This is not yet complete, it is a mathematical
exploration using MiHsC, and I'm not sure of it, but
I'm including it here to stimulate or support discussion (updated, 18/10/1014).
Assume an asymmetric resonant cavity, with microwave photons bouncing around inside it. They carry a force F=2P/c, where P is power and c is the speed of light, due to the inertial mass of light (light does have an inertial mass, or Solar sails wouldn't work). Including the Q factor (number of photon 'bounces') gives F=2PQ/c. Now MiHsC says the inertial mass is caused by Unruh radiation, and so it is affected by the Hubble horizon since Unruh waves must fit exactly within this horizon. In MiHsC the inertial mass (mi) is modified as mi=m(1-L/4T) where m is the unmodified mass, L is the Unruh wavelength determined by the acceleration, and T is the Hubble distance (see McCulloch, 2007, eq. 8) so for the low accelerations seen in deep space, hence long Unruh waves which 'feel' the Hubble horizon, inertia decreases in a new way which fixes the galaxy rotation problem (McCulloch, 2012).
Assume an asymmetric resonant cavity, with microwave photons bouncing around inside it. They carry a force F=2P/c, where P is power and c is the speed of light, due to the inertial mass of light (light does have an inertial mass, or Solar sails wouldn't work). Including the Q factor (number of photon 'bounces') gives F=2PQ/c. Now MiHsC says the inertial mass is caused by Unruh radiation, and so it is affected by the Hubble horizon since Unruh waves must fit exactly within this horizon. In MiHsC the inertial mass (mi) is modified as mi=m(1-L/4T) where m is the unmodified mass, L is the Unruh wavelength determined by the acceleration, and T is the Hubble distance (see McCulloch, 2007, eq. 8) so for the low accelerations seen in deep space, hence long Unruh waves which 'feel' the Hubble horizon, inertia decreases in a new way which fixes the galaxy rotation problem (McCulloch, 2012).
What if the resonant cavity walls acted like a Hubble horizon,
especially for Unruh waves of a similar length (as they are in this case)? Then the inertial
mass of the photons would increase towards the cavity's wide end, since more
Unruh waves would fit there, since mi=m(1-L/2w), where w is the
cavity width. The force carried by the photons then increases by this factor as they go from the narrow end (width w_small) towards the
wide end (width w_big). The force difference between ends is
dF = (PQ/c)*((L/w_big)-(L/w_small)) = (PQ/f)*((1/w_big)-(1/w_small)).
The leap is that the only way to conserve force (or conserve momentum) is to have an equal force pushing the whole system the other way towards the narrow end.
The Table below compares the predictions of MiHsC with the available data. The columns show, from left to right: the data source, the widths of the large and small ends of the cavity used, the Q factor, the power applied, the frequency applied, the thrust predicted by MiHsC and the observed thrust. The sources are Shawyer (2008) and Brady et al. (2014) (see their table on page 18). Dr Jose Rodal has provided some data for the Juan (2012) experiment (rows 3-4, italic), but their cavity geometry is unknown, so I've calculated the range of possible predictions due to MiHsC, given the range of geometries in the two Shawyer experiments (see red colour). The table:
dF = (PQ/c)*((L/w_big)-(L/w_small)) = (PQ/f)*((1/w_big)-(1/w_small)).
The leap is that the only way to conserve force (or conserve momentum) is to have an equal force pushing the whole system the other way towards the narrow end.
The Table below compares the predictions of MiHsC with the available data. The columns show, from left to right: the data source, the widths of the large and small ends of the cavity used, the Q factor, the power applied, the frequency applied, the thrust predicted by MiHsC and the observed thrust. The sources are Shawyer (2008) and Brady et al. (2014) (see their table on page 18). Dr Jose Rodal has provided some data for the Juan (2012) experiment (rows 3-4, italic), but their cavity geometry is unknown, so I've calculated the range of possible predictions due to MiHsC, given the range of geometries in the two Shawyer experiments (see red colour). The table:
Experiment w_big w_small Q Power in Freq' MiHsC Observed
cm cm Watts GHz (milliNewtons)
-------------------------------------------------------------------------------------------------------------
Shawyer (2008) a 16 11 5900 850 2.45 5.8 16
Shawyer (2008) b 28 17 45000 1000 2.45 44 80-214
Juan (2012) TE011 16/28 11/17 32000 1000 2.5 30-36 214
Juan (2012) TE012 16/28 11/17 50000 1000 2.45 47-58 315
Brady et al. (2014) a 24.75 16.5 7320 16.9 1.933 0.129 0.0912
Brady et al. (2014) b " " 18100 16.7 1.937 0.315 0.0501
Brady et al. (2014) c " " 22000 2.6 1.88 0.061 0.0554
The
MiHsC predictions vary in the same proportion, but typically underestimate the observations significantly (I don't know
what the error bars on the observations are). An increase in cavity size, power input and Q factor usually increases the observed force as predicted. Case 6 is a bit worrying. Here Brady et al. (NASA) increased the Q factor which according to the prediction, and Shawyer's previous results, should have boosted the force, but the observed force was smaller (but note that MiHsC-inertia also depends on whether the Unruh waves fit exactly into the cavity and this can change with slight changes in frequency, for a discussion, see McCulloch, 2007, link below, the first paragraph of the Discussion).
Thanks: The data for the 5th case and several mistakes in geometry kindly pointed out by aero & Dr Jose Rodal on an NSF forum and the comments section below.
Thanks: The data for the 5th case and several mistakes in geometry kindly pointed out by aero & Dr Jose Rodal on an NSF forum and the comments section below.
References
Brady, D., et al., 2014. Anomalous thrust production from an RF test device measured on a low-thrust torsion pendulum. Conference proceedings, see Table page 18. Link
Juan, W., 2012. Net thrust measurement of propellantless microwave thrusters. Acta Physica Sinica, 61, 11.
McCulloch, M.E., 2007. Modelling the Pioneer anomaly as modified inertia. MNRAS, 376, 338-342. Link.
McCulloch, M.E., 2012. Testing quantised inertia on galactic scales. Astrophys. & Space Sci., 342, 575-578. Link
Shawyer, R., 2008. Microwave propulsion - progress in the emdrive programme. Link. (see section 6, page 6).
66 comments:
Some minor corrections for the NASA Brady et.al. frequencies, case (a) 1932.6 MHz which rounds off to 1933 MHz rather 1932 MHz. Case (b) is 1936.7 MHz which rounds off to 1937 MHz rather than 1932 MHz.
You may also add the final case in page 18, Table 2 of NASA Brady et.al.'s report:
Q=22000; Power=2.6 watts; Frequency=1880 MHz; Predicted Force=61.4 microNewtons;Experimental measurement=55.4 microNewtons; so that actually the prediction for this case is pretty close to the measurement
I would appreciate your comments regarding NASA Brady et.al.'s statement (p.18):
"There appears to be a clear dependency between thrust magnitude and the presence of some sort of dielectric RF resonator in the thrust chamber. The geometry, location, and material properties of this resonator must be evaluated using numerous COMSOL® iterations to arrive at a viable thruster solution. 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."
Effectively, Brady et.al. did NOT measure any thrust with the dielectric resonator (PTFE "Teflon" thermoplastic) removed from the cavity.
How does MiHsC explain the extremely important role of the dielectric resonator in NASA's experiments?
Thanks.
You are being spoken of very highly over on NSF:
http://forum.nasaspaceflight.com/index.php?topic=29276.msg1266909#msg1266909
I'm just the class clown, the mathematicians are doing all the heavy lifting.
Essential dielectric?: interesting. MiHsC assumes that accelerating objects see Unruh waves that cause inertial mass, but are modified by horizons (cosmic, or cavity walls). I was looking at photons in the cavity, but it could more simply be the electrons in the dielectric whose inertia is being modified..
Thank you for your prompt reply, and again welcome to NASA SpaceFlight forum !
Concerning " I was looking at photons in the cavity, but it could more simply be the electrons in the dielectric whose inertia is being modified."
Q1)So do I understand correctly that it does not make any difference to your estimation and analysis whether it is the photons in the cavity or the electrons in the dielectric that are having their inertia modified?
Q2)If it is the electrons in the dielectric that are having their inertia modified, why would the Q factor enter into the equation ? Wouldn't the dielectric just get affected by the Electric Field and Magnetic Fields ?
Again case (b) in your table above (of NASA Brady's report) is very perplexing.
and the fact that Brady et.al state that "evaluations without the dielectric resonator ...measured no significant net thrust" is also very perplexing.
I need your help understanding your formulation for the truncated cone tested by NASA and Shawyer. As I understand your formulas (please forgive me if I am incorrect) the only dimensions that enter your formula are the flat ends of the truncated cone. Now, consider the radius of the smaller flat end get smaller, as this radius approaches zero (and therefore the cone is not truncated any more but ends at a point) your formula seems to go to infinity?
Correct. I always try to simplify the maths.. A proper derivation would consider how the 3-d cavity damps Unruh waves that don't fit exactly, and in all directions, but the formula I derived should suffice for the non-pointed cones used so far.
Thanks. So what would be the force for a cone shaped end? If a simple formula closed-form solution for a cone is not readily available, can you conceptualize whether a cone-shaped end would be a much superior form of electromagnetic thruster (of course I understand the speculative nature of this analysis, but since we are speculating we might as well consider the limit case of a cone).
Good point :) I'll think about it..
Please review your numbers for Shawyer (a) and (b) cases as presently listed in your table to be consistent with the units shown in your table:
1) the numbers you have for the (MiHsC and observed) forces for Shawyer are in milliNewtons but your table says microNewtons. That is a factor of 1000 between them.
2) Using the dimensions, Q, power, and frequency in your table, I obtain MiHsC predictions for Shawyer cases as follows:
(a) 12793 microNewtons
(b) 393586 microNewtons
Thanks, Dr. Jose' Rodal
Many thanks! I have corrected them. Unfortunately, I have already submitted the paper..
Some tentative numbers from Table 2 of the Chinese experiments (Yang Juan, Yang Le, Zhu Yu, Ma Nan) in http://www.emdrive.com/NWPU2010translation.pdf
TE011
P=1000 w
Q=32000
f=2.50 GHz
Measured Force= 214 milliNewtons
TE012
P=1000 w
Q=50000
f=2.45 GHz
Measured Force= 315 milliNewtons
The dimensions of the tested cavity are not clear to me. Assuming the same dimensions as Shawyer's case b in your table, I get the following MiHsC predictions:
TE011 MiHsC 437 milliNewtons vs. Measured= 315 milliNewtons
TE012 MiHsC 274 milliNewtons vs. Measured= 214 milliNewtons
Thanks, Dr. Jose' Rodal
We see, on the average, an overprediction by the simplified MiHsC formula used for the calculations here. This overprediction is not surprising mainly because the simplified MiHsC formula is not taking into account the contribution from the conical sides of the truncated cone. Is that correct?
Well, the main assumption is that the cavity-scale Casimir-effect is only disallowing Unruh waves in a direction perpendicular to the cone's axis (1-d). The waves will actually be affected in 2 other directions, which vary less: diluting the effect, & maybe accounting for the overestimate..
What gave you the intuition that the resonant cavity copper walls could possibly act like a Hubble horizon, especially for Unruh waves of a similar length? What enables a copper cavity to act like an event horizon? Can you provide an analogy or some physical reason for the cavity walls to act like a Hubble horizon? Thanks
OK. This is why I'm thinking the EmDrive walls might make a horizon: MiHsC assumes that inertia is caused by Unruh waves and the Hubble horizon is a boundary for information so all patterns within the cosmos must close there otherwise they let us deduce what lies beyond (this looks like a Hubble-scale Casimir effect) this includes the Unruh waves, so it affects inertia. Now, for normal accelerations a metal box will not effect Unruh waves because for typical accelerations (9.8m/s^2) they are light years long, but for huge accelerations (as I assume for the light/electrons in the EmDrive) the Unruh waves are affected by the copper wall because they are partly em waves and the electrons in the copper move to cancel the field, so the Unruh wave patterns have to close at the wall just as at the Hubble horizon (but for a different reason), so we have a mini-MiHsC going on. In both cosmic & mini cases it seems to explain anomalies.
Thanks. Dr. J. Rodal.
Prof. McCulloch, do I understand correctly the statement "a metal box will not effect Unruh waves because for typical accelerations (9.8m/s^2) they are light years long, but for huge accelerations (as I assume for the light/electrons in the EmDrive) the Unruh waves are affected by the copper wall" to mean that for your above simplified formula to be based on MiHsC, the accelerations of the electrons need to be large enough so that Unruh radiation can significantly affect the inertial mass such that milliNewton forces can be experienced?
Yes: the accelerating objects inside the shell/cavity must accelerate (a) fast enough that the Unruh waves they see become short enough to be damped by the shell. The formula is: wavelength~8c^2/a so, for example, to get Unruh waves 1 metre long you need a=7.2*10^17 m/s^2.
Thanks. Dr. J. Rodal.
As I said, this is a wild leap, but the acceleration of the photons is 2c^2/cavitysize~9*10^17 m/s^2.
Correction: wherever the previous message read "Radius" it should state "Diameter". (Thanks to @aero for noticing this error):
The acceleration of the photons transiting the cavity is
a = 2 c^2 / (CavityLength)
and recall that for Unruh radiation McCulloch inertial mass change we must have
a > 8 c^2 / (DiameterOfFlatSurface)
So we need,
2 c^2 / (CavityLength) > 8 c^2 / (DiameterOfFlatSurface)
or
(DiameterOfFlatSurface)/(CavityLength) > 4
Which is not satisfied for these EMDrives.
Actually
For the NASA Eagleworks truncated cone, using the radius of the larger flat surface:
(DiameterOfFlatSurface)/(CavityLength) ~ 1
So the acceleration required for Unruh radiation waves is about 4 times greater than the actual photon acceleration in the cavity.
My 1st comment is that the longest wave to fit inside a cavity is twice as long as the cavity, so this reduces the discrepancy to a factor of 2. I need to look at this more. I'll get back to you.
Extremely high accelerations are involved when photons are reflected at the copper surface. Velocity is a vector of course: a change in direction is a change in velocity. The highest acceleration is the one resulting from a photon traveling perpendicular to a flat surface, being reflected from the surface so that it travels in the opposite direction.
The photons reflected from the copper are identical to the incident ones, apart from the changed propagation direction. Some fraction of the photons are lost, while the energy content of each reflected photon is fully preserved. Which of the photons are lost is a matter of chance; there is a certain probability for each photon to be absorbed. There will be complete reflection (and no heating of the metal) in most cases and complete absorption with associated heating (creation of so-called phonons in the metal) in some cases.
Question: does acceleration due to reflection (due to a change in direction but no change in magnitude) satisfy the requirement of high acceleration for the Unruh radiation?
The "self accelerating box paradox"
_____________________________
Donald Marolf, Rafael Sorkin, Perfect mirrors and the self-accelerating box paradox, Phys.Rev. D66 (2002) 104004
http://arxiv.org/abs/hep-th/0201255
__________________________
William G. Unruh and Robert M. Wald, Acceleration radiation and the generalized second law of thermodynamics,Phys. Rev. D 25, 942 – Published 15 February 1982
http://journals.aps.org/prd/abstract/10.1103/PhysRevD.25.942
A popular account by Paul Davies of the "self accelerating box paradox" as it appeared in New Scientist Jan 14, 1982:
http://goo.gl/w7N6ir
"..by being unable to perceive the heat bath, he will be baffled by the levitation of the box.." Excellent find. Thanks!
I'm so glad you also appreciate it.
Dr. Jose' Rodal
I decided to post :)
I read your two linked papers and note that your model gives reasonable predictions for two difficult problems.
As I read the OP, the formula,
dF=(PQ/c)*((L/w_up)-(L/w_down))=(PQ/f)*((1/w_up)-(1/w_down))
L is the wavelength of the Unruh radiation which is related to the cavity dimensions. Is L expected to be 9 inches, the length of the truncated cone? Or is it expected to be 6 inches, the wavelength of the driving RF wave? On the far right hand side of the equation the Unruh wavelength is replaced with the RF drive wavelength(f = c/L) so evidently drive power wavelength is intended.
Are you sure about that?
And just in case you are unaware of it, the best estimate of the value of the Hubble constant has changed several times during the past 10 years. Current best estimate seems to be 2.19725E-18/s with uncertainty of about 5%.
It seems to be the bane of the theorist, shifting constants.
Sorry. Here's the value and link.
2013-03-21 67.80±0.77 Planck Mission
http://en.wikipedia.org/wiki/Hubble's_law
aero: on your 1st comment. Good point. I assumed the freq of the Unruh & em radiation to be the same since both are resonating in the same cavity, but as you say there may be a small difference. Pls note this is a work in progress.. Thanks for the info about Hubble's (not so) constant.
A small correction: in the text above the spreadsheet, the dimensions in the equation are called "w_up" and "w_down" but in the spreadsheet they are called "w_big" and "w_small." A uniform naming convention should be adopted.
Thanks. Corrected.
If I understand the theory, the Unruh radiation is due to the acceleration of the wall material driven by the RF waves. The lower the acceleration, the longer the Unruh wavelength.
Since the condition for resonance in a resonator is that the round trip distance, 2d, is equal to an integral number of wavelengths \lambda\, of the wave and the drive frequency wave length is like 6 inches, we have that resonance can occur for d = 3, 6, 9 or more inches. Distance is equal to 9 in the Eagleworks device.
This same resonance condition should hold for the Unruh waves. The distance is the same but the Unruh wavelength need not be. Since 2d = 18 inches = n lamda, Unruh wave length could be either 18 or 9 or 6 smaller. For the smaller wavelengths, the exciter, the drive frequency is not synchronous but it is for 18, 9 and 6 inch Unruh wavelengths.
Looking at Dr. Rodal's post here it seems that the Unruh wavelength should be 9 inches in order that the data best fits the theory.
http://forum.nasaspaceflight.com/index.php?topic=29276.msg1270419#msg1270419
Why 9 instead of 18 inches? I speculate that it has something to do with complete utilization of the exciting accelerations at the cavity ends. Its just a guess, and I don't see the justification now. I'll think about it.
The 1-D closed-form formula approximation neglects the contribution of the Unruh waves from the curved surfaces of the cavity, along the 1-D axis, related to the length of the cavity. The question from @aero relates to what should the "best" 1-D approximation. Such a question can only be answered taking into account the Unruh wave contributions from the curved surfaces from a 3-D solution.
I'm not sure that's right.
I see the 1-D model using the multiplicative terms L/w ... where L is the Unruh wavelength. Then in the next step L is set equal to the drive RF wavelength. I'm not sure this is a valid assumption even in the 1-D model. The cavity will support resonances at other frequencies and since the frequency of a 9 inch wavelength is 2/3 the frequency of the 6 inch wavelength, and frequency is the slope of the predicted Q plot,
PredictedQ = (ExperimentalForce)*Frequency/((PowerInput)*(1/Dsmall-1/Dbig))
lowering frequency by 33% gives best fit to the data. Almost perfect in fact.
Let me put it another way. The Unruh wavelength is constrained by the cavity height. For resonance the wavelengths can be 6, 9, or 18 inches giving frequencies of 5.08E-10, 7.63E-10, or 1.53E-09 Hz. The choice seems to be somewhat arbitrary.
The measurement data gives a best fit with frequency = 7.63E-10 Hz. Therefore, choosing frequency = 5.08 Hz corresponding to the 6 inch wavelength is counter to what the experimental data is telling us.
I see your point that it works, but with so much uncertainty due to the simplified maths, it's important not to choose the wavelength based solely on what works exactly, but to try to maintain a clear logic from the theory forward. As you say 'nothing arbitrary'. The Unruh wavelength L must come from the acceleration of either the photons or something else. By the way, I'm hugely grateful for both aero & Dr Rodal's professional contributions. Still some way to go yet..
Ok - This is just a thought, but isn't acceleration a vector? If it is pumping the Unruh waves at the boundaries then which phase of the RF wave driving the acceleration would be in the right direction?
All of them? The even numbered ones? The odd numbered ones?
Here I am speaking of n, as in 2d=n lamda, being odd or even.
I completely agree with "it's important not to choose the wavelength based solely on what works exactly, but to try to maintain a clear logic from the theory. As you say 'nothing arbitrary'."
It is a great mathematical beauty of McCulloch's formulation that it has a minimum of parameters and no fudge factors or arbitrary parameters. It is paramount to preserve that.
Having said that, if one can improve the 1-D formula based on clear logic, so much the better. Perhaps you can do that from a theoretical basis. However it is evident to me that one cannot do that from the EMDrive data at this point in time because a) only two frequencies really have been examined: 1.9 GHz in the USA and 2.5 GHz in the UK and China, and 2) as Ludwick has pointed out there are many questions regarding the robustness of the experimental frequency information.
I think I need to question which choice of Unruh wavelength is more arbitrary.
One choice is based on the RF drive frequency.
Another choice is based on the physical separation of the cavity walls, the walls which act like a Hubble event horizon.
In the experimental cases we are looking at the difference is small. But lets do a thought experiment.
How would it affect our choice of Unruh wavelength if the drive frequency were increased by a factor of 4, for example. The cavity would still resonate at the drive frequency, just for n = 12. But the RF wavelength would be ~1.5 inches while any Unruh waves within the cavity would still be constrained by the cavity walls acting as the Hubble horizon.
In this thought experiment it seems to me that the choice of 1.5 inch Unruh wavelength based on drive frequency is more arbitrary than choosing 9 inches based on cavity dimensions.
The above thought experiment is more philosophical than scientific.
It seems to me that a question I posed earlier could lead to the answer. The question, "Does the acceleration within the walls caused by the RF drive have a directional component?"
That is, taking both walls as drivers for the Unruh wave, is the acceleration additive for n odd and dissipative for n even?
For n even, the RF wave has the same phase at both walls, while for n odd, at the second wall the RF wave is 180 degrees out of phase with the wave at the first wall.
What can we say about the nature of the acceleration coupling to the Unruh wave? Could the situation be that the Unruh wave also resonates within the cavity, building in energy until the energy exceeded that imparted by the minimum acceleration limit posed?
(8 c^2 / (DiameterOfBaseOfCone).
Some impressive news: @frobnicat (France) examined 21769 formulas to explore the experimental data. There is no formula found using the brute-force computational approach that does appreciable better minimizing the Standard Deviation than McCulloch's formula to explain the experimental data of the EM Drive. See: http://forum.nasaspaceflight.com/index.php?topic=29276.msg1271847#msg1271847
Dr. J. Rodal
Also, I had previously statistically explored the experimental data with McCulloch's formula and found a high coefficient of determination (R^2):
http://forum.nasaspaceflight.com/index.php?topic=29276.msg1271227#msg1271227
http://forum.nasaspaceflight.com/index.php?topic=29276.msg1271390#msg1271390
http://forum.nasaspaceflight.com/index.php?topic=29276.msg1271562#msg1271562
Dr. J. Rodal
Prof. M
In your initial data set you use dimensions of the resonate cavities. In particular, Shawyer (2008) b 28 4 45000 1000 2.45 394 80-214
You use w_small as 4 cm. How did you derive that dimension? I have been measuring from photographs on my computer screen and I obtain values of 8 to 10 cm for the small end diameter. I use the photograph at the bottom of the page here. [url]http://emdrive.com/[/url]
If you have a better source of cavity dimension information, please let us know.
As you know, this suspect dimension is critical to the analysis.
aero
I've read so many papers & notes I've lost track, but I think I estimated 4cm using the design factor, probably wrongly. Your photographic method is better & it improves the prediction too.
Shawyer Demonstrator Dimension Estimates
_________________________
aero (updated based on pixels)
Large Base Diameter =28 cm
Small Base Diameter =16.7 cm
_________________________
NotSoSureOfIt Pot-Based
Large Base Diameter = 28 cm
Small Base Diameter = (18.8 cm/29.6 cm)*28 cm = 17.78 cm
NotSoSureOfIt RFConnector-Based
Large Base Diameter = 28 cm
Small Base Diameter =(15.3 cm / 24.1 cm) * 28 cm = 17.78 cm
_________________________
Rodal
Large Base Diameter = 28 cm
Small Base Diameter = 15.9 cm
_____________________________
_____________________________
CONCLUSION:
Average
Large Base Diameter = 28 cm
Small Base Diameter = 16.79 cm
Median = @aero
Large Base Diameter = 28 cm
Small Base Diameter =16.7 cm
Thanks for the updated geometry. I've updated the comparison table.
I've just proved 'properly' that cons of mtum for the emdrive microwaves does indeed lead to the formula I derived (more loosely) before. Feel better about it now.
Hi guys. I need some help. Does anyone know the axial length of the two Shawyer & 3 Brady cavities?
Shawyer (small) experimental
Small Diameter = 0.1075 m
Length= 0.156 m
Shawyer (large) demonstrator
Small Diameter= 0.1679 m
Length= 0.345 m
Brady et.al. (for all NASA experiments in your table)
Axial Length of cavity = 0.23 m
is the best estimate available at the moment, based on estimates from aero
Based on the cavity length for Shawyer's demonstrator (larger) drive, the predicted force should be about 4 times larger than in your table,
see:
http://forum.nasaspaceflight.com/index.php?topic=29276.msg1272895#msg1272895
http://forum.nasaspaceflight.com/index.php?topic=29276.msg1272925#msg1272925
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