The EmDrive is a fascinating anomaly. It consists of a truncated metal cone (cavity) with a magnetron inside that inputs EM radiation with the same wavelength as the size of the cavity (it's just like a loudspeaker-shaped microwave oven). It has been shown by three different groups (UK, China, US) that when a resonance is achieved the cavity moves slightly towards its narrow end in apparent violation of the conservation of momentum, since there is no expelled mass to cause this. There was a suspicion that the movement was due to air currents, but NASA have just this last week shown that the same thing happens in vacuo.

In previous blogs I showed that

MiHsC predicts the EmDrive thrust reasonably well, if it is assumed that photons have inertial mass which is caused by Unruh radiation whose wavelengths must fit inside the cone. MiHsC predicts that more Unruh waves fit in at the wide end of the EmDrive, so for photons traveling along the axis they always gain mass going towards the wide end and lose it going the other way. This is equivalent to expelling mass towards the wide end, so the cavity moves towards its narrow end to conserve momentum.

The equation I derived to apply MiHsC to the EmDrive setup (and published

here) was extremely simple and didn't take account of the 3-dimensional nature of the cavity. I have now worked out a short-cut way to calculate the effect in 3-d, and I've re-derived the equation I had before for the thrust (F), which was

F = PQL/c * (1/wb - 1/ws) (1)

so that in 3-d it is now

F = 6PQL/c * ( 1/(L+4wb) - 1/(L+4ws) ) (2)

where P is the power input (in Watts), Q is the Q-factor (number of bounces of a typical photon inside the cavity, L is the axial cavity length, c is the speed of light, ws and wb are the diameters of the small and big ends of the truncated cone. I have now applied Eq. 2 to the data I had before, and added the new vacuum result from NASA. I've put everything into Table 1 which shows results, row by row, for the two Shawyer (2008) tests (denoted Sa and Sb), the Cannae Drive test (Ca), the Chinese Juan et al. (2012) tests (J1 and J2), the NASA tests of Brady et al. (2014) (Ba, b, c), the recent NASA vacuum test (Bv), and last but not least I've just added Tajmar's (2015) vacuum test (T1).

Expt Q Power Freq' wb ws L

**Observed **MiHsC

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

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

S a 5900 850 2.45 16 12.750 15.6 **16** 3.84

S b 45000 1000 2.45 28 12.890 34.5 **80-214 ** 148

C a 1.1e7 10.5 1.047 22 20 3.0 ** 9** 7.34

J 1 32000 1000 2.45 28 12.89 34.5 **214 **106

J 2 50000 1000 2.45 28 12.89 34.5 **315 **165

B a 7320 16.9 1.933 27.94 15.88 22.86 **0.09** 0.23

B b 18100 16.7 1.937 " " " **0.05** 0.57

B c 22000 2.6 1.88 " " " **0.06** 0.11

B v 6730 50 1.937 " " " **0.03** 0.64

T 1 20.3 700 1.44 10.62 7.5 10.08 **0.02** 0.019

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Thanks to Dr J. Rodal for pointing out some errors in the NASA cavity's dimensions. I've now doubled the Tajmar dimensions too.

The results show a correlation between the observed thrusts (column 8) and the predictions of MiHsC (column 9), but with varying degrees of success: for the smaller NASA thrusts the error ratio is between 2 and 12, for the larger thrusts it is between 2 and 4. So, as usual, these results are interesting enough to record, but nothing yet to write to Nature about. Note that for J1 and J2 I've had to assume that their cavity dimensions were the same as those for Shawyer b, since their geometry was not documented. If anyone knows the dimensions, or notices any errors in the Table please do let me know! A summary of the Table is shown as a log-log plot below (I had to use a naughty log-log plot to separate the tiny NASA values).

Some of the discrepancy between MiHsC and the data could be due to an observation pointed out by Bob Ludwick that I read on a website somewhere: the Chinese noted that the correct parameter to use is not the Power P, but the power within the resonant bandwidth of the EmDrive, which is harder to calculate.

Some of my previous blog entries about MiHsC and the emdrive are

here and

here. My paper is

here.

**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., 2015. Can the EmDrive be predicted by quantised inertia? Progress in Physics, 11, 1, 78-80.

Link
Shawyer, R., 2008. Microwave propulsion - progress in the emdrive programme.

Link. (see section 6, page 6).

Tajmar, M., G. Fielder, 2015. Direct thrust measurements of an emdrive and evaluation of possible side effects. 51st AIAA/SAE/ASEE Joint Propulsion Conference, Orlando, Florida.