I have updated the Table comparing the predictions of MiHsC with the available, fully-documented, emdrive experimental results, including a 6th result that I've just found online: that of the Cannae drive of G. Fetta (I take it as an emdrive because the grooves cut into it were found by NASA to make little difference). I've shown the predictions of the 1-dimensional MiHsC formula (which is preliminary) which assumes that accelerations are produced by the radio frequency oscillations:

F = PQ/f * ((1/w_big)-(1/w_small)) MiHsC1

where P is the input power, Q is the Q factor, f is the input frequency, w_big and w_small are the widths of the end plates. I have also shown the predictions of an alternative formula (MiHsC 2) that assumes that the accelerations are caused by photons bouncing at the cavity ends, and includes the cavity length (s) and speed of light (c):

F = PQs/c * ((1/w_big)-(1/w_small)) MiHsC2

See the new table below. The first column shows the experiment (S=Shawyer, C=Cannae and B=Brady), the other columns show the diameters of the big and small (two estimates) cavity end plates, the Q factor, power input, frequency, and the last three columns compare the predictions of MiHsC1 and MiHsC2 with the observed force (in bold):

Expt Q Power Freq' w_big w_small s MiHsC1

**Observed**MiHsC2

Watts GHz cm cm cm (--------milliNewtons--------)

-----------------------------------------------------------------------------------------------------------

S a 5900 850 2.45 16 12.750 15.6 3.26

**16**4.15
S b 45000 1000 2.45 28 12.890 34.5 76.90

**80-214**216
C a 1.1e7 10.5 1.047 22 20 3.0 50.14

**8-10**5.25
B a 7320 16.9 1.933 39.7 24.4 33.2 0.10

**0.0912**0.22
B b 18100 16.7 1.937 " " 33.2 0.25

**0.0501**0.53
B c 22000 2.6 1.88 " " 33.2 0.05

**0.0554**0.10
MiHsC1 underestimates the Shawyer (2008) experiments (S), predicts five times the Cannae result (C), and agrees with the NASA / Brady et al. (2014) a and c results, but not case b where it overestimates by a factor of five. The Cannae drive (C) has a very different geometry to the others (the width is 22cm, the length is 1cm) and this difference is useful for testing. MiHsC2 is perhaps comparable in success, but does less well for the NASA results (the most accurate?) which may be because of the 1-d limitations of my approach, or it could mean that it is the radio frequency oscillation that is driving the acceleration that causes the Unruh radiation (MiHsC1) rather than the microwave photons physically bouncing between the plates (MiHsC2).

Thanks to Dr J. Rodal for correcting my cavity dimensions again! The source of the Cannae experiment geometry and results is: http://web.archive.org/web/20121104025749/http://www.cannae.com/proof-of-concept/design see also the experimental results section.

## 27 comments:

There are many reasons why it was a great idea for you to also incorporate the superconducting Cannae test. Besides the geometrical difference you pointed out, here are 2 more reasons:

1) The superonducting Cannae test has an extremely high Q=1.1e7 compared to the other devices. This test shows the validity of the Q dependence in your formula. There are explanations for the EM Drive tests as an experimental artifact where the artifact is not dependent on Q. Without this Cannae test there was no conclusive information to settle this issue because the Q varied in the other tests only by a factor of ~ 7. But incorporating the superconducting Cannae, now the Q varies by a factor exceeding 1000.

2) There are explanations of the EM Drive as an artifact that are nullified by the superonducting Cannae test due to its immersion in such a cold fluid.

By "rather than the light physically bouncing between the plates" you really mean "rather than the microwave-frequency photons physically bouncing between the plates" is that correct?

Correct. Useful comments, thanks.

A column for the cavity's axial length (which you called "s" in your previous table) is missing from this new table.

Did you use 0.1 cm for the cavity's axial length?

This dimension gives me the same value you show for MiHsC1 (4.3), while for MiHsC2, I get: 0.0149 milliNewtons.

With this same dimensions, using Shawyer's formula, for comparison, I get 0.0595 milliNewtons.

I used 1 cm for the Cannae axial length.

Aero just pointed out to me that the Cannae drawing says the units are in cm.

QUESTION: For the required dimensions (axial length, small diameter and large diameter) should one use the inner cavity dimensions ?

________

Please take a look at my post:

( http://forum.nasaspaceflight.com/index.php?topic=29276.msg1277322#msg1277322 )

...

B) For Shawyer's (both experimental and demo) I have used Shawyer's provided numbers for the large base diameter and the design factor. I have used Shawyer's equations to then derive what the small base diameter was.

C) For Shawyer's demo he provides 1) a range of force/powerInput and 2) a specific case where he provides the force/powerInput as well as the powerInput (from which one can derive the force). I therefore included that information on my table.

D) It still looks like your equation #1 based on frequency is closer to experiments overall.

The inner cavity dimensions would be more appropriate, yes, but it won't make a huge difference to MiHsC1 because the inner dimensions will all be slightly smaller, and in the same proportion. Thanks for the new Shawyer small diameter estimate, a few cms different to the photo-based estimates of aero.

The Cannae superconducting inner dimensions make a huge difference to both MiHsC 1 and 2. Please take a look at http://forum.nasaspaceflight.com/index.php?topic=29276.msg1277825#msg1277825

Based on the inner dimensions, the MiHsC 1 and 2 bracket the observed results. If you like further details on the source of the numbers I used please let me know.

If you can correct my numbers that will be strongly appreciated.

Dr. J. Rodal

I've updated my table using your Shawyer small diameters. One point: I still take the cannae cavity length as 1 cm since the important length is that length over which the lateral diameter changes. Also, nice to see some of you trying to keep it fact-based over at NSF.

"I still take the cannae cavity length as 1 cm since the important length is that length over which the lateral diameter changes"

Then for consistency we would have to change the cavity length for Shawyer Demo and for the NASA truncated cones. The Shawyer demo is externally a straight cylinder joined to a truncated cone. If we disregard the straight length for Cannae we have to also disregard the straight cylinder for Shawyer.

Ditto for NASA Brady: the INNER drawings show a straight cylinder section on the small base side of the truncated cone.

Also please consider that the INTERNAL inner diameters of the Cannae superconducting device are smaller than shown on your table and that strongly affects both MiHsC 1 and MiHsC 2 predictions, as indicated by my post.

Yes, I realised that just after I posted! I didn't correct for the wall. MiHsC1 now overestimates for the Cannae drive.

I get 5.255 for MiHsC 2 equation.

Please take a look at my post and dimensions. It depends on what one takes for the cavity length. You are still showing 1 cm for Cannae but the drawing shows it is around 3 cm if one consider the straight portion. If we disregard the straight portion we have to do the same for Shawyer Demo etc

We shld consider the whole straight portion because in MiHsC2 the cavity length comes in from the photons bouncing between the end walls so has to be the whole length. My thoughts on the sloping portion of the length apply to MiHsC1 only, and there 's' does not appear. So Cannae length=0.03m.

Given the extremely high Q reported for the Cannae superconducting device, there is an extremely small bandwitdth associated with it. As remarked by Ludwick in the NASASpaceFlight forum thread (e-mails sent to me by him and posted by me) none of the researchers appear to have the equipment necessary to keep the frequency precisely at the peak amplitude due to frequency drift. This problem is much more severe for the Cannae Superconducting due to the Q=1.1E07. Hence it is very understandable to have significant overpredictions, particularly for such a high Q. Thus the overprediction of MiHsC 1 for the Cannae superconducting case is much more understandable to me than the underprediction of MiHsC 2 for this case. It just means that the actual Q drifted to significantly lower values during the length of time upon which the observed force was measured. Another reason for drifting lower Q's during measurement is the reported boiling off of the hydrogen and the consequent sloping baseline of the experiment.

John Fornaro after much discussion, using AutoCAD independently came up with the same estimate for the Cannae superconducting cavity height = 3 cm (Fornaro AutoCAD drawing here: http://forum.nasaspaceflight.com/index.php?topic=29276.msg1278521#msg1278521 )

Hi, this is indeed fascinating.

I suggest that future researchers may need to include active feedback in experiments to counter the effect of Q factor on bandwidth.

Think of it as a tuned circuit in radio, higher Q = narrower bandwidth.

Eventually you reach a point where the bandwidth tends to zero as the Q approaches infinity, does this sound familiar?

(cough relativity /cough)

If so then a compromise between sensible bandwidth and Q may need to be found in order to guarantee thrust is generated under all operating modes, or pulse it to let the chamber recover thermally.

Also relevant, I am working on a variant of the EmDrive but using a much higher frequency (22 GHz) as the Gunn/IMPATT diodes are far easier to tune than a magnetron.

Simply adjusting the input voltage alters the frequency somewhat and keeping the chamber at a set temperature should help with the frequency drift too.

The source of these modules are old burglar alarms and the diodes can be found on Ebay cheaply although power is substantially limited to maybe 100mW; this could be a problem but I am hoping that the higher frequency and use of a superconducting cavity to begin with will offset this loss.

http://www.kwarc.org/10ghz/24g.html

Apologies, 24 GHz not 22 but the idea is otherwise sound.

It looks like the two modules I have are essentially intact and working, will have to build a converter and hook it up to my 2.4GHz frequency counter to be sure.

These diodes need 5-6V at a controlled current, as negative resistance devices there is a peak and a trough current. For those experimenting in this area please be careful as the diodes are *very* static sensitive and I learned this the hard way with 10.250 GHz diodes at £14 apiece..

note: higher frequency diodes need less voltage, hence earlier deletion.

see http://ea4eoz.blogspot.com/2012/10/24ghz-old-way.html

I'm very glad you're going to experiment. Please do tell me your setup & the result you get. For your proposed setup, and assuming P=100mW, Q=40,000?(superconductor?), f=24GHz, big end diameter = 2cm, small end = 1 cm (the cavity has to be smaller to resonate with higher freq, is this size possible?) I predict with MiHsC a force of 8.3 microNewtons (F=(PQ/f)*(1/wb-1/ws)).

Hi Dr Mike,update: intend to make a 24 GHz cavity using 3D printing of low melt alloy (BiSnIn)

The tuneable diodes are handy as the range is 23.7 to 24.3 GHz by the looks of things.

Also, the inner coating is likely to be YBaCuO7 powder as easyto make.

Fantastic! You could provide the 10th data point. I expect your high freq' will need a smaller cavity for maximum effect, see my comment above, though there could still be a smaller effect. If you're willing, please let me know your geometry, Q, P & thrust.

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