and see if it still works.
And this video @ 3:15
https://www.youtube.com/watch?v=nYDokJ2A_vU
I think I can safely believe Fermilab. Exchange photons are confined between two particles, so indeed they are also confined photons.
I never really approached photons from this perspective. I always assumed and was told they were always massless. What's the deal with confined photons? Confined photons seem to behave like massive particles.
Massive particles flowing into cavity, bouncing around a few thousand times, and then flowing out of a resonant cavity (by being absorbed) surely could make it move while conserving momentum. I picture a thrust nozzle when I think of it like this. Mass comes in, bounces around a bunch, finally comes out....and you have thrust.
Thanks for your patience. Would love some comments on this.
Edit:
Aha! http://www.livescience.com/45287howtotraplight.html A photon trapped in such a cavity behaves as if it had mass; in other words, the cavity creates a "trapping potential," keeping the photons from escaping.
http://www.desy.de/user/projects/Physics/Relativity/SR/light_mass.html However, if light is trapped in a box with perfect mirrors so the photons are continually reflected back and forth in both directions symmetrically in the box, then the total momentum is zero in the box's frame of reference but the energy is not. Therefore the light adds a small contribution to the mass of the box.
But then what? Can one really say with confidence that there exists a condition of "mass flow?"

A potentially interesting sidelight:
http://okomov.livejournal.com/577.html
The physics is descrived in vvery different terms ("Leonov’s superunification theory"?? "Antigravity"???) this has similar performance to what Shawyer predicts for a superconducting EmDrive thruster, i.e. 500 to 700 kg for 1kW power input.
Moreover, as soon as it starts to accelerate, the thrust ceases, hence the pulsed operation in the video, which is what Shawyer claims for a high Q EmDrive thruster without Doppler compensation.
What does the team think...?

....
Keeping first principles in mind concerning the QV model for how these thrusters may work. If they do interact with the QV somehow, their design should obviously be complimentary to the geometry of spacetime (there are crazy folks out there http://www.onlyspacetime.com/, I'm one of them, who believe spacetime emerges from the quantum world.) I wanted to test whether opening angle had any significance. When faced with choosing an opening angle amongst seemingly arbitrary angles I've found amongst Shawyer's prototypes, I wondered if a light cone opening angle of 45 degrees (measured from the longitudinal axis for a total of 90 as measured from outside) would be of any benefit or not. http://en.wikipedia.org/wiki/Minkowski_diagram After seeing that a light cone setup would be a ginormous cone after factoring in the necessary conical sections for front and end walls, I further halved it to 22.5 degrees (total of 45). That's why I have 2 drawn up in CAD. So it really came down to a question of what angle to pick out of so many choices. Those two I want to try.
Trying to reconcile the above ideas with simultaneously hunting a viable rf solution is proving daunting. Mostly due to the lack of resources. I may not be afforded the option to choose an opening angle and stay on freq and within reasonable size limits. As I'm researching this it is becoming clear that opening angle will be dominated by chosen frequency and practical considerations.
After following up on Aero's post: http://forum.nasaspaceflight.com/index.php?topic=29276.msg1274400#msg1274400 about this: http://www.emdrive.com/NWPU2010translation.pdf trying to see if I can find a good solution for calculating exact solutions for conical frustums, I learned that no such method exists to find closed form solutions to that problem. The Egan method is similar to what we need but it doesn't address the problem. None of what we're dealing here has spherical end caps. And honestly, the Egan way is way too high speed for me.
"Currently have two ways to find the electromagnetic field of the rectangular and circular waveguides, the eigenvalue equation which is an analytical method and numerical solution, when finding solution for the resonator, Maxwell equation in is need to be created in a spherical coordinate system, because the complexity of the spherical coordinate fielder equation, has not found anyone using eigenvalue method to calculated the distribution of the resonant field. Only find in Paper [4] using asymptotic method for conical waveguide. That method assume a equivalent radius ae, believes field of wavefront sphere of cone waveguide Eo,EФ,Ho,HФ can use its wavefront position radius ae equivalent circular waveguide field Er,EФ,Hr,HФ, this method of finding the field distribution within the conical resonator can be used as reference, but the accuracy reduced as the cone half opening angle increases. Using finite element to numerically simulate the Maxwell electromagnetic equation for the idealised conical resonator, the distribution of electromagnetic can be obtained directly, this method is not limited by the cavity structure and microwave mode."
By keep the diameter of the Small End constant, increase the large end of the cavity, in order to have the same resonant frequency, cavity height must be reduced, quality factor also reduce.
They're basically saying: (1) That I'm hosed trying to calculate such things. Simulating the conical frustum using FEM software is the way to go. Which I simply don't have access to. (2) Also they're saying that as the opening angle opens up, approximating the resonant modes becomes more and more difficult. (3) You have to shorten the cavity height as opening angle increases to maintain resonance at desired frequency, but it lowers Q. So I should probably (for now) rethink using such wide opening angles.
So I'm switching gears a bit using what I've learned from the above reporting.
(1) Keeping Cannae in mind, who says we need a cone anyway? We've discussed the commonality between Shawyer and Cannae in thread 1. http://forum.nasaspaceflight.com/index.php?topic=29276.msg1298712#msg1298712 So I'm thinking it would be smart to use what we've learned about cylinders and try a cylinder experiment.
(2) Instead of trying to optimize right out of the gate by throwing around light cones. It would be smarter to use the dims we already have for Shawyer experimental and demo, which you provided on the previous page.
(3) If I ever get this build going, I'm going to have to easter egg it anyway using a siggen and a power meter to find the resonant frequency (treat it like a filter, tune it until I get get an output from sample port), so I don't need to have exact calculations. I just need to be close enough to be within tunable limits.
1) Concerning a solution for the truncated cone EM Drive (the geometry used by Shawyer, NASA and Juan Yang in China), I can report the following progress. I have derived an exact, closedform solution for the integral of the longitudinal wavenumber "kz" (as proposed by @NotSoSureOfIt and hinted in the 1969 patent of Wolf) for a truncated cone or a cone. The solution contains square root terms and ArcTan terms. There is no question that when an exact solution is available it is always superior to any numerical method like Finite Element, Finite Difference, Boundary Element, etc. Even when exact solutions are not available, it is a standard methodology in any engineering department to start the design process with exact solutions to simplified geometries because of the considerable amount of time that it takes to generate a converged solution with Finite Element, Finite Difference, etc. Also because one can gain a much better understanding of the problem with a closedform solution (to quickly understand the influence of parameters).
2) It is not possible to solve the eigenvalue problem for the truncated cone cavity, or for a cone cavity, directly in terms of standard functions of the frequency (or the mode shape) because the longitudinal wavenumber kz expression for the truncated cone or a cone cannot be inverted (since the frequency is nonlinearly embedded in a number of square root and ArcTan terms).
3) The eigenvalue problem for the truncated cone can be solved by obtaining a numerical solution (finding roots of the nonlinear equation that arises from equating the longitudinal wavenumber "kz" to the mode shape quantum number "p" = 0,1,2,3,4...).
4) I will post the solution and numerical results in more detail, but meanwhile here is the main result:
the exact solution for the truncated cone gives results that are less than 1% different (for typical geometries with a cone angle equal or less than 20 degrees from the longitudinal axis comprising the NASA Brady et.al. , China (Juan Yang) and the UK (Shawyer) experiments) from the exact solution of a cylinder, if the cylinder diameter is expressed as the GeometricMean of the big and small diameters of the truncated cone. I have explored several mean measures, for example:
H, the Harmonic Mean ( https://en.wikipedia.org/wiki/Harmonic_mean ) ,
G, the Geometric Mean ( https://en.wikipedia.org/wiki/Geometric_mean ),
L, the Logarithmic Mean ( https://en.wikipedia.org/wiki/Logarithmic_mean ),
A, the Arithmetic Mean ( https://en.wikipedia.org/wiki/Arithmetic_mean ),
V, the Volumetric Mean (http://forum.nasaspaceflight.com/index.php?topic=36313.msg1319655#msg1319655 ),
R, the Root Mean Square ( https://en.wikipedia.org/wiki/Root_mean_square ),
C, the Contraharmonic mean ( https://en.wikipedia.org/wiki/Contraharmonic_mean ),
where:
SmallDiameter < H < G < L < A < V < R < C < BigDiameter
The closest results to the exact solution for the truncated cone are obtained using the GeometricMean of its big and small diameters, as the equivalent diameter of the cylinder cavity equation. I also found the value of the exponent of the Stolarsky Mean ( https://en.wikipedia.org/wiki/Stolarsky_mean ) that minimizes the error even further than the Geometric Mean, but the improvement is not dramatic and the Stolarsky exponent depends on the cone geometry, hence, for simplicity, one might as well use the GeometricMean=Sqrt[BigDiameter*SmallDiameter] in the cylinder equation to model the frequency and mode shapes of the truncated cone.
(http://www.gogeometry.com/geometry/geometric_mean_arithmetic.gif)
(http://forum.nasaspaceflight.com/index.php?action=dlattach;topic=29276.0;attach=620202;image)

As for the previous one, the level and quality of these comments is so high that the thread has become unreadable for nonphysicists.
Could you eventually, for the sake of not losing the majority of us too much behind, make a quick nontechnical summary of what are you discussing? is there any progress or barely nothing?
Thanks! :)

As for the previous one, the level and quality of these comments is so high that the thread has become unreadable for nonphysicists.
Could you eventually, for the sake of not losing the majority of us too much behind, make a quick nontechnical summary of what are you discussing? is there any progress or barely nothing?
Thanks! :)
1) We are exploring the validity of the claims of the different experimenters (NASA in the USA, Shawyer in the UK and Juan Yang in China) by systematically analyzing their experiments.
2) Some of the people in this forum are also designing and working to make their own prototypes and experiments.
3) One of the people in this forum (@NotSoSureOfIt), has made an outstanding contribution by independently deriving an equation that is not far from the claimed experimental results.
4) There are a number of possible physical reasons for the experimental results to be valid for space propulsion as well as for the results to be an experimental artifact that may not produce any propulsion in space.
5) There have been no further reports from NASA on the experiments that were supposed to be replicated at their other centers (JPL and Glenn) or at John Hopkins University. Actually @wembley, who is an aerospace technology reporter, reports that it is his opinion that NASA has a "news blackout" on this matter, and China's Juan Yang is not saying much either. The Chinese seem to be much further along than NASA, as they reported much greater thrust and they have conducted more thorough experiments (including being the first to numerically report the effects of temperature and temperature gradients with thermocouples embedded in the metal). Shawyer in the UK seems to be much further ahead than NASA as he claims he is exploring a superconducting design. Shawyer (UK) made a presentation in Canada late last year where he showed his latest design (using superconductivity) which he claims will result in much greater thrust/PowerInput (see image below).

A potentially interesting sidelight:
http://okomov.livejournal.com/577.html
The physics is descrived in vvery different terms ("Leonov’s superunification theory"?? "Antigravity"???) this has similar performance to what Shawyer predicts for a superconducting EmDrive thruster, i.e. 500 to 700 kg for 1kW power input.
Moreover, as soon as it starts to accelerate, the thrust ceases, hence the pulsed operation in the video, which is what Shawyer claims for a high Q EmDrive thruster without Doppler compensation.
What does the team think...?
I'm a newbie and not an expert, but I can give my opinion nonetheless: another proposal that needs strong evidence to give it any credence.
The material is somewhat scarce on technical details about the posited thruster, except the description of the author's theory.
It's not clear for me if this is another version of the Emdrive or something very different.
The videos of the moving chariot with inert wheels are interesting, but they can be done with many other things here on Earth, by using friction.

Longtime lurker here; I have to thank you all for your tireless contributions with very little data to go on. While it's too early to tell if anything will come of this, the potential payoff is earthchanging.
It does appear to me that @wembley is correct and there is indeed a de facto, if not formal, news blackout from NASA. Given the enormous level of interest in this over the last few months, isn't it odd that we haven't seen so much as a terse announcement to the effect of "We decided not to test this further at JPL after all, due to the fact we think it's nonsense, we have budget constraints, etc.". But as far as we know, they have said nothing at all since the initial announcement.
For people more familiar with NASA, is that common? Does NASA as a civilian agency have a history (or policy?) of suppressing experimental results that, like this, may have military applications? In other words, can the lack of any news at all one way or the other, be taken as a sign that there might be something to this? Or is that just conspiratorial nonsense?

For people more familiar with NASA, is that common? Does NASA as a civilian agency have a history (or policy?) of suppressing experimental results that, like this, may have military applications? In other words, can the lack of any news at all one way or the other, be taken as a sign that there might be something to this? Or is that just conspiratorial nonsense?
Rockets have military applications, but NASA does not suppress experimental results of rockets. To the contrary, they partner with companies such as SpaceX and share information for the advancement of space exploration. I'm not convinced there is a black out for EM drive technology. There appears to be a delay, which could have many causes. If there are people in the administration advocating for a black out, I think it is a mistake, and probably too late given the amount of information already in the public domain.

This is the latest official NASA media we have I think
Dr. Harold "Sonny" White  Eagleworks Laboratories: Advanced Propulsion
https://www.youtube.com/watch?v=Wokn7crjBbA
NASA Ames Research Director’s Colloquium, August 12, 2014
It is basically a rehash of the statements released in July, but gives some spaceflight context. In this presentation Dr White is very matter of fact about this concept. He seems to leave little doubt on how he feels about the effect's existence.
I hope he is right. He talks about some of the mission profiles.
But this year we have not heard anything since. It has been nearly 6 months, surely they know yay or nay by now. As some readers have pointed out, perhaps it has gone underground? Or maybe the results are so incredible that no one wants to be the first to report it for fear of ruining their career if they are wrong. If thats the case we just need someone to break the dam.

Interesting account relating to the history of Nasa and Darpa involvement with developing/testing advanced propulsion concepts.
http://www.bbc.com/future/story/20120321searchingforastarship
There is a lot of intriguing reading if you research the history and associations of the people named in the article.

For people more familiar with NASA, is that common? Does NASA as a civilian agency have a history (or policy?) of suppressing experimental results that, like this, may have military applications? In other words, can the lack of any news at all one way or the other, be taken as a sign that there might be something to this? Or is that just conspiratorial nonsense?
Rockets have military applications, but NASA does not suppress experimental results of rockets. To the contrary, they partner with companies such as SpaceX and share information for the advancement of space exploration. I'm not convinced there is a black out for EM drive technology. There appears to be a delay, which could have many causes. If there are people in the administration advocating for a black out, I think it is a mistake, and probably too late given the amount of information already in the public domain.
To be fair to NASA if this does work it's such a revolutionary technology that the reporting of it is not something to be rushed into. No doubt every result is having to be checked, checked again & then checked again etc etc which no doubt slows down the release of information. Especially if on top of that there are national security implications that have to be considered as well.

Anyone have the pdf?
http://arc.aiaa.org/doi/abs/10.2514/6.20143853
Also not exactly mainstream news but interesting nonetheless.
http://m.disclose.tv/news/NASA_Impossible_Quantum_Space_Engine_Actually_Works/113761#DTV

Anyone have the pdf?
http://arc.aiaa.org/doi/abs/10.2514/6.20143853
Also not exactly mainstream news but interesting nonetheless.
http://m.disclose.tv/news/NASA_Impossible_Quantum_Space_Engine_Actually_Works/113761#DTV
I have access to that conference paper. I won't give it out but if you have any specific questions about the contents I can try to answer them. (This topic is outside my area of expertise)
I only very briefly skimmed over the paper but it has a very amateur feel to it. For example the author claims ``numerical method analysis'' was used. Towards the end of the paper they clarify that they used the software packages HFSS and Analyst under an evaluation license. This does not give me high hopes that they were used correctly.

Anyone have the pdf?
http://arc.aiaa.org/doi/abs/10.2514/6.20143853
Yes, anything in particular you were after?
You may also want to look at his patents, eg from 2012
https://www.google.com/patents/US20140013724?dq=cannae+fetta&hl=en&sa=X&ei=4HvUVKaFIauV7AaCqYHABA&ved=0CCQQ6AEwAQ
and the earlier 2007 version which references Shawyer
https://www.google.com/patents/WO2007089284A2?cl=en&dq=fetta+thruster&hl=en&sa=X&ei=QHzUVJjuAsWP7AbMy4GYBQ&ved=0CEIQ6AEwBQ

For people more familiar with NASA, is that common? Does NASA as a civilian agency have a history (or policy?) of suppressing experimental results that, like this, may have military applications? In other words, can the lack of any news at all one way or the other, be taken as a sign that there might be something to this? Or is that just conspiratorial nonsense?
Rockets have military applications, but NASA does not suppress experimental results of rockets. To the contrary, they partner with companies such as SpaceX and share information for the advancement of space exploration. I'm not convinced there is a black out for EM drive technology. There appears to be a delay, which could have many causes. If there are people in the administration advocating for a black out, I think it is a mistake, and probably too late given the amount of information already in the public domain.
To be fair to NASA if this does work it's such a revolutionary technology that the reporting of it is not something to be rushed into. No doubt every result is having to be checked, checked again & then checked again etc etc which no doubt slows down the release of information. Especially if on top of that there are national security implications that have to be considered as well.
Folks:
The Eagleworks Lab is still working on the copper frustum thruster that was reported on last summer at the AIAA/JPC. We have now confirmed that there is a thrust signature in a hard vacuum (~5.0x10^6 Torr) in both the forward direction, (approx. +50 microNewton (uN) with 50W at 1,937.115 MHz), and the reversed direction, (up to 16uN with a failing RF amp), when the thruster is rotated 180 degrees on the torque pendulum. However we continue to fight through RF amplifier failures brought on by having to operate them in a hard vacuum with few $$$ resources to fix them when they break, so the desired data is coming along very slowly. We are still working on obtaining enough data though that will allow us to go to Glenn Research Center (GRC) for a replication effort in the next few months. However that will only happen if we can make the thrust signature large enough since the GRC thrust stand can only measure down to ~50uN, so we have to get the thrust signature up to at least 100uN before we can go to GRC.
As to the theoretical side of QThrusters, Dr. White has just developed the first cut at a quantum vacuum (QV) based plasma code written in C+ under Windows/Unix and VMD visualization software that utilizes the COMSOL E&M derived field data for a given thruster geometry that allows one to track the movement and velocity of a subset of the QV's electron/positron neutral plasma pairs in the thruster over time as they respond to the applied time varying RF E&M fields in the copper frustum resonant cavity and to each other. This package also allows one to calculate the expected thrust for a given input power and quality factor of the frustum resonant cavity based of standard plasma rocket physics. So far the estimated thrust verses experimental observations are within 2% for the first experimental data run I compared it to, but we still have a long, long road ahead of us of experimental validation before we have any real confidence in this very new QThruster design tool.
Best, Paul March

Wanted to examine the inventor's theory of operation. We spent a lot of time discussing Shawyer's theory, but Fetta didn't get much discussion. Probably because his paper is paywalled. Also @Wembley, thanks for the patents. There's plenty of free info there.
Break:
Neat I can hit zero every half wavelength with any frequency like this. (top)
Or if I mirror the diagonal of a cylinder, creating a cone I get pretty close sometimes after adjusted down 1 degree. (bottom)
http://goo.gl/jF8ZJB (shortened link to ebay)
Found these puppies. Emailed the seller to see what the dimensions are and to see if they are the manufacturer and whether they do custom sizes. Might be cheaper and less headache than buying a copper sheet.
Something very nice about the exact solution I obtained for the frequencies and mode shapes of a truncated cone, or for a cone, is that it implicitly, automatically, incorporates the condition of cutoff frequencies. The exact solution for a cylinder in Wikipedia (http://en.wikipedia.org/wiki/Microwave_cavity#Cylindrical_cavity) does not explicitly refer to the need for the condition of cutoff frequencies, and therefore the cutoff frequency condition (http://en.wikipedia.org/wiki/Cutoff_frequency ) has to be included in (http://en.wikipedia.org/wiki/Microwave_cavity#Cylindrical_cavity) as an additional condition (which we did not do in previous discussions of mode shapes: some of the mode shapes we discussed for certain geometries do not have Q resonance because they are cutoff ! ). Not all values of the longitudinal mode shape quantum number "p"=0,1,2,3,... are allowed. Low values of "p" (starting with p=0) are disallowed by the cutoff condition for small diameters.
The cutoff frequency condition (http://en.wikipedia.org/wiki/Cutoff_frequency ) is that the frequency of the cavity has to be greater than the speed of light in the medium times the appropriate zero Bessel function , divided by Pi*Diameter:
fmnp > cmedium Xfunction / (Diameter * Pi)
where
cmedium = c / Sqrt[epsilonr * mur] where epsilonr is the relative electric permittivity (dielectric constant), and mur is the relative magnetic permeability, and c is the speed of light in vacuum
and where
Xfunction=X_{mn} for TM modes and Xfunction = X'_{mn} for TE modes
Now, for a cylinder it is clear what "diameter" means, since the diameter is constant along the length. However, what is the cutoff condition for a truncated cone? This is included in the exact solution I obtained for a truncated cone and it is simply dictated by the small diameter of the truncated cone (which one would expect based on physical reasons):
fmnp > cmedium Xfunction / (Dsmall Pi)
where Xfunction=X_{mn} for TM modes and Xfunction = X'_{mn} for TE modes
This has very important consequences for a truncated cone, because as the small Diameter approaches zero, the cutoff frequency approaches infinity. This means that for a pointy cone, there can be no resonant Q solution possible. A pointy cone can only have evanescent waves (since only real solutions to the eigenvalue equation are standingwave resonant Q solutions, and the complex value solutions to the eigenvalue equation are evanescent waves).
EDIT:
This can also be stated as a cutoff wavelength, where the wavelength lambda_{mnp} is defined as the ratio of the speed of light in the medium, to the frequency f_{mnp}:
lambda_{mnp} = cmedium / f_{mnp}
substituting this, we obtain the following condition
lambda_{mnp} < (Dsmall * Pi) / Xfunction
the wavelength for a given mode mnp needs to be smaller than the smallDiameter*Pi /Xfunction
longer wavelengths get cutoff
Another very important consequence is that the cutoff frequency:
fmnp > cmedium Xfunction / (Dsmall Pi)
implies a minimum diameter for the truncated cone to support a given mode shape at a given frequency:
Dsmall > cmedium Xfunction / ( fmnp Pi)
where Xfunction=X_{mn} for TM modes and Xfunction = X'_{mn} for TE modes
For example, if one wants resonance at fmnp = 2.45 GHz, as @aero was proposing, then it immediately follows that the minimum diameter has to be
Dsmall > cmedium Xfunction / ( 2.45 GHz)
Since the Xfunction increases with m and n (except for one particular X' value for the TE mode with m=1: X'_{1n} or TE_{1n}) , small diameters cut off frequencies such that the mn modes can only occur at higher p values, that's why @aero found that the longitudinal mode shape quantum number p=3 for the NASA truncated cone with the dielectric, instead of p=0 or p=1 or p=2.
Dsmall > cmedium Xfunction / ( fmnp Pi)
or, since cmedium = c / Sqrt[epsilonr * mur]
Dsmall > c * Xfunction / (Sqrt[epsilonr * mur] * fmnp * Pi)
The higher the value of the dielectric constant epsilonr (everything else held constant), the lower the Diameter can be for a given frequency
The higher the value of the dielectric constant epsilonr (everything else held constant), the lower the frequency will be for a given mode shape mnp.
This clearly shows the function of the dielectric in the EM Drive: the dielectric allows mode shapes to occur at frequencies that would otherwise be cutoff for a given geometry.
The dielectric allows mode shapes to occur for smaller values of the small diameter.
Also, the cutoff frequency condition clearly shows why NASA and Shawyer located the dielectric at the small end of the cavity, since the cutoff frequency is a function of the the dielectric constant, such that lower dielectric constant allows for lower cutoff frequencies or equivalently smaller diameters. The best place to put the dielectric is at the small diameter in order to allow mode shapes to occur that would otherwise be precluded because of the cutoff frequency condition.
It is very interesting that there is a "sweet spot" of geometries for these EM Drives: too large a diameter leads to too many mode shapes very close to each other (and hence very difficult to tune and keep the EM Drive at a given resonant frequency) while too small diameters lead to cutoff of mode shapes. A pointy cone cannot have Q resonant modes, a pointy cone can only have evanescent waves. The closest one can come up to a pointy cone Q resonance would be to calculate and design a geometry with a dielectric located at the small end and a small but finite Dsmall diameter. Dsmall must be greater than zero, and for practical solutions this implies a minimum diameter.
(http://i.ebayimg.com/00/s/ODQ5WDg2Ng==/$(KGrHqZHJCkE63YKjOZMBO65s07Fn!~~60_35.JPG)
(http://forum.nasaspaceflight.com/index.php?action=dlattach;topic=29276.0;attach=620202;image)
I will write more on this and give numerical examples and mode shapes for the NASA and the Shawyer experiments. It is all falling into place very nicely now :)

Here's what I know about cutoff freqs of circular waveguide at least:
"The cutoff wavelength of a circular guide is 1.71 times the diameter of the
waveguide. Since the "a" dimension of a rectangular waveguide is approximately one halfwavelength at
the cutoff frequency, the diameter of an equivalent circular waveguide must be 2 ÷ 1.71, or approximately
1.17 times the "a" dimension of a rectangular waveguide."
Page 126
http://www.navymars.org/national/training/nmo_courses/nmo1/module11/14183_ch1.pdf
I've set the small diameter as 1 wavelength for the top cone. The bottom was set from calculating cylinders, so the guide wavelength in diameter is different than multiples of .5. See previous post.
The whole point of this exercise is to calculate the diameter of the "blanks" to insert into a cone of X angle and be resonant at the desired frequency and mode. I'm trying to figure this out by holding the small diameter as a constant.
Break:
@ Paul March, thank you for chiming in. All of us are chomping at the bit for ANY news whatsoever. Maybe Eagleworks could leverage its social media presence (https://www.facebook.com/eagleworksnasa) to keep the public engaged. As far as the lack of $$$ and resources go, I understand that Eagleworks works on a shoestring budget. Wish we could help. It probably isn't acceptable for us to try and crowdfund a government agency. Hopefully you achieve results that will turn heads. Godspeed.

It is all falling into place very nicely now :)
https://www.youtube.com/watch?v=EPX5IBbfmEQ ;)
In theory, could a dialectric be used to suppress resonance modes that might otherwise be present in an oversized cavity?

http://goo.gl/jF8ZJB (shortened link to ebay)
Found these puppies. Emailed the seller to see what the dimensions are and to see if they are the manufacturer and whether they do custom sizes. Might be cheaper and less headache than buying a copper sheet.
Got a supplier! They will do custom sizes and have their own shop. What they make is far superior than what I could slap together.
"apx. dimensions small= 6 5/8" x 3 3/8" medium= 8" x 5" large=11" x 7 3/4" all are 7 3/4" tall . yes we do make them @ our sheet metal shop & sure we can make custom sizes. Thanks Rick"

..
Folks:
The Eagleworks Lab is still working on the copper frustum thruster that was reported on last summer at the AIAA/JPC. We have now confirmed that there is a thrust signature in a hard vacuum (~5.0x10^6 Torr) in both the forward direction, (approx. +50 microNewton (uN) with 50W at 1,937.115 MHz), and the reversed direction, (up to 16uN with a failing RF amp), when the thruster is rotated 180 degrees on the torque pendulum. However we continue to fight through RF amplifier failures brought on by having to operate them in a hard vacuum with few $$$ resources to fix them when they break, so the desired data is coming along very slowly. We are still working on obtaining enough data though that will allow us to go to Glenn Research Center (GRC) for a replication effort in the next few months. However that will only happen if we can make the thrust signature large enough since the GRC thrust stand can only measure down to ~50uN, so we have to get the thrust signature up to at least 100uN before we can go to GRC.
As to the theoretical side of QThrusters, Dr. White has just developed the first cut at a quantum vacuum (QV) based plasma code written in C+ under Windows/Unix and VMD visualization software that utilizes the COMSOL E&M derived field data for a given thruster geometry that allows one to track the movement and velocity of a subset of the QV's electron/positron neutral plasma pairs in the thruster over time as they respond to the applied time varying RF E&M fields in the copper frustum resonant cavity and to each other. This package also allows one to calculate the expected thrust for a given input power and quality factor of the frustum resonant cavity based of standard plasma rocket physics. So far the estimated thrust verses experimental observations are within 2% for the first experimental data run I compared it to, but we still have a long, long road ahead of us of experimental validation before we have any real confidence in this very new QThruster design tool.
Best, Paul March
Thanks Paul for an excellent update, much appreciated.
Congratulations to the Eagleworks team for obtaining experimental force measurements in the torsional pendulum in a hard vacuum (~5.0x10^6 Torr) !
(http://i262.photobucket.com/albums/ii105/scoozna/misc/applause.gif)
It would be most helpful to the scientific/technical community if you could provide the dimensions of the frustum of a cone (truncated cone) used in the Brady et.al. "Anomalous ..." report.
Of several estimates of the geometry, we have established that this is the best estimate so far:
Aero Best estimate as of 11/9/2014 http://forum.nasaspaceflight.com/index.php?topic=29276.msg1285896#msg1285896
cavityLength = 0.24173 m
bigDiameter = 0.27246 m
smallDiameter = 0.15875 m
where "cavity length" is the axial length of the frustum measured along the longitudinal axis of the cone, perpendicular to both the small and big diameters. In other words, the dimension labeled "h" in the following image: (http://offshoremechanics.asmedigitalcollection.asme.org/data/Journals/JMOEEX/28400/031603_1_1.jpeg)
It would be most helpful if you could provide the actual (internal) dimensions of the frustum (or at least if you could provide its approximate dimensions).
Thanks :)

It is all falling into place very nicely now :)
...
In theory, could a dialectric be used to suppress resonance modes that might otherwise be present in an oversized cavity?
The dielectric reduces the frequencies at which resonance occurs, so it helps to avoid cutoff of mode shapes, and therefore there are more mode shapes with the dielectric (looking at all frequencies) if the relative permittivity > 1. Looking at all frequencies, if a given geometry has mode shapes cut off without the dielectric, the inclusion of a dielectric can bring some of the mode shapes back. This is only possible within the available material properties, for example for polymers, it reduces the frequencies (compared to the ones in air) by a factor of Sqrt[2.3] = 1.52. From the list below, Neoprene Rubber seems to have the highest dielectric constant of the solid materials in the list, it appears that Neoprene Rubber may reduce frequencies by a factor of Sqrt[6]=2.45. The liquids seem to have much higher dielectric constants.
The Wikipedia list ( See http://en.wikipedia.org/wiki/Relative_permittivity for a list of relative permittivites.) has listed "Calcium copper titanate" as having a dielectric constant of > 250,000 ! which would imply a factor of Sqrt[250000]=500 times !. It gives this link ( http://oatao.univtoulouse.fr/698/1/boulos_698.pdf ) that describes this multiphase ceramic material.
Unfortunately, relative permittivity strongly decreases with increasing frequency. Inspection of the graphs in ( http://oatao.univtoulouse.fr/698/1/boulos_698.pdf ) shows that the value of relative permittivity of this ceramic at frequencies > 10^5 Hz is less than 10,000 (Sqrt[10,000]=100). Unfortunately, it does not give values in the range of interest for EM Drives (10^9 Hz.)
To supress resonant modes (as compared to air or vacuum) one would need a dielectric with a relative permittivity less than one (resulting in an equivalent speed of light in the medium greater than the speed of light in vacuum "c" ).
(http://www.thelearningpit.com/hj/plcs_files/plcs72.gif)

Here's what I know about cutoff freqs of circular waveguide at least:
"The cutoff wavelength of a circular guide is 1.71 times the diameter of the
waveguide. ...
The US Navy reference should be corrected to read instead:
"The cutoff wavelength for the dominant mode TE_{11} of a circular guide is 1.71 times the diameter of the waveguide."
The dominant mode of a circular waveguide or cavity is the mode with the lowest value of Xfunction. This corresponds to X'_{11} which has a value of X'_{11} = 1.84118 (see: http://wwwal.kuicr.kyotou.ac.jp/www/accelerator/a4/besselroot.htmlx ) . Therefore the dominant mode is TE_{11}.
Using the equation in my post ( http://forum.nasaspaceflight.com/index.php?topic=36313.msg1326637#msg1326637 )
Dsmall > (cmedium * Xfunction) / (fmnp * Pi)
and since the wavelength is
lambda = cmedium / fmnp
where cmedium is the speed of light in the medium and fmnp is the frequency
this is equivalent to
Dsmall > (lambda* Xfunction) / Pi
For the dominant mode TE_{11}, Xfunction = X'_{11} = 1.84118 hence
Dsmall > (lambda* 1.84118) / Pi = lambda / 1.7063
or inverting:
lambda < 1.71 * Dsmall
"The cutoff wavelength for the dominant mode TE_{11} of a circular guide is 1.71 times the diameter of the waveguide."
quod erat demonstrandum
For a truncated cone, I would state:
"The cutoff wavelength for the dominant mode TE_{11} of a truncated cone cavity is 1.71 times the small diameter of the truncated cone."
Contour Plot of mode shape TE11:
Electrical field ____________(solid lines)
Magnetic field            (dashed lines)

Got the sample pack in the mail today. Will report on performance of 10 or 16 mil soon, specifically the ability to hold shape under its own weight while being as light as possible. Now, since I found the supplier, who uses heavier 22 Mil/16 Ounce Copper (see above), these will probably end up as end caps. I don't know what I'm going to do yet, buy or roll'n'solder myself. There's tradeoffs to consider. Like time and weight. So shiny :)
Edit:
It just occurred to me that I should have enough material in hand right now to make something happen if I can find a solution to a cone based off this cylinder: http://forum.nasaspaceflight.com/index.php?topic=36313.msg1320981#msg1320981
What do you think @Rodal? Do we have enough to confidently calculate a frustum of a cone that works and will fit within a 12"x12" sheet? The cylinder fits at least. I'm quite happy staying with 2.45ghz, TE111 for now. I don't care about finding the best mode for max thrust, just any thrust.

Got the sample pack in the mail today. Will report on performance of 10 or 16 mil soon, specifically the ability to hold shape under its own weight while being as light as possible. Now, since I found the supplier, who uses heavier 22 Mil/16 Ounce Copper (see above), these will probably end up as end caps. I don't know what I'm going to do yet, buy or roll'n'solder myself. There's tradeoffs to consider. Like time and weight. So shiny :)
Edit:
It just occurred to me that I should have enough material in hand right now to make something happen if I can find a solution to a cone based off this cylinder: http://forum.nasaspaceflight.com/index.php?topic=36313.msg1320981#msg1320981
What do you think @Rodal? Do we have enough to confidently calculate a frustum of a cone that works and will fit within a 12"x12" sheet? The cylinder fits at least. I'm quite happy staying with 2.45ghz, TE111 for now. I don't care about finding the best mode for max thrust, just any thrust.
First congratulations !
My main concern is being able to tune the EM Drive cavity to achieve Q resonance in the experiment.
Based on NASA's results I think that only the TE modes should provide a force measurement. I don't think that the TM modes will provide a force measurement.
As you know, the magnetron is not going to exactly deliver the nominal frequency of 2.45Ghz, and geometry imperfections are going to affect the natural frequency so that it will be different than the natural frequency of a perfect geometrical cone. Shawyer for the Demo had and adjustable end at the small end of the truncated cone that allowed him to mechanically tune the resonant, natural frequency of the drive (to match his nominal 2.45GHz excitation frequency).
(http://www.wired.com/images_blogs/dangerroom/images/2008/09/24/emdrive_2.jpg)
NASA had the ability to drive the cavity at different frequencies in order to find the natural frequency resonace "sweet spot"...
(http://d34s6f1vnlnqxq.cloudfront.net/11015598/e9f7781725f6444bbc2c7415f8edd698/norm/172484402_8.png)
It would be ideal to have both of those abilities as well :)

Not using a magnetron. I have test equipment. I can find the resonant frequency if we can calculate geometry close enough. The question is, in your opinion, is the math there to make an exact calculation yet?

Not using a magnetron. I have test equipment. I can find the resonant frequency if we can calculate geometry close enough. The question is, in your opinion, is the math there to make an exact calculation yet?
Definitely yes. :)
Please wait another week for me to post the numerical results for NASA and Shawyer vs equations.

Brainstorming some ideas here. So as far as an at home Cavendish, I want something that has the capability of spinning for days/weeks on wireless power (I understand the wireless power may affect the experiment so I'll have to control for it.) without getting wound up. I was thinking spherical magnets at the very top of the fishing line. Any thoughts? Or something better? The reason for this is. I'm using ultra low power, like 100mw low. The Rf source is going to have to ride along. Available electrical power will limit available rf power. Indeed if there is any thrust, it will be much smaller than anyone ever measured before. If it even works at all, it will probably take a long time to become evident on the balance. I want to give the device time to gain speed and keep going before I stop it and flip the "thruster" over. If it gets wound up, it'll just oscillate.
https://www.fourmilab.ch/gravitation/foobar/
http://www.intalek.com/Index/Projects/Research/CavendishExperiment.htm
http://www.ebay.com/bhp/spheremagnets
http://www.amazon.com/BeautyforallWirelessSupplyModuleCharger/dp/B00L19HE5I/ref=sr_1_37?ie=UTF8&qid=1423260545&sr=837&keywords=wireless+power

Break:
@ Paul March, thank you for chiming in. All of us are chomping at the bit for ANY news whatsoever. Maybe Eagleworks could leverage its social media presence (https://www.facebook.com/eagleworksnasa) to keep the public engaged. As far as the lack of $$$ and resources go, I understand that Eagleworks works on a shoestring budget. Wish we could help. It probably isn't acceptable for us to try and crowdfund a government agency. Hopefully you achieve results that will turn heads. Godspeed.
I would like to second this sentiment. Updates would be great!
Paul, If you feel crowdfunding would be worth it I am sure you could get lots of donors (including me). But like Mullerton said, may not be possible due to red tape.
And if not that we can call our congressmen and ask them to get this funded (for what its worth)

Well here's an open one...... http://scharstein.eng.ua.edu/electromagnetic.pdf

Found a nice little update article on nextbigfuture about the EM drive work. Dunno if you guys have seen this already but it might be of interest to a few of you following along intermittently! Enjoy.
http://nextbigfuture.com/2015/02/updateonemdriveworkatnasa.html#more

For people more familiar with NASA, is that common? Does NASA as a civilian agency have a history (or policy?) of suppressing experimental results that, like this, may have military applications? In other words, can the lack of any news at all one way or the other, be taken as a sign that there might be something to this? Or is that just conspiratorial nonsense?
Rockets have military applications, but NASA does not suppress experimental results of rockets. To the contrary, they partner with companies such as SpaceX and share information for the advancement of space exploration. I'm not convinced there is a black out for EM drive technology. There appears to be a delay, which could have many causes. If there are people in the administration advocating for a black out, I think it is a mistake, and probably too late given the amount of information already in the public domain.
To be fair to NASA if this does work it's such a revolutionary technology that the reporting of it is not something to be rushed into. No doubt every result is having to be checked, checked again & then checked again etc etc which no doubt slows down the release of information. Especially if on top of that there are national security implications that have to be considered as well.
Folks:
The Eagleworks Lab is still working on the copper frustum thruster that was reported on last summer at the AIAA/JPC. We have now confirmed that there is a thrust signature in a hard vacuum (~5.0x10^6 Torr) in both the forward direction, (approx. +50 microNewton (uN) with 50W at 1,937.115 MHz), and the reversed direction, (up to 16uN with a failing RF amp), when the thruster is rotated 180 degrees on the torque pendulum. However we continue to fight through RF amplifier failures brought on by having to operate them in a hard vacuum with few $$$ resources to fix them when they break, so the desired data is coming along very slowly. We are still working on obtaining enough data though that will allow us to go to Glenn Research Center (GRC) for a replication effort in the next few months. However that will only happen if we can make the thrust signature large enough since the GRC thrust stand can only measure down to ~50uN, so we have to get the thrust signature up to at least 100uN before we can go to GRC.
As to the theoretical side of QThrusters, Dr. White has just developed the first cut at a quantum vacuum (QV) based plasma code written in C+ under Windows/Unix and VMD visualization software that utilizes the COMSOL E&M derived field data for a given thruster geometry that allows one to track the movement and velocity of a subset of the QV's electron/positron neutral plasma pairs in the thruster over time as they respond to the applied time varying RF E&M fields in the copper frustum resonant cavity and to each other. This package also allows one to calculate the expected thrust for a given input power and quality factor of the frustum resonant cavity based of standard plasma rocket physics. So far the estimated thrust verses experimental observations are within 2% for the first experimental data run I compared it to, but we still have a long, long road ahead of us of experimental validation before we have any real confidence in this very new QThruster design tool.
Best, Paul March
Have you considered crowdfunding? I would absolutely donate to this testing endeavor.
How much money do you need to raise?

It's criminal in my view that this research isn't being better funded especially now that results are coming through.

I don't think funding discussions necessarily belong in this thread. Theory, potential application, and research results are one thing  figuring out how to pay for research on something that is not yet proven to create thrust (via the process of peer review and outside verification) is drifting dangerously close to territory that will earn a surefire thread closure.

I don't think funding discussions necessarily belong in this thread. Theory, potential application, and research results are one thing  figuring out how to pay for research on something that is not yet proven to create thrust (via the process of peer review and outside verification) is drifting dangerously close to territory that will earn a surefire thread closure.
But can you disentangle one from the other as easily as you suggest. I would say not.

We now have the shwayer, yang juan, fetta, nasa and vacuum test. This many tests almost are intriguing enough to warrant funding and lend credibility to the claims.
The only thing that remains is to build more prototypes and create a theory of operation that can be peer reviewed.
If the project lacks funding and it takes another 10 years to build the next prototypes we will have seriously hampered out development as a civilization.

..
Folks:
The Eagleworks Lab is still working on the copper frustum thruster that was reported on last summer at the AIAA/JPC. We have now confirmed that there is a thrust signature in a hard vacuum (~5.0x10^6 Torr) in both the forward direction, (approx. +50 microNewton (uN) with 50W at 1,937.115 MHz), and the reversed direction, (up to 16uN with a failing RF amp), when the thruster is rotated 180 degrees on the torque pendulum. However we continue to fight through RF amplifier failures brought on by having to operate them in a hard vacuum with few $$$ resources to fix them when they break, so the desired data is coming along very slowly. We are still working on obtaining enough data though that will allow us to go to Glenn Research Center (GRC) for a replication effort in the next few months. However that will only happen if we can make the thrust signature large enough since the GRC thrust stand can only measure down to ~50uN, so we have to get the thrust signature up to at least 100uN before we can go to GRC.
As to the theoretical side of QThrusters, Dr. White has just developed the first cut at a quantum vacuum (QV) based plasma code written in C+ under Windows/Unix and VMD visualization software that utilizes the COMSOL E&M derived field data for a given thruster geometry that allows one to track the movement and velocity of a subset of the QV's electron/positron neutral plasma pairs in the thruster over time as they respond to the applied time varying RF E&M fields in the copper frustum resonant cavity and to each other. This package also allows one to calculate the expected thrust for a given input power and quality factor of the frustum resonant cavity based of standard plasma rocket physics. So far the estimated thrust verses experimental observations are within 2% for the first experimental data run I compared it to, but we still have a long, long road ahead of us of experimental validation before we have any real confidence in this very new QThruster design tool.
Best, Paul March
Thanks Paul for an excellent update, much appreciated.
Congratulations to the Eagleworks team for obtaining experimental force measurements in the torsional pendulum in a hard vacuum (~5.0x10^6 Torr) !
(http://i262.photobucket.com/albums/ii105/scoozna/misc/applause.gif)
It would be most helpful to the scientific/technical community if you could provide the dimensions of the frustum of a cone (truncated cone) used in the Brady et.al. "Anomalous ..." report.
Of several estimates of the geometry, we have established that this is the best estimate so far:
Aero Best estimate as of 11/9/2014 http://forum.nasaspaceflight.com/index.php?topic=29276.msg1285896#msg1285896
cavityLength = 0.24173 m
bigDiameter = 0.27246 m
smallDiameter = 0.15875 m
where "cavity length" is the axial length of the frustum measured along the longitudinal axis of the cone, perpendicular to both the small and big diameters. In other words, the dimension labeled "h" in the following image: (http://offshoremechanics.asmedigitalcollection.asme.org/data/Journals/JMOEEX/28400/031603_1_1.jpeg)
It would be most helpful if you could provide the actual (internal) dimensions of the frustum (or at least if you could provide its approximate dimensions).
Thanks :)
The copper frustum we built and now are using has the following internal copper surface dimensions.
Large OD: 11.00" (0.2794m), Small OD: 6.25" (0.1588m) & Length: 9.00" (0.2286m) also see the attached slide with notes on the copper frustum's internal construction. I've also attached a slide with the TM212 E&M resonant mode we are currently exploring in this copper frustum cavity with a screen shot of the end on VMD display that shows the 100,000th simulation increment for this resonant mode. Each step in this plasma code is 1/72 of a full RF cycle, i.e., every 5.0 degrees of phase shift so each time step at 1,937.115 MHz is ~7.12 picoseconds (10^12s). Next is a picture of the forward thrust signature from this copper frustum taken in a ~5.0x10^6 Torr vacuum. However we are currently trying to investigate the thermal response of the is copper frustum on the baseline of the torque pendulum after learning that I made a poor choice in how I built and mounted the copper frustum since it makes these thermal effects more pronounced in these thrust plots than they had to be. I'm appending a partial COMSOL thermal analysis of the copper frustum and I would like to get someone better versed in the art of thermodynamics than I to see if they calculate the expected thermal expansion of the copper frustum AND the polyethylene discs over a 60 second data run with ~50W of 1,937.115 MHz RF applied inside the cavity via a 14mm OD magnetic loop antenna made from 20 gauge magnet wire.
BTW, we have found that both the TE and TM E&M modes of this copper frustum can produce a thrust signature, but so far the TM modes appear to be the better performer, at least for the few modes we have been able to study to date. (Shawyer and the Chinese used the magnetron excited TE012 mode in their frustum cavities without dielectrics being present.)
Lastly, like any busy lab, Eagleworks could always use extra funding to deal with its daily heart burns and required salaries to keep it going. However we are currently a NASA sponsored facility, which sadly precludes being able to accept crowd sourcing or any other outside source of funding, unless it's through a commercial NASA Space Act Agreement that has to be approved up through NASA headquarters in Washington DC. In the meantime we limp along with the meager funding we are allotted until we either run out of time, or we finally prove our QVF/MHD conjecture is close enough to the reality so that we can start building QThrusters with large enough thrusts, (tens to thousands of Newton), to be used on manned spaceflight missions.

...
The copper frustum we built and now are using has the following internal copper surface dimensions.
Large OD: 11.00" (0.2794m), Small OD: 6.25" (0.1588m) & Length: 9.00" (0.2286m) also see the attached slide with notes on the copper frustum's internal construction. I've also attached a slide with the TM212 E&M resonant mode we are currently exploring in this copper frustum cavity with a screen shot of the end on VMD display that shows the 100,000th simulation increment for this resonant mode. Each step in this plasma code is 1/72 of a full RF cycle, i.e., every 5.0 degrees of phase shift so each time step at 1,937.115 MHz is ~7.12 picoseconds (10^12s). Next is a picture of the forward thrust signature from this copper frustum taken in a ~5.0x10^6 Torr vacuum. However we are currently trying to investigate the thermal response of the is copper frustum on the baseline of the torque pendulum after learning that I made a poor choice in how I built and mounted the copper frustum since it makes these thermal effects more pronounced in these thrust plots than they had to be. I'm appending a partial COMSOL thermal analysis of the copper frustum and I would like to get someone better versed in the art of thermodynamics than I to see if they calculate the expected thermal expansion of the copper frustum AND the polyethylene discs over a 60 second data run with ~50W of 1,937.115 MHz RF applied inside the cavity via a 14mm OD magnetic loop antenna made from 20 gauge magnet wire.
BTW, we have found that both the TE and TM E&M modes of this copper frustum can produce a thrust signature, but so far the TM modes appear to be the better performer, at least for the few modes we have been able to study to date. (Shawyer and the Chinese used the magnetron excited TE012 mode in their frustum cavities without dielectrics being present.)
Lastly, like any busy lab, Eagleworks could always use extra funding to deal with its daily heart burns and required salaries to keep it going. However we are currently a NASA sponsored facility, which sadly precludes being able to accept crowd sourcing or any other outside source of funding, unless it's through a commercial NASA Space Act Agreement that has to be approved up through NASA headquarters in Washington DC. In the meantime we limp along with the meager funding we are allotted until we either run out of time, or we finally prove our QVF/MHD conjecture is close enough to the reality so that we can start building QThrusters with large enough thrusts, (tens to thousands of Newton), to be used on manned spaceflight missions.
Thanks so much, Paul for this excellent information.
(http://s3.amazonaws.com/remproduction/attachments/9800/full/9781618101204.jpg?1370989043)
I hope that all postings in this #2 thread will continue to abide by the guidelines here: http://forum.nasaspaceflight.com/index.php?topic=29276.msg1301657#msg1301657. The previous thread was locked because of "personal attacks" and "stupid" and "pointless" posts "that did not feel like this site's subject matter."
I hope that we can continue this thread in a professional manner concentrating on technical matters regarding EM Drive Developments related to space flight applications so that we maintain a healthy and open channel of communication with you (Paul March at NASA). Also with all others interested in the science and technology of EM Drive Developments related to space flight applications.

Rodal:
As a follow up to my previous post and in the spirit of open disclosure, I'm including our last nullthrust test that ran the RF amp at 10.0Adc while its RF power was being dissipated in a 100W, 50 ohm dummy load positioned in place of the test article on the torque pendulum (TP), a picture of the new heat shields for our torque pendulum's upper and lower torsion springs, (more belts and suspenders to mitigate thermal drifts in the TP baseline), the reversed test setup drawing and the best reversed thrust plot obtained just before or during when our second and last 120W max RF amplifier was dying from internal corona discharges around its RF output circulator. Apparently the RF amp's internal gas pressure had gone down from 1 Bar to an estimated 10 Torr or less after a few days leaking air in a hard vacuum. And 0.1to10.0 Torr is where glow discharges are the easiest to ignite with RF signals. So much for EMPower's "hermetic" sealed RF amplifiers...
Best, Paul March

Rodal:
As a follow up to my previous post and in the spirit of open disclosure, I'm including our last nullthrust test that ran the RF amp at 10.0Adc while its RF power was being dissipated in a 100W, 50 ohm dummy load positioned in place of the test article on the torque pendulum (TP), a picture of the new heat shields for our torque pendulum's upper and lower torsion springs, (more belts and suspenders to mitigate thermal drifts in the TP baseline), the reversed test setup drawing and the best reversed thrust plot obtained just before or during when our second and last 120W max RF amplifier was dying from internal corona discharges around its RF output circulator. Apparently the RF amp's internal gas pressure had gone down from 1 Bar to an estimated 10 Torr or less after a few days leaking air in a hard vacuum. And 0.1to10.0 Torr is where glow discharges are the easiest to ignite with RF signals. So much for EMPower's "hermetic" sealed RF amplifiers...
Best, Paul March
First off congratulations, and thank you very much for the information.
One question though. The use of a dummy load to the best of my understanding provides evidence to support that the thrust measurement device is not generating false positive data. Is it possible to run the Frustum in a null configuration? If so, is that in the plans before the next report is published?

Please be aware it wasn't me intention to take this thread off topic so apologies for that.

Has anyone notified Dr. M re. precise cavity dimensions and latest forces from Paul? I would but don't have his link handy.

Has anyone notified Dr. M re. precise cavity dimensions and latest forces from Paul? I would but don't have his link handy.
I sent Dr. McCulloch a message as soon as I saw the dimensions. Thanks

Well here's an open one...... http://scharstein.eng.ua.edu/electromagnetic.pdf
Thank you. That paper deals with the surface current induced by an incident plane wave on a truncated cone.
For electromagnetic transmission properties of spherical transverse electric(TE) and transversemagnetic (TM) eigenmodes within a truncated cone, see the enclosed paper.
(1) We have developed an exact analytical approach for the description of the electromagnetic
fields inside a hollow metallic waveguide with a taper. Analytical expressions for the spatital
distributions of electromagnetic field components, attenuation constant, phase constant and
wave impedance are derived.
(2)According to our theory the modes configurations inside a tapered hollow metallic
waveguide are similar to those in a cylindrical hollow metallic waveguide, but the
transmission characteristics and engergy densities distributions along propagating direction
have a different behavior. It is shown that all modes run continuously from a propagating
through a transition to an evanescent region and the value of the attenuation increases as the
distance from the cone vertex and the cone angle desrease. A strict distinction between pure
propagating and pure evanescent modes can not be achieved. There is no welldefined cutoff
wavelength but rather a cutoff radius. It is interesting to note that the magnitude of the cutoff
radius is related to the wavelength and the cone halfangle. The values of attenuation and
phase constants for the spherical TE and TM modes inside the tapered hollow metallic
waveguide depend on the cone halfangle very seriously. As the cone halfangle decreases, the
value of the attenuation increases. The smaller the cone halfangle is, the faster the modes
attenuate. This can explain why large taper angle may improve the light throughout in
aperture probe which finds an important application in scanning nearfield optical microscopy
(3) As follows from our calculations, we find that in the propagating region the attentuation of
some modes decays faster than those of others, and one mode after the other reaches cutoff in
the tapered hollow metallic waveguide as the distance from the cone vertex decreases.
4) In the tapered hollow metallic waveguide, light is well confined in the hollow core (air
region) because it is reflected back to the core by a metal wall.

Rodal:
As a follow up to my previous post and in the spirit of open disclosure, I'm including our last nullthrust test that ran the RF amp at 10.0Adc while its RF power was being dissipated in a 100W, 50 ohm dummy load positioned in place of the test article on the torque pendulum (TP), a picture of the new heat shields for our torque pendulum's upper and lower torsion springs, (more belts and suspenders to mitigate thermal drifts in the TP baseline), the reversed test setup drawing and the best reversed thrust plot obtained just before or during when our second and last 120W max RF amplifier was dying from internal corona discharges around its RF output circulator. Apparently the RF amp's internal gas pressure had gone down from 1 Bar to an estimated 10 Torr or less after a few days leaking air in a hard vacuum. And 0.1to10.0 Torr is where glow discharges are the easiest to ignite with RF signals. So much for EMPower's "hermetic" sealed RF amplifiers...
Best, Paul March
First off congratulations, and thank you very much for the information.
One question though. The use of a dummy load to the best of my understanding provides evidence to support that the thrust measurement device is not generating false positive data. Is it possible to run the Frustum in a null configuration? If so, is that in the plans before the next report is published?
Birchoff:
"Is it possible to run the Frustum in a null configuration? If so, is that in the plans before the next report is published?"
Yes and yes. In fact it was one of the requests made by the blue ribbon panel of PhDs that NASA/EP hired to review the Eagleworks Lab's theoretical and experimental work last summer. Even if will take a new mounting arrangement to get it accomplished.
Overall though the blue ribbon panel's experimentalists appeared to be pleased with our previous and upcoming lab work. However they ripped into Sonny's QVF/MHD conjecture because it relies on the quantum vacuum being mutable and engineerable whereas the current physics mainstream thinks that the quantum vacuum is an immutable ground energy state of the universe that canNOT be used to convey energy or momentum as proposed by Dr. White. However they brushed aside Sonny's QVF based derivation of the Bohr hydrogen atom electron radius as a "mathematical coincidence" and didn't have a word to say what the Casimir effect and other quantum vacuum phenomenon were caused by, that can only occur only if the QV is mutable and can convey energy and momentum. So Sonny and Jerry Vera took it upon themselves last fall to increase this mathematical coincidence from one to more than 47 times as they explored the QV created atomic electron shell radii for atoms up to atomic number 7 all based on the QV being the root cause for all of it including the origins of the electron and all other subatomic particles.
BTW, IMO Jim Woodward's MachEffect (ME) conjecture that is based primarily on SRT and GRT, is still in the running for a way to explain his and our test results to date. However the ME also has its detractors since it requires that instantaneous Wheeler/Feynman radiation reaction forces being required between a local time varying mass and all the other mass/energy in the casually connected universe, since this mechanism is used to balance the ME's energy & momentum conservation books. In the end analysis though I think that the ME will rest on the quantum nature of spacetime, since in Woodward's eyes the gravitational field IS spacetime, and in our eyes GRT's spacetime is in reality the quantum vacuum that probably has at least 4 spatial dimensions and one time dimension!
Best, Paul March

Thank you for the very interesting information about the "blue ribbon panel of PhDs that NASA/EP hired to review the Eagleworks Lab's theoretical and experimental work last summer." This is very relevant information to EM Drive Developments.
Paul, in your absence, the prior thread on EM Drives was derailed by polemical discussion of Woodward's MachEffect conjecture (more info here: http://forum.nasaspaceflight.com/index.php?topic=29276.msg1301657#msg1301657 ).
To avoid such issues, it may be preferable to continue discussion of that conjecture (Woodward's MachEffect) at this thread, dedicated exclusively to Woodward's MachEffect: http://forum.nasaspaceflight.com/index.php?topic=31037.460 )

Rodal:
As a follow up to my previous post and in the spirit of open disclosure, I'm including our last nullthrust test that ran the RF amp at 10.0Adc while its RF power was being dissipated in a 100W, 50 ohm dummy load positioned in place of the test article on the torque pendulum (TP), a picture of the new heat shields for our torque pendulum's upper and lower torsion springs, (more belts and suspenders to mitigate thermal drifts in the TP baseline), the reversed test setup drawing and the best reversed thrust plot obtained just before or during when our second and last 120W max RF amplifier was dying from internal corona discharges around its RF output circulator. Apparently the RF amp's internal gas pressure had gone down from 1 Bar to an estimated 10 Torr or less after a few days leaking air in a hard vacuum. And 0.1to10.0 Torr is where glow discharges are the easiest to ignite with RF signals. So much for EMPower's "hermetic" sealed RF amplifiers...
Best, Paul March
First off congratulations, and thank you very much for the information.
One question though. The use of a dummy load to the best of my understanding provides evidence to support that the thrust measurement device is not generating false positive data. Is it possible to run the Frustum in a null configuration? If so, is that in the plans before the next report is published?
Birchoff:
"Is it possible to run the Frustum in a null configuration? If so, is that in the plans before the next report is published?"
Yes and yes. In fact it was one of the requests made by the blue ribbon panel of PhDs that NASA/EP hired to review the Eagleworks Lab's theoretical and experimental work last summer. Even if will take a new mounting arrangement to get it accomplished.
Overall though the blue ribbon panel's experimentalists appeared to be pleased with our previous and upcoming lab work. However they ripped into Sonny's QVF/MHD conjecture because it relies on the quantum vacuum being mutable and engineerable whereas the current physics mainstream thinks that the quantum vacuum is an immutable ground energy state of the universe that canNOT be used to convey energy or momentum as proposed by Dr. White. However they brushed aside Sonny's QVF based derivation of the Bohr hydrogen atom electron radius as a "mathematical coincidence" and didn't have a word to say what the Casimir effect and other quantum vacuum phenomenon were caused by, that can only occur only if the QV is mutable and can convey energy and momentum. So Sonny and Jerry Vera took it upon themselves last fall to increase this mathematical coincidence from one to more than 47 times as they explored the QV created atomic electron shell radii for atoms up to atomic number 7 all based on the QV being the root cause for all of it including the origins of the electron and all other subatomic particles.
BTW, IMO Jim Woodward's MachEffect (ME) conjecture that is based primarily on SRT and GRT, is still in the running for a way to explain his and our test results to date. However the ME also has its detractors since it requires that instantaneous Wheeler/Feynman radiation reaction forces being required between a local time varying mass and all the other mass/energy in the casually connected universe, since this mechanism is used to balance the ME's energy & momentum conservation books. In the end analysis though I think that the ME will rest on the quantum nature of spacetime, since in Woodward's eyes the gravitational field IS spacetime, and in our eyes GRT's spacetime is in reality the quantum vacuum that probably has at least 4 spatial dimensions and one time dimension!
Best, Paul March
Thanks for the insight. what does Dr. White believe he has to do in order to prove or disprove that his conjecture explains the behavior observed when the truncated frustum is energized appropriately? Assuming all the testing currently being done is successful and you get a successful set of replications from other labs. The only thing we would be able to conclusively claim is that the device, built as describes, provides thrust. How does Dr. White plan to show that the device behaves as described by his theory? Also, if Dr. White cannot prove that his theory completely explains the observations, what would be the next steps to find an explanation for the observation? And would we need to have such a theory before we begin using this thing in well defined use cases like ISS or satelite station keeping?

Thank you for the very interesting information about the "blue ribbon panel of PhDs that NASA/EP hired to review the Eagleworks Lab's theoretical and experimental work last summer." This is very relevant information to EM Drive Developments.
Paul, in your absence, the prior thread on EM Drives was derailed by polemical discussion of Woodward's MachEffect (ME) conjecture (more info here: http://forum.nasaspaceflight.com/index.php?topic=29276.msg1301657#msg1301657 ).
To avoid such issues, it may be preferable to continue discussion of that conjecture (Woodward's MachEffect) can be pursued at this thread, dedicated exclusively to Woodward's MachEffect: http://forum.nasaspaceflight.com/index.php?topic=31037.460 )
Sorry, I didn't know that Jim Woodward's work had become a hot potato, so I'll go to the ME thread if the ME topic comes up again.
Best, PM

Thank you for the very interesting information about the "blue ribbon panel of PhDs that NASA/EP hired to review the Eagleworks Lab's theoretical and experimental work last summer." This is very relevant information to EM Drive Developments.
Paul, in your absence, the prior thread on EM Drives was derailed by polemical discussion of Woodward's MachEffect (ME) conjecture (more info here: http://forum.nasaspaceflight.com/index.php?topic=29276.msg1301657#msg1301657 ).
To avoid such issues, it may be preferable to continue discussion of that conjecture (Woodward's MachEffect) can be pursued at this thread, dedicated exclusively to Woodward's MachEffect: http://forum.nasaspaceflight.com/index.php?topic=31037.460 )
Sorry, I didn't know that Jim Woodward's work had become a hot potato, so I'll go to the ME thread if the ME topic comes up again.
Best, PM
I was trying to convey how pleased to hear back from you and how excited I was about the news you conveyed and how I wanted you to continue posting. It was my poor attempt at preventing this communication from being shut down again :)

Indeed we are all very delighted to hear from you Paul. This thread, and thread 1 has been a fury of activity trying to explore this proposition that we can possibly achieve all electric thrust in the vacuum of space without carrying propellant, and what it all means for science and humanity's future.
Given the reported results in vacuum, this is progress.
Patiently looking forward to reading "Anomalous Thrust Production from an RF Test Device Measured on a LowThrust Torsion Pendulum"

Indeed we are all very delighted to hear from you Paul. This thread, and thread 1 has been a fury of activity trying to explore this proposition that we can possibly achieve all electric thrust in the vacuum of space without carrying propellant, and what it all means for science and humanity's future.
Given the reported results in vacuum, this is progress.
Patiently looking forward to reading "Anomalous Thrust Production from an RF Test Device Measured on a LowThrust Torsion Pendulum"
seconded

Rodal:
As a follow up to my previous post and in the spirit of open disclosure, I'm including our last nullthrust test that ran the RF amp at 10.0Adc while its RF power was being dissipated in a 100W, 50 ohm dummy load positioned in place of the test article on the torque pendulum (TP), a picture of the new heat shields for our torque pendulum's upper and lower torsion springs, (more belts and suspenders to mitigate thermal drifts in the TP baseline), the reversed test setup drawing and the best reversed thrust plot obtained just before or during when our second and last 120W max RF amplifier was dying from internal corona discharges around its RF output circulator. Apparently the RF amp's internal gas pressure had gone down from 1 Bar to an estimated 10 Torr or less after a few days leaking air in a hard vacuum. And 0.1to10.0 Torr is where glow discharges are the easiest to ignite with RF signals. So much for EMPower's "hermetic" sealed RF amplifiers...
Best, Paul March
First off congratulations, and thank you very much for the information.
One question though. The use of a dummy load to the best of my understanding provides evidence to support that the thrust measurement device is not generating false positive data. Is it possible to run the Frustum in a null configuration? If so, is that in the plans before the next report is published?
Birchoff:
"Is it possible to run the Frustum in a null configuration? If so, is that in the plans before the next report is published?"
Yes and yes. In fact it was one of the requests made by the blue ribbon panel of PhDs that NASA/EP hired to review the Eagleworks Lab's theoretical and experimental work last summer. Even if will take a new mounting arrangement to get it accomplished.
Overall though the blue ribbon panel's experimentalists appeared to be pleased with our previous and upcoming lab work. However they ripped into Sonny's QVF/MHD conjecture because it relies on the quantum vacuum being mutable and engineerable whereas the current physics mainstream thinks that the quantum vacuum is an immutable ground energy state of the universe that canNOT be used to convey energy or momentum as proposed by Dr. White. However they brushed aside Sonny's QVF based derivation of the Bohr hydrogen atom electron radius as a "mathematical coincidence" and didn't have a word to say what the Casimir effect and other quantum vacuum phenomenon were caused by, that can only occur only if the QV is mutable and can convey energy and momentum. So Sonny and Jerry Vera took it upon themselves last fall to increase this mathematical coincidence from one to more than 47 times as they explored the QV created atomic electron shell radii for atoms up to atomic number 7 all based on the QV being the root cause for all of it including the origins of the electron and all other subatomic particles.
BTW, IMO Jim Woodward's MachEffect (ME) conjecture that is based primarily on SRT and GRT, is still in the running for a way to explain his and our test results to date. However the ME also has its detractors since it requires that instantaneous Wheeler/Feynman radiation reaction forces being required between a local time varying mass and all the other mass/energy in the casually connected universe, since this mechanism is used to balance the ME's energy & momentum conservation books. In the end analysis though I think that the ME will rest on the quantum nature of spacetime, since in Woodward's eyes the gravitational field IS spacetime, and in our eyes GRT's spacetime is in reality the quantum vacuum that probably has at least 4 spatial dimensions and one time dimension!
Best, Paul March
Thanks for the insight. what does Dr. White believe he has to do in order to prove or disprove that his conjecture explains the behavior observed when the truncated frustum is energized appropriately? Assuming all the testing currently being done is successful and you get a successful set of replications from other labs. The only thing we would be able to conclusively claim is that the device, built as describes, provides thrust. How does Dr. White plan to show that the device behaves as described by his theory? Also, if Dr. White cannot prove that his theory completely explains the observations, what would be the next steps to find an explanation for the observation? And would we need to have such a theory before we begin using this thing in well defined use cases like ISS or satelite station keeping?
Birchoff:
"What does Dr. White believe he has to do in order to prove or disprove that his conjecture explains the behavior observed when the truncated frustum is energized appropriately?"
Exactly what he and I have been doing. Fleshing out his QVF conjecture in papers for the appropriate peer reviewed journals. He is also continuing the generation of the COMSOL E&M and QVF based C++ plasma code that will allow us to compare the resonant cavity lab results with the QVF based force predictions using the volume integral of the ejected semivirtual e/p pairs for the resonant cavity geometry in question.
We have already performed the first step along this path with the preliminary results I provided in an earlier post today. In that slide which is based on the copper frustum cavity running in its TM212 mode with 50W of 1,937.188 MHz RF power applied, we showed that the predicted thrust that took over 18 hours to run the 150k time samples on an i5 PC, was 54uN and the average for five real data runs at 50W was 55uN. Is that another mathematical coincidence? I don't think so, but we won't know for sure until I have time to compare the rest of the 30W, 40W, and 60W averages on the attached slide with the same computer code that will take 17 hours to run on my lab PC for each additional example. We will also be looking at modeling and comparing the results of the Cannae test articles we tested in 2013 & 2014, along with the Shawyer/Chinese EMDrive results with and without dielectrics in the resonant cavities. If our plasma code predictions nail all those tests to say within +/10% of the experimental results then we can start using it to optimize the thrust output of these QVF/MHD based thrusters.
BTW, it appears that the dielectric discs may act as QV e/p pair reflectors that aid in the conical frustum shape's force symmetry breaking and force rectification process. Left to its own devices, the QV e/p pair spray generated by the applied RF energy tends to want to go in all directions instead of the desired tightly collimated unidirectional propellant beam that goes in one direction while the thruster backreacts in the opposite direction according to Newton's third law.
Best, Paul March

Rodal:
As a follow up to my previous post and in the spirit of open disclosure, I'm including our last nullthrust test that ran the RF amp at 10.0Adc while its RF power was being dissipated in a 100W, 50 ohm dummy load positioned in place of the test article on the torque pendulum (TP), a picture of the new heat shields for our torque pendulum's upper and lower torsion springs, (more belts and suspenders to mitigate thermal drifts in the TP baseline), the reversed test setup drawing and the best reversed thrust plot obtained just before or during when our second and last 120W max RF amplifier was dying from internal corona discharges around its RF output circulator. Apparently the RF amp's internal gas pressure had gone down from 1 Bar to an estimated 10 Torr or less after a few days leaking air in a hard vacuum. And 0.1to10.0 Torr is where glow discharges are the easiest to ignite with RF signals. So much for EMPower's "hermetic" sealed RF amplifiers...
Best, Paul March
First off congratulations, and thank you very much for the information.
One question though. The use of a dummy load to the best of my understanding provides evidence to support that the thrust measurement device is not generating false positive data. Is it possible to run the Frustum in a null configuration? If so, is that in the plans before the next report is published?
Birchoff:
"Is it possible to run the Frustum in a null configuration? If so, is that in the plans before the next report is published?"
Yes and yes. In fact it was one of the requests made by the blue ribbon panel of PhDs that NASA/EP hired to review the Eagleworks Lab's theoretical and experimental work last summer. Even if will take a new mounting arrangement to get it accomplished.
Overall though the blue ribbon panel's experimentalists appeared to be pleased with our previous and upcoming lab work. However they ripped into Sonny's QVF/MHD conjecture because it relies on the quantum vacuum being mutable and engineerable whereas the current physics mainstream thinks that the quantum vacuum is an immutable ground energy state of the universe that canNOT be used to convey energy or momentum as proposed by Dr. White. However they brushed aside Sonny's QVF based derivation of the Bohr hydrogen atom electron radius as a "mathematical coincidence" and didn't have a word to say what the Casimir effect and other quantum vacuum phenomenon were caused by, that can only occur only if the QV is mutable and can convey energy and momentum. So Sonny and Jerry Vera took it upon themselves last fall to increase this mathematical coincidence from one to more than 47 times as they explored the QV created atomic electron shell radii for atoms up to atomic number 7 all based on the QV being the root cause for all of it including the origins of the electron and all other subatomic particles.
BTW, IMO Jim Woodward's MachEffect (ME) conjecture that is based primarily on SRT and GRT, is still in the running for a way to explain his and our test results to date. However the ME also has its detractors since it requires that instantaneous Wheeler/Feynman radiation reaction forces being required between a local time varying mass and all the other mass/energy in the casually connected universe, since this mechanism is used to balance the ME's energy & momentum conservation books. In the end analysis though I think that the ME will rest on the quantum nature of spacetime, since in Woodward's eyes the gravitational field IS spacetime, and in our eyes GRT's spacetime is in reality the quantum vacuum that probably has at least 4 spatial dimensions and one time dimension!
Best, Paul March
Thanks for the insight. what does Dr. White believe he has to do in order to prove or disprove that his conjecture explains the behavior observed when the truncated frustum is energized appropriately? Assuming all the testing currently being done is successful and you get a successful set of replications from other labs. The only thing we would be able to conclusively claim is that the device, built as describes, provides thrust. How does Dr. White plan to show that the device behaves as described by his theory? Also, if Dr. White cannot prove that his theory completely explains the observations, what would be the next steps to find an explanation for the observation? And would we need to have such a theory before we begin using this thing in well defined use cases like ISS or satelite station keeping?
Birchoff:
"What does Dr. White believe he has to do in order to prove or disprove that his conjecture explains the behavior observed when the truncated frustum is energized appropriately?"
Exactly what he and I have been doing. Fleshing out his QVF conjecture in papers for the appropriate peer reviewed journals. He is also continuing the generation of the COMSOL E&M and QVF based C++ plasma code that will allow us to compare the resonant cavity lab results with the QVF based force predictions using the volume integral of the ejected semivirtual e/p pairs for the resonant cavity geometry in question.
We have already performed the first step along this path with the preliminary results I provided in an earlier post today. In that slide which is based on the copper frustum cavity running in its TM212 mode with 50W of 1,937.188 MHz RF power applied, we showed that the predicted thrust that took over 18 hours to run the 150k time samples on an i5 PC, was 54uN and the average for five real data runs at 50W was 55uN. Is that another mathematical coincidence? I don't think so, but we won't know for sure until I have time to compare the rest of the 30W, 40W, and 60W averages on the attached slide with the same computer code that will take 17 hours to run on my lab PC for each additional example. We will also be looking at modeling and comparing the results of the Cannae test articles we tested in 2013 & 2014, along with the Shawyer/Chinese EMDrive results with and without dielectrics in the resonant cavities. If our plasma code predictions nail all those tests to say within +/10% of the experimental results then we can start using it to optimize the thrust output of these QVF/MHD based thrusters.
BTW, it appears that the dielectric discs may act as QV e/p pair reflectors that aid in the conical frustum shape's force symmetry breaking and force rectification process. Left to its own devices, the QV e/p pair spray generated by the applied RF energy tends to want to go in all directions instead of the desired tightly collimated unidirectional propellant beam that goes in one direction while the thruster backreacts in the opposite direction according to Newton's third law.
Best, Paul March
Fantastic...
One last question if you dont mind indulging me in a bit of educated speculation. Can the copper frustum be made smaller while maintaining the same thrust performance? I would expect that the smaller frustum would lead to different parameters. But what I am trying to gauge is if there is some lower limit on the size of the frustum.

BTW, it appears that the dielectric discs may act as QV e/p pair reflectors that aid in the conical frustum shape's force symmetry breaking and force rectification process. Left to its own devices, the QV e/p pair spray generated by the applied RF energy tends to want to go in all directions instead of the desired tightly collimated unidirectional propellant beam that goes in one direction while the thruster backreacts in the opposite direction according to Newton's third law.
Best, Paul March
Kinda sounds like sail, like this:
http://forum.nasaspaceflight.com/index.php?topic=29276.msg1299424#msg1299424
There is a LOT of research in thread 1 that we dug up concerning transferring momentum from the QV to dielectrics and how the symmetry breaking works to enable momentum transfer under EM fields. I can dig it all up again for an executive summary.

Birchoff:
"What does Dr. White believe he has to do in order to prove or disprove that his conjecture explains the behavior observed when the truncated frustum is energized appropriately?"
Exactly what he and I have been doing. Fleshing out his QVF conjecture in papers for the appropriate peer reviewed journals. He is also continuing the generation of the COMSOL E&M and QVF based C++ plasma code that will allow us to compare the resonant cavity lab results with the QVF based force predictions using the volume integral of the ejected semivirtual e/p pairs for the resonant cavity geometry in question.
...
Thank you for taking time giving some valuable info on ongoing work to followers of this line of research. We all have certainly a ton of questions, hope you can shed some light on the frame of reference aspects (and energetic consequences) : in the present apparently successful simulation model (quantitatively predictive), in what frame of reference the e/p pairs are "found" before they are asymmetrically accelerated and ejected by the drive's power ? Are they always harvested "at rest" relative to the frustum ?
This would allow for more kinetic energy at the end of a mission than was injected into the drive (at the cost of a disturbed vacuum in the wake...). Sorry if it may sound controversial but I dare say we see two possible outcomes : tapping energy from the vacuum, or strange memory effect of "initial velocity" (for preventing such apparent overunit yield). Sounds like the working model validates the former and not the later ?
Third possibility : a preferred rest frame for the vacuum, since the specific speed of the present experimental thrust is 1000km/s we should expect some thrust/power variations relative to sidereal time (a few tens of % if this "aether" is cosmological, a few % if it is bound to galaxy rotation...) Any other alternative discussed ?
I guess those energetic aspects are asked again and again by sceptics, the "propeller" analogy needs clarification as for the implied instant velocity of the medium pushed against. I am sceptic but without an agenda. Just wonder where it leads.

Rodal:
As a follow up to my previous post and in the spirit of open disclosure, I'm including our last nullthrust test that ran the RF amp at 10.0Adc while its RF power was being dissipated in a 100W, 50 ohm dummy load positioned in place of the test article on the torque pendulum (TP), a picture of the new heat shields for our torque pendulum's upper and lower torsion springs, (more belts and suspenders to mitigate thermal drifts in the TP baseline), the reversed test setup drawing and the best reversed thrust plot obtained just before or during when our second and last 120W max RF amplifier was dying from internal corona discharges around its RF output circulator. Apparently the RF amp's internal gas pressure had gone down from 1 Bar to an estimated 10 Torr or less after a few days leaking air in a hard vacuum. And 0.1to10.0 Torr is where glow discharges are the easiest to ignite with RF signals. So much for EMPower's "hermetic" sealed RF amplifiers...
Best, Paul March
First off congratulations, and thank you very much for the information.
One question though. The use of a dummy load to the best of my understanding provides evidence to support that the thrust measurement device is not generating false positive data. Is it possible to run the Frustum in a null configuration? If so, is that in the plans before the next report is published?
Birchoff:
"Is it possible to run the Frustum in a null configuration? If so, is that in the plans before the next report is published?"
Yes and yes. In fact it was one of the requests made by the blue ribbon panel of PhDs that NASA/EP hired to review the Eagleworks Lab's theoretical and experimental work last summer. Even if will take a new mounting arrangement to get it accomplished.
Overall though the blue ribbon panel's experimentalists appeared to be pleased with our previous and upcoming lab work. However they ripped into Sonny's QVF/MHD conjecture because it relies on the quantum vacuum being mutable and engineerable whereas the current physics mainstream thinks that the quantum vacuum is an immutable ground energy state of the universe that canNOT be used to convey energy or momentum as proposed by Dr. White. However they brushed aside Sonny's QVF based derivation of the Bohr hydrogen atom electron radius as a "mathematical coincidence" and didn't have a word to say what the Casimir effect and other quantum vacuum phenomenon were caused by, that can only occur only if the QV is mutable and can convey energy and momentum. So Sonny and Jerry Vera took it upon themselves last fall to increase this mathematical coincidence from one to more than 47 times as they explored the QV created atomic electron shell radii for atoms up to atomic number 7 all based on the QV being the root cause for all of it including the origins of the electron and all other subatomic particles.
BTW, IMO Jim Woodward's MachEffect (ME) conjecture that is based primarily on SRT and GRT, is still in the running for a way to explain his and our test results to date. However the ME also has its detractors since it requires that instantaneous Wheeler/Feynman radiation reaction forces being required between a local time varying mass and all the other mass/energy in the casually connected universe, since this mechanism is used to balance the ME's energy & momentum conservation books. In the end analysis though I think that the ME will rest on the quantum nature of spacetime, since in Woodward's eyes the gravitational field IS spacetime, and in our eyes GRT's spacetime is in reality the quantum vacuum that probably has at least 4 spatial dimensions and one time dimension!
Best, Paul March
Thanks for the insight. what does Dr. White believe he has to do in order to prove or disprove that his conjecture explains the behavior observed when the truncated frustum is energized appropriately? Assuming all the testing currently being done is successful and you get a successful set of replications from other labs. The only thing we would be able to conclusively claim is that the device, built as describes, provides thrust. How does Dr. White plan to show that the device behaves as described by his theory? Also, if Dr. White cannot prove that his theory completely explains the observations, what would be the next steps to find an explanation for the observation? And would we need to have such a theory before we begin using this thing in well defined use cases like ISS or satelite station keeping?
Birchoff:
"What does Dr. White believe he has to do in order to prove or disprove that his conjecture explains the behavior observed when the truncated frustum is energized appropriately?"
Exactly what he and I have been doing. Fleshing out his QVF conjecture in papers for the appropriate peer reviewed journals. He is also continuing the generation of the COMSOL E&M and QVF based C++ plasma code that will allow us to compare the resonant cavity lab results with the QVF based force predictions using the volume integral of the ejected semivirtual e/p pairs for the resonant cavity geometry in question.
We have already performed the first step along this path with the preliminary results I provided in an earlier post today. In that slide which is based on the copper frustum cavity running in its TM212 mode with 50W of 1,937.188 MHz RF power applied, we showed that the predicted thrust that took over 18 hours to run the 150k time samples on an i5 PC, was 54uN and the average for five real data runs at 50W was 55uN. Is that another mathematical coincidence? I don't think so, but we won't know for sure until I have time to compare the rest of the 30W, 40W, and 60W averages on the attached slide with the same computer code that will take 17 hours to run on my lab PC for each additional example. We will also be looking at modeling and comparing the results of the Cannae test articles we tested in 2013 & 2014, along with the Shawyer/Chinese EMDrive results with and without dielectrics in the resonant cavities. If our plasma code predictions nail all those tests to say within +/10% of the experimental results then we can start using it to optimize the thrust output of these QVF/MHD based thrusters.
BTW, it appears that the dielectric discs may act as QV e/p pair reflectors that aid in the conical frustum shape's force symmetry breaking and force rectification process. Left to its own devices, the QV e/p pair spray generated by the applied RF energy tends to want to go in all directions instead of the desired tightly collimated unidirectional propellant beam that goes in one direction while the thruster backreacts in the opposite direction according to Newton's third law.
Best, Paul March
What about testing for a "wake"? I vaguely remember watching a presentation Dr. White gave where he said that one way of verifying conservation is being maintained would be to demonstrate the frustum creating some sort of "wake" or its equivalent. Will that also be tested before the next report?

Just checked in for a bit. WOW! Things have been busy!
Quickly plugged in those measurements. Used TM212, geometric mean. Needed effective n=1.38 to get the freq w/ dielectric. Q is down to 1000 for 50mmN at 50W.
Been chasing the selfacceleration papers, which looks good so far.
Hope to get some free time, too much nano going on.

Those are all good observations. Just as the speed of light is Lorentz invariant so too should be the vacuum. If symmetries were broken, there should be particles or phonons emerge that are detectable. Noether's theorem comes into play here and if the Emdrive does in fact work, we need to reexamine what we know about symmetries and conservation laws, because in the end, experiment always wins. Aside from being a neat thruster, it could be an instrument which enables a better understanding of the QV.
http://www.ovaltech.ca/pdfss/The_Challenge_to_Create_the_Space_Drive.pdf
One approach to conserve momentum is to consider space
itself as the reaction mass. This approach evokes the old idea
of an "ether." To be strictly consistent with empirical
evidence, such as the MichelsonMorely experiment, any
further research to revisit the idea of an ether would have to
impose the condition that an ether is electromagnetically
Lorentz invariant Note that this condition is a characteristic
of the ZPF [7].
So that approach is out because it is in opposition to MichelsonMorely.
An alternative to considering space as the reaction mass is
to further develop Mach's Principle. Mach's Principle asserts
that surrounding matter gives rise to inertial frames, and that
the inertial frames are somehow connected to the surrounding
matter [9]. Mach wrote that although he felt a connection to
the surrounding matter was required for the property of inertia
to be detectable, he also admitted that such a treatment was
not necessary to satisfactorily describe the laws of motion
[20]. Specifically, to be useful for propulsion physics, a
formalism of Mach's Principle is required that provides a
means to wansmit reaction forces to surrounding matter. This
implies developing a quantitative description for how the
surrounding matter creates an inertial frame, and how pushing
against that flame with a space drive is actually pushing
against the distant surrounding matter.
That sounds pretty good, but it leaves out two very important "sources" of inertia, which to Mach, were not directly observable to him. The quantum world, and the bound energy within the nucleus of atoms, and of course the QV. The philosophy of Mach valued what was directly observable. In modern times, materialism and physicalism are relics. So this approach is incomplete, thus a no go.
It is also possible to consider the very structure of
spacetime itself as a candidate for propulsive interactions. If it
were possible, for example, to create asymmetries in the very
properties of spacetime which give rise to inertial frames, it
may be possible to create net inertial forces. This is similar
to the"warp drive" suggested by Alcubierre [4]
Much better....
Uneven radiation pressure (from the QV and the RF simultaneously) across the cavity and the dielectric seems much more plausible than trying to accelerate virtual particle pairs in the style of MHD. Like Chuck Norris, you don't mess with virtual particles, virtual particles mess with you. :)

I still favor direct application of the Equivalence Principle ...night all

Folks:
If the quantum vacuum is degradable and malleable as we think it should be, then to conserve momentum a QV wake has to be generated in the QV media as a QThruster goes by just like a ship's propeller leaves a disturbance in the water as it goes by. We think that the density of the QV is normally around its cosmological average of 9.1x10^27 kg/m^3, but its density can be greatly increased by the presence of E&M fields and especially very strong and fast timevarying E&M fields that occur is microwave resonant cavities with large Quality Factors greater than say 1,000, or around elementary charged particles like electrons or protons where the QV density goes up to nuclear mass density as you approach the surface of the particle. Suggest anything? However in the paper we are now trying to get published with no takers so far, we find that the QV density should drop off very rapidly from a high density volume like a proton and in fact it follows the same drop off in density with distance as the Casimir effect does, i.e., 1 / r^4 where r = the distance from the resonant cavity boundary. With that being the case it would be near impossible to detect the QV wake behind a QThruster only generating milliNewtons or Newtons or even in tens of Newtons.
So what's to do? To detect a QV wake from a Qthruster at even short distances from the source we think we will have to use another RF excited resonant cavity in a form of QV parametric amplification that is designed to produce a high density QV state just like in a QThruster, but not to produce thrust. Instead it will be optimized to monitor its time varying QV density as various very weak QV wake fields come in, are amplified and detected, then pass out of it again to go back to the low density QV state once again. This has some interesting implications especially when you finish reading the attached paper from a PhD from Rice University here in Houston.
Last topic for the night for me. Someone on this list asked if one could extract energy from the QV. If the QV is GRT spacetime, and spacetime is the cosmological gravitational field that is created by all the causally connected mass/energy in our section of the universe, then we live in a high pressure sea of gravitational energy. Now if the QV energy state is degradable and locally changeable, then one can posit the possibility of a thermodynamic energy conversion cycle that can extract energy from a pressure difference created in this QV media relative to the QV background average pressure, with a net decrease in this universal gravitational pressure or temperature reflective of the amount of energy so extracted. And try to remember that gravitational energy is negative energy. I'll leave the rest to you folks to draw your own conclusions from what this might mean...
Best, Paul March

This news article got a lot of attention here:
http://www.sciencedaily.com/releases/2014/07/140722091425.htm
A couple of us posted that it feels very relevant to the dynamics inside of a resonant cavity. What is interesting is the end result of confining vacuum fluctuations:
In that case, the fluctuationmediated attraction between the atoms becomes orders of magnitude stronger than in free space. Usually, the force decreases rapidly with increasing distance between the atoms. Due to the transmission line, it falls off with one over the distance cubed, instead of one over the seventh power of the distance, as in the usual case.
As far as the difference in vacuum energy goes, we've discussed the possibility that there exists a "more negative" energy condition at the small end of the cavity WRT the large end. Less modes fit small end vs large end. No calculations were made.
http://forum.nasaspaceflight.com/index.php?topic=29276.msg1298712#msg1298712
Either way, I know there is vacuum energy difference in potential from the top to the bottom of the cavity and those relative differences are all that matter. From there, after mathematical conversion to momentum, it doesn't take a mathematician to know that the competing vacuum and RF momentum contributions to the dielectric aren't exactly equal.
Anyway it is just words without math to back it up.

Folks:
If the quantum vacuum is degradable and malleable as we think it should be, then to conserve momentum a QV wake has to be generated in the QV media as a QThruster goes by just like a ship's propeller leaves a disturbance in the water as it goes by. We think that the density of the QV is normally around its cosmological average of 9.1x10^27 kg/m^3, but its density can be greatly increased by the presence of E&M fields and especially very strong and fast timevarying E&M fields that occur is microwave resonant cavities with large Quality Factors greater than say 1,000, or around elementary charged particles like electrons or protons where the QV density goes up to nuclear mass density as you approach the surface of the particle. Suggest anything? However in the paper we are now trying to get published with no takers so far, we find that the QV density should drop off very rapidly from a high density volume like a proton and in fact it follows the same drop off in density with distance as the Casimir effect does, i.e., 1 / r^4 where r = the distance from the resonant cavity boundary. With that being the case it would be near impossible to detect the QV wake behind a QThruster only generating milliNewtons or Newtons or even in tens of Newtons.
So what's to do? To detect a QV wake from a Qthruster at even short distances from the source we think we will have to use another RF excited resonant cavity in a form of QV parametric amplification that is designed to produce a high density QV state just like in a QThruster, but not to produce thrust. Instead it will be optimized to monitor its time varying QV density as various very weak QV wake fields come in, are amplified and detected, then pass out of it again to go back to the low density QV state once again. This has some interesting implications especially when you finish reading the attached paper from a PhD from Rice University here in Houston.
Last topic for the night for me. Someone on this list asked if one could extract energy from the QV. If the QV is GRT spacetime, and spacetime is the cosmological gravitational field that is created by all the causally connected mass/energy in our section of the universe, then we live in a high pressure sea of gravitational energy. Now if the QV energy state is degradable and locally changeable, then one can posit the possibility of a thermodynamic energy conversion cycle that can extract energy from a pressure difference created in this QV media relative to the QV background average pressure, with a net decrease in this universal gravitational pressure or temperature reflective of the amount of energy so extracted. And try to remember that gravitational energy is negative energy. I'll leave the rest to you folks to draw your own conclusions from what this might mean...
Best, Paul March
Thank you for participating in the forum Paul. As far as the paper goes, why not publish publicly and let your peers see it and validate it without the "Star Chamber" reviewers?
Regarding the QV wake, does measuring it really matter in terms of validity if tens of Newtons of thrust (or more) are predictably being measured?
[Serious question]
As to your last few sentences. Woah!!!.......

Folks:
If the quantum vacuum is degradable and malleable as we think it should be, then to conserve momentum a QV wake has to be generated in the QV media as a QThruster goes by just like a ship's propeller leaves a disturbance in the water as it goes by. We think that the density of the QV is normally around its cosmological average of 9.1x10^27 kg/m^3, but its density can be greatly increased by the presence of E&M fields and especially very strong and fast timevarying E&M fields that occur is microwave resonant cavities with large Quality Factors greater than say 1,000, or around elementary charged particles like electrons or protons where the QV density goes up to nuclear mass density as you approach the surface of the particle. Suggest anything? However in the paper we are now trying to get published with no takers so far, we find that the QV density should drop off very rapidly from a high density volume like a proton and in fact it follows the same drop off in density with distance as the Casimir effect does, i.e., 1 / r^4 where r = the distance from the resonant cavity boundary. With that being the case it would be near impossible to detect the QV wake behind a QThruster only generating milliNewtons or Newtons or even in tens of Newtons.
So what's to do? To detect a QV wake from a Qthruster at even short distances from the source we think we will have to use another RF excited resonant cavity in a form of QV parametric amplification that is designed to produce a high density QV state just like in a QThruster, but not to produce thrust. Instead it will be optimized to monitor its time varying QV density as various very weak QV wake fields come in, are amplified and detected, then pass out of it again to go back to the low density QV state once again. This has some interesting implications especially when you finish reading the attached paper from a PhD from Rice University here in Houston.
Last topic for the night for me. Someone on this list asked if one could extract energy from the QV. If the QV is GRT spacetime, and spacetime is the cosmological gravitational field that is created by all the causally connected mass/energy in our section of the universe, then we live in a high pressure sea of gravitational energy. Now if the QV energy state is degradable and locally changeable, then one can posit the possibility of a thermodynamic energy conversion cycle that can extract energy from a pressure difference created in this QV media relative to the QV background average pressure, with a net decrease in this universal gravitational pressure or temperature reflective of the amount of energy so extracted. And try to remember that gravitational energy is negative energy. I'll leave the rest to you folks to draw your own conclusions from what this might mean...
Best, Paul March
Thank you for participating in the forum Paul. As far as the paper goes, why not publish publicly and let your peers see it and validate it without the "Star Chamber" reviewers?
Regarding the QV wake, does measuring it really matter in terms of validity if tens of Newtons of thrust (or more) are predictably being measured?
[Serious question]
As to your third to last sentence. Woah!!!.......
Well you have two issues at play here. First off is whether or not the device produces thrust. The second one is whether or not Dr. White's theory is the correct explanation for why the device produces thrust. being able to measure tens of newtons of thrust would simply get you easily verifiable proof that the device produces thrust. On the other hand it will not get your proof that Dr. White's proposed theory is the correct explanation. That said, showing a strong correlation between the observed scaling with predicted scaling and using the proposed theory to predict the null configuration of the device (verified by observation). All would strengthen the case for why the proposed theory that explains the operation of the device is correct. Assuming Dr. White had all those things, being able to observe some sort of "Wake" would be the icing on the cake, especially if the device used to detect the wake is predicted by the theory.

Hi Paul,
Glad to see some improvement on experiments!
In January 2015, Roger Shawyer put a document online entitled A Note on the Principles of EmDrive force measurement (http://www.emdrive.com/EmDriveForceMeasurement.pdf).
Please leave out his theoretical explanation about group velocities for now and let's focus on his experimental claims about measurements of reaction forces. He basically says:
1. The EmDrive creates two opposite forces:
 a thrust T
 a reaction force R = Ma
where M = mass of the thruster, and a = acceleration of the thruster.
2. Not net force can be measured if the cavity is absolutely static, because in this case T and R cancel out.
3. The cavity needs to move (to accelerate) even a bit for the forces to appear, even if the acceleration is tiny and due for example to a thermal expansion of the cavity walls.
4. According to the experimental setup, either T or R can be measured, hence a difference in the direction of the force (toward the smaller or bigger plate of the cavity).
What do you think about those claims? Especially the one about the reaction force R.

@ Mulletron
["As far as the difference in vacuum energy goes, we've discussed the possibility that there exists a "more negative" energy condition at the small end of the cavity WRT the large end. Less modes fit small end vs large end. No calculations were made."]
This is the dispersion relation calculation. The evaluation is made as the difference from one end of the cavity to the other. A "boost" is made to an accelerated frame of reference which eliminates that difference, ie. "v is everywhere close to c" This is just the "trivial" approximation as in:
* Hydrodynamics of the Vacuum_0409292v2.pdf
" However, the vacuum is a Lorentz invariant medium; it has no rest frame. The appropriate frame for the NFA is determined solely by the initial conditions. If in some frame the NFA conditions are satisfied at t = 0 then they will remain satisfied at all later times. One may trivially take a NFA solution and boost it by a large Lorentz boost to obtain an approximate solution to the original relativistic equations in which v is everywhere close to 1. Only when the range of v values is a significant fraction of unity is it necessary to abandon the NFA and return to the relativistic equations, (4.26, 4.27)."
The (static) force then appears as the equivalent "weight" of the photons in the AFR.
Edit: To get to the QM version you need to evaluate a total wavefunction and show that it satisfies (for example) the selfaccelerating condition, or the SachsSchwebel current, or some equivalent particlepair generation criteria. The selfacceleration looks good so far, and conserves momentum.

@ Mulletron
["As far as the difference in vacuum energy goes, we've discussed the possibility that there exists a "more negative" energy condition at the small end of the cavity WRT the large end. Less modes fit small end vs large end. No calculations were made."]
This is the dispersion relation calculation. The evaluation is made as the difference from one end of the cavity to the other. A "boost" is made to an accelerated frame of reference which eliminates that difference, ie. "v is everywhere close to c" This is just the "trivial" approximation as in:
* Hydrodynamics of the Vacuum_0409292v2.pdf
" However, the vacuum is a Lorentz invariant medium; it has no rest frame. The appropriate frame for the NFA is determined solely by the initial conditions. If in some frame the NFA conditions are satisfied at t = 0 then they will remain satisfied at all later times. One may trivially take a NFA solution and boost it by a large Lorentz boost to obtain an approximate solution to the original relativistic equations in which v is everywhere close to 1. Only when the range of v values is a significant fraction of unity is it necessary to abandon the NFA and return to the relativistic equations, (4.26, 4.27)."
The (static) force then appears as the equivalent "weight" of the photons in the AFR.
Good point, that's in page 8 of Hydrodynamics of the Vacuum_0409292v2.pdf
Also in page 9:
Although the flow velocity is nonrelativistic (v ≪ 1), disturbances tend to “propagate” superluminally, at 1/v. Hence, the NFA here is not a normal nonrelativistic reduction. The resulting equations are “antiGalilean” invariant...This is certainly strange, and takes some getting used to, but one should simply view it
as an approximation to the full Lorentz transformations, valid in the stated context. One
is used to dealing with small objects that move slowly, so that their density distributions
vary rapidly in space, but slowly in time. In the present case one is dealing with large
objects, slowly varying in space, but relatively rapidly varying in time. This is related to
the fact that the Higgs vacuum, as a spontaneous BoseEinstein condensate, has almost
all its particles in the same quantum state. Small disturbances of this state involve vast
numbers of particles, spread over long distances, all moving nearly in lockstep, so that
the disturbance varies only slowly with position while the whole collective has the same,
relatively rapid time dependence.
(Bold added for emphasis)

Yes, I have to look at that in the selfacceleration. Seems I thought they were using instantaneous, but I'll have to check. It's pretty heavy going for an old guy.

Paul, so last summer it was reported that TE012 was a top performer yet difficult to work with:
The measured power applied to the test article was measured to be 2.6 watts, and the (net) measured thrust was 55.4 micronewtons. With an input power of 2.6 watts, correcting for the quality factor, the predicted thrust is 50 micronewtons. However, since the TE012 mode had numerous other RF modes in very close proximity, it was impractical to repeatedly operate the system in this mode, so the decision was made to evaluate the TM211 modes instead.
The landscape appears to have changed somewhat:
approx. +50 microNewton (uN) with 50W at 1,937.115 MHz
BTW, we have found that both the TE and TM E&M modes of this copper frustum can produce a thrust signature, but so far the TM modes appear to be the better performer, at least for the few modes we have been able to study to date.
So a couple questions from this. It appears that TM modes are the top dogs now and at the same time performance has gone down significantly since vacuum testing began. See table below for what I mean. TM212 reported now vs TM211 reported then? Do you have any insight about this? Did the vacuum serve to eliminate artifact thrust signals significantly?
Also is TE012 still a good qthruster performer, but it is just a dog to work with? It showed promising results with only 2.6 watts input producing 55.4uN of thrust (only 1 run though). Is TE012 not so good after all? If so, what made the difference?
Finally, quoting from last summer's paper:
The tapered thruster has a mechanical design such that it will be able to hold pressure at 14.7 pounds per square inch (psi) inside of the thruster body while the thruster is tested at vacuum to preclude glow discharge within the thruster body while it is being operated at high power.
(http://forum.nasaspaceflight.com/index.php?action=dlattach;topic=36313.0;attach=634622;image)
So it appears the cavity contains atmospheric pressure air inside. Given the thin walls of the cavity and the end sections, did you experience any issues with the resonant cavity expanding under suction of vacuum? And did it affect your testing significantly?
Thanks in advance. There's likely to be a lot of questions coming. We really appreciate all that you have done so far.
On a separate note @Notsosureofit made a calculation based off the dispersion relation inside the cavity that yielded pretty tight results starting here: http://forum.nasaspaceflight.com/index.php?topic=36313.msg1317866#msg1317866

Paul, so last summer it was reported that TE012 was a top performer yet difficult to work with:
...
The landscape appears to have changed somewhat:
approx. +50 microNewton (uN) with 50W at 1,937.115 MHz
BTW, we have found that both the TE and TM E&M modes of this copper frustum can produce a thrust signature, but so far the TM modes appear to be the better performer, at least for the few modes we have been able to study to date.
So a couple questions from this. It appears that TM modes are the top dogs now and at the same time performance has gone down significantly since vacuum testing began. See table below for what I mean. TM212 reported now vs TM211 reported then? Do you have any insight about this? Did the vacuum serve to eliminate artifact thrust signals significantly?
Some caveats here:
1) When discussing mode shapes in experiments, the first question is whether the mode shape has been actually verified with experimental measurements. My reading of the information is that the answer is NO. There has been no experimental verification of what the actual mode shape was in the NASA experiments (either in the original "Anomalous ..." Brady et.al. report or in the new experiments). Is my reading correct? Has anyone actually measured the electric and magnetic fields inside the EM Drive during the experiments to experimentally verify what the actual mode shape was? Are there experimental measurements showing the orientation, gradient, and magnitude of the electrical and magnetic fields inside the EM Drive that can enable NASA to plot contour plots of the mode shapes to asses what particular mode shapes have taken place?
2) The mode shapes discussed in the original "Anomalous ..." Brady et.al. report or in the new experiments are based on COMSOL Finite Element modeling of the experiments. Having written Finite Element computer programs, having been involved in their theoretical formulation for very nonlinear problems at MIT and elsewhere, as well as their numerical implementation, and having used (and written constitutive equation subroutines for) commercial codes like ADINA, ANSYS, and others, I'm quite aware of issues dealing with a) theoretical formulation, b) numerical implementation and c) convergence of the Finite Element mesh. By no means one can accept a Finite Element solution as a correct modeling of reality. As a minimum one needs to a) show convergence of the finite element solution and preferably b) comparison of the Finite Element solver to exact solutions. In this case, there is a readily available solution for cylindrical cavities. I would like to see a comparison of COMSOL Finite Element (using a similar space and time domain discretization) to the exact solution.
3) For the problem at hand (truncated cone cavity) we know that exact solutions show that the truncated cone has mode shapes that are similar to those in a cylindrical cavity, but that the mode shapes in a truncated cone have a transition to an evanescent region. A strict distinction between pure propagating and pure evanescent modes in a truncated cone can not be achieved. Hence from a rigorous point of view, it is not correct to use the same terminology for the modes in a truncated cone than as used for the modes in a cylindrical cavity (TM212 or TE012, for example). If we are going to use the same terminology, we need to better define our convention: is this terminology used in the sense that only real solutions to the eigenvalue problem in a truncated cone are taken into account?
Therefore, there are very important issues discussing what the actual mode shape in these experiments are.
I suggest to proceed as follows. Let's first start with addressing whether the actual mode shapes were measured in the experiments and if so how they were measured.
If the answer is no, that they were not measured, then let's then proceed to validate a numerical solution. Can NASA show a comparison of a COMSOL Finite Element solution for a cylindrical cavity (with similar discretization as used for the truncated cone) vs. the exact solution?
Once that has been done, we should proceed to the next question: is the COMSOL Finite Element solution solving the eigenvalue problem for the truncated cone taking into account evanescent modes, that is, is it considering complex value solutions to the eigenvalue problem? or is it only considering real solutions to the eigenvalue problem?

Rodal:
Look at the copper frustum part2 COMSOL & IR thermal study that I submitted to this group yesterday for an answer to your "Have you experimentally verified that we are using the TM212 mode as predicted by our COMSOL simulations? The answer BTW is yes for the TM212 mode, but no for the TE012 mode, but since COMSOL predicted the right PE loaded resonant frequency for the TE212 mode as verified by my IR camera studies 1 & 2 of the copper frustum, I would assume that it got it right for the TE012 mode as well. In fact I should have provided you my IR study1 first, so find it attached.
Best, Paul M.

Folks:
If the quantum vacuum is degradable and malleable as we think it should be, then to conserve momentum a QV wake has to be generated in the QV media as a QThruster goes by just like a ship's propeller leaves a disturbance in the water as it goes by. We think that the density of the QV is normally around its cosmological average of 9.1x10^27 kg/m^3, but its density can be greatly increased by the presence of E&M fields and especially very strong and fast timevarying E&M fields that occur is microwave resonant cavities with large Quality Factors greater than say 1,000, or around elementary charged particles like electrons or protons where the QV density goes up to nuclear mass density as you approach the surface of the particle. Suggest anything? However in the paper we are now trying to get published with no takers so far, we find that the QV density should drop off very rapidly from a high density volume like a proton and in fact it follows the same drop off in density with distance as the Casimir effect does, i.e., 1 / r^4 where r = the distance from the resonant cavity boundary. With that being the case it would be near impossible to detect the QV wake behind a QThruster only generating milliNewtons or Newtons or even in tens of Newtons.
So what's to do? To detect a QV wake from a Qthruster at even short distances from the source we think we will have to use another RF excited resonant cavity in a form of QV parametric amplification that is designed to produce a high density QV state just like in a QThruster, but not to produce thrust. Instead it will be optimized to monitor its time varying QV density as various very weak QV wake fields come in, are amplified and detected, then pass out of it again to go back to the low density QV state once again. This has some interesting implications especially when you finish reading the attached paper from a PhD from Rice University here in Houston.
Last topic for the night for me. Someone on this list asked if one could extract energy from the QV. If the QV is GRT spacetime, and spacetime is the cosmological gravitational field that is created by all the causally connected mass/energy in our section of the universe, then we live in a high pressure sea of gravitational energy. Now if the QV energy state is degradable and locally changeable, then one can posit the possibility of a thermodynamic energy conversion cycle that can extract energy from a pressure difference created in this QV media relative to the QV background average pressure, with a net decrease in this universal gravitational pressure or temperature reflective of the amount of energy so extracted. And try to remember that gravitational energy is negative energy. I'll leave the rest to you folks to draw your own conclusions from what this might mean...
Best, Paul March
Thank you for participating in the forum Paul. As far as the paper goes, why not publish publicly and let your peers see it and validate it without the "Star Chamber" reviewers?
Regarding the QV wake, does measuring it really matter in terms of validity if tens of Newtons of thrust (or more) are predictably being measured?
[Serious question]
As to your last few sentences. Woah!!!.......
As too publishing publicly, where publicly would be the best place to publish to get the most eyes on it from the type of people you want to see it?

Rodal:
Look at the copper frustum part2 COMSOL & IR thermal study that I submitted to this group yesterday for an answer to your "Have you experimentally verified that we are using the TM212 mode as predicted by our COMSOL simulations? The answer BTW is yes for the TM212 mode, but no for the TE012 mode, but since COMSOL predicted the right PE loaded resonant frequency for the TE212 mode as verified by my IR camera studies 1 & 2 of the copper frustum, I would assume that it got it right for the TE012 mode as well. In fact I should have provided you my IR study1 first, so find it attached.
Best, Paul M.
Paul, thank you. This is the first time I see the attached IR study ("Comparison of COMSOL Predictions of Copper Frustrum Heat Dissipation with Dec 30 IR Data") . It was an excellent idea for NASA to conduct this experimental study to verify the TM212 mode. I congratulate you for that because it is of the utmost importance to understand the actual mode shapes being excited.
I attach the TM21 mode for a cylindrical cavity for comparison with TM21 in the truncated cone
Magnetic field:       dashed lines
Electric field: _______solid lines
PS: Concerning whether COMSOL's discretization predicting TE012 was correct, my attitude (based on conducting experiments and numerical analysis) is always I'm from Missouri "show me" :), so I would rather also have experimental verification for that experiment as well. But considering your tight budget constraints, you deserve congratulations for what has been done.

Rodal:
Look at the copper frustum part2 COMSOL & IR thermal study that I submitted to this group yesterday for an answer to your "Have you experimentally verified that we are using the TM212 mode as predicted by our COMSOL simulations? The answer BTW is yes for the TM212 mode, but no for the TE012 mode, but since COMSOL predicted the right PE loaded resonant frequency for the TE212 mode as verified by my IR camera studies 1 & 2 of the copper frustum, I would assume that it got it right for the TE012 mode as well. In fact I should have provided you my IR study1 first, so find it attached.
Best, Paul M.
Paul, thank you. This is the first time I see the attached IR study ("Comparison of COMSOL Predictions of Copper Frustrum Heat Dissipation with Dec 30 IR Data") . It was an excellent idea for NASA to conduct this experimental study to verify the TM212 mode. I congratulate you for that because it is of the utmost importance to understand the actual mode shapes being excited.
I attach the TM21 mode for a cylindrical cavity for comparison with TM21 in the truncated cone
Magnetic field:       dashed lines
Electric field: _______solid lines
PS: Concerning whether COMSOL's discretization predicting TE012 was correct, my attitude (based on conducting experiments and numerical analysis) is always I'm from Missouri "show me" :), so I would rather also have experimental verification for that experiment as well. But considering your tight budget constraints, you deserve congratulations for what has been done.
Notice from:
"Anomalous Thrust Production from an RF Test Device Measured on a LowThrust Torsion Pendulum" ( http://www.libertariannews.org/wpcontent/uploads/2014/07/AnomalousThrustProductionFromanRFTestDeviceBradyEtAl.pdf )
TE012 mode shape at 1.8804 GHz Table 2. Tapered Cavity Testing Summary (with the dielectric)
TM211 mode shape at 1.9326 GHz Table 2. Tapered Cavity Testing Summary (with the dielectric)
TM211 mode shape at 1.9367 GHz Table 2. Tapered Cavity Testing Summary (with the dielectric)
TM212 mode shape at 1.937188 GHz (Jan 2015 data (with the dielectric))
(TM212 mode shape at 1.937188 GHz from here http://forum.nasaspaceflight.com/index.php?topic=36313.msg1327177#msg1327177 )
(or an inconsequential difference 0.5%: TM212 mode shape at 1.946647 GHz http://forum.nasaspaceflight.com/index.php?action=dlattach;topic=36313.0;attach=634723 )
TM211 and TM212 have the same number of wave patterns in the circumferential and radial directions, but
TM211 has one halfwave pattern in the longitudinal direction
TM212 has two halfwave patterns in the longitudinal direction (twice as many as TM211)
yet they are reported to take place at practically the same frequency ?
Now, mode shapes also depend on:
a)geometry (I understand that the same tapered cone was used for all the above experiments, so that was not a variable)
b) relative electric permittivity and relative magnetic permeability (I understand that the same dielectric was used for all the above experiments, so that was not a variable)
So, if the geometry and the dielectric were the same in the above experiments:
QUESTION: 1.937188 GHz is only 0.025% different from 1.9367 GHZ.
It is not possible to have TM211 at 1.9367 GHz and TM212 at just 0.025% higher frequency, because TM211 has 1 halfwave in the longitudinal direction, while TM212 has 2 halfwaves in the longitudinal direction. Twice the number of halfwaves in the longitudinal direction imply a significantly higher frequency keeping the number of wavepatterns constant in the circumferential and radial directions (the same m=2 and n=1). Therefore doubling the number of halfwaves in the longitudinal direction with just a 0.025% increase in frequency cannot be justified.
Therefore it appears that the labeling of mode TM211 in the Brady et.al. NASA report was an error, and it really should have been TM212 based on the Jan 2015 IR data
If so, was there was an error in the COMSOL analysis for TE012 as well as for TM211 in the report since they may have used the same COMSOL analysis and mesh?
(http://www.optiqueingenieur.org/en/courses/OPI_ang_M01_C03/res/fig02_1.jpg)
Also, in "Anomalous Thrust Production from an RF Test Device Measured on a LowThrust Torsion Pendulum" ( http://www.libertariannews.org/wpcontent/uploads/2014/07/AnomalousThrustProductionFromanRFTestDeviceBradyEtAl.pdf )
page 18 (bottom) states (without the dielectric)
TE012 mode shape at 2.168 GHz .
So that the same mode shape (TE012) is stated to take place with the dielectric at 1.8804 GHz and without the dielectric at (15% higher frequency) 2.168 GHz, but there was no measurable response without the dielectric.
However,
Numerous COMSOL® analysis runs also indicated a strong dependency between thrust magnitude and antenna type, location, orientation, and number of antenna feeds. Slight changes in antenna design and number of feeds changed the COMSOL® thrust prediction by a factor of three which forced our team to implement tighter configuration control protocols during testing to ensure close representation of as built hardware to the analyzed configuration.
Finally, our experience with the TE012 mode indicated that it is important to design the RF prototype such that any target mode of operation is as isolated as possible in the frequency domain to help ensure that the system can be effectively tuned manually. This also protects for the ability to implement and use a phase lock loop (PLL) automated frequency control circuit. Due to the slow process commensurate with manual tuning, our future test articles will make use of a PLL whenever practical in order to increase the amount of data that can be collected for a given test article configuration and operating condition during a given amount of test time
(Bold added for emphasis)
So it is not clear whether the "no appreciable response without the dielectric at 2.168 GHz" may have been due to "slight changes in antenna location and orientation" in the 2.168 GHz experiment without the dielectric compared to the experiment at 1.8804 GHz with the dielectric.
Also the abovementioned report states:
the TE012 mode had numerous other RF modes in very close proximity, it was impractical to repeatedly operate the system in this mode, so the decision was made to evaluate the TM211 modes instead.
(Bold added for emphasis)
perhaps throwing further uncertainty as to what resonance took place at 1.8804 GHz

TM212 mode shape at 1.937188 GHz (Jan 2015 data (with the dielectric))
That comsol plot above says 1946.647. Where's the disconnect between numbers reported I wonder? Also unless comsol is taking into account all the little intricacies like heat expansion, bowing and buckling, simulation won't yield an exact result in reality. The thermal image pretty much nails whether or not the excited mode is actually being excited though.

TM212 mode shape at 1.937188 GHz (Jan 2015 data (with the dielectric))
That comsol plot above says 1946.647. Where's the disconnect between numbers reported I wonder? Also unless comsol is taking into account all the little intricacies like heat expansion, bowing and buckling, simulation won't yield an exact result in reality.
1) I took the 1.937188 GHz figure from here: http://forum.nasaspaceflight.com/index.php?topic=36313.msg1327177#msg1327177
In that slide which is based on the copper frustum cavity running in its TM212 mode with 50W of 1,937.188 MHz RF power applied
But 1946.647 makes practically NO difference. One cannot have TM212 at only 0.5% higher frequency than TM211
2) My reading is that the COMSOL Multiphysics simulation did not take into account buckling. Buckling is an instability that requires a nonlinear stability analysis.
3) "simulation won't yield an exact result in reality". No way this can justify TM212 at only 0.5% higher frequency than TM211 for the same known truncated cone geometry and identical dielectric material . A Finite Element calculation converges from below, it may produce too low a frequency for a given mode shape if the finite element mesh is too crude, but it is not going to give TM212 at only 0.5% higher frequency than TM211 for a cavity with the known dimensions of the NASA truncated cone, since TM212 has twice the number of longitudinal halfwave patterns as TM211

I get that, but with a cavity loaded with a dielectric, you can't add up wavelengths trying to satisfy E field requirements like we do with empty waveguides. With the dielectric inserted, there is a dielectric resonator inside the cavity resonator which means the solution is more complicated to figure out by hand.

I get that, but with a cavity loaded with a dielectric, you can't add up wavelengths trying to satisfy E field requirements like we do with empty waveguides. With the dielectric inserted, there is a dielectric resonator inside the cavity resonator which means the solution is more complicated to figure out by hand.
I am not figuring out the solution by hand. I am using Mathematica. Also, I have based my above statements on my extensive experience developing Finite Element formulations for nonlinear analysis, writing code for Finite Element programs and using commercial Finite Element codes to solve practical problems.
Concerning the dielectric, COMSOL uses the dielectric constant: the electric permittivity. My understanding is that the same dielectric was used for both the experiments for which COMSOL is stated as giving TM211 and TM212
If NASA used substantiallydifferent truncated cone geometry or substantiallydifferent dielectric geometry or materials for the experiments reportedly giving TM211 and TM212, it is useful to find out.
If I have made an error somewhere, I would appreciate it being pointed out.
If there is an error in the NASA report, it is useful to find out. It is not uncommon at all for articles to have errata, and in my experience, authors (certainly in the R&D field), are always appreciative when such errors are pointed out.

All:
Please note that our first COMSOL analyst who was volunteering his time for this activity while holding down his NASA day job, transcribed the dimensions for the copper frustum PE discs incorrectly when he did the analysis for the TE012 mode. He used 6.0" OD by 1.0" thick whereas the actual dimensions for the PE discs was 6.13" OD by 1.062" thick. The extra volume in the two PE discs lowered the actual observed resonant frequencies for all the resonant modes in the cavity down by about 8to10 MHz from COMSOL calculated. When you have to beg for help, one can't be too critical of the results. As to the TM212 mode analysis it was performed by another volunteer, so again I'm not going to complain that he didn't get these calculated frequencies spot on to what was measured with our Agilent FieldFox Vector Network Analyzer (VNA) measured.
Rodal:
The next time we look at the TE012 mode I will perform the same IR camera survey I did for the TM212 mode. The reason I didn't do the IR camera survey of the TE012 mode the first time around was that we didn't have that capability during March of 2014 when we ran that test series, since the IR camera didn't come along until the summer of 2014.
Best, Paul M.

OMG that is the best thing ever!!!! :) :D Thanks!
(http://forum.nasaspaceflight.com/index.php?action=dlattach;topic=36313.0;attach=634742;image)
(http://forum.nasaspaceflight.com/index.php?action=dlattach;topic=36313.0;attach=634740;image)
Wow, what a day. Thanks Paul March. Seriously thanks.
And there ya go, ISM band dimensions. Any competent tinkerer should be able to try it for themselves if they are so inclined. Be safe.
Let's not forget that if these Emdrives do work (looking pretty likely), Shawyer had the vision to make them happen. The folks at NASA had the courage to take a look.

All:
Please note that our first COMSOL analyst who was volunteering his time for this activity while holding down his NASA day job, transcribed the dimensions for the copper frustum PE discs incorrectly when he did the analysis for the TE012 mode. He used 6.0" OD by 1.0" thick whereas the actual dimensions for the PE discs was 6.13" OD by 1.062" thick. The extra volume in the two PE discs lowered the actual observed resonant frequencies for all the resonant modes in the cavity down by about 8to10 MHz from COMSOL calculated. When you have to beg for help, one can't be too critical of the results. As to the TM212 mode analysis it was performed by another volunteer, so again I'm not going to com