Author Topic: EM Drive Developments - related to space flight applications - Thread 2  (Read 2164343 times)

Offline Notsosureofit

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Yes, I added:

Where would the Q factor enter into consideration?

(Without the Q into the thrust force equation, we still have an inefficient photon rocket)

[and when one enters the Q factor for a closed cavity, I yet have to embrace an explanation for a closed cavity where I can fully see conservation of momentum and conservation of energy satisfied.  For example, Shawyer only takes into account the forces perpendicular to the bases and neglects the counterbalancing forces from the conical surface which result in zero net thrust force]

Ditto for the GR calculation: they are one-dimensional longitudinal approximations, where the index of refraction changes in the longitudinal direction: but the truncated cone is 3-D and has counterbalancing forces due to the forces on the conical surface which cancel the thrust

If I'm wrong, I would like someone to show what happens with the forces on the conical surface (which are at an angle to the longitudinal direction)

I need a free-body diagram showing the force vectors on all the copper surfaces for the 3-D problem force summation  :)

The Q only enters in the case of a gravitational interaction through its role in calculating the number of photons (Total mass/energy) in the cavity.  If it was a Newtonian momentum interaction only the Power enters.  (I get zero when I try Newtonian for the reasons you have mentioned)

Note: I should probably use "Classical" instead of "Newtonian" but I think you would get the idea that we are looking at the 4-volume as an invariant rather than an integration over the surface of the boundary conditions of classical momentum exchange. That can apply as the summation of the (false gravitational?, ie. frame-dependent) forces on the individual photons to give the resultant force on the cavity.
« Last Edit: 05/08/2015 01:40 PM by Notsosureofit »

Offline Rodal

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Yes, I added:

Where would the Q factor enter into consideration?

(Without the Q into the thrust force equation, we still have an inefficient photon rocket)

[and when one enters the Q factor for a closed cavity, I yet have to embrace an explanation for a closed cavity where I can fully see conservation of momentum and conservation of energy satisfied.  For example, Shawyer only takes into account the forces perpendicular to the bases and neglects the counterbalancing forces from the conical surface which result in zero net thrust force]

Ditto for the GR calculation: they are one-dimensional longitudinal approximations, where the index of refraction changes in the longitudinal direction: but the truncated cone is 3-D and has counterbalancing forces due to the forces on the conical surface which cancel the thrust

If I'm wrong, I would like someone to show what happens with the forces on the conical surface (which are at an angle to the longitudinal direction)

I need a free-body diagram showing the force vectors on all the copper surfaces for the 3-D problem force summation  :)

The Q only enters in the case of a gravitational interaction through its role in calculating the number of photons (Total mass/energy) in the cavity.  If it was a Newtonian momentum interaction only the Power enters.  (I get zero when I try Newtonian)
Another issue:  my understanding of your derivation is that it follows from the expression for the cylindrical cavity (cone angle = zero): hence it is a constant cross-section longitudinal approximation to the cone, where the index of refraction changes in the longitudinal direction: but the truncated cone is 3-D and has counterbalancing forces due to the forces on the conical surface which cancel the thrust

It seems that the forces on the conical surfaces of the cone are being ignored, and if one takes into account the forces on the cone surface, the "thrust" would be nullified: no thrust. 

Hence the only possible thrust is with a dielectric (either in the cylinder or in the truncated cone).

Is that correct ?
« Last Edit: 05/08/2015 01:21 PM by Rodal »

Offline maciejzi

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As I understand there are 2 possible setups: closed (tested) and open (one amateur video on youtube with kitchen microwave magnetron).
Regardless of the closed/open structure, shouldn't the cavity have form a reversed parabolic shape?
With the microwave injecting module on its side or in the middle, the reversed parabolic shape will send more microwaves in the required direction.



In my opinion the engine resembles a very stiff speaker calculated for resonance frequency of 2,45MHz. The stiffer the material the better it resonates in this frequency. It's not only the Q that matters. That may be the reason the Cannae engine has lower efficiency - it is made of thinner metal that is less stiff.


I propose 4 options, as in the picture (A,B,C,D).

Offline deuteragenie

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« Last Edit: 05/08/2015 01:35 PM by deuteragenie »

Offline maciejzi

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Like this ?

http://upload.wikimedia.org/wikipedia/commons/thumb/9/93/Horn_loudspeaker_animation.gif/250px-Horn_loudspeaker_animation.gif

Exactly, but calculated for the MW frequency, so it has to be very stiff. Actually, it has to have the exact stiffness of this frequency to send the maximum waves in the required direction of thrust.


The stiffness of the membrane (the drive cavity) has to be selected according to the medium it operates in. Different for air, different for cosmic vacuum.
« Last Edit: 05/08/2015 01:40 PM by maciejzi »

Offline Rodal

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As I understand there are 2 possible setups: closed (tested) and open (one amateur video on youtube with kitchen microwave magnetron).
Regardless of the closed/open structure, shouldn't the cavity have form a reversed parabolic shape?
With the microwave injecting module on its side or in the middle, the reversed parabolic shape will send more microwaves in the required direction.



In my opinion the engine resembles a very stiff speaker calculated for resonance frequency of 2,45MHz. The stiffer the material the better it resonates in this frequency. It's not only the Q that matters. That may be the reason the Cannae engine has lower efficiency - it is made of thinner metal that is less stiff.


I propose 4 options, as in the picture (A,B,C,D).
The problem is that I can hear music from an open speaker (a "waveguide") but I cannot hear anything out of a speaker that is a closed cavity, such that all internal surfaces are perfectly reflective (the closed cavity of the EM Drive).

And if you open the big base of the EM Drive cavity, so that it becomes a speaker, then it is a very inefficient photon rocket, and therefore the claims of Shawyer don't make sense because they are thousands of time greater thrust per input power than a photon rocket  :'(

Offline Notsosureofit

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Yes, I added:

Where would the Q factor enter into consideration?

(Without the Q into the thrust force equation, we still have an inefficient photon rocket)

[and when one enters the Q factor for a closed cavity, I yet have to embrace an explanation for a closed cavity where I can fully see conservation of momentum and conservation of energy satisfied.  For example, Shawyer only takes into account the forces perpendicular to the bases and neglects the counterbalancing forces from the conical surface which result in zero net thrust force]

Ditto for the GR calculation: they are one-dimensional longitudinal approximations, where the index of refraction changes in the longitudinal direction: but the truncated cone is 3-D and has counterbalancing forces due to the forces on the conical surface which cancel the thrust

If I'm wrong, I would like someone to show what happens with the forces on the conical surface (which are at an angle to the longitudinal direction)

I need a free-body diagram showing the force vectors on all the copper surfaces for the 3-D problem force summation  :)

The Q only enters in the case of a gravitational interaction through its role in calculating the number of photons (Total mass/energy) in the cavity.  If it was a Newtonian momentum interaction only the Power enters.  (I get zero when I try Newtonian)
Another issue:  my understanding of your derivation is that it follows from the expression for the cylindrical cavity (cone angle = zero): hence it is a constant cross-section longitudinal approximation to the cone, where the index of refraction changes in the longitudinal direction: but the truncated cone is 3-D and has counterbalancing forces due to the forces on the conical surface which cancel the thrust

It seems that the forces on the conical surfaces of the cone are being ignored, and if one takes into account the forces on the cone surface, the "thrust" would be nullified: no thrust. 

Hence the only possible thrust is with a dielectric (either in the cylinder or in the truncated cone).

Is that correct ?

You are too fast for my old fingers...

Ultimately, what needs to be shown here is that the "covariant force vector equal to zero" on a photon in the accelerated frame is the same vector in the cavity rest frame (ie. can be transformed to) such that the force on a photon in the rest frame is a result of the (velocity) dispersion due to the shape of the cavity boundary conditions.  That transformation would show that the effect is to be expected under General Relativity.

The Q only enters in the case of a gravitational interaction through its role in calculating the number of photons (Total mass/energy) in the cavity.  If it was a Newtonian momentum interaction only the Power enters.  (I get zero when I try Newtonian for the reasons you have mentioned)

Note: I should probably use "Classical" instead of "Newtonian" but I think you would get the idea that we are looking at the 4-volume as an invariant rather than an integration over the surface of the boundary conditions of classical momentum exchange. That can apply as the summation of the (false gravitational?, ie. frame-dependent) forces on the individual photons to give the resultant force on the cavity.

Offline Rodal

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....

You are too fast for my old fingers...

Ultimately, what needs to be shown here is that the "covariant force vector equal to zero" on a photon in the accelerated frame is the same vector in the cavity rest frame (ie. can be transformed to) such that the force on a photon in the rest frame is a result of the (velocity) dispersion due to the shape of the cavity boundary conditions.  That transformation would show that the effect is to be expected under General Relativity.

The Q only enters in the case of a gravitational interaction through its role in calculating the number of photons (Total mass/energy) in the cavity.  If it was a Newtonian momentum interaction only the Power enters.  (I get zero when I try Newtonian for the reasons you have mentioned)

Note: I should probably use "Classical" instead of "Newtonian" but I think you would get the idea that we are looking at the 4-volume as an invariant rather than an integration over the surface of the boundary conditions of classical momentum exchange. That can apply as the summation of the (false gravitational?, ie. frame-dependent) forces on the individual photons to give the resultant force on the cavity.

I very much appreciate the explanation, unfortunately, I may not be able to understand this until I see the explicit mathematical formula for the 4-volume invariant, particularly the derivation of that invariant  :)

Unfortunately, I cannot do it intuitively as you can.

Unfortunately I only have an intuition for linear differential equation Newtonian problems, very little intuition for nonlinear Newtonian problems and no intuition for nonlinear general relativity problems :(
« Last Edit: 05/08/2015 01:58 PM by Rodal »

Offline Notsosureofit

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You are too fast for my old fingers...

Ultimately, what needs to be shown here is that the "covariant force vector equal to zero" on a photon in the accelerated frame is the same vector in the cavity rest frame (ie. can be transformed to) such that the force on a photon in the rest frame is a result of the (velocity) dispersion due to the shape of the cavity boundary conditions.  That transformation would show that the effect is to be expected under General Relativity.

The Q only enters in the case of a gravitational interaction through its role in calculating the number of photons (Total mass/energy) in the cavity.  If it was a Newtonian momentum interaction only the Power enters.  (I get zero when I try Newtonian for the reasons you have mentioned)

Note: I should probably use "Classical" instead of "Newtonian" but I think you would get the idea that we are looking at the 4-volume as an invariant rather than an integration over the surface of the boundary conditions of classical momentum exchange. That can apply as the summation of the (false gravitational?, ie. frame-dependent) forces on the individual photons to give the resultant force on the cavity.

I very much appreciate the explanation, unfortunately, I may not be able to understand this until I see the explicit mathematical formula for the 4-volume invariant, particularly the derivation of that invariant  :)

Unfortunately, I cannot do it intuitively as you can.

That would, of course, constitute a proof.

Offline maciejzi

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The problem is that I can hear music from an open speaker (a "waveguide") but I cannot hear anything out of a speaker that is a closed cavity, such that all internal surfaces are perfectly reflective (the closed cavity of the EM Drive).

And if you open the big base of the EM Drive cavity, so that it becomes a speaker, then it is a very inefficient photon rocket, and therefore the claims of Shawyer don't make sense because they are thousands of time greater thrust per input power than a photon rocket  :'(


All right. Than maybe the magnetic field of the microwaves resonating inside the cavity "pushes" against the magnetic field of Earth. Anyway, the reversed parabolic (speaker-like) shape may send more waves to the wide end.

Whatever the reason it moves, all I am saying is that it has to be tested. Not only for different Q, but also different shapes, different MW injection positions and different stiffness of the 'emiting' structure.


Offline Rodal

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...Than maybe the magnetic field of the microwaves resonating inside the cavity "pushes" against the magnetic field of Earth. ...
If you believe Shawyer's experiments to not be artifacts, the effect of the Earth's magnetic field was nullified by the fact that Shawyer claims to have  tested the EM Drive UP, DOWN, and HORIZONTALLY oriented, measuring the same thrust/PowerInput  :(
« Last Edit: 05/08/2015 02:08 PM by Rodal »

Offline WarpTech

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And if you open the big base of the EM Drive cavity, so that it becomes a speaker, then it is a very inefficient photon rocket, and therefore the claims of Shawyer don't make sense because they are thousands of time greater thrust per input power than a photon rocket  :'(

I need to study @notsosureofit's GR calculation, but I think the point that is being missed here is, the resonant cavity acts as an EM Momentum amplifier. The Q factor comes in not "Just" as the number of photons stored, but also;  In GR as in PV, as the energy density inside the cavity increases, the wave velocity decreases. As velocity decreases, momentum increases. That "effective mass" of the photons in the cavity kicks in stronger.

p ~ E/v  and in the cavity v << c

This makes it a not-so "inefficient" photon rocket!

In the EM Drive design I proposed, we want the Q in the resonant cavity to be very high, but we do not want a high Q in the frustum. We want the backward-moving waves to expand, and the reflected waves moving forward to be attenuated. So we want a low Q, high attenuation in the frustum.

Todd

Offline Rodal

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And if you open the big base of the EM Drive cavity, so that it becomes a speaker, then it is a very inefficient photon rocket, and therefore the claims of Shawyer don't make sense because they are thousands of time greater thrust per input power than a photon rocket  :'(

I need to study @notsosureofit's GR calculation, but I think the point that is being missed here is, the resonant cavity acts as an EM Momentum amplifier. The Q factor comes in not "Just" as the number of photons stored, but also;  In GR as in PV, as the energy density inside the cavity increases, the wave velocity decreases. As velocity decreases, momentum increases. That "effective mass" of the photons in the cavity kicks in stronger.

p ~ E/v  and in the cavity v << c

This makes it a not-so "inefficient" photon rocket!

In the EM Drive design I proposed, we want the Q in the resonant cavity to be very high, but we do not want a high Q in the frustum. We want the backward-moving waves to expand, and the reflected waves moving forward to be attenuated. So we want a low Q, high attenuation in the frustum.

Todd

I see the need for:

*low Q
*high attenuation

(This maybe confirmed by the Chinese: Prof. Yang measured the highest thrust, and the highest thrust/PowerInput, using a Q~1500 (*) much lower than the other researchers)

in the truncated cone, but this is the complete opposite of what is claimed by Shawyer.

Actually Shawyer is proceeding in the completely opposite direction:

1) a superconducting truncated cone with Q>10^6 and

2) Shawyer threw away the dielectric, hence NO attenuation from the dielectric.

3) Also Shawyer increased the cone angle from 10 degrees to 35 degrees, which decreased the geometrical attenuation by a large factor.

How do you reconcile Shawyer going in the completely opposite direction ????

****On the other hand, we have not seen Shawyer flying around with his superconducting  EM Drive, and he hasn't reported any results in 6 months.  Companies are eager to publicize major positive breakthroughs as soon as possible, particularly when owning Intellectual Property, as patents suffer from exponentially decaying value with time, like long options, so you want to exercise their value as soon as possible ****

____________

(*) Readers just looking at the translation from the Chinese Paper: notice that the Q in the tables are computed by a very unorthodox method.  The Q of the Chinese experiments, calculated in the same way as in the West is very low
« Last Edit: 05/08/2015 02:47 PM by Rodal »

Offline deuteragenie

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The problem is that I can hear music from an open speaker (a "waveguide") but I cannot hear anything out of a speaker that is a closed cavity, such that all internal surfaces are perfectly reflective (the closed cavity of the EM Drive).

And if you open the big base of the EM Drive cavity, so that it becomes a speaker, then it is a very inefficient photon rocket, and therefore the claims of Shawyer don't make sense because they are thousands of time greater thrust per input power than a photon rocket  :'(


All right. Than maybe the magnetic field of the microwaves resonating inside the cavity "pushes" against the magnetic field of Earth. Anyway, the reversed parabolic (speaker-like) shape may send more waves to the wide end.

Whatever the reason it moves, all I am saying is that it has to be tested. Not only for different Q, but also different shapes, different MW injection positions and different stiffness of the 'emiting' structure.

Chapter 9 of Acoustics: Sound Fields and Transducers By Leo L. Beranek, Tim J. Mellow is dedicated to properties of Horn loudspeakers and studies different shapes (hyperbolic, conical, parabolic... finite / infinite) and provides many nice formulas that could stimulate your thinking. 

Offline Rodal

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The problem is that I can hear music from an open speaker (a "waveguide") but I cannot hear anything out of a speaker that is a closed cavity, such that all internal surfaces are perfectly reflective (the closed cavity of the EM Drive).

And if you open the big base of the EM Drive cavity, so that it becomes a speaker, then it is a very inefficient photon rocket, and therefore the claims of Shawyer don't make sense because they are thousands of time greater thrust per input power than a photon rocket  :'(


All right. Than maybe the magnetic field of the microwaves resonating inside the cavity "pushes" against the magnetic field of Earth. Anyway, the reversed parabolic (speaker-like) shape may send more waves to the wide end.

Whatever the reason it moves, all I am saying is that it has to be tested. Not only for different Q, but also different shapes, different MW injection positions and different stiffness of the 'emiting' structure.

Chapter 9 of Acoustics: Sound Fields and Transducers By Leo L. Beranek, Tim J. Mellow is dedicated to properties of Horn loudspeakers and studies different shapes (hyperbolic, conical, parabolic... finite / infinite) and provides many nice formulas that could stimulate your thinking.
May also be useful to look at how microwaves actually propagate in a cone, and different other shapes, as in the literature of radar, according to Maxwell's equations instead of acoustic waves.

See this for paraboloid cavities for example : http://forum.nasaspaceflight.com/index.php?topic=36313.msg1334659#msg1334659
« Last Edit: 05/08/2015 03:38 PM by Rodal »

Offline Einstein79

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The reason for the confusion over the violation of classical physics is because this system has nothing to do with classical physics. Moreover, the “thrust” that is being calculated is not thrust at all but space moving the drive from one position to another which can merely be related to thrust but is not, per se, thrust. The controlling factor here is, of course, the resonant frequency. If you match the resonant frequency that space uses to “hold” the object you will develop a “cavity” that the “object will move towards”. The reason why the device cannot be “pushed off of” for conservation of momentum to hold true is because space is already pushing on it satisfying the law.

A couple of postulates to keep in mind that will help with these experiments are:
1. Space creates light.
2. Space itself is a resonating chamber.
Interesting! Would you then be prepared to write down the equations of motion so that we can play with them?

The equations of motion do not exist from an inertial reference frame. We must assume that the object is not moving and that space is moving around and through the object. I am trying to develop the Hamiltonian for space but having difficulty because we have always assumed space to be a virtual plasma and it is not virtual at all, but real.

Offline maciejzi

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And if you open the big base of the EM Drive cavity, so that it becomes a speaker, then it is a very inefficient photon rocket, and therefore the claims of Shawyer don't make sense because they are thousands of time greater thrust per input power than a photon rocket  :'(

I need to study @notsosureofit's GR calculation, but I think the point that is being missed here is, the resonant cavity acts as an EM Momentum amplifier. The Q factor comes in not "Just" as the number of photons stored, but also;  In GR as in PV, as the energy density inside the cavity increases, the wave velocity decreases. As velocity decreases, momentum increases. That "effective mass" of the photons in the cavity kicks in stronger.

p ~ E/v  and in the cavity v << c

This makes it a not-so "inefficient" photon rocket!

What if the photon rocket utilized the same construction with a cavity that would make the light move slower?

http://news.harvard.edu/gazette/1999/02.18/light.html

As it is possible to slow the light, then the lower its speed the bigger its thrust.
That's one thing. The other is that the thrust is multiplied by the number of bounccs.
That applies to MW waves in the resonating cavity. Hence - the bigger the number of bounces, the bigger the thrust.
You can actually amplify the photon rocket thrust as well.
See here:

Source: Wiki, http://upload.wikimedia.org/wikipedia/commons/8/8e/Photon-Thrust-Amplification.jpg

Bend this light path with optical fiber and you receive a powerful thruster.
Like this:




A very simple idea... nobody ever checked it yet, I suppose. I think this setup may be worth checking.
Please consider the fact that it is not c in the nominator, but the actual speed of light in the optical fiber. The slower the speed of the light in this apparatus, the greater the thrust!
The EmDrive works based on similar principle.
« Last Edit: 05/08/2015 03:47 PM by maciejzi »

Offline Einstein79

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The reason for the confusion over the violation of classical physics is because this system has nothing to do with classical physics. Moreover, the “thrust” that is being calculated is not thrust at all but space moving the drive from one position to another which can merely be related to thrust but is not, per se, thrust. The controlling factor here is, of course, the resonant frequency. If you match the resonant frequency that space uses to “hold” the object you will develop a “cavity” that the “object will move towards”. The reason why the device cannot be “pushed off of” for conservation of momentum to hold true is because space is already pushing on it satisfying the law.

A couple of postulates to keep in mind that will help with these experiments are:
1. Space creates light.
2. Space itself is a resonating chamber.
Interesting! Would you then be prepared to write down the equations of motion so that we can play with them?

The Mexican hat potential is a good place to start, I think, but not sure yet. It seems reasonable because it might coalesce with symmetry breaking. 

Offline LasJayhawk

The reason for the confusion over the violation of classical physics is because this system has nothing to do with classical physics. Moreover, the “thrust” that is being calculated is not thrust at all but space moving the drive from one position to another which can merely be related to thrust but is not, per se, thrust. The controlling factor here is, of course, the resonant frequency. If you match the resonant frequency that space uses to “hold” the object you will develop a “cavity” that the “object will move towards”. The reason why the device cannot be “pushed off of” for conservation of momentum to hold true is because space is already pushing on it satisfying the law.

A couple of postulates to keep in mind that will help with these experiments are:
1. Space creates light.
2. Space itself is a resonating chamber.
Interesting! Would you then be prepared to write down the equations of motion so that we can play with them?

The Mexican hat potential is a good place to start, I think, but not sure yet. It seems reasonable because it might coalesce with symmetry breaking.

You and Mulletron seem to be going in the same direction, you might want to bounce ideas off each other...

Offline WarpTech

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And if you open the big base of the EM Drive cavity, so that it becomes a speaker, then it is a very inefficient photon rocket, and therefore the claims of Shawyer don't make sense because they are thousands of time greater thrust per input power than a photon rocket  :'(

I need to study @notsosureofit's GR calculation, but I think the point that is being missed here is, the resonant cavity acts as an EM Momentum amplifier. The Q factor comes in not "Just" as the number of photons stored, but also;  In GR as in PV, as the energy density inside the cavity increases, the wave velocity decreases. As velocity decreases, momentum increases. That "effective mass" of the photons in the cavity kicks in stronger.

p ~ E/v  and in the cavity v << c

This makes it a not-so "inefficient" photon rocket!

In the EM Drive design I proposed, we want the Q in the resonant cavity to be very high, but we do not want a high Q in the frustum. We want the backward-moving waves to expand, and the reflected waves moving forward to be attenuated. So we want a low Q, high attenuation in the frustum.

Todd

I see the need for:

*low Q
*high attenuation

(This maybe confirmed by the Chinese: Prof. Yang measured the highest thrust, and the highest thrust/PowerInput, using a Q~1500 (*) much lower than the other researchers)

in the truncated cone, but this is the complete opposite of what is claimed by Shawyer.

Actually Shawyer is proceeding in the completely opposite direction:

1) a superconducting truncated cone with Q>10^6 and

2) Shawyer threw away the dielectric, hence NO attenuation from the dielectric.

3) Also Shawyer increased the cone angle from 10 degrees to 35 degrees, which decreased the geometrical attenuation by a large factor.

How do you reconcile Shawyer going in the completely opposite direction ????

****On the other hand, we have not seen Shawyer flying around with his superconducting  EM Drive, and he hasn't reported any results in 6 months.  Companies are eager to publicize major positive breakthroughs as soon as possible, particularly when owning Intellectual Property, as patents suffer from exponentially decaying value with time, like long options, so you want to exercise their value as soon as possible ****

____________

(*) Readers just looking at the translation from the Chinese Paper: notice that the Q in the tables are computed by a very unorthodox method.  The Q of the Chinese experiments, calculated in the same way as in the West is very low

I'm still studying "everything" from Shawyer, but so far I am not sure he really understands the principle of operation. His force calculation is insightful but it does not explain the "extra" momentum.

FYI: Marco's 1st draft paper went out on an email today from Paul M. and was distributed to about 35 individuals, including myself to my surprise. A swath of replies went back and forth, including a copy and paste of one of our posts here, between Dr. Rodal and myself. The comments were not constructive, as both Jack S. and Eric D. discarded the notion of gravity in the frustum, because GR would require overcoming the G/c^4 factor.

What these Dr's are missing is that we are not effecting the full spectrum from long wavelength RF to high energy quarks with what is happening in the frustum. It is only mimicking what gravity does in a very narrow bandwidth of the EM spectrum. The factor G/c^4 is only applicable for gravity that affects the FULL bandwidth of all energy and particles. G/c^4 comes from the integral over all modes in the field. We are not affecting all modes, just a few in a relatively low energy regime.

That's IMO of course.

Todd

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