It's a gamble, but I think it's important to focus on anomalous experimental results since the new stuff always comes from there so I thought it would be useful to recap what I have been thinking about regarding Shawyer's EmDrive results. You should bear in mind that this is an example of me wildly playing around with ideas and I may decide tomorrow it is wrong. So, just to remind you that the EmDrive is a cone-shaped microwave resonant cavity, like a microwave oven built into a megaphone. When microwaves are resonated in there, it has been shown by Roger Shawyer, also a Chinese group and recently a NASA group that a small anomalous force is produced and the cavity moves towards its narrow end. This apparent violation of the conservation of momentum has not been explained.

To explain it, I've assumed the following: the microwaves bouncing around within the cavity have inertial mass (em radiation does: that's why it can push a Solar sail) and their inertia is determined by MiHsC (quantised inertia). In MiHsC the Unruh waves are allowed only if they fit exactly within the Hubble horizon or within a local Rindler horizon, but what if the cavity wall in this case was acting like a horizon? Well, then the microwaves at the wide end would have more inertia than those at the narrow end since more Unruh waves would fit. This means that as a microwave beam goes from the narrow end to the wide end it gains inertial mass. Now I can try something I've used before (for the Tajmar effect) and say, in order to still conserve momentum (mass*velocity) for the whole system, if mass goes up then velocity must go down, and the only way to achieve that is to have the whole structure move towards the narrow end.

I've done the calculation using MiHsC for Shawyer's EmDrive assuming an input power of 850W, a frequency of 2.45GHz and a Q factor (number of times the waves bounce before dissipating) of 5900 and I predict a force of 12.75mN, close to the 16 mN they saw.

Again, do take this in the spirit of 'playfulness'. There are huge questions: How can I throw out the rule book on photons like a hippy on LSD, and then insist on conserving momentum like an accountant with OCD? It could be a just a coincidence that it works, but it is interesting. Comments welcome!

## 12 comments:

I want to invite you over to the discussion at:

http://forum.nasaspaceflight.com/index.php?topic=29276.0

I know they all would be thrilled to hear your ideas.

Thank you.

Could you please provide the equations you used, or more details on how you calculated a force of 12.75 mN ?

"I've done the calculation using MiHsC for Shawyer's EmDrive assuming an input power of 850W, a frequency of 2.45GHz and a Q factor (number of times the waves bounce before dissipating) of 5900 and I predict a force of 12.75mN, close to the 16 mN they saw."

Thanks

Jeremiah Mullikin: thanks for the invitation. I'm not used to forums, but I'll have a look at yours over the next day or so and try and write something for it.

Be aware this is speculative, but look at eq. 8 in McCulloch (2007) (MNRAS, 376, 338-342). Replace big Theta with the cavity width (w). Calculate inertia at bottom & top, impose m'tum conservation so change in mass means change in v, and multiply by number of photon 'bounces' (Q) to give:

Force=(PQ/f)*((1/w_up)-(1/w_down)) where P is power (Watts), Q is the Q factor, f is frequency (Hz). I need more data (including Q factors) to test it..

Thanks for your prompt answer.

Shouldn't the frequency in the following expression be omega (the angular frequency)= 2 Pi f ?

"Force=(PQ/f)*((1/w_up)-(1/w_down))", so that really

Force=(PQ/(2 Pi f))*((1/w_up)-(1/w_down)); which gives a force 6.28 times smaller ?

The f comes in from f=c/lambda so no 2*pi needed.

Yes, that makes sense. Thank you for pointing it out.

"I need more data (including Q factors) to test it."

Here is a link to the NASA paper:

http://www.libertariannews.org/wp-content/uploads/2014/07/AnomalousThrustProductionFromanRFTestDevice-BradyEtAl.pdf Please see p.18 Table 2 for data: frequency, Q factor, Input Power, Peak Force and Mean Force. Concerning the dimensions, one can have a rough idea of the truncated cone (they call it "tapered cavity")dimensions from the pictures and knowing that they used Faztek beams with cross section of 1.5 inch x 1.5 inch

The picture of the tapered cavity seems to show a diameter ratio ( (large diameter)/(small diameter) ) = 9.9"/6.6" = 1.50 based on the photograph and the cross-section of the Faztek beam. Also the picture seems to show a ( (large diameter)/(length) ) = 9.9"/9.0" = 1.10, and ( (length)/( small diameter) ) = 9.0"/6.6" = 1.36.

I missed your comment "4 October 2014 14:57" with equations, which I did not have a chance to look at for as long as I wanted to. I would appreciate re-posting it if you have the time. Thanks

Thanks for the data. I deleted the derivation because I wasn't happy with part of the explanation, but will repost today.

The following NASA Eagleworks excerpts indicate that the resonant MODE SHAPE of operation is more important than the Q factor for the following microwave frequencies 1933 and 1937 MHz:

p. 14 "B. Tapered Cavity RF Evaluation and Testing, First TM211 mode Figures 18 and 19 chronicle the activities surrounding a series of five test runs at 1932.6 MHz corresponding to the first TM211 mode. In this test configuration, the VNA system indicated a quality factor of ~7320, and the difference of power forward and power reflected as reported by the power meters was indicated to be ~16.92 watts as a result of manual tuning to maximize the power difference. The (net) peak thrust observed for this tested configuration was 116 micronewtons and the (net) mean thrust over the five runs was 91.2 micronewtons.".....

p. 16 "C. Tapered Cavity RF Evaluation and Testing, Second TM211 mode

COMSOL® analysis indicates that there are two TM211 modes within a couple of MHz of one another for the as-built tapered thruster. The higher frequency TM211 mode has a much higher predicted quality factor (32,125), but considerably lower thrust to power performance (5 micronewtons per watt). The tapered RF system was tuned and operated at this mode for evaluation on the low thrust torsion pendulum. The measured quality factor was 18,100 with a power-forward/power-reflected difference of 16.74 watts and the average measured thrust was 50.1 micronewtons. With an input power of 16.74 watts, correcting for the quality factor, the predicted thrust was 47 micronewtons."

Unfortunately, the NASA report only shows the frequencies, but it does not show a figure with the MODE SHAPES in the cavity.

One cannot tell why operating at a frequency of 1937 MHz has a Q more than 4 times higher but a thrust force 1/2 as much as operating at a frequency of 1933 MHz. It would be nice to have a picture of the mode shapes to tell what is the difference: what gets excited in the cavity at 1933 MHz that makes a difference of 2 times in thrust force compared to operating at 1937 MHz.

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