Author Topic: EM Drive Developments - related to space flight applications - Thread 2  (Read 2167893 times)

Offline Rodal

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... 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/propellentless-space-propulsion-research-continues):

Quote from: David-Hambling  http://aviationweek.com/awin/propellentless-space-propulsion-research-continues
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 non-standard 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.
« Last Edit: 01/12/2015 09:25 PM by Rodal »

Offline Rodal

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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 velocity-frame of observance) directly as

(delta velocity)=(ThrustForce/Mass)*(delta time).

Of course, changes in velocity produced by external forces (for example by gravitational sling-shot) are not part of this consideration, only the ThrustForce is under consideration.
« Last Edit: 01/12/2015 09:37 PM by Rodal »

Offline frobnicat

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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/s²  Final velocity at 2000s vf=a*2000=2000m/s. DeltaV is 2km/s.
Kinetic energy Ek=.5*1*2000²=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 = (Vf-Vr)²-(Vi-Vr)² = Vf²-Vi²+2Vr(Vi-Vf)  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, 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(1-v²/c²), v in the rest frame where the device is not (yet) moving.
E = gamma m c²  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/c²

The consequences are
thrust/power < 1/c => v/c² < 1/c => v<c    classical rocket, reaction on usual mass
thrust/power = 1/c => v/c² = 1/c => v=c    photon rocket, reaction on particles of 0 rest mass
thrust/power > 1/c => v/c² > 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.

Offline Rodal

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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 time-component of the energy-momentum vector. Then if you change frames, what you called energy partly becomes momentum, and it is the conservation law of the total energy-momentum vector which is frame independent."

I would have written this instead as "the total energy-momentum vector is covariant, not invariant".

See:
 http://physics.stackexchange.com/questions/23323/is-the-change-in-kinetic-energy-of-a-particle-frame-independent

and

http://www.quora.com/Does-the-kinetic-energy-of-an-object-depend-on-the-reference-frame-of-the-observer-Why-or-why-not

and

http://physics.stackexchange.com/questions/23734/is-the-energy-conserved-in-a-moving-frame-of-reference

and

http://www.loreto.unican.es/Carpeta2012/TPT%28Tefft%29RelativityGalilean2007.pdf

2) The frame-of-reference kinetic energy issues (for non-relativistic 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 velocity-frame-of-reference) 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 frame-independent 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 time-history 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 19-1 Rocket propulsion elements 7th edition- Sutton)).

Quote from: equation 19-1 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:

Quote from: Ron Maimon
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.
« Last Edit: 01/14/2015 01:04 AM by Rodal »

Offline ThinkerX

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Quote
3) You are correct, for the EM Drive to make any sense it implies having memory of its time-history 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.

Offline Rodal

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....
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 Q-Thruster 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.


« Last Edit: 01/14/2015 01:42 AM by Rodal »

Online Stormbringer

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http://www.technologyreview.com/view/426281/giant-casimir-effect-predicted-inside-metamaterials/

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?  :-\
When antigravity is outlawed only outlaws will have antigravity.

Offline Rodal

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http://www.technologyreview.com/view/426281/giant-casimir-effect-predicted-inside-metamaterials/

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

Quote from: Tian-Ming Zhao, Rong-Xin Miao
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?   :-\
« Last Edit: 01/14/2015 02:25 PM by Rodal »

Offline Notsosureofit

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http://www.mouser.com/new/teampconnectors/te-connectivity-ariso/?utm_medium=email&utm_source=january2015&utm_campaign=cm-enews-tech2015&utm_content=p2-lm

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 ball-a-wax by this weekend.
« Last Edit: 01/15/2015 02:49 AM by Notsosureofit »

Offline Notsosureofit

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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 mass-less, perfectly conducting cavity)

Unlike the previous waveguide attempt, this wasn't done on a series of scribbled post-it 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 n-th zero of the m-th 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 n-th zero of the derivative of the m-th 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= 1.04e-4 vs 9.12e-5 Pwr= 16.9 Q=7320  TM122 or TE022
Bradyb NT= 4.80e-5 vs 5.01e-5 Pwr= 16.7 Q=18100 TE213
Bradyc NT= 4.78e-5 vs 5.54e-5 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.

« Last Edit: 01/19/2015 06:50 PM by Notsosureofit »

Offline Mulletron

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Keeping my eyes on the conference scene, nothing out of this one: http://www.aiaa-scitech.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.aiaa-propulsionenergy.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?
« Last Edit: 01/17/2015 03:32 PM by Mulletron »
Challenge your preconceptions, or they will challenge you. - Velik

Offline Star One

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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 Talk-Polywell as there's probably people on there who might have an answer for you?
« Last Edit: 01/17/2015 07:26 PM by Star One »

Online RotoSequence

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Poking around the internet, I ended up at this paper on Arxiv: http://arxiv.org/abs/1411.3987

Quote
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 time-correlated 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?
« Last Edit: 01/18/2015 10:07 AM by RotoSequence »

Offline Mulletron

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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 Talk-Polywell 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/Ohio-class_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/the-space-station-as-an-interplanetary-transport-vehicle/
« Last Edit: 01/18/2015 12:52 PM by Mulletron »
Challenge your preconceptions, or they will challenge you. - Velik

Offline Rodal

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....
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= 1.04e-4 vs 9.12e-5 Pwr= 16.9 Q=7320  TM122 or TE022
Bradyb NT= 4.80e-5 vs 5.01e-5 Pwr= 16.7 Q=18100 TE213
Bradyc NT= 4.78e-5 vs 5.54e-5 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 Low-Thrust Torsion Pendulum", Propulsion and Energy Forum, Cleveland, OH
AIAA 2014-4029, (http://www.libertariannews.org/wp-content/uploads/2014/07/AnomalousThrustProductionFromanRFTestDevice-BradyEtAl.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 full-wave 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 half-wave 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 half-wave 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):


NASA-Test  NASA-mode-reported Kwok#   @NotSoSureOfIt-mode        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

« Last Edit: 05/19/2015 04:43 PM by Rodal »

Offline Notsosureofit

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@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 !
« Last Edit: 01/18/2015 09:16 PM by Notsosureofit »

Offline Rodal

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Poking around the internet, I ended up at this paper on Arxiv: http://arxiv.org/abs/1411.3987

Quote
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 time-correlated 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:

Quote
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.

Online Stormbringer

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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.
« Last Edit: 01/18/2015 09:58 PM by Stormbringer »
When antigravity is outlawed only outlaws will have antigravity.

Offline ThinkerX

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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.


Offline Rodal

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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:



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.
« Last Edit: 01/19/2015 12:33 AM by Rodal »

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