Author Topic: EM Drive Developments - related to space flight applications - Thread 2  (Read 2171300 times)

Offline Mulletron

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Struck out on finding a lathe to use. My belt sander did a fantastic job too. So now I have 2, 1" thick x 6.25" wide HDPE discs. Now I have to figure out how to mount them....

Where there's a will, there's a way.



« Last Edit: 03/24/2015 04:19 PM by Mulletron »
Challenge your preconceptions, or they will challenge you. - Velik

Offline Rodal

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Struck out on finding a lathe to use. My belt sander did a fantastic job too. So now I have 2, 1" thick x 6.25" wide HDPE discs. Now I have to figure out how to mount them....

Where there's a will, there's a way.

QUESTION 1: Before mounting the discs, could you please run a couple of tests without the HDPE discs?

If, so I can send you a post showing the mode shapes at the two frequencies near 2.45 GHz and why .

There is a mode shape at 2.49 GHz (or at 2.46 GHz according to NASA's COMSOL calculations) that should produce no force without the dielectric disc (because the Poynting vector practically cancels out)

There is a mode shape at 2.46 GHz (or at 2.41 GHz according to NASA's COMSOL calculations) that may produce an electromagnetic force without the dielectric disc (because the Poynting vector does not cancel out)

QUESTION 2: Do you have access to a thermal IR camera (to identify the mode shapes, etc.)  ?
« Last Edit: 03/24/2015 06:55 PM by Rodal »

Offline jmossman

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Struck out on finding a lathe to use. My belt sander did a fantastic job too. So now I have 2, 1" thick x 6.25" wide HDPE discs. Now I have to figure out how to mount them....

Where there's a will, there's a way.

Congratulations on your build progress!

As for the HDPE mounting solution...

If the initial intention is to replicate the Eagleworks' configuration, I'd propose mimicking the Eagleworks' mounting technique.  I've seen at least two different bolt hole patterns in posted images, and some of the verbiage suggesting that different bolt hole patterns are best for different excited modes.  (as an aside, since the bolt holes pierce both the dielectric and the copper frustum's plate, I've wondered what the RF field looks like outside of the cavity near those holes; I don't recall seeing any bolt holes in the previously posted/discussed meep sims)

http://forum.nasaspaceflight.com/index.php?action=dlattach;topic=36313.0;attach=803831
Quote
(There are three ~1.00" 1/4-20 nylon bolts mounted on a ~2.00" radius spaced every 120 degrees that hold the first PE disc to the PCB end cap.   There is then a layer of 3/4" wide office scotch tape at the interface between the first and second PE discs and the center 1/4"-20 nylon bolt that hold second PE disc to the first PE disc.)
Quote
it looks like there is a high E-field volume where this center nylon bolt hangs out while running in the TM212 resonant mode.

(Image 1 below)

http://forum.nasaspaceflight.com/index.php?topic=36313.msg1335785#msg1335785
Quote
we tested the copper frustum in its TM010 mode and mounted a 5.0 inch OD by 1.0" thick PTFE disk at the center of the large OD end cap of the copper frustum with one 1/4-20 nylon bolt.


(Image 2 below)




[Mod Edit:  Images were stretching page, moved to attachments.  Please attach rather than embed in the future.]
« Last Edit: 03/24/2015 09:36 PM by Ford Mustang »

Offline Rodal

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Struck out on finding a lathe to use. My belt sander did a fantastic job too. So now I have 2, 1" thick x 6.25" wide HDPE discs. Now I have to figure out how to mount them....

Where there's a will, there's a way.

Congratulations on your build progress!

As for the HDPE mounting solution...

If the initial intention is to replicate the Eagleworks' configuration, I'd propose mimicking the Eagleworks' mounting technique.  I've seen at least two different bolt hole patterns in posted images, and some of the verbiage suggesting that different bolt hole patterns are best for different excited modes. ...

@Mulletron:

Please clarify whether your intention is indeed to identically "replicate Eagleworks" tests (as per the post above).  In other words: are you going to be testing at exactly the same frequencies (under the same configuration) as NASA Eagleworks?

My understanding was that you were not going to (initially at least) be testing at the same frequencies as NASA Eagleworks but instead you were going to be testing near 2.45 GHz.

If you are going to be testing near ~2.45 GHz (instead of ~1.9 Ghz) then the mode shapes are going to be different, and therefore one should not use the same bolt mounting configuration as Eagleworks.

 I can send you images of the mode shapes at nearby frequencies, if you confirm at what frequency you are going to test.


« Last Edit: 03/24/2015 07:18 PM by Rodal »

Offline Mulletron

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Struck out on finding a lathe to use. My belt sander did a fantastic job too. So now I have 2, 1" thick x 6.25" wide HDPE discs. Now I have to figure out how to mount them....

Where there's a will, there's a way.

QUESTION 1: Before mounting the discs, could you please run a couple of tests without the HDPE discs?

If, so I can send you a post showing the mode shapes at the two frequencies near 2.45 GHz and why .

There is a mode shape at 2.49 GHz (or at 2.46 GHz according to NASA's COMSOL calculations) that should produce no force without the dielectric disc (because the Poynting vector practically cancels out)

There is a mode shape at 2.46 GHz (or at 2.41 GHz according to NASA's COMSOL calculations) that may produce an electromagnetic force without the dielectric disc (because the Poynting vector does not cancel out)

QUESTION 2: Do you have access to a thermal IR camera (to identify the mode shapes, etc.)  ?

I'm going to try and run it with and without the HDPE discs in there. I can zero in on modes using the test equipment at work....but there's no way to verify really.

At home, there's no way of zeroing in on and exciting particular modes during the force testing. I'm just brute forcing this with wideband RF. I'm only interested in frequencies between 2400-2500mhz. I'm going for the same effect as a magnetron, but with much less power. So clearly defined mode shapes are out for now.

If a force is evident while the frustum is on the balance, I'll invest in one of those USB programmable signal generators. But for now, I'll just be happy if it even moves. I'm using the crawl, walk, run approach to things.

I don't have an IR camera btw.
« Last Edit: 03/24/2015 07:18 PM by Mulletron »
Challenge your preconceptions, or they will challenge you. - Velik

Offline Mulletron

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Struck out on finding a lathe to use. My belt sander did a fantastic job too. So now I have 2, 1" thick x 6.25" wide HDPE discs. Now I have to figure out how to mount them....

Where there's a will, there's a way.

Congratulations on your build progress!

As for the HDPE mounting solution...

If the initial intention is to replicate the Eagleworks' configuration, I'd propose mimicking the Eagleworks' mounting technique.  I've seen at least two different bolt hole patterns in posted images, and some of the verbiage suggesting that different bolt hole patterns are best for different excited modes.  (as an aside, since the bolt holes pierce both the dielectric and the copper frustum's plate, I've wondered what the RF field looks like outside of the cavity near those holes; I don't recall seeing any bolt holes in the previously posted/discussed meep sims)


My leading intention is to use the 3 Nylon bolt approach like Paul March, but it really pains me to drill holes into perfectly good dielectric resonators. All the Nylon bolts I have at the moment aren't long enough, and if the holes are too big, RF can escape.

I'm looking for a better way if there is one.
Challenge your preconceptions, or they will challenge you. - Velik

Offline Rodal

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Struck out on finding a lathe to use. My belt sander did a fantastic job too. So now I have 2, 1" thick x 6.25" wide HDPE discs. Now I have to figure out how to mount them....

Where there's a will, there's a way.

Congratulations on your build progress!

As for the HDPE mounting solution...

If the initial intention is to replicate the Eagleworks' configuration, I'd propose mimicking the Eagleworks' mounting technique.  I've seen at least two different bolt hole patterns in posted images, and some of the verbiage suggesting that different bolt hole patterns are best for different excited modes.  (as an aside, since the bolt holes pierce both the dielectric and the copper frustum's plate, I've wondered what the RF field looks like outside of the cavity near those holes; I don't recall seeing any bolt holes in the previously posted/discussed meep sims)


My leading intention is to use the 3 Nylon bolt approach like Paul March, but it really pains me to drill holes into perfectly good dielectric resonators. All the Nylon bolts I have at the moment aren't long enough, and if the holes are too big, RF can escape.

I'm looking for a better way if there is one.

Why don't you try this:

A single bolt through the center (which for sure is a node ).  See whether that's enough.

If it is not enough:

 Adhesion could be permanent and removing the dielectric from the copper base plate may involve damage.

Primers are solvent-based systems in which a reactive species is dissolved. Applied to a surface using a brush or spray, the primer’s solvent evaporates, leaving behind the reactive species on the substrate. The reactive species acts as a linking pin or bridge between an adhesive and the substrate Polyolefin primers are frequently used on hard-to-bond substrates joined with traditional and/or light curing cyanoacrylates ("superGlue").

Look at page 51 of this report from Loctite: http://www.henkelna.com/us/content_data/237471_LT2197_Plastic_Guide_v6_LR7911911.pdf

which are specifically recommended for polyethylene (a very hard to bond polymer)

(Ethyl Cyanoacrylate) Loctite 401 Prism from Amazon:

http://www.amazon.com/Loctite-Instant-Adhesive-Prism-Bottle/dp/B006GOKRSY/ref=pd_sim_sbs_indust_1?ie=UTF8&refRID=14RMFHYMSB2780RR33CY

Primer for Loctite 401 Prism from Amazon:

http://www.amazon.com/Loctite-LOC-18396-770-Cyanoacrylate-Adhesive/dp/B001OBQ8VO/ref=sr_1_fkmr0_1?s=hi&ie=UTF8&qid=1427237585&sr=1-1-fkmr0&keywords=Loctite%C2%AE+770%E2%84%A2+Prism%C2%AE+Primer
« Last Edit: 03/24/2015 09:58 PM by Rodal »

Offline Notsosureofit

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??  Replaceable end plates ?  One w/ and one w/o glued disks ?

Check w/ http://www.masterbond.com/?utm_source=jan14&utm_medium=email&utm_content=signature&utm_campaign=cpf
« Last Edit: 03/24/2015 07:37 PM by Notsosureofit »

Offline Mulletron

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Something cool I just found and have been fiddling around with:

http://www.i-logic.com/conecalc.htm (online version)
http://www.i-logic.com/conecalc/conecalc.htm (desktop download)

Plugged in the inside dimensions of the Eagleworks/Shawyer replication frustum, see screenshot. It generated a cut sheet. I added in some dimensions and a .25" offset in red, but not dimensioned. The sheet is 24"x48". The green rectangle is the sheet rotated for more efficient use of the copper.

http://basiccopper.com/22mil16oz24x4.html

Files are here: (click this line)




[Mod Edit:  Link was stretching page, changed to hyperlink]
« Last Edit: 03/24/2015 09:37 PM by Ford Mustang »
Challenge your preconceptions, or they will challenge you. - Velik

Offline flux_capacitor

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If your copper in the endplate is thick enough, surface roughening of the copper and of the HD PE results in mechanical interlocking sites and causes bond strength to increase dramatically.

I asked this before but my question wasn't answered (perhaps it is a stupid question):
Wouldn't roughening the copper internal surface of the end plates (to better bond the glue) dramatically reduce the surface reflectivity, hence the Q factor of the cavity?

Offline jmossman

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My leading intention is to use the 3 Nylon bolt approach like Paul March, but it really pains me to drill holes into perfectly good dielectric resonators. All the Nylon bolts I have at the moment aren't long enough, and if the holes are too big, RF can escape.

I'm looking for a better way if there is one.

http://forum.nasaspaceflight.com/index.php?topic=36313.msg1335766#msg1335766
Quote
Quote
tried epoxy and superglue bonding the PE and PTFE discs to the frustum end-caps, but these two plastics just happen to be the slickest and hardest plastics to bond to anything else.  Drat!
The marine adhesive made by 3M  (5200 or 5220 fast cure) will stick to anything

I too suspect 5200/5220 will work, but would eliminate any option of removing the HDPE discs without causing some damage.   High-temperature automotive RTV also comes to mind.  How transparent 5200/5220 or RTV are at these RF frequencies, I do not know.

Offline dustinthewind

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I don't understand the (analogy ?) in the following statement:

Quote
the circulating currents in the bottom plate observe the circulating current in the top plate as circulating in the same direction and so they are attracted to the top plate.  However, the top plate may observe the bottom plate having current circulating in the opposite direction and so it is repelled from the bottom plate.  The result is a unidirectional force. 

How are the circulating currents in the bottom plate "observing" the circulating currents in the top plate?
The magnetic electromagnetic fields are out of phase (see the plots below).  Why would the bottom circulating current "observe" the top one as circulating in the same direction: "in phase"?

(Dustinthewind - [bold with my name is me] in other words information only travels at the speed of light or , dx=c*dt.  The key to the image attached is:
Reference Numeral - Diagram illustrations as shown in FIGS. 1-2:
1 - Electromagnetic force
2 - Current in upper wire
3 - Current in middle wire
4 - Current in lower wire
5 - Apparent current of the upper wire
6 - Apparent current of the middle wire
7 - Apparent current of the lower wire
8 - Frame one of six
9 - Frame two of six
10 - frame three of six
11 - frame four of six
12 - frame five of six
13 - frame six of six

The image only considers parallel wires but the idea could be extended to make the wires equivalent to the circulating currents in the top and bottom plates or maybe the top plate and some distance down the sidewalls.

P.S. the diagram considers three wires but the simplest to consider is only two wires.  Ignore one color if you like as they are color coded depending on the wire and limit to two wires.  In the three wire diagram the top and bottom wires are out of phase 180 degrees so there is no unidirectional force between them.  The wires next to each other are only 90 degrees out of phase.  In time what happens is the bottom wire observes the current above it as moving in the same direction = attraction.  The top wire observes the current below it as moving in the opposite direction = repulsion
)


And most important, how does this get around the conservation of momentum problem (if one considers the EM Drive as a closed system with no internal sources) ?

(Dustinthewind - here is a quote from the other thread, "A scientific paper that clarifies how newtons 3rd law does not apply to the time delay of information and how it can be used for electromagnetic propulsion.  It provides a mathematical background for the time delayed magnetic fields but first illustrating how the static equations miss the effect.  https://scholar.google.com/scholar?cluster=7136673109349846373&hl=en&as_sdt=0,48" it is titled, "Newton's Third Law in the Framework of Special Relativity" ) - Dustinthewind - Please disregard this reference as I was in error in assuming this paper was dealing with two current loops changing in time 90 degrees out of phase.

Assuming no internal magnetic sources (no magnetic monopoles) and no internal electric sources, the divergence of Maxwell's stress tensor is zero (due to the lack of internal sources inside the cavity).
The derivative with respect to time of Poynting's vector is zero (if the electromagnetic fields are a harmonic function of time). These conditions lead to no electromagnetic force on the center of mass, even when considering a fully general-relativistic formulation of the principle of conservation of energy-momentum (http://en.wikipedia.org/wiki/Electromagnetic_stress%E2%80%93energy_tensor#Conservation_laws ), because the divergence (in 3D+1 spacetime) of the stress–energy tensor is zero under those previously-stated conditions.

In order to have a force and acceleration of the EM Drive one needs electromagnetic sources inside the EM Drive cavity (as assumed for example in Brandenburg's equations) and/or the electromagnetic fields to be a nonlinear non-harmonic function of time.

(Dustinthewind - It sounds like you have already considered the time dependent interactions from the sound of it so maybe I'm wrong in speculating on the propulsive effect.)
« Last Edit: 03/26/2015 12:51 AM by dustinthewind »

Offline Rodal

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If your copper in the endplate is thick enough, surface roughening of the copper and of the HD PE results in mechanical interlocking sites and causes bond strength to increase dramatically.

I asked this before but my question wasn't answered (perhaps it is a stupid question):
Wouldn't roughening the copper internal surface of the end plates (to better bond the glue) dramatically reduce the surface reflectivity, hence the Q factor of the cavity?

Good point, I presume that surface roughness features with height comparable to the penetration length would have a significant effect on the power loss ratio, so I deleted the mention of roughening to improve adhesion.
The effect of roughening on polyethylene does not seem to have universal acceptance: Loctite (see report below) states that they did not find a statistical difference when bonding LDPE (they don't say anything about roughening HD PE)

That leaves solvent-based primers as a good option to improve adhesion.

Look at page 51 of this report from Henkel North America (Loctite): http://www.henkelna.com/us/content_data/237471_LT2197_Plastic_Guide_v6_LR7911911.pdf

which are specifically recommended for polyethylene (a very hard to bond polymer)

(Ethyl Cyanoacrylate) Loctite 401 Prism from Amazon:

http://www.amazon.com/Loctite-Instant-Adhesive-Prism-Bottle/dp/B006GOKRSY/ref=pd_sim_sbs_indust_1?ie=UTF8&refRID=14RMFHYMSB2780RR33CY

Primer for Loctite 401 Prism from Amazon:

http://www.amazon.com/Loctite-LOC-18396-770-Cyanoacrylate-Adhesive/dp/B001OBQ8VO/ref=sr_1_fkmr0_1?s=hi&ie=UTF8&qid=1427237585&sr=1-1-fkmr0&keywords=Loctite%C2%AE+770%E2%84%A2+Prism%C2%AE+Primer

THIS GLUE IS STRONG AND FAST ACTING - MAKE SURE TO WEAR GLOVES AND PROTECT YOURSELF
« Last Edit: 03/25/2015 12:31 AM by Rodal »

Offline Rodal

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If your copper in the endplate is thick enough, surface roughening of the copper and of the HD PE results in mechanical interlocking sites and causes bond strength to increase dramatically.

I asked this before but my question wasn't answered (perhaps it is a stupid question):
Wouldn't roughening the copper internal surface of the end plates (to better bond the glue) dramatically reduce the surface reflectivity, hence the Q factor of the cavity?

Good point, I presume that surface roughness features with height comparable to the penetration length would have a significant effect on the power loss ratio, so I deleted the mention of roughening to improve adhesion.
The effect of roughening on polyethylene does not seem to have universal acceptance: Loctite (see report below) states that they did not find a statistical difference when bonding LDPE (they don't say anything about roughening HD PE)

That leaves solvent-based primers as a good option to improve adhesion.

Look at page 51 of this report from Henkel North America (Loctite): http://www.henkelna.com/us/content_data/237471_LT2197_Plastic_Guide_v6_LR7911911.pdf

which are specifically recommended for polyethylene (a very hard to bond polymer)

(Ethyl Cyanoacrylate) Loctite 401 Prism from Amazon:

http://www.amazon.com/Loctite-Instant-Adhesive-Prism-Bottle/dp/B006GOKRSY/ref=pd_sim_sbs_indust_1?ie=UTF8&refRID=14RMFHYMSB2780RR33CY

Primer for Loctite 401 Prism from Amazon:

http://www.amazon.com/Loctite-LOC-18396-770-Cyanoacrylate-Adhesive/dp/B001OBQ8VO/ref=sr_1_fkmr0_1?s=hi&ie=UTF8&qid=1427237585&sr=1-1-fkmr0&keywords=Loctite%C2%AE+770%E2%84%A2+Prism%C2%AE+Primer

THIS GLUE IS STRONG AND FAST ACTING - MAKE SURE TO WEAR GLOVES AND PROTECT YOURSELF

Notice that http://www.henkelna.com/us/content_data/237471_LT2197_Plastic_Guide_v6_LR7911911.pdf
shows on page 51 that adhesion to HDPE for Loctite 401 Prism alone gives 50 psi adhesive shear strength, while Loctite 401 Prism   with Loctite® 7701™ Prism® Primer (the medical version of 770 primer) gives 2000 psi adhesive shear strength (40 times greater adhesive shear strength when using the primer).

This adhesive + primer combination should amply exceed the adhesive shear strength to HDPE (and to PTFE "Teflon") of polyurethane-based marine adhesives according to published data.
« Last Edit: 03/25/2015 12:59 AM by Rodal »

Offline Rodal

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https://scholar.google.com/scholar?cluster=7136673109349846373&hl=en&as_sdt=0,48....
....

@frobnicat: please notice this paper, published in The European Physical Journal Plus
November 2014, 129:240; which was brought up by @dustinthewind:

https://scholar.google.com/scholar?cluster=7136673109349846373&hl=en&as_sdt=0,48

that states:

Quote from: Miron Tuval and Asher Yahalom Newton’s Third Law in the Framework of Special
Relativity
Most locomotive systems of today are based on open systems. A rocket sheds exhaust gas to propel itself, a speeding bullet generates recoil. A car pushes the road with the same force that is used to accelerate it, the same is true regarding the interaction of a plane with air and of a ship with water. However, the above relativistic considerations suggest’s a new type of motor which is not based on a open system but rather on a closed one
....
As a final remark we will address the problem of achieving constant force which may be of interest for locomotive applications. A constant force may be achieved by having a direct current in one loop and a current of uniform second derivative on the other. For the choice of values given in table 2 we obtained FT z ∼= 2.74 Newton.
Obviously the switching time may represent some difficulty which one may overcome with advanced enough switching technology perhaps using low resistivity superconducting materials. Another possibility for constructing a relativistic motor is using numerous modular solid-state devices each with fast switching and small current such that an appreciable amount of cumulative forcing will result.

The European Physical Journal arose in 1998 as a merger and continuation of the very prestigious journals Zeitschrift für Physik, Journal de Physique,  Il Nuovo Cimento, and other journals.

The authors are associated with the renowned Isaac Newton Institute for Mathematical Sciences, an international research institute for mathematics and theoretical physics adjoining the Cambridge University Centre for Mathematical Sciences. In 1993 the British mathematician Andrew Wiles announced at the Institute his proof of Fermat's last theorem. Its director as of May 2012 was Cambridge University Professor John Toland (who is famous for formally proving in 1978, Stokes' conjecture on the existence of gravity waves of maximum height on deep water, a previously open problem in mathematical hydrodynamics which dated back to the 19th century).

QUESTION: Can you identify fast switching (for tauc=10 nano seconds -> 2.7 Newtons; hence for tauc=3 microseconds -> 30 microNewtons, but for 100 Amps ?) and/or non-harmonic time-response of the electromagnetic fields in these EM Drive experiments?

(If there would be nonlinear, non-harmonic time response of the electromagnetic fields, then the derivative with respect to time of the Poynting vector would not be null, which indeed would result in a net longitudinal force, all that would be needed is special relativity, without the need of any esoteric physics: no need for Quantum Vacuum esoterica, no need for the "Mach Effect", no need for coupling of electromagnetism with gravity, no need for Unruh radiation, no need for superluminal tachyons, no need for extra dimensions of space (Kaluza-Klein or multidimensional branes), no need to appeal to Dark Energy, etc.)
« Last Edit: 03/25/2015 01:40 PM by Rodal »


Offline bad_astra

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I wonder if the harmonics of the microwave pulses from an EMDRIVE would sound like a WOW signal
"Contact Light" -Buzz Aldrin

Offline Rodal

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....
The copper frustum thrust reversal due to only its dielectric placement came when I was experimenting with the TM010 mode,...
... I think that this mode shape correct designation is TM011 instead of TM010 because:

1) There can be no TMmn0 modes for a truncated cone.  TMmn0 modes need to have a constant electromagnetic field in the longitudinal direction of the cavity.  This is possible for a cylindrical cavity (containing no other dielectrics inside besides the cavity medium) because it has constant geometrical and material properties in the longitudinal direction.  But a conical cavity has variable cross-section in the longitudinal direction, therefore the  TMnn0 mode is not possible.  The first possible mode (if it is not cut-off) is TMmn1.  The exact solution for the truncated cone shows this.  See for example:  http://gregegan.customer.netspace.net.au/SCIENCE/Cavity/Cavity.html   :The quantum mode number "p" for a truncated cone is related to k.   k cannot be zero for a truncated cone, since k = ω/c for a truncated cone , therefore k = 0 implies zero frequency for a truncated cone. 

2) As the attached plot shows, COMSOL's FEA plot shows an electromagnetic field that is not constant in the longitudinal direction, therefore this is not TM010, it looks instead as TM011 upon closer inspection.

(Therefore the analyst's designation for TM011 should be changed to TM012 and so forth for TM01p modes)
I have been examining higher modes for the truncated cone cavity and mode shapes for truncated cones with larger cone angle and for smaller base diameters at the same cone angle.

For these cases (mode shapes with higher "m" azimuthal quantum number, and those with smaller base diameters compared to the big base diameter) the difference between the truncated mode shapes and the cylindrical mode shape becomes more significant.

Ultimately this was unavoidable, because the only quantum number that the truncated cone and the cylindrical cavity have in common is "m" the azimuthal quantum mode number.  The variation along the circumference is described by a harmonic function in both the truncated cone and the cylindrical cavity.

On the other hand, the variation along "n" is described by Associated Legendre P functions in terms of the cone's angle for the truncated cone while it is described in terms of zero Bessel functions of the radial polar coordinate for the cylindrical cavity.  Different functions in terms of different variables.

And the variation along "p" is described by Spherical Bessel functions in terms of the spherical radial coordinate for the truncated cone, while it is described in terms of harmonic functions of the longitudinal polar coordinate for the cylindrical cavity.  Different functions in terms of different variables.

I have not found in the literature a commonly accepted nomenclature to designate mode shapes for the truncated cone.

Furthermore, for this thread's audience, the cylindrical mode shapes are something that the audience can more immediately relate to, since the cylindrical mode shape nomenclature is found in the literature, and @Notsosureofit's formula is based on an analogy to the cylindrical cavity mode shapes (using the Bessel zero functions to characterize the mode shapes).

Therefore, to better communicate these mode shapes, and to avoid confusion I have decided to identify the truncated mode shapes in future communications as follows:

1. Always specifying the frequency at which they take place.
2. Whenever possible to provide plots to illustrate the actual mode shape.
3. Whenever possible to provide the designation for the closest cylindrical mode shape.  I will identify these as "Cyl. TMmnp"

Of course, for high mode numbers and/or large cone angles we will find mode shapes that cannot be described in terms of a cylindrical cavity analogy.  In those cases those modes are best described by their frequency and a plot showing the actual mode shape.




Therefore, I will describe what NASA Eagleworks describes as mode TM212 as "Cyl. TM212" from now on.

There is still a discrepancy regarding what NASA Eagleworks describes as mode TM010, which I think should be described "Cyl. TM011" because this mode shape for the truncated cone is not constant along the longitudinal axis of the truncated cone (as NASA Eagleworks's own plot shows).


« Last Edit: 03/25/2015 06:15 PM by Rodal »

Offline flux_capacitor

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@frobnicat: please notice this paper, published in The European Physical Journal Plus
November 2014, 129:240; which was brought up by @dustinthewind:

https://scholar.google.com/scholar?cluster=7136673109349846373&hl=en&as_sdt=0,48

that states:

Quote from: Miron Tuval and Asher Yahalom Newton’s Third Law in the Framework of Special
Relativity
Most locomotive systems of today are based on open systems. A rocket sheds exhaust gas to propel itself, a speeding bullet generates recoil. A car pushes the road with the same force that is used to accelerate it, the same is true regarding the interaction of a plane with air and of a ship with water. However, the above relativistic considerations suggest’s a new type of motor which is not based on a open system but rather on a closed one
....
As a final remark we will address the problem of achieving constant force which may be of interest for locomotive applications. A constant force may be achieved by having a direct current in one loop and a current of uniform second derivative on the other. For the choice of values given in table 2 we obtained FT z ∼= 2.74 Newton.
Obviously the switching time may represent some difficulty which one may overcome with advanced enough switching technology perhaps using low resistivity superconducting materials. Another possibility for constructing a relativistic motor is using numerous modular solid-state devices each with fast switching and small current such that an appreciable amount of cumulative forcing will result.

The European Physical Journal arose in 1998 as a merger and continuation of the very prestigious journals Zeitschrift für Physik, Journal de Physique,  Il Nuovo Cimento, and other journals.

The authors are associated with the renowned Isaac Newton Institute for Mathematical Sciences, an international research institute for mathematics and theoretical physics adjoining the Cambridge University Centre for Mathematical Sciences. In 1993 the British mathematician Andrew Wiles announced at the Institute his proof of Fermat's last theorem. Its director as of May 2012 was Cambridge University Professor John Toland (who is famous for formally proving in 1978, Stokes' conjecture on the existence of gravity waves of maximum height on deep water, a previously open problem in mathematical hydrodynamics which dated back to the 19th century).

Very interesting paper! Especially considering what Roger Shawyer says about conservation of momentum in "open systems"… To summarize his point of view, standard Newtonian mechanics and thus the law of conservation of momentum indicate that, no matter what shape the cavity is, the forces exerted upon it from within must balance to zero. Shawyer claims this statement ignores special relativity, in which separate frames of reference have to be applied when velocities approach the speed of light. He declares that in the EmDrive, the system of electromagnetic waves and the waveguide can be regarded as an open system, both having separate frames of reference. He also says this effect is similar to the principle of the laser gyroscope, which is also an apparently closed system device, but where the beams act as if having an external frame of reference (which they have, since the speed of light is constant).

However, Shawyer was severely criticized by the scientific community for this "not even wrong" idea. And frankly, I wonder if Tuval & Yahalom's initial assumption regarding the "transmission of any information limited by the speed of light" is really correct, since it is established the Abraham–Lorentz force and inertial reaction forces are instantaneous. Another counterexample involving instantaneousness is quantum entanglement.

[EDIT]I didn't saw at first that Roger Shawyer's idea is opposite (the "open system") than the "closed system" treatment in special relativity by Miron Tuval & Asher Yahalom. It's weird because both seem to claim the same idea: decoupling the EM effects between two interacting electric circuits.
« Last Edit: 03/25/2015 07:56 PM by flux_capacitor »

Offline Notsosureofit

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The idea is correct, often used to demonstrate the twin paradox in General Relativity not Special Relativity.  (My pet peeve)  Special is only for Inertial frames.  Forces and acceleration require General Relativity, so they wind up using the limit of an approximation instead.

Edit: I have to read this paper in more detail, but first glance, it looks like you might get an impulse during this rather select interval but I don't (yet) see any consideration of the recovery of initial conditions w/o reversing it.
« Last Edit: 03/25/2015 08:06 PM by Notsosureofit »

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