Author Topic: EM Drive Developments - related to space flight applications - Thread 2  (Read 2107220 times)

Online Mulletron

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IRT the last couple posts, the unlicensed ISM band is more approachable for enthusiasts. I want folks like us to explore this proposition that we can achieve all electric thrust in the vacuum of space without propellant. I'm awaiting word from our academic institutions and NASA about what is really going on here, but that word may not come. Part of my mission on here, besides hopefully bringing attention to the underlying research which could support this (Tiggelen et al), and trying to figure this out myself with the help of my fellow posters, is also to inspire builders to take up experimentation by providing as much research and backup as possible. At the end, I want this thread (or the derivative of) to mature from "advanced concepts" to proven flight ready in my lifetime. There is NO way humanity is going to be stuck on this planet forever.

I in particular am trying fervently to find a solution for an unloaded conical frustum geometry resonant at 2437mhz at TE111 to start with. 2450mhz is a good start. From there you can perturb the cavity down to 2437mhz at will (mostly trial and error). I am still unsure if angle by the apex is truly important for resonance, but according to Egan, it is: http://www.gregegan.net/SCIENCE/Cavity/Cavity.html But if my hunch about the importance of the QV to spacetime is correct (pretty much has to be), 45 and 90 degrees by the apex is important. Since there appears to not be a ready made solution for this available to me in the world (short of simulating it like buying COMSOL and learning it, or hints from that patent), I(we) have to figure it out, somehow.

So in short. I want to crowdsource this problem. We need help! We all sink or swim together, as they say.
« Last Edit: 01/30/2015 07:15 PM by Mulletron »
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Offline Rodal

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....

I in particular am trying fervently to find a solution for an unloaded conical frustum geometry resonant at 2437mhz at TE111 to start with. 2450mhz is a good start. From there you can perturb the cavity down to 2437mhz at will (mostly trial and error)...
I think one has a greater chance of achieving thrust (it that is indeed possible) with mode shape TE01p than with mode TE11p, for any p. The images below illustrate the difference between them. 

Also, NASA reported mode TE012 for their experiment that gave greatest thrust/PowerInput.

More discussion of this here:  http://forum.nasaspaceflight.com/index.php?topic=36313.msg1322952#msg1322952

As to calculations for a cone geometry, there is Greg Egan's http://gregegan.customer.netspace.net.au/SCIENCE/Cavity/Cavity.html .  We will be reporting on a comparison as well.



Images of modes TE01p, and TE11p  (where p can be any p=0,1,2,3,...):

electric field ________________    solid lines

magnetic field - - - - - - - - - - - - -  dashed lines
« Last Edit: 01/30/2015 07:31 PM by Rodal »

Offline Rodal

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...I am still unsure if angle by the apex is truly important for resonance, but according to Egan, it is: http://www.gregegan.net/SCIENCE/Cavity/Cavity.html But if my hunch about the importance of the QV to spacetime is correct (pretty much has to be), 45 and 90 degrees by the apex is important. ..

@Mulletron, why do you think that the cone angle (thetaw in Egan's nomenclature), of an EM Drive, should (ideally) be 45 degrees ? (I don't recall the reasons(s), please refresh my mind). 



In Egan's geometry, the cone angle  (thetaw)  is measured from the longitudinal axis of the cone, "z", therefore this picture should show a negative cone angle  ( - thetaw) on the left, and a positive  ( + thetaw) on the right.



For reference. the tangent of thetaw and the angle thetaw, for the following cases are:


Example (and geometry)                    { Tan[thetaw],thetaw (degrees) }

NASA Brady et.al. (Fornaro)                {0.230422, 12.9757}
NASA Brady et.al. (Aero)                     {0.2352,     13.2354}
NASA Brady et.al. (Mulletron)              {0.257318, 14.4302}

Shawyer Experimental                        {0.104019,   5.93851}
Shawyer Demo                                    {0.219054, 12.3557}
Shawyer Superconducting 2014          {0.7002,     35}

Egan's example                                   {0.36397 ,  20}

We see that the cone angle thetaw for NASA's Brady et.al. truncated cone was about 14 degrees, Shawyer's Experimental  was only 6 degrees, Shawyer's Demo  was 12 degrees, and Egan's only example is 20 degrees (Egan's example has a cone angle much larger than the cone angle of experiments). The "cone angle thetaw" for a cylinder is zero, Shawyer's Experimental was closest to a cylinder, and NASA's Brady et.al. was the experiment with the largest cone angle.

Shawyer's latest (2014) superconducting design (see image, presented at the IAC 2014 conference in Toronto), for which there are no experimental results reported yet, appears to have a significantly larger cone angle than his previous experimental and demo geometries, and significantly larger than NASA's Brady et.al.'s.

EDIT: Shawyer's (2014) superconducting EM Drive design has a cone angle  thetaw of about 35 degrees.





(*

Fornaro estimate \
http://forum.nasaspaceflight.com/index.php?topic=36313.msg1302455#msg1302455;

fornaroLength=0.332 m
fornaroBigDiameter=0.397 m
fornaroSmallDiameter=0.244 m

*)

(*

Aero Best estimate as of 11/9/2014 \
http://forum.nasaspaceflight.com/index.php?topic=29276.msg1285896#msg1285896 ;

aeroLength=0.24173 m
aeroBigDiameter=0.27246 m
aeroSmallDiameter=0.15875 m

*)

(*
Mulletron Best estimate as of 11/9/2014
http://forum.nasaspaceflight.com/index.php?topic=36313.msg1320903#msg1320903;

mulletronLength=0.27637 m
mulletronBigDiameter=0.30098 m
mulletronSmallDiameter=0.15875 m

*)

(*
"Shawyer EXPERIMENTAL geometry"

shawyerExpLength=0.156 meter;
shawyerExpBigDiameter=0.16 meter
shawyerExpSmallDiameter=0.127546 meter;
*)

(*
" Shawyer DEMO geometry"

shawyerDemoLength=0.345 meter;
shawyerDemoBigDiameter=0.28 meter;
shawyerDemoSmallDiameter=0.128853 meter;

*)
« Last Edit: 01/31/2015 07:47 PM by Rodal »

Offline Rodal

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Also, the larger the cone angle thetaw, the more important is to have EM Drive spherical ends rather than flat ends.  The curvature of the spherical ends is more pronounced for larger cone angle thetaw.  Shawyer realized this: he has spherical ends in his 2014 superconducting design shown in the above image.
« Last Edit: 01/31/2015 04:49 PM by Rodal »

Online aero

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I learned a new trick.  :) Here are some images of the ez field along the x coordinate.

The imaginary and real parts are shown at x=194, because that showed a powerful signal.
The imaginary and real parts are shown at x=216, because that is the big end of the cavity.
The imaginary and real parts are shown at x=39, because that is the just inside the dielectric at the small end.

I'll see if I can get some magnetic field images.
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Offline Rodal

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I learned a new trick.  :) Here are some images of the ez field along the x coordinate.

The imaginary and real parts are shown at x=194, because that showed a powerful signal.
The imaginary and real parts are shown at x=216, because that is the big end of the cavity.
The imaginary and real parts are shown at x=39, because that is the just inside the dielectric at the small end.

I'll see if I can get some magnetic field images.

The real parts of the electric field shape at the location of highest intensity (x=194) and at the small end dielectric ( x=39) look like mode shape TE12 (see image attached).  Looking forward to seeing the magnetic field, to be sure what mode it is.

electric field ________________    solid lines

magnetic field - - - - - - - - - - - - -  dashed lines
« Last Edit: 02/01/2015 11:20 PM by Rodal »

Offline Rodal

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I learned a new trick.  :) Here are some images of the ez field along the x coordinate.

The imaginary and real parts are shown at x=194, because that showed a powerful signal.
The imaginary and real parts are shown at x=216, because that is the big end of the cavity.
The imaginary and real parts are shown at x=39, because that is the just inside the dielectric at the small end.

I'll see if I can get some magnetic field images.
Are you running the same dielectric properties, overall geometry and source frequency as in your message http://forum.nasaspaceflight.com/index.php?topic=36313.msg1321460#msg1321460 ?

It the answer is yes, then it looks like the mode shape was TE123 , that is m=1, n=2, p =3. 

Based just on the limited information from the movie's image of the z,r plane I previously thought ( http://forum.nasaspaceflight.com/index.php?action=post;msg=1321476;topic=36313.320 ) the mode shape could be TE013: m=0, n=1, p=3.  Based on the z,r plane previously shown one could not tell what m was.  The field does not look constant in the circumferential direction (which would be needed for m=0).  It seems to have a full wave, which means m=1.  I previously thought that n=1 , but n =2 can look like n=1  on the z,r plane at the right circumferential (azimuthal ) angle. 

To be 100% sure one would need an image of the plane z , r, showing a still picture of the electric field in the longitudinal direction, like you did in the movie (where z is the longitudinal axis of the cone and r is the radial axis) rotated (around the longitudinal axis z) at an angle 90 degrees from the previous circumferential angle.
 
(Or even better, get two new still images showing the electric field in the longitudinal direction:

1) of a plane z , r located at a circumferential angle theta1 and

2) of another plane z, r located at a different circumferential angle theta2

such that theta2 is rotated  (around the longitudinal axis z) by 90 degrees from theta1 so that  theta2=  theta1 + 90 degrees
)






The magnetic field images will also be helpful to understand what mode shape it is.
« Last Edit: 02/02/2015 02:37 PM by Rodal »

Online aero

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I will try to get additional views as time and health permits. My boy brought something home from school and we've all contracted it. Unfortunately for me, I didn't throw it off like the wife and boy did.

This image is in 3D, which means very low resolution, so no its not like the other one. It's the same cavity and same drive frequency though so it should be generally very similar.
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Offline Rodal

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I will try to get additional views as time and health permits. My boy brought something home from school and we've all contracted it. Unfortunately for me, I didn't throw it off like the wife and boy did.

This image is in 3D, which means very low resolution, so no its not like the other one. It's the same cavity and same drive frequency though so it should be generally very similar.
Thanks for updating us on your great progress.  Hope you feel better soon  :)

Offline Rodal

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I learned a new trick.  :) Here are some images of the ez field along the x coordinate.

The imaginary and real parts are shown at x=194, because that showed a powerful signal.
The imaginary and real parts are shown at x=216, because that is the big end of the cavity.
The imaginary and real parts are shown at x=39, because that is the just inside the dielectric at the small end.

I'll see if I can get some magnetic field images.


For these truncated cone calculations, you reported (in the movie attachment to http://forum.nasaspaceflight.com/index.php?topic=36313.msg1321460#msg1321460 ) that the value of the relative permittivity (dielectric constant) you used was 2.3.

I did not find the value of relative permeability ( the degree of magnetization of the material ) you used for your truncated cone (NASA Brady et.al.) calculations.

Just to be sure, could you please confirm that you used a value of 1 (one) for the relative permeability in the above calculations ?
« Last Edit: 02/02/2015 02:14 PM by Rodal »

Online aero

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I learned a new trick.  :) Here are some images of the ez field along the x coordinate.

The imaginary and real parts are shown at x=194, because that showed a powerful signal.
The imaginary and real parts are shown at x=216, because that is the big end of the cavity.
The imaginary and real parts are shown at x=39, because that is the just inside the dielectric at the small end.

I'll see if I can get some magnetic field images.


For these truncated cone calculations, you reported (in the movie attachment to http://forum.nasaspaceflight.com/index.php?topic=36313.msg1321460#msg1321460 ) that the value of the relative permittivity (dielectric constant) you used was 2.3.

I did not find the value of relative permeability ( the degree of magnetization of the material ) you used for your truncated cone (NASA Brady et.al.) calculations.

Just to be sure, could you please confirm that you used a value of 1 (one) for the relative permeability in the above calculations ?
I used the dielectric constant of 1.76 for the dielectric disk. That number was 2.3 in the movie but I only use 1.76 now that I've decided that 1.76 is the correct value. To investigate resonance of an empty cavity I can replace the dielectric material with "air." The value is 1.76 for the above runs.

In all cases the cone material, which should be copper, is a material defined by meep as a "Perfect Metal."  The content of the cavity is another material defined by meep as "air." The material outside the cavity, the environment, defaults to "vacuum." I do move the antenna location around and often forget to put it back to the most representative location for the run type. I move it because when I run Harminv using Cylindrical coordinates, the antenna must be on the central axis of rotation of the cone. If it is not, then in Cylindrical coordinates, nothing excites the cavity.

You can most likely tell by looking at the images, where the antenna was located for a particular run.
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Offline Rodal

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I learned a new trick.  :) Here are some images of the ez field along the x coordinate.

The imaginary and real parts are shown at x=194, because that showed a powerful signal.
The imaginary and real parts are shown at x=216, because that is the big end of the cavity.
The imaginary and real parts are shown at x=39, because that is the just inside the dielectric at the small end.

I'll see if I can get some magnetic field images.


For these truncated cone calculations, you reported (in the movie attachment to http://forum.nasaspaceflight.com/index.php?topic=36313.msg1321460#msg1321460 ) that the value of the relative permittivity (dielectric constant) you used was 2.3.

I did not find the value of relative permeability ( the degree of magnetization of the material ) you used for your truncated cone (NASA Brady et.al.) calculations.

Just to be sure, could you please confirm that you used a value of 1 (one) for the relative permeability in the above calculations ?
I used the dielectric constant of 1.76 for the dielectric disk. That number was 2.3 in the movie but I only use 1.76 now that I've decided that 1.76 is the correct value. To investigate resonance of an empty cavity I can replace the dielectric material with "air." The value is 1.76 for the above runs.
..

As I understand, the z,r (axial,radial) plane image in the movie was based on a relative permittivity of 2.3, while the theta, r (circumferential, radial) plane images of your above message are based on the different value of relative permittivity of 1.76.

Therefore it is possible that the mode shape in the z,r (axial,radial) plane image in the movie is different than the mode shape of the theta, r (circumferential, radial) plane images of your above message, the different mode shapes being due to the different values of  relative permittivity that were used in each calculation.
« Last Edit: 02/02/2015 05:01 PM by Rodal »

Offline Rodal

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I learned a new trick.  :) Here are some images of the ez field along the x coordinate.

The imaginary and real parts are shown at x=194, because that showed a powerful signal.
The imaginary and real parts are shown at x=216, because that is the big end of the cavity.
The imaginary and real parts are shown at x=39, because that is the just inside the dielectric at the small end.

I'll see if I can get some magnetic field images.


For these truncated cone calculations, you reported (in the movie attachment to http://forum.nasaspaceflight.com/index.php?topic=36313.msg1321460#msg1321460 ) that the value of the relative permittivity (dielectric constant) you used was 2.3.

I did not find the value of relative permeability ( the degree of magnetization of the material ) you used for your truncated cone (NASA Brady et.al.) calculations.

Just to be sure, could you please confirm that you used a value of 1 (one) for the relative permeability in the above calculations ?
..." I do move the antenna location around and often forget to put it back to the most representative location for the run type. I move it because when I run Harminv using Cylindrical coordinates, the antenna must be on the central axis of rotation of the cone. If it is not, then in Cylindrical coordinates, nothing excites the cavity.

For the calculations for the movie (with relative permittivity of 2.3) you used an excitation frequency of 1.76365 GHz.

What excitation frequency did you use for the calculations in your above message (with relative permittivity of 1.76) ?

Online Mulletron

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...I am still unsure if angle by the apex is truly important for resonance, but according to Egan, it is: http://www.gregegan.net/SCIENCE/Cavity/Cavity.html But if my hunch about the importance of the QV to spacetime is correct (pretty much has to be), 45 and 90 degrees by the apex is important. ..

@Mulletron, why do you think that the cone angle (thetaw in Egan's nomenclature), of an EM Drive, should (ideally) be 45 degrees ? (I don't recall the reasons(s), please refresh my mind). 


Keeping first principles in mind concerning the QV model for how these thrusters may work. If they do interact with the QV somehow, their design should obviously be complimentary to the geometry of spacetime (there are crazy folks out there http://www.onlyspacetime.com/, I'm one of them, who believe spacetime emerges from the quantum world.) I wanted to test whether opening angle had any significance. When faced with choosing an opening angle amongst seemingly arbitrary angles I've found amongst Shawyer's prototypes, I wondered if a light cone opening angle of 45 degrees (measured from the longitudinal axis for a total of 90 as measured from outside) would be of any benefit or not. http://en.wikipedia.org/wiki/Minkowski_diagram After seeing that a light cone setup would be a ginormous cone after factoring in the necessary conical sections for front and end walls, I further halved it to 22.5 degrees (total of 45). That's why I have 2 drawn up in CAD. So it really came down to a question of what angle to pick out of so many choices. Those two I want to try.

Trying to reconcile the above ideas with simultaneously hunting a viable rf solution is proving daunting. Mostly due to the lack of resources. I may not be afforded the option to choose an opening angle and stay on freq and within reasonable size limits. As I'm researching this it is becoming clear that opening angle will be dominated by chosen frequency and practical considerations.

After following up on Aero's post: http://forum.nasaspaceflight.com/index.php?topic=29276.msg1274400#msg1274400 about this: http://www.emdrive.com/NWPU2010translation.pdf trying to see if I can find a good solution for calculating exact solutions for conical frustums, I learned that no such method exists to find closed form solutions to that problem. The Egan method is similar to what we need but it doesn't address the problem. None of what we're dealing here has spherical end caps. And honestly, the Egan way is way too high speed for me.
Quote
"Currently have two ways to find the electromagnetic field of the rectangular and circular waveguides, the eigen-value equation which is an analytical method and numerical solution, when finding solution for the resonator, Maxwell equation in is need to be created in a spherical coordinate system, because the complexity of the spherical coordinate fielder equation, has not found anyone using eigen-value method to calculated the distribution of the resonant field. Only find in Paper [4] using asymptotic method for conical waveguide. That method assume a equivalent radius ae, believes field of wavefront sphere of cone waveguide Eo,EФ,Ho,HФ can use its wavefront position radius ae equivalent circular waveguide field Er,EФ,Hr,HФ, this method of finding the field distribution within the conical resonator can be used as reference, but the accuracy reduced as the cone half opening angle increases. Using finite element to numerically simulate the Maxwell electromagnetic equation for the idealised conical resonator, the distribution of electromagnetic can be obtained directly, this method is not limited by the cavity structure and microwave mode."

Quote
By keep the diameter of the Small End constant, increase the large end of the cavity, in order to have the same resonant frequency, cavity height must be reduced, quality factor also reduce.

They're basically saying: (1) That I'm hosed trying to calculate such things. Simulating the conical frustum using FEM software is the way to go. Which I simply don't have access to. (2) Also they're saying that as the opening angle opens up, approximating the resonant modes becomes more and more difficult. (3) You have to shorten the cavity height as opening angle increases to maintain resonance at desired frequency, but it lowers Q. So I should probably (for now) re-think using such wide opening angles.

So I'm switching gears a bit using what I've learned from the above reporting.
(1) Keeping Cannae in mind, who says we need a cone anyway? We've discussed the commonality between Shawyer and Cannae in thread 1. http://forum.nasaspaceflight.com/index.php?topic=29276.msg1298712#msg1298712 So I'm thinking it would be smart to use what we've learned about cylinders and try a cylinder experiment.
(2) Instead of trying to optimize right out of the gate by throwing around light cones. It would be smarter to use the dims we already have for Shawyer experimental and demo, which you provided on the previous page.
(3) If I ever get this build going, I'm going to have to easter egg it anyway using a sig-gen and a power meter to find the resonant frequency (treat it like a filter, tune it until I get get an output from sample port), so I don't need to have exact calculations. I just need to be close enough to be within tunable limits.
« Last Edit: 02/02/2015 07:55 PM by Mulletron »
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Online Mulletron

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(*
"Shawyer EXPERIMENTAL geometry"

shawyerExpLength=0.156 meter;
shawyerExpBigDiameter=0.16 meter
shawyerExpSmallDiameter=0.127546 meter;
*)

(*
" Shawyer DEMO geometry"

shawyerDemoLength=0.345 meter;
shawyerDemoBigDiameter=0.28 meter;
shawyerDemoSmallDiameter=0.128853 meter;

*)

These were both 2450mhz experiments. Where did the small diameters and lengths come from? I see the Large diameters here: http://www.emdrive.com/yang-juan-paper-2012.pdf.
Challenge your preconceptions, or they will challenge you. - Velik

Offline Rodal

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(*
"Shawyer EXPERIMENTAL geometry"

shawyerExpLength=0.156 meter;
shawyerExpBigDiameter=0.16 meter
shawyerExpSmallDiameter=0.127546 meter;
*)

(*
" Shawyer DEMO geometry"

shawyerDemoLength=0.345 meter;
shawyerDemoBigDiameter=0.28 meter;
shawyerDemoSmallDiameter=0.128853 meter;

*)

These were both 2450mhz experiments. Where did the small diameters and lengths come from? I see the Large diameters here: http://www.emdrive.com/yang-juan-paper-2012.pdf.

If I my memory is correct, we worked this out in Thread 1, the major contribution by far being from aero (aero deserves all the praise, if there are any mistakes in the above figures, they are mine).  I recall feeling very confident about the rationale that aero used to estimate these numbers, which I remember had a very solid foundation. 
« Last Edit: 02/02/2015 08:07 PM by Rodal »

Online Mulletron

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Well if they are correct, they are a ready made solution for ISM band experimentation.

Break:
So I swore off the theory bug a few weeks ago but I've got a bug I need swatting concerning the behavior of confined photons vs the usual free range variety. Here's a quote and a video, both of which have bells ringing and light bulbs floating over my head.
Quoting John A. Macken, from http://www.onlyspacetime.com/HiggsBoson
Quote
Suppose that there was a box with hypothetical 100% reflecting internal walls. It would be possible to trap some light energy in such a box. A freely propagating photon is a massless particle, but what about a “confined photon” trapped in the box. That photon is forced to have the box’s specific frame of reference. A calculation at the end of chapter 1 shows that the photon pressure exerted on the walls of the box is uniform if the box is not accelerating, but the pressure becomes unequal if the box is accelerated. This difference in pressure results in a net force which resists acceleration. This is the inertia of the confined photon energy and it exactly equals the inertia of an equal amount of energy in the form of matter particles. This is not a coincidence.
That scenario sure sounds familiar......like within magic resonant cavity thrusters. I read that a few days ago and really didn't believe any of it, but I filed it away for later.

Now I'm going to re arrange a portion of the above quote and put out a RFC on it:
Quote
.......the photon pressure exerted on the walls of the box is uniform if the box is not accelerating, but the pressure becomes unequal if the box is accelerated. This difference in pressure results in a net force which resists acceleration.

Let's assume that if the author were correct, is it logical to say the flipside is also correct?

.......if the photon pressure exerted on the walls of the box is non uniform if the box is not accelerating accelerates, but the pressure becomes unequal if when the box is accelerated. This difference in pressure results in a net force which resists enables acceleration.

Perhaps it is better to find his calculation at the end of chapter 1 and rearrange it and see if it still works.

And this video @ 3:15


I think I can safely believe Fermilab. Exchange photons are confined between two particles, so indeed they are also confined photons.

I never really approached photons from this perspective. I always assumed and was told they were always massless. What's the deal with confined photons? Confined photons seem to behave like massive particles.

Massive particles flowing into cavity, bouncing around a few thousand times, and then flowing out of a resonant cavity (by being absorbed) surely could make it move while conserving momentum. I picture a thrust nozzle when I think of it like this. Mass comes in, bounces around a bunch, finally comes out....and you have thrust.

Thanks for your patience. Would love some comments on this.

Edit:
Aha! http://www.livescience.com/45287-how-to-trap-light.html
Quote
A photon trapped in such a cavity behaves as if it had mass; in other words, the cavity creates a "trapping potential," keeping the photons from escaping.
http://www.desy.de/user/projects/Physics/Relativity/SR/light_mass.html
Quote
However, if light is trapped in a box with perfect mirrors so the photons are continually reflected back and forth in both directions symmetrically in the box, then the total momentum is zero in the box's frame of reference but the energy is not.  Therefore the light adds a small contribution to the mass of the box.
But then what? Can one really say with confidence that there exists a condition of "mass flow?"
« Last Edit: 02/03/2015 08:44 PM by Mulletron »
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Offline wembley

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A potentially interesting sidelight:

http://okomov.livejournal.com/577.html

The physics is descrived in vvery different terms ("Leonov’s superunification theory"?? "Antigravity"???) this has similar performance to what Shawyer predicts for a superconducting EmDrive thruster, i.e. 500 to 700 kg for 1kW power input.

Moreover, as soon as it starts to accelerate,  the thrust ceases, hence the pulsed operation in the video, which is what Shawyer claims for a high Q EmDrive thruster without Doppler compensation.

What does the team think...?
« Last Edit: 02/04/2015 08:57 AM by wembley »

Offline Rodal

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....
Keeping first principles in mind concerning the QV model for how these thrusters may work. If they do interact with the QV somehow, their design should obviously be complimentary to the geometry of spacetime (there are crazy folks out there http://www.onlyspacetime.com/, I'm one of them, who believe spacetime emerges from the quantum world.) I wanted to test whether opening angle had any significance. When faced with choosing an opening angle amongst seemingly arbitrary angles I've found amongst Shawyer's prototypes, I wondered if a light cone opening angle of 45 degrees (measured from the longitudinal axis for a total of 90 as measured from outside) would be of any benefit or not. http://en.wikipedia.org/wiki/Minkowski_diagram After seeing that a light cone setup would be a ginormous cone after factoring in the necessary conical sections for front and end walls, I further halved it to 22.5 degrees (total of 45). That's why I have 2 drawn up in CAD. So it really came down to a question of what angle to pick out of so many choices. Those two I want to try.

Trying to reconcile the above ideas with simultaneously hunting a viable rf solution is proving daunting. Mostly due to the lack of resources. I may not be afforded the option to choose an opening angle and stay on freq and within reasonable size limits. As I'm researching this it is becoming clear that opening angle will be dominated by chosen frequency and practical considerations.

After following up on Aero's post: http://forum.nasaspaceflight.com/index.php?topic=29276.msg1274400#msg1274400 about this: http://www.emdrive.com/NWPU2010translation.pdf trying to see if I can find a good solution for calculating exact solutions for conical frustums, I learned that no such method exists to find closed form solutions to that problem. The Egan method is similar to what we need but it doesn't address the problem. None of what we're dealing here has spherical end caps. And honestly, the Egan way is way too high speed for me.
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"Currently have two ways to find the electromagnetic field of the rectangular and circular waveguides, the eigen-value equation which is an analytical method and numerical solution, when finding solution for the resonator, Maxwell equation in is need to be created in a spherical coordinate system, because the complexity of the spherical coordinate fielder equation, has not found anyone using eigen-value method to calculated the distribution of the resonant field. Only find in Paper [4] using asymptotic method for conical waveguide. That method assume a equivalent radius ae, believes field of wavefront sphere of cone waveguide Eo,EФ,Ho,HФ can use its wavefront position radius ae equivalent circular waveguide field Er,EФ,Hr,HФ, this method of finding the field distribution within the conical resonator can be used as reference, but the accuracy reduced as the cone half opening angle increases. Using finite element to numerically simulate the Maxwell electromagnetic equation for the idealised conical resonator, the distribution of electromagnetic can be obtained directly, this method is not limited by the cavity structure and microwave mode."

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By keep the diameter of the Small End constant, increase the large end of the cavity, in order to have the same resonant frequency, cavity height must be reduced, quality factor also reduce.

They're basically saying: (1) That I'm hosed trying to calculate such things. Simulating the conical frustum using FEM software is the way to go. Which I simply don't have access to. (2) Also they're saying that as the opening angle opens up, approximating the resonant modes becomes more and more difficult. (3) You have to shorten the cavity height as opening angle increases to maintain resonance at desired frequency, but it lowers Q. So I should probably (for now) re-think using such wide opening angles.

So I'm switching gears a bit using what I've learned from the above reporting.
(1) Keeping Cannae in mind, who says we need a cone anyway? We've discussed the commonality between Shawyer and Cannae in thread 1. http://forum.nasaspaceflight.com/index.php?topic=29276.msg1298712#msg1298712 So I'm thinking it would be smart to use what we've learned about cylinders and try a cylinder experiment.
(2) Instead of trying to optimize right out of the gate by throwing around light cones. It would be smarter to use the dims we already have for Shawyer experimental and demo, which you provided on the previous page.
(3) If I ever get this build going, I'm going to have to easter egg it anyway using a sig-gen and a power meter to find the resonant frequency (treat it like a filter, tune it until I get get an output from sample port), so I don't need to have exact calculations. I just need to be close enough to be within tunable limits.

1) Concerning a solution for the truncated cone EM Drive (the geometry used by Shawyer, NASA and Juan Yang in China), I can report the following progress.  I have derived an exact, closed-form solution for the integral of the longitudinal wavenumber "kz" (as proposed by @NotSoSureOfIt and hinted in the 1969 patent of Wolf) for a truncated cone or a cone. The solution contains square root terms and ArcTan terms.  There is no question that when an exact solution is available it is always superior to any numerical method like Finite Element, Finite Difference, Boundary Element, etc. Even when exact solutions are not available, it is a standard methodology in any engineering department to start the design process with exact solutions to simplified geometries because of the considerable amount of time that it takes to generate a converged solution with Finite Element, Finite Difference, etc. Also because one can gain a much better understanding of the problem with a closed-form solution (to quickly understand the influence of parameters).

2) It is not possible to solve the eigenvalue problem for the truncated cone cavity, or for a cone cavity, directly in terms of standard functions of the frequency (or the mode shape) because the longitudinal wavenumber kz expression for the truncated cone or a cone cannot be inverted (since the frequency is nonlinearly embedded in a number of square root and ArcTan terms).

3) The eigenvalue problem for the truncated cone can be solved by obtaining a numerical solution (finding roots of the nonlinear equation that arises from equating the longitudinal wavenumber "kz" to the mode shape quantum number "p" = 0,1,2,3,4...).

4) I will post the solution and numerical results in more detail, but meanwhile here is the main result:

the exact solution for the truncated cone gives results that are less than 1% different (for typical geometries with a cone angle equal or less than 20 degrees from the longitudinal axis -comprising the NASA Brady et.al. , China (Juan Yang) and the UK (Shawyer) experiments) from the exact solution of a cylinder, if the cylinder diameter is expressed as the GeometricMean of the big and small diameters of the truncated cone.  I have explored several mean measures, for example:

H, the Harmonic Mean ( https://en.wikipedia.org/wiki/Harmonic_mean ) ,
G, the Geometric Mean ( https://en.wikipedia.org/wiki/Geometric_mean ),
L, the Logarithmic Mean ( https://en.wikipedia.org/wiki/Logarithmic_mean ),
A, the Arithmetic Mean ( https://en.wikipedia.org/wiki/Arithmetic_mean ),
V, the Volumetric Mean (http://forum.nasaspaceflight.com/index.php?topic=36313.msg1319655#msg1319655 ),
R, the Root Mean Square ( https://en.wikipedia.org/wiki/Root_mean_square ),
C, the Contraharmonic mean ( https://en.wikipedia.org/wiki/Contraharmonic_mean ),

where:

SmallDiameter < H < G < L < A < V < R < C < BigDiameter

The closest results to the exact solution for the truncated cone are obtained using the GeometricMean of its big and small diameters, as the equivalent diameter of the cylinder cavity equation.  I also found the value of the exponent of the Stolarsky Mean ( https://en.wikipedia.org/wiki/Stolarsky_mean )  that minimizes the error even further than the Geometric Mean, but the improvement is not dramatic and the Stolarsky exponent depends on the cone geometry, hence, for simplicity, one might as well use the GeometricMean=Sqrt[BigDiameter*SmallDiameter] in the cylinder equation to model the frequency and mode shapes of the truncated cone.


« Last Edit: 02/04/2015 02:40 PM by Rodal »

Offline francesco nicoli

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As for the previous one, the level and quality of these comments is so high that the thread has become unreadable for non-physicists.
Could you eventually, for the sake of not losing the majority of us too much behind, make a quick non-technical summary of what are you discussing? is there any progress or barely nothing?

Thanks! :)

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