NSF Thread 4
From EM Drive
NASASpaceFlight.com Forum
General Discussion => Advanced Concepts => Topic started by: Rodal on 08/07/2015 06:19 PM

This is a thread  Thread 4 in the series  focused on objective analysis of whether the EM Drive (a cavity resonating at microwave frequencies) reported "thrust force" is an experimental artifact or whether it is a real propulsion effect that can be used for space applications, and if so, in discussing those possible space propulsion applications.
Objective skeptical inquiry is strongly welcome. Disagreements should be expressed politely, concentrating on the technical, engineering and scientific aspects, instead of focusing on people. As such, the use of experimental data, mathematics, physics, engineering, drawings, spreadsheets and computer simulations are strongly encouraged, while subjective wordy statements are discouraged. Peerreviewed information from reputable journals is strongly encouraged. Please acknowledge the authors and respect copyrights.
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Links to previous threads:
Thread 1:
http://forum.nasaspaceflight.com/index.php?topic=29276.0
Thread 2:
http://forum.nasaspaceflight.com/index.php?topic=36313.0
Thread 3:
http://forum.nasaspaceflight.com/index.php?topic=37642.0

Entry level thread:
http://forum.nasaspaceflight.com/index.php?topic=37438.0
Baseline NSF Article:
http://www.nasaspaceflight.com/2015/04/evaluatingnasasfuturisticemdrive/
This is the link to the EM Drive wiki that users are encouraged to contribute to, edit for accuracy, and build as a knowledge resource for the EM Drive:
http://emdrive.wiki
Chris note: Please note all posts need to be useful and worthwhile or they will be removed via moderation. This subject has large interest, with over 2.5 million thread reads and 750,000 article reads. Most people are reading and not posting, so when you post it is in front of a very large audience.
Also, and it should go without saying, amateur experiments are discouraged unless you have gained educated and/or professional advice for safety reasons.
()

Ok, I made some additions, modifications and improvements to my .xls spreadsheet (see attached).
I've created an alternate version of McCulloch's 3D equation because, why not. I substituted area for diameter and that allowed me to drop that 6 off the front. The McCulloch 3D Modified equation is (I know it's messy):
((P*Q*L)/c)*((1/L+Pi*Br^2)(1/L+Pi*Sr^2))
P = Power in Watts
Q = Q
L = Length
c = Speed of Light
Br = Radius of the Large End
Sr = Radius of the Small End
Pi = π
Anyway, the above modifications just felt more natural than McCulloch's original 3D derivation and it brought the Tajmar prediction back into line.
One other interesting thing I found was that many of the extremely large Q frustums can be brought back into line with predicted values by simply dividing the provided Q value by 10. It works with Shawyer and with Juan. The predictions hold up with the Cannae drive for some reason, but fall flat on their face with the NASA tested Brady drive. Once again, all specifications have been stolen from McCulloch's blog (with the exceptions of my daydream, rfmwguy and TheTraveller).
My predicted thrust for rfmwguy's build works out to 226.00mN!
McCulloch's unedited 3D equation (assuming I entered it into the spreadsheet correctly) works out a prediction of 157.70mN!
Can't wait!

I have a thought for anyone doing this experiment, both in the open air and in a vacume chamber.
I would be interested in seeing what the total mass of the complete experiment rig is before and during the actual experiment. I fully expect there to be some "noise" in the measurement, but I think a short series of these experiments should be able to average out the real mass measurements. I have a couple of theories as to what might be going on, depending on what the actual mass readings are compared to before and during the experiment.
I don't want to really go into the theories as it may affect the results.

Thinking about the ongoing controversy regarding TheTraveller's and Shawyer's theory raises a question for me. Please forgive if this has been addressed in one of the earlier threads.
If Shawyer's theory is wrong then is Cullen's eqn 15 also incorrect?? Eqn 15 seems to be the bedrock of the theory (the bible they punch :D).
I am trying to unpack the controversy a bit from the recent standard of "the physics/theory is wrong".
Edit: Clarification.

One other interesting thing I found was that many of the extremely large Q frustums can be brought back into line with predicted values by simply dividing the provided Q value by 10.
Why would you do that?
The Demonstrator EMDrive has a stated Q of 45,000 and Df of 0.844.
The data is what it is.

One other interesting thing I found was that many of the extremely large Q frustums can be brought back into line with predicted values by simply dividing the provided Q value by 10.
Why would you do that?
The Demonstrator EMDrive has a stated Q of 45,000 and Df of 0.844.
The data is what it is.
Because, as we've tried to explain countless times, the Qs in Yang/Shell were grossly overstated. I think Thor is generous when he only divides it by 10.
Want proof? Look at Tajmar's Q, then look at yang/shawyers and tell me why there is a so much disparity. The disparity lies in yang/shawyers unfamiliarity with cavity Q measurement.

One other interesting thing I found was that many of the extremely large Q frustums can be brought back into line with predicted values by simply dividing the provided Q value by 10.
Why would you do that?
The Demonstrator EMDrive has a stated Q of 45,000 and Df of 0.844.
The data is what it is.
Obviously Q isn't Q if everybody's measuring it differently and getting different values.
But mostly, I noticed a trend and thought it was interesting. There was so much controversy swirling around with the whole "how do you calculate Q" thing, and since Q is an integral part of the McCulloch equation I thought I'd play around with it a bit.

One other interesting thing I found was that many of the extremely large Q frustums can be brought back into line with predicted values by simply dividing the provided Q value by 10.
Why would you do that?
The Demonstrator EMDrive has a stated Q of 45,000 and Df of 0.844.
The data is what it is.
Obviously Q isn't Q if everybody's measuring it differently and getting different values.
But mostly, I noticed a trend and thought it was interesting. There was so much controversy swirling around with the whole "how do you calculate Q" thing, and since Q is an integral part of the McCulloch equation I thought I'd play around with it a bit.
About the only way to resolve this Thor, is to do what you did, adjust reported Q to achieve the reported thrust, given the other parameters remain constant. Once you have static formulae, use Q as the variable to equate reported thrust. Nicely done...

I am sure many people know the Smith program. For all other here are the links.
Note the Icon/subprogram "circles".
Circles for Q, SWR and more are addable.
( Be careful while interpretating: Q of the cavity it selves for example is one thing the coupling factor of the antenna another, both are important!)
It's a very helpful program for the toolbox and RF engineering. :)
http://www.fritz.dellsperger.net/smith.html
http://fritz.dellsperger.net/downloads/Help%20V3.10.pdf
My wine don't like it at the moment >:( :\ for windows it works fine

One other interesting thing I found was that many of the extremely large Q frustums can be brought back into line with predicted values by simply dividing the provided Q value by 10.
Why would you do that?
The Demonstrator EMDrive has a stated Q of 45,000 and Df of 0.844.
The data is what it is.
Obviously Q isn't Q if everybody's measuring it differently and getting different values.
But mostly, I noticed a trend and thought it was interesting. There was so much controversy swirling around with the whole "how do you calculate Q" thing, and since Q is an integral part of the McCulloch equation I thought I'd play around with it a bit.
In the experimental EMDrive world of Shawyer, Prof Yang, Eagleworks and Tajmar, unloaded Q is measured and reported as the 3dB down bandwidth from the max return loss dB divided into the resonant frequency.
As Tajmar reported in the attachment.

One other interesting thing I found was that many of the extremely large Q frustums can be brought back into line with predicted values by simply dividing the provided Q value by 10.
Why would you do that?
The Demonstrator EMDrive has a stated Q of 45,000 and Df of 0.844.
The data is what it is.
And beside, when you use your spreadsheet from May and plug in a Df of .0844 and a Q of 45,000 you know what the mN of thrust predicted is? It's 253.4 mN. You know what my prediction is with the adjusted Q? It's 251.24 mN (and I used 3.14 for Pi). I'd say that's pretty darn close, wouldn't you? And with observed results as high as 214, I'd say we're both in the same ballpark.

One other interesting thing I found was that many of the extremely large Q frustums can be brought back into line with predicted values by simply dividing the provided Q value by 10.
Why would you do that?
The Demonstrator EMDrive has a stated Q of 45,000 and Df of 0.844.
The data is what it is.
Because, as we've tried to explain countless times, the Qs in Yang/Shell were grossly overstated. I think Thor is generous when he only divides it by 10.
Want proof? Look at Tajmar's Q, then look at yang/shawyers and tell me why there is a so much disparity. The disparity lies in yang/shawyers unfamiliarity with cavity Q measurement.
They all measure their unloaded Q the same way.
Measured resonant frequency at max return loss dB / bandwidth at 3dB down from the peak return loss dBs.
Examples from Eagleworks, Tajmar and Prof Yang. All using the same method to calc unloaded Q.

One other interesting thing I found was that many of the extremely large Q frustums can be brought back into line with predicted values by simply dividing the provided Q value by 10.
Why would you do that?
The Demonstrator EMDrive has a stated Q of 45,000 and Df of 0.844.
The data is what it is.
Obviously Q isn't Q if everybody's measuring it differently and getting different values.
But mostly, I noticed a trend and thought it was interesting. There was so much controversy swirling around with the whole "how do you calculate Q" thing, and since Q is an integral part of the McCulloch equation I thought I'd play around with it a bit.
In the experimental EMDrive world of Shawyer, Prof Yang, Eagleworks and Tajmar, unloaded Q is measured and reported as the 3dB down bandwidth from the max return loss dB divided into the resonant frequency.
As Tajmar reported in the attachment.
I will take the time to explain this one more time, Mr T. after that, either you are deliberately trying to confuse the issue or you simply cannot comprehend.
Q = Ctr freq of resonance/3dB bandwidth (total half power bandwidth). Return loss has no bearing on a Q measurement, it MUST be a 2 port measurement, otherwise it is a singleport device akin to an antenna, not a cavity. The calculations used in virtually all relative RF and Microwave circuits calculate Q in the same way, not what yang/shawyer invented.
http://docs.lumerical.com/en/diffractive_optics_cavity_q_calculation.html
"High Q cavities
Derivation of Q factor formula:
The quality factor (Q) is defined as (see image) where wr is the resonant frequency ( ωr=2π fR) and FWHM is the full width half max of the resonance intensity spectrum."

They all measure their unloaded Q the same way.
Measured resonant frequency at max return loss dB / bandwidth at 3dB down from the peak return loss dBs.
Examples from Eagleworks, Tajmar and Prof Yang. All using the same method to calc unloaded Q.
You are absolutely, 100% right. I hereby defer to you in all future disagreements. I apologize for my impertinence. My spreadsheet is wrong and your spreadsheet is right.

I will take the time to explain this one more time, Mr T. after that, either you are deliberately trying to confuse the issue or you simply cannot comprehend.
Q = Ctr freq of resonance/3dB bandwidth (total half power bandwidth). Return loss has no bearing on a Q measurement, it MUST be a 2 port measurement, otherwise it is a singleport device akin to an antenna, not a cavity. The calculations used in virtually all relative RF and Microwave circuits calculate Q in the same way, not what yang/shawyer invented.
http://docs.lumerical.com/en/diffractive_optics_cavity_q_calculation.html
"High Q cavities
Derivation of Q factor formula:
The quality factor (Q) is defined as (see image) where wr is the resonant frequency ( ωr=2π fR) and FWHM is the full width half max of the resonance intensity spectrum."
That may be how you would do it but it is not how Shawyer, Prof Yang, Eagleworks and Prof Tajmar measure their frustums unloaded Q as I just showed you.

They all measure their unloaded Q the same way.
Measured resonant frequency at max return loss dB / bandwidth at 3dB down from the peak return loss dBs.
Examples from Eagleworks, Tajmar and Prof Yang. All using the same method to calc unloaded Q.
You are absolutely, 100% right. I hereby defer to you in all future disagreements. I apologize for my impertinence. My spreadsheet is wrong and your spreadsheet is right.
It has nothing to do with me nor my spreadsheet.
I just showed you how Prof Yang, Eagleworks and Prof Tajmar measured their frustums unloaded Q. Note Prof Tajmar used an expert professor in uW engineering to measure his frustums unloaded Q by using the same 1 port S11 return loss method as used by Shawyer, Prof Yang and Eagleworks.

The testiness of this current discussion aside, I am genuinely interested in the reason why there is a difference between these two Q value viewpoints.

The calculations used in virtually all relative RF and Microwave circuits calculate Q in the same way, not what yang/shawyer invented.
An EMDrive cavity is not a standard cavity.
As I have shown you before, it is industry standard practice, maybe not yours, to use 1 port S11 return loss to measure unloaded cavity Q. You may disagree with the information on the slide but it is incorrect to say Shawyer and Prof Yang invented this method to measure unloaded Q.
As the slide clearly shows, to some it is the way to do the measurement.

The testiness of this current discussion aside, I am genuinely interested in the reason why there is a difference between these two Q value viewpoints.
In the EMDrive world measuring unloaded Q via S11 return loss at the 3bd down bandwidth is how it is measured.
So say Shawyer, Prof Yang, Eagleworks and Prof Tajmar.

The testiness of this current discussion aside, I am genuinely interested in the reason why there is a difference between these two Q value viewpoints.
As far as I can gather, @TT is saying, "How they did it". @rfmwguy is saying "How it should've been done." and @tleach is saying "This is how it seems to fit McCulloch's formula."
Which BTW, McCulloch doesn't define how to measure Q. He simply redefines it as the number of bounces (reflections), in the time it takes the photon to decay to zero. So that's not even the same definition of the Q that is being kicked around here. @tleach was trying to bridge that gap.
What I conclude is, the experimenters may or may not be measuring it consistently using the same methodology, but in all cases, they are doing it wrong and should be using 2 ports to measure cavity resonance. We have yet to see anyone do it this way.
Todd

but in all cases, they are doing it wrong and should be using 2 ports to measure cavity resonance. We have yet to see anyone do it this way.
Todd
So Dr. Ray Kwok is also wrong?

The testiness of this current discussion aside, I am genuinely interested in the reason why there is a difference between these two Q value viewpoints.
As far as I can gather, @TT is saying, "How they did it". @rfmwguy is saying "How it should've been done." and @tleach is saying "This is how it seems to fit McCulloch's formula."
Which BTW, McCulloch doesn't define how to measure Q. He simply redefines it as the number of bounces (reflections), in the time it takes the photon to decay to zero. So that's not even the same definition of the Q that is being kicked around here. @tleach was trying to bridge that gap.
What I conclude is, the experimenters may or may not be measuring it consistently using the same methodology, but in all cases, they are doing it wrong and should be using 2 ports to measure cavity resonance. We have yet to see anyone do it this way.
Todd
Thank you for summarizing the case, clarifying the problem and providing a conclusion. Well done.

The testiness of this current discussion aside, I am genuinely interested in the reason why there is a difference between these two Q value viewpoints.
In the EMDrive world measuring unloaded Q via S11 return loss at the 3bd down bandwidth is how it is measured.
So say Shawyer, Prof Yang, Eagleworks and Prof Tajmar.
I have to agree at this point, BUT for that you MUST know the coupling factor between your generatorantennacavity, only for the coupling factor K=1 the full 3dB BW is usable.
PDF: copy and past for translation somewhere ;)

The testiness of this current discussion aside, I am genuinely interested in the reason why there is a difference between these two Q value viewpoints.
As far as I can gather, @TT is saying, "How they did it". @rfmwguy is saying "How it should've been done." and @tleach is saying "This is how it seems to fit McCulloch's formula."
Which BTW, McCulloch doesn't define how to measure Q. He simply redefines it as the number of bounces (reflections), in the time it takes the photon to decay to zero. So that's not even the same definition of the Q that is being kicked around here. @tleach was trying to bridge that gap.
What I conclude is, the experimenters may or may not be measuring it consistently using the same methodology, but in all cases, they are doing it wrong and should be using 2 ports to measure cavity resonance. We have yet to see anyone do it this way.
Todd
It would be ohsosimple to resolve this. Send a closed, resonant cavity to NIST, the British Standards Institute (BSI) or other reputable body with ONLY 1 PORT and have them measure Q. After they ask where the other port is, they would ask, why would you want to measure a closed cavity system with only one port? IOW, an open system, like an antenna, only needs a single port. A resonant cavity needs 2 to properly measure Q.
I'll stand by this (un)controversial position regardless of the previous experimenters. Quite frankly, I'm surprised at their apparent lack of RF familiarity. This is not a slam, it is a known fact that RF engineering is taught less, practiced less and is receeding into the background of companies and institutions. Reason? Computer science boom and the "plug and play & throw away" mentality of electronics in general.
Open system = 1 port
Closed system (frustum) = 2 port
Case closed. Its the last I will post on this matter at NSF.

The testiness of this current discussion aside, I am genuinely interested in the reason why there is a difference between these two Q value viewpoints.
As far as I can gather, @TT is saying, "How they did it". @rfmwguy is saying "How it should've been done." and @tleach is saying "This is how it seems to fit McCulloch's formula."
Which BTW, McCulloch doesn't define how to measure Q. He simply redefines it as the number of bounces (reflections), in the time it takes the photon to decay to zero. So that's not even the same definition of the Q that is being kicked around here. @tleach was trying to bridge that gap.
What I conclude is, the experimenters may or may not be measuring it consistently using the same methodology, but in all cases, they are doing it wrong and should be using 2 ports to measure cavity resonance. We have yet to see anyone do it this way.
Todd
It would be ohsosimple to resolve this. Send a closed, resonant cavity to NIST, the British Standards Institute (BSI) or other reputable body with ONLY 1 PORT and have them measure Q. After they ask where the other port is, they would ask, why would you want to measure a closed cavity system with only one port? IOW, an open system, like an antenna, only needs a single port. A resonant cavity needs 2 to properly measure Q.
I'll stand by this (un)controversial position regardless of the previous experimenters. Quite frankly, I'm surprised at their apparent lack of RF familiarity. This is not a slam, it is a known fact that RF engineering is taught less, practiced less and is receeding into the background of companies and institutions. Reason? Computer science boom and the "plug and play & throw away" mentality of electronics in general.
Open system = 1 port
Closed system (frustum) = 2 port
Case closed. Its the last I will post on this matter at NSF.
???
It may be much more easy to measure with a calibrated(!) 2 port system...
But one can derive the Sparameter based on a 1 port measurement!
In doubt use a circulator and a load..

I think the reason why all the EmDrive experimenters to date (Shawyer, Yang, Brady/White, Tajmar) measured the unloaded Q (or Q_{u}) as the S11 1 port return loss (resonant frequency at maximum return loss dB 3dB off this peak return loss dB value) is not because they would not know or don't want to use the more official S22 2port method, but because the Q_{u} they get from the S11 1port method is a suitable value that can be plugged readily into their equations to calculate and predict theoretical thrust. Obviously the S22 2port method does not provide a value for Q usable to calculate thrust, at least according to their equations.

I think the reason why all the EmDrive experimenters to date (Shawyer, Yang, Brady/White, Tajmar) measured the unloaded Q (or Q_{u}) as the S11 1 port return loss (resonant frequency at maximum return loss dB 3dB off this peak return loss dB value) is not because they would not know or don't want to use the more official S22 2port method, but because the Q_{u} they get from the S11 1port method is just a suitable value that can be plugged readily into their equations to calculate and predict theoretical thrust. Obviously the S22 2port value does not provide a value usable to calculate thrust, at least according to their equations.
transmission measurement is S12 or S21

I think the reason why all the EmDrive experimenters to date (Shawyer, Yang, Brady/White, Tajmar) measured the unloaded Q (or Q_{u}) as the S11 1 port return loss (resonant frequency at maximum return loss dB 3dB off this peak return loss dB value) is not because they would not know or don't want to use the more official S22 2port method, but because the Q_{u} they get from the S11 1port method is just a suitable value that can be plugged readily into their equations to calculate and predict theoretical thrust. Obviously the S22 2port value does not provide a value usable to calculate thrust, at least according to their equations.
transmission measurement is S12 or S21
Ok thanks but you know what I meant ;)

but in all cases, they are doing it wrong and should be using 2 ports to measure cavity resonance. We have yet to see anyone do it this way.
Todd
So Dr. Ray Kwok is also wrong?
I see nothing incorrect about what Dr. Kwok said. He said "Resonators". An antenna is a resonator and so is a cavity. One is an open system, the other is a closed system. The preferred methods are different at a "National Standards" level, according to @rfmwguy. While I agree 100% that the experimenters to date have consistently used the S11 method, that does not mean it is the "standard" way to do it. You are arguing that "In the EM Drive world" this is how it's done. Perhaps this is true, but is no less true that this is NOT the "standard" way to do it.
Stop arguing about it and accept that fact please. You're driving everyone bonkers with your obstinance and defense of obvious incongruences. I do not follow others. I make mistakes, try to understand learn from them and forge my own path and from what I've seen, that is how most of us here operate.
Todd

I'll provide as much clear clean precise data as I can from my tests. That is my goal. There is no bad Data.
What theorists and nontheorists do with it by massaging it, reformulating it, how they plug it into those theories is beyond my control, but the Data rules here in this level of the EMDrive's development.
Back to //lurking//
Shell

Just a question regarding the Q measurement :
Even if we know that the Q's are/were measured in the wrong way, wouldn't it be wise to continue with the faulty system, in order to make all those test comparative?
If measurement standards are changed now to the correct method, all the data we have up till now becomes inaccurate or no longer useable, no?
One can question the validity of the previous information bits that have been gathered, but this sure will not help... throw it all overboard then? ???

Just a question regarding the Q measurement :
Even if we know that the Q's are/were measured in the wrong way, wouldn't it be wise to continue with the faulty system, in order to make all those test comparative?
If measurement standards are changed now to the correct method, all the data we have up till now becomes inaccurate or no longer useable, no?
One can question the validity of the previous information bits that have been gathered, but this sure will not help... throw it all overboard then? ???
Does everyone knows about the inner impedance of a oven magnetron?
If it is still ~50 Ohm there is no problem, the antenna coupling is as good in as out. 2 port measurement is equal to second port out at 50 Ohm...
In the 2 port case you have 2 times 50 Ohm(simple case) of out coupling means
1/50+1/50=25 Ohm
Thats the difference, nothing else (with respect to the coupling factor of each single antenna).
1/Q_eff=1/Q_int+1/Q_ext
If Q_ext(ernal) is known, whats the problem to derive Q_int(ernal) based on the measurement data ???
Sparameter (of a calibrated system) at each antenna(impedance) is all you need to derive the unloaded Q. It does'nt matter if 1 or 2 antennas will be used.

All this discussion about Q is relevant if the expression of the force on total system ( cavity +microwave source) is correct.
Any closed cavity can suffer of a non null net force produced by a electromagnetic field inside it acting on its HOLE INTERNAL SURFACE, but the source of the EM field is under force too, and MUST be accounted too.
No expression until now, shows the force calculated on entire surface, or take the source of the EM fields into account simultaneously.

Q = f / deltaF
where deltaF is the frequency spread between lower and upper 3 dB points.
I think the differences discussed stem from how that 3 dB is measured, no?

Q = f / deltaF
where deltaF is the frequency spread between lower and upper 3 dB points.
I think the differences discussed stem from how that 3 dB is measured, no?
If this is true then Q should not be used for any kind of thrust estimation or calculation. This kind of Qfactor is a human construct to facilitate easy discussion about simplified performance of RF/microwave things, with some sort of consensus of how to measure it reached 60 years ago (more or less, as demonstrated by this thread). It is essentially distilling the whole spectrum measurement into 3 points. It's very difficult to believe that this would produce better thrust estimation than utilizing the full integrated frequency spectrum of stored energy within the cavity.
In short, Q in this case is just an aspect of a design that should be used to make high level engineering decisions about multiple designs. It should not be used as a direct input to try and find quantitative values of physical phenomena.

Q = f / deltaF
where deltaF is the frequency spread between lower and upper 3 dB points.
I think the differences discussed stem from how that 3 dB is measured, no?
For a 1 port measurement may be.
http://forum.nasaspaceflight.com/index.php?topic=38203.msg1414228#msg1414228

@rfmwguy
"Thermal tests done including 5 minute run at 30% power, which is what I'll use for fulcrum test." So you're actually putting in 30% of 900W which would be approximately 270W.
And then there's the conversion of electrical energy into microwave energy. If we assume that wikepedia is correct, a 900W microwave oven magnetron should run with approximately 64% efficiency.
https://en.wikipedia.org/wiki/Microwave_oven#Heating_efficiency
That means you're magnetron is only putting 172.8W of energy into your frustum. I'm officially revising my force prediction (based on my v3 spreadsheet and a projected S12 Q factor of 7000) down 43.41 mN.
Sorry :)

Not coming from the RF world, I wonder why this whole discussion about Q can't settle on Q=2*π*energy_stored/energy_dissipated_per_cycle as a standard. Out of curiosity, isn't it possible to switch off a RF source fast enough (a few cycles) and get this Q value by observing only the time constant of the decay of amplitude with a minimally invasive probe ?
BTW, not wanting to sound insistent but there is no answer to my questions about the relation of Q and "losses per round trip" (http://forum.nasaspaceflight.com/index.php?topic=37642.msg1414001#msg1414001) (in the context of a linear resonant set up). If I am making a mistake by thinking "number of bounces" when hearing Q, then I'm not the only one : Think of it like the number of times a photon bounces inside a mirrored cavity. (https://www.reddit.com/r/EmDrive/comments/3fz91k/in_an_emdrive_q_rules/cttks09) A clarification might be useful.

Not coming from the RF world, I wonder why this whole discussion about Q can't settle on Q=2*π*energy_stored/energy_dissipated_per_cycle as a standard. Out of curiosity, isn't it possible to switch off a RF source fast enough (a few cycles) and get this Q value by observing only the time constant of the decay of amplitude with a minimally invasive probe ?
BTW, not wanting to sound insistent but there is no answer to my questions about the relation of Q and "losses per round trip" (http://forum.nasaspaceflight.com/index.php?topic=37642.msg1414001#msg1414001) (in the context of a linear resonant set up). If I am making a mistake by thinking "number of bounces" when hearing Q, then I'm not the only one : Think of it like the number of times a photon bounces inside a mirrored cavity. (https://www.reddit.com/r/EmDrive/comments/3fz91k/in_an_emdrive_q_rules/cttks09) A clarification might be useful.
My conjecture on this would be that, a small cone angle will cause more bounces and a higher Q. However, my feeling is that as the wave propagates from the small end to the big end, it is reflecting off the side walls. Each reflection off the side walls imparts a tiny bit of momentum to the frustum. So the more bounces off the side walls (not the end plates) will produce more thrust. This means that a slower group velocity, bouncing over a longer period of time, would give higher thrust. This leads to the idea that the frustum should be shaped more like a trombone with a long throat. But... none of the theories so far support this idea, but none have tried either.
Todd

Not coming from the RF world, I wonder why this whole discussion about Q can't settle on Q=2*π*energy_stored/energy_dissipated_per_cycle as a standard. Out of curiosity, isn't it possible to switch off a RF source fast enough (a few cycles) and get this Q value by observing only the time constant of the decay of amplitude with a minimally invasive probe ?
BTW, not wanting to sound insistent but there is no answer to my questions about the relation of Q and "losses per round trip" (http://forum.nasaspaceflight.com/index.php?topic=37642.msg1414001#msg1414001) (in the context of a linear resonant set up). If I am making a mistake by thinking "number of bounces" when hearing Q, then I'm not the only one : Think of it like the number of times a photon bounces inside a mirrored cavity. (https://www.reddit.com/r/EmDrive/comments/3fz91k/in_an_emdrive_q_rules/cttks09) A clarification might be useful.
My conjecture on this would be that, a small cone angle will cause more bounces and a higher Q. However, my feeling is that as the wave propagates from the small end to the big end, it is reflecting off the side walls. Each reflection off the side walls imparts a tiny bit of momentum to the frustum. So the more bounces off the side walls (not the end plates) will produce more thrust. This means that a slower group velocity, bouncing over a longer period of time, would give higher thrust. This leads to the idea that the frustum should be shaped more like a trombone with a long throat. But... none of the theories so far support this idea, but none have tried either.
Todd
Todd, but the axial force component due to the side walls equals Sin[theta]*SideWallForce, where theta is the cone halfangle. For theta = 0 ( a cylinder) the axial component due to the SideWallForce is Sin[0]*SideWallForce=0, it is zero no matter how large is the SideWallForce. For small theta, the SideWallForce axial component is very low. So, even if one grants you that the SideWallForce may be larger for small cone angle, the axial component is small. Comments?

Not coming from the RF world, I wonder why this whole discussion about Q can't settle on Q=2*π*energy_stored/energy_dissipated_per_cycle as a standard. Out of curiosity, isn't it possible to switch off a RF source fast enough (a few cycles) and get this Q value by observing only the time constant of the decay of amplitude with a minimally invasive probe ?
BTW, not wanting to sound insistent but there is no answer to my questions about the relation of Q and "losses per round trip" (http://forum.nasaspaceflight.com/index.php?topic=37642.msg1414001#msg1414001) (in the context of a linear resonant set up). If I am making a mistake by thinking "number of bounces" when hearing Q, then I'm not the only one : Think of it like the number of times a photon bounces inside a mirrored cavity. (https://www.reddit.com/r/EmDrive/comments/3fz91k/in_an_emdrive_q_rules/cttks09) A clarification might be useful.
My conjecture on this would be that, a small cone angle will cause more bounces and a higher Q. However, my feeling is that as the wave propagates from the small end to the big end, it is reflecting off the side walls. Each reflection off the side walls imparts a tiny bit of momentum to the frustum. So the more bounces off the side walls (not the end plates) will produce more thrust. This means that a slower group velocity, bouncing over a longer period of time, would give higher thrust. This leads to the idea that the frustum should be shaped more like a trombone with a long throat. But... none of the theories so far support this idea, but none have tried either.
Todd
Todd, but the axial force component due to the side walls equals Sin[theta]*SideWallForce, where theta is the cone halfangle. For theta = 0 ( a cylinder) the axial component due to the SideWallForce is Sin[0]*SideWallForce=0, it is zero no matter how large is the SideWallForce. For small theta, the SideWallForce axial component is very low. So, even if one grants you that the SideWallForce may be larger for small cone angle, the axial component is small. Comments?
But, say Sin(Theta) were decreased by 1% value, how many additional bounces will that deliver? It's nonlinear, so I don't know where the sweet spot is. Could a slightly lower cone angle provide much higher thrust because there are millions of more bounces at that angle? In other words, less thrust per bounce, but many more bounces. I don't know yet, but it is interesting and is yet "another" way of replacing Q with something else.
Todd

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Thanks Shell...it was fun...a dry run for the fulcrum test in a couple of weeks. Think we had 24 viewers, not bad for short notice only here on NSF.

Great work rfmwguy, watched the webcast and everything worked fine , look forward to the "real run"  best of luck!
And thanks to Dr Rodal for being a really effective ringmaster of this fringe circus!!!!

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Thinking about the ongoing controversy regarding TheTraveller's and Shawyer's theory raises a question for me. Please forgive if this has been addressed in one of the earlier threads.
If Shawyer's theory is wrong then is Cullen's eqn 15 also incorrect?? Eqn 15 seems to be the bedrock of the theory (the bible they punch :D).
I am trying to unpack the controversy a bit from the recent standard of "the physics/theory is wrong".
Cullen is discussing a constant cross section wave guide the resonator that Shawyer is trying to analyze is a more complicated shape so Cullen's equation may or may not be applicable. There is probably something wrong with Shawyer's equation 7 since it ignores forces on the side walls. There are proofs in EM theory that show that EM waves will produces a time averaged net 0 force for any shape cavity, and any result that contradicts this either has incorrect math, or an assumption inconsistent with Maxwell's equations i.e. new physics.
If you are looking for a specific part of Shawyer's paper that is wrong, just after equation 7, he applies the special relativity velocity addition formula. This formula is used to transform the velocity of something measured in one reference frame to the velocity that object would appear to have in another reference frame. Shawyer applies it to a random equation that he had rearranged to have a subtraction of velocities. He is not transforming reference frames, so applying the formula there is nonsense.
When he calculates the forces on the 2 plates separately for a waveguide moving at a different velocity, he is using the equation in the right context, but fails to account for the fact that he has to transform all of the variables into the moving reference frame. Some quantities that change are the cavity length, resonance frequency, injected frequency, and the energy stored in the waves. His claims of thrust reversing at a high fraction of the speed of light are a symptom of this misapplication of special relativity.
The fact that his paper's conclusions are completely wrong is sufficiently obvious to most experts that they don't even bother looking for what his specific mistakes are. The experimental results from multiple labs are another story, and those results are the only reason the EM drive is not completely dismissed.

Thinking about the ongoing controversy regarding TheTraveller's and Shawyer's theory raises a question for me. Please forgive if this has been addressed in one of the earlier threads.
If Shawyer's theory is wrong then is Cullen's eqn 15 also incorrect?? Eqn 15 seems to be the bedrock of the theory (the bible they punch :D).
I am trying to unpack the controversy a bit from the recent standard of "the physics/theory is wrong".
Cullen is discussing a constant cross section wave guide the resonator that Shawyer is trying to analyze is a more complicated shape so Cullen's equation may or may not be applicable. There is probably something wrong with Shawyer's equation 7 since it ignores forces on the side walls. There are proofs in EM theory that show that EM waves will produces a time averaged net 0 force for any shape cavity, and any result that contradicts this either has incorrect math, or an assumption inconsistent with Maxwell's equations i.e. new physics.
If you are looking for a specific part of Shawyer's paper that is wrong, just after equation 7, he applies the special relativity velocity addition formula. This formula is used to transform the velocity of something measured in one reference frame to the velocity that object would appear to have in another reference frame. Shawyer applies it to a random equation that he had rearranged to have a subtraction of velocities. He is not transforming reference frames, so applying the formula there is nonsense.
When he calculates the forces on the 2 plates separately for a waveguide moving at a different velocity, he is using the equation in the right context, but fails to account for the fact that he has to transform all of the variables into the moving reference frame. Some quantities that change are the cavity length, resonance frequency, injected frequency, and the energy stored in the waves. His claims of thrust reversing at a high fraction of the speed of light are a symptom of this misapplication of special relativity.
The fact that his paper's conclusions are completely wrong is sufficiently obvious to most experts that they don't even bother looking for what his specific mistakes are. The experimental results from multiple labs are another story, and those results are the only reason the EM drive is not completely dismissed.
Excellent!. Exactly the kind of detail I was looking for! I think the discussion in this series of threads has reached a point where even folks who are not experts in this domain are interested in detailed critiques like this.
The detailed dialog of WarpTech and DeltaMass has given me a much deeper appreciation of what might or might not be happening. Your excellent post also does this. Thank you.
And I certainly hope for more of this from both sides of the various controversies here! :D

No matter if the EM drive theory fails or not I do have a more basic physics question.
Back up to a simple situation where my finger or something pushes something else. The actual protons and neutrons (maybe electron clouds) do not touch (unless in a particle collision device like Fermi or Cern) so what wavefronts or fields are coming into play to transfer the force from the pusher object? Strong? Weak? Gravity? Magnetic? Electrical? A mixture?
Has touching like that been modeled down to the field level?
Has its relationship to reference frames in space been modeled?
I keep thinking rocket exhaust throwing mass out the back of the rocket  what does it really imply for different reference planes and the structure of space.
+ added later: And then there is the bit with particles that don't react with reference frames or matter unless they do a head on collision like the neutrino flashes in huge pools of carbontet. So what's the traction factor?

but in all cases, they are doing it wrong and should be using 2 ports to measure cavity resonance. We have yet to see anyone do it this way.
Todd
So Dr. Ray Kwok is also wrong?
I see nothing incorrect about what Dr. Kwok said. He said "Resonators". An antenna is a resonator and so is a cavity. One is an open system, the other is a closed system. The preferred methods are different at a "National Standards" level, according to @rfmwguy. While I agree 100% that the experimenters to date have consistently used the S11 method, that does not mean it is the "standard" way to do it. You are arguing that "In the EM Drive world" this is how it's done. Perhaps this is true, but is no less true that this is NOT the "standard" way to do it.
Stop arguing about it and accept that fact please. You're driving everyone bonkers with your obstinance and defense of obvious incongruences. I do not follow others. I make mistakes, try to understand learn from them and forge my own path and from what I've seen, that is how most of us here operate.
Todd
My point is Shawyer, Prof Yang, Eagleworks & Prof Tajmar measured unloaded Q via a 1 port S11 3dB off the max return loss dB and frequency.
Why did they do it that way?
Because the cavity in operation has no load, no output port. A high Q cavity is like a high impedance parallel LC circuit where any external load on the circuit / cavity will introduce additional circuit / cavity losses and thus drop circuit / cavity Q.
The EMDrive operates as a high Q unloaded cavity and doing 2 port S21 cavity Q measurement, where the 2nd port or probe removes some of the cavity energy, which increases cavity losses, reducing unloaded Q, is just nuts.
I have explained why EMDrive cavity Q must be measured via unloaded via S11 return loss and how it is done. I also explained using a 2 port S21 can measure Q but it is not unloaded Q as the 2nd port sample probe increases cavity losses and reduces the unloaded cavity Q.
But hey do it your way as all these arm chair experts who have never built an EMDrive and got it to produce Force know better than Shawyer, Prof Yang, Eagleworks, Prof Tajmar's & Prof Tajmar's uW expert prof.

The testiness of this current discussion aside, I am genuinely interested in the reason why there is a difference between these two Q value viewpoints.
As far as I can gather, @TT is saying, "How they did it". @rfmwguy is saying "How it should've been done." and @tleach is saying "This is how it seems to fit McCulloch's formula."
Which BTW, McCulloch doesn't define how to measure Q. He simply redefines it as the number of bounces (reflections), in the time it takes the photon to decay to zero. So that's not even the same definition of the Q that is being kicked around here. @tleach was trying to bridge that gap.
What I conclude is, the experimenters may or may not be measuring it consistently using the same methodology, but in all cases, they are doing it wrong and should be using 2 ports to measure cavity resonance. We have yet to see anyone do it this way.
Todd
Can we simply agree to some notation to indicate which measurement scheme for Q we are talking about. I'm sure there is a definitive answer for how to measure Q, but I get the feeling that deriving it involves complex math and probably deserves a paper of its own. Can we simply agree on some way to easily notate which measuring scheme a poster is using and agree to disagree which is correct pending further data?
I mean hell, with the falloff in power requirements that TT was going on about on Reddit I'm not at all sure that the Q of the device isn't increasing the longer it is active. (Which reminds me, has anybody pointed a geiger counter at one of these things to make sure it isn't throwing off unexpected radiation).

Investing in Innovation for the Common Good
http://t.co/6feZnFeHlr
True for my totally open EMDrive work as well.

Jose,
In Zeng & Fan they define the complex wave number propagating toward the small end as;
k = j*α  β, where j is the imaginary coordinate.
Momentum is directly proportional to k. So the squared magnitude of the momentum vector is proportional to;
k^{2} = α^{2} + β^{2}
Now, take a gander at the plots for attenuation and phase constant in Zeng & Fan. Which mode and cone halfangle do you think will have the highest momentum?
For TE modes, as β goes to 0, the wave is 100% attenuated at the small end. They refer to this as the cutoff.
Wouldn't you agree, that the waves have the highest momentum when the cone angle is smallest and k*r is the largest?
Also, if the attenuation, α is asymmetrical, would the equation above not (rather simply) explain beyond doubt why momentum transfer is also asymmetrical?
@TheTraveler likes to use Guide wavelength, rather than phase velocity. So be it. The guide wavelength is the inverse;
λ_{guide} = 2*pi/β
Per Z&F, as α increases, β goes to 0, the guide wavelength will become infinitely long and momentum of the wave goes to zero. It is 100% attenuated and absorbed at the front end.
Going the other way, toward the big end, β is increasing and α is decreasing rapidly. The momentum of the wave is increasing.
In both directions, the force on the frustum which balances the change in momentum is "forward". It is only the reflection at the big end that opposes this force. Anything that can be done to minimize the "z" component of this reflection, will add to the thrust.
Todd

SPR has declined my license request.
Too much red tape with using Chinese frustum fabricators and my Australian company would need to be approved by both UK and Australian Depts of Defense.
Oh well at least I tried to do the right thing.

SPR has declined my license request.
Too much red tape with using Chinese frustum fabricators and my Australian company would need to be approved by both UK and Australian Depts of Defense.
Oh well at least I tried to do the right thing.
As a practical matter will this affect you much? Just trying to understand the implications of this. Thanks!

SPR has declined my license request.
Too much red tape with using Chinese frustum fabricators and my Australian company would need to be approved by both UK and Australian Depts of Defense.
Oh well at least I tried to do the right thing.
As a practical matter will this affect you much? Just trying to understand the implications of this. Thanks!
Should have very little effect.
Was just trying to do the right thing by Shawyer / SPR and not be called out for ripping off the IP.
Told Shawyer I'll still give him / SPR 25% of any gross profit made.

SPR has declined my license request.
Too much red tape with using Chinese frustum fabricators and my Australian company would need to be approved by both UK and Australian Depts of Defense.
Oh well at least I tried to do the right thing.
As a practical matter will this affect you much? Just trying to understand the implications of this. Thanks!
Should have very little effect.
Was just trying to do the right thing by Shawyer / SPR and not be called out for ripping off the IP.
Told Shawyer I'll still give him / SPR 25% of any gross profit made.
So they'll still allow you manufacture in China/Australia and import the components? That's good at least. Bummer they won't let you give Shawyer some (financial) credit though...
EDIT: Oops! Yeah, looks like you're going to give him 25%. Sorry, it's getting late. I misread that last line.

SPR has declined my license request.
Too much red tape with using Chinese frustum fabricators and my Australian company would need to be approved by both UK and Australian Depts of Defense.
Oh well at least I tried to do the right thing.
As a practical matter will this affect you much? Just trying to understand the implications of this. Thanks!
Should have very little effect.
Was just trying to do the right thing by Shawyer / SPR and not be called out for ripping off the IP.
Told Shawyer I'll still give him / SPR 25% of any gross profit made.
There is nothing to stop you from experimenting since you do believe in it. That would be a better way to start anyway.

Wouldn't you agree, that the waves have the highest momentum when the cone angle is smallest and k*r is the largest?
Did you change your mind about k*r? In previous thread you implied the opposite, that it had to be the lowest possible in order to increase thrust.
It is only the reflection at the big end that opposes this force. Anything that can be done to minimize the "z" component of this reflection, will add to the thrust.
Todd
Anything decreasing the reflection at the big end would also dramatically decrease the Q of the cavity. Do you think about a particular method? EDIT: slotting maybe ;)

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Thermal tests done including 5 minute run at 30% power, which is what I'll use for fulcrum test. What I learned: Matching into frustum is good, magnetron ran at temperatures well below 200°C. Still had minor arcing, corrected it with full teardown and replacement of Db with mesh only, no copper clad. IOW, frustum is now all mesh except for Ds where magnetron is mounted. There was no arcing on Ds throughout any thermal testing. Plasma focused on Db, interestingly enough diagonally across from radome, not directly across axially.
@rfmwguy
"Thermal tests done including 5 minute run at 30% power, which is what I'll use for fulcrum test." So you're actually putting in 30% of 900W which would be approximately 270W.
And then there's the conversion of electrical energy into microwave energy. If we assume that wikepedia is correct, a 900W microwave oven magnetron should run with approximately 64% efficiency.
https://en.wikipedia.org/wiki/Microwave_oven#Heating_efficiency
That means you're magnetron is only putting 172.8W of energy into your frustum. I'm officially revising my force prediction (based on my v3 spreadsheet and a projected S12 Q factor of 7000) down 43.41 mN.
Sorry :)
Hi Thor,
No, 30% is the amount of time power is at 100%, so it will "pulse" at full power for 30% of the time.

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When you do the real thing are you going to publicise more widely?
I dunno, Star, have given that some thought, even getting some of my film crew buddies out to the shop to document it 3rdparty...but have enough reservations remaining that I'll just let NSF pals spread the word themselves.
Should positive results be achieved, and I believe enough in them, I'll get a film crew out to professionally video it. I'm sure they or perhaps a local TV station would be interested in shooting a "mad scientist" feature spot.
Way too early for that. Getting them out for null results would be a bad deal for everyone. Besides, I have to clean up the shop first ;)

Jose,
In Zeng & Fan they define the complex wave number propagating toward the small end as;
k = j*α  β, where j is the imaginary coordinate.
Momentum is directly proportional to k. So the squared magnitude of the momentum vector is proportional to;
k^{2} = α^{2} + β^{2}
Now, take a gander at the plots for attenuation and phase constant in Zeng & Fan. Which mode and cone halfangle do you think will have the highest momentum?
For TE modes, as β goes to 0, the wave is 100% attenuated at the small end. They refer to this as the cutoff.
Wouldn't you agree, that the waves have the highest momentum when the cone angle is smallest and k*r is the largest?
Also, if the attenuation, α is asymmetrical, would the equation above not (rather simply) explain beyond doubt why momentum transfer is also asymmetrical?
@TheTraveler likes to use Guide wavelength, rather than phase velocity. So be it. The guide wavelength is the inverse;
λ_{guide} = 2*pi/β
Per Z&F, as α increases, β goes to 0, the guide wavelength will become infinitely long and momentum of the wave goes to zero. It is 100% attenuated and absorbed at the front end.
Going the other way, toward the big end, β is increasing and α is decreasing rapidly. The momentum of the wave is increasing.
In both directions, the force on the frustum which balances the change in momentum is "forward". It is only the reflection at the big end that opposes this force. Anything that can be done to minimize the "z" component of this reflection, will add to the thrust.
Todd
Momentum is a vector. What matters is the component of the momentum on the lateral walls acting along the longitudinal axis, so you have to multiply it by Sin[θ]:
Sin[θ]*MomentumLateralWalls where θ=cone halfangle
()
while the transverse components
Cos[θ]*MomentumLateralWalls
are selfcancelling (since the component on the left wall act in opposite direction to the one in the right wall). Thus, if one assumes what you propose is correct (*), what matters is the vector component of momentum on the lateral walls, the component oriented along the longitudinal axis of the cone: Sin[θ]*Abs[k] where θ is the halfcone angle, so for θ=0, this component is zero. Any finite magnitude multiplied by zero gives a zero result. So obviously a cylinder (θ=0) is the worst situation, as the longitudinal component of lateralwall momentum is zero. For θ=0, Sin[θ]*Abs[k] is zero, as θ increases, k decreases, but Sin[θ] increases. As to what is the optimal value of the cone halfangle θ, one would have to calculate the expressions to find out.
If you don't multiply the Momentum by Sin[θ], then one arrives at the wrong conclusion: that a cylinder is best. To arrive at the correct conclusion, one has to multiply Momentum by Sin[θ].
(*) To know, one would have to calculate the Hankel functions and see how the absolute value of k varies as a function of cone angle θ and k r

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When you do the real thing are you going to publicise more widely?
I dunno, Star, have given that some thought, even getting some of my film crew buddies out to the shop to document it 3rdparty...but have enough reservations remaining that I'll just let NSF pals spread the word themselves.
Should positive results be achieved, and I believe enough in them, I'll get a film crew out to professionally video it. I'm sure they or perhaps a local TV station would be interested in shooting a "mad scientist" feature spot.
Way too early for that. Getting them out for null results would be a bad deal for everyone. Besides, I have to clean up the shop first ;)
Good to hear and good luck with the tests.:)

Not making any claims here, just reporting what I read. Keeping an open mind and poking around a bit.
Been reading up on how Shawyer "opens" up the Emdrive in his theory paper.
http://www.emdrive.com/theorypaper94.pdf
Specifically his use of Einstein's law of addition of velocities:
We note that if the forces had been the mechanical result of a working fluid
within the closed waveguide assembly, then the resultant force would merely
introduce a mechanical strain in the waveguide walls. This would be the result of a
closed system of waveguide and working fluid.
In the present system the working fluid is replaced by an electromagnetic
wave propagating close to the speed of light and Newtonian mechanics must be
replaced with the special theory of relativity. There are two effects to be considered
in the application of the special theory of relativity to the waveguide. The first effect
is that as the two forces Fg1 and Fg2 are dependent upon the velocities vg1 and vg2, the
thrust T should be calculated according to Einstein’s law of addition of velocities
given by
()
The second effect is that as the beam velocities are not directly dependent on
any velocity of the waveguide, the beam and waveguide form an open system. Thus
the reactions at the end plates are not constrained within a closed system of
waveguide and beam but are reactions between waveguide and beam, each operating
within its own reference frame, in an open system.
Source of image:
https://en.wikipedia.org/wiki/Velocityaddition_formula#Special_relativity
I remember reading lots of criticism for Shawyer using the addition of velocities from SR.
So I went looking around for where it is okay to use the addition of velocities. I went poking around to see what I could learn while keeping in mind that the EMdrives have air within the cavity with a refractive index not equal to 1 (1.000277) have been shown to present more thrust than airless cavities.
Ended up here:
https://en.wikipedia.org/wiki/Sagnac_effect (yeah I know, it's been brought up before)
When light propagates in fibre optic cable, the setup is effectively a combination of a Sagnac experiment and the Fizeau experiment. In glass the speed of light is slower than in vacuum, and the optical cable is the moving medium. In that case the relativistic velocity addition rule applies.
So it looks like the line in the sand is centered around the invariant speed of light in vacuum vs the speed of light in a medium (not a constant). Anyone able to mythbust any of this? Is the criticism that Shawyer is wrong in using the above addition of velocities warranted?
Which lead me to poke around looking for info related to the Fizeau experiment.
https://en.wikipedia.org/wiki/Fizeau_experiment (there was some dragging detected)
But then I was thinking of old MichelsonMorley experiment and those that followed:
https://en.wikipedia.org/wiki/Michelson%E2%80%93Gale%E2%80%93Pearson_experiment
http://www.kritikrelativitaetstheorie.de/Anhaenge/WolfgangEngelhardtSagnac.pdf (Originally posted in thread 2 by @Rodal)
So all I have to say after all that, it seems very important to see whether or not thrust differs when the frustum is oriented both parallel and perpendicular to Earth's rotation.

Not making any claims here, just reporting what I read. Keeping an open mind and poking around a bit.
Been reading up on how Shawyer "opens" up the Emdrive in his theory paper.
http://www.emdrive.com/theorypaper94.pdf
Specifically his use of Einstein's law of addition of velocities:
We note that if the forces had been the mechanical result of a working fluid
within the closed waveguide assembly, then the resultant force would merely
introduce a mechanical strain in the waveguide walls. This would be the result of a
closed system of waveguide and working fluid.
In the present system the working fluid is replaced by an electromagnetic
wave propagating close to the speed of light and Newtonian mechanics must be
replaced with the special theory of relativity. There are two effects to be considered
in the application of the special theory of relativity to the waveguide. The first effect
is that as the two forces Fg1 and Fg2 are dependent upon the velocities vg1 and vg2, the
thrust T should be calculated according to Einstein’s law of addition of velocities
given by
()
The second effect is that as the beam velocities are not directly dependent on
any velocity of the waveguide, the beam and waveguide form an open system. Thus
the reactions at the end plates are not constrained within a closed system of
waveguide and beam but are reactions between waveguide and beam, each operating
within its own reference frame, in an open system.
Source of image:
https://en.wikipedia.org/wiki/Velocityaddition_formula#Special_relativity
I remember reading lots of criticism for Shawyer using the addition of velocities from SR.
So I went looking around for where it is okay to use the addition of velocities. I went poking around to see what I could learn while keeping in mind that the EMdrives have air within the cavity with a refractive index not equal to 1 (1.000277) have been shown to present more thrust than airless cavities.
Ended up here:
https://en.wikipedia.org/wiki/Sagnac_effect (yeah I know, it's been brought up before)
When light propagates in fibre optic cable, the setup is effectively a combination of a Sagnac experiment and the Fizeau experiment. In glass the speed of light is slower than in vacuum, and the optical cable is the moving medium. In that case the relativistic velocity addition rule applies.
So it looks like the line in the sand is centered around the invariant speed of light in vacuum vs the speed of light in a medium (not a constant). Anyone able to mythbust any of this? Is the criticism that Shawyer is wrong in using the above addition of velocities warranted?
Which lead me to poke around looking for info related to the Fizeau experiment.
https://en.wikipedia.org/wiki/Fizeau_experiment (there was some dragging detected)
But then I was thinking of old MichelsonMorley experiment and those that followed:
https://en.wikipedia.org/wiki/Michelson%E2%80%93Gale%E2%80%93Pearson_experiment
http://www.kritikrelativitaetstheorie.de/Anhaenge/WolfgangEngelhardtSagnac.pdf (Originally posted in thread 2 by @Rodal)
So all I have to say after all that, it seems very important to see whether or not thrust differs when the frustum is oriented both parallel and perpendicular to Earth's rotation.
If you really want to dive deep, look at Orbital Angular Momentum of circular radiation:
http://arxiv.org/ftp/arxiv/papers/0905/0905.0190.pdf

Jose,
In Zeng & Fan they define the complex wave number propagating toward the small end as;
k = j*α  β, where j is the imaginary coordinate.
Momentum is directly proportional to k. So the squared magnitude of the momentum vector is proportional to;
k^{2} = α^{2} + β^{2}
Now, take a gander at the plots for attenuation and phase constant in Zeng & Fan. Which mode and cone halfangle do you think will have the highest momentum?
For TE modes, as β goes to 0, the wave is 100% attenuated at the small end. They refer to this as the cutoff.
Wouldn't you agree, that the waves have the highest momentum when the cone angle is smallest and k*r is the largest?
Also, if the attenuation, α is asymmetrical, would the equation above not (rather simply) explain beyond doubt why momentum transfer is also asymmetrical?
@TheTraveler likes to use Guide wavelength, rather than phase velocity. So be it. The guide wavelength is the inverse;
λ_{guide} = 2*pi/β
Per Z&F, as α increases, β goes to 0, the guide wavelength will become infinitely long and momentum of the wave goes to zero. It is 100% attenuated and absorbed at the front end.
Going the other way, toward the big end, β is increasing and α is decreasing rapidly. The momentum of the wave is increasing.
In both directions, the force on the frustum which balances the change in momentum is "forward". It is only the reflection at the big end that opposes this force. Anything that can be done to minimize the "z" component of this reflection, will add to the thrust.
Todd
Momentum is a vector. What matters is the component of the momentum on the lateral walls acting along the longitudinal axis, so you have to multiply it by Sin[θ]:
Sin[θ]*MomentumLateralWalls where θ=cone halfangle
()
while the transverse components
Cos[θ]*MomentumLateralWalls
are selfcancelling (since the component on the left wall act in opposite direction to the one in the right wall). Thus, if one assumes what you propose is correct (*), what matters is the vector component of momentum on the lateral walls, the component oriented along the longitudinal axis of the cone: Sin[θ]*Abs[k] where θ is the halfcone angle, so for θ=0, this component is zero. Any finite magnitude multiplied by zero gives a zero result. So obviously a cylinder (θ=0) is the worst situation, as the longitudinal component of lateralwall momentum is zero. For θ=0, Sin[θ]*Abs[k] is zero, as θ increases, k decreases, but Sin[θ] increases. As to what is the optimal value of the cone halfangle θ, one would have to calculate the expressions to find out.
If you don't multiply the Momentum by Sin[θ], then one arrives at the wrong conclusion: that a cylinder is best. To arrive at the correct conclusion, one has to multiply Momentum by Sin[θ].
(*) To know, one would have to calculate the Hankel functions and see how the absolute value of k varies as a function of cone angle θ and k r
But Z&F give k in the direction of r, not perpendicular to the axis. So the k value I'm using is already "in" that direction. What am I missing in Z&F that says otherwise?
Todd

...But Z&F give k in the direction of r, not perpendicular to the axis. So the k value I'm using is already "in" that direction. What am I missing in Z&F that says otherwise?
Todd
In expression 9 of Zeng and Fan's paper
Electromagnetic fields and transmission properties in tapered hollow metallic waveguides
Xiahui Zeng and Dianyuan Fan
https://www.osapublishing.org/oe/fulltext.cfm?uri=oe17134&id=175583
Zeng and Fan define k sub r in the r direction
Then suddenly in expressions 12, 13 and 14 they give an expression for gamma sub [θ ,φ] in terms of a k that has no subscript.
Ricvl has called these expressions 12 to 14 into question, as to whether they satisfy the Boundary Conditions. I find it peculiar that Zeng and Fan dropped the r subscript in these expressions 1214, and that they replace gamma with gamma sub [θ, φ]
I have not rederived them on my own to see whether they are correct, or whether they satisfy the Boundary Conditions or what does k stand for in these expressions.
From a physical standpoint it does not make any sense to me that the longitudinal component should be maximum for θ =0. For θ =0 the longitudinal component of momentum should be zero, so either Ricvl is correct that these expressions do not satisfy the Boundary Conditions, or gamma is not in the r direction.
Inspection of the subscript for gamma in equations 12 to 14 reveals that this is indeed the case.
The expressions 12 to 14 are labeled as gamma sub [θ, φ], therefore my interpretation is that they clearly are the components perpendicular to r, since the coordinates θ, φ are perpendicular to r.
Therefore it seems to me that a gamma component in the θ direction should be multplied by Sin[θ] to get the component in the longitudinal direction.
At the bottom of page 14, Zeng and Fan write:
Based on the Eqs. (12), (13) and (14), a variation of the attenuation α and phase constants β
for the spherical TE and TM modes as a function of kr with cone halfangle 0 θ as a
parameter has been studied and the results are presented in Figs. 25.
So Figs. 2 to 5 that you are using to base your conclusions on, are based on gamma sub [ θ, φ ] instead of gamma sub r.

...But Z&F give k in the direction of r, not perpendicular to the axis. So the k value I'm using is already "in" that direction. What am I missing in Z&F that says otherwise?
Todd
In expression 9 of Zeng and Fan's paper
Electromagnetic fields and transmission properties in tapered hollow metallic waveguides
Xiahui Zeng and Dianyuan Fan
https://www.osapublishing.org/oe/fulltext.cfm?uri=oe17134&id=175583
Zeng and Fan define k sub r in the r direction
Then suddenly in expressions 12, 13 and 14 they give an expression for gamma sub [θ ,φ] in terms of a k that has no subscript.
Ricvl has called these expressions 12 to 14 into question, as to whether they satisfy the Boundary Conditions. I find it peculiar that Zeng and Fan droped the r subscript in these expressions 1214, and that they replace gamma with gamma sub [θ, φ]
I have not rederived them on my own to see whether they are correct, or whether they satisfy the Boundary Conditions or what does k stand for in these expressions.
From a physical standpoint it does not make any sense to me that the longitudinal component should be maximum for θ =0. For θ =0 the longitudinal component of momentum should be zero, so either Ricvl is correct that these expressions do not satisfy the Boundary Conditions, or k in these expresssions is not k sub r and gamma is not in the r direction.
Inspection of the subscript for gamma in equations 12 to 14 reveals that this is indeed the case.
The expressions 12 to 14 are labeled as gamma sub [θ, φ], therefore my interpretation is that they clearly are the components perpendicular to r, since the coordinates θ, φ are perpendicular to r.
Therefore it seems to me that a gamma component in the θ direction should be multplied by Sin[θ] to get the component in the longitudinal direction.
Okay, back to the drawing board!
Thanks!
Todd

...
Okay, back to the drawing board!
Thanks!
Todd
Please notice that while Fig. 2 and 3 in Zeng and Fan correspond to the electric field in the θ and φ directions, Fig 4 and 5 correspond to the electric field in the r direction. Only the TM modes have an electric field in the r direction.
They define the attenuation only for the electric field, so they don't have a figure for magnetic field in the r direction corresponding to the TE modes.

For those who are too skittish to be associated with doing Emdrive experiments, would recasting it as yet another Aether drag experiment sound any better?
https://en.wikipedia.org/wiki/Michelson%E2%80%93Morley_experiment#Recent_optical_resonator_experiments
Have any recent experiments featured any intentional symmetry breaking?

For those who are too skittish to be associated with doing Emdrive experiments, would recasting it as yet another Aether drag experiment sound any better?
https://en.wikipedia.org/wiki/Michelson%E2%80%93Morley_experiment#Recent_optical_resonator_experiments
Have any recent experiments featured any intentional symmetry breaking?
Which kind of symmetry do you mean?
complex issue...
That's symmetry breaking par excellence, never the B field curls in the opposite direction while the current flows in the direction like in the drawing ;)
source of the picture: http://wiki.bnvbamberg.de/flgwiki/index.php/SchulheftPh9
Gravity is another example (till now there is only attractive force). :)

Parity and Time

Parity and Time
spontaneous symmetry breaking is the why we(and the universe) are here and the why we can ask such questions 8)
I will hope we will find out why symmetry is broken inside the conical cavity. May be it acts weak on some unknown scalar field in a asymmetrically way

...
Okay, back to the drawing board!
Thanks!
Todd
Please notice that while Fig. 2 and 3 in Zeng and Fan correspond to the electric field in the θ and φ directions, Fig 4 and 5 correspond to the electric field in the r direction. Only the TM modes have an electric field in the r direction.
They define the attenuation only for the electric field, so they don't have a figure for magnetic field in the r direction corresponding to the TE modes.
Correct. The attenuation is on E perpendicular to the walls, since there is no radial component and no component tangential to the walls. However, the momentum in the r direction, depends on E perpendicular to r. So the attenuation of E perpendicular to r, affects the momentum in the r direction without multiplication by Sin(theta).
If you follow from equation 8 to 9, the expression j*k_{r}=(1/E)*dE/dr, is an expression for momentum in the r direction. To get momentum in the z direction, you would multiply by Cos(theta), but for small cone angles it's negligible.
Equation 8 is fairly straight forward, the wave is propagating in the r direction, and equation 9 shows it is expanding or contracting depending on direction. Take the derivative of 9 wrt t and multiply by Planck's constant to get the force, dp/dt. For which I get; (E is the electric field, not energy!!!)
F_{r} = (hbar*k_{r}/E)*dE/dt j*hbar*d/dt(dE/dr)
= (hbar*k_{r}/E)*dE/dt j*(hbar/c)*d^{2}E/dt^{2}) (I don't think I should use c here for dr/dt, but you get the idea. It's a wave equation.)
For F_{z} = F_{r} * Cos(theta)
Comments?
Todd

For those who are too skittish to be associated with doing Emdrive experiments, would recasting it as yet another Aether drag experiment sound any better?
https://en.wikipedia.org/wiki/Michelson%E2%80%93Morley_experiment#Recent_optical_resonator_experiments
Have any recent experiments featured any intentional symmetry breaking?
Which kind of symmetry do you mean?
complex issue...
That's symmetry breaking par excellence, never the B field curls in the opposite direction while the current flows in the direction like in the drawing ;)
source of the picture: http://wiki.bnvbamberg.de/flgwiki/index.php/SchulheftPh9
Gravity is another example (till now there is only attractive force). :)
Gravity is the result of breaking the symmetry of the equilibrium power exchange, (photons, gluons, etc..) between particleoscillators and the applicable ZPF. If you can produce a gradient in the opposite direction...
Todd

...
Okay, back to the drawing board!
Thanks!
Todd
Please notice that while Fig. 2 and 3 in Zeng and Fan correspond to the electric field in the θ and φ directions, Fig 4 and 5 correspond to the electric field in the r direction. Only the TM modes have an electric field in the r direction.
They define the attenuation only for the electric field, so they don't have a figure for magnetic field in the r direction corresponding to the TE modes.
Correct. The attenuation is on E perpendicular to the walls, since there is no radial component and no component tangential to the walls. However, the momentum in the r direction, depends on E perpendicular to r. So the attenuation of E perpendicular to r, affects the momentum in the r direction without multiplication by Sin(theta).
If you follow from equation 8 to 9, the expression j*k_{r}=(1/E)*dE/dr, is an expression for momentum in the r direction. To get momentum in the z direction, you would multiply by Cos(theta), but for small cone angles it's negligible.
Equation 8 is fairly straight forward, the wave is propagating in the r direction, and equation 9 shows it is expanding or contracting depending on direction. Take the derivative of 9 wrt t and multiply by Planck's constant to get the force, dp/dt. For which I get; (E is the electric field, not energy!!!)
F_{r} = (hbar*k_{r}/E)*dE/dt j*hbar*d/dt(dE/dr)
= (hbar*k_{r}/E)*dE/dt j*(hbar/c)*d^{2}E/dt^{2}) (I don't think I should use c here for dr/dt, but you get the idea. It's a wave equation.)
For F_{z} = F_{r} * Cos(theta)
Comments?
Todd
I would have to rederive them myself, but:
1) From a physical standpoint it does not make any sense to me that the longitudinal component should be maximum for θ =0. For θ =0 the longitudinal component of momentum should be zero, so either Ricvl is correct that these expressions do not satisfy the Boundary Conditions, or gamma is not in the r direction.
2) The expressions 12 to 13 are labeled as gamma sub [θ, φ], therefore my interpretation is that they clearly are the components perpendicular to r, since the coordinates θ, φ are perpendicular to r. Therefore it seems to me that a gamma component in the θ direction should be multplied by Sin[θ] to get the component in the longitudinal direction.
I have to rederive them myself to make any further comments. #1 ( it does not make any sense to me that the longitudinal component should be maximum for θ =0 which implies that a cylinder is best) is a big obstacle in me being able to agree that it is correct without mulitplying by Sin[θ]
Sorry, I cannot take Zeng and Fan's results for granted if they imply that the longitudinal component of momentum should be maximum for θ =0

...
Okay, back to the drawing board!
Thanks!
Todd
Please notice that while Fig. 2 and 3 in Zeng and Fan correspond to the electric field in the θ and φ directions, Fig 4 and 5 correspond to the electric field in the r direction. Only the TM modes have an electric field in the r direction.
They define the attenuation only for the electric field, so they don't have a figure for magnetic field in the r direction corresponding to the TE modes.
Correct. The attenuation is on E perpendicular to the walls, since there is no radial component and no component tangential to the walls. However, the momentum in the r direction, depends on E perpendicular to r. So the attenuation of E perpendicular to r, affects the momentum in the r direction without multiplication by Sin(theta).
If you follow from equation 8 to 9, the expression j*k_{r}=(1/E)*dE/dr, is an expression for momentum in the r direction. To get momentum in the z direction, you would multiply by Cos(theta), but for small cone angles it's negligible.
Equation 8 is fairly straight forward, the wave is propagating in the r direction, and equation 9 shows it is expanding or contracting depending on direction. Take the derivative of 9 wrt t and multiply by Planck's constant to get the force, dp/dt. For which I get; (E is the electric field, not energy!!!)
F_{r} = (hbar*k_{r}/E)*dE/dt j*hbar*d/dt(dE/dr)
= (hbar*k_{r}/E)*dE/dt j*(hbar/c)*d^{2}E/dt^{2}) (I don't think I should use c here for dr/dt, but you get the idea. It's a wave equation.)
For F_{z} = F_{r} * Cos(theta)
Comments?
Todd
I would have to rederive them myself, but:
1) From a physical standpoint it does not make any sense to me that the longitudinal component should be maximum for θ =0. For θ =0 the longitudinal component of momentum should be zero, so either Ricvl is correct that these expressions do not satisfy the Boundary Conditions, or gamma is not in the r direction.
2) The expressions 12 to 13 are labeled as gamma sub [θ, φ], therefore my interpretation is that they clearly are the components perpendicular to r, since the coordinates θ, φ are perpendicular to r. Therefore it seems to me that a gamma component in the θ direction should be multplied by Sin[θ] to get the component in the longitudinal direction.
I have to rederive them myself to make any further comments. #1 ( it does not make any sense to me that the longitudinal component should be maximum for θ =0 which implies that a cylinder is best) is a big obstacle in me being able to agree that it is correct without mulitplying by Sin[θ]
Sorry, I cannot take Zeng and Fan's results for granted if they imply that the longitudinal component of momentum should be maximum for θ =0
You can't form a cylinder this way, r is the distance from the apex ;) that's never parallel. For the boundary conditions i have to think about, but your comment 2) make sense to me

...
You can't form a cylinder this way, r is the distance from the apex ;) that's never parallel. For the boundary conditions i have to think about, but your comment 2) make sense to me
I had that discussion with Todd in a previous thread, where he wrote the same thing you wrote above.
That's wrong.
I submitted a formal proof that a cylinder is the limit for r2 >Infinity with (r2  r1) kept constant and theta > 0. Although I derived my proof independently you can also find in Euclidean geometry books, it emanates from the last of Euclid's postulate (parallell lines never meet) that is supplanted in Lobatchesky and Riemannian geometries.

...
Okay, back to the drawing board!
Thanks!
Todd
Please notice that while Fig. 2 and 3 in Zeng and Fan correspond to the electric field in the θ and φ directions, Fig 4 and 5 correspond to the electric field in the r direction. Only the TM modes have an electric field in the r direction.
They define the attenuation only for the electric field, so they don't have a figure for magnetic field in the r direction corresponding to the TE modes.
Correct. The attenuation is on E perpendicular to the walls, since there is no radial component and no component tangential to the walls. However, the momentum in the r direction, depends on E perpendicular to r. So the attenuation of E perpendicular to r, affects the momentum in the r direction without multiplication by Sin(theta).
If you follow from equation 8 to 9, the expression j*k_{r}=(1/E)*dE/dr, is an expression for momentum in the r direction. To get momentum in the z direction, you would multiply by Cos(theta), but for small cone angles it's negligible.
Equation 8 is fairly straight forward, the wave is propagating in the r direction, and equation 9 shows it is expanding or contracting depending on direction. Take the derivative of 9 wrt t and multiply by Planck's constant to get the force, dp/dt. For which I get; (E is the electric field, not energy!!!)
F_{r} = (hbar*k_{r}/E)*dE/dt j*hbar*d/dt(dE/dr)
= (hbar*k_{r}/E)*dE/dt j*(hbar/c)*d^{2}E/dt^{2}) (I don't think I should use c here for dr/dt, but you get the idea. It's a wave equation.)
For F_{z} = F_{r} * Cos(theta)
Comments?
Todd
I would have to rederive them myself, but:
1) From a physical standpoint it does not make any sense to me that the longitudinal component should be maximum for θ =0. For θ =0 the longitudinal component of momentum should be zero, so either Ricvl is correct that these expressions do not satisfy the Boundary Conditions, or gamma is not in the r direction.
2) The expressions 12 to 14 are labeled as gamma sub [θ, φ], therefore my interpretation is that they clearly are the components perpendicular to r, since the coordinates θ, φ are perpendicular to r. Therefore it seems to me that a gamma component in the θ direction should be multplied by Sin[θ] to get the component in the longitudinal direction.
I have to rederive them myself to make any further comments. #1 ( it does not make any sense to me that the longitudinal component should be maximum for θ =0 which implies that a cylinder is best) is a big obstacle in me being able to agree that it is correct without mulitplying by Sin[θ]
In a cylinder, the longitudinal component of momentum is the wave propagating down the waveguide. The momentum is in the z direction, not radial toward the walls. In Z&F, they are depicting a waveguide, not a cavity. The momentum is propagating down the waveguide. Changing the angle > 0, changes the momentum in the z direction for a tapered waveguide, relative to a cylindrical waveguide. In the case of the wave moving toward the apex, what Z&F show is that the waves are attenuated and all of the momentum in the z direction is phase shifted and absorbed.
Essentially, attenuation of the E field in the perpendicular directions, "IS" attenuation of momentum in the r direction, because S_{r} = E x H perpendicular to S. The wave traveling toward the apex is losing momentum to the waveguide, in the z direction. The wave traveling toward the big end is gaining momentum in the z direction. In a cylinder, neither is true because the wave does not change momentum in either direction. So the kvector reflecting off the wall is not (theta, phi) in Z&F, it is in the r direction. So it is r*Cos(theta) to get z direction thrust.
Todd

I have a real concern with TheTraveller's Excel spreadsheet. The values I get from the first basic dimensions are inconsistent. I'm talking of the file EMDriveCalc20150617b.xls available from emdrive.wiki (http://emdrive.wiki/Useful_EMDrive_Design_and_Test_Tools) as well as TT's Gdrive (https://drive.google.com/folderview?id=0B7kgKijop0ifk9EakZfbW9aZGMwNWZMQ01xVnBON0tkM2w0Q1NLbmtjRFFwMXBuNVlVN0U&usp=sharing#list).
Let's take know values, for example Eagleworks' frustum:
D_{b} = 0.2794 m
D_{s} = 0.15875 m
Frustum length = 0.2286 m
cone halfangle = 14.78°
Input the first three values, and the spreadsheet returns a cone halfangle of 24.5° :(
Calculate the hypotenuse or draw the plan in a CAD software with the know values, you will easily get the frustum side length at 0.2364256 m. But the spreadsheet returns 0.2584848 m!
The formula for the cone halfangle (cell D8) in the spreadsheet is :
=DEGREES(ATAN((D3÷2)÷((D5×(D4÷2))+((D3÷2)−(D4÷2))+D5)))
Whereas it could use arccosine, frustum centre length (diameter center to diameter center) and frustum side length:
=DEGREES(ACOS(D5/D9)
Talking about the frustum side length (cell D9), its formula is wrong:
= SQRT(D5^2+(D3−D4)^2)
The correct formula should use end radii squared instead of end diameters squared:
= SQRT(D5^2+((D3−D4)÷2)^2)
How is the rest right or wrong? I can't even get D_{f} right with the available spreadsheet. When inputing the Baby EmDrive data for example, D_{f} becomes negative which is impossible (it should be comprised between 0 and 1) EDIT: my mistake, 24 GHz instead of 2.4 GHz resolved this issue.
Whatever, I don't get the same D_{f} as TheTraveller for the same untouched spreadsheet and same input values. See fourth attachement below. Those differences are quite small, but everything else following in the spreadsheet gets very different values from those discrepancies.
@TheTraveller: can you please doublecheck those basic values in the spreadsheet, and upload a corrected version to the emdrive.wiki? This would be much appreciated by the EmDrive community :)
Below, I show two hypothesis for TT's EmDrive Mark 2, according to how the "Frustum centre length" is defined in the spreadsheet.
 The first with Frustum centre length = 208.71 mm has a cone halfangle (corrected formula) of 30°
 The second with Frustum centre length = 240.7 mm has a cone halfangle (corrected formula) of 26.6° (instead of 27.7° with the wrong angle formula).
What is important to note is that "Frustum centre length" as defined in the spreadsheet is the length between the centers of the two end diameters, and not the length defined by TheTraveller in his drawing where it is the apex r_{2}r_{1} length. All the misunderstanding comes from the difference in that drawing (attached in third position below).

By the way those of you supporting the EM drive want an example of a theory that started out on the fringes but has gradually moved more centre wise then they only have to look at holographic theory for the universe.
http://www.sciencedaily.com/releases/2015/04/150427101633.htm

...
In a cylinder, the longitudinal component of momentum is the wave propagating down the waveguide. The momentum is in the z direction, not radial toward the walls. In Z&F, they are depicting a waveguide, not a cavity. The momentum is propagating down the waveguide. Changing the angle > 0, changes the momentum in the z direction for a tapered waveguide, relative to a cylindrical waveguide. In the case of the wave moving toward the apex, what Z&F show is that the waves are attenuated and all of the momentum in the z direction is phase shifted and absorbed.
Essentially, attenuation of the E field in the perpendicular directions, "IS" attenuation of momentum in the r direction, because S_{r} = E x H perpendicular to S. The wave traveling toward the apex is losing momentum to the waveguide, in the z direction. The wave traveling toward the big end is gaining momentum in the z direction. In a cylinder, neither is true because the wave does not change momentum in either direction. So the kvector reflecting off the wall is not (theta, phi) in Z&F, it is in the r direction. So it is r*Cos(theta) to get z direction thrust.
Todd
A cylinder is a geometrical concept. It is perfectly OK for me to speak of a cylinder as something that has open ends, it carries no implications of a being a cavity.
As to Zeng and Fan, as I said, I would have to rederive their equations and see whether they satisfy the boundary conditions (Ricvl said that they don't) or if there is something else amiss.

...
You can't form a cylinder this way, r is the distance from the apex ;) that's never parallel. For the boundary conditions i have to think about, but your comment 2) make sense to me
I had that discussion with Todd in a previous thread, where he wrote the same thing you wrote above.
That's wrong.
I submitted a formal proof that a cylinder is the limit for r2 >Infinity with (r2  r1) kept constant and theta > 0. Although I derived my proof independently you can also find in Euclidean geometry books, it emanates from the last of Euclid's postulate (parallell lines never meet) that is supplanted in Lobatchesky and Riemannian geometries.
Yeah right it's negligible for huge values of r, sometime the difference of r1 and r2 reach Plank length and there is no longer a difference in a physical sense.
For me this point is done!
Thanks Doc

... Anything that can be done to minimize the "z" component of this reflection, will add to the thrust.
Todd
Since it is unlikely that I will have the time to rederive Zeng and Fan's equations any time soon, please allow me to pursue this (it is much less time consuming :) )
1) What, specifically, can be done to minimize the "z component of the reflection at the Big End, to add to thrust?"
2) Do I understand you correctly that you think that the net force is pointing from the Big End towards the Small End? (in the opposite direction to Shawyer's thrust which he posits to be pointed from the Small End to the Big End?)

need it 3D :)

...
In a cylinder, the longitudinal component of momentum is the wave propagating down the waveguide. The momentum is in the z direction, not radial toward the walls. In Z&F, they are depicting a waveguide, not a cavity. The momentum is propagating down the waveguide. Changing the angle > 0, changes the momentum in the z direction for a tapered waveguide, relative to a cylindrical waveguide. In the case of the wave moving toward the apex, what Z&F show is that the waves are attenuated and all of the momentum in the z direction is phase shifted and absorbed.
Essentially, attenuation of the E field in the perpendicular directions, "IS" attenuation of momentum in the r direction, because S_{r} = E x H perpendicular to S. The wave traveling toward the apex is losing momentum to the waveguide, in the z direction. The wave traveling toward the big end is gaining momentum in the z direction. In a cylinder, neither is true because the wave does not change momentum in either direction. So the kvector reflecting off the wall is not (theta, phi) in Z&F, it is in the r direction. So it is r*Cos(theta) to get z direction thrust.
Todd
A cylinder is a geometrical concept. It is perfectly OK for me to speak of a cylinder as something that has open ends, it carries no implications of a being a cavity.
As to Zeng and Fan, as I said, I would have to rederive their equations and see whether they satisfy the boundary conditions (Ricvl said that they don't) or if there is something else amiss.
I think that you would not need to confirm anything more than equations 8 and 9. Forget the Hankel functions. Z&F say this equation for E is valid
For all electric field components of the spherical TE and TM modes mentioned previously, one can expressed them as... [equation 8]
You have the exact solution for E and H in a frustum cavity. Simply plug in the E vector into equation 9,
k_{r} = j*(1/E)*dE/dr
where E is the electric field vector, all 3 components, which you already have in Mathematica. I think it should be just a few lines of code to take the derivative of a vector you already have, and multiply by the inverse. Once you have k_{r}, take the derivative of that wrt time to get the force equation, and multiply by Cos(theta) to get the force in the z direction. No?
Todd

... Anything that can be done to minimize the "z" component of this reflection, will add to the thrust.
Todd
Since it is unlikely that I will have the time to rederive Zeng and Fan's equations any time soon, please allow me to pursue this (it is much less time consuming :) )
1) What, specifically, can be done to minimize the "z component of the reflection at the Big End, to add to thrust?"
2) Do I understand you correctly that you think that the net force is pointing from the Big End towards the Small End? (in the opposite direction to Shawyer's thrust which he posits to be pointed from the Small End to the Big End?)
1) At one time I suggested cutting slots in it to eliminate the DC component of current density. Settling for a lower Q and more leakage out the big end. Or a partially reflecting surface, like a Laser uses to allow a beam to escape. I am also thinking that the angle of incidence is important too, after looking at the Meep gifs. The energy does not appear to reflect perpendicular to the big end.
2a) I support the idea that dp/dt of the "frustum" is always forward, meaning small end leading.
2b) The dp/dt of the EM waves inside the frustum are such that dp/dt is positive when the wave is moving backwards, and negative when the wave is moving forward. So in one direction it is like "Shawyer's notion of thrust" and in the other direction it is like a solar wind behind a sail. Waves moving in BOTH directions, exert a force Forward on the frustum. It is only when the wave reflects from the big end that a force is being exerted that opposes that force.
I have calculated the DC Bfield inside a frustum cavity and proven to myself that Maxwell's equations yield 0 net force on the system, provided I do not include any kind of nonlinear GR or PV affects on the permeability function. However, if the current is interrupted through the big end, i.e., if there is leakage flux escaping at the big end, then the force is asymmetrical.
Todd

...
In a cylinder, the longitudinal component of momentum is the wave propagating down the waveguide. The momentum is in the z direction, not radial toward the walls. In Z&F, they are depicting a waveguide, not a cavity. The momentum is propagating down the waveguide. Changing the angle > 0, changes the momentum in the z direction for a tapered waveguide, relative to a cylindrical waveguide. In the case of the wave moving toward the apex, what Z&F show is that the waves are attenuated and all of the momentum in the z direction is phase shifted and absorbed.
Essentially, attenuation of the E field in the perpendicular directions, "IS" attenuation of momentum in the r direction, because S_{r} = E x H perpendicular to S. The wave traveling toward the apex is losing momentum to the waveguide, in the z direction. The wave traveling toward the big end is gaining momentum in the z direction. In a cylinder, neither is true because the wave does not change momentum in either direction. So the kvector reflecting off the wall is not (theta, phi) in Z&F, it is in the r direction. So it is r*Cos(theta) to get z direction thrust.
Todd
A cylinder is a geometrical concept. It is perfectly OK for me to speak of a cylinder as something that has open ends, it carries no implications of a being a cavity.
As to Zeng and Fan, as I said, I would have to rederive their equations and see whether they satisfy the boundary conditions (Ricvl said that they don't) or if there is something else amiss.
Yes Dr Rodal, to me Zeng and Fan don't write the correct expressions for the problem of propagation on a tapered conical waveguide.
One way is solve the helmoltz equations respecting directly the physical boundary conditions under the geometry of problem.
This will implies that standard solutions of wave equation in spherical coordinates ( in general, bessel and legendre functions of integer order), must be subtituted by specific solutions with fractionary order legendre/ bessel functions, to respect the angular (theta) PEC boundary condition.
Other way, more complicated, is find solutions using the called "coupledmode theory in instantaneous eigenmode (quasimode) basis ", where one can use a superposition cilindrical modes, evolving a coupledmode equation along the longitudinal axis of propagation, where each cilindrical mode has a instantaneous dependence on the radii of tapered section of conical waveguide.
Of course, there are many others forms to solve this problem.

...
In a cylinder, the longitudinal component of momentum is the wave propagating down the waveguide. The momentum is in the z direction, not radial toward the walls. In Z&F, they are depicting a waveguide, not a cavity. The momentum is propagating down the waveguide. Changing the angle > 0, changes the momentum in the z direction for a tapered waveguide, relative to a cylindrical waveguide. In the case of the wave moving toward the apex, what Z&F show is that the waves are attenuated and all of the momentum in the z direction is phase shifted and absorbed.
Essentially, attenuation of the E field in the perpendicular directions, "IS" attenuation of momentum in the r direction, because S_{r} = E x H perpendicular to S. The wave traveling toward the apex is losing momentum to the waveguide, in the z direction. The wave traveling toward the big end is gaining momentum in the z direction. In a cylinder, neither is true because the wave does not change momentum in either direction. So the kvector reflecting off the wall is not (theta, phi) in Z&F, it is in the r direction. So it is r*Cos(theta) to get z direction thrust.
Todd
A cylinder is a geometrical concept. It is perfectly OK for me to speak of a cylinder as something that has open ends, it carries no implications of a being a cavity.
As to Zeng and Fan, as I said, I would have to rederive their equations and see whether they satisfy the boundary conditions (Ricvl said that they don't) or if there is something else amiss.
Yes Dr Rodal, to me Zeng and Fan don't write the correct expressions for the problem of propagation on a tapered conical waveguide.
One way is solve the helmoltz equations respecting directly the physical boundary conditions under the geometry of problem.
This will implies that standard solutions of wave equation in spherical coordinates ( in general, bessel and legendre functions of integer order), must be subtituted by specific solutions with fractionary order legendre/ bessel functions.
Other way, more complicated, is find solutions using the called "coupledmode theory in instantaneous eigenmode (quasimode) basis ", where one can use a superposition cilindrical modes, evolving a coupledmode equation along the longitudinal axis of propagation, where each cilindrical mode has a instantaneous dependence on the radii of tapered section of conical waveguide.
Of course, there are many others forms to solve this problem.
I set to bold because, to my understanding, this is precisely what they did. Look at equations 2 & 3, and the associated text that follows it, through to equation 8. This part of their work is not that difficult to follow, so I don't see precisely where they make any error or assumptions that would cause it to be wrong. Their answer includes everything you just said, and the derivatives are Hankel functions of "fractional order". Where is the error?
Todd

I have a real concern with TheTraveller's Excel spreadsheet. The values I get from the first basic dimensions are inconsistent. I'm talking of the file EMDriveCalc20150617b.xls available from emdrive.wiki (http://emdrive.wiki/Useful_EMDrive_Design_and_Test_Tools) as well as TT's Gdrive (https://drive.google.com/folderview?id=0B7kgKijop0ifk9EakZfbW9aZGMwNWZMQ01xVnBON0tkM2w0Q1NLbmtjRFFwMXBuNVlVN0U&usp=sharing#list).
Let's take know values, for example Eagleworks' frustum:
D_{b} = 0.2794 m
D_{s} = 0.15875 m
Frustum length = 0.2286 m
cone halfangle = 14.78°
Input the first three values, and the spreadsheet returns a cone halfangle of 24.5° :(
Calculate the hypotenuse or draw the plan in a CAD software with the know values, you will easily get the frustum side length at 0.2364256 m. But the spreadsheet returns 0.2584848 m!
The formula for the cone halfangle (cell D8) in the spreadsheet is :
=DEGREES(ATAN((D3÷2)÷((D5×(D4÷2))+((D3÷2)−(D4÷2))+D5)))
Whereas it could use arccosine, frustum centre length (diameter center to diameter center) and frustum side length:
=DEGREES(ACOS(D5/D9)
Talking about the frustum side length (cell D9), its formula is wrong:
= SQRT(D5^2+(D3−D4)^2)
The correct formula should use end radii squared instead of end diameters squared:
= SQRT(D5^2+((D3−D4)÷2)^2)
How is the rest right or wrong? I can't even get D_{f} right with the available spreadsheet. When inputing the Baby EmDrive data for example, D_{f} becomes negative which is impossible (it should be comprised between 0 and 1) >:(
@TheTraveller: can you please doublecheck those basic values in the spreadsheet, and upload a corrected version to the emdrive.wiki? This would be much appreciated by the EmDrive community :)
Below, I show two hypothesis for TT's EmDrive Mark 2, according to how the "Frustum centre length" is defined in the spreadsheet.
 The first with Frustum centre length = 208.71 mm has a cone halfangle (corrected formula) of 30°
 The second with Frustum centre length = 240.7 mm has a cone halfangle (corrected formula) of 26.6° (instead of 27.7° with the wrong angle formula).
What is important to note is that "Frustum centre length" as defined in the spreadsheet is the length between the centers of the two end diameters, and not the length defined by TheTraveller in his drawing where it is the apex r_{2}r_{1} length. All the misunderstanding comes from the difference in that drawing (attached in third position below).
Didn't the traveler say this came from Shawyer and SPR and the software they used?
Shell
P: Good catch //flux_capacitor

By the way those of you supporting the EM drive want an example of a theory that started out on the fringes but has gradually moved more centre wise then they only have to look at holographic theory for the universe.
http://www.sciencedaily.com/releases/2015/04/150427101633.htm
I honestly love this theory, simply it fits so much (but what do I know?). I've been following it for the last few months. Good post Star One!
I've been kicked out of the shop while other work goes on so I've been reading way too much tech.
Shell

need it 3D :)
Needs a Heat Shield......

Something has been bothering me since last night and I couldn't help but watching the modes change and flip in meep.
How can you calculate seriously any Q in a cavity that simply jumps around from one T mode decaying and building into another in such a short time? And they all do it, every simulation with varying speeds.
Just something to mull over on a day away from the shop.
Shell
Added: Back to lurk mode and I'll be quiet.

If EmDrive "thrust" is an artifact of the experimental measurement process, as most people believe it is, then what is your favoured candidate for such an artifact?
I vote for thermalrelated.

...
In a cylinder, the longitudinal component of momentum is the wave propagating down the waveguide. The momentum is in the z direction, not radial toward the walls. In Z&F, they are depicting a waveguide, not a cavity. The momentum is propagating down the waveguide. Changing the angle > 0, changes the momentum in the z direction for a tapered waveguide, relative to a cylindrical waveguide. In the case of the wave moving toward the apex, what Z&F show is that the waves are attenuated and all of the momentum in the z direction is phase shifted and absorbed.
Essentially, attenuation of the E field in the perpendicular directions, "IS" attenuation of momentum in the r direction, because S_{r} = E x H perpendicular to S. The wave traveling toward the apex is losing momentum to the waveguide, in the z direction. The wave traveling toward the big end is gaining momentum in the z direction. In a cylinder, neither is true because the wave does not change momentum in either direction. So the kvector reflecting off the wall is not (theta, phi) in Z&F, it is in the r direction. So it is r*Cos(theta) to get z direction thrust.
Todd
A cylinder is a geometrical concept. It is perfectly OK for me to speak of a cylinder as something that has open ends, it carries no implications of a being a cavity.
As to Zeng and Fan, as I said, I would have to rederive their equations and see whether they satisfy the boundary conditions (Ricvl said that they don't) or if there is something else amiss.
Yes Dr Rodal, to me Zeng and Fan don't write the correct expressions for the problem of propagation on a tapered conical waveguide.
One way is solve the helmoltz equations respecting directly the physical boundary conditions under the geometry of problem.
This will implies that standard solutions of wave equation in spherical coordinates ( in general, bessel and legendre functions of integer order), must be subtituted by specific solutions with fractionary order legendre/ bessel functions.
Other way, more complicated, is find solutions using the called "coupledmode theory in instantaneous eigenmode (quasimode) basis ", where one can use a superposition cilindrical modes, evolving a coupledmode equation along the longitudinal axis of propagation, where each cilindrical mode has a instantaneous dependence on the radii of tapered section of conical waveguide.
Of course, there are many others forms to solve this problem.
I set to bold because, to my understanding, this is precisely what they did. Look at equations 2 & 3, and the associated text that follows it, through to equation 8. This part of their work is not that difficult to follow, so I don't see precisely where they make any error or assumptions that would cause it to be wrong. Their answer includes everything you just said, and the derivatives are Hankel functions of "fractional order". Where is the error?
Todd
Not only half interger order Todd, but a real order associated legendre and bessel functions.
I need go to a party now ;D , but latter I will try explain better, but basicaly, boundary conditions under a adapted coordinate system for the problem, are satisfied only with the use of the free parameters of the general solution, and must have no dependence with the independent variables of the differential problem, or will not sove bc conditions and the differential equation simultaneously.

Something has been bothering me since last night and I couldn't help but watching the modes change and flip in meep.
How can you calculate seriously any Q in a cavity that simply jumps around from one T mode decaying and building into another in such a short time? And they all do it, every simulation with varying speeds.
Just something to mull over on a day away from the shop.
Shell
Added: Back to lurk mode and I'll be quiet.
Excellent question. I hope that you don't shy away from asking such questions because it is only this way that one can understand what is being output.
My understanding (aero to confirm) is that the quality factor is calculated by aero using the routine Harminv.
Please notice that Meep has this disclaimer for using Hamrinv to calculate the quality factor Q:
http://abinitio.mit.edu/wiki/index.php/Meep_Reference#Harminv
Important: normally, you should only use harminv to analyze data after the sources are off. Wrapping it in (aftersources (harminv ...)) is sufficient.
Thus, the Quality factor and the frequency (also obtained by Harminv) should properly be obtained after the sources are OFF, not when they are on.
This takes us back to the whole discussion about Q quality factor in experiments. The problem is not only how to best experimentally measure and report Q, but it seems not ideal to me to discuss and report a Q (as first done by Shawyer and then imitated by all other EM Drive experimenters) with the source ON.
It seems to me that proper measurement of Q also in experiments should be done upon turning the source off and examining the decay (as posted by Frobnicat in a separate post).
With the sources OFF, the definition of Q (inverse to damping) is wellposed.
With the sources ON, the meaning of Q is tricky. It seems to me that when people are measuring Q with the sources on they are assuming a wellposed problem with "nice" properties (symmetry, etc.) that may not be fulfilled. This is particularly contradictory with TheTraveller: who rejects Finite Element solutions (using COMSOL or ANSYS) and exact solutions of the problem saying that only a solution that calculates a force can properly calculate the frequency and at the same time Shawyer "measures" Q with the RF feed ON which assumes a well posed nice solution amenable to presentation of Q as if it would be the same Q as the one calculated with the RF feed off.
The way that the Q is being measured experimentally by Shawyer and others using S11 and the 3db width is similar to a common method in structural vibration analysis. Of course, this presupposes a steadystate response. In reality with the RF feed ON, the measurement may be a transient instead.
_______________________________________________________
QUESTION TO aero: have you been calculating the quality factor Q with Harminv, and if so, have you been doing so with the sources ON or OFF. Have you been wrapping with (aftersources (harminv ...)) ?

I set to bold because, to my understanding, this is precisely what they did. Look at equations 2 & 3, and the associated text that follows it, through to equation 8. This part of their work is not that difficult to follow, so I don't see precisely where they make any error or assumptions that would cause it to be wrong. Their answer includes everything you just said, and the derivatives are Hankel functions of "fractional order". Where is the error?
Todd
Not only half interger order Todd, but a real order associated legendre and bessel functions.
I need go to a party now ;D , but latter I will try explain better, but basicaly, boundary conditions under a adapted coordinate system for the problem, are satisfied only with the use of the free parameters of the general solution, and must have no dependence with the independent variables of the differential problem, or will not sove bc conditions and the differential equation simultaneously.
Just tell me if equations 8 and 9 are correct or not please. It is a simple enough wave function and its first derivative. Is it representative of the electric field for TE and TM modes as they say, or isn't it? I don't need anything past equation 9 from Z&F to calculate the momentum and forces from the wave vector. @Rodal has an exact solution for the fields in his Mathematica program, and we have numbers from Meep. Therefore, regardless if Zeng and Fan derived those fields correctly, if equation 9 is correct, (which I think it is) then what's the problem? Just plug in the E vector from Mathematica or Meep, and its inverse, and take a couple of derivatives... and we have a force equation in both directions of propagation.
Todd

...
In a cylinder, the longitudinal component of momentum is the wave propagating down the waveguide. The momentum is in the z direction, not radial toward the walls. In Z&F, they are depicting a waveguide, not a cavity. The momentum is propagating down the waveguide. Changing the angle > 0, changes the momentum in the z direction for a tapered waveguide, relative to a cylindrical waveguide. In the case of the wave moving toward the apex, what Z&F show is that the waves are attenuated and all of the momentum in the z direction is phase shifted and absorbed.
Ui
Essentially, attenuation of the E field in the perpendicular directions, "IS" attenuation of momentum in the r direction, because S_{r} = E x H perpendicular to S. The wave traveling toward the apex is losing momentum to the waveguide, in the z direction. The wave traveling toward the big end is gaining momentum in the z direction. In a cylinder, neither is true because the wave does not change momentum in either direction. So the kvector reflecting off the wall is not (theta, phi) in Z&F, it is in the r direction. So it is r*Cos(theta) to get z direction thrust.
Todd
A cylinder is a geometrical concept. It is perfectly OK for me to speak of a cylinder as something that has open ends, it carries no implications of a being a cavity.
As to Zeng and Fan, as I said, I would have to rederive their equations and see whether they satisfy the boundary conditions (Ricvl said that they don't) or if there is something else amiss.
Yes Dr Rodal, to me Zeng and Fan don't write the correct expressions for the problem of propagation on a tapered conical waveguide.
One way is solve the helmoltz equations respecting directly the physical boundary conditions under the geometry of problem.
This will implies that standard solutions of wave equation in spherical coordinates ( in general, bessel and legendre functions of integer order), must be subtituted by specific solutions with fractionary order legendre/ bessel functions.
Other way, more complicated, is find solutions using the called "coupledmode theory in instantaneous eigenmode (quasimode) basis ", where one can use a superposition cilindrical modes, evolving a coupledmode equation along the longitudinal axis of propagation, where each cilindrical mode has a instantaneous dependence on the radii of tapered section of conical waveguide.
Of course, there are many others forms to solve this problem.
I set to bold because, to my understanding, this is precisely what they did. Look at equations 2 & 3, and the associated text that follows it, through to equation 8. This part of their work is not that difficult to follow, so I don't see precisely where they make any error or assumptions that would cause it to be wrong. Their answer includes everything you just said, and the derivatives are Hankel functions of "fractional order". Where is the error?
Todd
Not only half interger order Todd, but a real order associated legendre and bessel functions.
I need go to a party now ;D , but latter I will try explain better, but basicaly, boundary conditions under a adapted coordinate system for the problem, are satisfied only with the use of the free parameters of the general solution, and must have no dependence with the independent variables of the differential problem, or will not sove bc conditions and the differential equation simultaneously.
I opted out of a summer end party tonight mainly because Monday is a milestone birthday. Think I will celebrate with the sense that the next generation will question everything and challenge the status quo. Here's to nonconformity...

I love this thread and am totally addicted, can't put it down. Thanks for all the work and information! Discussions about Q, oxidation, broad / narrow spectrum and the shape of the ends have got me thinking about an alternate configuration. It has many of the same characteristics but might be slightly easier to build / find parts / work with. It is an ordinary cylinder with a cone inside. Maybe something to consider once folks are enjoying consistent thrust (lifting small objects and pets, etc... ;)
Keep up the great work!

(https://encryptedtbn0.gstatic.com/images?q=tbn:ANd9GcQ_05_4foqMCaIOwvjdhDM9TC1aHo21AriJlRVkkOXgzXbncvpCCw)
The Eggcelerator

I love this thread and am totally addicted, can't put it down. Thanks for all the work and information! Discussions about Q, oxidation, broad / narrow spectrum and the shape of the ends have got me thinking about an alternate configuration. It has many of the same characteristics but might be slightly easier to build / find parts / work with. It is an ordinary cylinder with a cone inside. Maybe something to consider once folks are enjoying consistent thrust (lifting small objects and pets, etc... ;)
Keep up the great work!
WELCOME to the thread. :)
That looks similar to an early patent by Shawyer, as I recall Shawyer had a cylinder with a dielectric insert inside it in the shape of a cone. Maybe somebody can find it.

Todd
I opted out of a summer end party tonight mainly because Monday is a milestone birthday. Think I will celebrate with the sense that the next generation will question everything and challenge the status quo. Here's to nonconformity...
Many years ago my first electronics teacher upon graduation from high school and before I set off to collage told me something I thought was kind of silly (you know 17 and so) HE said: "The is the golden age of mediocre conformity, never let yourself be trapped". As I got older I realized what a gift of wisdom he had said.
Happy Birthday to a very nonmediocre person. :)
Shell

Something has been bothering me since last night and I couldn't help but watching the modes change and flip in meep.
How can you calculate seriously any Q in a cavity that simply jumps around from one T mode decaying and building into another in such a short time? And they all do it, every simulation with varying speeds.
Just something to mull over on a day away from the shop.
Shell
Added: Back to lurk mode and I'll be quiet.
Excellent question. I hope that you don't shy away from asking such questions because it is only this way that one can understand what is being output.
My understanding (aero to confirm) is that the quality factor is calculated by aero using the routine Harminv.
Please notice that Meep has this disclaimer for using Hamrinv to calculate the quality factor Q:
http://abinitio.mit.edu/wiki/index.php/Meep_Reference#Harminv
Important: normally, you should only use harminv to analyze data after the sources are off. Wrapping it in (aftersources (harminv ...)) is sufficient.
Thus, the Quality factor and the frequency (also obtained by Harminv) should properly be obtained after the sources are OFF, not when they are on.
This takes us back to the whole discussion about Q quality factor in experiments. The problem is not only how to best experimentally measure and report Q, but it seems not ideal to me to discuss and report a Q (as first done by Shawyer and then imitated by all other EM Drive experimenters) with the source ON.
It seems to me that proper measurement of Q also in experiments should be done upon turning the source off and examining the decay (as posted by Frobnicat in a separate post).
With the sources OFF, the definition of Q (inverse to damping) is wellposed.
With the sources ON, the meaning of Q is tricky. It seems to me that when people are measuring Q with the sources on they are assuming a wellposed problem with "nice" properties (symmetry, etc.) that may not be fulfilled. This is particularly contradictory with TheTraveller: who rejects Finite Element solutions (using COMSOL or ANSYS) and exact solutions of the problem saying that only a solution that calculates a force can properly calculate the frequency and at the same time Shawyer "measures" Q with the RF feed ON which assumes a well posed nice solution amenable to presentation of Q as if it would be the same Q as the one calculated with the RF feed off.
The way that the Q is being measured experimentally by Shawyer and others using S11 and the 3db width is similar to a common method in structural vibration analysis. Of course, this presupposes a steadystate response. In reality with the RF feed ON, the measurement may be a transient instead.
??????????????????????????????????????????????????????????
QUESTION TO aero: have you been calculating the quality factor Q with Harminv, and if so, have you been doing so with the sources ON or OFF. Have you been wrapping with (aftersources (harminv ...)) ?
I've been researching this today and I've about reached one days brain drain.
Dr. Rodal, it's not only in meep that it's happening it's in the cavity as well, under power and I know It's driven by Maxwell's equations for a specific time set with in a finite computational defined area.
(http://abinitio.mit.edu/wiki/index.php/Meep)
Resonant modes and frequencies — by analyzing the response of the system to a short pulse, one can extract the frequencies, decay rates, and field patterns of the harmonic modes of a system (including waveguide and cavity modes, and including losses).

I feel there is much more going on that meep cannot show because of some of the inherent limitations. What I'd like to see is a round tube ends capped off as a resonate chamber with a RF input, measure the Q in meep. Would you look at the CSV files from aero and do a simple compare of the Q and stress values between the two?
Maybe it's nothing but this old gal has a bone and maybe you have another way of looking at it. I think simply the decaying and mode switching in the frustum are a great red flag.
Back to lurk
Shell

...I feel there is much more going on that meep cannot show because of some of the inherent limitations. What I'd like to see is a round tube ends capped off as a resonate chamber with a RF input, measure the Q in meep. Would you look at the CSV files from aero and do a simple compare of the Q and stress values between the two? ...
Shell
Two possible ways to calculate Q from Meep, and none are possible at the moment with the output available:
1) To calculate the Q one needs to have access to all the Meep output: all the fields at all the nodes. This is necessary to calculate the energy over the whole volume (which would be divided by the power loss on the copper surface). That output information is not available for any of the Meep runs.
2) Alternatively one could calculate the Q from the time decay with the RF feed off. This cannot be done at the present time either because there has not been any runs with the RF feed off. All the runs are with the RF feed ON, for a total of 0.013 microseconds (if my memory is correct). During this time period there is no decay, on the contrary there is exponential magnification, so the calculated Q would be an imaginary number.

Something has been bothering me since last night and I couldn't help but watching the modes change and flip in meep.
How can you calculate seriously any Q in a cavity that simply jumps around from one T mode decaying and building into another in such a short time? And they all do it, every simulation with varying speeds.
Just something to mull over on a day away from the shop.
Shell
Added: Back to lurk mode and I'll be quiet.
Excellent question. I hope that you don't shy away from asking such questions because it is only this way that one can understand what is being output.
My understanding (aero to confirm) is that the quality factor is calculated by aero using the routine Harminv.
Please notice that Meep has this disclaimer for using Hamrinv to calculate the quality factor Q:
http://abinitio.mit.edu/wiki/index.php/Meep_Reference#Harminv
Important: normally, you should only use harminv to analyze data after the sources are off. Wrapping it in (aftersources (harminv ...)) is sufficient.
Thus, the Quality factor and the frequency (also obtained by Harminv) should properly be obtained after the sources are OFF, not when they are on.
This takes us back to the whole discussion about Q quality factor in experiments. The problem is not only how to best experimentally measure and report Q, but it seems not ideal to me to discuss and report a Q (as first done by Shawyer and then imitated by all other EM Drive experimenters) with the source ON.
It seems to me that proper measurement of Q also in experiments should be done upon turning the source off and examining the decay (as posted by Frobnicat in a separate post).
With the sources OFF, the definition of Q (inverse to damping) is wellposed.
With the sources ON, the meaning of Q is tricky. It seems to me that when people are measuring Q with the sources on they are assuming a wellposed problem with "nice" properties (symmetry, etc.) that may not be fulfilled. This is particularly contradictory with TheTraveller: who rejects Finite Element solutions (using COMSOL or ANSYS) and exact solutions of the problem saying that only a solution that calculates a force can properly calculate the frequency and at the same time Shawyer "measures" Q with the RF feed ON which assumes a well posed nice solution amenable to presentation of Q as if it would be the same Q as the one calculated with the RF feed off.
The way that the Q is being measured experimentally by Shawyer and others using S11 and the 3db width is similar to a common method in structural vibration analysis. Of course, this presupposes a steadystate response. In reality with the RF feed ON, the measurement may be a transient instead.
_______________________________________________________
QUESTION TO aero: have you been calculating the quality factor Q with Harminv, and if so, have you been doing so with the sources ON or OFF. Have you been wrapping with (aftersources (harminv ...)) ?
(set! sources drivesrcGaus)
(runsources+ (* gc T_meep) ; This time, # peroids, is for nonresonant frequencies dissapation (startup).
; Lower Q, shorter time, higher Q, longer time before measurement made. Take your best guess.
(aftersources (harminv Ez (vector3 0.05 0.05 0.05) fmeep BW 5)) )
(exit)

A couple of key points I found about Harminv in this description of operational programing of Harminv in wiki.

(Quote)
Important: normally, you should only use harminv to analyze data after the sources are off. Wrapping it in (aftersources (harminv ...)) is sufficient. (end Quote)
Also.
Can we access this in meep to analyze?
(harminverr result)

(Quote)
http://abinitio.mit.edu/wiki/index.php/Meep_Reference#Harminv
Harminv
The following step function collects field data from a given point and runs Harminv on that data to extract the frequencies, decay rates, and other information.
(harminv c pt fcen df [maxbands])
Returns a step function that collects data from the field component c (e.g. Ex, etc.) at the given point pt (a vector3). Then, at the end of the run, it uses Harminv to look for modes in the given frequency range (center fcen and width df), printing the results to standard output (prefixed by harminv:) as commadelimited text, and also storing them to the variable harminvresults. The optional argument maxbands is the maximum number of modes to search for; defaults to 100.
Important: normally, you should only use harminv to analyze data after the sources are off. Wrapping it in (aftersources (harminv ...)) is sufficient.
In particular, Harminv takes the time series f(t) corresponding to the given field component as a function of time and decomposes it (within the specified bandwidth) as:
f(t) = \sum_n a_n e^{i\omega_n t}
The results are stored in the list harminvresults, which is a list of tuples holding the frequency, amplitude, and error of the modes. Given one of these tuples, you can extract its various components with one of the accessor functions:
(harminvfreq result)
Return the complex frequency ω (in the usual Meep 2πc units).
(harminvfreqre result)
Return the real part of the frequency ω.
(harminvfreqim result)
Return the imaginary part of the frequency ω.
(harminvQ result)
Return dimensionless lifetime, or "quality factor", Q, defined as \mathrm{Re}\,\omega / 2 \mathrm{Im}\,\omega.
(harminvamp result)
Return the complex amplitude a.
(harminverr result)
A crude measure of the error in the frequency (both real and imaginary)...if the error is much larger than the imaginary part, for example, then you can't trust the Q to be accurate. Note: this error is only the uncertainty in the signal processing, and tells you nothing about the errors from finite resolution, finite cell size, and so on!
For example, (map harminvfreqre harminvresults) gives you a list of the real parts of the frequencies, using the Scheme builtin map.

Yes, analyse away: Data table is to wide to format nicely here, so a spread sheet is attached.

My Frustum dimensions, resonant frequency and Df are now locked and loaded:
Frustum big diameter m 0.40000
Frustum small diameter m 0.15900
Frustum centre length m 0.24070
External Rf Hz 2,450,250,000
Calculated Df Df 0.857
The SPR and my resonance models agree to within 4.6MHz or 0.178% which is close enough for me.

I love this thread and am totally addicted, can't put it down. Thanks for all the work and information! Discussions about Q, oxidation, broad / narrow spectrum and the shape of the ends have got me thinking about an alternate configuration. It has many of the same characteristics but might be slightly easier to build / find parts / work with. It is an ordinary cylinder with a cone inside. Maybe something to consider once folks are enjoying consistent thrust (lifting small objects and pets, etc... ;)
Keep up the great work!
See Shawyer's patent as attached.

Yes, analyse away: Data table is to wide to format nicely here, so a spread sheet is attached.
So what are we seeing? Do you need for me to dig into it?

Yes, analyse away: Data table is to wide to format nicely here, so a spread sheet is attached.
So what are we seeing? Do you need for me to dig into it?
You are seeing several cases of exactly what was described in your post above. If you want to analyse it, it is available. It tells me that the software thinks it is operating successfully, maybe it will tell you something different.

I have a real concern with TheTraveller's Excel spreadsheet. The values I get from the first basic dimensions are inconsistent. I'm talking of the file EMDriveCalc20150617b.xls available from emdrive.wiki (http://emdrive.wiki/Useful_EMDrive_Design_and_Test_Tools) as well as TT's Gdrive (https://drive.google.com/folderview?id=0B7kgKijop0ifk9EakZfbW9aZGMwNWZMQ01xVnBON0tkM2w0Q1NLbmtjRFFwMXBuNVlVN0U&usp=sharing#list).
Let's take know values, for example Eagleworks' frustum:
D_{b} = 0.2794 m
D_{s} = 0.15875 m
Frustum length = 0.2286 m
cone halfangle = 14.78°
Input the first three values, and the spreadsheet returns a cone halfangle of 24.5° :(
Calculate the hypotenuse or draw the plan in a CAD software with the know values, you will easily get the frustum side length at 0.2364256 m. But the spreadsheet returns 0.2584848 m!
The formula for the cone halfangle (cell D8) in the spreadsheet is :
=DEGREES(ATAN((D3÷2)÷((D5×(D4÷2))+((D3÷2)−(D4÷2))+D5)))
Whereas it could use arccosine, frustum centre length (diameter center to diameter center) and frustum side length:
=DEGREES(ACOS(D5/D9)
Talking about the frustum side length (cell D9), its formula is wrong:
= SQRT(D5^2+(D3−D4)^2)
The correct formula should use end radii squared instead of end diameters squared:
= SQRT(D5^2+((D3−D4)÷2)^2)
How is the rest right or wrong? I can't even get D_{f} right with the available spreadsheet. When inputing the Baby EmDrive data for example, D_{f} becomes negative which is impossible (it should be comprised between 0 and 1) EDIT: my mistake, 24 GHz instead of 2.4 GHz resolved this issue.
Whatever, I don't get the same D_{f} as TheTraveller for the same untouched spreadsheet and same input values. See fourth attachement below. Those differences are quite small, but everything else following in the spreadsheet gets very different values from those discrepancies.
@TheTraveller: can you please doublecheck those basic values in the spreadsheet, and upload a corrected version to the emdrive.wiki? This would be much appreciated by the EmDrive community :)
Below, I show two hypothesis for TT's EmDrive Mark 2, according to how the "Frustum centre length" is defined in the spreadsheet.
 The first with Frustum centre length = 208.71 mm has a cone halfangle (corrected formula) of 30°
 The second with Frustum centre length = 240.7 mm has a cone halfangle (corrected formula) of 26.6° (instead of 27.7° with the wrong angle formula).
What is important to note is that "Frustum centre length" as defined in the spreadsheet is the length between the centers of the two end diameters, and not the length defined by TheTraveller in his drawing where it is the apex r_{2}r_{1} length. All the misunderstanding comes from the difference in that drawing (attached in third position below).
Thanks for finding that. Fixed. There may be other such errors as a lot of that work was done when I was taking strong pain killing tables. These formula are not involved in the resonance calc.
My resonant calc matches the SPR model by 0.178%, so I'm happy with that. They were 4.6MHz higher.
The frustum length is the distance in meters between the centre points of the end plates. If the end plates are spherical then the frustum side wall length is also the centre separation length.
Have modified the spreadsheet to show Vertex length and spherical end plate radius as attached.
Also modified the drawing to show the same data.

Yes, analyse away: Data table is to wide to format nicely here, so a spread sheet is attached.
No wonder it's too[sic] wide. You really don't want, or need, all those significant digits.

The Eggcelerator
Thanks for your eggcellent idea! Might want to run it through MEEP...JIK. It may crack interstellar flight. 8)
(Sorry couldn't resist, Good Morning!)
https://twitter.com/EggPuns/status/545618667481096193
Image: http://www.rt17.hr/teslaseggofcolumbus/

The Eggcelerator
Dimensions?
Frequency?
And where does the magnetron go?
Hey, sort of the right shape and everything. A run through with MEEP probably wouldn't hurt anything.

Stranger things have happened. I looked at that "inverted cone" drawing and it sort of instantly generalised itself to an ovoid :)

Stranger things have happened. I looked at that "inverted cone" drawing and it sort of instantly generalised itself to an ovoid :)
Think that would do a better job of confining the fields to 1d. As per this:
http://www.pnas.org/content/111/29/10485.full (paper)
http://www.sciencedaily.com/releases/2014/07/140722091425.htm (newsy)

Delta Mass...and others.
I keep coming back to David Bae's photon recycling laser two platform system.
To me, it looks like a weird photon rocket variant  yet one that produces thousands of times the amount of thrust a photon rocket should be able to produce. It also appears legit.
With Bae's device you get around over unity / conservation of energy via redshift and a statement that only a small fraction of each photonic bounce is used for propulsion. Yet, at the same time, another implication is missed:
For that to be true, the total energy potential of a photon would have to be many thousands of time greater than what the standard photon rocket calculations allow for. Anybody care to dispute or comment on this?
Therefor, while the calculations for maximum thrust for the classic photon rocket are correct, you HAVE to allow for the possibility of much higher thrust IF the photons greater energy can be tapped. Bae's device shows one way of doing this.
Something else I have been wondering ever since Doctor Rodal first posted it. Specifically, from MEEP based calculations and a program of his own, he stated that if the cavity had the right angle, the forces within it did three things:
1  they went exponential, at least for the duration of the MEEP run (roughly 1/1000th of a second?)
2  did not sum to zero, at least within that time period. (But sooner or later, to satisfy the laws of thermodynamics, they would have to sum to zero).
3  and these forces were nowhere near the levels reported in the EM Drive experiments.
So I have been wondering. The relevant law of thermodynamics is Time Averaged. Suppose this device breaks or twists the average, enough to where the 'step down cycle' doesn't kick in for say....several seconds, or even a minute. That the forces within the EM Drive continued to build exponentially in mostly one direction not for just a few thousandths of a second, but several actual seconds. Would the exponential force by that point be on a par with the typically reported results?
A larger wave or cycle of some sort.
Two other relevant tidbits here:
Best I can recollect, no EM Drive test has lasted more than a couple minutes.
Something that has been pointed out by Rodal, Paul March, and others: maintaining the relevant frequency to produce thrust is a severe pain. Suppose, due to something we cannot see at the moment, the frequency is impossible to maintain for whatever reason for more than a minute or two? And must be reset afterwards.

If you really want to dive deep, look at Orbital Angular Momentum of circular radiation:
http://arxiv.org/ftp/arxiv/papers/0905/0905.0190.pdf
You think it is converting OAM to LM in there?
Didn't someone detect rotation in MEEP a few pages back?

.. maintaining the relevant frequency to produce thrust is a severe pain. Suppose, due to something we cannot see at the moment, the frequency is impossible to maintain for whatever reason for more than a minute or two? And must be reset afterwards.
I believe the reason to be purely thermal, and so it can be adjusted to remain on tune until the cows come home.

Something that has been pointed out by Rodal, Paul March, and others: maintaining the relevant frequency to produce thrust is a severe pain. Suppose, due to something we cannot see at the moment, the frequency is impossible to maintain for whatever reason for more than a minute or two? And must be reset afterwards.
By monitoring the VSWR of the driven frustum and automatically adjusting the freq every 50ms to find the lowest VSWR, it is possible to track any frustum resonant change and keep the freq in centre of the bandwidth, so to produce max Force.
Attached is my rough schematic of the Raspberry 2B based Control and Monitoring system I'm developing to do just that.
Should add that to get a low VSWR you need to 1st have a way to adjust the frustum's impedance to match that of the Rf generator, which in my case is a solid state 100W Rf amp. I will be using an inline coax 3 stub tuner as used by Paul at Eagleworks.

.. maintaining the relevant frequency to produce thrust is a severe pain. Suppose, due to something we cannot see at the moment, the frequency is impossible to maintain for whatever reason for more than a minute or two? And must be reset afterwards.
I believe the reason to be purely thermal, and so it can be adjusted to remain on tune until the cows come home.
720mNs of Force being generated by thermal radiation differential toward the small end?
Care to do the math as to what the surface temp differential of the big end to small end would need to be for that to happen? Lets assume Prof Yang's frustum had flat end plates but otherwise was similar to the attached.

believe the reason to be purely thermal, and so it can be adjusted to remain on tune until the cows come home.
thermal is the usual reason cited. (should have included that). But should still be confirmed.
I take it, then, apart from that, you agree with or at least do not have any major issues with the rest of my reasoning?

believe the reason to be purely thermal, and so it can be adjusted to remain on tune until the cows come home.
thermal is the usual reason cited. (should have included that). But should still be confirmed.
I take it, then, apart from that, you agree with or at least do not have any major issues with the rest of my reasoning?
Well, I don't subscribe to the "borrowing energy for a long time" theory. Who would?
As for Bae, I'm still on the fence with that. I'll be staying there until I think I really understand it. Right now, I'm pretty sure I don't!
p.s. Watch your quotes. The admin police will be after you :P

By the way those of you supporting the EM drive want an example of a theory that started out on the fringes but has gradually moved more centre wise then they only have to look at holographic theory for the universe.
http://www.sciencedaily.com/releases/2015/04/150427101633.htm
I honestly love this theory, simply it fits so much (but what do I know?). I've been following it for the last few months. Good post Star One!
I've been kicked out of the shop while other work goes on so I've been reading way too much tech.
Shell
It's the fact that the maths fits so well to reality as we understand it. Also that they've now built an experiment to help prove the theory to detect an effect people might have never imagined before this could have existed. Rather like the EM drive.:)

Well, I don't subscribe to the "borrowing energy for a long time" theory. Who would?
'borrowing energy?' Where do you come up with that?
The closest I came was in my commentary on Rodal's analysis of the MEEP results and his own independent program. The claims there were the forces had a nonnetzero average, and were starting to go exponential. That was Rodal, not me.
I am merely wondering out loud if these forces continued on an exponential track for a few seconds they might not result in thrusts comparable to that reported by the experimenters. Are you taking issue with a simple extrapolation?
And yes, I suspect that something causes the exponentially increasing cycle to collapse or reverse itself after a while. (a few seconds? a minute? two?)
As for Bae, I'm still on the fence with that. I'll be staying there until I think I really understand it. Right now, I'm pretty sure I don't!
Yet Bae's device has more experimental evidence going for it than the EM Drive.

@TheTraveller: thanks, your Mark 2 drawing is consistent now. May you share the new spreadsheet on your Google Drive? Still the wrong one there.
But your cone halfangle is still wrong. Your frustum has a halfcone angle of 30.04°, not 27.7°. This is because the formula for the angle assumes the old version of Frustum centre length (D_{b} to D_{s}) and not the new one (r_{2}r_{1}).
Could you please share the new spreadsheet after this last correction?
Below, the confirmed version. We're finally in agreement…

With Bae's device you get around over unity / conservation of energy via redshift and a statement that only a small fraction of each photonic bounce is used for propulsion. Yet, at the same time, another implication is missed:
For that to be true, the total energy potential of a photon would have to be many thousands of time greater than what the standard photon rocket calculations allow for. Anybody care to dispute or comment on this?
This is correct and the mechanics behind it are well understood. A photon's energymomentum relationship is given by: E = p*c, where E = the photon's energy, p = the photon's momentum and c = speed of light (in vacuum). So, what happens when you shine a laser out the back of the photon rocket? Each photon has momentum p and by conservation of momentum, your ship's momentum increases by p (i.e. the momentum you add is the opposite of the photon's momentum) and the kinetic energy increases accordingly, only by a small fraction of the energy you spent on creating the photon. The energy of the departed photon is "wasted" in this case, as it should be for energy to be conserved.
Therefor, while the calculations for maximum thrust for the classic photon rocket are correct, you HAVE to allow for the possibility of much higher thrust IF the photons greater energy can be tapped. Bae's device shows one way of doing this.
Right, in order to get more energy out of that same photon, it first has to come back to you after being reflected off of something. Then it can be reflected off of your ship giving you more momentum and so on. But the critical part here is that every time the photon gets reflected, its direction reverses and so it imparts momentum to the reflector in the direction the photon was moving and the opposite of the direction into which it is reflected.
So, each time, you will get more momentum in your desired direction and the reflector on the other side will get momentum in the opposite direction. Another such idea is to have the other reflector on the Earth as described by Meyer et al in "Laser Elevator: Momentum Transfer Using an Optical Resonator" and also explained by XKCD here: https://blog.xkcd.com/2008/02/15/thelaserelevator/.

@TheTraveller: thanks, your Mark 2 drawing is consistent now. May you share the new spreadsheet on your Google Drive? Still the wrong one there.
But your cone halfangle is still wrong. Your frustum has a halfcone angle of 30.04°, not 27.7°. This is because the formula for the angle assumes the old version of Frustum centre length (D_{b} to D_{s}) and not the new one (r_{2}r_{1}).
Could you please share the new spreadsheet after this last correction?
Below, the confirmed version. We're finally in agreement…
Shared: https://drive.google.com/file/d/0B7kgKijop0iNjlZSmtuMHBzY28/view?usp=sharing
Has a better explanation on how to use it and how to use Goal Seek to find the resonant frequency.
Calcs Frustum slant angle correctly. This calc is not used in the spreadsheet.

...If you follow from equation 8 to 9, the expression j*k_{r}=(1/E)*dE/dr, is an expression for momentum in the r direction. ...
Comments?
Todd
I went over this reference again:
Electromagnetic fields and transmission properties in tapered hollow metallic waveguides
Xiahui Zeng and Dianyuan Fan
https://www.osapublishing.org/oe/fulltext.cfm?uri=oe17134&id=175583
and I cannot agree that <<the expression j*k_{r}=(1/E)*dE/dr, is an expression for momentum in the r direction>>
The subscript "r" in k_{r} does NOT indicate vector direction, instead it indicates that the scalar k_{r} only depends on "r".
Looking at equation (8) in page 38 of their article, you will notice that what they do is a separation of variables where they separate the dependence on "r" multiplicatively as an exponential that depends on r:
E(r,θ,φ) = A (θ,φ) e ^ [  γ * r ] (Notice that here the vector E is replaced by a scalar function E(r,θ,φ), as is usually done when solving the scalar Helmholtz equation)
where e ^ [  γ * r ] shows:
* explicit dependence on r
* implicit dependence on r, since γ depends on r: γ = γ (r)
Equations 8 and 9 are scalar equations. Neither equations 8 or 9 are vector equations and a vector basis is not given, thus there is no vector dependence provided. All that is being done here is a separation of variables of a scalar: the scalar E(r,θ,φ) is separated into two scalar variables: A and e ^ [  γ * r ], multiplying each other, where A does not depend on r, and e ^ [  γ * r ] only depends on r.
Zeng and Fan use the subscript "r' for k (and then they soon stop using it) just to indicate that k only depends on r, NOT that k is the vector component of a k vector.
Please notice that the solution of the problem comprises electromagnetic field vectors, where each electromagnetic component may have a dependence on any of the spherical components: r, θ, φ
Having a dependence on r, does NOT mean that the field is directed along "r"
For example, the vector component of the electric field in the φ direction, E_{φ} for TEmnp has a dependence on r, such that for p=1 it varies like half a wave pattern in the r direction, while for p=2 it varies with r as a fullwave pattern for example. That does NOT mean that E_{φ} is directed along the r direction, it just indicates the r variation of the component Eφ that is directed along the φ direction (which is perpendicular to r).
To see the direction you have to express the electromagnetic fields as vectors using unit vectors (which Zeng and Fan don't show explicitly):
E = E_{r} e_{r} + E_{θ} e_{θ} + E_{φ} e_{φ}
where in general, all three components depend on each three directions:
E_{r} = E_{r} (r,θ,φ)
E_{θ} = E_{θ} (r,θ,φ)
E_{φ} = E_{φ} (r,θ,φ)
here, dependence on r does not mean r direction of the vector: E_{θ} (r,θ,φ) depends on r but it is not directed along r, E_{φ} (r,θ,φ) depends on r but it is not directed along r.
The momentum of E_{θ} is directed along θ. In general dE_{θ}/dr depends on r,θ and φ , but its momentum is directed along θ.
The momentum of E_{φ} is directed along φ. In general dE_{φ}/dr depends on r,θ and φ , but its momentum is directed along φ.
Only the momentum of E_{r} is directed along r, but there is no E_{r} component in a TE mode. Hence in a TE mode there is no E component with electric momentum directed along r.

from thread 3 page 329
http://forum.nasaspaceflight.com/index.php?topic=37642.6560
quote rodal
"Here I present the Poynting vector field for the final 14 time slices. It would be fun if somebody makes this into a movie"
So in movie form

Also that they've now built an experiment to help prove the theory to detect an effect people might have never imagined before this could have existed.
I can't find any details on such an experiment. Link, please?

Yes, analyse away: Data table is to wide to format nicely here, so a spread sheet is attached.
No wonder it's too[sic] wide. You really don't want, or need, all those significant digits.
Another drive by Pasting.
I'm wondering if we could limit some of the overhead in meep right here... need to dig.
Shell

Also that they've now built an experiment to help prove the theory to detect an effect people might have never imagined before this could have existed.
I can't find any details on such an experiment. Link, please?
http://holometer.fnal.gov/index.html
Don't see a connection to Emdrive unless their results somehow change our conservation laws.

Yes, analyse away: Data table is to wide to format nicely here, so a spread sheet is attached.
So what are we seeing? Do you need for me to dig into it?
You are seeing several cases of exactly what was described in your post above. If you want to analyse it, it is available. It tells me that the software thinks it is operating successfully, maybe it will tell you something different.
First look, I see a column with error on it and numbers beneath it. Why do you see it operating correctly aero? Is it because it gave Q's for those associated frequencies on the rows? What does that number in the error column mean?

The Eggcelerator
Thanks for your eggcellent idea! Might want to run it through MEEP...JIK. It may crack interstellar flight. 8)
(Sorry couldn't resist, Good Morning!)
https://twitter.com/EggPuns/status/545618667481096193
Image: http://www.rt17.hr/teslaseggofcolumbus/
We all just See Shell. ;)

Think I got this correct.
Rotary table time to target RPM calculator screen shot as attached.
Looks like 4 minutes per 30 rpm, assuming very little air resistance due to a circular plastic air resistance shield that fits on the outer radius of the table base.

http://arxiv.org/abs/1508.00626
The Reality of Casimir Friction
K. A. Milton, J. S. Høye, I. Brevik
Theoretical consensus is emerging.

http://arxiv.org/abs/1508.00626
The Reality of Casimir Friction
K. A. Milton, J. S. Høye, I. Brevik
Theoretical consensus is emerging.
Thank you for posting this reference. It would be very much appreciated any other references you may find on this subject (Casimir friction)

.. maintaining the relevant frequency to produce thrust is a severe pain. Suppose, due to something we cannot see at the moment, the frequency is impossible to maintain for whatever reason for more than a minute or two? And must be reset afterwards.
I believe the reason to be purely thermal, and so it can be adjusted to remain on tune until the cows come home.
It may be an analog of an "Electromagnetic Dean Drive" where the phenomenon may be due to the boundary conditions between the electromagnetic fields and the copper cavity instead of mechanical friction as a boundary condition between two solid surfaces. Many things point towards this:
1) Shawyer acknowledging that nothing much can be measured unless there are background dynamic forces
2) Effect is much larger (orders of magnitude) with air than in a partial vacuum
3) Postprocessing stress tensor analysis of Meep with Wolfram Mathematica visavis exact solution analysis of stress tensor.
Don't know yet whether it may have any practical use in deep space (wouldn't it require a framedependent medium ? ). Not ready to present the mathematics behind this. Intuitively, I think it may be best understood by those working with elastic fluid flow (and the breaking of the noslip boundary condition for fluids) than those working with electromagnetics. The problem is that most work in electromagnetics does not analyze the stress tensor and the proper boundary conditions because electromagnetic stresses are so small (a very different situation from fluid flow, where the flow boundary conditions have been well studied for over a century). The paper presented by Mulletron on Casimir friction is a big exception to this lack of discussion. Encouraging to see Mulletron also looking at Casimir friction.

.. maintaining the relevant frequency to produce thrust is a severe pain. Suppose, due to something we cannot see at the moment, the frequency is impossible to maintain for whatever reason for more than a minute or two? And must be reset afterwards.
I believe the reason to be purely thermal, and so it can be adjusted to remain on tune until the cows come home.
I would expect thermal as well to be causing the drift, mode changes into ranges that cannot be recovered from. And you can't change the input frequency when the cavity has deformed in a nonuniform way. It can be defined further to localized hot spots on the end plates, those need to be addressed.
So I'm going to disclose just part of my next build.
Two step process. First a ceramic plate, nice stuff. Since they are down the road from me I've planned a visit. Did some work with them on their saws to cut those ceramics and I think I still have some good contacts there.
http://www.coorstek.com/markets/aerospace_defense/armor_protection.php
Then have it gold plated.
Do the same for the small end plate.
This simple solution coupled with an active transducer feedback system in the small plate will keep the hot spots from warping the modes and changing the cavity resonance. The sidewall thermal expansion, which is a lateral down the length can be corrected by the small end transducer compensator.
I'm still using a heavier perforated copper on the sides (I'm going to be drilling the holes ... sigh for the sides to allow for greater cooling.
So what I hope to have is a nonsuper conducting very high Q cavity that doesn't shift modes and frequency demands, with a long run time.
On the methods used to hold resonance now. Even if I shift input frequencies the hot spots will have already caused an issue in mode deformation and a input frequency change will not address those. The only way is to maintain the endplates integrity is with this configuration and simply adjust the length of the cavity with the small end.
I've been thinking about this ever since Dr. Rodal sent me those images a couple months ago of the DUT by EagleWorks that showed the hotspots in simulation and the real world DUT. I was hoping to have a little more gofundme to start the build of this but it's not quite there yet.
This is the first time I have disclosed this idea of the second generation ERD ... Electromagnetic Reaction Drive except to mail it to someone else a bit ago. I would love to have inputs on what everyone thinks about it.
Shell
edit readibility

@TheTraveller:
About that triple tuning stub  am I correct in assuming that this must be operated manually, or have you come up with a motorised solution?
As a general comment  when thermal effects drive the system off tune, there are in fact two independent adjustments to be made  a frequency adjustment to find the new resonance, and an impedance adjustment to minimise VSWR.

@TheTraveller:
About that triple tuning stub  am I correct in assuming that this must be operated manually, or have you come up with a motorised solution?
As a general comment  when thermal effects drive the system off tune, there are in fact two independent adjustments to be made  a frequency adjustment to find the new resonance, and an impedance adjustment to minimise VSWR.
In my second generation of the Electromagnetic Reaction Drive EMD, the first adjustment is the cavity length to the input frequency (a manual lead screw) then fine tune through the transducer compensator. Very simple. Once the VSWR is set in the very first run it should remain set in this configuration.
The whole key i this is the Magnetron and also why I was jazzed to find that simple way to stabilize it's output and also mod it to be a 100% duty cycle,
I'm keeping the hexagonal side walls simply because it leads to a very nice way to physically mount waveguides on the 180 degree sidewalls. Should give me a solid TE012.
Frequency and power stabilized magnetron 100% duty cycle
Symmetrical waveguide inputs (I hated seeing the microwaves being pushed around by the single input deforming the modes). It's as simple as the incoming wave hitting a opposing wall of the cavity and bouncing at an obscure angle or the mode being pushed by the incoming wave pressures to switch physical positions. Seen this every since our first sim with meep. The only time is when we inserted the antenna into the endplates, that was very nice.
I figure I can at least double or more the force from a cavity by stabilizing these two variables.
Shell
boobboos

...
I'm keeping the hexagonal side walls simply because it leads to a very nice way to physically mount waveguides on the 180 degree sidewalls. Should give me a solid TE012. ...
Is your first test EM Drive test going to have two symmetrically placed waveguides exciting the cavity or are you planing to use waveguides only in later tests? (If so, how are you going to feed the RF on your first test?)

Then have it gold plated.
Do the same for the small end plate.
Do you know the needed gold thickness for good resonance and high Qfactor, and if that firm can reach that requirement?
This simple solution coupled with an active transducer feedback system in the small plate will keep the hot spots from warping the modes and changing the cavity resonance. The sidewall thermal expansion, which is a lateral down the length can be corrected by the small end transducer compensator.
Is this "transducer" similar to Shawyer's piezoelectric actuator (moving within a fraction of a millimeter) or is it a simpler and cheaper but slower system, like a stepper motor or a more expensive but more precise servomotor?
So what I hope to have is a nonsuper conducting very high Q cavity that doesn't shift modes and frequency demands, with a long run time.
Does "a long run time" mean you want to make a rotary test like TheTraveller, to let the frustum accelerate?
This is the first time I have disclosed this idea of the second generation ERD ... Electromagnetic Reaction Drive except to mail it to someone else a bit ago. I would love to have inputs on what everyone thinks about it.
Shell
This is exciting! :)
Frequency and power stabilized magnetron 100% duty cycle
Symmetrical waveguide inputs (I hated seeing the microwaves being pushed around by the single input deforming the modes). It's as simple as the incoming wave hitting a opposing wall of the cavity and bouncing at an obscure angle or the mode being pushed by the incoming wave pressures to switch physical positions. Seen this every since our first sim with meep. The only time is when we inserted the antenna into the endplates, that was very nice.
I figure I can at least double or more the force from a cavity by stabilizing these two variables.
Shell
You could increase the force even further, as your symmetrical doubleinput waveguide could allow two magnetrons operating at the same time, autotuning each other through a slaving process known as injection locking (https://en.wikipedia.org/wiki/Injection_locking).
See this prior post by ElizabethGreene (http://forum.nasaspaceflight.com/index.php?topic=37642.msg1401433#msg1401433) in thread 3 for that matter, as well as this post by AnalogMan (http://forum.nasaspaceflight.com/index.php?topic=37642.msg1397636#msg1397636) that has a reference paper attached. As it went almost unnoticed the first time, I attach again this document: "Noise Performance of Frequency and PhaseLocked CW Magnetrons Operated as CurrentControlled Oscillators".

@TheTraveller:
About that triple tuning stub  am I correct in assuming that this must be operated manually, or have you come up with a motorised solution?
As a general comment  when thermal effects drive the system off tune, there are in fact two independent adjustments to be made  a frequency adjustment to find the new resonance, and an impedance adjustment to minimise VSWR.
It is manually tuned.
Expected thermal frustum resonant freq changes should not cause much if any VSWR change but for sure it is an unknown. The data collection and logging system should show if there is any forward power to frustum thermal heating to resonant freq to VSWR change and to what extent, if any, it changes.
Power is only max 100W and the wall and end plate thickness are 2mm oxygen free copper so the frustum should be fairly dimensionally stable at this power level. BTW the outside of the frustum will be painted with a pot belly wood stove high carbon black paint to aid heat radiation and reduce thermal movement.
Copper expands approx 0.0167mm/m/degC. For a 20 deg C temp increase (25C to 45C which will never happen), averaged over the entire frustum side wall area, with a starting length of 0.2407m, would result in a 0.08mm increase in length. Would have very little measurable effect on frustum resonance nor on impedance tuning.

...
I'm keeping the hexagonal side walls simply because it leads to a very nice way to physically mount waveguides on the 180 degree sidewalls. Should give me a solid TE012. ...
Is your first test EM Drive test going to have two symmetrically placed waveguides exciting the cavity or are you planing to use waveguides only in later tests? (If so, how are you going to feed the RF on your first test?)
The opposed waveguides are on the second revised frustum. Have the copper for it. Still working on the waveguides and ceramics and another magnetron and power supply.
Somewhat simple process to couple into a coaxial cable which is then going to be run into the frustum to dual dipole antennas in the frustum supported by a ceramic rod through the sidewalls. The nice thing about a cavity with holes in it I can pop the antenna(s) anywhere I want quite easily.
I was thinking about this dual configuration. see pic. I'm still working on the actual placement but I'm using a 1/16" ceramic rod that fits very tightly onto the holes on the side walls to support the antenna. By the time the Rf gets to the antennas I'll be dealing with maybe 30 watts of RF. Not like the magnetron waveguide into the sidewalls.

So for say TE01X modes, what kind of beam is that? Is it a Gaussian beam? Or a LaguerreGaussian beam? Jim Beam?
In return, here's some info on resonant cavity accelerators:
http://uspas.fnal.gov/materials/09UNM/ResonantCavities.pdf (big file be patient)
Also in there is info to end the Sparameter fight from page 1.
S11 VSWR (Translated to English means measuring at input port only.) (This test should reflect conditions one would expect when the frustum is in operation so keep sample port high Z. In my test, since the sample port was "hobbled" aka just solder cup, it didn't make a difference if it was terminated, shorted, or even left open.)
S21 Measure Q via transmission method. (Input to output) (You gotta have a well matched sample port for the test. What I did after the test was "hobble" the sample port by just leaving a stubby solder cup. This was also recommended by StarDrive. I quickly realized that since I'm interested in NOT coupling energy back out of the cavity, I had to hobble the sample port.)

Then have it gold plated.
Do the same for the small end plate.
Do you know the needed gold thickness for good resonance and high Qfactor, and if that firm can reach that requirement?
This simple solution coupled with an active transducer feedback system in the small plate will keep the hot spots from warping the modes and changing the cavity resonance. The sidewall thermal expansion, which is a lateral down the length can be corrected by the small end transducer compensator.
Is this "transducer" similar to Shawyer's piezoelectric actuator (moving within a fraction of a millimeter) or is it a simpler and cheaper but slower system, like a stepper motor or a more expensive but more precise servomotor?
So what I hope to have is a nonsuper conducting very high Q cavity that doesn't shift modes and frequency demands, with a long run time.
Does "a long run time" mean you want to make a rotary test like TheTraveller, to let the frustum accelerate?
This is the first time I have disclosed this idea of the second generation ERD ... Electromagnetic Reaction Drive except to mail it to someone else a bit ago. I would love to have inputs on what everyone thinks about it.
Shell
This is exciting! :)
Frequency and power stabilized magnetron 100% duty cycle
Symmetrical waveguide inputs (I hated seeing the microwaves being pushed around by the single input deforming the modes). It's as simple as the incoming wave hitting a opposing wall of the cavity and bouncing at an obscure angle or the mode being pushed by the incoming wave pressures to switch physical positions. Seen this every since our first sim with meep. The only time is when we inserted the antenna into the endplates, that was very nice.
I figure I can at least double or more the force from a cavity by stabilizing these two variables.
Shell
You could increase the force even further, as your symmetrical doubleinput waveguide could allow two magnetrons operating at the same time, autotuning each other through a slaving process known as injection locking (https://en.wikipedia.org/wiki/Injection_locking).
See this prior post by ElizabethGreene (http://forum.nasaspaceflight.com/index.php?topic=37642.msg1401433#msg1401433) in thread 3 for that matter, as well as this post by AnalogMan (http://forum.nasaspaceflight.com/index.php?topic=37642.msg1397636#msg1397636) that has a reference paper attached. As it went almost unnoticed the first time, I attach again this document: "Noise Performance of Frequency and PhaseLocked CW Magnetrons Operated as CurrentControlled Oscillators".
I know about the dual phase locked magnetrons and that will be in the third series tests. first is to see if I can truly be stable and control the environment in this second series.
No. not like TT's Simply if I ramp up the thrusts like the designs in the third level with dual magnetrons I should be hitting a high acceleration and rotational rate in a almost frictionless air bearing (my design) rotary table and that is another issue, plus a lot more money. No, it as simple for me to monitor thrust pressures on my test platform and then remove the scales and time the acceleration for a given distance with the same test and test platform. No I'm after thrust measurements from a long burn. ;)
BTW: the magnetron is just popped into the frustum for looks.
The pizo is OTS and after I posted a PM to someone here I read that RS's next was going to be using the same idea. interesting hum?
Added: The pizoelectric is an OTS and I will drive it with a simple Pi, very cool little board. http://www.amazon.com/gp/product/B00PWYK2V6?psc=1&redirect=true&ref_=oh_aui_detailpage_o04_s00
Added after shower.. lol
Ys I'm very aware of the thickness of gold and who can do it and I'm going to hold that one close for now and the actual ceramic I'll be using. Sorry
shell

Interesting Russian EMDrive like patent:
http://bankpatentov.ru/node/123593
and comment received on Reddit EMDrive forum:
https://www.reddit.com/r/EmDrive/comments/3ceyjv/email_from_roger_shawyer/ctww6rd
As Dr. Vladimir Leonov claims the "Shawyer Effect" works via the QV, Dr. White might be interested.

So for say TE01X modes, what kind of beam is that? Is it a Gaussian beam? Or a LaguerreGaussian beam? Jim Beam?
In return, here's some info on resonant cavity accelerators:
http://uspas.fnal.gov/materials/09UNM/ResonantCavities.pdf (big file be patient)
Also in there is info to end the Sparameter fight from page 1.
S11 VSWR (Translated to English means measuring at input port only.) (This test should reflect conditions one would expect when the frustum is in operation so keep sample port high Z. In my test, since the sample port was "hobbled" aka just solder cup, it didn't make a difference if it was terminated, shorted, or even left open.)
S21 Measure Q via transmission method. (Input to output) (You gotta have a well matched sample port for the test. What I did after the test was "hobble" the sample port by just leaving a stubby solder cup. This was also recommended by StarDrive. I quickly realized that since I'm interested in NOT coupling energy back out of the cavity, I had to hobble the sample port.)
Right now it's a Jim Bean... I'm having a birthday party today and do have to get going to set up. I'll be back a little later to detail out more. Thanks for the link, I think I know these guys. ;)
Shell

It just occurred to me while I was typing all that out. I bet I could use that sample port as a way to tune the cavity somehow. Not sure how. Any ideas? Is there something I could screw onto the NF connector which would allow me to use it as a tuner?

It just occurred to me while I was typing all that out. I bet I could use that sample port as a way to tune the cavity somehow. Not sure how. Any ideas? Is there something I could screw onto the NF connector which would allow me to use it as a tuner?
Yes, just use an amplifier and the sample port as the input signal. Start with a pulse that "rings" inside the frustum at resonance. Take the output from the sample port and feed it into the input of the amplifier. Then feed the output of the amplifier back into the frustum. The output of the amplifier will "track" the resonance of the chamber automatically, due to the feedback loop. No mechanical adjustments required.
Todd

If you really want to dive deep, look at Orbital Angular Momentum of circular radiation:
http://arxiv.org/ftp/arxiv/papers/0905/0905.0190.pdf
The reason I'm asking about beams is because I'm following up on @rfmwguy's reference above, specifically this quote from it:
3.3 LaguerreGaussian Beams
In order to endow our EM beam with orbital angular momentum, let us search for
a solution of the Helmholtz equation with an azimuthal e−il' dependence because,
according to Simpson et al. [46], such a beam will carry OAM. Let us use our uG
25
https://en.wikipedia.org/wiki/Orbital_angular_momentum_of_light#cite_ref1
edit:
I'm somewhat confused by this whole beam situation. Maybe it is Bessel beams.

So for say TE01X modes, what kind of beam is that? Is it a Gaussian beam? Or a LaguerreGaussian beam? Jim Beam?
In return, here's some info on resonant cavity accelerators:
http://uspas.fnal.gov/materials/09UNM/ResonantCavities.pdf (big file be patient)
Also in there is info to end the Sparameter fight from page 1.
S11 VSWR (Translated to English means measuring at input port only.) (This test should reflect conditions one would expect when the frustum is in operation so keep sample port high Z. In my test, since the sample port was "hobbled" aka just solder cup, it didn't make a difference if it was terminated, shorted, or even left open.)
S21 Measure Q via transmission method. (Input to output) (You gotta have a well matched sample port for the test. What I did after the test was "hobble" the sample port by just leaving a stubby solder cup. This was also recommended by StarDrive. I quickly realized that since I'm interested in NOT coupling energy back out of the cavity, I had to hobble the sample port.)
In and out for some supplies.
Look at the piece of RF equipment behind me in the picture... :). It was the start of it all for the SSC.
http://www.gofundme.com/yy7yz3k
Back to the party. Ya'll have a great Sunday (if in your time zone).
Shell

TheTraveller provided this link re some Russian work on microwave thrusters:
Interesting Russian EMDrive like patent:
http://bankpatentov.ru/node/123593 
Wonder if that is related to this little (~0.3 m) Russian spacecraft, with no announced purpose, that was launched in May of 2014 with three other spacecraft and has apparently been scurrying around in orbit visiting some of the other payloads/booster.
http://conspiracycafe.blogspot.com/2015/03/kosmos2499isitspyorassassinor.html
Lots of speculation as to its purpose, but, given its small size, not much speculation about how it was doing its ‘scurrying’.

Just to bring it back to the surface : is any one going to try with Matglas 2714A at the big end?
To see if extreme magnetic permeability has any impact on EMdrive performances?
If too expensive, a second option would be an iron plate ( as noted on the wiki list : (99.95% pure Fe annealed in H) )

TheTraveller provided this link re some Russian work on microwave thrusters:
Interesting Russian EMDrive like patent:
http://bankpatentov.ru/node/123593 
Wonder if that is related to this little (~0.3 m) Russian spacecraft, with no announced purpose, that was launched in May of 2014 with three other spacecraft and has apparently been scurrying around in orbit visiting some of the other payloads/booster.
http://conspiracycafe.blogspot.com/2015/03/kosmos2499isitspyorassassinor.html
Lots of speculation as to its purpose, but, given its small size, not much speculation about how it was doing its ‘scurrying’.
Great link about the little Russian spacecraft (Kosmos2499), thanks.
May not be related, because TheTraveller also gave this link to a comment received on Reddit EMDrive forum from somebody claiming to be the author of the Russian EMDrivelike invention:
https://www.reddit.com/r/EmDrive/comments/3ceyjv/email_from_roger_shawyer/ctww6rd
where somebody claiming to be the patent's author (http://bankpatentov.ru/node/123593)  writes:
I suggest along with Shawyer establish an independent international company in Cyprus with the participation of enthusiasts of new space technologies. Funding for this project can be ensured. I am ready to participate in the project.
Dr. Vladimir Leonov
...
I doubt that somebody involved in a Russian Defense Department project (Kosmos2499) would be posting in Reddit (given his name, email address and phone number) suggesting to << along with Shawyer establish an independent international company >> in a foreign country (Cyprus) known as a haven to escape Russian taxes (http://www.nytimes.com/2014/02/18/business/international/russianbusinesstargetofcypriotbailoutstilllovestheisland.html?_r=0).

Just to bring it back to the surface : is any one going to try with Matglas 2714A at the big end?
To see if extreme magnetic permeability has any impact on EMdrive performances?
If too expensive, a second option would be an iron plate ( as noted on the wiki list : (99.95% pure Fe annealed in H) )
This is particularly suitable for TE (transverse electric) modes, because they have a magnetic field in the axial direction. Thus it may be something that SeeShells may want to consider if she succeeds in exciting a TE mode.
TE modes ==> particularly suitable to a ferromagnetic end (magnetic field in longitudinal direction)
TM modes ==> particularly suitable to a dielectric end (electric field in longitudinal direction)
(as used for example by NASA Eagleworks)

Also that they've now built an experiment to help prove the theory to detect an effect people might have never imagined before this could have existed.
I can't find any details on such an experiment. Link, please?
It's in the link I originally posted on this topic up thread.
Posted again for ease of reference.
http://motherboard.vice.com/read/thereisgrowingevidencethatouruniverseisagianthologram
The actual experiment that will decipher this involves measuring the relative positions of large mirrors separated by 40 meters, using two Michelson laser interferometers with a precision 1 billion times smaller than an atom. If, as according to the holographic noise hypothesis, information about the positions of the two mirrors is finite, then the researchers should ultimately hit a limit in their ability to resolve their respective positions.
“What happens then?” Lanza said. “We expect to simply measure noise, as if the positions of the optics were dancing around, not able to be pinned down with more precision. So in the end, the experimental signature we are looking for is an irreducible noise floor due to the universe not actually storing more information about the positions of the mirrors.”
The team is currently collecting and analyzing data, and expects to have their first results by the end of the year. Lanza told me they are encouraged by the fact that their instruments have achieved by far the best sensitivity ever to gravitational waves at high frequencies.
“The physics of gravitational waves is unrelated to holographic noise, however, the gravity wave results demonstrate that our instrument is operating at top notch science quality, and we are now poised to experimentally dig into the science of holographic noise,” Lanza said.
You can find more details & relevant links here.
http://www.sciencedaily.com/releases/2015/04/150427101633.htm
Here's the paper.
http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.114.111602

Just to bring it back to the surface : is any one going to try with Matglas 2714A at the big end?
To see if extreme magnetic permeability has any impact on EMdrive performances?
If too expensive, a second option would be an iron plate ( as noted on the wiki list : (99.95% pure Fe annealed in H) )
This is particularly suitable for TE (transverse electric) modes, because they have a magnetic field in the axial direction. Thus it may be something that SeeShells may want to consider if she succeeds in exciting a TE mode.
TE modes ==> particularly suitable to a ferromagnetic end
TM modes ==> particularly suitable to a dielectric end (as used for example by NASA Eagleworks)
The russian patent is hard to read even with automatic translation, but quite interesting :)
µ, epsilon dependence make sense
The same like in the picture for the Efield is true for the Hfield using high µ_r
I remember there was a discussion based on permeability and susceptibility and losses in the last thread.

...
You have the exact solution for E and H in a frustum cavity. Simply plug in the E vector into equation 9,
k_{r} = j*(1/E)*dE/dr
where E is the electric field vector, all 3 components, which you already have in Mathematica. I think it should be just a few lines of code to take the derivative of a vector you already have, and multiply by the inverse.
My solution is in terms of real valued functions (Spherical Bessel functions), while Zeng and Fan used the complexvalued spherical Hankel functions (or Spherical Bessel functions of the third kind same thing).
A complex valued solution is needed to separate the real and imaginary terms alpha and beta. So I would need to spend the time to recast the solution in terms of complexvalued Spherical Hankel functions (or Spherical Bessel functions of the third kind same thing). To do this I would need to review Hankel functions (I think that they are usually used for theoretical work to express outward and inwardpropagating wave solutions of the wave equation) and make sure that all the terms are correct, including defining factors.
***************
I still think that you can use Zeng and Fan's results, the only difference is that you have to multiply the results in Fig 2 and Fig 3 by Sin[θ] to get the momentum component in the longitudinal direction, but I haven't checked this.

...
In a cylinder, the longitudinal component of momentum is the wave propagating down the waveguide. The momentum is in the z direction, not radial toward the walls. In Z&F, they are depicting a waveguide, not a cavity. The momentum is propagating down the waveguide. Changing the angle > 0, changes the momentum in the z direction for a tapered waveguide, relative to a cylindrical waveguide. In the case of the wave moving toward the apex, what Z&F show is that the waves are attenuated and all of the momentum in the z direction is phase shifted and absorbed.
Essentially, attenuation of the E field in the perpendicular directions, "IS" attenuation of momentum in the r direction, because S_{r} = E x H perpendicular to S. The wave traveling toward the apex is losing momentum to the waveguide, in the z direction. The wave traveling toward the big end is gaining momentum in the z direction. In a cylinder, neither is true because the wave does not change momentum in either direction. So the kvector reflecting off the wall is not (theta, phi) in Z&F, it is in the r direction. So it is r*Cos(theta) to get z direction thrust.
Todd
A cylinder is a geometrical concept. It is perfectly OK for me to speak of a cylinder as something that has open ends, it carries no implications of a being a cavity.
As to Zeng and Fan, as I said, I would have to rederive their equations and see whether they satisfy the boundary conditions (Ricvl said that they don't) or if there is something else amiss.
Yes Dr Rodal, to me Zeng and Fan don't write the correct expressions for the problem of propagation on a tapered conical waveguide.
One way is solve the helmoltz equations respecting directly the physical boundary conditions under the geometry of problem.
This will implies that standard solutions of wave equation in spherical coordinates ( in general, bessel and legendre functions of integer order), must be subtituted by specific solutions with fractionary order legendre/ bessel functions.
Other way, more complicated, is find solutions using the called "coupledmode theory in instantaneous eigenmode (quasimode) basis ", where one can use a superposition cilindrical modes, evolving a coupledmode equation along the longitudinal axis of propagation, where each cilindrical mode has a instantaneous dependence on the radii of tapered section of conical waveguide.
Of course, there are many others forms to solve this problem.
I set to bold because, to my understanding, this is precisely what they did. Look at equations 2 & 3, and the associated text that follows it, through to equation 8. This part of their work is not that difficult to follow, so I don't see precisely where they make any error or assumptions that would cause it to be wrong. Their answer includes everything you just said, and the derivatives are Hankel functions of "fractional order". Where is the error?
Todd
Sorry Todd, Dr Rodal and all people from this forum.
My fault. The zeng and fan field solutions are correct and the table 1 shows the order of associated legendre/bessel functions for some values of cone angle thetazero.
But together,the definitions in ( 8 ), (9) , (10), (11), (12), (13), and (14) make no sense to me.
A "constant" kr while defining the exponential in ( 8 ) and (9) , or in other words, kr is not a function of any spatial variable at this point, but becomes a function of r later.
The same for "constant" gamma definition in (10) and (11).
Suddenly, these "constants" becomes functions in (12), (13) and (14).
Magic?

If you really want to dive deep, look at Orbital Angular Momentum of circular radiation:
http://arxiv.org/ftp/arxiv/papers/0905/0905.0190.pdf
You think it is converting OAM to LM in there?
Didn't someone detect rotation in MEEP a few pages back?
Its possible oam is the reason for force variants in different orientations. IOW cosmic speed limit might create a localized force to shed photon speed. Obviously not sure but the brick wall of C is there in our reference frame...in which we are in orbital motion...something to ponder perhaps.

http://arxiv.org/abs/1508.00626
The Reality of Casimir Friction
K. A. Milton, J. S. Høye, I. Brevik
Theoretical consensus is emerging.
Thank you for posting this reference. It would be very much appreciated any other references you may find on this subject (Casimir friction)
Found some.
Casimir friction force and energy dissipation for moving harmonic oscillators  J. S. Høye; I. Brevik
Casimir friction at zero and finite temperatures  Høye, Johan S.; Brevik, Iver (2014)
Macroscopic approach to the Casimir friction force  V. V. Nesterenko,A. V. Nesterenko (2014)

I can understand the attraction of taking the idea of Casimir friction in order to explain an EmDrive as some sort of ZeroPoint Dean Drive. A pawl and ratchet into spacetime. What I don't understand is how people can make such a proposal when there is no Casimir effect in an EmDrive in the first place.

...
In a cylinder, the longitudinal component of momentum is the wave propagating down the waveguide. The momentum is in the z direction, not radial toward the walls. In Z&F, they are depicting a waveguide, not a cavity. The momentum is propagating down the waveguide. Changing the angle > 0, changes the momentum in the z direction for a tapered waveguide, relative to a cylindrical waveguide. In the case of the wave moving toward the apex, what Z&F show is that the waves are attenuated and all of the momentum in the z direction is phase shifted and absorbed.
Essentially, attenuation of the E field in the perpendicular directions, "IS" attenuation of momentum in the r direction, because S_{r} = E x H perpendicular to S. The wave traveling toward the apex is losing momentum to the waveguide, in the z direction. The wave traveling toward the big end is gaining momentum in the z direction. In a cylinder, neither is true because the wave does not change momentum in either direction. So the kvector reflecting off the wall is not (theta, phi) in Z&F, it is in the r direction. So it is r*Cos(theta) to get z direction thrust.
Todd
A cylinder is a geometrical concept. It is perfectly OK for me to speak of a cylinder as something that has open ends, it carries no implications of a being a cavity.
As to Zeng and Fan, as I said, I would have to rederive their equations and see whether they satisfy the boundary conditions (Ricvl said that they don't) or if there is something else amiss.
Yes Dr Rodal, to me Zeng and Fan don't write the correct expressions for the problem of propagation on a tapered conical waveguide.
One way is solve the helmoltz equations respecting directly the physical boundary conditions under the geometry of problem.
This will implies that standard solutions of wave equation in spherical coordinates ( in general, bessel and legendre functions of integer order), must be subtituted by specific solutions with fractionary order legendre/ bessel functions.
Other way, more complicated, is find solutions using the called "coupledmode theory in instantaneous eigenmode (quasimode) basis ", where one can use a superposition cilindrical modes, evolving a coupledmode equation along the longitudinal axis of propagation, where each cilindrical mode has a instantaneous dependence on the radii of tapered section of conical waveguide.
Of course, there are many others forms to solve this problem.
I set to bold because, to my understanding, this is precisely what they did. Look at equations 2 & 3, and the associated text that follows it, through to equation 8. This part of their work is not that difficult to follow, so I don't see precisely where they make any error or assumptions that would cause it to be wrong. Their answer includes everything you just said, and the derivatives are Hankel functions of "fractional order". Where is the error?
Todd
Sorry Todd, Dr Rodal and all people from this forum.
My fault. The zeng and fan field solutions are correct and the table 1 shows the order of associated legendre/bessel functions for some values of cone angle thetazero.
But together,the definitions in ( 8 ), (9) , (10), (11), (12), (13), and (14) make no sense to me.
A "constant" kr while defining the exponential in ( 8 ) and (9) , or in other words, kr is not a function of any spatial variable at this point, but becomes a function of r later.
The same for "constant" gamma definition in (10) and (11).
Suddenly, these "constants" becomes functions in (12), (13) and (14).
Magic?
Agreed, they misuse the word "constant" when pertaining to the variables, alpha and beta. It is a terminology issue though, not math that is incorrect.
It is not magic. Equation 12 is the derivative of equation 2, per equations 9 and 10, for TE modes. Equations 13 and 14 are the derivatives of equation 5, for TM modes. Since there is no component of Er in equation 2, there is no radial component of attenuation for the E field in the r direction. But there is for the TM mode, in equation 5 to give equation 14.
Todd

...
Agreed, they misuse the word "constant" when pertaining to the variables, alpha and beta. It is a terminology issue though, not math that is incorrect.
It is not magic. Equation 12 is the derivative of equation 2, per equations 9 and 10, for TE modes. Equations 13 and 14 are the derivatives of equation 5, for TM modes. Since there is no component of Er in equation 2, there is no radial component of attenuation for the E field in the r direction. But there is for the TM mode, in equation 5 to give equation 14.
Todd
It may be interesting to plot the γ function, the logarithmic gradient of the electric field:
γ =  dLog[E]/dr =  (1/E)*dE/dr
defined by Zeng and Fan, and apply it to the case of standing waves in a closed resonant cavity: Yang/Shell for TE011 and TE012, to see what it looks like.
In this case γ = γ_{θ} = γ_{φ}
γ_{θ} =  (1/E_{θ})*dE_{θ}/dr = γ_{φ} =  (1/E_{φ})*dE_{φ}/dr
γ is real, these are standing waves hence there is no imaginary component of γ.
γ grows without bounds, to Infinity, at each end because the transverse electric fields are zero at the big base and at the small base in order to satisfy the boundary condition that electric fields parallel to a metal boundary must be zero. Since γ is defined as the ratio of the gradient of the electric field with respect to r, divided by the electric field, when the field is zero at the bases, while the numerator is maximum, γ is infinite at the boundaries.
For TE012, γ also grows without bounds at the middle node of the two halfwave patterns because at that point the transverse electric field is zero while its gradient with respect to r is maximum.
Notice that γ is negative at the small base (small r) and positive at the big base (large r).

...
In a cylinder, the longitudinal component of momentum is the wave propagating down the waveguide. The momentum is in the z direction, not radial toward the walls. In Z&F, they are depicting a waveguide, not a cavity. The momentum is propagating down the waveguide. Changing the angle > 0, changes the momentum in the z direction for a tapered waveguide, relative to a cylindrical waveguide. In the case of the wave moving toward the apex, what Z&F show is that the waves are attenuated and all of the momentum in the z direction is phase shifted and absorbed.
Essentially, attenuation of the E field in the perpendicular directions, "IS" attenuation of momentum in the r direction, because S_{r} = E x H perpendicular to S. The wave traveling toward the apex is losing momentum to the waveguide, in the z direction. The wave traveling toward the big end is gaining momentum in the z direction. In a cylinder, neither is true because the wave does not change momentum in either direction. So the kvector reflecting off the wall is not (theta, phi) in Z&F, it is in the r direction. So it is r*Cos(theta) to get z direction thrust.
Todd
A cylinder is a geometrical concept. It is perfectly OK for me to speak of a cylinder as something that has open ends, it carries no implications of a being a cavity.
As to Zeng and Fan, as I said, I would have to rederive their equations and see whether they satisfy the boundary conditions (Ricvl said that they don't) or if there is something else amiss.
Yes Dr Rodal, to me Zeng and Fan don't write the correct expressions for the problem of propagation on a tapered conical waveguide.
One way is solve the helmoltz equations respecting directly the physical boundary conditions under the geometry of problem.
This will implies that standard solutions of wave equation in spherical coordinates ( in general, bessel and legendre functions of integer order), must be subtituted by specific solutions with fractionary order legendre/ bessel functions.
Other way, more complicated, is find solutions using the called "coupledmode theory in instantaneous eigenmode (quasimode) basis ", where one can use a superposition cilindrical modes, evolving a coupledmode equation along the longitudinal axis of propagation, where each cilindrical mode has a instantaneous dependence on the radii of tapered section of conical waveguide.
Of course, there are many others forms to solve this problem.
I set to bold because, to my understanding, this is precisely what they did. Look at equations 2 & 3, and the associated text that follows it, through to equation 8. This part of their work is not that difficult to follow, so I don't see precisely where they make any error or assumptions that would cause it to be wrong. Their answer includes everything you just said, and the derivatives are Hankel functions of "fractional order". Where is the error?
Todd
Sorry Todd, Dr Rodal and all people from this forum.
My fault. The zeng and fan field solutions are correct and the table 1 shows the order of associated legendre/bessel functions for some values of cone angle thetazero.
But together,the definitions in ( 8 ), (9) , (10), (11), (12), (13), and (14) make no sense to me.
A "constant" kr while defining the exponential in ( 8 ) and (9) , or in other words, kr is not a function of any spatial variable at this point, but becomes a function of r later.
The same for "constant" gamma definition in (10) and (11).
Suddenly, these "constants" becomes functions in (12), (13) and (14).
Magic?
Agreed, they misuse the word "constant" when pertaining to the variables, alpha and beta. It is a terminology issue though, not math that is incorrect.
It is not magic. Equation 12 is the derivative of equation 2, per equations 9 and 10, for TE modes. Equations 13 and 14 are the derivatives of equation 5, for TM modes. Since there is no component of Er in equation 2, there is no radial component of attenuation for the E field in the r direction. But there is for the TM mode, in equation 5 to give equation 14.
Todd
If one has a function with exponential format F=exp(k.x) and k is a constant then one can write k=(dF/dx)/F.
But if one has a function F=exp(k(x).x) then (dF/dx)/F=k(x) + xdk(x)/dx
If F has no exponential format is worse.
The wave solutions in spherical coodinates are the form exp(+ik.r)/r and exp(ik.r)/r only when r goes to infinity.
Of couse, the 1/r dependence of the asymptotic fields becomes a 1/r^2 of poynting vector dependence and describes the natural decay/ enhancement of outward/inward spherical waves from/to cone apex, and this factor will cancel with ds=r^2domega infinitesimal area element of a radial power flux calculation, where domega is a infinitesimal solid angle.

...
If one has a function with exponential format F=exp(k.x) and k is a constant then one can write k=(dF/dx)/F.
But if one has a function F=exp(k(x).x) then (dF/dx)/F=k(x) + xdk(x)/dx
If F has no exponential format is worse.
The wave solutions in spherical coodinates are the form exp(+ik.r)/r and exp(ik.r)/r only when r goes to infinity.
Yes, basically γ = γ (r) hence it does not make sense that γ is treated as a constant to define
E = A e^{  γ r}
γ =  (1/E) dE/dr = α + j β
because this is only true for γ = constant

...
If one has a function with exponential format F=exp(k.x) and k is a constant then one can write k=(dF/dx)/F.
But if one has a function F=exp(k(x).x) then (dF/dx)/F=k(x) + xdk(x)/dx
If F has no exponential format is worse.
The wave solutions in spherical coodinates are the form exp(+ik.r)/r and exp(ik.r)/r only when r goes to infinity.
Yes, basically γ = γ (r) hence it does not make sense that γ is treated as a constant to define
E = A e^{  γ r}
γ =  (1/E) dE/dr = α + j β
because this is only true for γ = constant
So, really
 (1/E) dE/dr = γ + r dγ/dr
So Zeng and Fan's expression is exact when dγ/dr = 0, that is when γ is constant.
and approximate for dγ/dr ~ 0 (γ nearly constant)
so in the images shown in http://forum.nasaspaceflight.com/index.php?topic=38203.msg1414705#msg1414705 above and in Zeng and Fan's figures, the γ expression is more accurate as a measure of attenuation where γ is flat (where the gradient dγ/dr ~ 0 ) and nearly constant, which is more nearly the case for values such that:
γ = 0 (NO ATTENUATION)

I took a break today and let my computer run 64 cycles of the Shell conic frustum cavity model. The png views and csv data of the final 14 time slices is available here. To me, it does look to be much more "converged" than 32 cycle runs.
https://drive.google.com/folderview?id=0B1XizxEfB23tfmVCZlhnNUVtTGRoTTlZSGJiT3ZfSHBvYnNELUc1WlN0Sk15ZDZud3pSWmM&usp=sharing (https://drive.google.com/folderview?id=0B1XizxEfB23tfmVCZlhnNUVtTGRoTTlZSGJiT3ZfSHBvYnNELUc1WlN0Sk15ZDZud3pSWmM&usp=sharing)
Please read the data description file for the details of the run.

...
If one has a function with exponential format F=exp(k.x) and k is a constant then one can write k=(dF/dx)/F.
But if one has a function F=exp(k(x).x) then (dF/dx)/F=k(x) + xdk(x)/dx
If F has no exponential format is worse.
The wave solutions in spherical coodinates are the form exp(+ik.r)/r and exp(ik.r)/r only when r goes to infinity.
Yes, basically γ = γ (r) hence it does not make sense that γ is treated as a constant to define
E = A e^{  γ r}
γ =  (1/E) dE/dr = α + j β
because this is only true for γ = constant
So, really
 (1/E) dE/dr = γ + r dγ/dr
So Zeng and Fan's expression is exact when dγ/dr = 0, that is when γ is constant.
and approximate for dγ/dr ~ 0 (γ nearly constant)
so in the images shown in http://forum.nasaspaceflight.com/index.php?topic=38203.msg1414705#msg1414705 above and in Zeng and Fan's figures, the γ expression is more accurate as a measure of attenuation where γ is flat (where the gradient dγ/dr ~ 0 ) and nearly constant, which is more nearly the case for values such that:
γ = 0 (NO ATTENUATION)
Gamma = alfa (attenuation) + jbeta (propagation)
No attenuation = zero alfa
Be careful. The expression for gamma does not make sense for stationary waves ( a superposition of two counter propagating waves and, of course, with diferent gammas)

...
Gamma = alfa (attenuation) + jbeta (propagation)
No attenuation = zero alfa
Becareful. The expression for gamma do not make sense for stationary waves ( two counter propagating waves and, of course, with diferent gammas)
Yes I realize that. There is no harm in showing it simply as (1/E)dE/dr without the meaning attached by Zeng and Fan, to understand what (1/E)dE/dr looks like.
(1/E)dE/dr is only dependent on r since E is separated into multiplicative components of the three spherical coordinates
(1/E)dE/dr just means the gradient of the logarithmic of the electric field, since
(1/E)dE/dr =  d(Log[E]/dr (no approximation here, this is a correct expression for the logarithmic gradient)

Pedantically it's the gradient of the log of the field, rather than the log of the gradient

Interesting reddit link... https://neolegesmotus.wordpress.com
Seems like a similar senario to spr, tho design is different. Italian non newtonian propulsion company. Hmmmmm
https://youtu.be/1rOvWi5QNZE

Pedantically it's the gradient of the log of the field, rather than the log of the gradient
The term "logarithmic gradient" (not log of a gradient) has been employed in the Mathematics, Continuum Mechanics, Fluid Mechanics and Heat Transfer literature short for "the gradient of the log of the field"
http://bit.ly/1IDbv4a
because "logarithmic gradient" is less awkward and its precise meaning is given by the equation

Interesting reddit link... https://neolegesmotus.wordpress.com
Seems like a similar senario to spr, tho design is different. Italian non newtonian propulsion company. Hmmmmm
What's up with the Iron Cross on it ?

Interesting reddit link... https://neolegesmotus.wordpress.com
Seems like a similar senario to spr, tho design is different. Italian non newtonian propulsion company. Hmmmmm
What's up with the Iron Cross on it ?
You've got me doc...not a company logo...decoration apparently.

Interesting reddit link... https://neolegesmotus.wordpress.com
Seems like a similar senario to spr, tho design is different. Italian non newtonian propulsion company. Hmmmmm
What's up with the Iron Cross on it ?
You've got me doc...not a company logo...decoration apparently.
and the inscription on it reading:
"Fear of the Lord"

Interesting reddit link... https://neolegesmotus.wordpress.com
Seems like a similar senario to spr, tho design is different. Italian non newtonian propulsion company. Hmmmmm
What's up with the Iron Cross on it ?
You've got me doc...not a company logo...decoration apparently.
and the inscription on it reading:
"Fear of the Lord"
Thks, my italian is lame. strange thing to put on something someone wants to solicit funding for. Guess they're religious minded...

Interesting reddit link... https://neolegesmotus.wordpress.com
Seems like a similar senario to spr, tho design is different. Italian non newtonian propulsion company. Hmmmmm
What's up with the Iron Cross on it ?
You've got me doc...not a company logo...decoration apparently.
and the inscription on it reading:
"Fear of the Lord"
The symbol is a "Cross Pattee" often associated with the Knights Templar. The Iron Cross has a different shape. See: https://en.m.wikipedia.org/wiki/Cross_pattée

GrailShip, then.
You probably already realised that "Ni" is the first two letters of "inertia", reversed. 8) 8) 8)

Grail Ship indeed. From: https://neolegesmotus.wordpress.com/2015/08/04/aspsselectromagneticenginetdsvf2/
Last but not least, when functioning PNNE produces massive E.M radiation, so who works in proximity of the prototype must wear a protective suit. Laureti found a curious but effective solution: he modified a medieval chain mail to work as a Faraday cage.
Wonder if he wore a Templar white tunic over the chain mail? :)
If he had a sword then it would be very easy for him to "cut the power!" :D

I just realized that my thinking has been a bit off. Seeing those things mounted to the back of a ship was interesting but not necessary. Theoretically it isn't necessary that the frustum be in a vacuum at all (certainly useful in the analysis phase). If it works best with air in it, then mount it in a canister with air. If nitrogen, helium, xenon or even water vapor is best then that is what it runs in. Which got me thinking, for the upcoming tests a measurement of the relative humidity would be very interesting given the interaction between microwaves and water molecules. Back to bed...

Has anyone, in the thousands of posts here, calculated how much water (gm/s) it would take to generate X N of thrust by evaporation and steam jetting?

Seems like a similar scenario to SPR, though the design is different. Italian non Newtonian propulsion company. Hmmmmm
It looks cool, but the video is...unimpressive.
And while I can't quite put my finger on it, the basic concept seems flawed. Maybe it would work for a ground effect device, say some sort of hovercraft?
Also, I note that like Shawyer, this guy immediately ventures into 'flying car' territory on rather lackluster experimental evidence.
I mean, using David Bae's work as a sort of rough measure, I can almost buy a weird fluke or loophole that would permit propellentless thrust for a sustained period on the order of a few Newton's, but more than that...

Has the article "Resonant cavities and spacetime thrust" from Marco Frasca been discussed on this forum ? A quick search on "frasca" keyword gave no result.
This article, dated May 20, 2015, analyses, by solving Einstein ﬁeld equations, the geometry of spacetime in a cavity when a plane electromagnetic wave is present. Influence of cavity shape is also considered.
It looks a pretty serious work ... but I am not operational enough in General Relativity to make a deep referee of it.

Has the article "Resonant cavities and spacetime thrust" from Marco Frasca been discussed on this forum ? A quick search on "frasca" keyword gave no result.
This article, dated May 20, 2015, analyses, by solving Einstein ﬁeld equations, the geometry of spacetime in a cavity when a plane electromagnetic wave is present. Influence of cavity shape is also considered.
It looks a pretty serious work ... but I am not operational enough in General Relativity to make a deep referee of it.
http://forum.nasaspaceflight.com/index.php?topic=37642.msg1378648#msg1378648

I can understand the attraction of taking the idea of Casimir friction in order to explain an EmDrive as some sort of ZeroPoint Dean Drive. A pawl and ratchet into spacetime. What I don't understand is how people can make such a proposal when there is no Casimir effect in an EmDrive in the first place.
Sure there is. It is very easy to justify in a type 2* EmDrive, as the gap between the dielectric insert **and small end plate. For a type 3 this geometry is satisfied by the close proximity of air molecules to the copper walls.
Linked to is a study using CO2 and CH4 molecules which illustrates this.
http://arxiv.org/abs/1506.01673
My attempts to study Casimir friction are related to the type 3 cavity, even though it applies equally to a type 2. All the info I dug up throughout threads 1 and 2 were related to the dielectric insert in a type 2 cavity and were geared toward the Casimir momentum phenomena.
*Emdrive types in image at bottom.
Type 1: Cavity with dielectric insert
Type 2: Tapered cavity with dielectric insert
Type 3: Tapered cavity with no dielectric insert
A side note, there is no way to justify a copper or aluminum cavity that is "dielectric free". The oxides of both are dielectrics, as is the air.
**StarDrive reported interesting thrust reversal effects in thread 2, when a bolt holding the dielectric down melted and came loose.
http://forum.nasaspaceflight.com/index.php?topic=36313.msg1335190#msg1335190
I know from studying Casimir geometry that, Casimir energy can be switched from negative to positive simply by disturbing the geometry. For example, corners are positive, while parallel plates are negative.

http://forum.nasaspaceflight.com/index.php?topic=37642.msg1378648#msg1378648
Thank you for the link. So Marco Fresca is still working to improve his paper and will publish it on arxiv when ready with numerical results on the predicted thrust (apparently this day is not yet arrived).

Interesting reddit link... https://neolegesmotus.wordpress.com
Seems like a similar senario to spr, tho design is different. Italian non newtonian propulsion company. Hmmmmm
What's up with the Iron Cross on it ?
You've got me doc...not a company logo...decoration apparently.
and the inscription on it reading:
"Fear of the Lord"
The symbol is a "Cross Pattee" often associated with the Knights Templar. The Iron Cross has a different shape. See: https://en.m.wikipedia.org/wiki/Cross_pattée
Reminds me of the early Crookes tubes experiments with "Maltese cross" mask :
()
Last but not least, when functioning PNNE produces massive E.M radiation, so who works in proximity of the prototype must wear a protective suit. Laureti found a curious but effective solution: he modified a medieval chain mail to work as a Faraday cage.
Space knights... their hopes make other propellentless propulsion claims pale in comparison :
However, while testing PNNE and in particular TDS VF2, ASPS discovered that the thruster doesn’t follow the common law of inertia, because E.M propulsion literally “accelerates on its own acceleration”. Hence there is the need for ASPS to define a totally new law of inertia that would allow an E.M starship to cover several light years in few seconds! It sounds astonishing but ASPS seems confident in theory effectiveness.
:o

Frobnicat, that smiley was perfect. Definitely a WTF moment.

http://forum.nasaspaceflight.com/index.php?topic=37642.msg1378648#msg1378648
Thank you for the link. So Marco Fresca is still working to improve his paper and will publish it on arxiv when ready with numerical results on the predicted thrust (apparently this day is not yet arrived).
The author is a NSF member named StrongGR:
http://forum.nasaspaceflight.com/index.php?action=profile;u=47907
Maybe try PMing him for more info?

http://forum.nasaspaceflight.com/index.php?topic=37642.msg1378648#msg1378648
Thank you for the link.
So Marco Fresca is still working to improve his paper and will publish it on arxiv when ready with numerical results on the predicted thrust (apparently this day is not yet arrived).
No, the message linked by TheTraveller is just an old message, one of several messages posted by the author.
Marco's (Frasca not "Fresca" ;) ) paper has already been published in ResearchGate some time ago. We discussed Marco's paper in detail with him prior to publication. We discussed limits of expressions, the perturbation approach and numerical results. The conclusion was that General Relativity could not be used to justify the claimed thrust for the EM Drive because the GR effect discussed by Frasca happens very close to the singularity at the vertex of the cone (as it is evident from his paper). Shawyer by intentional design on his part (claiming a waveguide cutoff effect on the small diameter although there is no such cutoff for tapered waveguides) stopped the EM Drive geometry very far away from the vertex of the cone, hence the effect discussed by Frasca is several orders of magnitude much smaller that what is claimed as thrust by EM Drive researchers.

Off topic alert  Today, I turned the big sixzero; a milestone birthday. Which should be used to convince others that one can still think, dream and build well into their senior era. So many companies and institutions look to replace older folks once they turn 50...I know from experience. I also know that its a waste of talent to do this.
So, here's to the older generation still plugging away at science. How I wish something like this project were around when I was much younger. THAT should be a message to the young folks out there to get involved in science early. Push the envelope, think outside the box, do something different...who knows, what you may come up with could change the world.
Onward and upward  Dave (rfmwguy)

Off topic alert  Today, I turned the big sixzero; a milestone birthday. Which should be used to convince others that one can still think, dream and build well into their senior era. So many companies and institutions look to replace older folks once they turn 50...I know from experience. I also know that its a waste of talent to do this.
So, here's to the older generation still plugging away at science. How I wish something like this project were around when I was much younger. THAT should be a message to the young folks out there to get involved in science early. Push the envelope, think outside the box, do something different...who knows, what you may come up with could change the world.
Onward and upward  Dave (rfmwguy)
Happy Birthday :)

No, the message linked by TheTraveller is just an old message, one of several messages posted by the author.
Marco's paper has already been published in Arxiv and ResearchGate some time ago. We discussed Marco's paper in detail with him prior to publication. We discussed limits of expressions, the perturbation approach and numerical results. The conclusion was that General Relativity could not be used to justify the claimed thrust for the EM Drive because the GR effect discussed by Frasca happens very close to the singularity at the vertex of the cone (as it is evident from his paper). Shawyer by intentional design on his part (claiming a waveguide cutoff effect on the small diameter although there is no such cutoff for tapered waveguides) stopped the EM Drive geometry very far away from the vertex of the cone, hence the effect discussed by Frasca is several orders of magnitude much smaller that what is claimed as thrust by EM Drive researchers.
Ok, I have found the final article at ResearchGate (apparently it is not in Arxiv). Effectively the predicted thrust of 6*10^22 N is realy too small to be a candidate explanation to the fantastic EMDrive test results.
By the way it is interresting to learn that Electromagnetic plane wave and Gravitational plane wave produce the same gravitational attractions on test particles (they dont need to have an electrical charge).

Frobnicat, that smiley was perfect. Definitely a WTF moment.
LOL...yep :o was perfect. Funny how people jump to extreme applications without duediligence on prototypes...i.e. replication, explanation and 3rd party verification. That leads to speculation on whether its all a funding scheme.
On NSF1701, if I've detected any force whatsoever, I'll try and figure out why only to a point. After that, I would prefer to offer it (for free) to a reputable institution that is willing to duplicate tests under (expensive) laboratory conditions.
Of course, if they break it...that would spoil my day ;)

I was asking myself how long it would take to empty the frustum of the energy stored, now I know, not long :)
Extracting microwave energy from a cavity by mode conversion at a coupling window
http://rd.springer.com/article/10.1134/1.1259080
"It is shown that microwave rf pulse compressors with copper storage cavities and energy extraction by mode conversion at a coupling window can provide gains of 5–13 dB with output signal durations of 20–150 ns and peak powers of 5–10 MW in the 3cm band and 50–100 MW in the 10cm band. "

Off topic alert  Today, I turned the big sixzero; a milestone birthday. Which should be used to convince others that one can still think, dream and build well into their senior era. So many companies and institutions look to replace older folks once they turn 50...I know from experience. I also know that its a waste of talent to do this.
So, here's to the older generation still plugging away at science. How I wish something like this project were around when I was much younger. THAT should be a message to the young folks out there to get involved in science early. Push the envelope, think outside the box, do something different...who knows, what you may come up with could change the world.
Onward and upward  Dave (rfmwguy)
And a very happy birthday from another of the older generation. As my mom said to me many times Dave. Make it so!
Michelle

I was asking myself how long it would take to empty the frustum of the energy stored, now I know, not long :)
Extracting microwave energy from a cavity by mode conversion at a coupling window
http://rd.springer.com/article/10.1134/1.1259080
"It is shown that microwave rf pulse compressors with copper storage cavities and energy extraction by mode conversion at a coupling window can provide gains of 5–13 dB with output signal durations of 20–150 ns and peak powers of 5–10 MW in the 3cm band and 50–100 MW in the 10cm band. "
Perfect! Was looking this morning at how much the mode changes could kill off the Q and the time frame needed. Thanks
back to reading and lurking.

Has anyone, in the thousands of posts here, calculated how much water (gm/s) it would take to generate X N of thrust by evaporation and steam jetting?
I can do it, but require more data. It's F= (p_exit  p_0) A_e + _mdot V_e
The terms are, in order, pressure at the nozzle, ambient pressure, Area of the nozzle exit, Mass flow rate (in kilograms per second), and exit velocity.
For forces ~ 1 N in air I "feel" like...
A.) You would notice it.
B.) The cavity would exhaust the available water vapor in the cavity very rapidly.
For short bursts of power or muN force levels steam jetting or hot air jets do "feel" like realistic sources of experimental error. Putting symmetrical (relatively) big holes in the sidewalls and doing longer runs should reduce these by maximizing Ae, minimizing p, and exhausting the available water vapor.
I have similar concerns with hot air in the cavity causing ballooning error. I don't know how to eliminate that effect while retaining a gasfilled cavity. Advice in that direction would be appreciated.

Off topic alert  Today, I turned the big sixzero; a milestone birthday. Which should be used to convince others that one can still think, dream and build well into their senior era. So many companies and institutions look to replace older folks once they turn 50...I know from experience. I also know that its a waste of talent to do this.
So, here's to the older generation still plugging away at science. How I wish something like this project were around when I was much younger. THAT should be a message to the young folks out there to get involved in science early. Push the envelope, think outside the box, do something different...who knows, what you may come up with could change the world.
Onward and upward  Dave (rfmwguy)
Happy birthday, youngster.

Hi Thor,
No, 30% is the amount of time power is at 100%, so it will "pulse" at full power for 30% of the time.
Sorry, busy weekend! Happy birthday!
Ok, right. That's makes the spreadsheet spit out (assuming 64% efficiency in converting electrical input into RF) a figure of up to 100.93mN or 144.71 mN for 30% of the time.

Conical Waves Producing Longitudinal Power Flows
http://rd.springer.com/article/10.1134/1.1307823#page1
"A conical electromagnetic wave converging to its axis is studied theoretically. It is
demonstrated that the wave produces an intense selfaccelerating flow of energy
(momentum)"
Seem to me a bit strange but... [EDIT] Do not stay in front, very barsoonian ;)

Hi Thor,
No, 30% is the amount of time power is at 100%, so it will "pulse" at full power for 30% of the time.
Sorry, busy weekend! Happy birthday!
Ok, right. That's makes the spreadsheet spit out (assuming 64% efficiency in converting electrical input into RF) a figure of up to 100.93mN or 144.71 mN for 30% of the time.
Please notice that McCulloch's formula is completely unable to distinguish between TM (transverse magnetic) from TE (transverse electric) modes. Actually McCulloch's formula completely ignores the mode shape (it ignores not only whether TE or TM but also it ignores the quantum mode shape numbers m,n,p). This is a weakness in McCulloch's formula (not present in Notsosureofit's formula that does take into account the mode shapes).
Those claiming much larger thrust and thrust/InputPower claim to use TE modes: Shawyer and Yang.
NASA also reported much larger thrust/InputPower when using TE modes but could not excite it consistently so they switched to TM modes.
So, there is considerable uncertainty when predicting thrust with a formula that ignores the mode shape of EM Drive operation.

Nice work aero. I like this and your run file is very easy to read.
I organized the images in a equal grid
My question is, are the vertical columns when arranged like this showing the same time stamp through the frustum for the sample on the waveform showing the mode?
Shell
First column
ex.t00
ey.t00
ez.000
etc....
I took a break today and let my computer run 64 cycles of the Shell conic frustum cavity model. The png views and csv data of the final 14 time slices is available here. To me, it does look to be much more "converged" than 32 cycle runs.
https://drive.google.com/folderview?id=0B1XizxEfB23tfmVCZlhnNUVtTGRoTTlZSGJiT3ZfSHBvYnNELUc1WlN0Sk15ZDZud3pSWmM&usp=sharing (https://drive.google.com/folderview?id=0B1XizxEfB23tfmVCZlhnNUVtTGRoTTlZSGJiT3ZfSHBvYnNELUc1WlN0Sk15ZDZud3pSWmM&usp=sharing)
Please read the data description file for the details of the run.

Thanks.
Yes, all of the slices labelled t 00 are taken just after the 62.7^{th} cycle, those labelled t 01 just after the 62.8^{th} cycle and so forth, up to the slice labelled t13 which is taken at the end of the run, at the 64^{th} cycle.
Nice work aero. I like this and your run file is very easy to read.
I organized the images in a equal grid
My question is, are the vertical columns when arranged like this showing the same time stamp through the frustum for the sample on the waveform showing the mode?
Shell
First column
ex.t00
ey.t00
ez.000
etc....
I took a break today and let my computer run 64 cycles of the Shell conic frustum cavity model. The png views and csv data of the final 14 time slices is available here. To me, it does look to be much more "converged" than 32 cycle runs.
https://drive.google.com/folderview?id=0B1XizxEfB23tfmVCZlhnNUVtTGRoTTlZSGJiT3ZfSHBvYnNELUc1WlN0Sk15ZDZud3pSWmM&usp=sharing (https://drive.google.com/folderview?id=0B1XizxEfB23tfmVCZlhnNUVtTGRoTTlZSGJiT3ZfSHBvYnNELUc1WlN0Sk15ZDZud3pSWmM&usp=sharing)
Please read the data description file for the details of the run.

Please notice that McCulloch's formula is completely unable to distinguish between TM (transverse magnetic) from TE (transverse electric) modes. Actually McCulloch's formula completely ignores the mode shape (it ignores not only whether TE or TM but also it ignores the quantum mode shape numbers m,n,p). This is a weakness in McCulloch's formula (not present in Notsosureofit's formula that does take into account the mode shapes).
Those claiming much larger thrust and thrust/InputPower claim to use TE modes: Shawyer and Yang.
NASA also reported much larger thrust/InputPower when using TE modes but could not excite it consistently so they switched to TM modes.
So, there is considerable uncertainty when predicting thrust with a formula that ignores the mode shape of EM Drive operation.
The derivation (F = 6PQL/c * [1/(L+4wb)  1/(L+4ws) ] which I found on http://physicsfromtheedge.blogspot.co.uk/2015/02/mihscvsemdrivedata3d.html) that I'm using in my spreadsheet doesn't take into account the input frequency of the radiation either, just the Power and the "Q".
EDIT: If I get a chance tonight I'll try to add Notsosureofit's formula to my spreadsheet and see what happens

Frobnicat, that smiley was perfect. Definitely a WTF moment.
LOL...yep :o was perfect. Funny how people jump to extreme applications without duediligence on prototypes...i.e. replication, explanation and 3rd party verification. That leads to speculation on whether its all a funding scheme.
On NSF1701, if I've detected any force whatsoever, I'll try and figure out why only to a point. After that, I would prefer to offer it (for free) to a reputable institution that is willing to duplicate tests under (expensive) laboratory conditions.
Of course, if they break it...that would spoil my day ;)
Is it legally possible and ethically right for us to try and open source this Resonant Cavity Thruster? I mean seriously, nobody owns the wheel. If this approach proves to be a viable means for propellantless propulsion, then the impact factor is no less important.
For Shawyer to try and patent this before there was even a dream of a viable commercial product is ludicrous.
He should have opened it up to research at the beginning.
Based on what I know, the current iteration is obviously not viable.
So, what do we have now that is truly unique and novel with which we can package up and give to the world?
If members of the public are able to own a personal stake in something as evolutionary as this, some will gladly invest enormous amounts of effort, even with no guarantee of any financial reward or any success; like us.
So can it be done? Should it be done? If so, we need help...
We just have to make it roll. The rest is history.

Please notice that McCulloch's formula is completely unable to distinguish between TM (transverse magnetic) from TE (transverse electric) modes. Actually McCulloch's formula completely ignores the mode shape (it ignores not only whether TE or TM but also it ignores the quantum mode shape numbers m,n,p). This is a weakness in McCulloch's formula (not present in Notsosureofit's formula that does take into account the mode shapes).
Those claiming much larger thrust and thrust/InputPower claim to use TE modes: Shawyer and Yang.
NASA also reported much larger thrust/InputPower when using TE modes but could not excite it consistently so they switched to TM modes.
So, there is considerable uncertainty when predicting thrust with a formula that ignores the mode shape of EM Drive operation.
The derivation (F = 6PQL/c * [1/(L+4wb)  1/(L+4ws) ] which I found on http://physicsfromtheedge.blogspot.co.uk/2015/02/mihscvsemdrivedata3d.html) that I'm using in my spreadsheet doesn't take into account the input frequency of the radiation either, just the Power and the "Q".
EDIT: If I get a chance tonight I'll try to add Notsosureofit's formula to my spreadsheet and see what happens
Of course there are many ways to look at this, to play devil's advocate:
1) It may be that Shawyer's and Yang's claims are unreliable and the only reliable claims are those of NASA using TM modes
2) Since so little is known with certainty at this point in time, the simplicity of McCulloch's formula at this stage may be justified, as there is no point in overfitting unreliable data.

Interesting Russian EMDrive like patent:
http://bankpatentov.ru/node/123593
and comment received on Reddit EMDrive forum:
https://www.reddit.com/r/EmDrive/comments/3ceyjv/email_from_roger_shawyer/ctww6rd
As Dr. Vladimir Leonov claims the "Shawyer Effect" works via the QV, Dr. White might be interested.
Thanks for posting this TT. Warping space is a requirement of the EMDrive and as the author states it can be done through an EM interaction.

Off topic alert  Today, I turned the big sixzero; a milestone birthday. Which should be used to convince others that one can still think, dream and build well into their senior era. So many companies and institutions look to replace older folks once they turn 50...I know from experience. I also know that its a waste of talent to do this.
So, here's to the older generation still plugging away at science. How I wish something like this project were around when I was much younger. THAT should be a message to the young folks out there to get involved in science early. Push the envelope, think outside the box, do something different...who knows, what you may come up with could change the world.
Onward and upward  Dave (rfmwguy)
Just think of it, Dave: Donald Trump is over 69 years old, so you have more than 9 years left for you to run for President of the US :)

Just think of it, Dave: Donald Trump is over 69 years old, so you have more than 9 years left for you to run for President of the US :)
13 years if you wait as long as Bernie Sanders did. ;D

https://drive.google.com/folderview?id=0B1XizxEfB23tfmVCZlhnNUVtTGRoTTlZSGJiT3ZfSHBvYnNELUc1WlN0Sk15ZDZud3pSWmM&usp=sharing
I took both Center x and Center Y pages and opened them into separate folders, sized them so one row was 14 images across and the vertical columns were synced 00, 01, 02, 03, 04... same time slice. Then switched back and forth between the pages comparing a image and mode for X to Y and at the same position.
In some cases the modes match X and Y but several they don't even come close. Just another flag of an interesting anomaly of how you could see in a relatively symmetrical cavity mode variation just between a X slice through the middle and a Y slice through the middle in the same time stamp.
Or has everyone seen this weirdness and you're going to go... phhhsst, silly old woman...
Shell

https://drive.google.com/folderview?id=0B1XizxEfB23tfmVCZlhnNUVtTGRoTTlZSGJiT3ZfSHBvYnNELUc1WlN0Sk15ZDZud3pSWmM&usp=sharing
I took both Center x and Center Y pages and opened them into separate folders, sized them so one row was 14 images across and the vertical columns were synced 00, 01, 02, 03, 04... same time slice. Then switched back and forth between the pages comparing a image and mode for X to Y and at the same position.
In some cases the modes match X and Y but several they don't even come close. Just another flag of an interesting anomaly of how you could see in a relatively symmetrical cavity mode variation just between a X slice through the middle and a Y slice through the middle in the same time stamp.
Or has everyone seen this weirdness and you're going to go... phhhsst, silly old woman...
Shell
Since the mode shapes are shown on different scales, without showing the numbers, a mode shape that has magnitude that is dozens or hundreds of times smaller amplitude (and thus insignficant) looks significant when compared without numbers. Hence the images are very difficult to understand .
Remember how we progressed:
1) At the beginning of MEEP runs, the same fields were shown on different scales from time step to time step. It looked so crazy that even the field outside the EM Drive had flashing colors. And inside the EM Drive we could see fractals that were numerical artifacts.
This was fixed by showing all the time steps at the same final scale. This fixed the fractals and the crazy colors outside the EM Drive.
2) We still have the problem that different fields in different directions: Ex, Ey, Ez, Hx, Hy, and Hz, are shown with different scales. Thus one is not able to distinguish, say if E in the x direction is 1000 times less than E in the y direction. Thus we cannot distinguish "noise" from signal.
ALL electric fields should be shown on the same scale and all magnetic fields should be shown to the same scale. Otherwise there is no comprehension.
3) I cannot tell what the mode shape being excited is, from looking at these images: is it TE ? is it TM? nobody knows. Why is it that nobody knows? Because the fields are not shown to the same scale, thus nobody can tell whether it is TE or TM. We don't know what is noise and what is signal.
Is the field in the longitudinal z direction an electric field (and hence a TM mode) or is it a magnetic field (and thus a TE mode). We cannot tell, both mode shapes are being shown and we don't know which is large and which is negligible.
If they would be shown to the same scale, and one mode shape happens to be 100 times smaller magnitude than another one, it would look like zero, and we would not look at it, thus we would better understand because we would be looking ONLY at the mode shapes that are high in magnitude. The way it is now, we don't know what is high magnitude and what is low magnitude.
Imagine what life would be like if your senses would be such that we would not be able to distinguish between what is near and what is far, between what is high and what is low, we would be lost.

Happy birthday rfmwguy :)

Happy birthday rfmwguy :)
Danke, herr x_ray!

Off topic alert  Today, I turned the big sixzero; a milestone birthday. Which should be used to convince others that one can still think, dream and build well into their senior era. So many companies and institutions look to replace older folks once they turn 50...I know from experience. I also know that its a waste of talent to do this.
So, here's to the older generation still plugging away at science. How I wish something like this project were around when I was much younger. THAT should be a message to the young folks out there to get involved in science early. Push the envelope, think outside the box, do something different...who knows, what you may come up with could change the world.
Onward and upward  Dave (rfmwguy)
Just think of it, Dave: Donald Trump is over 69 years old, so you have more than 9 years left for you to run for President of the US :)
Thanks, Doc...you cheered me up enough that I feel like this ;)

Happy birthday rfmwguy :)
Danke, herr x_ray!
Is it possible to record your next live run?
I have little problems with the time difference between our countries, last time i was sleeping, dont see your live show :[
Did you see this file?
There is a description for possible Q measurement with only one port.
The problem with a magnetron is that is only a source, there is no IQ mixer (or six port) inside the magnetron... So it may be the simplest way is to use a probe port in that case.
http://uspas.fnal.gov/materials/09UNM/ResonantCavities.pdf (big file be patient)
Thanks Mulletron for post the link
BTW: I hope you got a great party today! :P

Happy birthday rfmwguy :)
Danke, herr x_ray!
Is it possible to record your next live run?
I have little problems with the time difference between our countries, last time i was sleeping, dont see your live show :[
Did you see this file?
There is a description for possible Q measurement with only one port.
The problem with a magnetron is that is only a source, there is no IQ mixer (or six port) inside the magnetron... So it may be the simplest way is to use a probe port in that case.
http://uspas.fnal.gov/materials/09UNM/ResonantCavities.pdf (big file be patient)
Thanks Mulletron for post the link
BTW: I hope you got a great party today! :P
I will have a live session the day before I run the actual live test, basically walking throught the setup. This should be 2 weeks or less and hope to announce it next week sometime.
Last thing I need to to get the Galinstan for the liquid metal power connectors.

@rfmwguy: Happy Birthday!
About that spendy Galinstan: did you at least consider a fullyselfcontained rig using batteries?  and what put you off it?

@rfmwguy: Happy Birthday!
About that spendy Galinstan: did you at least consider a fullyselfcontained rig using batteries?  and what put you off it?
Thks dm...I was going to use battery until the junk exciter spoiled my day. It was only going to put out about 8 watts after amplification...far too low power for me to be able to measure on the Floobie Stick balance beam...so, the magnetron was chosen.
I agree, batteries would have been best, but 4kV bias?...uhhh maybe not so much.

Yeah, the inverter is the tricky bit. But...
http://powersupply33.com/converter9vto135kv.html

I was thinking about the air ballooning effect... again ::)
And yes i am sure that was already discussed several times. ;)
It is cause by the higher kinetic energy of the particles, they need more space and generate a pressure at the surrounded walls...
I think that effect is only true for a cavity that allow to escape the gas while heating. If it is airtight the number of gas molecules per volume stays constant.
But than there is more energy inside the cavity and based on the restmass+velocity of the gas particles the system will be a little bit heavier the higher the temperature is in contrast to the surrounding.
The gas around the cavity also heats up, that causes a upstream of air.
The last effect is already true for rfmwguy and SheShells
This can be eliminated by testing the cone in the "up" and "down" direction.
In the horizontal direction using perforated copper a force based on this effect would always working forward the small diameter(inner sidewall) same would act at the lower outside wall but forward the big end, so it cancels each other...
Is there some argument i miss in my memory?
(only for my brain protocol...)
https://www.youtube.com/watch?v=PvZoSugrz24
https://en.wikipedia.org/wiki/Schlieren_imaging

For Shawyer to try and patent this before there was even a dream of a viable commercial product is ludicrous.
I vigorously disagree. Mr. Shawyer has, hypothetically, discovered something that we thought was impossible. As such, in addition to his Nobel prize, he is fully entitled to own that intellectual property for the full duration of the patent and take full financial advantage of it. His right to make a billion dollars on this is just as real as your right to make a billion dollars on any improvements you make to it.
A patent is a reward and incentive for the inventor's investment of effort, risk, failures, money, time, and life in creating a device or idea. If they choose to open source it or freely license it then that is their choice. They are under no ethical or moral obligation to do so.
He should have opened it up to research at the beginning.
He did. He's been writing about it publicly for a decade to anyone who would listen. For his trouble he's been called a fraud and charlatan. He's been mocked and ridiculed. To imply that he's hoarded this to himself is a particularly bitter insult.
Based on what I know, the current iteration is obviously not viable.
Your knowledge is incorrect. He discovered the Shawyer effect and then spent years inventing, experimenting, and refining devices that generated thrust from RF energy. The device accomplished the "impossible". That certainly seems "viable" to me.
If members of the public are able to own a personal stake in something as evolutionary as this, some will gladly invest enormous amounts of effort, even with no guarantee of any financial reward or any success; like us.
Mr. Shawyer built this technology "with no guarantee of any financial reward or any success." How is his contribution somehow inferior to what we would create?
So can it be done? Should it be done? If so, we need help...
We just have to make it roll. The rest is history.
Patent law is not simple at all. Even worse, it varies wildly by country and it changes over time. In the US, there is a tiny window for building a copy of a device to determine the accuracy of the specification, for the sole purpose of gratifying a philosophical taste, or curiosity, or for mere amusement. I currently work within those exceptions. Any use beyond that should be negotiated with Mr. Shawyer.
eag
P.s. ... don't forget that Cannae has patents on this kit too. Even though their drive !did not work! they still own part of the IP.

I call it "ballooning" when the cavity is perfectly airtight and the walls bulge slightly  the thinner the walls, the greater this effect. Due to the increase in external volume at constant contained mass, the cavity density decreases and thus experiences increased buoyancy in air. There is however a countereffect present; because the air around the cavity is also heated, it enjoys a lower density, which in turn reduces this buoyancy. Which of these two competing effects wins out depends on all the details.
When the cavity is not airtight, there are two effects to be expected:
a) a loss of allup cavity mass due to the mass of the expelled air with increased heating
b) the possibility of a rocket effect due to convection of cavity gas in a preferred direction, which in turn depends on where it's leaking. Note that, for certain leakage patterns, one would see the artifact of reversed thrust when the cavity is flipped, since now the "jet" direction is also flipped.
Note that, in vacuum, none of the above occur if care is taken to evacuate the cavity.

I call it "ballooning" when the cavity is perfectly airtight and the walls bulge slightly  the thinner the walls, the greater this effect. Due to the increase in external volume at constant contained mass, the cavity density decreases and thus experiences increased buoyancy in air. There is however a countereffect present; because the air around the cavity is also heated, it enjoys a lower density, which in turn reduces this buoyancy. Which of these two competing effects wins out depends on all the details.
When the cavity is not airtight, there are two effects to be expected:
a) a loss of allup cavity mass due to the mass of the expelled air with increased heating
b) the possibility of a rocket effect due to convection of cavity gas in a preferred direction, which in turn depends on where it's leaking. Note that, for certain leakage patterns, one would see the artifact of reversed thrust when the cavity is flipped, since now the "jet" direction is also flipped.
Note that, in vacuum, none of the above occur if care is taken to evacuate the cavity.
This thought was based on inelastic walls who are thick enough..

@rfmwguy: Happy Birthday!
About that spendy Galinstan: did you at least consider a fullyselfcontained rig using batteries?  and what put you off it?
You can buy a cheap UPS Puresine inverter relatively cheap, and use that to power the magnetron transformer.
Todd

https://drive.google.com/folderview?id=0B1XizxEfB23tfmVCZlhnNUVtTGRoTTlZSGJiT3ZfSHBvYnNELUc1WlN0Sk15ZDZud3pSWmM&usp=sharing
I took both Center x and Center Y pages and opened them into separate folders, sized them so one row was 14 images across and the vertical columns were synced 00, 01, 02, 03, 04... same time slice. Then switched back and forth between the pages comparing a image and mode for X to Y and at the same position.
In some cases the modes match X and Y but several they don't even come close. Just another flag of an interesting anomaly of how you could see in a relatively symmetrical cavity mode variation just between a X slice through the middle and a Y slice through the middle in the same time stamp.
Or has everyone seen this weirdness and you're going to go... phhhsst, silly old woman...
Shell
Since the mode shapes are shown on different scales, without showing the numbers, a mode shape that has magnitude that is dozens or hundreds of times smaller amplitude (and thus insignficant) looks significant when compared without numbers. Hence the images are very difficult to understand .
Remember how we progressed:
1) At the beginning of MEEP runs, the same fields were shown on different scales from time step to time step. It looked so crazy that even the field outside the EM Drive had flashing colors. And inside the EM Drive we could see fractals that were numerical artifacts.
This was fixed by showing all the time steps at the same final scale. This fixed the fractals and the crazy colors outside the EM Drive.
2) We still have the problem that different fields in different directions: Ex, Ey, Ez, Hx, Hy, and Hz, are shown with different scales. Thus one is not able to distinguish, say if E in the x direction is 1000 times less than E in the y direction. Thus we cannot distinguish "noise" from signal.
ALL electric fields should be shown on the same scale and all magnetic fields should be shown to the same scale. Otherwise there is no comprehension.
3) I cannot tell what the mode shape being excited is, from looking at these images: is it TE ? is it TM? nobody knows. Why is it that nobody knows? Because the fields are not shown to the same scale, thus nobody can tell whether it is TE or TM. We don't know what is noise and what is signal.
Is the field in the longitudinal z direction an electric field (and hence a TM mode) or is it a magnetic field (and thus a TE mode). We cannot tell, both mode shapes are being shown and we don't know which is large and which is negligible.
If they would be shown to the same scale, and one mode shape happens to be 100 times smaller magnitude than another one, it would look like zero, and we would not look at it, thus we would better understand because we would be looking ONLY at the mode shapes that are high in magnitude. The way it is now, we don't know what is high magnitude and what is low magnitude.
Imagine what life would be like if your senses would be such that we would not be able to distinguish between what is near and what is far, between what is high and what is low, we would be lost.
Sigh. Lost? No, just regroup.
Thanks for the recap, I did't realize we handicapped the visual data as much as we did in truncating data simply making it unusable as a visual aid.
I hope the numbers haven't been truncated in the CSV files as well. Back to lurk and dig.
Shell

...
Sigh. Lost? No, just regroup.
Thanks for the recap, I did't realize we handicapped the visual data as much as we did in truncating data simply making it unusable as a visual aid.
I hope the numbers haven't been truncated in the CSV files as well. Back to lurk and dig.
Shell
The numbers are in the csv files, but it is much more time consuming to postprocess the csv files than to just click and look at the images. All my 3 computers are otherwise occupied at the moment. I had a small window of time in one computer which I used to calculate something that Todd will be interested in :) Hope to get to this soon.

...
Agreed, they misuse the word "constant" when pertaining to the variables, alpha and beta. It is a terminology issue though, not math that is incorrect.
It is not magic. Equation 12 is the derivative of equation 2, per equations 9 and 10, for TE modes. Equations 13 and 14 are the derivatives of equation 5, for TM modes. Since there is no component of Er in equation 2, there is no radial component of attenuation for the E field in the r direction. But there is for the TM mode, in equation 5 to give equation 14.
Todd
It may be interesting to plot the γ function, the logarithmic gradient of the electric field:
γ =  dLog[E]/dr =  (1/E)*dE/dr
defined by Zeng and Fan, and apply it to the case of standing waves in a closed resonant cavity: Yang/Shell for TE011 and TE012, to see what it looks like.
In this case γ = γ_{θ} = γ_{φ}
γ_{θ} =  (1/E_{θ})*dE_{θ}/dr = γ_{φ} =  (1/E_{φ})*dE_{φ}/dr
γ is real, these are standing waves hence there is no imaginary component of γ.
γ grows without bounds, to Infinity, at each end because the transverse electric fields are zero at the big base and at the small base in order to satisfy the boundary condition that electric fields parallel to a metal boundary must be zero. Since γ is defined as the ratio of the gradient of the electric field with respect to r, divided by the electric field, when the field is zero at the bases, while the numerator is maximum, γ is infinite at the boundaries.
For TE012, γ also grows without bounds at the middle node of the two halfwave patterns because at that point the transverse electric field is zero while its gradient with respect to r is maximum.
Notice that γ is negative at the small base (small r) and positive at the big base (large r).
...
If one has a function with exponential format F=exp(k.x) and k is a constant then one can write k=(dF/dx)/F.
But if one has a function F=exp(k(x).x) then (dF/dx)/F=k(x) + xdk(x)/dx
If F has no exponential format is worse.
The wave solutions in spherical coodinates are the form exp(+ik.r)/r and exp(ik.r)/r only when r goes to infinity.
Yes, basically γ = γ (r) hence it does not make sense that γ is treated as a constant to define
E = A e^{  γ r}
γ =  (1/E) dE/dr = α + j β
because this is only true for γ = constant
So, really
 (1/E) dE/dr = γ + r dγ/dr
So Zeng and Fan's expression is exact when dγ/dr = 0, that is when γ is constant.
and approximate for dγ/dr ~ 0 (γ nearly constant)
so in the images shown in http://forum.nasaspaceflight.com/index.php?topic=38203.msg1414705#msg1414705 above and in Zeng and Fan's figures, the γ expression is more accurate as a measure of attenuation where γ is flat (where the gradient dγ/dr ~ 0 ) and nearly constant, which is more nearly the case for values such that:
γ = 0 (NO ATTENUATION)
Thanks to our "NSF Peer Review Committee" with members Ricvl, Todd "WarpTech" and yours truly we have peerreviewed Zeng and Fan's paper better than was done by the original editiorial review by Optics Express Journal:
Electromagnetic fields and transmission properties in tapered hollow metallic waveguides
Xiahui Zeng and Dianyuan Fan
https://www.osapublishing.org/oe/fulltext.cfm?uri=oe17134&id=175583
Ricvl uncovered the important error that Zeng and Fan failed to properly derive the γ exponent, as they improperly considered it to be a constant in the initial part of their derivation and then a posteriori they inconsistently considered it to be a function of r.
I have properly solved the first order differential equation for γ(r):
r dγ/dr + γ =  (1/E_{θ})*dE_{θ}/dr
that arises from solving for the exponent γ in the following expression:
E_{θ} = A e^{  γ r}
(observe that Zeng and Fan did not solve this equation, instead they considered r dγ/dr << γ and hence assumed
γ =  (1/E_{θ})*dE_{θ}/dr).
When properly solving the differential equation (numerically, since it does not have a closed form solution, and it is quite difficult to solve numerically because it contains highly oscillating functions and it diverges at the boundaries)
I get the enclosed attenuation curve for γ for Yang/Shell in TE011 mode, with the RF feed off, standing waves, which does make sense (the solution based on Zeng & Fan's equation γ =  (1/E_{θ})*dE_{θ}/dr does not make sense because it contains a large geometrical magnification at the small end).
The attenuation is positive over the whole EM Drive, being close to zero over most of it but diverging to high attenuation at both ends because (1/E_{θ})*dE_{θ}/dr) diverges at the ends as previously explained due to the fact that the electric field E_{θ} must be zero at the bases. Therefore the tangent electric field E_{θ} gets 100% attenuated at the small base and at the big base. The attenuation curve for the other tangent electric field E_{φ} is identical.
Notice the asymmetry: there is more attenuation going on towards the small base.
Thus we have properly solved this problem for the case in which E_{θ} satisfies the bondary conditions for a resonant cavity.
Recall
1) Yang/Shell geometry:
bigDiameter = 0.201(*meter*);
smallDiameter = 0.1492(*meter*);
axialLength = 0.24(*meter*);
equivalently:
r1 = 0.693281 (*meter*); (*spherical small radius *)
r2 = 0.933978 (*meter*); (*spherical large radius *)
θ_{w} = 6.15933 (*degrees*); (*halfcone angle*)
2) the geometry we consider is as shown in this image:
()

...
Sigh. Lost? No, just regroup.
Thanks for the recap, I did't realize we handicapped the visual data as much as we did in truncating data simply making it unusable as a visual aid.
I hope the numbers haven't been truncated in the CSV files as well. Back to lurk and dig.
Shell
The numbers are in the csv files, but it is much more time consuming to postprocess the csv files than to just click and look at the images. All my 3 computers are otherwise occupied at the moment. I had a small window of time in one computer which I used to calculate something that Todd will be interested in :) Hope to get to this soon.
That's ok Jose, I'm going to take some time and do it. I need to.
Thanks,
Shell

Hi everyone...
Been in lurking mode for a while now, and have been wringing my head for answers. No joy. I do have an idea, but I need to see the results of more vacuum tests to be reasonably confident.
I would like to take this opportunity to say this to the DIY guys. I would dearly love to build myself, but simply have no time or shop. I can only think in the rare moments I have. You really are pulling together and doing a great job.
But I need more null tests! I need someone to put a heating element in and test for deformation etc...
From different shaped frustums.
I need to see possible radiation leakage from the endplate.
I need a ramped test in a vacuum chamber bringing the power up to 100% and I need to see what happens when the magnetron pops. And in atmosphere too!
I need this because if on the off chance that this thing works, it will help me to understand the underlying process.
And I'm saying this because I believe that we are exciting a very particular set of circumstances. I honestly don't believe for a moment that the shape of the frustum is THAT important. After all, we have seen potential thrust from varying designs. I mean look at the Cannae drive  Totally different. I can understand Temjar. He realized this too. Hence a hole you could stick your head through and peek around in.
MEEP will prove powerful in the end, I'm sure of it. But just not for the moment. Don't kill me Aero, I know you have done such fine work there...It can help guide us. But should not be considered so pertinent until we have figured the basics.
I think its time to balance the tests, and not get overloaded with results. There is also a high chance I've missed out on stuff here. It's been a busy month. And @Shell how goes the measurement setup? Sorry to hear about your loss.
Bedtime now.

It is thanks to aero running Meep that we are able to calculate and show:
1) The huge difference between having RF feed ON with travelling waves vs. the case examined by Greg Egan (RF feed OFF with standing waves)
2) The fact that there is Poynting vector directionally oriented with the RF feed ON that keeps growing with time exponentially, with the RF Feed on.
3) The fact that the stresses and hence the forces at the small and big bases are greatly influenced by the antenna with the RF feed ON
4) The difference between placing the antenna at the small end vs the big end
5) The difference between placing the antenna at the axis of axisymmetry vs being offset
6) The difficulties of exciting TE modes with dipole antennas
I say no, nobody here is overloaded, rfmwguy and SeeShells can carry much more on their shoulders, so aero, keep it going with
7) Loop antennas to excite TE modes
8 ) Showing what happens when your turn the RF feed OFF
9) Modeling a waveguide entering the cavity to excite a TE mode in the cavity
10) Showing how steadystate is approached
etc.
:)

Dr Rodal, I think there is a problem again.
Standing waves.
In the cavity, at least, the fields are superpositions of two counter propagating waves, then one has (to simplify)
E=[a.exp(gamma.r)+b.exp(gamma.r)].F(tetha,phi)
Repair, the expression above is just a aproximate model to fit the fields by exponential functions, where the correct is to use fractional spherical hankel functions (for spherical ends cavitys), where a,b and gamma will fataly be functions of r. At r>>1 the spherical hankel function decay with 1/r.
Then how to differentiate a destructive interference at node fields from a infinity attenuation?
Worse, even with a,b and gamma being constants, when one take the derivative of E above, because the two signals of gamma (outward/inward from/to apex cone) one has
dE/dr=gamma[a.exp(gamma.r) b.exp(gamma.r)].F(theta,phi), and we lost original E function, then imagine with a,b and gamma being r functions.
This is just my way to think. You may, of course, disagree. :)

It is thanks to aero running Meep that we are able to calculate and show:
1) The huge difference between having RF feed ON with travelling waves vs. the case examined by Greg Egan (RF feed OFF with standing waves)
2) The fact that there is Poynting vector directionally oriented with the RF feed ON that keeps growing with time exponentially, with the RF Feed on.
3) The fact that the stresses and hence the forces at the small and big bases are greatly influenced by the antenna with the RF feed ON
4) The difference between placing the antenna at the small end vs the big end
5) The difference between placing the antenna at the axis of axisymmetry vs being offset
6) The difficulties of exciting TE modes with dipole antennas
I say no, nobody here is overloaded, rfmwguy and SeeShells can carry much more on their shoulders, so aero, keep it going with
7) Loop antennas to excite TE modes
8 ) Showing what happens when your turn the RF feed OFF
9) Modeling a waveguide entering the cavity to excite a TE mode in the cavity
10) Showing how steadystate is approached
etc.
:)
I also am very glad aero is here doing work that has effectively moved this group forward with answers garnered in meep that simply were not available to the group in any other fashion. And with your help we got some very good answers.
But a couple of questions arise in how we can accomplish this with the data being displayed as it currently is.
How can we even know that a TM mode can be excited when you declared that the displayed modes were of little value after the filtering of the data files to rid the display of the artifacts and flashing colors. The only way I can see is not to be dependent on the display of meep and postprocess but use another program, Wolfram or something else?
I need to know how to forecast the future use of meep and post processing because this second build I'll be going after building a stable frustum with ceramic gold plated endplates and an active feedback system to assure mode and frequency lock. If I can't get the answers here than I'll need to take a longer path.
I was busy today tracking down and talking with old contacts that are going to try to get me the ceramics for the endplates. I'll need to tell them before too long what size I want them to be. The final shape of the ERD frustum will depend on how well meep and post processing can show what shape is optimal for it. For that we need as stable of an answer we can get. Simply for keeping a TE mode in a stabilized frustum, I think this is needed.
Shell

...
I also am very glad aero is here doing work that has effectively moved this group forward with answers garnered in meep that simply were not available to the group in any other fashion. And with your help we got some very good answers.
But a couple of questions arise in how we can accomplish this with the data being displayed as it currently is.
How can we even know that a TM mode can be excited when you declared that the displayed modes were of little value after the filtering of the data files to rid the display of the artifacts and flashing colors. The only way I can see is not to be dependent on the display of meep and postprocess but use another program, Wolfram or something else?
I need to know how to forecast the future use of meep and post processing because this second build I'll be going after building a stable frustum with ceramic gold plated endplates and an active feedback system to assure mode and frequency lock. If I can't get the answers here than I'll need to take a longer path.
I was busy today tracking down and talking with old contacts that are going to try to get me the ceramics for the endplates. I'll need to tell them before too long what size I want them to be. The final shape of the ERD frustum will depend on how well meep and post processing can show what shape is optimal for it. For that we need as stable of an answer we can get. Simply for keeping a TE mode in a stabilized frustum, I think this is needed.
Shell
Perhaps aero (or somebody else) will find a way to:
1) Plot all the electric fields with the same magnitude scale, and plot all the magnetic fields with the same magnitude scales
2) Plot the contour plots for the electromagnetic fields with an attached color bar showing the numerical magnitude of the contour colors.
I am not conversant with Meep but it seems to me that this need is something that many other users of Meep also have (to plot all the fields with the same magnitude and to be able to show the numerical value of the contours) and therefore may be an already existing command or something that somebody may have already documented how to do.
I know that other codes with which I am conversant (ANSYS, etc.) this is standard. Actually the ability to show the numerical value of the contours was available in ANSYS from its first versions back in the early 1980's.

...
...
...
Thanks to our "NSF Peer Review Committee" with members Ricvl, Todd "WarpTech" and yours truly we have peerreviewed Zeng and Fan's paper better than was done by the original editiorial review by Optics Express Journal:
Electromagnetic fields and transmission properties in tapered hollow metallic waveguides
Xiahui Zeng and Dianyuan Fan
https://www.osapublishing.org/oe/fulltext.cfm?uri=oe17134&id=175583
Ricvl uncovered the important error that Zeng and Fan failed to properly derive the γ exponent, as they improperly considered it to be a constant in the initial part of their derivation and then a posteriori they inconsistently considered it to be a function of r.
I have properly solved the first order differential equation for γ(r):
r dγ/dr + γ =  (1/E_{θ})*dE_{θ}/dr
that arises from solving for the exponent γ in the following expression:
E_{θ} = A e^{  γ r}
(observe that Zeng and Fan did not solve this equation, instead they considered r dγ/dr << γ and hence assumed
γ =  (1/E_{θ})*dE_{θ}/dr).
When properly solving the differential equation (numerically, since it does not have a closed form solution, and it is quite difficult to solve numerically because it contains highly oscillating functions and it diverges at the boundaries)
I get the enclosed attenuation curve for γ for Yang/Shell in TE011 mode, with the RF feed off, standing waves, which does make sense (the solution based on Zeng & Fan's equation γ =  (1/E_{θ})*dE_{θ}/dr does not make sense because it contains a large geometrical magnification at the small end).
The attenuation is positive over the whole EM Drive, being close to zero over most of it but diverging to high attenuation at both ends because (1/E_{θ})*dE_{θ}/dr) diverges at the ends as previously explained due to the fact that the electric field E_{θ} must be zero at the bases. Therefore the tangent electric field E_{θ} gets 100% attenuated at the small base and at the big base. The attenuation curve for the other tangent electric field E_{φ} is identical.
Notice the asymmetry: there is more attenuation going on towards the small base.
Thus we have properly solved this problem for the case in which E_{θ} satisfies the bondary conditions for a resonant cavity.
Recall
...
This is great! I have a question though. How can gamma be 0 at r = .85? It is not the attenuation exactly.
gamma = alpha + j*beta
You said "there is no imaginary part of gamma", meaning beta = 0 because it's a standing wave. Fine, but if gamma = 0, then what happened to the momentum of the wave?
gamma = j*k ~ p
Also, by assuming a standing wave solution, you are precluding there is any effect due to propagating waves. As @Ricvil said, the standing wave is the superposition of two propagating waves. The effect we are looking for pretty much requires that these two waves are not equal. So I don't think the assumption that beta=0 because they are standing waves is a good idea. It is like assuming the force we are looking for, doesn't exist.
I think it is required that beta =/= 0, or else the wave has no momentum to transfer to the frustum.
Thanks.
Todd

Dr Rodal, I think there is a problem again.
Standing waves.
In the cavity, at least, the fields are superpositions of two counter propagating waves, then one has (to simplify)
E=[a.exp(gamma.r)+b.exp(gamma.r)].F(tetha,phi)
Repair, the expression above is just a aproximate model to fit the fields by exponential functions, where the correct is to use fractional spherical hankel functions (for spherical ends cavitys), where a,b and gamma will fataly be functions of r. At r>>1 the spherical hankel function decay with 1/r.
Then how to differentiate a destructive interference at node fields from a infinity attenuation?
Worse, even with a,b and gamma being constants, when one take the derivative of E above, because the two signals of gamma (outward/inward from/to apex cone) one has
dE/dr=gamma[a.exp(gamma.r) b.exp(gamma.r)].F(theta,phi), and we lost original E function, then imagine with a,b and gamma being r functions.
This is just my way to think. You may, of course, disagree. :)
There is NO approximation, and there is no fitting. There is NO exponential fit, because γ is not a constant here, γ is a function of r, defined to give the identical part of E_{θ} that is solely expressible in term of r . The meaning of γ is only as described by the mathematical expression, not more and not less.
γ is not a closedform expression, it is not expressible by any known function known in any text. γ is given by Wolfram Mathematica as the solution of the differential equation, it is NOT a known classical function, it is NOT an exponential with a constant exponent multiplying r.
It is just a mapping of the original function into another function that gives exactly the same result.
It is exactly the same.
The solution E_{θ} in terms of γ exponential and A is identical to the one expressed in terms of Spherical Bessel functions and the Legendre Associated functions, it is just expressed in a different form.
Tomorrow I will post a comparison plot to show this identity. It is identical by construction
/////////////////////////////////////////////////////////////////
As to interference, separate waves and other issues present in the transient when the RF feed is ON, I have not dealt with those aspects. I have only dealt with the standing wave solution. To deal with the transient with the RF feed ON, yes I would have to use Hankel functions.

...
This is great! I have a question though. How can gamma be 0 at r = .85? ..
gamma is zero at r=0.85 because at r=0.85 the rdependent part of E_{θ} is 1. An exponential raised to a zero value gives you 1. The constants defining E_{θ} (as well as the θ and phi dependent variables) are absorbed into "A":
E_{θ} = A e^{  γ r}
for γ = 0
gives
E_{θ} /A = 1
one is the maximum value of E_{θ} /A, which has been normalized to have a maximum value of 1 by construction.

...
Also, by assuming a standing wave solution, you are precluding there is any effect due to propagating waves. As @Ricvil said, the standing wave is the superposition of two propagating waves. The effect we are looking for pretty much requires that these two waves are not equal. So I don't think the assumption that beta=0 because they are standing waves is a good idea. It is like assuming the force we are looking for, doesn't exist.
I think it is required that beta =/= 0, or else the wave has no momentum to transfer to the frustum.
Thanks.
Todd
Of course. But that is all that I solved. As I wrote in my post I only used the standing wave solution. Unequal travelling waves in opposite directions, interference, or other effects present with the RF feed on, or a force, are not going to be found here. I used only the standing wave solution, for which there is no force according to Maxwell's solution.
Before we go to Hankel functions we have to start from a known solution to see whether the method is sound and gives a correct solution to a known problem.
Particularly when Zeng and Fan have the incorrect solution and nobody from the peer reviewers caught it.
To consider a waveguide or an RF cavity transient solution I would have to use the same methodology using spherical Hankel functions instead of spherical Bessel functions, as I had posted previously :)
Piano piano si va sano e lontano
()

...
I also am very glad aero is here doing work that has effectively moved this group forward with answers garnered in meep that simply were not available to the group in any other fashion. And with your help we got some very good answers.
But a couple of questions arise in how we can accomplish this with the data being displayed as it currently is.
How can we even know that a TM mode can be excited when you declared that the displayed modes were of little value after the filtering of the data files to rid the display of the artifacts and flashing colors. The only way I can see is not to be dependent on the display of meep and postprocess but use another program, Wolfram or something else?
I need to know how to forecast the future use of meep and post processing because this second build I'll be going after building a stable frustum with ceramic gold plated endplates and an active feedback system to assure mode and frequency lock. If I can't get the answers here than I'll need to take a longer path.
I was busy today tracking down and talking with old contacts that are going to try to get me the ceramics for the endplates. I'll need to tell them before too long what size I want them to be. The final shape of the ERD frustum will depend on how well meep and post processing can show what shape is optimal for it. For that we need as stable of an answer we can get. Simply for keeping a TE mode in a stabilized frustum, I think this is needed.
Shell
Perhaps aero (or somebody else) will find a way to:
1) Plot all the electric fields with the same magnitude scale, and plot all the magnetic fields with the same magnitude scales
2) Plot the contour plots for the electromagnetic fields with an attached color bar showing the numerical magnitude of the contour colors.
I am not conversant with Meep but it seems to me that this need is something that many other users of Meep also have (to plot all the fields with the same magnitude and to be able to show the numerical value of the contours) and therefore may be an already existing command or something that somebody may have already documented how to do.
I know that other codes with which I am conversant (ANSYS, etc.) this is standard. Actually the ability to show the numerical value of the contours was available in ANSYS from its first versions back in the early 1980's.
The numerical field intensity values may be available in some convenient way that I just don't know about, but I have looked. Other meepers looking would be very helpful.
They are available, just not convenienly, by using the "verbose" switch on h5topng. Unfortunately, using that will require two separate runs, but I guess any method would require two separate runs at some level. Here is the verbose output from generating one png file.
steve@stevep6720f:~$ h5topng v t 0 z 214 ./Shell2ddipoleloopout/hx.h5
Using colormap "gray" in file "/usr/share/h5utils/colormaps/gray".
grayscale color map (white to black)
2 color entries read from colormap file.
Scaling opacity by 1
data rank = 4

reading from "./Shell2ddipoleloopout/hx.h5", slice at 214 in z dimension, slice at 0 in t dimension.
data ranges from 0.00012754 to 0.00012754.
writing "./Shell2ddipoleloopout/hx.png" from 196x196 input data.
all data range from 0.00012754 to 0.00012754.
I manually made 12 runs of h5topng, and extracted the following data ranges.
Range of data values in Shell2ddipoleloop64out
slice t 00, z 15 Big end
ex all data range from 3.67269e05 to 3.67269e05.
ey all data range from 1.42517e05 to 1.42517e05.
ez all data range from 0.000245405 to 0.000245405.
hx all data range from 0.000538633 to 0.000538633.
hy all data range from 0.000356036 to 0.000356036.
hz all data range from 4.65749e05 to 3.78542e05.
slice t 00 z 214 Small end
ex all data range from 1.60461e05 to 1.60461e05.
ey all data range from 3.20985e05 to 3.20985e05.
ez all data range from 4.04811e05 to 4.04811e05.
hx all data range from 0.00012754 to 0.00012754.
hy all data range from 0.000287974 to 0.000287974.
hz all data range from 1.07156e05 to 1.61666e05.
As I understand you, what you need is to have three png files, ex, ey, ez scaled to the maximum range of the E components and three, hx hy, hz scaled to the maximum range for the H component  for each time slice and each of the 4 geometry slices per time slice. That would be the ez range and the hx range for the first case above, but note that max value and min value won't necessarily always be from the same component as the second hz range above indicates.
Scaling the range of values using this approach is quite unwieldy to do manually, as there are I believe 336 pngs for a standard data set as I have been using, but also, we might benefit by extending that data set to 2 full cycles, or even more.
Does anyone here want to volunteer to create a bash shell file that runs the data set in verbose mode capturing the terminal output in the log file, then scan that log file, extract the correct range of values and scale the h5topng max and min switches, then run the data set again for upload? Conceptually it should be straight forward but I only recognize bash in passing, are almost strangers. Of course one could use Octave or MatLab to read the log file and extract the pertinent data, or even write a purpose program that simply scans and extracts the data then writes a new shell file with as many h5topng command lines as needed. That might be safer and the 336 + command line shell file would be "throw away" so it wouldn't need to be "slick."

EDIT: If I get a chance tonight I'll try to add Notsosureofit's formula to my spreadsheet and see what happens
Oh my gosh.
Notsureofit's formula is much more difficult to program into excel. You have to calculate TM modes, TE modes, Angular Frequency, and p (quantum number in the longitudinal direction, for modes TMmnp and TEmnp) and use them as inputs. This will take much longer than I realized.

ALL electric fields should be shown on the same scale and all magnetic fields should be shown to the same scale. Otherwise there is no comprehension.
A common dB scale should be appropriate.

ALL electric fields should be shown on the same scale and all magnetic fields should be shown to the same scale. Otherwise there is no comprehension.
A common dB scale should be appropriate.
Why use a logarithm scale for showing the magnitude of the electromagnetic fields?
What advantage is there in using a logarithmic scale? I see disadvantages as a logarithmic scale would distort the fields and really distort the mode shapes which are usually displayed in texts with a linear scale and hence become difficult to recognize. We want to be able to identify the mode shapes so that we know whether TE or TM, etc.
(http://forum.nasaspaceflight.com/index.php?action=dlattach;topic=36313.0;attach=632192;image)

ALL electric fields should be shown on the same scale and all magnetic fields should be shown to the same scale. Otherwise there is no comprehension.
A common dB scale should be appropriate.
Why use a logarithm scale for showing the magnitude of the electromagnetic fields?
What advantage is there in using a logarithmic scale? I see disadvantages as a logarithmic scale would distort the fields and really distort the mode shapes which are usually displayed in texts with a linear scale and hence become difficult to recognize. We want to be able to identify the mode shapes so that we know whether TE or TM, etc.
(http://forum.nasaspaceflight.com/index.php?action=dlattach;topic=36313.0;attach=632192;image)
Dr. Rodal just s curious question. Do you consider to use fractal geometry when trying to identify the mode shapes? I was just wondering, when I know fractal geometry actually works with all kinds of crazy repeating patterns as far as I know. EmDrive might be the case.
"A fractal is a natural phenomenon or a mathematical set that exhibits a repeating pattern that displays at every scale" https://en.wikipedia.org/wiki/Fractal

Why use a logarithm scale for showing the magnitude of the electromagnetic fields?
What advantage is there in using a logarithmic scale? I see disadvantages as a logarithmic scale would distort the fields and really distort the mode shapes which are usually displayed in texts with a linear scale and hence become difficult to recognize. We want to be able to identify the mode shapes so that we know whether TE or TM, etc.
If your concern is to appreciate level ratio of more than 1000 on a screen, a dB scale makes sense.
Efield pattern for the TE01 mode below cutoff, plotted with a dB scale and a lower limit of 40 dB.
()

https://people.math.osu.edu/gerlach.1/math/BVtypset/node122.html
About hankel and bessel, see (512) and (513) of property 14 of above reference.
For non integer order, just a linear combination and can be inverted, expressing hankel functions by bessel functions and vice versa. The boundary conditions will set the coeficients of one or other representation.
The spherical ones are basicaly related by a (1/r)^0.5 factor.
You prefer bessel, and I prefer hankel.
"É trocar seis por meia dúzia".
:)
...
Also, by assuming a standing wave solution, you are precluding there is any effect due to propagating waves. As @Ricvil said, the standing wave is the superposition of two propagating waves. The effect we are looking for pretty much requires that these two waves are not equal. So I don't think the assumption that beta=0 because they are standing waves is a good idea. It is like assuming the force we are looking for, doesn't exist.
I think it is required that beta =/= 0, or else the wave has no momentum to transfer to the frustum.
Thanks.
Todd
Of course. But that is all that I solved. As I wrote in my post I only used the standing wave solution. Unequal travelling waves in opposite directions, interference, or other effects present with the RF feed on, or a force, are not going to be found here. I used only the standing wave solution, for which there is no force according to Maxwell's solution.
Before we go to Hankel functions we have to start from a known solution to see whether the method is sound and gives a correct solution to a known problem.
Particularly when Zeng and Fan have the incorrect solution and nobody from the peer reviewers caught it.
To consider a waveguide or an RF cavity transient solution I would have to use the same methodology using spherical Hankel functions instead of spherical Bessel functions, as I had posted previously :)
Piano piano si va sano e lontano
()

Several of the EM Drive builders have experienced differences in measured thrust based on the direction that the Frustums smaller end was facing at the time ("Horizontally") during testing. Should some other test data be included as standard test data, to better exclude/include possible contributing factors to current test results?
a) Could this be somehow related to what direction the earth is rotating in comparison to the longitude, latitude and altitude and starting position relative to degrees from true north of the Frustums small end when the Frustum is mounted facing horizontally, at the testers location at the time of testing?
b) Could this be somehow related to what the earths current magnetic field is at any given longitude, latitude and altitude of the testers location at the time of testing?
c) Could the Atmospheric pressure/Barometric Pressure at the testers location be contributing to differences in measured thrust at the time of testing? After all some of the measured thrust has been no greater than enough to move a snowflake.
d) Could Relative Humidity at a specific temperature at the testers location at the time of testing be contributing to measured thrust at the testers location?
e) Include vertical thrust measurements when the Frustum is mounted and facing horizontally as secondary test data. During the same test window and starting with the Frustums small end being at the same degree from true north postion as any horizontal test which was done in the same test window. Vice versa ("minus any need to start at any true north position") for Frustums being tested with their smaller end being tested vertically.
Point being: Could any of the above, be causing any differences in measured thrust during testing?
Would it not be a prudent thing to be including all the above information at least at this time with other test data results?
At time of test:
1. Longitude
2. Latitude
3. Altitude
4. Barometric Pressure
5, Relative Humidity ("With temperature for reference")
6. Horizontal starting direction of Frustum smaller end in degrees from true north, when the Frustum is mounted facing horizontally
7. Measurements of vertical thrust not just horizontal thrust when the Frustums small end is mounted and facing horizontally. Using the same starting position that any prior test, during the same test window that horizontal thrust testing started from. Vice versa for Frustums being tested with their smaller end being tested vertically ("minus any need to start at any true north position").
To be able to see if any of the above are somehow involved or have any impact on whatever test results are being seen and produced at any specific time. Even when using the same EM Drive build, at the same location, during different testing times.
Any anomalies or even valid and real EM results which might be involved in producing thrust results during testing of EM Drives, most likely are not likely to always present themselves currently, as being exclusively limited to only a pure horizontal or vertical thrust plane of a Frustum undergoing a test.
Any thrust being generated for any reasons. Must be being currently generated at different angles ("Simultaneously in both the horizontal and vertical directions") in reference to the mounting plane of any given Frustum build and test setup. Yet thrust is only being measured ("currently") in the absolute direction that the Frustum small/large end was currently pointing in. At the time of any given test.
Edit: Typos
Don

For Shawyer to try and patent this before there was even a dream of a viable commercial product is ludicrous.
I vigorously disagree. Mr. Shawyer has, hypothetically, discovered something that we thought was impossible. As such, in addition to his Nobel prize, he is fully entitled to own that intellectual property for the full duration of the patent and take full financial advantage of it. His right to make a billion dollars on this is just as real as your right to make a billion dollars on any improvements you make to it.
A patent is a reward and incentive for the inventor's investment of effort, risk, failures, money, time, and life in creating a device or idea. If they choose to open source it or freely license it then that is their choice. They are under no ethical or moral obligation to do so.
He should have opened it up to research at the beginning.
He did. He's been writing about it publicly for a decade to anyone who would listen. For his trouble he's been called a fraud and charlatan. He's been mocked and ridiculed. To imply that he's hoarded this to himself is a particularly bitter insult.
Based on what I know, the current iteration is obviously not viable.
Your knowledge is incorrect. He discovered the Shawyer effect and then spent years inventing, experimenting, and refining devices that generated thrust from RF energy. The device accomplished the "impossible". That certainly seems "viable" to me.
If members of the public are able to own a personal stake in something as evolutionary as this, some will gladly invest enormous amounts of effort, even with no guarantee of any financial reward or any success; like us.
Mr. Shawyer built this technology "with no guarantee of any financial reward or any success." How is his contribution somehow inferior to what we would create?
So can it be done? Should it be done? If so, we need help...
We just have to make it roll. The rest is history.
Patent law is not simple at all. Even worse, it varies wildly by country and it changes over time. In the US, there is a tiny window for building a copy of a device to determine the accuracy of the specification, for the sole purpose of gratifying a philosophical taste, or curiosity, or for mere amusement. I currently work within those exceptions. Any use beyond that should be negotiated with Mr. Shawyer.
eag
P.s. ... don't forget that Cannae has patents on this kit too. Even though their drive !did not work! they still own part of the IP.
Good, thank you for lighting off discussion. Now I want to make it clear that my intent is NOT to deprive Shawyer of his rights to anything. The intent is to spur development. Simple as that.
The intent is to first find any evidence whatsoever which will prove the existence of the "Shawyer effect." Nobody has been able to prove that these devices function as useful thrusters. Folks may argue, well Shaywer himself proved it or Eagleworks did. There is no consensus that the "Shawyer effect" exists, therefore any utility to such an invention is simply conjecture. So as it stands right now, Shawyer owns the patent to a bet, a gamble. A 50/50 yes or no that he has something useful. The consensus of the world is that it doesn't work. I am agnostic.
I might as well patent the light saber right now because eventually somebody else will figure out the details for me, right?
I did bring up the idea to him of opening up his invention for open source development*. I got no answer. No surprise there. I will absolutely tell you, that if the answer is eureka it really works..and the consensus is that it works, he'll get his Nobel and loads of cash.
But there will be no protection provided by his patents. Bigger businesses with deeper pockets will just take it. I don't want to see that happen. It happens all the time, especially in tech.
So my vision here is:
1) Confirm that the Shawyer effect even really exists (which is what we're all doing here right now). If not, then put it in the closet with the lifters.
2) If we learn enough so as to make a meaningful contribution to theory or engineering which can warrant a clear reason to say we have something unique, then
3) Fork it and open it up.
Your knowledge is incorrect. He discovered the Shawyer effect and then spent years inventing, experimenting, and refining devices that generated thrust from RF energy. The device accomplished the "impossible". That certainly seems "viable" to me.
This quote tells me that you believe EmDrive really works and is absolutely useful.
* http://www.teslamotors.com/blog/allourpatentarebelongyou (like this)
Edits: readability

https://www.reddit.com/r/EmDrive/comments/3gkwcz/build_complete_initial_testing_done_emdrive_build/
New EmDrive test results by PaulTheSwag posted few minutes ago on the reddit.

Shawyer has enough problems with the theory people, and is utterly out of his depth in that domain. Therefore for Shawyer to win, he has to succeed experimentally. This means inter alia reproducibility. Unfortunately for Shawyer, he has not opened up in the sense of seeding several different labs with identical devices whose parameters can be varied so as to enact various control protocols. Nobody knows the true details of that turntable device. He fails by not sharing. He will not be believed.
What else is there? Low SNR from EW, confusing results from Cannae, but stellar reports from Yang whose lab is protected by the Chinese military. That's about as opposite to "open" as you can get, and therefore the most suspicious. We draw a blank experimentally too, across the board.
So the only way out here is what people on this forum are doing  building it themselves. It doesn't have to be this way, but it's been forced to be this way.

https://www.reddit.com/r/EmDrive/comments/3gkwcz/build_complete_initial_testing_done_emdrive_build/
New EmDrive test results by PaulTheSwag posted few minutes ago on the reddit.
Dramatic in terms of the large measured thrust levels, but confusing too. Why does the measured thrust bang up and down like that under constant input power? Is this oscillation about the fulcrum? Is it a ballistic measuring device?

just a note on the theory side
it's interesting to find that resonant cavities in particle accelerators (and other applications) there is an unwanted effect called lorentz force which i've seen mention here before a few times. they fight against this effect because it induces various distortions including to the body of the cavity. maybe what the EM drive does is to amplify this effect instead.
the very name 'lorentz' in interesting as his equations are at the core of relativity, in terms of the lorentz transformation in special relativity, and the lorentz force equation as an input to the electromagnetic stress–energy tensor in general relativity.

Dr Rodal, I think there is a problem again.
Standing waves.
In the cavity, at least, the fields are superpositions of two counter propagating waves, then one has (to simplify)
E=[a.exp(gamma.r)+b.exp(gamma.r)].F(tetha,phi)
Repair, the expression above is just a aproximate model to fit the fields by exponential functions, where the correct is to use fractional spherical hankel functions (for spherical ends cavitys), where a,b and gamma will fataly be functions of r. At r>>1 the spherical hankel function decay with 1/r.
Then how to differentiate a destructive interference at node fields from a infinity attenuation?
Worse, even with a,b and gamma being constants, when one take the derivative of E above, because the two signals of gamma (outward/inward from/to apex cone) one has
dE/dr=gamma[a.exp(gamma.r) b.exp(gamma.r)].F(theta,phi), and we lost original E function, then imagine with a,b and gamma being r functions.
This is just my way to think. You may, of course, disagree. :)
There is NO approximation, and there is no fitting. There is NO exponential fit, because γ is not a constant here, γ is a function of r, defined to give the identical part of E_{θ} that is solely expressible in term of r . The meaning of γ is only as described by the mathematical expression, not more and not less.
γ is not a closedform expression, it is not expressible by any known function known in any text. γ is given by Wolfram Mathematica as the solution of the differential equation, it is NOT a known classical function, it is NOT an exponential with a constant exponent multiplying r.
It is just a mapping of the original function into another function that gives exactly the same result.
It is exactly the same.
The solution E_{θ} in terms of γ exponential and A is identical to the one expressed in terms of Spherical Bessel functions and the Legendre Associated functions, it is just expressed in a different form.
Tomorrow I will post a comparison plot to show this identity. It is identical by construction
/////////////////////////////////////////////////////////////////
As to interference, separate waves and other issues present in the transient when the RF feed is ON, I have not dealt with those aspects. I have only dealt with the standing wave solution. To deal with the transient with the RF feed ON, yes I would have to use Hankel functions.
As promised, I attach a plot showing that the result of exponentiating the gamma function γ I derived (times r)
E_{θ} = A e^{  γ r}
results in exactly the same function as the exact electric field E_{θ} divided by A: E_{θ} /A. There is no approximation.
Again, this is by construction. The gamma function γ(r) cannot be expressed in terms of any known function appearing in any textbook, it has to be obtained as a numerical solution to the differential equation:
r dγ/dr + γ =  (1/E_{θ})*dE_{θ}/dr
By contrast, the γ function as defined by Zeng and Fan (who define it as γ =  (1/E_{θ})*dE_{θ}/dr )
does not result in E_{θ} / A = e^{  γ r} as is easy to show. See the bottom attached image, showing divergence at small radius near the small base.
A plot of what proper definition of the gamma function γ(r) looks like is shown here:
http://forum.nasaspaceflight.com/index.php?topic=38203.msg1415088#msg1415088

https://www.reddit.com/r/EmDrive/comments/3gkwcz/build_complete_initial_testing_done_emdrive_build/
New EmDrive test results by PaulTheSwag posted few minutes ago on the reddit.
Dramatic in terms of the large measured thrust levels, but confusing too. Why does the measured thrust bang up and down like that under constant input power? Is this oscillation about the fulcrum? Is it a ballistic measuring device?
Apply a sudden force to a undamped fulcrum and it will do as shown. Oscillate up and down before settling into the final displacement.
His non lengthened frustum resonants in TE212 mode at 2.4219 GHz, which should be inside the magnetron's output freq range. Predicted Force generation is around 200mN at 1,000Ws, assuming a Q of 50,000.
At his +50mm length extension, should get TE013 resonance at 2.4439GHz. Assuming the Q stays the same, Force grows to around 240mN. Additionally this frequency is closer to the centre frequency of the magnetron and should get more power inside the cavity.
My latest EMDrive calculator is here:
https://drive.google.com/file/d/0B7kgKijop0iUnlaXzc0OFVvc00/view?usp=sharing

https://www.reddit.com/r/EmDrive/comments/3gkwcz/build_complete_initial_testing_done_emdrive_build/
New EmDrive test results by PaulTheSwag posted few minutes ago on the reddit.
Dramatic in terms of the large measured thrust levels, but confusing too. Why does the measured thrust bang up and down like that under constant input power? Is this oscillation about the fulcrum? Is it a ballistic measuring device?
He says that he got much larger results with the extension to the truncated cone. I could not find an image for what the extension to the cone looks like, nor its dimensions. Could somebody please be so kind as to link to the image showing the extension and its dimensions ?
PS: I understand he says he used the NASA Eagleworks dimensions, if that is the case, the resonant frequency at near 2.45 GHz should be TM212 (transverse magnetic, same mode excited by Iulian Berca), instead of TE212 (transverse electric)

PS: I understand he says he used the NASA Eagleworks dimensions, if that is the case, the resonant frequency at near 2.45 GHz should be TM212 (transverse magnetic, same mode excited by Iulian Berca), instead of TE212 (transverse electric)
As calculated.

PS: I understand he says he used the NASA Eagleworks dimensions, if that is the case, the resonant frequency at near 2.45 GHz should be TM212 (transverse magnetic, same mode excited by Iulian Berca), instead of TE212 (transverse electric)
As calculated.
As calculated by NASA: 2.45 GHz TM212 (transverse MAGNETIC mode) (not TE212) for NASA's truncated cone dimensions (no dielectric insert)
My exact solution agrees with NASA
Full NASA report attached below

PS: I understand he says he used the NASA Eagleworks dimensions, if that is the case, the resonant frequency at near 2.45 GHz should be TM212 (transverse magnetic, same mode excited by Iulian Berca), instead of TE212 (transverse electric)
As calculated.
As calculated by NASA: 2.45 GHz TM212 (transverse MAGNETIC mode) (not TE212) for NASA's truncated cone dimensions (no dielectric insert)
My exact solution agrees with NASA
As calculated by NASA: 1.88 GHz TE212 (transverse ELECTRIC mode occurs at a much lower frequency than 2.45 GHz) for NASA's truncated cone dimensions (no dielectric insert)
My exact solution agrees with NASA

I'm still confused. Are we looking at a single impulsive event, or a steadystate force?

As calculated by NASA: 2.45 GHz TM212 (transverse MAGNETIC mode) (not TE212) for NASA's truncated cone dimensions (no dielectric insert)
My exact solution agrees with NASA
Full NASA report attached below
And the Force they measured when they excited the frustum in TM213 mode at the predicted freq was?

I'm still confused. Are we looking at a single impulsive event, or a steadystate force?
The unraveling of the EM Drive "force measurement" this is what is great about replications.
The South African experiment does not show a constant steadystate force.
His fulcrum is undamped and will oscillate for some time before settling at the final value. You know that so why the comment?

Calculation of resonant frequencies in cavities is wellknown and established. Has been replicated routinely in thousands of carefully designed experiments. Routinely done at CERN and other particle accelerators using Finite Element Analysis . The hundreds of thousands of readers of this thread can conduct their own calculations based on the NASA dimensions (see attached NASA report for dimensions frequencies and mode shape) and independently verify whether the mode shape at 2.45 GHz is TM212 or TE212

I'm still confused. Are we looking at a single impulsive event, or a steadystate force?
The unraveling of the EM Drive "force measurement" this is what is great about replications.
The South African experiment does not show a constant steadystate force.
His fulcrum is undamped and will oscillate for some time before settling at the final value. You know that so why the comment?
There is always some amount of damping in any setup (if there would be no damping we would be able to have perpetual motion machines, which is impossible). But fair enough, since I have not had a chance to do detailed modeling of his setup (I don't even know his dimensions) I withdraw my comments until I have the chance to model his setup.
Can you provide a link to his cone dimensions, masses, displacement/force measuring device, etc., for me to model his experiment?

PS: I understand he says he used the NASA Eagleworks dimensions, if that is the case, the resonant frequency at near 2.45 GHz should be TM212 (transverse magnetic, same mode excited by Iulian Berca), instead of TE212 (transverse electric)
As calculated.
As calculated by NASA: 2.45 GHz TM212 (transverse MAGNETIC mode) (not TE212) for NASA's truncated cone dimensions (no dielectric insert)
My exact solution agrees with NASA
As calculated by NASA: 1.88 GHz TE212 (transverse ELECTRIC mode occurs at a much lower frequency than 2.45 GHz) for NASA's truncated cone dimensions (no dielectric insert)
My exact solution agrees with NASA
Proof of frustum resonance in any mode is measured Force generation. No Force generation, means the mode and resonance calc is not correct.
What NASA needs to show is the S11 return loss scans for those frequencies. When you see the return loss dB dips, then you know there is a resonant mode. Need a different antenna to properly excite TE and TM modes.
EW's internal frustum length only needs to be 3mm longer than SA Paul's frustum length for the 2.445GHz resonance to turn into a 2.422GHz resonance.
Thus I suggest the attached does show a TE213 resonance that EW found, Paul in SA found and my spreadsheet predicts.

There is always some amount of damping in any setup (if there would be no damping we would be able to have perpetual motion machines, which is impossible). But fair enough, since I have not had a chance to do detailed modeling of his setup (I don't even know his dimensions) I withdraw my comments until I have the chance to model his setup.
Can you provide a link to his cone dimensions, masses, displacement/force measuring device, etc., for me to model his experiment?
https://www.reddit.com/r/EmDrive/comments/3gkwcz/build_complete_initial_testing_done_emdrive_build/

...
Proof of frustum resonance in any mode is measured Force generation. No Force generation, means the mode and resonance calc is not correct.
What NASA needs to show is the S11 return loss scans for those frequencies. When you see the return loss dB dips, then you know there is a resonant mode. Need a different antenna to properly excite TE and TM modes.
EW's internal frustum length only needs to be 3mm longer than SA Paul's frustum length for the 2.445GHz resonance to turn into a 2.422GHz resonance.
Thus I suggest the attached does show a TE212 resonance that EW found, Paul in SA found and my spreadsheet predicts.
Therefore according to you CERN, MIT, CalTech, Princeton, etc., and anybody that calculates frequencies and mode shapes of resonant cavities using Finite Element analysis and exact solutions are getting wrong results and they should immediately switch to using your Excel spreadsheet to calculate resonant frequencies and mode shapes of resonant cavities?
XRay and others in this thread, for example should replace their methods of analysis and start using your Excel spreadsheet to calculate resonant frequencies and mode shapes?

Calculation of resonant frequencies in cavities is wellknown and established. Has been replicated routinely in thousands of carefully designed experiments. Routinely done at CERN and other particle accelerators using Finite Element Analysis . The hundreds of thousands of readers of this thread can conduct their own calculations based on the NASA dimensions (see attached NASA report for dimensions frequencies and mode shape) and independently verify whether the mode shape at 2.45 GHz is TM212 or TE212
As I said proof of the calc is seeing a S11 return loss dip at the calculated freq. Is easy to do. EW has the VNA to do the scan. So why no scans to back the calcs?

...
Proof of frustum resonance in any mode is measured Force generation. No Force generation, means the mode and resonance calc is not correct.
What NASA needs to show is the S11 return loss scans for those frequencies. When you see the return loss dB dips, then you know there is a resonant mode. Need a different antenna to properly excite TE and TM modes.
EW's internal frustum length only needs to be 3mm longer than SA Paul's frustum length for the 2.445GHz resonance to turn into a 2.422GHz resonance.
Thus I suggest the attached does show a TE212 resonance that EW found, Paul in SA found and my spreadsheet predicts.
Therefore according to you CERN, MIT, CalTech, Princeton, etc., and anybody that calculates frequencies and mode shapes of resonant cavities using Finite Element analysis and exact solutions are getting wrong results and they should immediately switch to using your Excel spreadsheet to calculate resonant frequencies and mode shapes?
Point was if NASA had done a S11 return loss scan on the real frustum, to find the freq the return loss dB drops, they would have confirmed their calcs were correct.
As for the other guys they probably use SuperFish to model and design their cavities.
http://www.lanl.gov/projects/feynmancenter/technologies/software/poissonsuperfish.php
Do a Google search for superfish resonant cavity to turn up a lot of hits.
https://www.google.com.au/search?q=superfish+resonant+cavity&oq=superfish+resonant+cavity&aqs=chrome..69i57.7017j0j4&sourceid=chrome&es_sm=122&ie=UTF8

There is always some amount of damping in any setup (if there would be no damping we would be able to have perpetual motion machines, which is impossible). But fair enough, since I have not had a chance to do detailed modeling of his setup (I don't even know his dimensions) I withdraw my comments until I have the chance to model his setup.
Can you provide a link to his cone dimensions, masses, displacement/force measuring device, etc., for me to model his experiment?
https://www.reddit.com/r/EmDrive/comments/3gkwcz/build_complete_initial_testing_done_emdrive_build/
I see the dimensions of the truncated cone there but I don't see enough details to do any modeling: no masses and most bothersome, no dimensions or description of the testing setup except:
A knifeedge fulcrum is composed of a long balancing beam which rests on two razor edges. This allows for very sensitive measurement of minuscule forces such as those produced by an EMDrive.
One issue that could become a problem is air currents which could potentially give false positives. Once the frustum is set up on the fulcrum with a counterweight the fulcrum will be left for 10 minutes in the testing room. The setup will then be powered on for a burst of 10 seconds.
The frustum will be suspended in an upright position below the beam of the fulcrum. A laser will be attached to the other end of the beam which will project onto graph paper. This setup will detect any upwards or downwards forces on the frustum. A camera is positioned perpendicular to the graph paper to make measurements of the laser point.
One for example could say that the erratic oscillations are just due to convection currents in the air and unrelated to the EM Drive (as shown by the videos of rfmwguy). Not way to know from this brief description.

Calculation of resonant frequencies in cavities is wellknown and established. Has been replicated routinely in thousands of carefully designed experiments. Routinely done at CERN and other particle accelerators using Finite Element Analysis . The hundreds of thousands of readers of this thread can conduct their own calculations based on the NASA dimensions (see attached NASA report for dimensions frequencies and mode shape) and independently verify whether the mode shape at 2.45 GHz is TM212 or TE212
As I said proof of the calc is seeing a S11 return loss dip at the calculated freq. Is easy to do. EW has the VNA to do the scan. So why no scans to back the calcs?
My limited experience with the comsol EM module is it works fine!
Without calculations it is difficult(not possible) to say a specific peak in the Sparameter plot is the target resonance. I am sure EW did both, calculations and measurements

My limited experience with the comsol EM module is it works fine!
Without calculations it is difficult(not possible) to say a specific peak in the Sparameter plot is the target resonance.
Sure understand that. But if you do a scan on a cavity and the predicted resonance is not there, then what?
As far as I know, there were no scans to back up all the mode and freq calculations that EW did.

I see the dimensions of the truncated cone there but I don't see enough details to do any modeling: no masses and most bothersome, no dimensions or description of the testing setup except:
This info is in his report. How is this not enough info to do an analysis?
Hypothesis Test 1 – NASA cavity size at 2450MHz
When microwaves are supplied into the cavity, a thrust will be produced by the frustum.
Hypothesis Test 2 – Frustum extended by 50 mm excited at 2450MHz
When microwaves are supplied into the cavity, a greater thrust will be produced by the increase in resonance.
The specifications of the frustum are as follows
Height (perpendicular): 228 mm (1) 278mm (2)
Big Diameter: 279.4mm
Small Diameter: 158.8mm
Material: Copper
Antenna location: 34.29 mm from Big Diameter

I see the dimensions of the truncated cone there but I don't see enough details to do any modeling: no masses and most bothersome, no dimensions or description of the testing setup except:
This info is in his report. How is this not enough info to do an analysis?
Hypothesis Test 1 – NASA cavity size at 2450MHz
When microwaves are supplied into the cavity, a thrust will be produced by the frustum.
Hypothesis Test 2 – Frustum extended by 50 mm excited at 2450MHz
When microwaves are supplied into the cavity, a greater thrust will be produced by the increase in resonance.
The specifications of the frustum are as follows
Height (perpendicular): 228 mm (1) 278mm (2)
Big Diameter: 279.4mm
Small Diameter: 158.8mm
Material: Copper
Antenna location: 34.29 mm from Big Diameter
Do you understand how to model the dynamic oscillations of the knifeedge fulcrum composed of a long balancing beam which rests on two razor edges ? :)
You repeated the dimensions of the truncated cone, again, as I wrote:
I see the dimensions of the truncated cone there but I don't see enough details to do any modeling: no masses and most bothersome, no dimensions or description of the testing setup except
no dimensions of the knifeedge fulcrum composed of a long balancing beam which rests on two razor edges
no masses
Is there even a photograph from which one can guesstimate dimensions of the "long balancing beam", etc.?

Do you understand how to model the dynamic oscillations in a testing setup ?
1st you need to confirm resonance. Last time that I remember you commented there was no resonance for the EW copper frustum at 2.45GHz. Might try that again and over the range +30MHz.

Do you understand how to model the dynamic oscillations in a testing setup ?
1st you need to confirm resonance. Last time that I remember you commented there was no resonance for the EW copper frustum at 2.45GHz. Might try that again and over the range +30MHz.
Sigh. Hand over the discussion with TheTraveller of the South African experiment to you deltaMass and Frobnicat ;)
PS: I never said that there was no resonance for the EW copper frustum at 2.45GHz
that is a complete canard.
I even gave the TM212 resonance frequencies to Mulletron for his NASAdimensioned experiment at 2.45 GHz and put the Iulian Berca mode shape TM212 at 2.45GHz in the EM Drive wiki accordingly.
Unbelievable for TheTraveller to say such a canard. I even submitted to his attention (and SeeShell quoted in one of her messages) a complete table, for all NASA calculated frequencies from below 1GHz to 2.5GHz comparing my exact solution results to NASA results including TM212 at 2.45Ghz

It becomes obvious that not every DIY builder has the same experience level of building experimental setups. By this I do not mean that there is a lack of experience on a technical skilllevel, but on the data reporting...
Would it make sense to build some sort of checklist that would include all the needed required data, so that it can better assist those who work on a theoretical level?
Seeshell , fe, has many years of experience in building experimental devices, but not everybody is used to work in a scientific research environment and knows how to bring all their data.
Some guidelines for experimental reporting could help everybody, no?

My limited experience with the comsol EM module is it works fine!
Without calculations it is difficult(not possible) to say a specific peak in the Sparameter plot is the target resonance.
Sure understand that. But if you do a scan on a cavity and the predicted resonance is not there, then what?
As far as I know, there were no scans to back up all the mode and freq calculations that EW did.
I had this problem several times. Scan a larger bandwidth and you will find the modes not very far away. The problem is not the calculation (that works), the problems are imperfections in the builded cavity itself namy the dimensions, the antenna feed, the cavity material and so on. All that are systematic errors and causes frequency offsets to the calculated target frequencies.
I don't know why EW don't show these plots ??? looks good in such a paper ;)
EDIT
Different calculation methods also leads to different Resultats (often only a few MHz).

https://www.reddit.com/r/EmDrive/comments/3gkwcz/build_complete_initial_testing_done_emdrive_build/
New EmDrive test results by PaulTheSwag posted few minutes ago on the reddit.
Interesting build, well documented. Would have liked to have seen some video. Seems like a similar setup to my fulcrum, which is all mechanical...eliminates sevaral digital variables. Nice use of solid copper. His extended fulcrum is similar to my nsf1701. Feedpoint similat to spr and julians null point. Julian moved feedpoint halfway up frustum to get results. Congrats to his gold medal! That opens doors for further research for this young DIYer...bravo.

My limited experience with the comsol EM module is it works fine!
Without calculations it is difficult(not possible) to say a specific peak in the Sparameter plot is the target resonance.
Sure understand that. But if you do a scan on a cavity and the predicted resonance is not there, then what?
As far as I know, there were no scans to back up all the mode and freq calculations that EW did.
I have a simple VNA I plan to use to find resonance frequencies and it's simply a verification to the calculations. Over the years I know formulas are fine but deal in a virtual world and the calculated vs the real world seldom agree 100%. That's why the some of the waveguides are tuned with guys with tiny little hammers or with stub tuner screws.
Even NASA should have used VNAs in air and vacuum just to check and I'm not sure they did.
Back to working and lurking.
shell

It becomes obvious that not every DIY builder has the same experience level of building experimental setups. By this I do not mean that there is a lack of experience on a technical skilllevel, but on the data reporting...
Would it make sense to build some sort of checklist that would include all the needed required data, so that it can better assist those who work on a theoretical level?
Seeshell , fe, has many years of experience in building experimental devices, but not everybody is used to work in a scientific research environment and knows how to bring all their data.
Some guidelines for experimental reporting could help everybody, no?
I second this and have also posted suggestions on additional standard test data that at this stage of testing EM Drives might be helpful to include or at least consider:
http://forum.nasaspaceflight.com/index.php?topic=38203.msg1415202#msg1415202
At some point should there not be at least suggested test data result standards that all EM Drive builders could reference in the Wiki? Not mandating that they be used. But suggesting they should be.
Don

https://www.reddit.com/r/EmDrive/comments/3gkwcz/build_complete_initial_testing_done_emdrive_build/
New EmDrive test results by PaulTheSwag posted few minutes ago on the reddit.
Interesting build, well documented. Would have liked to have seen some video. Seems like a similar setup to my fulcrum, which is all mechanical...eliminates sevaral digital variables. Nice use of solid copper. His extended fulcrum is similar to my nsf1701. Feedpoint similat to spr and julians null point. Julian moved feedpoint halfway up frustum to get results. Congrats to his gold medal! That opens doors for further research for this young DIYer...bravo.
That does my heart wonders to see a young man tackel this. Good for him!

It becomes obvious that not every DIY builder has the same experience level of building experimental setups. By this I do not mean that there is a lack of experience on a technical skilllevel, but on the data reporting...
Would it make sense to build some sort of checklist that would include all the needed required data, so that it can better assist those who work on a theoretical level?
Seeshell , fe, has many years of experience in building experimental devices, but not everybody is used to work in a scientific research environment and knows how to bring all their data.
Some guidelines for experimental reporting could help everybody, no?
I agree. I had mentioned a while ago that it would be nice to create a NI labview standard for all drives to tested against. We should think about the methods and data logging. From that point, we test at a single test bed. I think shell is well on her way to creating a standardized test facility. With that will come the need to develop standardized test software, sensors., et al.
Of course I have not asked shell if she's interested in becoming THE global test facility...;)

It becomes obvious that not every DIY builder has the same experience level of building experimental setups. By this I do not mean that there is a lack of experience on a technical skilllevel, but on the data reporting...
Would it make sense to build some sort of checklist that would include all the needed required data, so that it can better assist those who work on a theoretical level?
Seeshell , fe, has many years of experience in building experimental devices, but not everybody is used to work in a scientific research environment and knows how to bring all their data.
Some guidelines for experimental reporting could help everybody, no?
I agree. I had mentioned a while ago that it would be nice to create a NI labview standard for all drives to tested against. We should think about the methods and data logging. From that point, we test at a single test bed. I think shell is well on her way to creating a standardized test facility. With that will come the need to develop standardized test software, sensors., et al.
Of course I have not asked shell if she's interested in becoming THE global test facility...;)
I might be up for it and I kind of like the idea. I cringe at the lack of safety used to get something to thrust and I see so many coming online right now. It's going to be desperately needed and standardized... but...
We're gonna need a bigger boat.
https://www.youtube.com/watch?v=QT9BeGNnCqw

Apologies.
The mode I reported for the South African frustum as TE212 was actually TE213 as can be clearly seen on the screenshot.

Unbelievable for TheTraveller to say such a canard. I even submitted to his attention (and SeeShell quoted in one of her messages) a complete table, for all NASA calculated frequencies from below 1GHz to 2.5GHz comparing my exact solution results to NASA results including TM212 at 2.45Ghz
We were discussing the EW frustum and the lack of any 2.45GHz resonance in any mode, which we both agreed with. We both ending up suggested the EW copper frustum's length needed to be increased.
Remember or shall I dig it out? Trust me my memory is VERY good.

Unbelievable for TheTraveller to say such a canard. I even submitted to his attention (and SeeShell quoted in one of her messages) a complete table, for all NASA calculated frequencies from below 1GHz to 2.5GHz comparing my exact solution results to NASA results including TM212 at 2.45Ghz
We were discussing the EW frustum and the lack of any 2.45GHz resonance in any mode, which we both agreed with. We both ending up suggested the EW copper frustum's length needed to be increased.
Remember or shall I dig it out? Trust me my memory is VERY good.
That is a canard. For you to insist on these false accusations without even bothering to verify whether your longterm memory is correct, after you just had to apologize for your shortterm memory confusion (http://forum.nasaspaceflight.com/index.php?topic=38203.msg1415282#msg1415282) is just unfathomable :) .

Does anyone have any experience with this?
http://www.amazon.com/ADXL345DigitalSensorsAccelerationArduino/dp/B008B4W1QS/ref=sr_1_2?s=automotive&ie=UTF8&qid=1439307463&sr=12&keywords=sensor+acceleration
Never mind I found a spec sheet on it.... thx
Just to log data for the stand... I'm liking the Pi
compass magnetometer IC, I2C, HMC5883L, PCB module, for Arduino microcontroller
http://www.gearbest.com/developmentboards/pp_156161.html?currency=USD&gclid=CNLS1LCzoccCFQkFaQod43IBVg
http://www.gearbest.com/developmentboards/pp_156161.html?currency=USD&gclid=CNLS1LCzoccCFQkFaQod43IBVg

I had mentioned a while ago that it would be nice to create a NI labview standard for all drives to tested against.
Would it be possible to use:
http://www.myopenlab.de/startseite.html
Open source but simple, (too simple?)..

Unbelievable for TheTraveller to say such a canard. I even submitted to his attention (and SeeShell quoted in one of her messages) a complete table, for all NASA calculated frequencies from below 1GHz to 2.5GHz comparing my exact solution results to NASA results including TM212 at 2.45Ghz
We were discussing the EW frustum and the lack of any 2.45GHz resonance in any mode, which we both agreed with. We both ending up suggested the EW copper frustum's length needed to be increased.
Remember or shall I dig it out? Trust me my memory is VERY good.
That is a canard. For you to insist on these false accusations without even bothering to verify whether your longterm memory is correct, after you just had to apologize for your shortterm memory confusion (http://forum.nasaspaceflight.com/index.php?topic=38203.msg1415282#msg1415282) is just unfathomable.
As for my long term memory it is correct:
http://forum.nasaspaceflight.com/index.php?topic=37642.msg1390632#msg1390632
What about yours?
As for the mode confusion, we all make mistakes, shall I point out a few of yours?

It becomes obvious that not every DIY builder has the same experience level of building experimental setups. By this I do not mean that there is a lack of experience on a technical skilllevel, but on the data reporting...
Would it make sense to build some sort of checklist that would include all the needed required data, so that it can better assist those who work on a theoretical level?
Seeshell , fe, has many years of experience in building experimental devices, but not everybody is used to work in a scientific research environment and knows how to bring all their data.
Some guidelines for experimental reporting could help everybody, no?
I agree. I had mentioned a while ago that it would be nice to create a NI labview standard for all drives to tested against. We should think about the methods and data logging. From that point, we test at a single test bed. I think shell is well on her way to creating a standardized test facility. With that will come the need to develop standardized test software, sensors., et al.
Of course I have not asked shell if she's interested in becoming THE global test facility...;)
I regard your work & Shell's as being the high bar that other DIY builders should aspire too.

I had mentioned a while ago that it would be nice to create a NI labview standard for all drives to tested against.
Would it be possible to use:
http://www.myopenlab.de/startseite.html
Open source but simple, (too simple?)..
Not a bad thought, it is a little simple but somewhat unknown for many. Maybe we can still use Wiki but setup a spread sheet layout with most of the information and a link to more detailed data. I know every test will not use or need some of the data points.
I've just ordered magnetic compass detectors and acceleration detectors on the fulcrum beam. Not extremely sensitive stuff, but it will give some needed baseline data. I'll also be recording date, time, temp, humidity of the lab.

Unbelievable for TheTraveller to say such a canard. I even submitted to his attention (and SeeShell quoted in one of her messages) a complete table, for all NASA calculated frequencies from below 1GHz to 2.5GHz comparing my exact solution results to NASA results including TM212 at 2.45Ghz
We were discussing the EW frustum and the lack of any 2.45GHz resonance in any mode, which we both agreed with. We both ending up suggested the EW copper frustum's length needed to be increased.
Remember or shall I dig it out? Trust me my memory is VERY good.
That is a canard. For you to insist on these false accusations without even bothering to verify whether your longterm memory is correct, after you just had to apologize for your shortterm memory confusion (http://forum.nasaspaceflight.com/index.php?topic=38203.msg1415282#msg1415282) is just unfathomable.
As for my long term memory it is correct:
http://forum.nasaspaceflight.com/index.php?topic=37642.msg1390632#msg1390632
What about yours?
As for the mode confusion, we all make mistakes, shall I point out a few of yours?
There is something wrong with your comprehension:
1)The quotation you provide is NOT for the NASA dimensions it is for RFMwguy dimensions
2) In the quotation you provide I explicitly say that there is no such thing as "no resonance" because of mode participation at these frequencies, the complete opposite of what you claim
Sorry, I don't agree with the word "will not resonate" in absolute terms. You probably mean "will not resonate at the highest Q". There is always a spectral response of resonance, which will contains peaks with different amplitude at different frequencies.
3) I never stated "will not resonate". You are the one that stated that, and I explicitly answered that I did not agree with you.
4) There are many frequencies in the spectrum around 2.45 GHz for NASA and for RFMWguy. I would never state "not resonate" it is just a matter of what modes will participate the most.

It becomes obvious that not every DIY builder has the same experience level of building experimental setups. By this I do not mean that there is a lack of experience on a technical skilllevel, but on the data reporting...
Would it make sense to build some sort of checklist that would include all the needed required data, so that it can better assist those who work on a theoretical level?
Seeshell , fe, has many years of experience in building experimental devices, but not everybody is used to work in a scientific research environment and knows how to bring all their data.
Some guidelines for experimental reporting could help everybody, no?
I agree. I had mentioned a while ago that it would be nice to create a NI labview standard for all drives to tested against. We should think about the methods and data logging. From that point, we test at a single test bed. I think shell is well on her way to creating a standardized test facility. With that will come the need to develop standardized test software, sensors., et al.
Of course I have not asked shell if she's interested in becoming THE global test facility...;)
I regard your work & Shell's as being the high bar that other DIY builders should aspire too.
That's the nicest thing someone has said in a long time. I'm flattered and thank you.
Added: I think I'd like rfmwguy do the narration on my tests. I'll send you a script rfmwguy. ;)

Unbelievable for TheTraveller to say such a canard. I even submitted to his attention (and SeeShell quoted in one of her messages) a complete table, for all NASA calculated frequencies from below 1GHz to 2.5GHz comparing my exact solution results to NASA results including TM212 at 2.45Ghz
We were discussing the EW frustum and the lack of any 2.45GHz resonance in any mode, which we both agreed with. We both ending up suggested the EW copper frustum's length needed to be increased.
Remember or shall I dig it out? Trust me my memory is VERY good.
That is a canard. For you to insist on these false accusations without even bothering to verify whether your longterm memory is correct, after you just had to apologize for your shortterm memory confusion (http://forum.nasaspaceflight.com/index.php?topic=38203.msg1415282#msg1415282) is just unfathomable.
As for my long term memory it is correct:
http://forum.nasaspaceflight.com/index.php?topic=37642.msg1390632#msg1390632
What about yours?
As for the mode confusion, we all make mistakes, shall I point out a few of yours?
You are either very confused or there is something very wrong with you insisting with this canard:
1) The quotation you provide is NOT for the NASA dimensions it is for RFMwguy dimensions
2) In the quotation you provide I explicitly say that there is no such thing as "no resonance" because of mode participation at these frequencies, the complete opposite of what you claim
Sorry, I don't agree with the word "will not resonate" in absolute terms. You probably mean "will not resonate at the highest Q". There is always a spectral response of resonance, which will contains peaks with different amplitude at different frequencies.
3) I never stated "will not resonate". You are the one that stated that, and I explicitly answered that I did not agree with you.
The frustum dimensions quoted are for the copper EW frustum as the post clearly says.
At least Dr Rodal and I agree the standard EW frustum
Frustum big diameter m 0.2794000
Frustum small diameter m 0.1588000
Frustum centre length m 0.2286000
External Rf Hz 2,450,000,000
will not resonate at 2.45GHz.
What you said was while there were no high Q resonances at 2.45GHz, there may be low Q resonances, even though you gave no proof that there were any low Q resonances around 2.45GHz. Which there are not.
Point is we both agreed the EW frustum length needed to be increased and following that advise RFMwguy increased his frustum length.
So please now show me any modes that resonant at 2.45GHz with the EW copper frustum. If you can't then thanks for the verification that we agree there are no resonant modes at 2.45GHz for the EW frustum.

...
Point is we both agreed the EW frustum length needed to be increased and following that advise RFMwguy increased his frustum length.
So please now show me any modes that resonant at 2.45GHz with the EW copper frustum. If you can't then thanks for the verification that we agree there are no resonant modes at 2.45GHz for the EW frustum.
As I said before :
Sorry, I don't agree with the word "will not resonate" in absolute terms. You probably mean "will not resonate at the highest Q". There is always a spectral response of resonance, which will contains peaks with different amplitude at different frequencies.
I didn't agree with you then, and I don't agree with you now. Period. Case in point: the recent Meep runs showing mode participation from different modes. Nothing unusual about that.. :)
The only mode shape that has ever been verified for an EM Drive has been TM212 for NASA with a dielectric insert that matched TM212 NASA prediction at 1.94GHz. NASA predicts TM212 at 2.45GHz with the NASA dimensions and no dielectric. (It is well known that dielectric insert lower the natural frequency of a mode shape)
(http://forum.nasaspaceflight.com/xindex.php,qaction=dlattach,3Btopic=36313.0,3Battach=846719,3Bimage.pagespeed.ic.KVIUQGgNKt.webp)

...
Point is we both agreed the EW frustum length needed to be increased and following that advise RFMwguy increased his frustum length.
So please now show me any modes that resonant at 2.45GHz with the EW copper frustum. If you can't then thanks for the verification that we agree there are no resonant modes at 2.45GHz for the EW frustum.
As I said before :
Sorry, I don't agree with the word "will not resonate" in absolute terms. You probably mean "will not resonate at the highest Q". There is always a spectral response of resonance, which will contains peaks with different amplitude at different frequencies.
I didn't agree with you then, and I don't agree with you now. Period.
As I said in a previous email I don't plan to ever spend any time showing you anything.
Which say to me your exact solution can't predict the resonance mode for:
1) The Flight Thruster
2) The EW frustum
3) The SA replication of the EW frustum
4) The Tajmar frustum
5) The Iulian frustum
So of what value is a exact solution that can't match real world data.
Should add your exact solution for my frustum design, that was verified by the latest SPR design software, was so far off as to again show your so called "exact solution" is far from exact.

The only mode shape that has ever been verified for an EM Drive has been TM212 for NASA with a dielectric that matched TM212 NASA prediction. NASA predicts TM212 at 2.45GHz with the NASA dimensions.
And that is working well for them?
Getting lots of Force generation in atmo and vac are they?
BTW, the EW copper frustum is operating in a claimed TM212 mode at 1.937GHz and not at 2.45GHz.

Here are the two png sets scaled to the maximum range of the E and H fields for the t=0 time slice. The ranges are from field components as follows:
# ez all data range from 0.000245405 to 0.000245405. E field big end
# hx all data range from 0.000538633 to 0.000538633. H field big end
# ez all data range from 4.04811e05 to 4.04811e05. E field small end
# hy all data range from 0.000287974 to 0.000287974. H field small end
Please look these png's over closely to be sure that this is what you want to see as it will be considerable effort to scale the png files in this way for the general case.
Or do you need to see the side views for this t = 0 case?

Here are the two png sets scaled to the maximum range of the E and H fields for the t=0 time slice. The ranges are from field components as follows:
# ez all data range from 0.000245405 to 0.000245405. E field big end
# hx all data range from 0.000538633 to 0.000538633. H field big end
# ez all data range from 4.04811e05 to 4.04811e05. E field small end
# hy all data range from 0.000287974 to 0.000287974. H field small end
Please look these png's over closely to be sure that this is what you want to see as it will be considerable effort to scale the png files in this way for the general case.
Or do you need to see the side views for this t = 0 case?
Thank you for going through the trouble to do this.
1) Assuming that the longitudinal axis is the z axis, this looks indeed like a TE mode (transverse electric) as the Hz mode (magnetic field in the longitudinal direction) is strong and the Ez (electric field in the longitudinal direction) is weak
however...
2) The blue areas in the fields: they look like the magnitude has been clipped.
(http://forum.nasaspaceflight.com/xindex.php,qaction=dlattach,3Btopic=38203.0,3Battach=1055383,3Bimage.pagespeed.ic.hjMMacoPKv.webp)
They look like ContourPlots in Mathematica when I use PlotRange with a range smaller than the full magnitude, so the contours get cliped. I would double check whether magnitudes have not been clipped.
3) Is there some means to control the number of contour values in the contour plots? It looks to me like there are more contour levels than the number of colors available, as a result colors keep repeating themselves. What one wants is to have blue represent the lowest magnitude and red the highest magnitude, instead of red/green/blue/yellow patterns being repeated cyclically.
(http://forum.nasaspaceflight.com/xindex.php,qaction=dlattach,3Btopic=38203.0,3Battach=1055381,3Bimage.pagespeed.ic.p_0CAdsbWT.webp)

The numerical field intensity values may be available in some convenient way that I just don't know about, but I have looked. Other meepers looking would be very helpful.
They are available, just not convenienly, by using the "verbose" switch on h5topng. Unfortunately, using that will require two separate runs, but I guess any method would require two separate runs at some level. Here is the verbose output from generating one png file.
steve@stevep6720f:~$ h5topng v t 0 z 214 ./Shell2ddipoleloopout/hx.h5
Using colormap "gray" in file "/usr/share/h5utils/colormaps/gray".
grayscale color map (white to black)
2 color entries read from colormap file.
Scaling opacity by 1
data rank = 4

reading from "./Shell2ddipoleloopout/hx.h5", slice at 214 in z dimension, slice at 0 in t dimension.
data ranges from 0.00012754 to 0.00012754.
writing "./Shell2ddipoleloopout/hx.png" from 196x196 input data.
all data range from 0.00012754 to 0.00012754.
I manually made 12 runs of h5topng, and extracted the following data ranges.
Range of data values in Shell2ddipoleloop64out
slice t 00, z 15 Big end
ex all data range from 3.67269e05 to 3.67269e05.
ey all data range from 1.42517e05 to 1.42517e05.
ez all data range from 0.000245405 to 0.000245405.
hx all data range from 0.000538633 to 0.000538633.
hy all data range from 0.000356036 to 0.000356036.
hz all data range from 4.65749e05 to 3.78542e05.
slice t 00 z 214 Small end
ex all data range from 1.60461e05 to 1.60461e05.
ey all data range from 3.20985e05 to 3.20985e05.
ez all data range from 4.04811e05 to 4.04811e05.
hx all data range from 0.00012754 to 0.00012754.
hy all data range from 0.000287974 to 0.000287974.
hz all data range from 1.07156e05 to 1.61666e05.
As I understand you, what you need is to have three png files, ex, ey, ez scaled to the maximum range of the E components and three, hx hy, hz scaled to the maximum range for the H component  for each time slice and each of the 4 geometry slices per time slice. That would be the ez range and the hx range for the first case above, but note that max value and min value won't necessarily always be from the same component as the second hz range above indicates.
Scaling the range of values using this approach is quite unwieldy to do manually, as there are I believe 336 pngs for a standard data set as I have been using, but also, we might benefit by extending that data set to 2 full cycles, or even more.
Does anyone here want to volunteer to create a bash shell file that runs the data set in verbose mode capturing the terminal output in the log file, then scan that log file, extract the correct range of values and scale the h5topng max and min switches, then run the data set again for upload? Conceptually it should be straight forward but I only recognize bash in passing, are almost strangers. Of course one could use Octave or MatLab to read the log file and extract the pertinent data, or even write a purpose program that simply scans and extracts the data then writes a new shell file with as many h5topng command lines as needed. That might be safer and the 336 + command line shell file would be "throw away" so it wouldn't need to be "slick."
Please find attached a simple python program. Rename to h5topng_range.py. Usage:
python h5topng_range.py logfile filename.txt
Output is to stdout, so some post processing will be necessary to get this to run in bash (I'm on windows, no access to bash until tonight). Tested with version 3.x should work with 2.5+ but I haven't tested. Uses the argparse library which is standard in version 3.x.
For the sample h5topng output quoted above, contained in "filename.txt", this produces the output:
h5topng t 0 z 214 m 0.00012754 M 0.00012754 ./Shell2ddipoleloopout/hx.h5
The numbers are pulled from the "all range data from" line and not the "data ranges from" line. The "z" switch is parametric based on the "reading from" line. The "t" is hardcoded, but can be made parametric if necessary, the value after "t" is, of course, parametric.

About PaulTheSwag's experiment:
1. What differentiates the thrust profile from one where only an initial impulse was produced?
2. What is a "double knifeedge fulcrum"? It makes no sense to me.
3. Do we know the power value?

About PaulTheSwag's experiment:
1. What differentiates the thrust profile from one where only an initial impulse was produced?
2. What is a "double knifeedge fulcrum"? It makes no sense to me.
3. Do we know the power value?
2. Did you saw the pictures? http://imgur.com/a/iO7er

Ok since the photons inside the cavity are traveling in a medium at a group velocity <c, we can technically define a frame where the photon is at rest relative to the cavity walls. I can't justify a reason to not treat them as massive particles in calculations.
This is a special case since we're not dealing with photons in vacuum. Does this sound controversial to anyone? That means switching to relativistic momentum.
http://hyperphysics.phyastr.gsu.edu/hbase/relativ/relmom.html
This ref was shared by someone else recently and I think it is significant.
http://arxiv.org/abs/0708.3519

About PaulTheSwag's experiment:
1. What differentiates the thrust profile from one where only an initial impulse was produced?
2. What is a "double knifeedge fulcrum"? It makes no sense to me.
3. Do we know the power value?
2. Did you saw the pictures? http://imgur.com/a/iO7er
OK. I now understand the double knife edge (actually triple).

About PaulTheSwag's experiment:
1. What differentiates the thrust profile from one where only an initial impulse was produced?
2. What is a "double knifeedge fulcrum"? It makes no sense to me.
3. Do we know the power value?
2. Did you saw the pictures? http://imgur.com/a/iO7er
Nah  viel zu langsam.
Do you have a helpful answer?
Ich denke es ist dieses Teil auf dem Foto ;)

Dr Rodal, I think there is a problem again.
Standing waves.
In the cavity, at least, the fields are superpositions of two counter propagating waves, then one has (to simplify)
E=[a.exp(gamma.r)+b.exp(gamma.r)].F(tetha,phi)
Repair, the expression above is just a aproximate model to fit the fields by exponential functions, where the correct is to use fractional spherical hankel functions (for spherical ends cavitys), where a,b and gamma will fataly be functions of r. At r>>1 the spherical hankel function decay with 1/r.
Then how to differentiate a destructive interference at node fields from a infinity attenuation?
Worse, even with a,b and gamma being constants, when one take the derivative of E above, because the two signals of gamma (outward/inward from/to apex cone) one has
dE/dr=gamma[a.exp(gamma.r) b.exp(gamma.r)].F(theta,phi), and we lost original E function, then imagine with a,b and gamma being r functions.
This is just my way to think. You may, of course, disagree. :)
There is NO approximation, and there is no fitting. There is NO exponential fit, because γ is not a constant here, γ is a function of r, defined to give the identical part of E_{θ} that is solely expressible in term of r . The meaning of γ is only as described by the mathematical expression, not more and not less.
γ is not a closedform expression, it is not expressible by any known function known in any text. γ is given by Wolfram Mathematica as the solution of the differential equation, it is NOT a known classical function, it is NOT an exponential with a constant exponent multiplying r.
It is just a mapping of the original function into another function that gives exactly the same result.
It is exactly the same.
The solution E_{θ} in terms of γ exponential and A is identical to the one expressed in terms of Spherical Bessel functions and the Legendre Associated functions, it is just expressed in a different form.
Tomorrow I will post a comparison plot to show this identity. It is identical by construction
/////////////////////////////////////////////////////////////////
As to interference, separate waves and other issues present in the transient when the RF feed is ON, I have not dealt with those aspects. I have only dealt with the standing wave solution. To deal with the transient with the RF feed ON, yes I would have to use Hankel functions.
As promised, I attach a plot showing that the result of exponentiating the gamma function γ I derived (times r)
E_{θ} = A e^{  γ r}
results in exactly the same function as the exact electric field E_{θ} divided by A: E_{θ} /A. There is no approximation.
Again, this is by construction. The gamma function γ(r) cannot be expressed in terms of any known function appearing in any textbook, it has to be obtained as a numerical solution to the differential equation:
r dγ/dr + γ =  (1/E_{θ})*dE_{θ}/dr
By contrast, the γ function as defined by Zeng and Fan (who define it as γ =  (1/E_{θ})*dE_{θ}/dr )
does not result in E_{θ} / A = e^{  γ r} as is easy to show. See the bottom attached image, showing divergence at small radius near the small base.
A plot of what proper definition of the gamma function γ(r) looks like is shown here:
http://forum.nasaspaceflight.com/index.php?topic=38203.msg1415088#msg1415088
We continue this discussion now with the TE012 mode of Yang/Shell.
Unfortunately for TEmnp mode shapes with p>1 we encounter the problem that Ricvl was discussing:
1) γ is positive whether E_{θ} is positive or negative. The sign (whether + or  ) of E_{θ} is lost upon computation of γ(r) as a solution of
r dγ/dr + γ =  (1/E_{θ})*dE_{θ}/dr
because the sign of E_{θ} appears both in the numerator and the denominator of the right hand side, hence it cancels out, and it gets lost unless we account for it.
Therefore we can calculate γ(r) accurately, but upon substitution in
A e^{  γ r}
we have to account for whether the value corresponds to positive or negative values of the half wavepattern of E_{θ}. This is similar to inverse functions that lose track of sign information (for example the Square Root function). It is not a problem in computing γ(r), it is just a problem in inverting (which is not required) to verify that it corresponds to E_{θ}.
2) When p>1, we have more than one half wavepattern to match, normalization is more elaborate:
a) we normalize the maximum of the maximum halfwave pattern to one.
b) we scale the lower value of the maximum of the other halfwave pattern as follows:
Ln[(lower max halfwave pattern)/(max halfwave pattern)]/r (of lower max halfwave pattern)
We show below what γ(r) looks like using this scaling. We also show the Electric Field wave patterns for TE011 and TE012.
Both issues perhaps can be addressed by using Hankel functions and then taking E_{θ} as the real part. We will investigate this in the future.

Here are the two png sets scaled to the maximum range of the E and H fields for the t=0 time slice. The ranges are from field components as follows:
# ez all data range from 0.000245405 to 0.000245405. E field big end
# hx all data range from 0.000538633 to 0.000538633. H field big end
# ez all data range from 4.04811e05 to 4.04811e05. E field small end
# hy all data range from 0.000287974 to 0.000287974. H field small end
Please look these png's over closely to be sure that this is what you want to see as it will be considerable effort to scale the png files in this way for the general case.
Or do you need to see the side views for this t = 0 case?
Thank you for going through the trouble to do this.
1) Assuming that the longitudinal axis is the z axis, this looks indeed like a TE mode (transverse electric) as the Hz mode (magnetic field in the longitudinal direction) is strong and the Ez (electric field in the longitudinal direction) is weak
however...
2) The blue areas in the fields: they look like the magnitude has been clipped.
(http://forum.nasaspaceflight.com/xindex.php,qaction=dlattach,3Btopic=38203.0,3Battach=1055383,3Bimage.pagespeed.ic.hjMMacoPKv.webp)
They look like ContourPlots in Mathematica when I use PlotRange with a range smaller than the full magnitude, so the contours get cliped. I would double check whether magnitudes have not been clipped.
3) Is there some means to control the number of contour values in the contour plots? It looks to me like there are more contour levels than the number of colors available, as a result colors keep repeating themselves. What one wants is to have blue represent the lowest magnitude and red the highest magnitude, instead of red/green/blue/yellow patterns being repeated cyclically.
(http://forum.nasaspaceflight.com/xindex.php,qaction=dlattach,3Btopic=38203.0,3Battach=1055381,3Bimage.pagespeed.ic.p_0CAdsbWT.webp)
ex all data range from 3.67269e05 to 3.67269e05.
ey all data range from 1.42517e05 to 1.42517e05.
ez all data range from 0.000245405 to 0.000245405.
Of course they have been clipped. Look at the data ranges for the three E field components. Anything below the data range (or above, but that won't happen) are well ....from the manual: "Data values below or above this range will be treated as if they were min or max respectively." I suppose I could use the range from the minimum of the field to the maximum. Not minimum/ maximum of the most energetic component. To do so would be only a little more difficult, but would that be better? I can't guess without looking.

...
ex all data range from 3.67269e05 to 3.67269e05.
ey all data range from 1.42517e05 to 1.42517e05.
ez all data range from 0.000245405 to 0.000245405.
Of course they have been clipped. Look at the data ranges for the three E field components. Anything below the data range (or above, but that won't happen) are well ....from the manual: "Data values below or above this range will be treated as if they were min or max respectively." I suppose I could use the range from the minimum of the field to the maximum. Not minimum/ maximum of the most energetic component. To do so would be only a little more difficult, but would that be better? I can't guess without looking.
Yes, it would be better to have everything under
Electric field with highest absolute magnitude Universal Minimum /
Electric field with highest absolute magnitude Universal Maximum
for the electric fields
and
Magnetizing field with highest absolute magnitude Universal Minimum /
Magnetizing field with highest absolute magnitude Universal Maximum
because the Universal Min/Max doesn't discriminate based on sign of the field.
Since the values in the pictures are clipped, does that mean that the mode is really TM because what is shown is the minimum range instead of the maximum universal range?

About PaulTheSwag's experiment:
1. What differentiates the thrust profile from one where only an initial impulse was produced?
2. What is a "double knifeedge fulcrum"? It makes no sense to me.
3. Do we know the power value?
2. Did you saw the pictures? http://imgur.com/a/iO7er
Nah  viel zu langsam.
Do you have a helpful answer?
Ich denke es ist dieses Teil auf dem Foto ;)
Danke Ihnen so sehr für dieses Foto :)
I had missed it

How about my other two questions  the power? and why not just an impulse?

I missed this post. https://hackaday.io/project/5596emdrive/log/22182silverhiresprint
It is really wonderful to see how many people are working on their own EmDrive.
NASA EW guys join the fray please ;) That is if they let you....One post would not kill you you know and it can inspire more people.
Also storm after Prof. Tajmar first paper calmed down, but EmDrive now have more attention than before.
By the way any idea if Prof. Tajmar listens to this forum? It would be great to try to invite him here. His ideas and knowledge would be great addition here and can further boost incredible share of ideas here.
Maybe send an email signed by our science people here? :)

How about my other two questions  the power? and why not just an impulse?
I can't give you a answer, but ask him self :)
Here is the report of this young guy...
Source: https://www.reddit.com/r/EmDrive/comments/3gkwcz/build_complete_initial_testing_done_emdrive_build/
Pictures can be load from: http://imgur.com/a/iO7er
in a .zip file

About PaulTheSwag's experiment:
1. What differentiates the thrust profile from one where only an initial impulse was produced?
2. What is a "double knifeedge fulcrum"? It makes no sense to me.
3. Do we know the power value?
double edge knife
And here is his report
https://docs.google.com/document/d/10uC31tfb6sGAouICB1x7wF3F17qcBO5oie5_07Ethk/edit?pli=1
Links to it all.
https://www.reddit.com/r/EmDrive/comments/3gkwcz/build_complete_initial_testing_done_emdrive_build/

Here are the two png sets scaled to the maximum range of the E and H fields for the t=0 time slice. The ranges are from field components as follows:
# ez all data range from 0.000245405 to 0.000245405. E field big end
# hx all data range from 0.000538633 to 0.000538633. H field big end
# ez all data range from 4.04811e05 to 4.04811e05. E field small end
# hy all data range from 0.000287974 to 0.000287974. H field small end
Please look these png's over closely to be sure that this is what you want to see as it will be considerable effort to scale the png files in this way for the general case.
Or do you need to see the side views for this t = 0 case?
Thank you for going through the trouble to do this.
1) Assuming that the longitudinal axis is the z axis, this looks indeed like a TE mode (transverse electric) as the Hz mode (magnetic field in the longitudinal direction) is strong and the Ez (electric field in the longitudinal direction) is weak
however...
2) The blue areas in the fields: they look like the magnitude has been clipped.
(http://forum.nasaspaceflight.com/xindex.php,qaction=dlattach,3Btopic=38203.0,3Battach=1055383,3Bimage.pagespeed.ic.hjMMacoPKv.webp)
They look like ContourPlots in Mathematica when I use PlotRange with a range smaller than the full magnitude, so the contours get cliped. I would double check whether magnitudes have not been clipped.
3) Is there some means to control the number of contour values in the contour plots? It looks to me like there are more contour levels than the number of colors available, as a result colors keep repeating themselves. What one wants is to have blue represent the lowest magnitude and red the highest magnitude, instead of red/green/blue/yellow patterns being repeated cyclically.
(http://forum.nasaspaceflight.com/xindex.php,qaction=dlattach,3Btopic=38203.0,3Battach=1055381,3Bimage.pagespeed.ic.p_0CAdsbWT.webp)
ex all data range from 3.67269e05 to 3.67269e05.
ey all data range from 1.42517e05 to 1.42517e05.
ez all data range from 0.000245405 to 0.000245405.
Of course they have been clipped. Look at the data ranges for the three E field components. Anything below the data range (or above, but that won't happen) are well ....from the manual: "Data values below or above this range will be treated as if they were min or max respectively." I suppose I could use the range from the minimum of the field to the maximum. Not minimum/ maximum of the most energetic component. To do so would be only a little more difficult, but would that be better? I can't guess without looking.
I have a silly question. If the data values are clipped why am I still seeing artifacts on the side walls?
shell

The numerical field intensity values may be available in some convenient way that I just don't know about, but I have looked. Other meepers looking would be very helpful.
They are available, just not convenienly, by using the "verbose" switch on h5topng. Unfortunately, using that will require two separate runs, but I guess any method would require two separate runs at some level. Here is the verbose output from generating one png file.
steve@stevep6720f:~$ h5topng v t 0 z 214 ./Shell2ddipoleloopout/hx.h5
Using colormap "gray" in file "/usr/share/h5utils/colormaps/gray".
grayscale color map (white to black)
2 color entries read from colormap file.
Scaling opacity by 1
data rank = 4

reading from "./Shell2ddipoleloopout/hx.h5", slice at 214 in z dimension, slice at 0 in t dimension.
data ranges from 0.00012754 to 0.00012754.
writing "./Shell2ddipoleloopout/hx.png" from 196x196 input data.
all data range from 0.00012754 to 0.00012754.
I manually made 12 runs of h5topng, and extracted the following data ranges.
Range of data values in Shell2ddipoleloop64out
slice t 00, z 15 Big end
ex all data range from 3.67269e05 to 3.67269e05.
ey all data range from 1.42517e05 to 1.42517e05.
ez all data range from 0.000245405 to 0.000245405.
hx all data range from 0.000538633 to 0.000538633.
hy all data range from 0.000356036 to 0.000356036.
hz all data range from 4.65749e05 to 3.78542e05.
slice t 00 z 214 Small end
ex all data range from 1.60461e05 to 1.60461e05.
ey all data range from 3.20985e05 to 3.20985e05.
ez all data range from 4.04811e05 to 4.04811e05.
hx all data range from 0.00012754 to 0.00012754.
hy all data range from 0.000287974 to 0.000287974.
hz all data range from 1.07156e05 to 1.61666e05.
As I understand you, what you need is to have three png files, ex, ey, ez scaled to the maximum range of the E components and three, hx hy, hz scaled to the maximum range for the H component  for each time slice and each of the 4 geometry slices per time slice. That would be the ez range and the hx range for the first case above, but note that max value and min value won't necessarily always be from the same component as the second hz range above indicates.
Scaling the range of values using this approach is quite unwieldy to do manually, as there are I believe 336 pngs for a standard data set as I have been using, but also, we might benefit by extending that data set to 2 full cycles, or even more.
Does anyone here want to volunteer to create a bash shell file that runs the data set in verbose mode capturing the terminal output in the log file, then scan that log file, extract the correct range of values and scale the h5topng max and min switches, then run the data set again for upload? Conceptually it should be straight forward but I only recognize bash in passing, are almost strangers. Of course one could use Octave or MatLab to read the log file and extract the pertinent data, or even write a purpose program that simply scans and extracts the data then writes a new shell file with as many h5topng command lines as needed. That might be safer and the 336 + command line shell file would be "throw away" so it wouldn't need to be "slick."
Please find attached a simple python program. Rename to h5topng_range.py. Usage:
python h5topng_range.py logfile filename.txt
Output is to stdout, so some post processing will be necessary to get this to run in bash (I'm on windows, no access to bash until tonight). Tested with version 3.x should work with 2.5+ but I haven't tested. Uses the argparse library which is standard in version 3.x.
For the sample h5topng output quoted above, contained in "filename.txt", this produces the output:
h5topng t 0 z 214 m 0.00012754 M 0.00012754 ./Shell2ddipoleloopout/hx.h5
The numbers are pulled from the "all range data from" line and not the "data ranges from" line. The "z" switch is parametric based on the "reading from" line. The "t" is hardcoded, but can be made parametric if necessary, the value after "t" is, of course, parametric.
That looks very promising.
No, the t is what it is, the x y and z are parameters, (one set per png file). But it looks like the shell file will need to undergo major changes. I've attached my shell file (change the extension to .sh). It works for what I have been doing but I am forced by h5topng to copy the .png files into the subfolders from the out folder. The new desire to set min/max for each value of t, x, y, z will force us to discard this approach and adopt a naming convention something like I use for the csv files. That shell file is also attached (changed extension) but h5totxt handles the subdirectory correctly so no file moving is needed.
As for running it in bash? Not necessary until the h5topng commands are fully formulated and written to a shell file. You can do all of that in Python if that is your language of choice. Then run that shell file in bash.
You will likely need to create a set of h5 files to run your tests against. Don't go to to much work until you do that because I'm not sure that the single case of data that I generated and posted is representative of what h5topng outputs when multiple files are generated. It's sure not what the attached shell file logs, but then, the attached is probably not representative of the ultimate design, either.
and see the manual, it's short:
http://abinitio.mit.edu/h5utils/h5topngman.html (http://abinitio.mit.edu/h5utils/h5topngman.html)

Here are the two png sets scaled to the maximum range of the E and H fields for the t=0 time slice. The ranges are from field components as follows:
# ez all data range from 0.000245405 to 0.000245405. E field big end
# hx all data range from 0.000538633 to 0.000538633. H field big end
# ez all data range from 4.04811e05 to 4.04811e05. E field small end
# hy all data range from 0.000287974 to 0.000287974. H field small end
Please look these png's over closely to be sure that this is what you want to see as it will be considerable effort to scale the png files in this way for the general case.
Or do you need to see the side views for this t = 0 case?
Thank you for going through the trouble to do this.
1) Assuming that the longitudinal axis is the z axis, this looks indeed like a TE mode (transverse electric) as the Hz mode (magnetic field in the longitudinal direction) is strong and the Ez (electric field in the longitudinal direction) is weak
however...
2) The blue areas in the fields: they look like the magnitude has been clipped.
(http://forum.nasaspaceflight.com/xindex.php,qaction=dlattach,3Btopic=38203.0,3Battach=1055383,3Bimage.pagespeed.ic.hjMMacoPKv.webp)
They look like ContourPlots in Mathematica when I use PlotRange with a range smaller than the full magnitude, so the contours get cliped. I would double check whether magnitudes have not been clipped.
3) Is there some means to control the number of contour values in the contour plots? It looks to me like there are more contour levels than the number of colors available, as a result colors keep repeating themselves. What one wants is to have blue represent the lowest magnitude and red the highest magnitude, instead of red/green/blue/yellow patterns being repeated cyclically.
(http://forum.nasaspaceflight.com/xindex.php,qaction=dlattach,3Btopic=38203.0,3Battach=1055381,3Bimage.pagespeed.ic.p_0CAdsbWT.webp)
ex all data range from 3.67269e05 to 3.67269e05.
ey all data range from 1.42517e05 to 1.42517e05.
ez all data range from 0.000245405 to 0.000245405.
Of course they have been clipped. Look at the data ranges for the three E field components. Anything below the data range (or above, but that won't happen) are well ....from the manual: "Data values below or above this range will be treated as if they were min or max respectively." I suppose I could use the range from the minimum of the field to the maximum. Not minimum/ maximum of the most energetic component. To do so would be only a little more difficult, but would that be better? I can't guess without looking.
I have a silly question. If the data values are clipped why am I still seeing artifacts on the side walls?
shell
Maybe artefacts from the grid but there are strong currents in the wall and corresponding fields...

Dr. Rodal,
I was trying to figure out a way to communicate what I thought was going on, but I think I was wrong. It's simple 
Draw 3 sine waves on a sheet of paper, xy axis, each symmetric about the x axis, but with different amplitudes. Then draw horizontal lines tangent to the extreme positive and negative values of each sine wave. I used the y value of the top and bottom horizontal line.
So the weaker sign waves are not clipped, they just don't have enough power to show up on the scale of the strongest.
I'll see about using a different color map.

Dr. Rodal,
I was trying to figure out a way to communicate what I thought was going on, but I think I was wrong. It's simple 
Draw 3 sine waves on a sheet of paper, xy axis, each symmetric about the x axis, but with different amplitudes. Then draw horizontal lines tangent to the extreme positive and negative values of each sine wave. I used the y value of the top and bottom horizontal line.
So the weaker sign waves are not clipped, they just don't have enough power to show up on the scale of the strongest.
I'll see about using a different color map.
Today (morning) someone pointed out that it may be helpful to use a logarithmic scale, did you try that in the actual case? (one try to compare with the mag. scale?)
Other color map for the mag. scale like you sad could be also helpful i think.
BTW: great work, thanks for spend your time!

Dr. Rodal,
I was trying to figure out a way to communicate what I thought was going on, but I think I was wrong. It's simple 
Draw 3 sine waves on a sheet of paper, xy axis, each symmetric about the x axis, but with different amplitudes. Then draw horizontal lines tangent to the extreme positive and negative values of each sine wave. I used the y value of the top and bottom horizontal line.
So the weaker sign waves are not clipped, they just don't have enough power to show up on the scale of the strongest.
I'll see about using a different color map.
bluered (opaque blue to transparent white to opaque red). I have several color maps available, this is just the first try. I personally don't like it very much.

Dr. Rodal,
I was trying to figure out a way to communicate what I thought was going on, but I think I was wrong. It's simple 
Draw 3 sine waves on a sheet of paper, xy axis, each symmetric about the x axis, but with different amplitudes. Then draw horizontal lines tangent to the extreme positive and negative values of each sine wave. I used the y value of the top and bottom horizontal line.
So the weaker sign waves are not clipped, they just don't have enough power to show up on the scale of the strongest.
I'll see about using a different color map.
Today (morning) someone pointed out that it may be helpful to use a logarithmic scale, did you try that in the actual case? (one try to compare with the mag. scale?)
Other color map for the mag. scale like you sad could be also helpful i think.
BTW: great work, thanks for spend your time!
I saw that and frankly it gave me a nice chuckle. Two points on a log scale?
See: http://abinitio.mit.edu/h5utils/h5topngman.html (http://abinitio.mit.edu/h5utils/h5topngman.html) Look really, really closely for the log scale output, then tell me what you find.
Or maybe it would be more fruitful to look here: http://www.hdfgroup.org/products/java/hdfview/UsersGuide/ug05spreadsheet.html#ug05subset_transpose (http://www.hdfgroup.org/products/java/hdfview/UsersGuide/ug05spreadsheet.html#ug05subset_transpose)
My point is that logarithmic seems to be an alien concept to meep and it's support software.

....
bluered (opaque blue to transparent white to opaque red). I have several color maps available, this is just the first try. I personally don't like it very much.
This is much better.
I would definitely use this from now on.
This way we can tell what is high amplitude and what is low amplitude. The previous way....just say no good

Dr. Rodal,
I was trying to figure out a way to communicate what I thought was going on, but I think I was wrong. It's simple 
Draw 3 sine waves on a sheet of paper, xy axis, each symmetric about the x axis, but with different amplitudes. Then draw horizontal lines tangent to the extreme positive and negative values of each sine wave. I used the y value of the top and bottom horizontal line.
So the weaker sign waves are not clipped, they just don't have enough power to show up on the scale of the strongest.
I'll see about using a different color map.
Today (morning) someone pointed out that it may be helpful to use a logarithmic scale, did you try that in the actual case? (one try to compare with the mag. scale?)
Other color map for the mag. scale like you sad could be also helpful i think.
BTW: great work, thanks for spend your time!
I saw that and frankly it gave me a nice chuckle. Two points on a log scale?
See: http://abinitio.mit.edu/h5utils/h5topngman.html (http://abinitio.mit.edu/h5utils/h5topngman.html) Look really, really closely for the log scale output, then tell me what you find.
Or maybe it would be more fruitful to look here: http://www.hdfgroup.org/products/java/hdfview/UsersGuide/ug05spreadsheet.html#ug05subset_transpose (http://www.hdfgroup.org/products/java/hdfview/UsersGuide/ug05spreadsheet.html#ug05subset_transpose)
My point is that logarithmic seems to be an alien concept to meep and it's support software.
For very good reasons: IMHO a logarithmic scale is the complete opposite of what one wants to do to display mode shapes for these purposes: it will increase the number of contours in the low range and it will decrease them in the high range.
A logarithmic scale is a nonlinear scale used when there is a large range of quantities. Common uses include the earthquake strength, sound loudness, light intensity, and pH of solutions.
It is based on orders of magnitude, rather than a standard linear scale, so each mark on the scale is the previous mark multiplied by a value.
It will distort all the shapes. Logarithmic scales are suitable when you have an exponential increasing behavior. Not suitable for the fields.
May be suitable to plot attenuation, not for discriminating mode shapes from the electromagnetic fields.
Suitable for earthquake strength, sound loudness
()

Dr. Rodal,
I was trying to figure out a way to communicate what I thought was going on, but I think I was wrong. It's simple 
Draw 3 sine waves on a sheet of paper, xy axis, each symmetric about the x axis, but with different amplitudes. Then draw horizontal lines tangent to the extreme positive and negative values of each sine wave. I used the y value of the top and bottom horizontal line.
So the weaker sign waves are not clipped, they just don't have enough power to show up on the scale of the strongest.
I'll see about using a different color map.
Today (morning) someone pointed out that it may be helpful to use a logarithmic scale, did you try that in the actual case? (one try to compare with the mag. scale?)
Other color map for the mag. scale like you sad could be also helpful i think.
BTW: great work, thanks for spend your time!
I saw that and frankly it gave me a nice chuckle. Two points on a log scale?
See: http://abinitio.mit.edu/h5utils/h5topngman.html (http://abinitio.mit.edu/h5utils/h5topngman.html) Look really, really closely for the log scale output, then tell me what you find.
Or maybe it would be more fruitful to look here: http://www.hdfgroup.org/products/java/hdfview/UsersGuide/ug05spreadsheet.html#ug05subset_transpose (http://www.hdfgroup.org/products/java/hdfview/UsersGuide/ug05spreadsheet.html#ug05subset_transpose)
My point is that logarithmic seems to be an alien concept to meep and it's support software.
For very good reasons: a logarithmic scale is the opposite of what one wants to do to display mode shapes for these purposes: it will increase the number of contours in the low range and it will decreased them in the high range.
A logarithmic scale is a nonlinear scale used when there is a large range of quantities. Common uses include the earthquake strength, sound loudness, light intensity, and pH of solutions.
It is based on orders of magnitude, rather than a standard linear scale, so each mark on the scale is the previous mark multiplied by a value.
It will distort all the shapes. Logarithmic scales are suitable when you have an exponential increasing behavior. Not suitable for the fields.
May be suitable to plot attenuation, not for the fields
OK i can follow your explanation (high vs. low field strength), but i am not sure in view of the resulting pictures. It would be soften the edges we look since the rescaling.
You are the expert here, if you think i isn't helpful then forget it, no problem with that.
And yes it's much better with the new color map!!

...
OK i can follow your explanation (high vs. low field strength), but i am not sure in view of the resulting pictures. It would be soften the edges we look since the rescaling.
You are the expert here, if you think i isn't helpful then forget it, no problem with that.
And yes it's much better with the new color map!!
Well it is just my opinion of course.
Let's clarify it with an example: a logarithmic scale is eminently suited to rank earthquakes because each level changes by an order of magnitude. The difference between an earthquake with a level of 9 from a level of 8 is much greater than the difference between an earthquake between a level of 5 and a level of 4.
Ditto for sound.
Both for sound and earthquakes it makes sense to have a scale that has more levels at low magnitude and less levels at high magnitude.
Now, for the electromagnetic fields, we do not have a scale of electromagnetism where we want to minimize the number of levels at high magnitude and maximize the number of levels at low magnitude.
A linear scale for the mode shapes in EM Drive cavities is fine because we don't have singularities.
A logarithmic scale would make sense for this kind of shape: see the attachment for attenuation where the attenuation goes to Infinity at each end, the plot is clipped at the ends because a linear scale cannot show the singularities at each end.

...
OK i can follow your explanation (high vs. low field strength), but i am not sure in view of the resulting pictures. It would be soften the edges we look since the rescaling.
You are the expert here, if you think i isn't helpful then forget it, no problem with that.
And yes it's much better with the new color map!!
Well it is just my opinion of course.
Let's clarify it with an example: a logarithmic scale is eminently suited to rank earthquakes because each level changes by an order of magnitude. The difference between an earthquake with a level of 9 from a level of 8 is much greater than the difference between an earthquake between a level of 5 and a level of 4.
Ditto for sound.
Both for sound and earthquakes it makes sense to have a scale that has more levels at low magnitude and less levels at high magnitude.
Now, for the electromagnetic fields, we do not have a scale of electromagnetism where we want to minimize the number of levels at high magnitude and maximize the number of levels at low magnitude.
A linear scale for the mode shapes in EM Drive cavities is fine because we don't have singularities.
A logarithmic scale would make sense for this kind of shape: see the attachment for attenuation where the attenuation goes to Infinity at each end, the plot is clipped at the ends because a linear scale cannot show the singularities at each end.
Yes you should be right, its a little bi t late and i am tired today.
I just take a look of a random sonnetEM plot with both scalings... have to agree.
Wish a good night (later for you).

Ok since the photons inside the cavity are traveling in a medium at a group velocity <c, we can technically define a frame where the photon is at rest relative to the cavity walls. I can't justify a reason to not treat them as massive particles in calculations.
This is a special case since we're not dealing with photons in vacuum. Does this sound controversial to anyone? That means switching to relativistic momentum.
http://hyperphysics.phyastr.gsu.edu/hbase/relativ/relmom.html
This ref was shared by someone else recently and I think it is significant.
http://arxiv.org/abs/0708.3519
I have found this paper useful and the mathematics makes sense. The relativistic treatment of photons in a waveguide gives them a rest mass, that is proportional to the cutoff frequency of the waveguide.
I've used this in a tapered cylinder waveguide approximation to derive the thrust equation. I've just been too busy to work on my paper for the past couple of weeks.
Todd

My limited experience with the comsol EM module is it works fine!
Without calculations it is difficult(not possible) to say a specific peak in the Sparameter plot is the target resonance.
Sure understand that. But if you do a scan on a cavity and the predicted resonance is not there, then what?
As far as I know, there were no scans to back up all the mode and freq calculations that EW did.
I have a simple VNA I plan to use to find resonance frequencies and it's simply a verification to the calculations.
...
Even NASA should have used VNAs in air and vacuum just to check and I'm not sure they did.
...
I'd like to propose a logical progression to the VNA analysis: characterize each experimental frustum at multiple temperatures
@deltaMass recently proposed that thermal data could be used as an approximation to how well tuned the frustum was to the source RF feed. To continue the line of thought, if one could characterize a frustum at discrete temperatures using a VNA , then one could theoretically build a control loop using frustum temperature that varied frequency and/or impedance controls without having to perform realtime VSWR or sample port analysis.
Effectively I'm proposing that a lookup table could be constructed that indicates the optimal experimental control settings for each temperature point. As the frustum heats up, the optimal experimental control settings can be obtained from the table. As an implementation detail, one could use curvefitting to build an equation or use simplistic "ifthenelse" to drive the control loop outputs.
While the temperature is likely to be the dominant frustum parameter than impact bandpass characteristics and impedance, other parameters may also be important to in order to implement a control loop that yields repeatable results (i.e. frustum orientation, humidity, etc).
EDIT: On further thought, one might need multiple temperature inputs from different areas on the frustum geometry. The backofnapkin reasoning being that temperature differences at certain key locations may have a more pronounced effect on bandpass characteristics and impedance than a single "average" frustum temperature. I'd guess that the temperature of the "big end" and "small end" are the two dominant parameters.

I'm still confused. Are we looking at a single impulsive event, or a steadystate force?
The unraveling of the EM Drive "force measurement" this is what is great about replications.
The South African experiment does not show a constant steadystate force.
His fulcrum is undamped and will oscillate for some time before settling at the final value. You know that so why the comment?
Your Quote link to Rodal's comment (about "unraveling") does not work. Can you please provide a working link?

About PaulTheSwag's experiment:
1. What differentiates the thrust profile from one where only an initial impulse was produced?
2. What is a "double knifeedge fulcrum"? It makes no sense to me.
3. Do we know the power value?
2. Did you saw the pictures? http://imgur.com/a/iO7er
OK. I now understand the double knife edge (actually triple).
Same as mine, 3 blades, 2 balance points.

About PaulTheSwag's experiment:
1. What differentiates the thrust profile from one where only an initial impulse was produced?
2. What is a "double knifeedge fulcrum"? It makes no sense to me.
3. Do we know the power value?
2. Did you saw the pictures? http://imgur.com/a/iO7er
OK. I now understand the double knife edge (actually triple).
Same as mine, 3 blades, 2 balance points.
()

How about my other two questions  the power? and why not just an impulse?
An impulse would give an undamped massspring* harmonic oscillator an initial velocity to the mass but would not change the equilibrium point : the oscillations would have a mean position around the same equilibrium (before excitation). This is not what we see, even if the time axis lacks of resolution it looks like the response to a step, the mean after excitation is above the preexcitation position. Too bad the record is too short to see what happens after poweroff (why ?) : the undamped oscillator should continue to oscillate, more or less depending on phase at power off, but back around the initial equilibrium point, at least if there is a steep step down back to 0 force at poweroff (which somehow often proves elusive with the emdrive experiments).
* in this case the "springiness" is actually a centre of mass below axis (by what amount ?) restoring torque, but this is the same dynamic harmonic oscillator for small linearisable displacements.

Ok since the photons inside the cavity are traveling in a medium at a group velocity <c, we can technically define a frame where the photon is at rest relative to the cavity walls. I can't justify a reason to not treat them as massive particles in calculations.
This is a special case since we're not dealing with photons in vacuum. Does this sound controversial to anyone? That means switching to relativistic momentum.
http://hyperphysics.phyastr.gsu.edu/hbase/relativ/relmom.html
This ref was shared by someone else recently and I think it is significant.
http://arxiv.org/abs/0708.3519
What do you think happens at the height of a mode switch, right at the phase change peak. Time freezes.
Kidding aside, I want to read those papers, but later tonight. Thanks.
Shell

About PaulTheSwag's experiment:
1. What differentiates the thrust profile from one where only an initial impulse was produced?
2. What is a "double knifeedge fulcrum"? It makes no sense to me.
3. Do we know the power value?
2. Did you saw the pictures? http://imgur.com/a/iO7er
OK. I now understand the double knife edge (actually triple).
Same as mine, 3 blades, 2 balance points.
()
Two balance points for me.

NSF1701 Update 8/11/15. Assembly of frustum complete. Final weighin 2.383 kg. (grill) Thermometer installed, thanks to an idea from a pal here on NSF. Electrodes (solid copper wire) and terminal strip attached. Frustum is pictured upside down, as test will have small end closest to floor.
Final assembly on microwave (oven) controller just about done. Terminal strip on back and all wired up. Outside case reinstalled, fan and turntable motor disabled. All that's left is to attach copper wire and galinstan copper cups.
Just about at the end of the build phase!!!!!!!!!!!

That looks very promising.
No, the t is what it is, the x y and z are parameters, (one set per png file). But it looks like the shell file will need to undergo major changes. I've attached my shell file (change the extension to .sh). It works for what I have been doing but I am forced by h5topng to copy the .png files into the subfolders from the out folder. The new desire to set min/max for each value of t, x, y, z will force us to discard this approach and adopt a naming convention something like I use for the csv files. That shell file is also attached (changed extension) but h5totxt handles the subdirectory correctly so no file moving is needed.
As for running it in bash? Not necessary until the h5topng commands are fully formulated and written to a shell file. You can do all of that in Python if that is your language of choice. Then run that shell file in bash.
You will likely need to create a set of h5 files to run your tests against. Don't go to to much work until you do that because I'm not sure that the single case of data that I generated and posted is representative of what h5topng outputs when multiple files are generated. It's sure not what the attached shell file logs, but then, the attached is probably not representative of the ultimate design, either.
and see the manual, it's short:
http://abinitio.mit.edu/h5utils/h5topngman.html (http://abinitio.mit.edu/h5utils/h5topngman.html)
Please find attached a shell script generator file (rename from .txt to .py). Usage:
python generate_shell.py colormap dkbluered zbigend 15 zsmallend 214 outdir ./output_dir time 0:13
For now, the "m" minimum, "M" maximum, and "2dloop64" prefix are hard coded. You may change these manually on lines 42 and 5357. I have not completely coded different min/max values for the ex, ey, ez, hx, hy, hz directions, for now the e/h min/max are the same (e.g. ex min/max is the same as hx min/max). The input files are assumed to be in outdir and have the format of dir.h5 where dir is one of ex, ey, ez, hx, hy, hz.
The output is also attached. Since I am on windows, the file separator is "\", however in unix it should switch to "/" automagically.
This may be useful to you for generating shell scripts using custom min/max values pending the creation of a script to extract the min/max from log files. If you can post or PM me an actual log file, I can see about creating a new parser that can automate the whole process. Also, maybe the "h5ls" command can extract the min/max values without having to generate a set of "throwaway" png files?
EDIT: I threw in the h5totxt for free, took about 30 sec once I had the h5topng coded. Feel free to remove that part. Also, the output.txt was generated using a slightly different command line than the example from above. :)

NSF1701 Update 8/11/15. Assembly of frustum complete. Final weighin 2.383 kg. (grill) Thermometer installed, thanks to an idea from a pal here on NSF. Electrodes (solid copper wire) and terminal strip attached. Frustum is pictured upside down, as test will have small end closest to floor.
Final assembly on microwave (oven) controller just about done. Terminal strip on back and all wired up. Outside case reinstalled, fan and turntable motor disabled. All that's left is to attach copper wire and galinstan copper cups.
Just about at the end of the build phase!!!!!!!!!!!
That is simply beautiful. Nice looking build!
So you got to work on your build I got to smear some tar a roof that was leaking. Something isn't right here.... hmmmm
Very nice.
Shell

NSF1701 Update 8/11/15. Assembly of frustum complete. Final weighin 2.383 kg. (grill) Thermometer installed, thanks to an idea from a pal here on NSF. Electrodes (solid copper wire) and terminal strip attached. Frustum is pictured upside down, as test will have small end closest to floor.
Final assembly on microwave (oven) controller just about done. Terminal strip on back and all wired up. Outside case reinstalled, fan and turntable motor disabled. All that's left is to attach copper wire and galinstan copper cups.
Just about at the end of the build phase!!!!!!!!!!!
That is simply beautiful. Nice looking build!
So you got to work on your build I got to smear some tar a roof that was leaking. Something isn't right here.... hmmmm
Very nice.
Shell
Thanks shell. Get that roof fixed, we can't have leaks at our global test facility ;)

@Imbfan
Making good progress. One simple thing
Direction('0x0', 'x', .456, .567),
Direction('0y0', 'y', .678, .789),
should be
Direction('0 x 0', 'x', .456, .567),
Direction('0 y 0', 'y', .678, .789),
The 0 is a switch telling h5totxt to use the center of the lattice as the origin, the x is a switch telling to cut the x axis, that is, look at the y,z plane, and of course the 0 says cut along the x=0 value. Similar for y. And h5totxt and h5topng requires a space to separate switches/values.
I'll look in more detail soon but that was all I saw on first read.
aero

@Imbfan
Making good progress. One simple thing
Direction('0x0', 'x', .456, .567),
Direction('0y0', 'y', .678, .789),
should be
Direction('0 x 0', 'x', .456, .567),
Direction('0 y 0', 'y', .678, .789),
The 0 is a switch telling h5totxt to use the center of the lattice as the origin, the x is a switch telling to cut the x axis, that is, look at the y,z plane, and of course the 0 says cut along the x=0 value. Similar for y. And h5totxt and h5topng requires a space to separate switches/values.
I'll look in more detail soon but that was all I saw on first read.
aero
From the manual you linked earlier:
0
Shift the origin of the x/y/z slice coordinates to the dataset center, so that e.g. 0 x 0 (or more compactly 0x0) returns the central x plane of the dataset instead of the edge x plane. (t coordinates are not affected.)
I could not test, but it's no problem to switch it if it doesn't work.

My limited experience with the comsol EM module is it works fine!
Without calculations it is difficult(not possible) to say a specific peak in the Sparameter plot is the target resonance.
Sure understand that. But if you do a scan on a cavity and the predicted resonance is not there, then what?
As far as I know, there were no scans to back up all the mode and freq calculations that EW did.
I have a simple VNA I plan to use to find resonance frequencies and it's simply a verification to the calculations.
...
Even NASA should have used VNAs in air and vacuum just to check and I'm not sure they did.
...
I'd like to propose a logical progression to the VNA analysis: characterize each experimental frustum at multiple temperatures
@deltaMass recently proposed that thermal data could be used as an approximation to how well tuned the frustum was to the source RF feed. To continue the line of thought, if one could characterize a frustum at discrete temperatures using a VNA , then one could theoretically build a control loop using frustum temperature that varied frequency and/or impedance controls without having to perform realtime VSWR or sample port analysis.
Effectively I'm proposing that a lookup table could be constructed that indicates the optimal experimental control settings for each temperature point. As the frustum heats up, the optimal experimental control settings can be obtained from the table. As an implementation detail, one could use curvefitting to build an equation or use simplistic "ifthenelse" to drive the control loop outputs.
While the temperature is likely to be the dominant frustum parameter than impact bandpass characteristics and impedance, other parameters may also be important to in order to implement a control loop that yields repeatable results (i.e. frustum orientation, humidity, etc).
EDIT: On further thought, one might need multiple temperature inputs from different areas on the frustum geometry. The backofnapkin reasoning being that temperature differences at certain key locations may have a more pronounced effect on bandpass characteristics and impedance than a single "average" frustum temperature. I'd guess that the temperature of the "big end" and "small end" are the two dominant parameters.
That's a good idea.
Here is how I see it when using copper endplates and copper side walls. Remember, movement the thickness of a piece of paper can trash your Q and resonance.
Upon power you will begin to deform the copper endplates and adjusting the incoming frequency to try to correct will not correct the heat in the mode shapes that is deforming the copper and mode.
The excess heat will migrate through conduction and thermal convection to the side walls where due to the thermal expansion the cavity length will slowly increase pushing you out of tune.
The ideal way would be to keep the endplates from deforming in the first place. By using ceramic plates. I'm going to have mine electroplated, with gold (very thin). Gold is a great heat conductor but what is good about this setup the plate will not deform under mode hotspots like copper causing mode and cavity degradation.
There is little i can do on the sidewalls thermal expansion but move the small end plate via flat transducers that control positioning by feed back and that would be from a probe in the frustum. I have a coarse lead screw adjustment for the small plate and flat transducers to fine control the Z position as the sidewalls expand.
oops brain spasm!
Thinking out loud here... If I muck it up just shout "danger, danger engineer thinking, please step back"!
To do it right I should couple the small endplate externally to the large with ceramic rods, avoiding the issue of the cavity walls heating and changing length. Then I'll free float the plate in the small end, therefor the expanding side walls will just slide on by the plate and not change the distance between the plates, thereby keeping Q and mode. I grok this.
This idea is a brain spasm in progress, but dang it sounds good. (It would look a little like rfmwguy's frustum build with the external rods between the plates, but free floating one plate). I bet I could do it without any major looped feedback just by building a solid thermal compensating cavity. but ...
Let me recap.
That way I've stabilized the endplates from thermal hot spot mode expansion effects and compensated the cavity growth down the Y axis that changes tune. Maybe I'll need a little snub to control and fine tune the resonance in the end of the cavity driven by a transducer, and that would work easier than pushing a piece of ceramic around.
I've diner waiting, will be back.
Shell
PS: You know I may change my second build, heck I may build it first.

We continue our calculations of the gamma function γ as a measure of exponential geometrical attenuation:
E_{θ} = A e^{  γ r}
where the gamma function γ(r) (which cannot be expressed in terms of any known function appearing in any textbook), has to be obtained as a numerical solution to the differential equation
r dγ/dr + γ =  (1/E_{θ})*dE_{θ}/dr
for what we think is most likely the Yang EM Drive geometry:
bigDiameter = 0.247 (*meter*);
smallDiameter = 0.1144253 (*meter*);
axialLength = 0.24 (*meter*);
r1 = 0.211022 (*meter*);
r2 = 0.455515 (*meter*);
θ = 15.44 °
We show below:
1) γ(r) vs. r for TE011 to max attenuation of 5
2) γ(r) vs. r for TE011 to max attenuation of 25
3) E_{θ}/A vs. r for TE011
Clearly, the geometrical attenuation γ(r) is much greater for the Yang cavity at 15 ° and smaller distance to the vertex than the previously calculated for 6 ° and larger distance to the vertex

We continue by showing γ for the Yang cavity at 15 ° to the previously calculated for 6 ° side by side.
1) The 6 ° Yang/Shell geometry:
bigDiameter = 0.201(*meter*);
smallDiameter = 0.1492(*meter*);
axialLength = 0.24(*meter*);
r1 = 0.693281 (*meter*); (*spherical small radius *)
r2 = 0.933978 (*meter*); (*spherical large radius *)
θ_{w} = 6.15933 ° (*degrees*); (*halfcone angle*)
2) The 15 ° Yang EM Drive geometry:
bigDiameter = 0.247 (*meter*);
smallDiameter = 0.1144253 (*meter*);
axialLength = 0.24 (*meter*);
r1 = 0.211022 (*meter*);
r2 = 0.455515 (*meter*);
θ_{w} = 15.44 ° (*degrees*); (*halfcone angle*)
the geometry we consider is as shown in this image:
()
We show below:
1) γ(r) vs. r for TE011 15 ° geometry
2) γ(r) vs. r for TE011 6 ° geometry
Clearly, the geometrical attenuation γ(r) is much greater for the Yang cavity at 15 ° and closer to the vertex than the previously calculated for 6 ° and farther from the vertex . When the attenuation gradient is correctly calculated, the attenuation is clearly greater for higher angles and closer to the vertex.
__________________________
These are calculations of the gamma function γ as a measure of exponential geometrical attenuation:
E_{θ} = A e^{  γ r}
where the gamma function γ(r) (which cannot be expressed in terms of any known function appearing in any textbook), has to be obtained as a numerical solution to the differential equation
r dγ/dr + γ =  (1/E_{θ})*dE_{θ}/dr

@Imbfan
Making good progress. One simple thing
Direction('0x0', 'x', .456, .567),
Direction('0y0', 'y', .678, .789),
should be
Direction('0 x 0', 'x', .456, .567),
Direction('0 y 0', 'y', .678, .789),
The 0 is a switch telling h5totxt to use the center of the lattice as the origin, the x is a switch telling to cut the x axis, that is, look at the y,z plane, and of course the 0 says cut along the x=0 value. Similar for y. And h5totxt and h5topng requires a space to separate switches/values.
I'll look in more detail soon but that was all I saw on first read.
aero
From the manual you linked earlier:
0
Shift the origin of the x/y/z slice coordinates to the dataset center, so that e.g. 0 x 0 (or more compactly 0x0) returns the central x plane of the dataset instead of the edge x plane. (t coordinates are not affected.)
I could not test, but it's no problem to switch it if it doesn't work.
I remember that now that you mention it. So it likely works as you have it.
I did look at the h5ls statement. I don't think it works for what we want, but it may. There is no question that a Scilab program could be written to do what we need with the .h5 files, but I'm not going to even think about doing it. It looks to me like a life's work to decipher that language but it looks like it does everything and probably in several ways. Here.
https://help.scilab.org/doc/5.5.2/en_US/index.html (https://help.scilab.org/doc/5.5.2/en_US/index.html)

Because nobody seems to have posted it (yet)...
...some details on the size of the new Hackaday Rig (directly from the builders post) :
Height without the cylindrical endpart: 21.87mm
Height of cylindrical endpart: 5mm
Diameter small end: 16.12mm
Diameter big end: 29.64mm
Frequency is tuneable within 23 to 25 GHz (maybe more, but then the generator works out of spec)
The small end wall will be movable within the cylindrical endpart by a servo for automatic testing.
The endplates are flat  but a sphrical mod is also possible, because the cavity ends are open so we can flange different endplates to it.
Many thanx for your analysis, it´s really amazing that you´re doing that for us.
Do you also need the antenna position/antenna length, or does it not matter?
The current board uses a 3/4 lambda of 24.125GHz
The antenna hole is 5.55mm below the cylindrical endpart.
If this is wrong, we can make another drill. Unfortunately I could not find much information about the antenna position in EMdrives, just the standard 1/4lambda distance from the wall for usual waveguides.
May I suggest somebody add this info to the wiki very shortly?
A couple observations:
First, this device is tiny. I think I might have junked copper fittings of comparable dimensions out in the garage. Makes a shot glass look huge by comparison.
Second, note his uncertainty about antenna placement  something we have also been wrestling with.

...May I suggest somebody add this info to the wiki very shortly?...
Thanks very much for posting the information.
I agree that it should be posted once they get results, but can we wait to put it in the wiki until they have reported a measurement?
Presently only data for EM Drives that have been tested are included in the EM Drive wiki

NSF1701 Update 8/11/15. Assembly of frustum complete. Final weighin 2.383 kg. (grill) Thermometer installed, thanks to an idea from a pal here on NSF. Electrodes (solid copper wire) and terminal strip attached. Frustum is pictured upside down, as test will have small end closest to floor.
Final assembly on microwave (oven) controller just about done. Terminal strip on back and all wired up. Outside case reinstalled, fan and turntable motor disabled. All that's left is to attach copper wire and galinstan copper cups.
Just about at the end of the build phase!!!!!!!!!!!
I suggest you twist the wires tightly and put shielding around all the voltage terminals, wires, etc. up to the contact cups. So that there are no spurious Lorentz forces acting on it.
Todd

We continue by showing γ for the Yang cavity at 15 ° to the previously calculated for 6 ° side by side.
1) The 6 ° Yang/Shell geometry:
bigDiameter = 0.201(*meter*);
smallDiameter = 0.1492(*meter*);
axialLength = 0.24(*meter*);
r1 = 0.693281 (*meter*); (*spherical small radius *)
r2 = 0.933978 (*meter*); (*spherical large radius *)
θ_{w} = 6.15933 ° (*degrees*); (*halfcone angle*)
2) The 15 ° Yang EM Drive geometry:
bigDiameter = 0.247 (*meter*);
smallDiameter = 0.1144253 (*meter*);
axialLength = 0.24 (*meter*);
r1 = 0.211022 (*meter*);
r2 = 0.455515 (*meter*);
θ_{w} = 15.44 ° (*degrees*); (*halfcone angle*)
the geometry we consider is as shown in this image:
()
We show below:
1) γ(r) vs. r for TE011 15 ° geometry
2) γ(r) vs. r for TE011 6 ° geometry
Clearly, the geometrical attenuation γ(r) is much greater for the Yang cavity at 15 ° and closer to the vertex than the previously calculated for 6 ° and farther from the vertex . When the attenuation gradient is correctly calculated, the attenuation is clearly greater for higher angles and closer to the vertex.
__________________________
These are calculations of the gamma function γ as a measure of exponential geometrical attenuation:
E_{θ} = A e^{  γ r}
where the gamma function γ(r) (which cannot be expressed in terms of any known function appearing in any textbook), has to be obtained as a numerical solution to the differential equation
r dγ/dr + γ =  (1/E_{θ})*dE_{θ}/dr
By that conclusion, we can practically guarantee that a smaller cone angle will have a higher Q, because the loss due to attenuation is much smaller.
FYI: What you're doing makes a lot more sense to me than what Z&F were showing. No wonder I was having such a difficult time interpreting their results.
Now, my question is, was Yang right when she said that the more cylindrical frustum with higher Q had the greatest thrust? Shell may do better than we expect with her 6deg. frustum, but not because of what we thought we knew 2 months ago.
Todd

@Imbfan
Here are your files back to you. You will note that I tinkered with them but not for posterity.
 I put the run command at the top of the executable files as a comment  Just so I won't forget what it is.
 I added the "2>&1  tee nemonicname.log" bash switch to the run commands to save the std output to a log file.
 I commented the csv file print output statements, don't want or need csv's to find the min/max values >>> unless the v switch on h5totxt also gives the min/max values, then because it's faster we will use it instead.
 I edited in the v (verbose) option to the .py run log file and changed the extension to .sh  also changed the name of the output directory to "garbage" and removed the color map trying to speed things up. Didn't help much.
 I ran the resulting shell file and obtained a verbose.log file >>> this is the one that has the real min/max values...
Unfortunately I wasn't very careful with saving the files so in particular the "generate_shell.log" file may be partly or mostly edited, not the actual output from your Python program.

Looking for litterature on the subject of forces and momentum in electromagnetic systems, I have found this article dated from october 2002 : "On an Additional Magnetic Force Present in a System of Coaxial Solenoids", http://pdf.lu/72oA (http://pdf.lu/72oA). The conclusion of this paper is the following :
More generally, experiments to validate or disconﬁrm, in suitable geometries, the various terms of our proposed generalized equation of motion (7) would evidently be desirable. The Lorentz force is the only one of those terms currently known beyond doubt to be physically valid. For a century too much has been left to accepted electromagnetic theory and not enough to empirical inquiry.
Phenomenology and empirical investigation seem well today be the future of electromagnetism !

Looking for litterature on the subject of forces and momentum in electromagnetic systems, I have found this article dated from october 2002 : "On an Additional Magnetic Force Present in a System of Coaxial Solenoids", http://pdf.lu/72oA (http://pdf.lu/72oA). The conclusion of this paper is the following :
More generally, experiments to validate or disconﬁrm, in suitable geometries, the various terms of our proposed generalized equation of motion (7) would evidently be desirable. The Lorentz force is the only one of those terms currently known beyond doubt to be physically valid. For a century too much has been left to accepted electromagnetic theory and not enough to empirical inquiry.
Phenomenology and empirical investigation seem well today be the future of electromagnetism !
That was written 13 years ago. Can you hear the crickets?

NSF1701 Update 8/11/15. Assembly of frustum complete. Final weighin 2.383 kg. (grill) Thermometer installed, thanks to an idea from a pal here on NSF. Electrodes (solid copper wire) and terminal strip attached. Frustum is pictured upside down, as test will have small end closest to floor.
Final assembly on microwave (oven) controller just about done. Terminal strip on back and all wired up. Outside case reinstalled, fan and turntable motor disabled. All that's left is to attach copper wire and galinstan copper cups.
Just about at the end of the build phase!!!!!!!!!!!
Now the NSF1701 looks like a very important part of the NCC1701 ;D ;)
Good luck for your coming tests :)
pictures: rfmwguy and http://www.cygnusx1.net/links/lcars/ksyenterprise.php

About PaulTheSwag's experiment:
1. What differentiates the thrust profile from one where only an initial impulse was produced?
2. What is a "double knifeedge fulcrum"? It makes no sense to me.
3. Do we know the power value?
2. Did you saw the pictures? http://imgur.com/a/iO7er
OK. I now understand the double knife edge (actually triple).
Same as mine, 3 blades, 2 balance points.
()
Two balance points for me.
Shell your bearing is able to produce a lot of friction.. ???
What do you think about commercial bearings for your carbon construction? metal, plastic or ceramic

.......
Clearly, the geometrical attenuation γ(r) is much greater for the Yang cavity at 15 ° and closer to the vertex than the previously calculated for 6 ° and farther from the vertex . When the attenuation gradient is correctly calculated, the attenuation is clearly greater for higher angles and closer to the vertex.
........
Dr. Rodal,
For a while i was wondering what you were doing as I did not understand the purpose of the graphs, but your last explanation made it clear for me. Thanks for that....
As you have the opportunity now to calculate the attenuation gradient for a half cone angle, do you think it is possible to investigate if there is an optimal angle?
fe, calculate the gamma for each 5° incremental to see how the attenuation evolves through the different angles? Does attenuation continue to increase with the increasing angle or is there an optimum angle?
Information like this would be crucial for redesigning frustums to achieve max attenuation and would consequently assist in answering the question to what gives the most net force result in a frustum : a high Q, or a high attenuation or maybe, as Todd previously suggested, Q and attenuation needs to balance each other?

To do it right I should couple the small endplate externally to the large with ceramic rods, avoiding the issue of the cavity walls heating and changing length. Then I'll free float the plate in the small end, therefor the expanding side walls will just slide on by the plate and not change the distance between the plates, thereby keeping Q and mode. I grok this...
Great idea! This is what I liked about the Tajmar setup. His small plate appears to be mechanically connected to the large plate via the external adjustment mechanism, isolating it from the frustum... Pity about that 'Great Bloody Hole'^{TM} in the side of it though... With your added ceramicendplate goodness, you have a recipe for some interesting tests... 8)
Another idea that's been knocking around in my skull for a while would be to fabricate a frustum shaped block out of a highk ceramic and then plate the whole thing... ???

... Another idea that's been knocking around in my skull for a while would be to fabricate a frustum shaped block out of a highk ceramic and then plate the whole thing... ???
Do we have and orde of magnitude for the Q reduction due to copper oxydation by the oxygen of air ?

...
Two balance points for me.
Shell your bearing is able to produce a lot of friction.. ???
What do you think about commercial bearings for your carbon construction? metal, plastic or ceramic
Why not a short hardened steel tubing sheath around the carbon tube where it rests on the knife edge ?

Can't stop thinking about @Notsosureofit's accelerated frame of reference model.

.......
Clearly, the geometrical attenuation γ(r) is much greater for the Yang cavity at 15 ° and closer to the vertex than the previously calculated for 6 ° and farther from the vertex . When the attenuation gradient is correctly calculated, the attenuation is clearly greater for higher angles and closer to the vertex.
........
Dr. Rodal,
For a while i was wondering what you were doing as I did not understand the purpose of the graphs, but your last explanation made it clear for me. Thanks for that....
As you have the opportunity now to calculate the attenuation gradient for a half cone angle, do you think it is possible to investigate if there is an optimal angle?
fe, calculate the gamma for each 5° incremental to see how the attenuation evolves through the different angles? Does attenuation continue to increase with the increasing angle or is there an optimum angle?
Information like this would be crucial for redesigning frustums to achieve max attenuation and would consequently assist in answering the question to what gives the most net force result in a frustum : a high Q, or a high attenuation or maybe, as Todd previously suggested, Q and attenuation needs to balance each other?
Unfortunately, calculating this for just one geometry is very time consuming . At the moment the best I can do is to compare a few geometries (so far I have only compared two geometries). So all I can see at the moment is:
if the hypothesis that an increasing gradient of attenuation towards the vertex is good is true
1) The Yang geometry with 15 degrees and closer to the vertex is better than the Yang geometry with 6 degrees and further from the vertex
2) The lower mode shape TE011 looks better than TE012
Need to look at other geometries and mode shapes.

We continue our calculations of the gamma function γ as a measure of exponential geometrical attenuation:
E_{θ} = A e^{  γ r}
where the gamma function γ(r) (which cannot be expressed in terms of any known function appearing in any textbook), has to be obtained as a numerical solution to the differential equation
r dγ/dr + γ =  (1/E_{θ})*dE_{θ}/dr
for what we think is most likely the Yang EM Drive geometry:
bigDiameter = 0.247 (*meter*);
smallDiameter = 0.1144253 (*meter*);
axialLength = 0.24 (*meter*);
r1 = 0.211022 (*meter*);
r2 = 0.455515 (*meter*);
θ = 15.44 °
We show below:
1) γ(r) vs. r for TE011 to max attenuation of 5
2) γ(r) vs. r for TE011 to max attenuation of 25
3) E_{θ}/A vs. r for TE011
Clearly, the geometrical attenuation γ(r) is much greater for the Yang cavity at 15 ° and smaller distance to the vertex than the previously calculated for 6 ° and larger distance to the vertex
We continue the above study by showing the results for mode shape TE012
We show below:
1) γ(r) vs. r for TE012 to max attenuation of 5
2) γ(r) vs. r for TE012 to max attenuation of 25
3) E_{θ}/A vs. r for TE012

We continue by showing γ for the Yang cavity at 15 ° to the previously calculated for 6 ° side by side.
1) The 6 ° Yang/Shell geometry:
bigDiameter = 0.201(*meter*);
smallDiameter = 0.1492(*meter*);
axialLength = 0.24(*meter*);
r1 = 0.693281 (*meter*); (*spherical small radius *)
r2 = 0.933978 (*meter*); (*spherical large radius *)
θ_{w} = 6.15933 ° (*degrees*); (*halfcone angle*)
2) The 15 ° Yang EM Drive geometry:
bigDiameter = 0.247 (*meter*);
smallDiameter = 0.1144253 (*meter*);
axialLength = 0.24 (*meter*);
r1 = 0.211022 (*meter*);
r2 = 0.455515 (*meter*);
θ_{w} = 15.44 ° (*degrees*); (*halfcone angle*)
the geometry we consider is as shown in this image:
()
We show below:
1) γ(r) vs. r for TE011 15 ° geometry
2) γ(r) vs. r for TE011 6 ° geometry
Clearly, the geometrical attenuation γ(r) is much greater for the Yang cavity at 15 ° and closer to the vertex than the previously calculated for 6 ° and farther from the vertex . When the attenuation gradient is correctly calculated, the attenuation is clearly greater for higher angles and closer to the vertex.
__________________________
These are calculations of the gamma function γ as a measure of exponential geometrical attenuation:
E_{θ} = A e^{  γ r}
where the gamma function γ(r) (which cannot be expressed in terms of any known function appearing in any textbook), has to be obtained as a numerical solution to the differential equation
r dγ/dr + γ =  (1/E_{θ})*dE_{θ}/dr
We continue the above study by showing the results for TE012 comparing the 6 degree and the 15 degree Yang geometries
We show below:
1) γ(r) vs. r for TE012 15 ° geometry
2) γ(r) vs. r for TE012 6 ° geometry
Clearly, the geometrical attenuation γ(r) is much greater for the Yang cavity at 15 ° and closer to the vertex than the previously calculated for 6 ° and farther from the vertex . When the attenuation gradient is correctly calculated, the attenuation is clearly greater for higher angles and closer to the vertex.

...By that conclusion, we can practically guarantee that a smaller cone angle will have a higher Q, because the loss due to attenuation is much smaller.
FYI: What you're doing makes a lot more sense to me than what Z&F were showing. No wonder I was having such a difficult time interpreting their results.
Now, my question is, was Yang right when she said that the more cylindrical frustum with higher Q had the greatest thrust? Shell may do better than we expect with her 6deg. frustum, but not because of what we thought we knew 2 months ago.
Todd
Actually, calculating the Q factor as
qualityFactor = (2/skinDepth)*(energyVolumeIntegral/energySurfaceIntegral)
results in slightly higher Q for the 15 degree geometry than for the 6 degree geometry:
Mode shape TE012
Q (6 degree geometry) = 71,173
Q (15 degree geometry) = 73,658
using resistivity = 1.678*10^(8)(*copper*);
(For impure copper or other alloys the Q will decrease with the increasing resistivity)
And a calculation for TheTraveller's 30 degree geometry showed a theoretical Q near 100,000
So, calculating
qualityFactor = (2/skinDepth)*(energyVolumeIntegral/energySurfaceIntegral)
although higher angles result in greater attenuation, the Q actually goes up rather than down because less of the energy is exposed to the surface
Everything I have looked at so far consistently points toward higher cone angles and being closer to the vertex as being better, which is in agreement with Shawyer's, McCulloch's and Notsosureofit's formulas.
(As long as there is an electromagnetic field mode shape filling the cavity towards the small base: extending the cone with a mode that doesn't reach the small base is wasted volume: it results in lower Q)
TE modes have higher Q than TM modes.
___________________
1) The 6 ° Yang/Shell geometry:
bigDiameter = 0.201(*meter*);
smallDiameter = 0.1492(*meter*);
axialLength = 0.24(*meter*);
r1 = 0.693281 (*meter*); (*spherical small radius *)
r2 = 0.933978 (*meter*); (*spherical large radius *)
θ_{w} = 6.15933 ° (*degrees*); (*halfcone angle*)
2) The 15 ° Yang EM Drive geometry:
bigDiameter = 0.247 (*meter*);
smallDiameter = 0.1144253 (*meter*);
axialLength = 0.24 (*meter*);
r1 = 0.211022 (*meter*);
r2 = 0.455515 (*meter*);
θ_{w} = 15.44 ° (*degrees*); (*halfcone angle*)

About PaulTheSwag's experiment:
1. What differentiates the thrust profile from one where only an initial impulse was produced?
2. What is a "double knifeedge fulcrum"? It makes no sense to me.
3. Do we know the power value?
2. Did you saw the pictures? http://imgur.com/a/iO7er
OK. I now understand the double knife edge (actually triple).
Same as mine, 3 blades, 2 balance points.
()
Two balance points for me.
Shell your bearing is able to produce a lot of friction.. ???
What do you think about commercial bearings for your carbon construction? metal, plastic or ceramic
It could if I wasn't using a trick here that I needed to mention and I'm really sorry it slipped my mind. The knife edge really isn't a knife edge anymore, it has been rounded off using a belt sander and the tube simply rolls over the rounded surface of the blade that was a sharp edge.
I liked the strength of the blade but I disliked the friction and stresses when using 2 blades one on top of each other or the way the blade could slice into a metal or a carbon fiber tube. In testing I had the blades chip and shatter against each other and glued steel plates end up getting a grove from the blade in just a couple runs up and down with weights on the fulcrum.
A mental calculation thinking about the small radii the tube would roll over changing the length over 1 meter was around 5 microns. It's acceptable.
Added: What do you think xray? Do you think this will work ok? I wanted to try and avoid any bearing for they seem to always have the issued of initial movement from stiction.

@Dr. Rodal ("And/Or curious others")
Would you be able to produce output using the tool or formula of your choice at your leisure to see how relative humidity might impact results?
If you already know. Please don't waste your time.
I just am curious that I have not seen any mention about RH having any cause or effect or that the impact of RH differences are so small, that they don't need to be considered.
With the large differences in thrust results for tests done in a vacuum compared to testing under normal atmospheric pressure conditions. I've been wondering if RH could be a major contributing cause to those differences.
Note: I just can't help having "flashbacks" to my U.S. Air Force days as a Wideband Communications Equipment 304x0 equipment repair person (http://oai.dtic.mil/oai/oai?verb=getRecord&metadataPrefix=html&identifier=ADA201690) in the 1970's who maintained microwave equipment using near these same microwave frequencies.
One of my many maintenance duties was to replace desiccant in every waveguide we used and it was not simply to avoid only rust and/or condensation, in those waveguides.
It has been awhile. But I think one of the reasons why we used desiccant and replaced it so often in all our waveguides had to do with standing waves. I could be remembering this incorrectly. But that's what I recall today. That said. The situation I am referencing was at a site where our microwave transmit power was 10 KW per 60 foot parabolic antenna. Shown below.
(http://www.saveontelephonebills.com/camera/MartinaFrancaItaly.jpg)
Thanks
Edited: For photo
Don

@Dr. Rodal ("And/Or curious others")
Would you be able to produce output using the tool or formula of your choice at your leisure to see how relative humidity might impact results?
If you already know. Please don't waste your time.
I just am curious that I have not seen any mention about RH having any cause or effect or that the impact of RH differences are so small, that they don't need to be considered.
With the large differences in thrust results for tests done in a vacuum compared to testing under normal atmospheric pressure conditions. I've been wondering if RH could be a major contributing cause to those differences.
Thanks
Don
Hi, I have not taken the time to consider how to calculate how humidity may affect the results. I agree that it sounds very interesting for many reasons. For example, we know how microwave ovens preferentially excite a water molecule and they mostly heat food by heating water, so moist air is most relevant. I would have to think about how to include that effect in calculations :)
For the time being it would be useful if experimenters would record and report the relative humidity of the environment when they performed their tests.

EMDrive Rotary Test Table and 5GHz WiFi USB comms
Have gone with a single wireless USB to USB connection between the Laptop and the Raspberry 2B control and monitoring system using a 5GHz WiFi HotSpot generated by my mobile phone. This should eliminate USB to USB comms interference by any 2.45GHz stray Rf that gets out of the Faraday Cage around the EMDrive and the 100W Rf amp. Will be using the high power upper band 5GHz WiFi channels to be sure to get a good connection.
The wireless Raspberry 2B USB to Laptop USB link will enable live, real time data to be displayed on the LapTop and to allow real time control over all EMDrive operational parameters.
Using the 5GHz WiFi HotSpot generated by my mobile phone, means there is no need for the test / demo site to have 5GHz WiFi availability.
Doing this saves me a few modules to write the code for, debug and interface.
The raspberry 2B Control and Monitoring System will collect in real time and log the following data every 10ms or 100 samples per second:
Force generated  calculated
Angular velocity  measured
Angular acceleration  calculated & measured by a 3 axis onboard axis accelerometer
Forward Rf power  measured
Reflected Rf power  measured
VSWR  calculated
Frustum Q  measured
Frustum bandwidth  measured
Frequency  as generated and measured
Rf amp Voltage, Current and Power consumed  measured
Internal frustum pressure  measured
End plate, side wall, ambient and Rf amp temperature  measured
Date and Time to a sub millisecond accuracy  measured
Latitude, Longitude and elevation from mobile phone GPS data  measured.
Rotary table layout as attached.
As always comments most welcome.

...By that conclusion, we can practically guarantee that a smaller cone angle will have a higher Q, because the loss due to attenuation is much smaller.
FYI: What you're doing makes a lot more sense to me than what Z&F were showing. No wonder I was having such a difficult time interpreting their results.
Now, my question is, was Yang right when she said that the more cylindrical frustum with higher Q had the greatest thrust? Shell may do better than we expect with her 6deg. frustum, but not because of what we thought we knew 2 months ago.
Todd
Actually, calculating the Q factor as
qualityFactor = (2/skinDepth)*(energyVolumeIntegral/energySurfaceIntegral)
results in slightly higher Q for the 15 degree geometry than for the 6 degree geometry:
Mode shape TE012
Q (6 degree geometry) = 71,173
Q (15 degree geometry) = 73,658
using resistivity = 1.678*10^(8)(*copper*);
(For impure copper or other alloys the Q will decrease with the increasing resistivity)
And a calculation for TheTraveller's 30 degree geometry showed a theoretical Q near 100,000
So, calculating
qualityFactor = (2/skinDepth)*(energyVolumeIntegral/energySurfaceIntegral)
although higher angles result in greater attenuation, the Q actually goes up rather than down because less of the energy is exposed to the surface
Everything I have looked at so far consistently points toward higher cone angles and being closer to the vertex as being better, which is agreement with Shawyer's, McCulloch's and Notsosureofit's formulas.
(As long as there is an electromagnetic field mode shape filling the cavity towards the small base: extending the cone with a mode that doesn't reach the small base is wasted volume: it results in lower Q)
TE modes have higher Q than TM modes.
___________________
1) The 6 ° Yang/Shell geometry:
bigDiameter = 0.201(*meter*);
smallDiameter = 0.1492(*meter*);
axialLength = 0.24(*meter*);
r1 = 0.693281 (*meter*); (*spherical small radius *)
r2 = 0.933978 (*meter*); (*spherical large radius *)
θ_{w} = 6.15933 ° (*degrees*); (*halfcone angle*)
2) The 15 ° Yang EM Drive geometry:
bigDiameter = 0.247 (*meter*);
smallDiameter = 0.1144253 (*meter*);
axialLength = 0.24 (*meter*);
r1 = 0.211022 (*meter*);
r2 = 0.455515 (*meter*);
θ_{w} = 15.44 ° (*degrees*); (*halfcone angle*)
Some very nice work, over the top for the both of you, hats off to warptech and Dr. Rodal.
Since this build has had input from so many of you and has been a creative mindsink that I've never been involved with or even have seen. I'd like some input on what you think for the second build dimensions.
I'll still be using the octagonal 6 sided shape for several reasons.
Mounting of the waveguides is much easier to the flat walls and making them 180 degrees out from each other and in the same plane.
The ceramic plates are easier to get with flat sides (think of cutting a circle with a circular blade like in a dicing saw).
If I go with ceramics for the side walls later they also are easier to cut.
I'll still use a perforated side wall copper O2 free sheet to downsize the ballooning effects but with smaller holes with wider spacing.
PM me if you would like or throw it out in the forum.
Shell
PS: I think I know what you would like to see Dr. Rodal. ;)

@Dr. Rodal ("And/Or curious others")
Would you be able to produce output using the tool or formula of your choice at your leisure to see how relative humidity might impact results?
If you already know. Please don't waste your time.
I just am curious that I have not seen any mention about RH having any cause or effect or that the impact of RH differences are so small, that they don't need to be considered.
With the large differences in thrust results for tests done in a vacuum compared to testing under normal atmospheric pressure conditions. I've been wondering if RH could be a major contributing cause to those differences.
Thanks
Don
Hi, I have not taken the time to consider how to calculate how humidity may affect the results. I agree that it sounds very interesting for many reasons. For example, we know how microwave ovens preferentially excite a water molecule and they mostly heat food by heating water, so moist air is most relevant. I would have to think about how to include that effect in calculations :)
For the time being it would be useful if experimenters would record and report the relative humidity of the environment when they performed their tests.
Another sign of getting older. Sigh.....
I forgot to mention, that we also used both horizontal and vertical polarity with our microwave antennas for diversity. In some cases vertical or horizontal polarities made major differences with different atmospheric conditions.
Antennas which received our microwave signals ("Using tropospheric scatter") were as much as 400 miles away. So there were multiple weather conditions which our microwave transmissions could encounter as they tried to reach our distant ends.
I have no idea if this applies to EM Drives or not.
But I am surprised that there has been little test data to compare when a waveguide is used to inject the microwave signal into the EM Drive if the waveguide was in a horizontal or vertical mounting position on the EM Drive and if the polarity of that waveguide, could have any effect on measured results when using the same sized EM Drive with the opposite polarity to compare horizontal to vertical polarities. Near or about at the same mounting position.
I'm not sure if any of your test tools or formulas allow waveguides to use horizontal or vertical polarities as input data to see if any polarity differences might make the output of same, have different results.
Don

@Dr. Rodal ("And/Or curious others")
Would you be able to produce output using the tool or formula of your choice at your leisure to see how relative humidity might impact results?
If you already know. Please don't waste your time.
I just am curious that I have not seen any mention about RH having any cause or effect or that the impact of RH differences are so small, that they don't need to be considered.
With the large differences in thrust results for tests done in a vacuum compared to testing under normal atmospheric pressure conditions. I've been wondering if RH could be a major contributing cause to those differences.
Thanks
Don
Hi, I have not taken the time to consider how to calculate how humidity may affect the results. I agree that it sounds very interesting for many reasons. For example, we know how microwave ovens preferentially excite a water molecule and they mostly heat food by heating water, so moist air is most relevant. I would have to think about how to include that effect in calculations :)
For the time being it would be useful if experimenters would record and report the relative humidity of the environment when they performed their tests.
Another sign of getting older. Sigh.....
I forgot to mention, that we also used both horizontal and vertical polarity with our microwave antennas for diversity. In some cases vertical or horizontal polarities made major differences with different atmospheric conditions.
Antennas which received our microwave signals ("Using tropospheric scatter") were as much as 400 miles away. So there were multiple weather conditions which our microwave transmission could encounter to reach our distant ends.
I have no idea if this applies to EM Drives or not.
But I am surprised that there has been little test data to compare when a waveguide is used to inject the microwave signal into the EM Drive if the waveguide was in a horizontal or vertical mounting position on the EM Drive and if the polarity of that waveguide, could have any effect on measured results when using the same sized EM Drive with the opposite polarity to compare horizontal to vertical polarities. Near or about at the same mounting position.
I'm not sure if any of your test tools or formulas allow waveguides to use horizontal or vertical polarities as input data to see if any polarity differences might make the output of same, have different results.
Don
Good points Don, nice post.
Ok... this is from a gal who though she knew something about antennas and I'd like your input because I found out I really don't. I would guess over the last couple months this group has dug into antennas quite deep and I've read more about them than I care to think of. Weird and beautiful stuff.
A couple of things that are on the the forefront that to me have seemed to be of importance.
First off is the radiation patterns and how they must be aligned correctly to excite one or the other, TE or TM mode pattern in the frustum.
Second is the radiation pattern needs to be as uniform as it can, with no funny lobes. A simple snub @ 2.45GHz in a TE insertion point towards the bottom leads to rotational effects of the modes around the cavity. As they build and collapse it kills off the Q of the cavity.
Third is the losses associated with an antenna into the cavity. We have calculated only 4050 watts of effective RF being available to cause a thrust effect in the cavity.
Fourth that low output is why many (Including me) have elected to treat the Frustum like part of a waveguide and directly inject the output of a magnetron down a waveguide into the cavity. rfmwguy coupled his magnetron directly into his cavity, the man is awsum.

NSF1701 live test...Galinstan ordered and should be here within a week. Will do the live test either 8/18 or 8/25 depending on the delivery.

@Dr. Rodal ("And/Or curious others")
Would you be able to produce output using the tool or formula of your choice at your leisure to see how relative humidity might impact results?
If you already know. Please don't waste your time.
I just am curious that I have not seen any mention about RH having any cause or effect or that the impact of RH differences are so small, that they don't need to be considered.
With the large differences in thrust results for tests done in a vacuum compared to testing under normal atmospheric pressure conditions. I've been wondering if RH could be a major contributing cause to those differences.
Thanks
Don
Hi, I have not taken the time to consider how to calculate how humidity may affect the results. I agree that it sounds very interesting for many reasons. For example, we know how microwave ovens preferentially excite a water molecule and they mostly heat food by heating water, so moist air is most relevant. I would have to think about how to include that effect in calculations :)
For the time being it would be useful if experimenters would record and report the relative humidity of the environment when they performed their tests.
For a nonsealed EMDrive cavity that's exposed to the air, any humidity in the cavity will heat up and vent out of any openings including waveguides and wiring harnesses, but eventually, it'll all be gone, so the longer the magnetron is turned on, the more steam will evaporate and escape. Any anomalous thrust would tend towards zero over time because of humidity as the device clears out the water vapor in the form of pressurized steam.
For an EMDrive operated in a vacuum, any humidity would get flushed out as the pump reduces the air pressure inside the chamber.
For a "perfectly" sealed EM Drive, the steam would build up pressure inside the EMDrive as energy is added to the system, but no thrust would be measured external to the system. Until, of course, the balloon pops.
Trusting a vaccum to get rid of water is not quite that simple:
see: http://cas.web.cern.ch/cas/Spain2006/PDFs/Dylla2.pdf
You're looking at hours to eliminate water, even with heat.
They don't characterize copper in the citation above, which would probably make things worse. Copper is on the list of metals to avoid in high vacuum systems due to outgassing issues.
Also note that outgassing torr has a conversion to gramforce/centimeter2 or newtons/centimeter2
You will get thrust from outgassing based on the surface area. Not a lot, but some.

@Imbfan
I sent a PM to you just now describing the attached. Here is a complete log file to work with.
aero

NSF1701 live test...Galinstan ordered and should be here within a week. Will do the live test either 8/18 or 8/25 depending on the delivery.
I think X_Ray asked this earlier but I didn't see your response: do you have any plans to record your tests, so people who aren't able to watch it live can still watch the video? (Depending on what streaming program you're using, this may be a builtin function.)

I am a Newbie and a lurker I bow to all of you for your unbounded enthusiasm and hardwork. While I am not a DIYer, I have been following with all the DIY projects. I have a humble suggestion.
I was changing the parameters in the McCalloch Thrust calculation Spreadsheet. (Excellent work!)
By having the same power and changing the geometry and size of the frustum, more than 1 N can be achived, it looks like.
(Changed based on Juan 2 corrected values)
Updated
Input Reference Value
Big Diameter 28
Small Diameter 1
Cavity Length 100
Q 5000
Frequency 2.45
Power 1000
Big Radius 14
Small Radius 0.5
mN Force 1608.75
mN Force 1081.08
mN Force 1025.45
This could prove the validity of McCalloch calculations.
Just a humble suggestion.

@Dr. Rodal ("And/Or curious others")
Would you be able to produce output using the tool or formula of your choice at your leisure to see how relative humidity might impact results?
If you already know. Please don't waste your time.
I just am curious that I have not seen any mention about RH having any cause or effect or that the impact of RH differences are so small, that they don't need to be considered.
With the large differences in thrust results for tests done in a vacuum compared to testing under normal atmospheric pressure conditions. I've been wondering if RH could be a major contributing cause to those differences.
Thanks
Don
Hi, I have not taken the time to consider how to calculate how humidity may affect the results. I agree that it sounds very interesting for many reasons. For example, we know how microwave ovens preferentially excite a water molecule and they mostly heat food by heating water, so moist air is most relevant. I would have to think about how to include that effect in calculations :)
For the time being it would be useful if experimenters would record and report the relative humidity of the environment when they performed their tests.
Another sign of getting older. Sigh.....
I forgot to mention, that we also used both horizontal and vertical polarity with our microwave antennas for diversity. In some cases vertical or horizontal polarities made major differences with different atmospheric conditions.
Antennas which received our microwave signals ("Using tropospheric scatter") were as much as 400 miles away. So there were multiple weather conditions which our microwave transmission could encounter to reach our distant ends.
I have no idea if this applies to EM Drives or not.
But I am surprised that there has been little test data to compare when a waveguide is used to inject the microwave signal into the EM Drive if the waveguide was in a horizontal or vertical mounting position on the EM Drive and if the polarity of that waveguide, could have any effect on measured results when using the same sized EM Drive with the opposite polarity to compare horizontal to vertical polarities. Near or about at the same mounting position.
I'm not sure if any of your test tools or formulas allow waveguides to use horizontal or vertical polarities as input data to see if any polarity differences might make the output of same, have different results.
Don
Good points Don, nice post.
Ok... this is from a gal who though she knew something about antennas and I'd like your input because I found out I really don't. I would guess over the last couple months this group has dug into antennas quite deep and I've read more about them than I care to think of. Weird and beautiful stuff.
A couple of things that are on the the forefront that to me have seemed to be of importance.
First off is the radiation patterns and how they must be aligned correctly to excite one or the other, TE or TM mode pattern in the frustum.
Second is the radiation pattern needs to be as uniform as it can, with no funny lobes. A simple snub @ 2.45GHz in a TE insertion point towards the bottom leads to rotational effects of the modes around the cavity. As they build and collapse it kills off the Q of the cavity.
Third is the losses associated with an antenna into the cavity. We have calculated only 4050 watts of effective RF being available to cause a thrust effect in the cavity.
Fourth that low output is why many (Including me) have elected to treat the Frustum like part of a waveguide and directly inject the output of a magnetron down a waveguide into the cavity. rfmwguy coupled his magnetron directly into his cavity, the man is awsum.
Thanks.
First, by no means is my experience even close to yours or others here.
That said. I can't see how when mounting a waveguide to a EM Drive in a horizontal vs. vertical position could not have major effects on how the microwave transmission propagates in a closed Frustum cavity.
After all. It was one of only two of the levels of diversity, which were used by the U.S. Air Force High Power Tropospheric Scatter long distance microwave transmissions. The other being two antennas, sending to the same distant ends.
I have no math or science experience to back this up other than it's my personal belief that many measured factors which are being calculated using formulas and test tools for EM Drives which are using waveguides as their input source. Would change in major ways. When using a horizontal or vertical polarity of the mounting position on or near the same mounting position used with the other polarity. For the same EM Drive. Which factors and/or how much. I have no idea.
I wish I had a better answer for you. But I think some of the test tools and/or formulas being used here if they have the ability to use input data using a different polarity for EM Drives using waveguide input as input data. That this would and could be quickly confirmed as fact or be ruled out as "Junk Science".
If I had any worries about this it would be. How accurately some test tools or formulas account for horizontal and vertical waveguide mounts to a Frustum, when calculating how the microwave transmission propagates.
I say this because of the Frustum cavity not being a normal cylinder. So the polarity of how the waveguide is mounted on a Frustum cavity would predispose the initial microwave transmission as it's leaving the waveguide, to less or more of the Frustum cavity wall angle changes based on the polarity of how the waveguide was mounted. Because of the waveguide being a rectangle and not a square.
I can't see how that would not change how the microwave transmission propagated when the waveguide polarity is changed from horizontal to vertical or vise versa.
For me to simply disregard what polarity the waveguide entered the Frustum cavity for testing purposes. Would be equal to saying if you added or removed 2 inches in length to a Frustum that one would not see any noticeable test result differences. Which I think virtually everyone here would say would be an incorrect assumption.
A funny aside when saying "My EM Drive used a waveguide with a horizontal polarity" We need to create a common reference to should the waveguide polarity be considered to be in reference to the small and large end of a Frustum or the sides of a Frustum. My vote is to use the small and large ends as the reference point as what polarity a waveguide is using to enter a Frustum.
Don

I am a Newbie and a lurker I bow to all of you for your unbounded enthusiasm and hardwork. While I am not a DIYer, I have been following with all the DIY projects. I have a humble suggestion.
I was changing the parameters in the McCalloch Thrust calculation Spreadsheet. (Excellent work!)
By having the same power and changing the geometry and size of the frustum, more than 1 N can be achived, it looks like.
(Changed based on Juan 2 corrected values)
Updated
Input Reference Value
Big Diameter 28
Small Diameter 1
Cavity Length 100
Q 5000
Frequency 2.45
Power 1000
Big Radius 14
Small Radius 0.5
mN Force 1608.75
mN Force 1081.08
mN Force 1025.45
This could prove the validity of McCalloch calculations.
Just a humble suggestion.
Welcome to the forum. :)
Unfortunately McCulloch has many formulas that are different from the one in the spreadsheet. See his blog for all his formulas:
http://physicsfromtheedge.blogspot.com/
I noticed that in the above calculation the length is 100 times the small diameter.
To confuse the problem further, besides having more than one formula, McCulloch in his blog has written that large length/diameter ratios are bad for actual thrust. Since McCulloch has a number of formulas I suggest that you post your above suggestion as a question in his blog and see what McCulloch responds, as he is pretty good at answering questions.
If he answers you, I would appreciate your posting back here at NSF and letting us know what he answered.

NSF1701 live test...Galinstan ordered and should be here within a week. Will do the live test either 8/18 or 8/25 depending on the delivery.
I think X_Ray asked this earlier but I didn't see your response: do you have any plans to record your tests, so people who aren't able to watch it live can still watch the video? (Depending on what streaming program you're using, this may be a builtin function.)
Yes, I think I can record on Ustream as I do it. If I cannot, I'll simply do a recorded video.

...
Note: I just can't help having "flashbacks" to my U.S. Air Force days as a Wideband Communications Equipment 304x0 equipment repair person (http://oai.dtic.mil/oai/oai?verb=getRecord&metadataPrefix=html&identifier=ADA201690) in the 1970's who maintained microwave equipment using near these same microwave frequencies.
One of my many maintenance duties was to replace desiccant in every waveguide we used and it was not simply to avoid only rust and/or condensation, in those waveguides.
It has been awhile. But I think one of the reasons why we used desiccant and replaced it so often in all our waveguides had to do with standing waves. I could be remembering this incorrectly. But that's what I recall today. That said. The situation I am referencing was at a site where our microwave transmit power was 10 KW per 60 foot parabolic antenna. Shown below.
Don
I would suspect the main reason was to prevent arcing in the waveguide. It's pretty common to find desiccant in the X band aircraft weather radars operating above 67 KW but not in the lower powered ones...

...
Note: I just can't help having "flashbacks" to my U.S. Air Force days as a Wideband Communications Equipment 304x0 equipment repair person (http://oai.dtic.mil/oai/oai?verb=getRecord&metadataPrefix=html&identifier=ADA201690) in the 1970's who maintained microwave equipment using near these same microwave frequencies.
One of my many maintenance duties was to replace desiccant in every waveguide we used and it was not simply to avoid only rust and/or condensation, in those waveguides.
It has been awhile. But I think one of the reasons why we used desiccant and replaced it so often in all our waveguides had to do with standing waves. I could be remembering this incorrectly. But that's what I recall today. That said. The situation I am referencing was at a site where our microwave transmit power was 10 KW per 60 foot parabolic antenna. Shown below.
Don
I would suspect the main reason was to prevent arcing in the waveguide. It's pretty common to find desiccant in the X band aircraft weather radars operating above 67 KW but not in the lower powered ones...
Yes, that was also one of the reasons but as I stated in my prior post I seem to recall it helping with standing waves as well. So it was not simply for condensation reasons but also for RH water vapor reasons in the waveguide.
Again, I could be wrong about this but this is what I recall today. Many decades later.
Don

So what did you use? Just a bag of desiccant sitting in the wave guide? How big?

So what did you use? Just a bag of desiccant sitting in the wave guide? How big?
Sometimes simply a bag of desiccant about the size of a sugar packet in a restaurant. Other times raw desiccant powder of varying quantities which had it's own pouch that also needed to be replaced when the desiccant was replaced.
Desiccant quantity would depend on the type of waveguide, how the waveguide ran vertically or horizontally and for how long of a distance.
Generally, minus the bendable waveguide runs to the antennas. The moment a waveguide went from vertical to horizontal after the initial waveguide bend a new section of waveguide would be used. Which is where virtually all the desiccant was located and placed.
Don

NSF1701 live test...Galinstan ordered and should be here within a week. Will do the live test either 8/18 or 8/25 depending on the delivery.
I think X_Ray asked this earlier but I didn't see your response: do you have any plans to record your tests, so people who aren't able to watch it live can still watch the video? (Depending on what streaming program you're using, this may be a builtin function.)
Yes, I think I can record on Ustream as I do it. If I cannot, I'll simply do a recorded video.
Frustumapaloosa?! :D
If the timing's right, you, Shells and TT could put on a show!

About PaulTheSwag's experiment:
1. What differentiates the thrust profile from one where only an initial impulse was produced?
2. What is a "double knifeedge fulcrum"? It makes no sense to me.
3. Do we know the power value?
2. Did you saw the pictures? http://imgur.com/a/iO7er
OK. I now understand the double knife edge (actually triple).
Same as mine, 3 blades, 2 balance points.
()
Two balance points for me.
Shell your bearing is able to produce a lot of friction.. ???
What do you think about commercial bearings for your carbon construction? metal, plastic or ceramic
It could if I wasn't using a trick here that I needed to mention and I'm really sorry it slipped my mind. The knife edge really isn't a knife edge anymore, it has been rounded off using a belt sander and the tube simply rolls over the rounded surface of the blade that was a sharp edge.
I liked the strength of the blade but I disliked the friction and stresses when using 2 blades one on top of each other or the way the blade could slice into a metal or a carbon fiber tube. In testing I had the blades chip and shatter against each other and glued steel plates end up getting a grove from the blade in just a couple runs up and down with weights on the fulcrum.
A mental calculation thinking about the small radii the tube would roll over changing the length over 1 meter was around 5 microns. It's acceptable.
Added: What do you think xray? Do you think this will work ok? I wanted to try and avoid any bearing for they seem to always have the issued of initial movement from stiction.
The stiction at initial movement is inherent for any conventional bearing. Rounded blades will work better i think, use a drop of oil and all will be good :)
Ballbearing is even better...
picture source:http://www.gsstoedtlen.homepage.tonline.de/rad/geschichte_rad3.htm

I am a Newbie and a lurker I bow to all of you for your unbounded enthusiasm and hardwork. While I am not a DIYer, I have been following with all the DIY projects. I have a humble suggestion.
I was changing the parameters in the McCalloch Thrust calculation Spreadsheet. (Excellent work!)
By having the same power and changing the geometry and size of the frustum, more than 1 N can be achived, it looks like.
(Changed based on Juan 2 corrected values)
Updated
Input Reference Value
Big Diameter 28
Small Diameter 1
Cavity Length 100
Q 5000
Frequency 2.45
Power 1000
Big Radius 14
Small Radius 0.5
mN Force 1608.75
mN Force 1081.08
mN Force 1025.45
This could prove the validity of McCalloch calculations.
Just a humble suggestion.
Did you plug the same values into @Notsosureofit's equation and see how it compares? His equation is more likely correct than McCulloch's.
Todd

[quote author=TheUberOverLord link=topic=38203.msg1415594#msg1415594
Should have said insertion points for the waveguide instead.
Each will excite a different mode.
Top magnetron
Side magnetron waveguide
Dual Dipoles top
Opposing RF injection points

NSF1701 live test...Galinstan ordered and should be here within a week. Will do the live test either 8/18 or 8/25 depending on the delivery.
I think X_Ray asked this earlier but I didn't see your response: do you have any plans to record your tests, so people who aren't able to watch it live can still watch the video? (Depending on what streaming program you're using, this may be a builtin function.)
Yes, I think I can record on Ustream as I do it. If I cannot, I'll simply do a recorded video.
Frustumapaloosa?! :D
If the timing's right, you, Shells and TT could put on a show!
There you go...might be as interesting as most the stuff on basic cable ;)

NSF1701 live test...Galinstan ordered and should be here within a week. Will do the live test either 8/18 or 8/25 depending on the delivery.
I think X_Ray asked this earlier but I didn't see your response: do you have any plans to record your tests, so people who aren't able to watch it live can still watch the video? (Depending on what streaming program you're using, this may be a builtin function.)
Yes, I think I can record on Ustream as I do it. If I cannot, I'll simply do a recorded video.
Frustumapaloosa?! :D
If the timing's right, you, Shells and TT could put on a show!
I'm pushing as hard as I can. ;)
Would be a great show.
Shell

http://cas.web.cern.ch/cas/Germany2009/Lectures/PDFWeb/Jensen.pdf
Back to the grind
good reading...

[quote author=TheUberOverLord link=topic=38203.msg1415594#msg1415594
Should have said insertion points for the waveguide instead.
Each will excite a different mode.
Top magnetron
Side magnetron waveguide
Dual Dipoles top
Opposing RF injection points
Your flexible cone is a good idea i think!
All the modes are excitable, more or less good with the antenna at each position/orientation.
VNA wide band measurements show that.(it is hard work to suppress a resonance nearly complete) ;)
At a wrong position and/or orientation you will see only a little dip in the plot. Better you look in the complex xyplane (Magnitude and Phase or Re/Im).
Over as under coupling looks equal in a simple magnitude/frequency plot!
You are able to change the length, that is need to get resonance for the different modes (and high Q).
It's a good plan and i am sure a lot of work!
Can you post some pictures of the present state? Would be very interesting.
picture 1: coplanar transmission line with sonnetEM
pictures 2 and 3: magnitude vs complex

http://cas.web.cern.ch/cas/Germany2009/Lectures/PDFWeb/Jensen.pdf
Back to the grind
good reading...
It's a very nice read. Notice that, because the R,L,C components in the cavity model are in shunt configuration, the usual expression for Q is reciprocated (e.g. Q = R/(w L) ). Also note that maximum attainable Q's (nonsuperconducting) are pegged around 41,000.

http://cas.web.cern.ch/cas/Germany2009/Lectures/PDFWeb/Jensen.pdf
Back to the grind
good reading...
It's a very nice read. Notice that, because the R,L,C components in the cavity model are in shunt configuration, the usual expression for Q is reciprocated (e.g. Q = R/(w L) ). Also note that maximum attainable Q's (nonsuperconducting) are pegged around 41,000.
The file looks good! Thanks for the quote

Hi
This is what Mike McCulloch had replied
//Dear Ramachandra, The formula I published, and that you are using, was an approximation that assumed the Unruh waves can only resonate perpendicular to the emdrive's cavity axis. This is an approximation because the Unruh waves can also resonate along the axis, and in diagonal directions. If you had a pointed cone, this formula would then predict no waves at all at the pointed end, and an infinite thrust since Wsmall=0, but in the real emdrive Unruh waves would still be able to exist at the small end by resonating along the length of the axis. This limitation of the formula is not so bad for the emdrive because it is a truncated cone, but a better formula is needed and I've been trying to calculate the exact analytic formula to take account of resonance in all directions. In lieu of that I've developed a simple formula that does take account of resonance along the axis. It is:
F = 6PQL/c * ( 1/(L+4wb)  1/(L+4ws) )
L=axial length. You can also see my discussion of this formula here:
http://physicsfromtheedge.blogspot.co.uk/2015/02/mihscvsemdrivedata3d.html//
As for these calculations, the original post did contain those numbers
mN Force 1608.75
mN Force 1081.08
mN Force 1025.45
These three numbers are from three of his equations.
When I put these numbers in @notsureofit xls
Big Diameter 28
Small Diameter 1
Cavity Length 100
Q 5000
Frequency 2.45
Power 1000
I get 1144 mN!
But If I keep the original length 0.164m, i get 6980 mN.
Such testing could prove which one can be counted on.
Just a suggestion.

So what did you use? Just a bag of desiccant sitting in the wave guide? How big?
aero, the csv files you run for:
\\64 cycle Shell 2D loop ant \\ 64cyclerun 2d loop antcsv \\ 2dloop64
show a TE (transverse electric) mode.
Unfortunately, we cannot tell for sure what mode it is unless we get a circular crosssection (with normal z) at a location away from the bases. The reason for this is that the electric modes in the transverse direction are zero at the bases due to the boundary conditions. (This was not a problem for TM mode shapes because the transverse magnetic field is not zero at the bases)
I would like the same information (all 6 fields, using the same mesh, etc.) as for the other runs at the following location, for a circular crosssection (with normal z):
Column 30(columns ranging from 0 to 228)
in order to ascertain what TE mode shape it is
If you have to rerun, it may be advantageous to rerun for the regular amount of time instead of 64 cycles because that way we can accomplish two things:
1) ascertain what TE mode shape it is
2) compare the stresses, forces, etc at the bases and the Poynting vector in the trapezium plane with the previous runs for Yang Shell that had transverse magnetic modes
Thanks

http://cas.web.cern.ch/cas/Germany2009/Lectures/PDFWeb/Jensen.pdf
Back to the grind
good reading...
It's a very nice read. Notice that, because the R,L,C components in the cavity model are in shunt configuration, the usual expression for Q is reciprocated (e.g. Q = R/(w L) ). Also note that maximum attainable Q's (nonsuperconducting) are pegged around 41,000.
If you think those dual ported cavity designs are like a non ported and unloaded EMDrive cavity well good luck.
BTW that looks like a Superfish field drawing.

By the way those of you supporting the EM drive want an example of a theory that started out on the fringes but has gradually moved more centre wise then they only have to look at holographic theory for the universe.
http://www.sciencedaily.com/releases/2015/04/150427101633.htm
Is that theory the one that leads down the path to... everything around us including us is just a simulation.

Looks like I am going to be interviewed on a live radio talk show about my NSF1701 experiment in the near future. When it becomes finalized, I'll post the info I have. Can't discuss any details yet...
They always said I had a Face made for the Radio ;)

By the way those of you supporting the EM drive want an example of a theory that started out on the fringes but has gradually moved more centre wise then they only have to look at holographic theory for the universe.
http://www.sciencedaily.com/releases/2015/04/150427101633.htm
Is that theory the one that leads down the path to... everything around us including us is just a simulation.
Actually, no. They are separate. But note that they are not mutually exclusive 8)

Interesting Russian EMDrive like patent:
http://bankpatentov.ru/node/123593
and comment received on Reddit EMDrive forum:
https://www.reddit.com/r/EmDrive/comments/3ceyjv/email_from_roger_shawyer/ctww6rd
As Dr. Vladimir Leonov claims the "Shawyer Effect" works via the QV, Dr. White might be interested.
Yes Interesting
(snip)
...The invention relates to the space industry and is designed to create traction in the new generations of interplanetary spacecraft by using superstrong interactions with the vacuum field. The proposed method of propulsion is carried out in a vacuum due to redistribution of medium density quantum vacuum field within the working fluid in a direction opposite to the vector thrust by deformation of the vacuum field, acting on the working fluid system of rotating nonuniform electric and magnetic fields of skew, intensity gradient of which coincides with the direction thrust vector, and the working fluid is set at the same time, electric and magnetic properties. According to the first embodiment of the motor field for a spacecraft equipped with a generator, the voltage converter and activators vacuum field comprising a motor rotor formed as a working fluid of a dielectric and ferromagnetic material in the shape of a truncated cone, the base of which is coaxially aligned with the rotor of the motor, advantageously giromotora, magnetic system bipolar electrodes that cover a clearance taper working fluid. In a second embodiment of the field drive for spacecraft includes a housing field engine that serves as the body of the spacecraft, equipped with activators of the vacuum field, ring generator, battery, battery current converter, traction control field Motor, motors to drive the rotor activators vacuum field. ..
(snip)

I keep thinking about the idea (http://forum.nasaspaceflight.com/index.php?topic=37642.msg1412971#msg1412971) I had a few days ago and pushed it further. I thought about Rodal and WarpTech's advice of increasing cone angle and keeping the apex as near as possible of the small end. I also kept Shawyer's high D_{f} and concentric spherical ends to maintain a high Q, and I've ended up with this wide and shallow resonant design, with incredible large spherical ends, making the frustum almost a halfsphere:
D_{b} = 600 mm
D_{s} = 150 mm
L = 51.20 mm
r_{1} = 76.92 mm
r_{2} = 307.67 mm
r_{2}r_{1} = 230.75 mm
θ = 77.18°
Resonance at 2.45 GHz in TE013 mode, D_{f} = 0.96
Would be a challenge to build but nevertheless interesting to test. What could be the Q of such a cavity?

I keep thinking about the idea (http://forum.nasaspaceflight.com/index.php?topic=37642.msg1412971#msg1412971) I had a few days ago and pushed it further. I thought about Rodal and WarpTech's advice of increasing cone angle and keeping the apex as near as possible of the small end. I also kept Shawyer's high D_{f} and concentric spherical ends to maintain a high Q, and I've ended up with this wide and shallow resonant design, with incredible large spherical ends, making the frustum almost a halfsphere:
D_{b} = 600 mm
D_{s} = 150 mm
L = 51.20 mm
r_{1} = 76.92 mm
r_{2} = 307.67 mm
r_{2}r_{1} = 230.75 mm
θ = 77.18°
Resonance at 2.45 GHz in TE013 mode, D_{f} = 0.96
Would be a challenge to build but nevertheless interesting to test. What could be the Q of such a cavity?
That's an interesting shape!
How did you calculate <<Resonance at 2.45 GHz in TE013 mode>> ?

That's an interesting shape!
How did you calculate <<Resonance at 2.45 GHz in TE013 mode>> ?
Thanks doc!
I used TheTraveller's latest's spreadsheet (http://emdrive.wiki/Useful_EMDrive_Design_and_Test_Tools) to tune the various dimensions. I do not know any software or technique to do those calcs.

That's an interesting shape!
How did you calculate <<Resonance at 2.45 GHz in TE013 mode>> ?
Thanks doc!
I used TheTraveller's latest's spreadsheet (http://emdrive.wiki/Useful_EMDrive_Design_and_Test_Tools) to tune the various dimensions. I do not know any software or technique to do those calcs.
It is quite an interesting shape to explore for example whether there is a limit to the notion of large angles and proximity to the base. I will calculate the attenuation shape, Q and resonance when I have a chance :)

Sorry for crashing in but I must ask.
Is Neon light usefull for detecting RF leaks outside frustum?
Sorry if it`s been proposed.
Keep up, we are counting on you! :)

Sorry for crashing in but I must ask.
Is Neon light usefull for detecting RF leaks outside frustum?
Sorry if it`s been proposed.
Keep up, we are counting on you! :)
From what I have seen, a neon tube must be almost in contact with the source. Not a good idea.

Well :(
But there are some crazy rigs:
https://www.youtube.com/watch?v=NIjcNIR_Yg8
https://www.youtube.com/watch?v=_fqYusKZC38

Looks like I am going to be interviewed on a live radio talk show about my NSF1701 experiment in the near future. When it becomes finalized, I'll post the info I have. Can't discuss any details yet...
They always said I had a Face made for the Radio ;)
I just asked him for details and I might do it with you. No weirdness and space aliens allowed. ;)

Dr. Rodal,
I was trying to figure out a way to communicate what I thought was going on, but I think I was wrong. It's simple 
Draw 3 sine waves on a sheet of paper, xy axis, each symmetric about the x axis, but with different amplitudes. Then draw horizontal lines tangent to the extreme positive and negative values of each sine wave. I used the y value of the top and bottom horizontal line.
So the weaker sign waves are not clipped, they just don't have enough power to show up on the scale of the strongest.
I'll see about using a different color map.
bluered (opaque blue to transparent white to opaque red). I have several color maps available, this is just the first try. I personally don't like it very much.
Some of these images seem wrong.
Example:
bighz
(http://forum.nasaspaceflight.com/xindex.php,qaction=dlattach,3Btopic=38203.0,3Battach=1055446,3Bimage.pagespeed.ic.JnWBLMhTwp.webp)
as I interpret this, it is the Hz field, the magnetic field normal to the Big Base, with the z axis longitudinal, normal to the Big Base.
the magnetic field normal to a surface should be zero at a surface. It should be zero at the Big Base.
It is close to zero when I postprocess the csv files with Wolfram Mathematica
Yet in the above images you show this bighz as having the highest magnitude magnetic field at the Big Base?
Ditto for smallhz
(http://forum.nasaspaceflight.com/xindex.php,qaction=dlattach,3Btopic=38203.0,3Battach=1055434,3Bimage.pagespeed.ic.1L14N7WegQ.webp)
_____________
PS: I verified that the end cuts:
End cuts are at: Big end .h5 row 15
Small end .h5 row 214
are at the correct location, so that is not the source of the problem.

Have decided to dump 9kgs of rotary table mass by using 1kg of Lithium Ion rechargeable batteries (28 x 3.7v 3.8Ah = approx 400Whs of energy) instead of 7kgs of SLA batteries and reduce the frustum thickness from 2mm (4.2kg) to 0.5mm (1kg).
Expected frustum temp rise and pressure calcs show 0.5mm sidewall and end plate thickness is more than enough.
Should now take about 2 minutes per 30 rpm increase versus 4 minutes at the old mass.

I keep thinking about the idea (http://forum.nasaspaceflight.com/index.php?topic=37642.msg1412971#msg1412971) I had a few days ago and pushed it further. I thought about Rodal and WarpTech's advice of increasing cone angle and keeping the apex as near as possible of the small end. I also kept Shawyer's high D_{f} and concentric spherical ends to maintain a high Q, and I've ended up with this wide and shallow resonant design, with incredible large spherical ends, making the frustum almost a halfsphere:
D_{b} = 600 mm
D_{s} = 150 mm
L = 51.20 mm
r_{1} = 76.92 mm
r_{2} = 307.67 mm
r_{2}r_{1} = 230.75 mm
θ = 77.18°
Resonance at 2.45 GHz in TE013 mode, D_{f} = 0.96
Would be a challenge to build but nevertheless interesting to test. What could be the Q of such a cavity?
Glad you found the spreadsheet useful. Using Goal Seek has made it super fast to find the exact resonance in the desired mode or not.
Interesting design.
As I understand the momenta gradient driven opposite Frustum movement and resultant Force vectors, they "PUSH" the frustum from the outer big end edge toward the vertex. Would not this design result in a lot of Force vectors pushing toward the vertex but not really helping axial Force generation so much?

I keep thinking about the idea (http://forum.nasaspaceflight.com/index.php?topic=37642.msg1412971#msg1412971) I had a few days ago and pushed it further. I thought about Rodal and WarpTech's advice of increasing cone angle and keeping the apex as near as possible of the small end. I also kept Shawyer's high D_{f} and concentric spherical ends to maintain a high Q, and I've ended up with this wide and shallow resonant design, with incredible large spherical ends, making the frustum almost a halfsphere:
D_{b} = 600 mm
D_{s} = 150 mm
L = 51.20 mm
r_{1} = 76.92 mm
r_{2} = 307.67 mm
r_{2}r_{1} = 230.75 mm
θ = 77.18°
Resonance at 2.45 GHz in TE013 mode, D_{f} = 0.96
Would be a challenge to build but nevertheless interesting to test. What could be the Q of such a cavity?
I might be able to model it. Can you export an STL of the part?

Dr. Rodal,
I was trying to figure out a way to communicate what I thought was going on, but I think I was wrong. It's simple 
Draw 3 sine waves on a sheet of paper, xy axis, each symmetric about the x axis, but with different amplitudes. Then draw horizontal lines tangent to the extreme positive and negative values of each sine wave. I used the y value of the top and bottom horizontal line.
So the weaker sign waves are not clipped, they just don't have enough power to show up on the scale of the strongest.
I'll see about using a different color map.
bluered (opaque blue to transparent white to opaque red). I have several color maps available, this is just the first try. I personally don't like it very much.
Some of these images seem wrong.
Example:
bighz
(http://forum.nasaspaceflight.com/xindex.php,qaction=dlattach,3Btopic=38203.0,3Battach=1055446,3Bimage.pagespeed.ic.JnWBLMhTwp.webp)
as I interpret this, it is the Hz field, the magnetic field normal to the Big Base
the magnetic field normal to a surface should be zero at a surface. It should be zero at the Big Base.
It is close to zero when I postprocess the csv files with Wolfram Mathematica
Yet in the above images you show this bighz as having the highest magnitude magnetic field at the Big Base?
Ditto for smallhz
(http://forum.nasaspaceflight.com/xindex.php,qaction=dlattach,3Btopic=38203.0,3Battach=1055434,3Bimage.pagespeed.ic.1L14N7WegQ.webp)
Interesting  We'll need to wait until Imbfan gets the automated field intensity extraction software running. That won't be to long based on the progress she is making.
Earlier today I was looking at the field intensity of the images around the base ends using hdfview. It seems clear from looking at adjacent slices that something may be not right. See the attached jpgs for z slice 14, 15, 16 and 17. Slice z14 is within the metal, so nothing. Slice z15 is the cut we have been taking as at the big base, while z16 is one pixel inward and z17 is 2 pixels inward. With the lattice measuring 0.275 meters (rounded up in deference to DeltaMass) and resolution 250, the distance between pixels is 1.1 mm so z15 should be well out of the metal if z14 is the metal surface. But the images seem to say that z14 is well inside the metal and z15 is somewhere close to the surface while z16 is well outside the metal.
I wonder if the meep "subpixel averaging" is blending the dielectric constant at the edge of the metal with the air, also at the edge? If so, maybe I should quit using "subpixel averaging." On the other hand, the characteristic you wrote about above seems different than the one I observed.
Let's see what it looks like when the field intensities are automatically and correctly extracted for the images. Then we'll have something that we can fix, if it is broken. Fixing my fat fingers is much more difficult and they are not even broken  yet :o
P.S. I see you looked at this while I was typing.

Looks like I am going to be interviewed on a live radio talk show about my NSF1701 experiment in the near future. When it becomes finalized, I'll post the info I have. Can't discuss any details yet...
They always said I had a Face made for the Radio ;)
I just asked him for details and I might do it with you. No weirdness and space aliens allowed. ;)
That's a fact...he just called and said it might be tonight...will call me back in abt 1 hr. Love to have you there as well. Told them my belief was seeing is believing...not willing to take others word on it. had to try it for myself.

Looks like I am going to be interviewed on a live radio talk show about my NSF1701 experiment in the near future. When it becomes finalized, I'll post the info I have. Can't discuss any details yet...
They always said I had a Face made for the Radio ;)
I just asked him for details and I might do it with you. No weirdness and space aliens allowed. ;)
That's a fact...he just called and said it might be tonight...will call me back in abt 1 hr. Love to have you there as well. Told them my belief was seeing is believing...not willing to take others word on it. had to try it for myself.
Don't suppose we'll be able to listen or you record? Likely will be copyrighted.

Looks like I am going to be interviewed on a live radio talk show about my NSF1701 experiment in the near future. When it becomes finalized, I'll post the info I have. Can't discuss any details yet...
They always said I had a Face made for the Radio ;)
I just asked him for details and I might do it with you. No weirdness and space aliens allowed. ;)
That's a fact...he just called and said it might be tonight...will call me back in abt 1 hr. Love to have you there as well. Told them my belief was seeing is believing...not willing to take others word on it. had to try it for myself.
Don't suppose we'll be able to listen or you record? Likely will be copyrighted.
I suppose that rfmwguy is the legal owner of whatever he produces, including what he speaks and articulates.

Will be talking NSF1701 on art bells dark matters digital radio network tomorrow at midnight PST.
Guest info to appear tomorrow abt 7:30 PM on othersideofmidnight.com website
Show is a mixture of science fiction, fantasy and science fact...I'll stay with facts and hope to still be entertaining, but understand its show biz. Will not over promise and under deliver however ;)
Its late for sure but they archive shows. Will talk how and why I jumped in and where it could lead.
Sounds like fun...

Will be talking NSF1701 on art bells dark matters digital radio network tomorrow at midnight PST.
Guest info to appear tomorrow abt 7:30 PM on othersideofmidnight.com website
Show is a mixture of science fiction, fantasy and science fact...I'll stay with facts and hope to still be entertaining, but understand its show biz. Will not over promise and under deliver however ;)
Its late for sure but they archive shows. Will talk how and why I jumped in and where it could lead.
Sounds like fun...
Even money says Art brings up UFO's in the first 5 min.

Will be talking NSF1701 on art bells dark matters digital radio network tomorrow at midnight PST.
Guest info to appear tomorrow abt 7:30 PM on othersideofmidnight.com website
Show is a mixture of science fiction, fantasy and science fact...I'll stay with facts and hope to still be entertaining, but understand its show biz. Will not over promise and under deliver however ;)
Its late for sure but they archive shows. Will talk how and why I jumped in and where it could lead.
Sounds like fun...
Even money says Art brings up UFO's in the first 5 min.
Course my reply would be I will believe it when I see it personally ;)
Sorta the reason I started my build...

Will be talking NSF1701 on art bells dark matters digital radio network tomorrow at midnight PST.
Guest info to appear tomorrow abt 7:30 PM on othersideofmidnight.com website
Show is a mixture of science fiction, fantasy and science fact...I'll stay with facts and hope to still be entertaining, but understand its show biz. Will not over promise and under deliver however ;)
Its late for sure but they archive shows. Will talk how and why I jumped in and where it could lead.
Sounds like fun...
Even money says Art brings up UFO's in the first 5 min.
Course my reply would be I will believe it when I see it personally ;)
Sorta the reason I started my build...
Be prepared what to answer if he asks you:
1) Whether Shawyer invented the EM Drive as a result of a close encounter of the 3rd kind with UFO's that allowed him to get access to UFO's propulsion technology?
2) Whether the EM Drive is derived from Die Glocke Wunderwaffe antigravity research from WWII ?
3) What are you going to do if you accidentally create a wormhole in your garage as a result of your EM Drive research
4) if the EM Drive works, how long will a trip to Alpha Centauri take.
:)

Be prepared what to answer if he asks you:
1) Whether Shawyer invented the EM Drive as a result of a close encounter of the 3rd kind with UFO's that allowed him to get access to UFO's propulsion technology?
Art has been doing this a long time. Surely he knows the UFOs use Zero time zero space motion frozen 500KV (DC) repulsive electrostatic counter rotating vortexes in glass and copper plate capacitors radially around a central magnetic generator. Everyone knows that, right?*
Ref:
Supreme Cosmic Secret Vol. 1, p2, publisher unknown.
* One observes that the rotation of static fields is, by definition, proportional to Maxwell's 1880 rotation rate.

...
Some of these images seem wrong.
Example:
bighz
(http://forum.nasaspaceflight.com/xindex.php,qaction=dlattach,3Btopic=38203.0,3Battach=1055446,3Bimage.pagespeed.ic.JnWBLMhTwp.webp)
as I interpret this, it is the Hz field, the magnetic field normal to the Big Base
the magnetic field normal to a surface should be zero at a surface. It should be zero at the Big Base.
It is close to zero when I postprocess the csv files with Wolfram Mathematica
Yet in the above images you show this bighz as having the highest magnitude magnetic field at the Big Base?
Ditto for smallhz
(http://forum.nasaspaceflight.com/xindex.php,qaction=dlattach,3Btopic=38203.0,3Battach=1055434,3Bimage.pagespeed.ic.1L14N7WegQ.webp)
Interesting  We'll need to wait until Imbfan gets the automated field intensity extraction software running. That won't be to long based on the progress she is making.
Earlier today I was looking at the field intensity of the images around the base ends using hdfview. It seems clear from looking at adjacent slices that something may be not right. See the attached jpgs for z slice 14, 15, 16 and 17. Slice z14 is within the metal, so nothing. Slice z15 is the cut we have been taking as at the big base, while z16 is one pixel inward and z17 is 2 pixels inward. With the lattice measuring 0.275 meters (rounded up in deference to DeltaMass) and resolution 250, the distance between pixels is 1.1 mm so z15 should be well out of the metal if z14 is the metal surface. But the images seem to say that z14 is well inside the metal and z15 is somewhere close to the surface while z16 is well outside the metal.
I wonder if the meep "subpixel averaging" is blending the dielectric constant at the edge of the metal with the air, also at the edge? If so, maybe I should quit using "subpixel averaging." On the other hand, the characteristic you wrote about above seems different than the one I observed.
Let's see what it looks like when the field intensities are automatically and correctly extracted for the images. Then we'll have something that we can fix, if it is broken. Fixing my fat fingers is much more difficult and they are not even broken  yet :o
P.S. I see you looked at this while I was typing.
Yes the Meep images are very wrong and misleading. Actually HXz is the largest, and HYz is close, but HZz at the Big Base is practically zero (contrary to the Meep images output that have it as the largest).
HZz must be zero at the Big Base to satisfy the Boundary Condition that the normal magnetic field must be zero at a conductor.
See my attachments below (using Wolfram Mathematica to postprocess the csv files) and compare with the Meep output.
NOTICE that my contour plots are rotated by 90 degress from your contour plots
It very much looks like the problem is due to the commands used to get the contour plots to be plotted within the same range. The plot commands are doing the opposite of what should be done. The commands are incorrectly clipping the data: they are only allowing the small HZz component to have contour plots.
It very much looks like the problem is due to the wrong range commands used to get the contour plots to be plotted within the same range. The plot commands are doing the opposite of what should be done. The commands are incorrectly clipping the data: they are only allowing the small HZz component to have contour plots.
The range used is the wrong range:
http://forum.nasaspaceflight.com/index.php?topic=38203.msg1415315#msg1415315
The ranges are from field components as follows:
# hx all data range from 0.000538633 to 0.000538633. H field big end
The correct range for HXz at the big end is 0.013 to +0.013
The contour plots are being clipped !!!!
Clipping is the complete opposite of what should be done. We are interested in the high values, not the low values !
QUESTION: At what time step did you output the pictures ?
(http://forum.nasaspaceflight.com/index.php?action=dlattach;topic=38203.0;attach=1055449;image)
(http://forum.nasaspaceflight.com/index.php?action=dlattach;topic=38203.0;attach=1055447;image)
(http://forum.nasaspaceflight.com/index.php?action=dlattach;topic=38203.0;attach=1055445;image)

Interesting  We'll need to wait until Imbfan gets the automated field intensity extraction software running. That won't be to long based on the progress she is making.
Please find a python file attached. It works well on my machine using the flags presented before. There remain some rough edges, but this should do the bulk of the work automagically. Enjoy!
I wonder if the meep "subpixel averaging" is blending the dielectric constant at the edge of the metal with the air, also at the edge? If so, maybe I should quit using "subpixel averaging." On the other hand, the characteristic you wrote about above seems different than the one I observed.
I'm pretty sure this is exactly what is happening. The boundary lies between pixels 14 and 16. It's late otherwise I'd math it out. If you don't subpixel average, the angled sides would go wonky, I bet.

I keep thinking about the idea (http://forum.nasaspaceflight.com/index.php?topic=37642.msg1412971#msg1412971) I had a few days ago and pushed it further. I thought about Rodal and WarpTech's advice of increasing cone angle and keeping the apex as near as possible of the small end. I also kept Shawyer's high D_{f} and concentric spherical ends to maintain a high Q, and I've ended up with this wide and shallow resonant design, with incredible large spherical ends, making the frustum almost a halfsphere:
D_{b} = 600 mm
D_{s} = 150 mm
L = 51.20 mm
r_{1} = 76.92 mm
r_{2} = 307.67 mm
r_{2}r_{1} = 230.75 mm
θ = 77.18°
Resonance at 2.45 GHz in TE013 mode, D_{f} = 0.96
Would be a challenge to build but nevertheless interesting to test. What could be the Q of such a cavity?
Glad you found the spreadsheet useful. Using Goal Seek has made it super fast to find the exact resonance in the desired mode or not.
Interesting design.
As I understand the momenta gradient driven opposite Frustum movement and resultant Force vectors, they "PUSH" the frustum from the outer big end edge toward the vertex. Would not this design result in a lot of Force vectors pushing toward the vertex but not really helping axial Force generation so much?
Yes. Every force vector in an EmDrive with spherical ends has an inner component (yet the vector on the axis) since they all point towards the vertex. With a side wall angle > 45° this component is maybe too much. Maybe the wall would need to be less angled.
Whatever, I did that to explore "extreme shapes" and these kinds of possibilities:
It is quite an interesting shape to explore for example whether there is a limit to the notion of large angles and proximity to the base. I will calculate the attenuation shape, Q and resonance when I have a chance :)

Using The Travellers spreadsheet to gauge resonance in the LBand to compare with other modelling.
Frustrum Big Diameter 0.4335m
Frustrum Small Diameter 0.2461m
Frustrum Centre Length 0.3543m
Frequency: 932.3Hz  close to TM011 Mode? Am I using the spreadsheet as intended?
Any idea what Q you end up with given the larger frustrum at TM011?
Thoughts as to TM011 EMDrive/QThruster phenomena at TM011 (vs. say TM010)? Would go TE012 but looks hard to do in the LBand according to this spreadsheet.

Please take a look at the conclusion of the below paper, it may explain why we have a decreasing force in vacuum.
When the particles in air (water,soot...) disappear the force decrease. What do you think of that? It could be an explanation for the thin shell frustums.
Lateral Chiralitysorting Optical Spin Forces in Evanescent Fields
http://arxiv.org/abs/1408.2268
"The transverse component of the spin angular momentum of evanescent waves gives rise to lateral optical forces on chiral particles, which have the unusual property of acting in a direction in which there is neither a field gradient nor wave propagation."

Interesting  We'll need to wait until Imbfan gets the automated field intensity extraction software running. That won't be to long based on the progress she is making.
Please find a python file attached. It works well on my machine using the flags presented before. There remain some rough edges, but this should do the bulk of the work automagically. Enjoy!
I wonder if the meep "subpixel averaging" is blending the dielectric constant at the edge of the metal with the air, also at the edge? If so, maybe I should quit using "subpixel averaging." On the other hand, the characteristic you wrote about above seems different than the one I observed.
I'm pretty sure this is exactly what is happening. The boundary lies between pixels 14 and 16. It's late otherwise I'd math it out. If you don't subpixel average, the angled sides would go wonky, I bet.
Subpixel averaging cannot be the cause of the problem because subpixel averaging should also affect the csv files, but as I show in message: http://forum.nasaspaceflight.com/index.php?topic=38203.msg1415788#msg1415788 the csv files do NOT have this problem: the csv files correctly show the HZz magnetic field normal to the big base to have the lowest magnitude (instead of the highest), the csv files show it to have a magnitude close to zero, and it should be zero to satisfy the boundary conditions.
So, the problem has everything to do with the routine and commands used to make the plots: it is a postprocessing problem, not a processing problem. Since subpixel avearaging affects processing itself, it should affect the csv files output, and hence subpixel averaging cannot be the source of the problem.
It very much looks like the problem is due to the wrong range commands used to get the contour plots to be plotted within the same range. The plot commands are doing the opposite of what should be done. The commands are incorrectly clipping the data: they are only allowing the small HZz component to have contour plots.
The range used is the wrong range:
http://forum.nasaspaceflight.com/index.php?topic=38203.msg1415315#msg1415315
The ranges are from field components as follows:
# hx all data range from 0.000538633 to 0.000538633. H field big end
The correct range for HXz at the big end is 0.013 to +0.013
The contour plots are being clipped at a very low value!!!!
Clipping is the complete opposite of what should be done. We are interested in the high values, not the low values !

Will be talking NSF1701 on art bells dark matters digital radio network tomorrow at midnight PST.
Guest info to appear tomorrow abt 7:30 PM on othersideofmidnight.com website
Show is a mixture of science fiction, fantasy and science fact...I'll stay with facts and hope to still be entertaining, but understand its show biz. Will not over promise and under deliver however ;)
Its late for sure but they archive shows. Will talk how and why I jumped in and where it could lead.
Sounds like fun...
Even money says Art brings up UFO's in the first 5 min.
Course my reply would be I will believe it when I see it personally ;)
Sorta the reason I started my build...
Be prepared what to answer if he asks you:
1) Whether Shawyer invented the EM Drive as a result of a close encounter of the 3rd kind with UFO's that allowed him to get access to UFO's propulsion technology?
2) Whether the EM Drive is derived from Die Glocke Wunderwaffe antigravity research from WWII ?
3) What are you going to do if you accidentally create a wormhole in your garage as a result of your EM Drive research
4) if the EM Drive works, how long will a trip to Alpha Centauri take.
:)
Lol...I've thought about that. Tho it will be my chance to get realistic conversation going, like let's get more data before we talk about a jetsons lifestyle ;)

Here are the two png sets scaled to the maximum range of the E and H fields for the t=0 time slice. The ranges are from field components as follows:
# ez all data range from 0.000245405 to 0.000245405. E field big end
# hx all data range from 0.000538633 to 0.000538633. H field big end
# ez all data range from 4.04811e05 to 4.04811e05. E field small end
# hy all data range from 0.000287974 to 0.000287974. H field small end
Please look these png's over closely to be sure that this is what you want to see as it will be considerable effort to scale the png files in this way for the general case.
Or do you need to see the side views for this t = 0 case?
...
They look like ContourPlots in Mathematica when I use PlotRange with a range smaller than the full magnitude, so the contours get cliped. I would double check whether magnitudes have not been clipped.
3) Is there some means to control the number of contour values in the contour plots? It looks to me like there are more contour levels than the number of colors available, as a result colors keep repeating themselves. What one wants is to have blue represent the lowest magnitude and red the highest magnitude, instead of red/green/blue/yellow patterns being repeated cyclically.
Yes, this whole problem was due to the fact that the command was doing the complete opposite of what is wanted: it was clipping the images at a value of +/ 0.0005 and preventing showing the actual values that go up to +/0.013, thus it was showing contours only for the contours that had values close to zero.
Values were being clipped at 3.8% of the full range ! Anything higher than 3.8% was being clipped.
This error would have been evident if the numerical values of the contours would have been displayed, as I display them in the attachments to the message http://forum.nasaspaceflight.com/index.php?topic=38203.msg1415788#msg1415788
This error was not evident to anybody because the numerical values of the contours are not being shown in the Meep image output. This shows the problem with these Meep images output: nobody can tell what they mean, or even tell when there is an error because numerical values are not being shown.
To prevent future errors and to be able to interpret the images, the best thing would be to display the numerical values of the contours
It looks like somebody realized that there was an issue with this and they wrote about this in the Wiki about the need to have numerical values shown in the Meep contour plots:
http://emdrive.wiki/MEEP#Contour_plots
Meep adventurers may wish to consider improving h5topng to produce images which contain:  The numerical value on the contour boundaries
()

Will be talking NSF1701 on art bells dark matters digital radio network tomorrow at midnight PST.
Guest info to appear tomorrow abt 7:30 PM on othersideofmidnight.com website
Show is a mixture of science fiction, fantasy and science fact...I'll stay with facts and hope to still be entertaining, but understand its show biz. Will not over promise and under deliver however ;)
Its late for sure but they archive shows. Will talk how and why I jumped in and where it could lead.
Sounds like fun...
Even money says Art brings up UFO's in the first 5 min.
Course my reply would be I will believe it when I see it personally ;)
Sorta the reason I started my build...
Be prepared what to answer if he asks you:
1) Whether Shawyer invented the EM Drive as a result of a close encounter of the 3rd kind with UFO's that allowed him to get access to UFO's propulsion technology?
2) Whether the EM Drive is derived from Die Glocke Wunderwaffe antigravity research from WWII ?
3) What are you going to do if you accidentally create a wormhole in your garage as a result of your EM Drive research
4) if the EM Drive works, how long will a trip to Alpha Centauri take.
:)
Lol...I've thought about that. Tho it will be my chance to get realistic conversation going, like let's get more data before we talk about a jetsons lifestyle ;)
http://www.enterprisemission.com/
rfmwguy this is so much right up your alley, you have a great way with words (great voice and face for radio I might add). In a email to me he said he was going to try to get Shawyer on as well.
I think I'll pass this time.
Shell

Today is going to be a busy day. I have my final 2 sheets of melamine white pressed white 3/4" 4x8' sheets being picked up and with some help start to get them laid out to cut for the remaining pieces of the stand. I had to wait for help as they just are too heavy for one old gal to move around.
Shell

Will be talking NSF1701 on art bells dark matters digital radio network tomorrow at midnight PST.
PST? Did you mean midnight Pacific Daylight Time?

I keep thinking about the idea (http://forum.nasaspaceflight.com/index.php?topic=37642.msg1412971#msg1412971) I had a few days ago and pushed it further. I thought about Rodal and WarpTech's advice of increasing cone angle and keeping the apex as near as possible of the small end. I also kept Shawyer's high D_{f} and concentric spherical ends to maintain a high Q, and I've ended up with this wide and shallow resonant design, with incredible large spherical ends, making the frustum almost a halfsphere:
I love this. I've been thinking about it since you first mentioned it too.
It reminds me of those Mirage 3D hologram generators they sell in expensive toy stores, but with a hemispheric "lid" inserted into the top opening to keep the reflections going.

Will be talking NSF1701 on art bells dark matters digital radio network tomorrow at midnight PST.
PST? Did you mean midnight Pacific Daylight Time?
Yes.

Will be talking NSF1701 on art bells dark matters digital radio network tomorrow at midnight PST.
PST? Did you mean midnight Pacific Daylight Time?
Yes, PDT, 3 hours behind EST

.................
D_{b} = 600 mm
D_{s} = 150 mm
L = 51.20 mm
r_{1} = 76.92 mm
r_{2} = 307.67 mm
r_{2}r_{1} = 230.75 mm
θ = 77.18°
Resonance at 2.45 GHz in TE013 mode, D_{f} = 0.96
.....
Yes. Every force vector in an EmDrive with spherical ends has an inner component (yet the vector on the axis) since they all point towards the vertex. With a side wall angle > 45° this component is maybe too much. Maybe the wall would need to be less angled.
Whatever, I did that to explore "extreme shapes" and these kinds of possibilities:
How did you determine the very wide angle for this setup?
On the assumption that an EMdrive does indeed produce a force, there is still the problem that we do not know where and how that force is produced. There are a few theories but we still have to see some tests that are specifically designed to eliminate or confirm one of the theories.
Some say the side wall contribute nothing to the created force others say just the opposite.
Some say the Q is THE factor to achieve a large force, others claim a low Q but high attenuation is the path to follow.
First step is to confirm the existence of a force that makes the EMdrive move. Once that done, the different experiments should focus in lining up with certain theories and then test them to find out what theory fits best. This is why attenuation calculations on ever wider angles would be interesting. If the attenuation keeps growing with the angle, you would end up with 90° halfcone angle, which doesn't make sense.. hence why I suspect there must be an optimal angle... somewhere...( if attenuation is indeed the key factor for force creation)
For that, a certain standardization in design might be needed, but with each type of cavity designed to maximize certain theoretical ideas....(fe, increase of angle design, increasing Q design, etc)
Too bad i don't have a real metal 3dprinter to create a few standard cavity models.
The best i could do is 3Dprint in copper filament, but I doubt the copper particles would be dense enough to give solid internal reflection. The plastic part of the filament would melt way sooner and the particles would give a very lousy Q... :'(
Unless someone can convince me that is not the case....and that it does make sense..

Please take a look at the conclusion of the below paper, it may explain why we have a decreasing force in vacuum.
When the particles in air (water,soot...) disappear the force decrease. What do you think of that? It could be an explanation for the thin shell frustums.
Lateral Chiralitysorting Optical Spin Forces in Evanescent Fields
http://arxiv.org/abs/1408.2268
"The transverse component of the spin angular momentum of evanescent waves gives rise to lateral optical forces on chiral particles, which have the unusual property of acting in a direction in which there is neither a field gradient nor wave propagation."
I like this.... Thanks for the post.
Several on here bend towards the evanescent decaying waves that have four distinct momenta and three distinct spins compared to the single momentum and single spin for a propagating EM wave as to providing a link to the "outside world".
It's interesting that traveling magnet can induce a action in a copper pipe.
http://video.mit.edu/watch/physicsdemolenzslawwithcopperpipe10268/
Coffee alert...
I theorise that the same is happening within the frustum with the traveling waves. We build up a DC magnetic component in the walls from the harmonic mode and when the mode collapses (they all have in every simulation) to form another mode. That switch decaying produces evanescent waves that push into the copper ~5um imparting momentum and force on the still decaying magnetic component left from the last mode.
It could be argued that the sum of the forces with mode changes and induced magnetic components in the side walls are zero with no net force using Maxwell's equations and be correct, although when one adds in the evanescent decaying waves that have four distinct momenta and three distinct spins things begin to look a little different and more complicated. As to how a standard propagating wave with a single momentum and single spin inducing in the walls a normal magnetic Dc component induced into the walls can be acted upon from a evanescent decaying wave with an extraordinary grouping of forces? I stumble.
My math falls short here and I've reached my limit with my first cup of coffee anyway.
Shell

Will be talking NSF1701 on art bells dark matters digital radio network tomorrow at midnight PST.
PST? Did you mean midnight Pacific Daylight Time?
Yes, PDT, 3 hours behind EST
LATE NITE, past my bedtime. :)

How did you determine the very wide angle for this setup?
If the attenuation keeps growing with the angle, you would end up with 90° halfcone angle, which doesn't make sense.
Actually the 90° halfcone angle, thus the perfect halfsphere, was the value and the shape I started from ;)
I first chose D_{s} = 150 mm (to be just above the cylindrical cutoff diameter at 2.45 GHz),
and D_{b} = 4x that value = 600 mm (arbitrarily, I just wanted to maximize the difference between the two end diameters).
So my "cavity" was at the beginning a perfect halfsphere of r_{2} = 300 mm… which could not resonate in TE013 mode (according to TT's spreadsheet) until I moved the ends a bit, slightly increasing the distance between them from 225 mm at the beginning to the optimal distance of 230.75 mm, keeping the end diameters constant. Hence the halfcone angle reduced from 90° initially to 77.18° after tweaking.

Will be talking NSF1701 on art bells dark matters digital radio network tomorrow at midnight PST.
PST? Did you mean midnight Pacific Daylight Time?
Yes, PDT, 3 hours behind EST
LATE NITE, past my bedtime. :)
Mine too, but I'll revert back to my college days one more time ;)

Will be talking NSF1701 on art bells dark matters digital radio network tomorrow at midnight PST.
PST? Did you mean midnight Pacific Daylight Time?
Yes, PDT, 3 hours behind EST
LATE NITE, past my bedtime. :)
Mine too, but I'll revert back to my college days one more time ;)
Well you're younger than I am kiddo. ;) 60...HA!
If I wake up early I might join in but don't count your chickens.

I keep thinking about the idea (http://forum.nasaspaceflight.com/index.php?topic=37642.msg1412971#msg1412971) I had a few days ago and pushed it further. I thought about Rodal and WarpTech's advice of increasing cone angle and keeping the apex as near as possible of the small end. I also kept Shawyer's high D_{f} and concentric spherical ends to maintain a high Q, and I've ended up with this wide and shallow resonant design, with incredible large spherical ends, making the frustum almost a halfsphere:
D_{b} = 600 mm
D_{s} = 150 mm
L = 51.20 mm
r_{1} = 76.92 mm
r_{2} = 307.67 mm
r_{2}r_{1} = 230.75 mm
θ = 77.18°
Resonance at 2.45 GHz in TE013 mode, D_{f} = 0.96
Would be a challenge to build but nevertheless interesting to test. What could be the Q of such a cavity?
I might be able to model it. Can you export an STL of the part?
Although SketchUp is not good at all with circles (it draws them as a series of segments) I updated the number of segments per circle from 24 to 240 in order to improve precision.
I don't know if you need the 2D plan or the 3D modeled object, so I created both versions and exported them in STL format. You can find them zipped below.

Wow this is like a mishmash of @Notsosureofit and @Mike McCulloch. It even has a tapered waveguide. Very excited to read this closely later.
http://arxiv.org/abs/physics/0606072

Will be talking NSF1701 on art bells dark matters digital radio network tomorrow at midnight PST.
PST? Did you mean midnight Pacific Daylight Time?
Yes, PDT, 3 hours behind EST
LATE NITE, past my bedtime. :)
Mine too, but I'll revert back to my college days one more time ;)
Well you're younger than I am kiddo. ;) 60...HA!
If I wake up early I might join in but don't count your chickens.
Too bad if you dont skype in...they mentioned they'd like to get more perspectives on builders and I mentioned you. Think if people hear realistic, serious stories on theory and build, it'll let them know its not a fringe element working on these things. Right now, my thought is many think it is another coldfusion type device. Lots of notions to clear up. Seems like a good place to start...

I keep thinking about the idea (http://forum.nasaspaceflight.com/index.php?topic=37642.msg1412971#msg1412971) I had a few days ago and pushed it further. I thought about Rodal and WarpTech's advice of increasing cone angle and keeping the apex as near as possible of the small end. I also kept Shawyer's high D_{f} and concentric spherical ends to maintain a high Q, and I've ended up with this wide and shallow resonant design, with incredible large spherical ends, making the frustum almost a halfsphere:
D_{b} = 600 mm
D_{s} = 150 mm
L = 51.20 mm
r_{1} = 76.92 mm
r_{2} = 307.67 mm
r_{2}r_{1} = 230.75 mm
θ = 77.18°
Resonance at 2.45 GHz in TE013 mode, D_{f} = 0.96
Would be a challenge to build but nevertheless interesting to test. What could be the Q of such a cavity?
I might be able to model it. Can you export an STL of the part?
Although SketchUp is not good at all with circles (it draws them as a series of segments) I updated the number of segments per circle from 24 to 240 in order to improve precision.
I don't know if you need the 2D plan or the 3D modeled object, so I created both versions and exported them in STL format. You can find them zipped below.
This is a very interesting shape to test the outer limits of the theories and methods involved.
Due to the extreme spherical conical shape of this cavity, the limitations of the spreadsheet approach (that in a kludgy way intends to model a spherical cone as a large series of cylindrical waveguides) is more crudely exposed:
the natural frequency of mode TE013 is 2.132 GHz (instead of 2.45 GHz), a difference of 15% in frequency (for cone angles of 15 degrees the spreadsheet is 1 to 2% different from the exact solution)
It does resonate, and it resonates well:
theoretical Q = 94,254
using a resistivity = 1.678*10^(8)(*copper*) (Q will go down with increasing resitivity materials and geometrical imperfections)
although this is not much more than the Q calculated for the 30 degrees cavity, so it looks like there are diminishing returns after 30 degrees
I attach below the contour plots for
1) the magnetic field in the spherical radial direction
2) the electric field in the azimuthal circumferential direction
Note how distorted is the magnetic field in the spherical radial direction

Although SketchUp is not good at all with circles (it draws them as a series of segments) I updated the number of segments per circle from 24 to 240 in order to improve precision.
I don't know if you need the 2D plan or the 3D modeled object, so I created both versions and exported them in STL format. You can find them zipped below.
Thanks for explaining how you got to that "apparent random" angle...It makes sense now.
STL files are the preferred choice for 3dprinting... ;)
It doesn't really matter because even if you model it with a nurbs modeler software package (smooth and continuous surfaces), in the end, an STL file is a format that only understands 3d points, so all the surfaces are automatically converted to polygons....hence always be an approximation of the real surface.
it is all a matter of conversion resolution then...
what would be the best placement for the waveguide entrance then?

I keep thinking about the idea (http://forum.nasaspaceflight.com/index.php?topic=37642.msg1412971#msg1412971) I had a few days ago and pushed it further. I thought about Rodal and WarpTech's advice of increasing cone angle and keeping the apex as near as possible of the small end. I also kept Shawyer's high D_{f} and concentric spherical ends to maintain a high Q, and I've ended up with this wide and shallow resonant design, with incredible large spherical ends, making the frustum almost a halfsphere:
D_{b} = 600 mm
D_{s} = 150 mm
L = 51.20 mm
r_{1} = 76.92 mm
r_{2} = 307.67 mm
r_{2}r_{1} = 230.75 mm
θ = 77.18°
Resonance at 2.45 GHz in TE013 mode, D_{f} = 0.96
Would be a challenge to build but nevertheless interesting to test. What could be the Q of such a cavity?
I might be able to model it. Can you export an STL of the part?
Although SketchUp is not good at all with circles (it draws them as a series of segments) I updated the number of segments per circle from 24 to 240 in order to improve precision.
I don't know if you need the 2D plan or the 3D modeled object, so I created both versions and exported them in STL format. You can find them zipped below.
This is a very interesting shape to test the outer limits of the theories and methods involved.
Due to the extreme spherical conical shape of this cavity, the limitations of the spreadsheet approach (that in a kludgy way intends to model a sherical cone as a large series of cylinders) is more crudely exposed:
the natural frequency of mode TE013 is 2.132 GHz (instead of 2.45 GHz), a difference of 15% in frequency (for cone angles of 15 degrees the spreadsheet is 1 to 2% different from the exact solution)
It does resonate, and it resonates well:
theoretical Q = 94,254
using a resistivity = 1.678*10^(8)(*copper*) (Q will go down with increasing resitivity materials and geometrical imperfections)
although this is not much more than the Q calculated for the 30 degrees cavity, so it looks like there are diminishing returns after 30 degrees
I attach below the contour plots for
1) the magnetic field in the spherical radial direction
2) the electric field in the azimuthal circumferential direction
Note how distorted is the magnetic field in the spherical radial direction
And these are the 3D plots of
1) the magnetic field in the spherical radial direction
2) the electric field in the azimuthal circumferential direction
The longitudinal magnetic field is the important field: it makes it look like a manta ray spaceship

theoretical Q = 94,254
using a resistivity = 1.678*10^(8)(*copper*) (Q will go down with increasing resitivity materials and geometrical imperfections)
Hello sir.
I'm just lurking here. Appreciation for all the work you sir and all you guys do for emdive community.
What if the the copper cavity is cooled down with liquid Nitrogen?
How does it affect the Qfactor in real?
Could the inner portion of the cavity be lined with YBCO thin film and N2 cooled? Does YBCO film do the job at 2.3G or 23G freq?
Best, Peter

theoretical Q = 94,254
using a resistivity = 1.678*10^(8)(*copper*) (Q will go down with increasing resitivity materials and geometrical imperfections)
Hello sir.
I'm just lurking here. Appreciation for all the work you sir and all you guys do for emdive community.
What if the the copper cavity is cooled down with liquid Nitrogen?
How does it affect the Qfactor in real?
Could the inner portion of the cavity be lined with YBCO thin film and N2 cooled? Does YBCO film do the job at 2.3G or 23G freq?
Best, Peter
Welcome to the forum !
Concerning operation of the cavity in the superconducting range, in my humble opinion that is way too complicated to give a thoughtful answer without doing the pertinent analysis, which I haven't done.
Shawyer claims to have been working on superconducting designs for years, but the very limited financial situation of his company reported in a number of posts by WallofWolfStreet in this forum (reported by WWS to be deeply in debt to hundreds of thousand of pounds, not a single employee, etc.) and the lack of experimental measurements (his latest paper in Acta Astronautica dealt mainly with futurustic designs) does not show progress that can be independently assessed.
(http://forum.nasaspaceflight.com/index.php?action=dlattach;topic=36313.0;attach=875941;image)

...
what would be the best placement for the waveguide entrance then?
For the 30 degree superconducting cavity Shawyer is entering asymmetrically from the lateral conical surface:
see above image