Author Topic: EM Drive Developments - related to space flight applications - Thread 3  (Read 1880014 times)

Offline rfmwguy

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FWIW, I admire the meepers doing what I cannot do, burn through iterations and generate 3D models. I vote for both us builders, meepers and theoretical types keep doing what we are doing...trying to help in our own way.

p.s. NSF-1701 exoskeleton needed some strengthening today. Just got that completed. I'll post a pic in a minute.

Offline tleach

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What I want to see is some of the qualitative behavior surmised by some where the wave dissipates into the big end, aliasing into the wall as dissipation (ultimately) into thermal energy, creating a kind of momentum sink.

"Momentum Sink" 

I like it.  If the frustum acts as a Momentum Sink, soaking ALL of the radiation's (microwaves') momentum up and converting it into momentum of the frustum, then we avoid the conservation of momentum issues, right?

An astronaut leaving right side of a space station (by pushing with feet, or repulsing with magnet, whatever) and coasting through and being "soaked" (grabbing) on the left side will move the space station to the right (by a few centimetres or millimetres), but that don't yield an acquired deltaV at end of the exercise. It is trivial to move a box "propellentless" by moving things (mass or energy) inside the box, but the centre of mass of the whole system (box + content of box) is not departing from inertial trajectory (no move overall). And this is one shot, can't be cycled for added displacement (can't be used to "crawl").

http://forum.nasaspaceflight.com/index.php?topic=37642.msg1402428#msg1402428
( for a 2kg 2m sized spacecraft on lithium ion battery such mass_energy displacement amounts for a one shot of one tenth of an angström... and it couldn't possibly exceed the size of the spacecraft even with antimatter batteries)

This is for deep space flat spacetime. In curved spacetime things can be a bit different and cycling can yield added displacement, but this is a very small magnitude effect : swimming in spacetime
(was already mentioned in thread 1)
The curvature of spacetime is very slight, so the ability to swim in spacetime is unlikely to  lead  to  new  propulsion  devices.  For  a meter-sized   object   performing   meter-sized deformations at the surface of the Earth, the displacement is of order 10^-23m

More accessible illustrated sciam article on the principle.  ( the article on the publisher's site is paywalled, not sure if this full length article copy is legit )

edited:left/right blunder

OK, but your example (and thank you for using a simple analogy that us non math people can follow) is... macroscopic.  Astronauts have mass and hence have inertia.  Photons do not.  I'm suggesting that perhaps the momentum is being directly transferred without changing the center of mass.

Edit:  I mean, ok, I guess the center of mass would change, but the center of mass would change as a result of the direct transfer of the momentum from the photons to the frustum, not as an intermediary step on the way to acceleration.
« Last Edit: 07/22/2015 12:53 AM by tleach »
T. Thor Leach

Offline deltaMass

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FWIW, I admire the meepers doing what I cannot do, burn through iterations and generate 3D models. I vote for both us builders, meepers and theoretical types keep doing what we are doing...trying to help in our own way.

p.s. NSF-1701 exoskeleton needed some strengthening today. Just got that completed. I'll post a pic in a minute.
Elon Musk found out that he had a similar problem this week too :P

Offline rfmwguy

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nsf-1701 exoskeleton complete today. copper tape with conductive adhesive added on top and bottom edge seams.

Offline aero

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Meep also allows a source (antenna) to be turned off at a specific time via the "end-time" parameter on the
"src-time" classes such as "continuous-src" and "gaussian-src".  I could run this when I get home tonight if no one beats me to the punch.

make a run and check the fields, (look at the antenna), but when I did it, it was clear that the gaussian-src did not turn off at the end time. That is consistent with the reference manual which gives "end-time" as a a parameter for continuous-src and for custom-src but not for gaussian-src. Unfortunately meep does not throw an error when this is used, so running and looking is the only way I know to determine what happens. When I searched on the meep mailing list for how to turn off a Gaussian,  that was one of those questions for which the answer was, "write your own function."
Retired, working interesting problems

Offline ArbitraryConstant

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I suspect everyone has seen some version of Escape Dynamic's microwave-powered shuttle at this point, but just in case, here's a short (and badly written) article that includes a nice bit of embedded animation. It's only vaguely related, but hey, it is a spacecraft proposal, and it is using microwaves, so... here you go.
They use reaction mass though. :)

Offline rfmwguy

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FWIW, I admire the meepers doing what I cannot do, burn through iterations and generate 3D models. I vote for both us builders, meepers and theoretical types keep doing what we are doing...trying to help in our own way.

p.s. NSF-1701 exoskeleton needed some strengthening today. Just got that completed. I'll post a pic in a minute.
Elon Musk found out that he had a similar problem this week too :P

Yes, calculating stresses and testing stress-strain properties is important in many fields  :P

<<The roughly 2-foot-long (0.6 meters) struts hold these bottles in place. Each strut is certified to withstand about 10,000 lbs. (4,500 kilograms) of force. Based on when the explosion happened — less than 3 minutes after liftoff — the strut in question apparently broke under a load of less than 2,000 lbs. (900 kg), Musk said.

"It's not something that should have ever failed at this force level," he said. The strut "would appear to be incorrectly made, but there was no visible way of telling that from the outside."

SpaceX sources these struts from an outside company and will probably change suppliers now, Musk added. In addition, SpaceX plans to individually test and certify every strut that will fly, to ensure that no faulty ones make it on board, he said>>
lol...I hope musk uses more than Cu foil to fix his rockets. Had I known I was going to use a heavy magnetron, i'd have started off with sturdier material...oh well, minor tweak...as it stands now, my weight budget is around 2kg, not 1.5. Still light enough to react to small forces on the fulcrum, or as deltamass would call it: floobie stick ;)

Offline rq3

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It is not just the gross mischaracterization of what is happening,  accompanied by an obvious misunderstanding of how the scientific process works , but the sheer pomposity of pretending to teach others how science should be conducted.  The question asked, has been answered repeatedly in this thread.  The people doing the testing (rfmwguy, SeeShells, etc.) have worked together with the people doing these simulations, whose object has been to understand the mode shapes, electromagnetic fields, flux and stresses excited in the microwave cavity, just like Prof. Yang conducted computer simulations (prior to her test results: the highest forces ever reported) and just like it has been done in all R&D since WWII.

The hubris of somebody that just joined this 600 pages long thread telling others to "stand by", is just outstanding.

All done anonymously, of course.

Please address sequentially. I asked no questions. I made clear statements. If you have issues with my clear statements, please don't wave your arms generically and discount my statements. Please address my statements.

I believe that this thread has devolved into:
1) Hardware experiments with no new data SO FAR
2) Software simulations, based on known physics, attempting to predict unknown physics based on no new data SO FAR

Also, please see my previous posts to this forum. If you have missed them, perhaps you are only paying attention to those that agree with you. Bad science.
« Last Edit: 07/22/2015 01:48 AM by rq3 »

Offline ElizabethGreene

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So why are folks relying on MEEP to model a physical process that, according to known physics, is impossible?

The answer is quite simple.  It takes me ~20 hours to build a bad emdrive.  Bad in this case doesn't mean non-functional, it means "I forgot to carry a 1 and now the resonant frequency is off by more than the 50Mhz window where I can reliably phase lock a magnetron."

Meep/Harminv, or in my case Comsol, allows me to moron-test a resonator before breaking out the tin snips.  It can tell me if I have a bunch of eigenvalues all piled up around my desired mode.  With Comsol and Solidworks integration I can adjust a cavity dimension, rebuild the model, and hit compute faster than I can type this message.  Further, by pulling my model directly from Solidworks and using it to create my sheetmetal template then I can cut out a dozen fidgety and error-prone fabrication steps.  This combination of tools enables me to do work I couldn't even dream of without them.

That's just the tip of the iceberg.  Plodding through the Comsol sample models has given me dozens of new ideas.  One example: Negative refraction index split ring and pole metamaterials.  Hypothetically, using these as the big end of the resonator can make the thrust higher for the same unit volume by pulling the big end and pushing the little one.  (Chalk that one up as today's idea book contribution.) 

I am firmly in the "build it and play with it" camp.  That said, I am willing to putz around in software for days if it will save me years of unproductive work.

Offline WarpTech

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Well, yes but when the antenna is on the axis of rotation and either a point source or axial in length, the frustum is rotationally symmetric. Meep also allows specification of mirror symmetry which reduces run time significantly but does not address the granularity issue.
Hey - as I was thinking about this, I think a cylindrical 2D model could be *very* helpful in understanding the qualitative behavior if Todd's theories or the ratchet theory are involved here.  We could do the sims in (1/261)th the time.  With a 2D cyl, we would assume a circular plate source (a line in the 2D plane)....  I'll check it out unless you beat me to it...

Unfortunately, 3D is needed to model an EM wave. If you want to do a scalar field in 2D, that may work but how well does that model EM, which is a vector field? Starting with an open ended 3D cylinder, rather than a frustum and determining the right antenna configuration at one end, to get resonance at near zero, 0 group velocity, without mode distortion would be closer to what we need.

Think of this, instead of a large Q, what we could have is a long, slow moving wave train. We are inputting energy at 2.4GHz, and the traveling wave is moving at "almost" zero velocity down a straight pipe. The energy will pile up into a very short wavelength "mass" that has an enormous amount of energy. At the end of the day, a slow moving wave-train or a high Q will both result in an enormous energy storage. The difference is, the moving wave-train has focused momentum, where a high Q has zero!

So, I shall reiterate. I believe what we want is the resonance of the circular Bessel function, Xmn mode, and a long, slow moving wave-train of "mass" moving down the pipe. Then the pipe starts to taper outward and all that mass "falls" to the bottom of the well, the big end. In response, the frustum-pipe thrusts the other way. As I've said, as long as that energy does not go all the way back "up" the hill to where it started, the potential energy has dropped and it cannot be recovered. The energy lost by the waves is gained by the frustum and so the frustum's CM is shifted forward. Conservation of energy and momentum is inherent. Regardless of the thrust-to-power ratio, it is a conserved system;

d(K + P)/dt = 0

where K is kinetic energy and P is potential energy input at the small end.

Regarding the ratchet, if this works, that works too. Same process, different design. I would optimize it differently if I wanted to design a ratchet. What I've proposed above is not optimized to be a ratchet. It is a thruster. I have the force equation. What I am still trying to determine is how to formulate the power "correctly". I would think this should be a piece of cake, but there are too many interrelated equations and options I am not 100% comfortable with ....yet. Thanks for thinking of me! I appreciate it. :)
Todd

Online ThinkerX

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Please address sequentially. I asked no questions. I made clear statements. If you have issues with my clear statements, please don't wave your arms generically and discount my statements. Please address my statements.

I believe that this thread has devolved into:
1) Hardware experiments with no new data SO FAR
2) Software simulations, based on known physics, attempting to predict unknown physics based on no new data SO FAR


'devolved' is probably the wrong word.  'focused' might be a better choice.

As to the 'so far,' bit much of the conversation is 'prep work' to ensure the best possible (new) results - positive or negative.  Plus, much of the modeling and test work is just barely getting started.  One does not immediately jump from highly preliminary tests, calculations, and models to a definitive conclusion.  That is the mistake too often made by those who claim to have invented perpetual motion machines or some such.


Offline SeeShells

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Very busy day here, getting all the little pieces and parts screws glues and soft pads to shine up the fulcrum, extra gas for the little torches...... Plenty of little details. Plus digging into dipoles and everything you ever wanted to know about that black art. ;) Thanks for the great help, you know who you are!

Meep is a tool nothing more and if you see everything as a hammer, well you know the saying.

The data needs to be flushed out with every tool we have. Meep is a tool that's not going to miraculously discover why this gives thrust but it can provide stress and wave densities that may be of use later after we plug in the real data.

This thing is simply going to take a engineering test bed to take it apart piece by piece and I've tried to build one to do just that. I hope to be able to provide quantified data on active and passive motions during power times, TE and TM modes and different power levels, different insertion sites. different models of cavity lengths different materials from perforated copper to solid to flat to convex end plates. I know there will be more from varying the duty cycles on the magnetron fro 10% up to 100%. I'm even going to use an old trick keeping the cavity resonate at a good Q from my sub hunting days but I'll detail that out later.

I'm remembering or relearning or just plain learning while I do all of this but in the end I hope to be able to provide a nice set of data to crunch on using the same test bed.

I want to thank everyone for the wonderful help, I've never been blessed in my career to have so much talent in one room. Well a blog room that is.

Shell

Offline DeWeave

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'Accepted physics' was rather inartful phrasing on my part.

A better summary would be, Mach effect and the Emdrive have both been shown to occur through initial testing.  Whether either or both evaporate into the Ether with closer examination remains to be seen, and further testing is the most useful next step either way. 

It just seems that the more the MEEp folks to try define exactly what happens to the fulstrum when you're running it, the more it sounds like Woodword theories.  I'm not saying this is necessarily the Mach effect, more that both theories sound similar enough that perhaps you're converging on the same principle from different sides.

At risk of over thinking it:
Woodword coming from the theory side is taking the simplest possible approach to validate his theory; using a capacitor.  But you could generate the same effect through a much more complex means, which could be what's happening here. 

Offline rfmwguy

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It is not just the gross mischaracterization of what is happening,  accompanied by an obvious misunderstanding of how the scientific process works , but the sheer pomposity of pretending to teach others how science should be conducted.  The question asked, has been answered repeatedly in this thread.  The people doing the testing (rfmwguy, SeeShells, etc.) have worked together with the people doing these simulations, whose object has been to understand the mode shapes, electromagnetic fields, flux and stresses excited in the microwave cavity, just like Prof. Yang conducted computer simulations (prior to her test results: the highest forces ever reported) and just like it has been done in all R&D since WWII.

The hubris of somebody that just joined this 600 pages long thread telling others to "stand by", is just outstanding.

All done anonymously, of course.

Please address sequentially. I asked no questions. I made clear statements. If you have issues with my clear statements, please don't wave your arms generically and discount my statements. Please address my statements.

I believe that this thread has devolved into:
1) Hardware experiments with no new data SO FAR
2) Software simulations, based on known physics, attempting to predict unknown physics based on no new data SO FAR

Also, please see my previous posts to this forum. If you have missed them, perhaps you are only paying attention to those that agree with you. Bad science.
And you would like the thread to be...uhhh, what? Opinions are only semi-welcomed, contructive critiques or suggestions are OK. Real work on hardware or software...even better. Find a niche and let's get this thing resolved: refuted or confirmed. After hundreds of pages, that is my takeaway fwiw.

Offline notarget

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Unfortunately, 3D is needed to model an EM wave. If you want to do a scalar field in 2D, that may work but how well does that model EM, which is a vector field? Starting with an open ended 3D cylinder, rather than a frustum and determining the right antenna configuration at one end, to get resonance at near zero, 0 group velocity, without mode distortion would be closer to what we need.
Hey Todd - the sim we're describing is actually a 3D sim, but assumes rotational symmetry.  We can have your blobs of EM traveling in 3D space as E + B vector fields with interlaced curl - no worries :-)

What would blow this sim is if there were something about this phenom that required a non-rotationally symmetric solution.  Even spiral eddy currents (helical) are admitted in rotational symmetric solutions, so I can't think of anything that rules it out for this case...

At this point, not being an EM person (more mechanical / Aero), I would just like to understand some of the EM physics better by doing some meaningful sims - particularly as your theories have turned toward an aliasing of momentum into entropy - which implies an interaction with the boundaries and materials...

Offline notarget

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Unfortunately, 3D is needed to model an EM wave. If you want to do a scalar field in 2D, that may work but how well does that model EM, which is a vector field? Starting with an open ended 3D cylinder, rather than a frustum and determining the right antenna configuration at one end, to get resonance at near zero, 0 group velocity, without mode distortion would be closer to what we need.
Hey Todd - the sim we're describing is actually a 3D sim, but assumes rotational symmetry.  We can have your blobs of EM traveling in 3D space as E + B vector fields with interlaced curl - no worries :-)
I now see the confusion - "cylindrical symmetry" is not what I've been thinking about, rather I'm referring to "axisymmetry" or periodic in the angular coordinate around the frustum's length axis.  We often exploited this in CFD for propulsion systems - I typically used a periodic boundary condition and was able to use one 2D plane worth of model space to do the sims.

Unfortunately - meep doesn't do that.  I can do quarter symmetry which will save 1/4 of the space / time but it doesn't seem to do axisymmetry per-se.

I'm going to run some more stuff and post what I get - too much talk on this stuff for this thread IMO.

Offline WarpTech

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Unfortunately, 3D is needed to model an EM wave. If you want to do a scalar field in 2D, that may work but how well does that model EM, which is a vector field? Starting with an open ended 3D cylinder, rather than a frustum and determining the right antenna configuration at one end, to get resonance at near zero, 0 group velocity, without mode distortion would be closer to what we need.
Hey Todd - the sim we're describing is actually a 3D sim, but assumes rotational symmetry.  We can have your blobs of EM traveling in 3D space as E + B vector fields with interlaced curl - no worries :-)

What would blow this sim is if there were something about this phenom that required a non-rotationally symmetric solution.  Even spiral eddy currents (helical) are admitted in rotational symmetric solutions, so I can't think of anything that rules it out for this case...

At this point, not being an EM person (more mechanical / Aero), I would just like to understand some of the EM physics better by doing some meaningful sims - particularly as your theories have turned toward an aliasing of momentum into entropy - which implies an interaction with the boundaries and materials...

At the moment, I'm concentrating on dispersion forces with an open-ended waveguide, not entropy. Once I discover what generates the high thrust-to-power ratios that Yang has reported, then I can turn my attention toward what happens when the big end is closed off. Right now, I've got my head wrapped around inverse metric coefficients acting on the phase velocity.

Break over...
Todd

Offline ElizabethGreene

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An astronaut leaving right side of a space station (by pushing with feet, or repulsing with magnet, whatever) and coasting through and being "soaked" (grabbing) on the left side will move the space station to the right (by a few centimetres or millimetres), but that don't yield an acquired deltaV at end of the exercise. It is trivial to move a box "propellentless" by moving things (mass or energy) inside the box, but the centre of mass of the whole system (box + content of box) is not departing from inertial trajectory (no move overall).

There is a fundamental difference between light bouncing around in an  emdrive and the astronaut in the space station.  It took me a while to grok this, but I think I can explain it now.

The astronaut pushes off of one side of the spacecraft with a specific amount of force.  He moves left, the spacecraft moves right.  These forces are balanced.  There is nothing he can do, Pre-emdrive, to accelerate himself left that doesn't generate a corresponding thrust on the spacecraft to the right.  He cannot change his mass or acceleration without a corresponding change to the spacecraft.  This is classic conservation of momentum.

Light does not obey conservation of momentum under specific conditions.

This has been demonstrated:
Optical diametric drive acceleration through action–reaction symmetry breaking
http://www.nature.com/nphys/journal/v9/n12/full/nphys2777.html

Under specific conditions, Light can push off the right wall of the spacecraft with a small force and hit the left wall with a large force, bounce off, and hit the right wall with a small force again.  This will move the spacecraft's CG.

How do you make light do this?  Take a look at the equation for radiation pressure.

F=hf/c
Force = Planck constant times frequency divided by the speed of light.

The c term is really important   It is not c0, 3x108 meters per second the speed of light in a vacuum.  The divisor is c, not c0.  It is the speed of light _in the medium_.

If that equation holds true, F=hf/c, then slowing light down INCREASES the force of radiation pressure.  That is completely non-intuitive for me.  It makes no sense whatsoever.  Slower should be less force, right?

No.  It's been demonstrated.
The Measurement of Optical Radiation Pressure in Dispersive Media
http://www.jstor.org/stable/79586

Abstract Snippet: "The new experiment confirms, to a  precision of about 0.05%, that the momentum associated with  electromagnetic radiation increases directly with the refractive index of the medium into which it passes."

Key: Radiation pressure varies inversely with the speed of light.

I'm still perplexed by this, and I wish to know more.

If you accept that slowing light down will increase its force, how does this work in a tapered non-dielectric emdrive waveguide?  How does it slow light down?

Answering this requires an understanding of light propagation in a waveguide.

In this video https://www.youtube.com/watch?v=NOW8Bgx-CU0?t=33m40s Professor Lewin demonstrates that polarized light with the E field perpendicular to two parallel plates will not propagate if the distance between them is less than half of the wavelength.

In waveguides you have a similar limitation.  If the longest dimension of the waveguide is less than half the wavelength then the light is absorbed.

The point where light will no longer propagate, i.e. where the light can no longer fit, is called the upper cutoff wavelength or the lower cutoff frequency.  You can see get formulas for these from the waveguide math page at microwaves101.com.  http://www.microwaves101.com/encyclopedias/waveguide-mathematics#cutoff

What's interesting for our purposes is not what happens at the cutoff frequency f=c/2a, but what happens between cutoff f=c/2a and where an entire wavelength will fit in the waveguide f=c/a.

When the wide part of the waveguide (a) is less than the wavelength then light has to reflect off the sides to fit in the guide.  This makes the light move more slowly, at a speed called the Group Velocity. 

.

Driving the point home, it is possible to make a waveguide small enough that you can outrun the light in it without breaking a sweat.

This explains the tapered waveguide emdrive.  At the big end the radiation pressure is close to hf/c0.  At the little end, the light is much slower, approaching zero, so the radiation pressure is radically larger.  The imbalance in forces makes the ship go.

That leaves the dielectric case unexplained.  The missing piece is that there is a connection between n (index of refraction) and the electric and magnetic permeabilities of dielectrics.  The dielectric slows light down, increasing its wavelength, and increasing radiation pressure .

In the non-dielectric end, the force is hf/c0. (a small number)
In the dielectric end, the force is hfn/c0. (a bigger number)

That's _almost_ enough to explain a dielectric emdrive in a closed waveguide, but not quite.  I'll dig into the remainder in a moment. 

Putting these together gives you the guts of Mr. Shawyer's emdrive theory, ignoring the bits around general relativity.  The net force is the large radiation pressure from the slow moving light in the near-cutoff or dielectric little end minus the small radiation pressure from the freespace propagating big end.

Back to the dielectric for a moment.

If you drew this out on paper you'd see that some radiation reflects from the dielectric instead of on the metal endcap.  This reflection is an impedance mismatch and it generates radiation pressure too.  You can eliminate this reflection and it's associated thrust in the wrong direction if you can find a place where the electric field in the waveguide is zero.  We're lucky.  In a standing wave like a waveguide or resonator there are points called nodes.  At a node the wave "stands still". 
  The electric field is zero, so a transition to a dielectric at that point yields no thrust in the wrong direction.

* elaborating:
Poynting gave us
S = E x H

In english, the Energy transferred is the cross product of the Electric and Magnetic field vectors.  If either of these vectors are zero, the energy transferred _and the radiation pressure_ are zero. 

Transitioning from freespace to dielectric propagation at a node yields no impedance mismatch reflection and no backwards radiation pressure.

This last component probably explains why some promising looking EmDrives don't work.  If the small end has a node parked in it then the energy transfer to the business end will be dramatically reduced.  Possibly reduced so much that you have to tap the emdrive to get it started.

... that ran long...
Bringing it back to the original comment:

Light bouncing in a space capsule is different from an astronaut bouncing because the Astronaut Force is constantly balanced, but the force exerted by the light varies based on the speed of light in the medium and the phase of light as it reflects.

Arc, this is the bit for your question:
I believe light can skirt conservation of momentum because it has no mass.  I do NOT believe it violates conservation of energy.  Some quantity of energy will be converted to motion by the work of accelerating the emDrive.  This energy has to come from absorption of the light or by decreasing its frequency.  Mr. Shawyer calls this Doppler shift, but I think it's closer to Compton scattering.  In either case, the energy will come from somewhere.

A bright fellow could answer this question with a specially designed reflector where the large waveguide dimension could be adjusted (changing Vg) and separate input and output ports.  A frequency shift between input and output ports that correlates to work would be an interesting clue.

This has some connotations for emdrive design.

You want the big end a >= lambda and the little end close to cutoff.  You want an antinode in the little end and a node (or several) at the big end.  The guide wavelength will change across the tapered section, so predicting the best cavity length requires compensating for that.  There may be some point where higher Q does not increase thrust because the frequency shift of doing work moves the little-end-bounced light out of the range of resonance or below cutoff.  This is frequency shift probably the limiting mechanism for maximum work.

Last piece.  I cannot see the emdrive as an overunity device.  Lifting a tennis ball from the floor to the ceiling is roughly 10 joules, and if done in one second 10 Watts.  I do not understand how less than half of that force (4 newton-meters) at a cost of 1,000 electrical watts begins to approach overunity.

What am I missing?

Edit: Changed Planck Length to Planck Constant. Again.
« Last Edit: 07/22/2015 12:16 PM by ElizabethGreene »

Offline X_RaY

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See that. :)

Another thougth.

upon reflection light undergoes a 180 degree phase change on metal surfaces

Yes, and this situation is modeled by a traveling wave with reverse propagation and exactly 180 degrees of phase difference producing a destructive interference exactly at the mirror position.
With two mirrors one has to satisfy the destructive interference at two points simultaneously, and this condition defines the possibles modes on "cavity".
This is a example of superposition  principle to model boundary conditions.

There isn't destructive interference at all (otherwise there isn't a propagating wave...). ;)
Into the direction of the small diameter there will be a gain in the field strength (see horn antennas)
I think the difference between a resonator and a waveguide is: (pre sign of the field
,see picture-example for TE011)

please correct me if i am wrong
Yes you are right.I was thinking about smith diagram. And yes there is a difference in the direction in the diagram if one looks into the propagation direction of the source or away from it. Yesterday I missed this fact in my mind  :-\ :-[

Offline aero

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@SeeShell -
Your .png and .csv files data is/are up have been uploaded here:

https://drive.google.com/folderview?id=0B1XizxEfB23tfm04QWNVVVVvT3gtcVAzRUp6T1BCLVpoV0EyeVVKR2ZxQkp2a3NKcUNPMU0&usp=sharing

I uploaded my meep data request file/form to hopefully explain what the data is, although it needs more English and fewer Scheme statements. The inside big end is at row 15 and small end at row 216 of the csv files, and the total run meep time t = 13.054 (6527 timesteps).
« Last Edit: 07/22/2015 07:10 AM by aero »
Retired, working interesting problems

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