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#2760 by X_RaY on 26 May, 2016 19:35
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The question re the NASA frustum and the TE012 mode was if there is such a "good" power/thrust radio in this mode, then why was there not more power >2.6 Watts "put/injected" into it? Sonny stated they were only "able" to get 2.6 Watts in the frustum into this mode. What did he mean by this? Why weren't they "able" to get more power into the frustum? Since predicted Q and actual Q were high and close to one another in TE012 might this not also speak to the "good" power/thrust" ratio?
28W output power at the amplifier. (typical 25W, see peport)
The neophyte looks at the data, sees the best thrust/power ratio, sees the high predicted and actual Q and asks why not up the power and generate a good deal more force? Dr. Rodal agreed "anomalous force/power" would be cumbersome (in the least!)
1. Losses of 0.3...-0,5dB at each connector
2. coaxial cable loss 1.5...2dB/m
3. circulator(+load=isolator) or dual directional coupler (DDC) losses up to 3dB per path
4. antenna feed and maybe some kind of tuner for impedance matching can also produce several dB of loss
All this together can easily produce a loss of 11.461dB.
And maybe the antenna shape and position/orientation was not the best? -
#2761 by zellerium on 26 May, 2016 19:47
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Didn't they have their amplifier in the vacuum chamber for this experiment? And didn't they say it was "dying"?The question re the NASA frustum and the TE012 mode was if there is such a "good" power/thrust radio in this mode, then why was there not more power >2.6 Watts "put/injected" into it? Sonny stated they were only "able" to get 2.6 Watts in the frustum into this mode. What did he mean by this? Why weren't they "able" to get more power into the frustum? Since predicted Q and actual Q were high and close to one another in TE012 might this not also speak to the "good" power/thrust" ratio?
30W output power at the amplifier.
The neophyte looks at the data, sees the best thrust/power ratio, sees the high predicted and actual Q and asks why not up the power and generate a good deal more force? Dr. Rodal agreed "anomalous force/power" would be cumbersome (in the least!)
1. Losses of 0.3...-0,5dB at each connector
2. coaxial cable loss 1.5...2dB/m
3. circulator(+load=isolator) losses up to 3dB per path
4. antenna feed and maybe some kind of tuner for impedance matching can also produce several dB of loss
All this together can easily produce a loss of 11.761dB.
And maybe the antenna shape and position/orientation was not the best?
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#2762 by X_RaY on 26 May, 2016 20:22
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Didn't they have their amplifier in the vacuum chamber for this experiment? And didn't they say it was "dying"?The question re the NASA frustum and the TE012 mode was if there is such a "good" power/thrust radio in this mode, then why was there not more power >2.6 Watts "put/injected" into it? Sonny stated they were only "able" to get 2.6 Watts in the frustum into this mode. What did he mean by this? Why weren't they "able" to get more power into the frustum? Since predicted Q and actual Q were high and close to one another in TE012 might this not also speak to the "good" power/thrust" ratio?
28W output power at the amplifier.
The neophyte looks at the data, sees the best thrust/power ratio, sees the high predicted and actual Q and asks why not up the power and generate a good deal more force? Dr. Rodal agreed "anomalous force/power" would be cumbersome (in the least!)
1. Losses of 0.3...-0,5dB at each connector
2. coaxial cable loss 1.5...2dB/m
3. circulator(+load=isolator) or dual directional coupler (DDC) losses up to 3dB per path
4. antenna feed and maybe some kind of tuner for impedance matching can also produce several dB of loss
All this together can easily produce a loss of 11.461dB.
And maybe the antenna shape and position/orientation was not the best?
Yes the capacitors was problematic as far as I remember but this was fixed.
On the other hand, the power was adjustable.Quote...
Testing of the tapered RF thruster at a particular mode started with some bench level evaluation of the choice of RF drive antenna (type, size, and mounting orientation), and likewise for the sense antenna. When this step was complete, the thruster was transferred to the low thrust torsion pendulum and connected to the manually tuned RF drive system (which simultaneously served as the counterbalance mass for the thruster at the opposite end of the torsion pendulum arm). The 25 watt amplifier was driven by a Mini-Circuits® voltage controlled oscillator (VCO) passed through a Mini-Circuits® variable voltage attenuator (VVA). The output of the RF amplifier was run through a dual directional coupler (DDC) with power meters positioned to measure forward and reflected power from the test article. For final tuning prior to testing on the rig, typically a stub tuner was placed between the DDC and the test article and the VNA’s Smith Chart and S11 plots were used to optimize coupling with the test article. Figure 17 shows the thruster mounted on the torsion pendulum arm and how it was connected to the RF amplifier.
...
Additional equipment for power, signal generation, and data collection and display resides in the lab equipment rack adjacent to the optical bench. From this location, our Test Engineer can provide test article primary power, RF signal generation, signal amplification, avionics control power, data acquisition, and data display.
...
With an input power of 2.6 watts, correcting for the quality factor, the predicted thrust is 50 micronewtons. However, since the TE012 mode had numerous other RF modes in very close proximity, it was impractical to repeatedly operate the system in this mode, so the decision was made to evaluate the TM211 modes instead.
...
We performed some very early evaluations without the dielectric resonator (TE012 mode at 2168 MHz, with power levels up to ~30 watts) and measured no significant net thrust.
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#2763 by Rodal on 26 May, 2016 20:39
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A common misconception in the literature (in several introductory books and, unfortunately in Wikipedia), and in the EM Drive thread is that the radiation pressure can always be obtained from the Poynting vector simply by the cyclic average of the Poynting vector divided by the speed of light:
In here: https://forum.nasaspaceflight.com/index.php?topic=39214.msg1532199#msg1532199 I discuss that:
one cannot simply calculate the radiation pressure in a resonant cavity using the cyclic average of the Poynting vector divided by the speed of light:
since 1) the Poynting vector is zero at the metal walls for TE modes and 2) the Poynting vector does not have a constant magnitude in the longitudinal direction for standing waves in a cavity, for any mode shape. On the other hand, as we have shown, one can certainly calculate the radiation pressure at the walls of resonant cavity based on the energy density value at the wall for TE modes, or in general, based on the energy density and the Coulomb pressure at the wall for any mode shape, hence obtaining the radiation pressure from the energy density approach is a more general approach than relying on the Poynting vector field. -
#2764 by zellerium on 26 May, 2016 20:58
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Dave, Jamie, that looks great! Dave, you have mentioned a few times that your frustum is high "Q" --- Do you have a +/- value for that? Best of luck! thanks, Kevin
Thanks Kevin. OK, the scan below is what I considered an ideal coupling with my VNA probe...everything was mechanically aligned perfectly, but subsequent scans showed slightly worse return loss peak. By the shape of this noisy 63dB RL, it appears the 3dB BW off best RL is about 10 MHz wide. Center was about 2440855 MHz and with a 3dB BW of 10 MHz, that give a Q of 244,085.
Now, This I believe is under perfect conditions. I am not convinced yet that the times I was able to see this value of return loss will be repeatable. However, under perfect matching/coupling/isolation conditions, this cavity has a Q capability of around 245K.
...
I think you meant 2440.885 MHz, right? Which would yield a much more reasonable Q of 244.085
Fantastic min RL though, I could never get ours below -50 dB -
#2765 by zellerium on 26 May, 2016 21:33
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Wait Kurt...better recheck that...Note the 3dB points off max peak of 63dB RL...that is not 10 MHz, its 10 kHz. You take a look at the trace again. If this is true, its 2440.850/0.01 = 244,085 as I originally stated. Granted, I am a bit punchy, but take a look for me. I estimated the 3dB BW (60dB points) to be about 0.010 MHz wide. Sheesh...better take a nap.
That's right Kurt...you can tell I'm running low on energy due to lack of sleep. You are correct.Dave, Jamie, that looks great! Dave, you have mentioned a few times that your frustum is high "Q" --- Do you have a +/- value for that? Best of luck! thanks, Kevin
Thanks Kevin. OK, the scan below is what I considered an ideal coupling with my VNA probe...everything was mechanically aligned perfectly, but subsequent scans showed slightly worse return loss peak. By the shape of this noisy 63dB RL, it appears the 3dB BW off best RL is about 10 MHz wide. Center was about 2440855 MHz and with a 3dB BW of 10 MHz, that give a Q of 244,085.
Now, This I believe is under perfect conditions. I am not convinced yet that the times I was able to see this value of return loss will be repeatable. However, under perfect matching/coupling/isolation conditions, this cavity has a Q capability of around 245K.
...
I think you meant 2440.885 MHz, right? Which would yield a much more reasonable Q of 244.085
Fantastic min RL though, I could never get ours below 50 dB
I wouldn't feel too bad about 40-50dB. This is what I would expect from a single can cavity from my past experience. When us RF types see some wildly good performance like 63dB RL, we usually say "Careful, don't flex that test cable!"
If we're going to start measuring quality like Mr. Shawyer, then yes I agree its 10 KHz and 244,000 Q. But as far as I can recall everyone else here has always measured quality from -3 dB below 0 which is how EW and NWPU measured theirs.
We would have definitely improved our quality by several orders of magnitude using this other technique.
How do RF component manufacturers typically measure it? There must be some industry standard... -
#2766 by Rodal on 26 May, 2016 21:45
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Correct Zellerium. Besides that, recall what is the actual definition of Q, it is:
If we're going to start measuring quality like Mr. Shawyer, then yes I agree its 10 KHz and 244,000 Q. But as far as I can recall everyone else here has always measured quality from -3 dB below 0 which is how EW and NWPU measured theirs.
We would have definitely improved our quality by several orders of magnitude using this other technique.
How do RF component manufacturers typically measure it? There must be some industry standard...
which does not depend on arbitrary definitions of 3 db etc.
NASA obtained excellent agreement between COMSOL calculations of Q (calculated from the above formula based on the conductivity of copper, and the geometry) and compared to their convention on how to measure Q experimentally.
On the other hand, a "measured Q" of 244,000 for this copper frustum does not make sense with any calculation, particularly for a TM013 mode shape, which should be under 100,000 under the best of circumstances. -
#2767 by Rodal on 26 May, 2016 22:00
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Is my memory correct that on your earlier threads discussions on Q, based on your life experience you thought that Q's of 80,000 to 100,000 were hard to believe and that Q of less than 20,000 were more in line for copper cavities?
Being around this stuff most my life, I have never seen a Q calculation like what you have stated a few times. 3dB bandwidth is half-power which is industry standard. I've posted several links that confirm this measurement convention amongst RF & Microwave design engineers....
Correct Zellerium. Besides that, recall what is the actual definition of Q, it is:
If we're going to start measuring quality like Mr. Shawyer, then yes I agree its 10 KHz and 244,000 Q. But as far as I can recall everyone else here has always measured quality from -3 dB below 0 which is how EW and NWPU measured theirs.
We would have definitely improved our quality by several orders of magnitude using this other technique.
How do RF component manufacturers typically measure it? There must be some industry standard...
which does not depend on arbitrary definitions of 3 db etc.
NASA obtained excellent agreement between COMSOL calculations of Q (calculated from the above formula based on the conductivity of copper, and the geometry) and compared to their convention on how to measure Q experimentally.
On the other hand, a "measured Q" of 244,000 for this copper frustum does not make sense with any calculation, particularly for a TM013 mode shape, which should be under 100,000 under the best of circumstances.
If so, how can a Q of 244,000 now be in the realm of possibility?
A Q of 244,000 for such a copper cavity is outside the realm of what is quoted in books, and most sources.
Concerning that formula for Q and experimental values, take a look for example at
"Systems with Small Dissipation" by Braginsky et. al (translated by Kip Thorne)
University of Chicago Press
including resonant copper cavities with non-uniform cross-section for accelerators. -
#2768 by Monomorphic on 26 May, 2016 22:12
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Are all these variables available from a return loss trace? What I have been using, and I think it is probably a short-hand way of calculating Q, is fc/Δf. Where Δf = f1 − f2.
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#2769 by rq3 on 26 May, 2016 22:26
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(Mod note - removed)
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#2770 by zellerium on 26 May, 2016 22:34
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If we're going to start measuring quality like Mr. Shawyer, then yes I agree its 10 KHz and 244,000 Q. But as far as I can recall everyone else here has always measured quality from -3 dB below 0 which is how EW and NWPU measured theirs.
We would have definitely improved our quality by several orders of magnitude using this other technique.
How do RF component manufacturers typically measure it? There must be some industry standard...
I was mistaken, in their 2013 and 2014 papers NWPU measured their Q from a position sqrt(2)/2 times their min return loss
But I agree with rq3 that you can get spurious noise that yields a trough far below the actual RL. But if it were to settle and maintain that position, could it still be classified as noise?
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#2771 by zellerium on 26 May, 2016 22:42
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If I were to measure my cylindrical cavity Q from 3dB above the minimum RL, we would have a Q of 2418.3 MHz / .1 MHz = 24,000 for a polished aluminum cavity with ~1 inch thick HDPE insert
For some reason that seems wrong to me...
Edit: the data points are too sparse at that zoom to get an accurate bandwidth
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#2772 by frobnicat on 26 May, 2016 22:56
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.../...
Didn't they have their amplifier in the vacuum chamber for this experiment? And didn't they say it was "dying"?
Yes the capacitors was problematic as far as I remember but this was fixed.
On the other hand, the power was adjustable.
... quote from Brady et al. 2014 report ...
None of the experiments covered in the 2014 Brady et al. report was actually in vacuum, although they were indeed in a vacuum chamber. The best "anomalous force/apparently spent power" ratio for TE012 with 2.6W was obtained at atmospheric pressure, and the comments about difficulty of getting a stable TE012 mode (that might explain the low absolute power and at least why it was not pursued) can't be linked to difficulties specific to vacuum, I think.
This asks also the question of what part (if any) of that good figure of merit ratio would subsist if it was tested in vacuum, all other things being equal at EagleWorks test stand, as with others modes the later communications by Paul March here at NSF indicated a very significant decrease in anomalous force per power when operated in vacuum conditions (for a very few shared plots actually), if I recall. Aside speculative hypothesis about the role of atmospheric pressure inside the vessel for a speculative real "propellantless thrust", the most natural interpretation for skeptics of such consequence is simply that vacuum removes one source (among others) of spurious coupling between tested device (and testing apparatus) and immediate surroundings : i.e. the role of atmospheric pressure in higher anomalous force magnitudes would to be found outside the vessel, convection etc... or between inside and outside in case of warm "jets" or other gas outbursts. More elaborate "pathological" conditions can also apply, for instance in vacuum less adsorbed water content in the nylon screws hence less bulk microwave induced heating of those. Mmm... melted nylon screws!
Those reports on anomalous measurements should come with a hundred pages of annexes or even just a link to scanned lab. notebook full of details... that would spare us months of discussions on interpretations (of what is a "reversal" for instance) and years of waiting the next report holding on silly hypothesis.
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#2773 by Rodal on 26 May, 2016 23:00
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No, the variables in the equation above are not meant to be used for quick experimental measurement, but instead they are meant to be calculated by a sophisticated mathematical model (this is the equation used by COMSOL FEA to assess the Q). They do not contain any arbitrary paramenters, like "3db" . However, one needs to know the mode shape for example, as the variables in the equation are again mode shape dependent.
Are all these variables available from a return loss trace? What I have been using, and I think it is probably a short-hand way of calculating Q, is fc/Δf. Where Δf = f1 − f2.
The experimental methods to calculate Q contain arbitrary parameters that are meant for quick approximate calculations, where one does not need to know the mode shape, etc..
Again, it is straightforward to show that one cannot have a Q=244,000 for a copper cavity of these dimensions even under perfect conditions.
It would be like having a discussion about damping (Q is an inverse measure of damping), with experimental people saying that they are measuring a damping value based on 3 db (such discussion of damping is very approximate and very dependent on the measuring equipment being used). The best way to calculate damping is analytically.
Other methods are for expediency. But what matters is that any approximate value of damping (or Q) has to make physical sense. -
#2774 by HMXHMX on 26 May, 2016 23:34
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Not followed Woodward's Mach Effect much, but know of no independent builds, tests or verifications outside of the good Professor. If there are some, let me know. Also, I don't recall seeing anything close to the design disclosure there is with the emdrive. EW tested it I believe, but moved on to something else. Any individuals replicating Mach Effect work or know of any, please point to the specifics. Not much time to dig into it myself. Running on 3 hours of sleep after the radio show...
Woodward's METs (Mach-Effect Thrusters) are not secret devices and any patient and dedicated DIYer could replicate them. They are quite simple in their construction: some disks about one inch diameter made of piezoelectric or electrostrictive high-k materials, like PZT or PMN, built from sintered powder (although PMN seems rather difficult to buy). Apart from that: Bonded copper electrodes. Screws. Electric wires. Liquid metal (Galinstan) contacts. Accelerometers. A very high-precision torsional pendulum. A vacuum pump. And some not-so-fancy electronics to generate the adequate HV/AC frequencies to drive the little test articles.
Honestly I think the main difficulty for a new DIYer in Mach Effect propulsion would be to acquire Woodward's knowledge and know-how about the very specific signal generation and how to carefully cancel spurious effects. This is touchy because the thrust signatures are so tiny, the signal needs to be very clean and the precision of the balance very high. The level of precision is what has prevented DIYers to replicate Woodward's work IMHO. Because of that, higher power METs from Woodward are long overdue.
For a start, before reading Woodward's book, perhaps you could have a look at Tom Mahood's summary of those devices on his personal page. Good close-up pictures of some METs there.
(Tom Mahood was Woodward's graduate student in the 90s)
Anyone who wants to attempt a serious replication is welcome to do so, and I'll work to facilitate that with the Woodward lab. SSI (www.ssi.org) may also be able to provide one or two METs from the lab for replication attempts, provided the attempts are done competently with due care, and results are made public. We'd prefer those few METs to go to academic labs but are open to talks with serious "pro-am" researchers. PM me or email to gary at ssi dot org. -
#2775 by mwvp on 26 May, 2016 23:50
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... 244K is not a repeatable Q, IMHO, nor is a Q of a million. The cavity is capable of it, but in real life where things are imperfect, sub 100K is the norm. I did some things traditionally not done in copper-can cavities which are 20K, so I believe its superior to them. Some things I've been open about, some things I have not. Designer's privilege, I guess.
Et tu, rfmwguy? First Shawyer, then TT, then Shells, now you. Hiding, suppressing, withholding. Keeping secrets. Doesn't inspire confidence.
...Unfortunately, most DIYers, are not working in the realm of micrometer accuracies in mechanical designs, especially at the signal injection point. This is the critical area where RL could fluctuate wildly with poor grounding, coupling, centering, etc.
Lets put it this way, my theoretical cavity design can yield a Q of up to 245K under the proper conditions - see the pic. In real-world practice, the resultant coupling of a standard magnetron will likely experience a Q of half of that...I have seen this, too.
Well, I could put an absorptive high-Q lumped-element filter with outrageous insertion loss in line with a frustrum and produce an extreme Q based on RL. Of course, the energy in the cavity, the EM momentum and radiation pressure would be practically zilch. As would any propulsive effect, unless somehow free energy is provoking annoyed quantum-vacuum fairies.
I've worked on more radios and instruments than I care to remember with crystal filters, saw filters, et. immense Q, passband-skirts and dispersion specs with 20dB+ insertion loss, and on antennas and ultrasonic transducers that would be called junk if they had near 3dB insertion loss, because they need to put energy on target, not filter a signal that will be trivially amplified back up again.
I don't think RL is the way to go to really measure Q, as has been discussed. I would use a tiny, little hole with a tiny, little amplified probe to sniff the signal. But that's me. Good luck to all.
Sorry for butting in. Back to lurking... -
#2776 by rq3 on 27 May, 2016 01:21
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(Mod note - removed)
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#2777 by birchoff on 27 May, 2016 03:31
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Not followed Woodward's Mach Effect much, but know of no independent builds, tests or verifications outside of the good Professor. If there are some, let me know. Also, I don't recall seeing anything close to the design disclosure there is with the emdrive. EW tested it I believe, but moved on to something else. Any individuals replicating Mach Effect work or know of any, please point to the specifics. Not much time to dig into it myself. Running on 3 hours of sleep after the radio show...
Woodward's METs (Mach-Effect Thrusters) are not secret devices and any patient and dedicated DIYer could replicate them. They are quite simple in their construction: some disks about one inch diameter made of piezoelectric or electrostrictive high-k materials, like PZT or PMN, built from sintered powder (although PMN seems rather difficult to buy). Apart from that: Bonded copper electrodes. Screws. Electric wires. Liquid metal (Galinstan) contacts. Accelerometers. A very high-precision torsional pendulum. A vacuum pump. And some not-so-fancy electronics to generate the adequate HV/AC frequencies to drive the little test articles.
Honestly I think the main difficulty for a new DIYer in Mach Effect propulsion would be to acquire Woodward's knowledge and know-how about the very specific signal generation and how to carefully cancel spurious effects. This is touchy because the thrust signatures are so tiny, the signal needs to be very clean and the precision of the balance very high. The level of precision is what has prevented DIYers to replicate Woodward's work IMHO. Because of that, higher power METs from Woodward are long overdue.
For a start, before reading Woodward's book, perhaps you could have a look at Tom Mahood's summary of those devices on his personal page. Good close-up pictures of some METs there.
(Tom Mahood was Woodward's graduate student in the 90s)
Anyone who wants to attempt a serious replication is welcome to do so, and I'll work to facilitate that with the Woodward lab. SSI (www.ssi.org) may also be able to provide one or two METs from the lab for replication attempts, provided the attempts are done competently with due care, and results are made public. We'd prefer those few METs to go to academic labs but are open to talks with serious "pro-am" researchers. PM me or email to gary at ssi dot org.
According to the last part of the conclusion of Theory of a Mach Effect Thruster 2. There have been two replications that are in the process of being published. HMXHMX you wouldnt happen to know anything about the status of those would you? -
#2778 by HMXHMX on 27 May, 2016 04:26
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Not followed Woodward's Mach Effect much, but know of no independent builds, tests or verifications outside of the good Professor. If there are some, let me know. Also, I don't recall seeing anything close to the design disclosure there is with the emdrive. EW tested it I believe, but moved on to something else. Any individuals replicating Mach Effect work or know of any, please point to the specifics. Not much time to dig into it myself. Running on 3 hours of sleep after the radio show...
Woodward's METs (Mach-Effect Thrusters) are not secret devices and any patient and dedicated DIYer could replicate them. They are quite simple in their construction: some disks about one inch diameter made of piezoelectric or electrostrictive high-k materials, like PZT or PMN, built from sintered powder (although PMN seems rather difficult to buy). Apart from that: Bonded copper electrodes. Screws. Electric wires. Liquid metal (Galinstan) contacts. Accelerometers. A very high-precision torsional pendulum. A vacuum pump. And some not-so-fancy electronics to generate the adequate HV/AC frequencies to drive the little test articles.
Honestly I think the main difficulty for a new DIYer in Mach Effect propulsion would be to acquire Woodward's knowledge and know-how about the very specific signal generation and how to carefully cancel spurious effects. This is touchy because the thrust signatures are so tiny, the signal needs to be very clean and the precision of the balance very high. The level of precision is what has prevented DIYers to replicate Woodward's work IMHO. Because of that, higher power METs from Woodward are long overdue.
For a start, before reading Woodward's book, perhaps you could have a look at Tom Mahood's summary of those devices on his personal page. Good close-up pictures of some METs there.
(Tom Mahood was Woodward's graduate student in the 90s)
Anyone who wants to attempt a serious replication is welcome to do so, and I'll work to facilitate that with the Woodward lab. SSI (www.ssi.org) may also be able to provide one or two METs from the lab for replication attempts, provided the attempts are done competently with due care, and results are made public. We'd prefer those few METs to go to academic labs but are open to talks with serious "pro-am" researchers. PM me or email to gary at ssi dot org.
According to the last part of the conclusion of Theory of a Mach Effect Thruster 2. There have been two replications that are in the process of being published. HMXHMX you wouldnt happen to know anything about the status of those would you?
I am aware of this, but since this is an EM thread we should take it to the Woodward thread. -
#2779 by X_RaY on 27 May, 2016 06:58
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#
No, the variables in the equation above are not meant to be used for quick experimental measurement, but instead they are meant to be calculated by a sophisticated mathematical model (this is the equation used by COMSOL FEA to assess the Q). They do not contain any arbitrary paramenters, like "3db" . However, one needs to know the mode shape for example, as the variables in the equation are again mode shape dependent.
Are all these variables available from a return loss trace? What I have been using, and I think it is probably a short-hand way of calculating Q, is fc/Δf. Where Δf = f1 − f2.
The experimental methods to calculate Q contain arbitrary parameters that are meant for quick approximate calculations, where one does not need to know the mode shape, etc..
Again, it is straightforward to show that one cannot have a Q=244,000 for a copper cavity of these dimensions even under perfect conditions.
It would be like having a discussion about damping (Q is an inverse measure of damping), with experimental people saying that they are measuring a damping value based on 3 db (such discussion of damping is very approximate and very dependent on the measuring equipment being used). The best way to calculate damping is analytically.
Other methods are for expediency. But what matters is that any approximate value of damping (or Q) has to make physical sense.
Fully agree!
Also there is a lot of good descriptions about Q measurement available at the net.
This for example:
http://www.engineering.olemiss.edu/~eedarko/experience/rfqmeas2b.pdf
http://forum.nasaspaceflight.com/index.php?topic=39214.msg1510595#msg1510595
