Derivation of an Equation for the Cut-Off Diameter of a Frustum-Shaped Cavity at a Specific Resonant Frequency

I am scheduled to speak at the SmallSat Conference 2017 in Logan, UT this August. It is just one of the Swifties, where you get 3 minutes to talk about a subject, but they are letting me include a paper on the subject into the proceedings, which I have never done before. It is essentially a summary of the state of the investigation of the EMDrive as I know it, and what I believe are testable predictions that would differentiate between possible explanations for the phenomenon. I cannot put the paper here, but I am going to link to a paper I wrote that is referenced by it.

One of the important features of a waveguide that some of the proposed explanations rely upon is the cut-off frequency of the waveguide, or the cut-off diameter of the frequency. The problem is that, because the cavities being used are in a shape that has not been considered useful before this, the cut-off diameter doesn't have a reliable equation in order to predict it. This is my attempt at deriving one, and I hope that it proves valuable. I don't have the tools to test it in a simulation, but some people on the EMDrive thread at the NASA Spaceflight Forum gave it a quick go and it looks promising.

AIAA Paper

The long-awaited paper from Eagleworks on their EMDrive experiments has come out and the short version is: they measured a thrust of about 2mN / kW. This is a huge step forward, and I'm struggling to understand it all. I have only had a chance to skim it, but here are my thoughts right now. 

The reference to the Pilot-Wave understanding of quantum dynamics is fascinating this is the second time in a few weeks something about this has been published; the first time was in Wired here. (Apparently this was published in 2014, but I only read it a week ago) This idea says that a photon isn't a single thing that is both a particle and a wave, but a literal pairing of a particle and a wave. I'm looking forward to better understanding how this ties into the EMDrive, but I don't really understand the explanation yet. I asked Dr. March the following two questions: 1. Is it fair to summarize the findings as "the EMDrive is not a reactionless thruster, but more like a propeller through the zero-point field, and 2. Does this mean that a second EMDrive would react to another's wake? His response to the first was a gracious and complicated cantata scored around the theme of "No", but I'll have to read a lot more to understand it (including a dictionary, in some cases). He did recommend Dr. White's papers on the Quantum Vaccuum, so I will be reading that, as well. His answer to the second was "Yes", so I find that a very tempting experiment to try, if I ever get any farther. 

I also contacted Dr. McCulloch at Plymouth University. The question was around Pilot-Wave theory in general. He has said that his modified Casimir affect theory of inertia (MiHsC) would require light to travel faster than the speed of light when in a wave guide. He very graciously corrected my understanding that it did, pointing out that what travels faster than c was the phase velocity, not the group velocity, of the wave. Having gone back and tried to understand the difference, I see he's right, but my question today was: if the particle and the wave are separate, wouldn't the individual particles start riding the phase velocity but arrive sporadically, while the average flux of particles would be consistent with them traveling the group velocity? It seems to me that the particles, being the parts with mass, would be the relevant part to his theories, so maybe it's an answer. I look forward to hearing what he thinks. 

I genuinely don't know what to think. The possibility that there are multiple theories, and possible experiments to find out which it could be, is very exciting. What do you think?


Tuesday, the hard work of the last four months finally produced some results. As you may recall, the last chamber I made was not able to resonate at the expected frequency. I originally thought it was, but then I discovered that it was actually a resonance in my measuring equipment and not in the chamber itself. I discovered this right before I presented my project at the International Space Development Conference in San Juan (it wasn't meant to be a scientific presentation, but it would have been pretty embarrassing to present something that turned out to be incorrect). Comparing the measurements of the cavity that the Tajmar team used in their model, I found that my chamber was 5 mm shorter. I've had trouble understanding why they made their model to those measurements. I didn't have the parts on hand to make a second chamber, and didn't have the money to buy new materials. Luckily, I did have the parts to try and make the variable-sized chamber that would be the next generation model. I've pressed on to try and finish that, and have made some progress on it, but most importantly I got much better at polishing. With a few new tools and learning new techniques that were better than just hand-polishing with sandpaper, I decided a couple of weeks ago to try polishing the original chamber with the new techniques and see if the problem with the resonance was actually due to incorrect measurements. 

And amazingly changing the polishing fixed the resonance problem! I got a resonance at about 2.40 GHz and at about 2.46 GHz. I didn't test it with the computer recording software plugged in, and when I attempted to show Mike Beach, the electronics expert that has been helping me at Artisan's Asylum, after the class he was teaching ended an hour and a half later it didn't work any more. I believe that this is because the copper oxidized enough in that hour and a half to reduce the reflectivity enough that it no longer resonated, but now I know how to fix that. (Really, Dr. Paul March gave me the hint about it months ago, but I thought I could get around it so I didn't buy the correct materials. Eight hours soaking in lemon juice, he told me, but I thought polishing right before the test was enough. I now keep all parts in a bath of 5% ascorbic acid whenever it's not in use).

The Q I measured yesterday was about 50, comparable to what the Tajmar experiments had, and I'm sure I can do better. Now that something is moving the needle, I am laying out a series of tests that I will be conducting over the next few days or weeks.

I am going to run tests, recording a control sweep and then recording frequency sweeps every 15 minutes to see the degradation of the resonance over time after at least a day of soaking in the ascorbic acid. The next step will be to see whether using galinstin as a liquid "gasket" between the copper parts of the chamber increases the Q factor; it may or it may not. The next step after that will be to incorporate the silicone spray Dr. March recommended to me to see how well it protects against oxidation. I didn't want to incorporate this spray until I knew the chamber worked in case a misapplication of the spray caused a problem that prevented the chamber from working.

Testing the chamber under full expected power will take a lot of preparation. I have partially constructed a faraday cage in which to test it that is big enough for some levers to amplify the measured force. It's a bit complicated, and getting power into the cage without it leaking the powerful microwaves out has been tricky.

I also have been starting to construct the experiment controller, with the foundation for control circuitry for the satellite inside it. That part is designed roughly in my head, and I've only just started to get it out into code.

I will keep you posted. 

International Space Development Conference

I recently presented the Build an EM Drive project to the International Space Development Conference in Puerto Rico. Puerto Rico was fun; the conference was sort of a bust for us. I got on the schedule late and, while they were great, it was so chaotic that I accidentally wasn't on the official schedule. A few people came. The presentation is included below. It's part of a change in the way we are promoting the project, as well. I will have more about that soon.

Why Metal Spinning?

I have a lot of trouble starting the blog for this project, because I have a million thoughts about it and I haven't known whetner the try and express them all in a shorter form and follow up with further detail, or some other approach. What I am actually going to do, is address one small thing, and see where it takes us.

If I were looking at the Facebook and Twitter feeds, one of the biggest questions I would have is, "why is he focusing on metal spinning?" It turns out I have reasons!

It comes down to the mechanics of how microwaves are reflected in a resonance chamber. The photon hits the walls and induces an electric current in the walls and this electric current in turn emits a new photon that follows a course as if it reflected off the wall. Which it did; that's how reflection works. Anyway, the point is that without the electric current, it doesn't work. So, the material needs to be highly conductive, and the current has to be complete, or nothing happens. And there's another piece of the puzzle: skin depth. Skin depth is how far into the copper the photon penetrates before it creates the current. A high frequency photon will go farther in, a low frequency photon will stop closer to the surface. So if the photon doesn't penetrate all the to some copper, it doesn't work. Say, if there's copper oxide or some schmutz on the wall. And the skin depth is micrometers thick; the copper can't have anything on it. And it should be very highly polished, forcing the current to flow around surface blemishes, like the tiny scratches the keep metal surfaces from having a "mirror finish", increases the electrical resistance and cuts down the reflectivity. This, in turn, reduces the "Q factor", which I will explain later and is really, really important for the EM drive.

Which brings us to metal spinning. My first attempt at building a cavity, in addition to having nearly every dimension wrong, was made by cutting the shape out of a single sheet of copper, wrapping it around a mandrel, and welding the ends together so that it was in the shape of a frustum.


Which went OK except that it wasn't very smooth, and I didn't make my own mandrel so it wasn't shaped smoothly, and a million other reasons I am unhappy with it. But I had my biggest problem with the seam. It really bothered me to have a seam, because:

  1. I expect it would interfere with the electrical connectivity, since the solder probably conducts less well than the copper,
  2. I expect the huge step between the two ends as they had to overlap to get the weld to stick to be a problem with the skin depth,
  3. It just didn't seem right.

I am also looking at other designs where other groups have created their walls and then bolted or affixed the base plates to flanges on the walls. A mechanical connection like that does not work as well as a solder connection, just because it often better to have a liquid that can flow into the little cracks between two objects. Now, I am not going to knock Anyone else; many of them know what they are doing better than I do; I am just saying that I cannot do things their way and feel comfortable that it is the best I can do.

Then, I heard about metal spinning. It is a technique that is not often done today, and actually uses a lot of tools in very unusually way and, in a space like the Artisan's Asylum, is very cross-disciplinary and complicated. We do not have any experience with it amongst our instructors, and just having some one trying it at the Asylum has generated a lot of interest. But, what it means, is: I can create a frustum whose walls and one of the base plates are all one single sheet of metal and there virtually no seams anywhere. This is very important to me; I think this will increase the Q of the chamber, and it may make fabricating multiple copies easier, if it comes to that.

Som, months of yak shaving later and I have started to produce some spun parts.
Metal Spinning Night 1 Metal Spinning Night 2
Nothing that looks completed, but I am almost there. 

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