### Author Topic: EM Drive Developments - related to space flight applications - Thread 3  (Read 2877453 times)

#### Rodal

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##### Re: EM Drive Developments - related to space flight applications - Thread 3
« Reply #5140 on: 07/25/2015 07:58 pm »

I agree. By accepted theory, there should be no thrust whatsoever beyond a photon rocket. If there really is verifiable excess thrust, no matter how small, then this a breakthrough.

If by accepted theory you include General Relativity, then there should be a small thrust as long as you can accept some deviation from perfectly "flat" space.  (the swimming spaceman was a good example)

Good point, but I believe conventional wisdom is that space is flat. Of course, conventional wisdom could be wrong. If space isn't perfectly flat, then maybe we are on to something that would make a good drive for spaceflight. Still, no flying cars.

space time is only flat where there is no gravity.  This is why light follows a curved path in the presence of a gravitational well.  http://www.math.brown.edu/~banchoff/STG/ma8/papers/dstanke/Project/curved_space.html

If you can artificially engineer a gravitational well of sorts, "maybe not exactly gravity but mimic it at a specific frequency", then you might be able to effectively curve space and time/energy at that particular wavelength.
Spacetime is curved in the presence of gravity but all measurements up to now is that space itself (not spacetime) is Euclidean flat.   RonM's statement was that space is (Euclidean) flat.  He is correct.

Experimental data from various, independent sources (WMAP, BOOMERanG and Planck for example) confirm that the universe is flat with only a 0.4% margin of error.

https://en.wikipedia.org/wiki/Shape_of_the_universe#Curvature_of_Universe

This is an important distinction.

Spacetime should not be confused with space.
« Last Edit: 07/25/2015 08:02 pm by Rodal »

#### dustinthewind

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##### Re: EM Drive Developments - related to space flight applications - Thread 3
« Reply #5141 on: 07/25/2015 08:00 pm »

space time is only flat where there is no gravity.  This is why light follows a curved path in the presence of a gravitational well.  http://www.math.brown.edu/~banchoff/STG/ma8/papers/dstanke/Project/curved_space.html

If you can artificially engineer a gravitational well of sorts, "maybe not exactly gravity but mimic it at a specific frequency", then you might be able to effectively curve space and time/energy at that particular wavelength.
Spacetime is curved in the presence of gravity but all measurements up to now is that space itself (not spacetime) is Euclidean flat.   RonM's statement was that space is (Euclidean) flat.  He is correct.

Experimental data from various, independent sources (WMAP, BOOMERanG and Planck for example) confirm that the universe is flat with only a 0.4% margin of error.

This is an important distinction.

Spacetime should not be confused with space.

Ok i see what was being referred to then.  Sorry for the confusion.
« Last Edit: 07/25/2015 08:02 pm by dustinthewind »

#### WarpTech

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##### Re: EM Drive Developments - related to space flight applications - Thread 3
« Reply #5142 on: 07/25/2015 08:03 pm »
Thrust To Power Derivation

I posted the attached derivation the other day. The only response was an off the cuff remark from @deltaMass. I guess what I'm looking for is some discussion on why this is wrong, or not. The algebra is correct, the interpretation is that as the Xmn "resonant" wave propagates down the expanding waveguide, the gradient enhances the thrust. I estimated using Wolfram Alpha's waveguide simulator (using 2 different size waveguides) that if the wavelength expansion follows the taper, and the frequency is very near the cut-off. The resulting thrust to power is several orders of magnitude greater than a photon rocket, over a short distance. If the waveguide is long, then it all reduces to 1/c at the far end. If there is no taper, it reduces to 1/v_phase. Taper adds a gradient that depends on the direction of the taper. In one direction it attenuates, in the other it accelerates.

Let me know what you think.
Todd
I applaud your effort to explain the magnification of thrust over a photon rocket.

My comment on the derivation is that you have to justify how you immediately go into a differential equation where the frequency omega and the wavenumber k are treated as differentials but the cylindrical Bessel function stays constant and unadulterated.

You need to justify the meaning of kdk.  You need to justify how can a cylindrical Bessel function enter into a tapered waveguide: which is a cone.  This is the same approximation that TheTraveller, Notsosureofit and others do ab initio.  It needs to be justified.   I agree that solving the exact solution in terms of Legendre Associated functions and Spherical Bessel functions does not appear feasible in terms of obtaining a closed-form solution, but perhaps you could attempt a perturbation analysis for example instead of jumping right away into a differential equation for a tapered waveguide with Bessel cylindrical functions.

A perturbation solution in terms of small cone half-angle, for example, where the cylinder is the limit geometry for cone half-angle approaching zero.  For small cone angles the solution should be close to a cylindrical Bessel function, but how close does it have to be?

If it is very close, the magnification factor may be negligible, as the magnification factor arises from the cone angle being different from zero.

The perturbation approach also would provide an estimate of the errors involved in the solution (an estimate of the size of the neglected higher order terms).

I haven't used perturbation theory since circa 1992. That would take a great deal of effort for something I find to be trivially obvious. Look at the attached equation for the wave vector in a circular waveguide. If w0 = wmn, there is no propagation. There can be however, periodic boundary conditions and localized standing waves. On the other hand, even if w0 > wmn such that it is a traveling wave. There is an inertial frame where the group velocity is zero, and the same situation applies, periodic in z, with a stationary resonant standing wave.

Now, what is the difference if I slowly increase w0, or slowly decrease wmn by introducing a taper? Nothing, as far as I can see. The end result is the same, a traveling wave that is accelerating. Why does this need to be proven? it's obvious. If not, why isn't it?

I am not considering a closed ended frustum here. Only the tapered waveguide vs a straight waveguide. It is only a resonant cavity in 2D, the circular cross section, not the length. Bessel function is the solution for a circle. It shifts frequency for the same reason "time dilation" occurs in a gravitational field. It is in a potential energy gradient.
Todd

#### Rodal

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##### Re: EM Drive Developments - related to space flight applications - Thread 3
« Reply #5143 on: 07/25/2015 08:04 pm »
That title was chosen I reckon because people searching for news on Pluto would get that article coming up as well.
That explains Pluto in the headline, but where did the duration: 18 months trip come from?

#### Rodal

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##### Re: EM Drive Developments - related to space flight applications - Thread 3
« Reply #5144 on: 07/25/2015 08:11 pm »
...
I haven't used perturbation theory since circa 1992. That would take a great deal of effort for something I find to be trivially obvious. Look at the attached equation for the wave vector in a circular waveguide. If w0 = wmn, there is no propagation. There can be however, periodic boundary conditions and localized standing waves. On the other hand, even if w0 > wmn such that it is a traveling wave. There is an inertial frame where the group velocity is zero, and the same situation applies, periodic in z, with a stationary resonant standing wave.

Now, what is the difference if I slowly increase w0, or slowly decrease wmn by introducing a taper? Nothing, as far as I can see. The end result is the same, a traveling wave that is accelerating. Why does this need to be proven? it's obvious. If not, why isn't it?

I am not considering a closed ended frustum here. Only the tapered waveguide vs a straight waveguide. It is only a resonant cavity in 2D, the circular cross section, not the length. Bessel function is the solution for a circle. It shifts frequency for the same reason "time dilation" occurs in a gravitational field. It is in a potential energy gradient.
Todd
It is the difference between a spherical wave and a flat wave.  The flat wave solution with the cylindrical Bessel function in the cross section applies to a perfect cylinder.  The tapered, conical waveguide does not have the flat wave solution in general, only as an approximation.  The flat wave solution does not respect the boundary conditions of the lateral surface of the cone.  See the paper of Yang and Fan: they consider an open waveguide and they had to use the spherical wave solution.

You asked for comments. Your solution is an approximation to the spherical wave solution.  The objection can be raised that the accuracy of the amplification factor is unknown, as the solution is predicated on a flat wave that does not exactly respect the boundary conditions for an open conical waveguide (or section of a cone).  The cylindrical Bessel function is assumed ab initio.  Satisfaction of boundary conditions is not discussed in your paper.
« Last Edit: 07/25/2015 08:18 pm by Rodal »

#### X_RaY

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##### Re: EM Drive Developments - related to space flight applications - Thread 3
« Reply #5145 on: 07/25/2015 08:13 pm »
Thrust To Power Derivation

I posted the attached derivation the other day. The only response was an off the cuff remark from @deltaMass. I guess what I'm looking for is some discussion on why this is wrong, or not. The algebra is correct, the interpretation is that as the Xmn "resonant" wave propagates down the expanding waveguide, the gradient enhances the thrust. I estimated using Wolfram Alpha's waveguide simulator (using 2 different size waveguides) that if the wavelength expansion follows the taper, and the frequency is very near the cut-off. The resulting thrust to power is several orders of magnitude greater than a photon rocket, over a short distance. If the waveguide is long, then it all reduces to 1/c at the far end. If there is no taper, it reduces to 1/v_phase. Taper adds a gradient that depends on the direction of the taper. In one direction it attenuates, in the other it accelerates.

Let me know what you think.
Todd
I applaud your effort to explain the magnification of thrust over a photon rocket.

My comment on the derivation is that you have to justify how you immediately go into a differential equation where the frequency omega and the wavenumber k are treated as differentials but the cylindrical Bessel function stays constant and unadulterated.

You need to justify the meaning of kdk.  You need to justify how can a cylindrical Bessel function enter into a tapered waveguide: which is a cone.  This is the same approximation that TheTraveller, Notsosureofit and others do ab initio.  It needs to be justified.   I agree that solving the exact solution in terms of Legendre Associated functions and Spherical Bessel functions does not appear feasible in terms of obtaining a closed-form solution, but perhaps you could attempt a perturbation analysis for example instead of jumping right away into a differential equation for a tapered waveguide with Bessel cylindrical functions.

A perturbation solution in terms of small cone half-angle, for example, where the cylinder is the limit geometry for cone half-angle approaching zero.  For small cone angles the solution should be close to a cylindrical Bessel function, but how close does it have to be?

If it is very close, the magnification factor may be negligible, as the magnification factor arises from the cone angle being different from zero.

The perturbation approach also would provide an estimate of the errors involved in the solution (an estimate of the size of the neglected higher order terms).

I haven't used perturbation theory since circa 1992. That would take a great deal of effort for something I find to be trivially obvious. Look at the attached equation for the wave vector in a circular waveguide. If w0 = wmn, there is no propagation. There can be however, periodic boundary conditions and localized standing waves. On the other hand, even if w0 > wmn such that it is a traveling wave. There is an inertial frame where the group velocity is zero, and the same situation applies, periodic in z, with a stationary resonant standing wave.

Now, what is the difference if I slowly increase w0, or slowly decrease wmn by introducing a taper? Nothing, as far as I can see. The end result is the same, a traveling wave that is accelerating. Why does this need to be proven? it's obvious. If not, why isn't it?

I am not considering a closed ended frustum here. Only the tapered waveguide vs a straight waveguide. It is only a resonant cavity in 2D, the circular cross section, not the length. Bessel function is the solution for a circle. It shifts frequency for the same reason "time dilation" occurs in a gravitational field. It is in a potential energy gradient.
Todd

It shifts frequency?  The frequency is determined by the EM source.
It shifts the wavenumber k
« Last Edit: 07/25/2015 08:37 pm by X_RaY »

#### rfmwguy

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##### Re: EM Drive Developments - related to space flight applications - Thread 3
« Reply #5146 on: 07/25/2015 08:22 pm »

Just a heads up you guys dont have to wait till tuesday to get tajmar's paper. its availabe from AIAA's archive for 25 bucks. Working my way through it and his other papers....
Excellent! Questions abound, obviously. Good luck digging thru it. While reposting may not be cool until after the presentation, summation is welcomed.

Wouldn't even a summation be rather rude until he's presented it himself?

I'd say yes, except for it is already available for download, therefore purchase and commentary. If it wasn't on-line, then courtesy would be to hold off...just my opinion however.

#### Rodal

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##### Re: EM Drive Developments - related to space flight applications - Thread 3
« Reply #5147 on: 07/25/2015 08:32 pm »

Just a heads up you guys dont have to wait till tuesday to get tajmar's paper. its availabe from AIAA's archive for 25 bucks. Working my way through it and his other papers....
Excellent! Questions abound, obviously. Good luck digging thru it. While reposting may not be cool until after the presentation, summation is welcomed.

Wouldn't even a summation be rather rude until he's presented it himself?

I'd say yes, except for it is already available for download, therefore purchase and commentary. If it wasn't on-line, then courtesy would be to hold off...just my opinion however.
Since when is the case that a paper that is already available for download to the general public cannot be freely discussed by the general public?

The conferences I'm familiar with show the complete opposite:  such papers are made available PRIOR to the oral presentation for scientific and engineering presentations ON PURPOSE so that the studious, well prepared participant at the audience can better listen to the presentation and ask questions at the conference.  The papers are made available ahead of time for scientific purposes.  We are not talking here about the remarks of a politician or a businessman or a drug company preparing to make a sensational announcement and surprise an unsuspecting audience willing to be amazed.  We are not talking here about an artist, a musician, painter or sculptor preparing to unveil to the public his/her latest creation.

A studious, well-informed audience is a much better audience than an ignorant, passive audience. Scientists are not people that are expected to just sit there "prepared to be amazed" sitting passively as a magical act is performed in front of them.  Discussion of papers before presentations is a tradition that goes back to Einstein, Pauli, Heissenberg and countless other presentations.

The presenter can say whatever he/she wants during his/her oral presentation.  There are countless famous cases: one of the most recent and well known ones is when Hawkings recanted (sort of) on the information paradox problem for the black hole, as his paper was made available prior to the presentation, and a number of people with different opinions were well prepared for the presentation by studying the paper ahead of the presentation.

Maybe a politician would not like that his/her remarks be made public before surprising his/her audience.  A teacher/Professor on the other hand would be delighted to have a studious audience that would have discussed and studied his/her lecture ahead of time.  We are talking about a full Professor of Astronautics, Head of Space Systems and Chair, at TU Dresden University here, not about a politician or a businessman.  We are not talking about the head of Apple preparing to amaze the customers and business community with the latest Apple device while Apple fans sit in a long line prepared to buy it.

This is the link to Martin Tajmar's EM Drive paper:

http://arc.aiaa.org/doi/pdf/10.2514/6.2015-4083
« Last Edit: 07/25/2015 09:59 pm by Rodal »

#### X_RaY

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##### Re: EM Drive Developments - related to space flight applications - Thread 3
« Reply #5148 on: 07/25/2015 09:05 pm »

Just a heads up you guys dont have to wait till tuesday to get tajmar's paper. its availabe from AIAA's archive for 25 bucks. Working my way through it and his other papers....
Excellent! Questions abound, obviously. Good luck digging thru it. While reposting may not be cool until after the presentation, summation is welcomed.

Wouldn't even a summation be rather rude until he's presented it himself?

I'd say yes, except for it is already available for download, therefore purchase and commentary. If it wasn't on-line, then courtesy would be to hold off...just my opinion however.
Since when is the case that a paper that is already available for download to the general public cannot be freely discussed by the general public?

The conferences I'm familiar show the complete opposite:  such papers are made available PRIOR to the oral presentation for scientific and engineering presentations ON PURPOSE so that the studious, well prepared participant at the audience can better listen to the presentation and ask questions at the conference.  The papers are made available ahead of time for scientific purposes.  We are not talking here about the remarks of a politician or a businessman or a drug company preparing to make a sensational announcement and surprise an unsuspecting audience willing to be amazed.  We are not talking here about an artist, a musician, painter or sculptor preparing to unveil to the public his/her latest creation.

An informed, studious, well-informed audience is a much better audience than an ignorant audience. Scientists are not people that are expected to just sit there "prepared to be amazed".  Discussion of papers before presentations is a tradition that goes back to Einstein, Pauli, Heissenberg and countless other presentations.

The presenter can say whatever he/she wants during his/her oral presentation.  There are countless famous cases: one of the most recent and well known ones is when Hawkings recanted (sort of) on the information paradox problem for the black hole, as his paper was made available prior to the presentation, and a number of people with different opinions were well prepared for the presentation by studying the paper ahead of the presentation.

Maybe a politician would not like that his/her remarks be made public before surprising his/her audience.  A teacher/Professor on the other hand would be delighted to have a studious audience that would have discussed and studied his/her lecture ahead of time.  We are talking about a full Professor of Astronautics, Head of Space Systems and Chair, at TU Dresden University here, not about a politician or a businessman.  We are not talking about the head of Apple preparing to amaze the customers and business community with the latest Apple device while Apple fans sit in a long line prepared to buy it.

This is the link to Martin Tajmar's EM Drive paper:

http://arc.aiaa.org/doi/pdf/10.2514/6.2015-4083
I fully agree with you at this point.
But a abstract is the one thing a full review paper another...
And hey this guy is paid with my tax, lets wait a few days we will see what's coming on of his research
« Last Edit: 07/25/2015 09:11 pm by X_RaY »

#### birchoff

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##### Re: EM Drive Developments - related to space flight applications - Thread 3
« Reply #5149 on: 07/25/2015 09:14 pm »
Tajmar Experimental results

Cavity Length(m) = 0.0686
Big Diameter(m) = 0.0541
Small Diameter(m) = 0.0385
Dielectric = None
Frequency = 2.44Ghz
Input Power = 700w (output of magnetron)

Balance Beam Test(Thermal Isolation + Magnetic Isolation + Circulation block)
Quote from: Direct Thrust Measurements of an EM Drive and Evaluation of Possible Side-Effects
We first tested our EMDrive on a beam balance setup using a sensitive Sartorius AX224 sxale with a resolution
of 0.1 mg which translates into 1 µN. Since the EMDrive was much heavier than the maximum 220 g which the
balance can support, the thruster was mounted inside a large aluminum box on one side and counter weights together with the balance on the other side using a knife-egde balance setup14 on top of a granite table to reduce vibrations as shown in Fig. 4. The magnetron was connected with three cables to the high-voltage electronics that was powered by a computer-controlled power supply (two from the HV transformer and one grounding cable). After installation, the box was sealed using an aluminum sheet and tape around the box such that hot air can not easily escape the measurement box. All other surface-edges inside the box where sealed using silicon.
In addition to testing the thruster in different directions (upwards, downwards and horizontally – the balance reading was such that an upwards oriented thruster shall give positive weight changes/thrusts), we implemented several different isolation methods (see Fig. 4c) in order to evaluate and remove possible effects from electromagnetic or buoyancy influence. Specifically, we implemented:

Thermal isolation: Glass whool wrapped around the thruster and fixed with tape in order to slow down heating of the air around the EMDrive
Magnetic isolation: Iron sheets with high magnetic permeability were also wrapped around the thruster
Air Circulation Block: The whole interior of the measurement box was filled up with glass whool in order to reduce any hot air currents inside the measurement box

Moreover, we also checked if the operation of the EMDrive itself does influence the Sartorius balance by powering it up in the same setup but using less counter weight such that the balance was free. The balance reading was stable during turn-on/off and therefore no electromagnetic influence was seen.

Pressure = Ambient
Q = 48.8 (measured and calculated before they started testing)
Force (mN) = 0.229

Torsion balance(Oil fluid damping + magnetron pointing outwards from liquid metal connections)
Quote from: Direct Thrust Measurements of an EM Drive and Evaluation of Possible Side-Effects
We have built a torsion balance for electric propulsion testing that can support 12 kg on a balance arm and features liquid metal power feeding (using Galinstan cups), magnetic and fluid damping. We use the attocube FPS laser interferometer with superior resolution and drift characteristics which results in sub nano-Newton thrust resolutions and very low drifts which makes it one of the best thrust balances available today15. The torsion balance is mounted inside a large vacuum chamber (1.5 m length and 0.9 m diameter) which sits on top of a Newport optical table to damp it from outside vibrations (see Fig. 6). In addition, rubber damping is used inside the vacuum  hamber to further isolate the balance. The chamber is equipped with an Edwards XDS35i scroll pump and a Pfeiffer HiPace 2300 turbo pump (>2000 l/s) to achieve a base pressure in the 10-7 mbar range. Fig. 7 shows the different thruster orientations on the balance that we tested: horizontal (positive and negative thrust directions) as well as vertical (pointing upwards). We believed that a vertical thruster orientation would be a better zero-reference compared to the resistor replacement of the thruster as done by Brady et al13 as here we can better catch the same thermal/magnetic signature. Also, we found out by using a microwave detector that during testing, some microwave radiation was leaking out into the vacuum chamber although the tapered cavity was soldered and glued together. In this setup, the power electronics were outside the chamber (HV transformer, capacitor, diode) and the three connections required by the magnetron (HV plus/minus and ground) were supplied via the liquid metal contacts next to the thruster.
Pressure = 4×10-6
Q = 20.3 (seems like this was measured and calculated after they finished all reported testing)
Force (mN) = 0.02

The results for the torsion balance test that I have summarized is the last reported run which they did. I opted to not summarize the second to last run for brevity. Let me know if you would like that summarized also. That particular run was meant to be closer to the Brady et al tapered frustum experiment. Where the vacuum chamber was not evacuated but closed. They got really weird results with the horizontal-left(positive) orientation reporting 96 microNewtons, horizontal-right (negative) orientation reported a POSITIVE 145 micro newtons. On top of that the vertical orientation which should have been null reporting 224 microNewtons. They suspected magnetic interaction to be the culprit and in their last test run, which I summarized above, evacuated the chamber; switched out the  magnetic eddy-current damping for oil damping and flipped the emdrive so that its attached magnetron would be pointing away (no longer adjacent) from the liquid metal connections.
« Last Edit: 07/25/2015 09:35 pm by birchoff »

#### birchoff

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##### Re: EM Drive Developments - related to space flight applications - Thread 3
« Reply #5150 on: 07/25/2015 09:24 pm »

Just a heads up you guys dont have to wait till tuesday to get tajmar's paper. its availabe from AIAA's archive for 25 bucks. Working my way through it and his other papers....
Excellent! Questions abound, obviously. Good luck digging thru it. While reposting may not be cool until after the presentation, summation is welcomed.

Wouldn't even a summation be rather rude until he's presented it himself?

I'd say yes, except for it is already available for download, therefore purchase and commentary. If it wasn't on-line, then courtesy would be to hold off...just my opinion however.
Since when is the case that a paper that is already available for download to the general public cannot be freely discussed by the general public?

The conferences I'm familiar show the complete opposite:  such papers are made available PRIOR to the oral presentation for scientific and engineering presentations ON PURPOSE so that the studious, well prepared participant at the audience can better listen to the presentation and ask questions at the conference.  The papers are made available ahead of time for scientific purposes.  We are not talking here about the remarks of a politician or a businessman or a drug company preparing to make a sensational announcement and surprise an unsuspecting audience willing to be amazed.  We are not talking here about an artist, a musician, painter or sculptor preparing to unveil to the public his/her latest creation.

An informed, studious, well-informed audience is a much better audience than an ignorant audience. Scientists are not people that are expected to just sit there "prepared to be amazed".  Discussion of papers before presentations is a tradition that goes back to Einstein, Pauli, Heissenberg and countless other presentations.

The presenter can say whatever he/she wants during his/her oral presentation.  There are countless famous cases: one of the most recent and well known ones is when Hawkings recanted (sort of) on the information paradox problem for the black hole, as his paper was made available prior to the presentation, and a number of people with different opinions were well prepared for the presentation by studying the paper ahead of the presentation.

Maybe a politician would not like that his/her remarks be made public before surprising his/her audience.  A teacher/Professor on the other hand would be delighted to have a studious audience that would have discussed and studied his/her lecture ahead of time.  We are talking about a full Professor of Astronautics, Head of Space Systems and Chair, at TU Dresden University here, not about a politician or a businessman.  We are not talking about the head of Apple preparing to amaze the customers and business community with the latest Apple device while Apple fans sit in a long line prepared to buy it.

This is the link to Martin Tajmar's EM Drive paper:

http://arc.aiaa.org/doi/pdf/10.2514/6.2015-4083

I agree with Rodal on this. which is why I put together a high level summary with enough information to at least fill out the emdrive wiki results page. and what I hope is sufficient context about the test runs they reported on in the paper.

That said, the paper is still a good read. All this time I was expecting Tajmar was doing another rought approximation of an emdrive similar to what Brady et al did. I was pleasantly surprised to see that it looks like he really did a replication. It looks like there was some collaboration with Shawyer to help with constructing the device. From my interpretation of the paper it looks like the theory Tajmar is using to evaluate the observed thrust is Shawyers and not Dr. White's. That said while Tajmar still observed thrust still an order of magnitude more effective than pure radiation thrust after removing thermal/magnetic/air circulation as possible measurement errors; there are still some anomalies.

#### WarpTech

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##### Re: EM Drive Developments - related to space flight applications - Thread 3
« Reply #5151 on: 07/25/2015 09:26 pm »
...
I haven't used perturbation theory since circa 1992. That would take a great deal of effort for something I find to be trivially obvious. Look at the attached equation for the wave vector in a circular waveguide. If w0 = wmn, there is no propagation. There can be however, periodic boundary conditions and localized standing waves. On the other hand, even if w0 > wmn such that it is a traveling wave. There is an inertial frame where the group velocity is zero, and the same situation applies, periodic in z, with a stationary resonant standing wave.

Now, what is the difference if I slowly increase w0, or slowly decrease wmn by introducing a taper? Nothing, as far as I can see. The end result is the same, a traveling wave that is accelerating. Why does this need to be proven? it's obvious. If not, why isn't it?

I am not considering a closed ended frustum here. Only the tapered waveguide vs a straight waveguide. It is only a resonant cavity in 2D, the circular cross section, not the length. Bessel function is the solution for a circle. It shifts frequency for the same reason "time dilation" occurs in a gravitational field. It is in a potential energy gradient.
Todd
It is the difference between a spherical wave and a flat wave.  The flat wave solution with the cylindrical Bessel function in the cross section applies to a perfect cylinder.  The tapered, conical waveguide does not have the flat wave solution in general, only as an approximation.  The flat wave solution does not respect the boundary conditions of the lateral surface of the cone.  See the paper of Yang and Fan: they consider an open waveguide and they had to use the spherical wave solution.

You asked for comments. Your solution is an approximation to the spherical wave solution.  The objection can be raised that the accuracy of the amplification factor is unknown, as the solution is predicated on a flat wave that does not exactly respect the boundary conditions for an open conical waveguide (or section of a cone).  The cylindrical Bessel function is assumed ab initio.  Satisfaction of boundary conditions is not discussed in your paper.

I appreciate the help. Now i understand the issue. However, wouldn't a ray-vector approach show the same behavior without the need for spherical harmonics?

Below is what Zeng & Fan wrote for impedances. Impedance is basically u0*velocity. The TE mode is the phase velocity, the TM mode is the group velocity. How do we plot this as a function of kr?  I can't interpret something I don't understand and this just looks like gibberish to me, without some way to plot it out and visualize it. Sorry, I'm an engineer not a mathematician.
Todd

#### birchoff

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##### Re: EM Drive Developments - related to space flight applications - Thread 3
« Reply #5152 on: 07/25/2015 09:27 pm »
Updated my summary to show that the input power reported is the power being outputted by the magnetron to the cavity not the power being fed to the magnetron. Something else to be aware of is that he used a wave guide instead of an RF antenna.

#### X_RaY

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##### Re: EM Drive Developments - related to space flight applications - Thread 3
« Reply #5153 on: 07/25/2015 09:42 pm »
...
I haven't used perturbation theory since circa 1992. That would take a great deal of effort for something I find to be trivially obvious. Look at the attached equation for the wave vector in a circular waveguide. If w0 = wmn, there is no propagation. There can be however, periodic boundary conditions and localized standing waves. On the other hand, even if w0 > wmn such that it is a traveling wave. There is an inertial frame where the group velocity is zero, and the same situation applies, periodic in z, with a stationary resonant standing wave.

Now, what is the difference if I slowly increase w0, or slowly decrease wmn by introducing a taper? Nothing, as far as I can see. The end result is the same, a traveling wave that is accelerating. Why does this need to be proven? it's obvious. If not, why isn't it?

I am not considering a closed ended frustum here. Only the tapered waveguide vs a straight waveguide. It is only a resonant cavity in 2D, the circular cross section, not the length. Bessel function is the solution for a circle. It shifts frequency for the same reason "time dilation" occurs in a gravitational field. It is in a potential energy gradient.
Todd
It is the difference between a spherical wave and a flat wave.  The flat wave solution with the cylindrical Bessel function in the cross section applies to a perfect cylinder.  The tapered, conical waveguide does not have the flat wave solution in general, only as an approximation.  The flat wave solution does not respect the boundary conditions of the lateral surface of the cone.  See the paper of Yang and Fan: they consider an open waveguide and they had to use the spherical wave solution.

You asked for comments. Your solution is an approximation to the spherical wave solution.  The objection can be raised that the accuracy of the amplification factor is unknown, as the solution is predicated on a flat wave that does not exactly respect the boundary conditions for an open conical waveguide (or section of a cone).  The cylindrical Bessel function is assumed ab initio.  Satisfaction of boundary conditions is not discussed in your paper.

I appreciate the help. Now i understand the issue. However, wouldn't a ray-vector approach show the same behavior without the need for spherical harmonics?

Below is what Zeng & Fan wrote for impedances. Impedance is basically u0*velocity. The TE mode is the phase velocity, the TM mode is the group velocity. How do we plot this as a function of kr?  I can't interpret something I don't understand and this just looks like gibberish to me, without some way to plot it out and visualize it. Sorry, I'm an engineer not a mathematician.
Todd

TE and TM are different field configurations. Not phase and group velocities..
For higher kr see the last picture please
« Last Edit: 07/25/2015 10:00 pm by X_RaY »

#### WarpTech

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##### Re: EM Drive Developments - related to space flight applications - Thread 3
« Reply #5154 on: 07/25/2015 09:56 pm »
...
I haven't used perturbation theory since circa 1992. That would take a great deal of effort for something I find to be trivially obvious. Look at the attached equation for the wave vector in a circular waveguide. If w0 = wmn, there is no propagation. There can be however, periodic boundary conditions and localized standing waves. On the other hand, even if w0 > wmn such that it is a traveling wave. There is an inertial frame where the group velocity is zero, and the same situation applies, periodic in z, with a stationary resonant standing wave.

Now, what is the difference if I slowly increase w0, or slowly decrease wmn by introducing a taper? Nothing, as far as I can see. The end result is the same, a traveling wave that is accelerating. Why does this need to be proven? it's obvious. If not, why isn't it?

I am not considering a closed ended frustum here. Only the tapered waveguide vs a straight waveguide. It is only a resonant cavity in 2D, the circular cross section, not the length. Bessel function is the solution for a circle. It shifts frequency for the same reason "time dilation" occurs in a gravitational field. It is in a potential energy gradient.
Todd
It is the difference between a spherical wave and a flat wave.  The flat wave solution with the cylindrical Bessel function in the cross section applies to a perfect cylinder.  The tapered, conical waveguide does not have the flat wave solution in general, only as an approximation.  The flat wave solution does not respect the boundary conditions of the lateral surface of the cone.  See the paper of Yang and Fan: they consider an open waveguide and they had to use the spherical wave solution.

You asked for comments. Your solution is an approximation to the spherical wave solution.  The objection can be raised that the accuracy of the amplification factor is unknown, as the solution is predicated on a flat wave that does not exactly respect the boundary conditions for an open conical waveguide (or section of a cone).  The cylindrical Bessel function is assumed ab initio.  Satisfaction of boundary conditions is not discussed in your paper.

I appreciate the help. Now i understand the issue. However, wouldn't a ray-vector approach show the same behavior without the need for spherical harmonics?

Below is what Zeng & Fan wrote for impedances. Impedance is basically u0*velocity. The TE mode is the phase velocity, the TM mode is the group velocity. How do we plot this as a function of kr?  I can't interpret something I don't understand and this just looks like gibberish to me, without some way to plot it out and visualize it. Sorry, I'm an engineer not a mathematician.
Todd

TE and TM are different field configurations. Not phase and group velocities..

Please stop nitpicking what I say. https://en.wikipedia.org/wiki/Wave_impedance
The equations below clearly show what I said is correct.

Z0=u0c,

So these show it to be;

ZTE = u0*phase velocity,
ZTM = u0*group velocity.

The same is true for what Zeng and Fan wrote for a tapered waveguide. Therefore, their two equations are proportional to the velocities by a constant, u0.
Todd

#### Rodal

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##### Re: EM Drive Developments - related to space flight applications - Thread 3
« Reply #5155 on: 07/25/2015 10:08 pm »
Tajmar Experimental results

Cavity Length(m) = 0.0686
Big Diameter(m) = 0.0541
Small Diameter(m) = 0.0385
Dielectric = None
Frequency = 2.44Ghz
Input Power = 700w (output of magnetron)

Balance Beam Test(Thermal Isolation + Magnetic Isolation + Circulation block)
Quote from: Direct Thrust Measurements of an EM Drive and Evaluation of Possible Side-Effects
We first tested our EMDrive on a beam balance setup using a sensitive Sartorius AX224 sxale with a resolution
of 0.1 mg which translates into 1 µN. Since the EMDrive was much heavier than the maximum 220 g which the
balance can support, the thruster was mounted inside a large aluminum box on one side and counter weights together with the balance on the other side using a knife-egde balance setup14 on top of a granite table to reduce vibrations as shown in Fig. 4. The magnetron was connected with three cables to the high-voltage electronics that was powered by a computer-controlled power supply (two from the HV transformer and one grounding cable). After installation, the box was sealed using an aluminum sheet and tape around the box such that hot air can not easily escape the measurement box. All other surface-edges inside the box where sealed using silicon.
In addition to testing the thruster in different directions (upwards, downwards and horizontally – the balance reading was such that an upwards oriented thruster shall give positive weight changes/thrusts), we implemented several different isolation methods (see Fig. 4c) in order to evaluate and remove possible effects from electromagnetic or buoyancy influence. Specifically, we implemented:

Thermal isolation: Glass whool wrapped around the thruster and fixed with tape in order to slow down heating of the air around the EMDrive
Magnetic isolation: Iron sheets with high magnetic permeability were also wrapped around the thruster
Air Circulation Block: The whole interior of the measurement box was filled up with glass whool in order to reduce any hot air currents inside the measurement box

Moreover, we also checked if the operation of the EMDrive itself does influence the Sartorius balance by powering it up in the same setup but using less counter weight such that the balance was free. The balance reading was stable during turn-on/off and therefore no electromagnetic influence was seen.

Pressure = Ambient
Q = 48.8 (measured and calculated before they started testing)
Force (mN) = 0.229

Torsion balance(Oil fluid damping + magnetron pointing outwards from liquid metal connections)
Quote from: Direct Thrust Measurements of an EM Drive and Evaluation of Possible Side-Effects
We have built a torsion balance for electric propulsion testing that can support 12 kg on a balance arm and features liquid metal power feeding (using Galinstan cups), magnetic and fluid damping. We use the attocube FPS laser interferometer with superior resolution and drift characteristics which results in sub nano-Newton thrust resolutions and very low drifts which makes it one of the best thrust balances available today15. The torsion balance is mounted inside a large vacuum chamber (1.5 m length and 0.9 m diameter) which sits on top of a Newport optical table to damp it from outside vibrations (see Fig. 6). In addition, rubber damping is used inside the vacuum  hamber to further isolate the balance. The chamber is equipped with an Edwards XDS35i scroll pump and a Pfeiffer HiPace 2300 turbo pump (>2000 l/s) to achieve a base pressure in the 10-7 mbar range. Fig. 7 shows the different thruster orientations on the balance that we tested: horizontal (positive and negative thrust directions) as well as vertical (pointing upwards). We believed that a vertical thruster orientation would be a better zero-reference compared to the resistor replacement of the thruster as done by Brady et al13 as here we can better catch the same thermal/magnetic signature. Also, we found out by using a microwave detector that during testing, some microwave radiation was leaking out into the vacuum chamber although the tapered cavity was soldered and glued together. In this setup, the power electronics were outside the chamber (HV transformer, capacitor, diode) and the three connections required by the magnetron (HV plus/minus and ground) were supplied via the liquid metal contacts next to the thruster.
Pressure = 4×10-6
Q = 20.3 (seems like this was measured and calculated after they finished all reported testing)
Force (mN) = 0.02

The results for the torsion balance test that I have summarized is the last reported run which they did. I opted to not summarize the second to last run for brevity. Let me know if you would like that summarized also. That particular run was meant to be closer to the Brady et al tapered frustum experiment. Where the vacuum chamber was not evacuated but closed. They got really weird results with the horizontal-left(positive) orientation reporting 96 microNewtons, horizontal-right (negative) orientation reported a POSITIVE 145 micro newtons. On top of that the vertical orientation which should have been null reporting 224 microNewtons. They suspected magnetic interaction to be the culprit and in their last test run, which I summarized above, evacuated the chamber; switched out the  magnetic eddy-current damping for oil damping and flipped the emdrive so that its attached magnetron would be pointing away (no longer adjacent) from the liquid metal connections.

That fully confirms what I posted:

* Q below 50

* Force in vacuum only 20 microNewtons for hundreds of watts.

* Orientation sensitivity is a problem

Even the test in air are orders of magnitude below what Shawyer and Yang have claimed.

The tests in air are close to what NASA and Iulian Berca reported in force/InputPower

The tests in vacuum are even lower than what NASA reported.

This can be taken as a confirmation of NASA Eagleworks excellent testing program.
« Last Edit: 07/25/2015 10:09 pm by Rodal »

#### flux_capacitor

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##### Re: EM Drive Developments - related to space flight applications - Thread 3
« Reply #5156 on: 07/25/2015 10:08 pm »
From the intro in the abstract paper:

How can Tajmar says:
Quote
After developing a numerical model to properly design our cavity for high efficiencies in close cooperation with the EM Drive's inventor
and then measure:
Quote
Due to a low Q factor of <50

Why was the Q so desperately low? What could possibly have gone wrong with all those experts onboard and Dresden leading-edge technologies?

#### Rodal

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##### Re: EM Drive Developments - related to space flight applications - Thread 3
« Reply #5157 on: 07/25/2015 10:10 pm »
From the intro in the abstract paper:

How can Tajmar says:
Quote
After developing a numerical model to properly design our cavity for high efficiencies in close cooperation with the EM Drive's inventor
and then measure:
Quote
Due to a low Q factor of <50

Why was the Q so desperately low? What could possibly have gone wrong with all those experts onboard and Dresden leading-edge technologies?

Take a look at my prior posts (the ones were I suggested questions for Dr. Bagelbytes to ask).  I think that there was gross overcoupling.

Perhaps intentional to the magnetron's bandwidth.
« Last Edit: 07/25/2015 10:13 pm by Rodal »

#### Rodal

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##### Re: EM Drive Developments - related to space flight applications - Thread 3
« Reply #5158 on: 07/25/2015 10:16 pm »
...
I haven't used perturbation theory since circa 1992. That would take a great deal of effort for something I find to be trivially obvious. Look at the attached equation for the wave vector in a circular waveguide. If w0 = wmn, there is no propagation. There can be however, periodic boundary conditions and localized standing waves. On the other hand, even if w0 > wmn such that it is a traveling wave. There is an inertial frame where the group velocity is zero, and the same situation applies, periodic in z, with a stationary resonant standing wave.

Now, what is the difference if I slowly increase w0, or slowly decrease wmn by introducing a taper? Nothing, as far as I can see. The end result is the same, a traveling wave that is accelerating. Why does this need to be proven? it's obvious. If not, why isn't it?

I am not considering a closed ended frustum here. Only the tapered waveguide vs a straight waveguide. It is only a resonant cavity in 2D, the circular cross section, not the length. Bessel function is the solution for a circle. It shifts frequency for the same reason "time dilation" occurs in a gravitational field. It is in a potential energy gradient.
Todd
It is the difference between a spherical wave and a flat wave.  The flat wave solution with the cylindrical Bessel function in the cross section applies to a perfect cylinder.  The tapered, conical waveguide does not have the flat wave solution in general, only as an approximation.  The flat wave solution does not respect the boundary conditions of the lateral surface of the cone.  See the paper of Yang and Fan: they consider an open waveguide and they had to use the spherical wave solution.

You asked for comments. Your solution is an approximation to the spherical wave solution.  The objection can be raised that the accuracy of the amplification factor is unknown, as the solution is predicated on a flat wave that does not exactly respect the boundary conditions for an open conical waveguide (or section of a cone).  The cylindrical Bessel function is assumed ab initio.  Satisfaction of boundary conditions is not discussed in your paper.

I appreciate the help. Now i understand the issue. However, wouldn't a ray-vector approach show the same behavior without the need for spherical harmonics?

Below is what Zeng & Fan wrote for impedances. Impedance is basically u0*velocity. The TE mode is the phase velocity, the TM mode is the group velocity. How do we plot this as a function of kr?  I can't interpret something I don't understand and this just looks like gibberish to me, without some way to plot it out and visualize it. Sorry, I'm an engineer not a mathematician.
Todd

I think they are Henkel spherical functions.  I could plot it with Mathematica but I have some \$\$\$ work to do.  Didn't Zeng and Fan have some plots of impedance in their paper?

#### ThereIWas3

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##### Re: EM Drive Developments - related to space flight applications - Thread 3
« Reply #5159 on: 07/25/2015 10:16 pm »
"Cavity Length(m) = 0.0686".   6cm?   Is this typical of the cavity sizes in the other experiments?

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