I formally challenge the EM drive to a race. CID on one torsion balance and the EM on another and you can only use 12V @ 3 amps. Lets see which one makes a rotation first.
Sincerely,
Harry Sprain
...How about I just re-write your result using the definition of skin depth... then the equation makes a lot more sense to me. Q increases as "resistivity" decreases, but the relationship to frequency and permeability would seem to suggest a small frustum with high permeability.
Consider these equations at constant frequency and constant dimensions. What two variables do we have left to play with, in terms of materials?
Again, "To continue this discussion both of us must stop writing Q ~ and instead write Q = , detailing what precise expression, in terms of what variables, we are talking about"
in your response, you continue to write Q~. You need to write Q= referring to something specific and preciseto be able to have a discussion.
EDIT: Basically, this is the issue, I realize that one has to be explicit as to what is the Q= expression also in your dQ/dr
because there are many ways to write Q~ that lead to completely different expressions depending on what multiplying factors one is referring to
Like this? It's non-linear.
Thinking more about your theory, please comment on whether (and if not, why not) your theory is effectively nullified by the test results of Zeller and Kraft, at California Polytechnic State University, San Luis Obispo, who performed experiments with a cylindrical cavity having a HDPE dielectric ( https://www.linkedin.com/in/kurtwadezeller ) (NSF member Zellerium https://forum.nasaspaceflight.com/index.php?action=profile;area=showposts;u=47993 ). The cylindrical metal cavity was symmetric, but the HDPE was placed asymmetrically in the cylindrical cavity. Their conclusion was that there was no thrust. This experiment by Zeller and Kraft is a falsification of a hypothesis that thrust is generated simply by the HDPE (whether by electrostriction or other means), when asymmetrically placed in a cylindrical cavity.
Their experiments at California Polytechnic State University, San Luis Obispo, showing no thrust when using HDPE dielectric asymmetrically placed in a cylindrical cavity, can be seen in the attachments on https://www.linkedin.com/in/kurtwadezeller under "Researcher" section on Kurt Zeller's LinkedIn profile.
A theory explaining thrust of the EM Drive based on HDPE dielectric would need to also explain Zeller's experiments showing no thrust.
I just read the paper on the cylindrical cavity with HDPE dielectric, and the results were "inconclusive", not "null". They did measure thrust, but the results were in either direction.
Primarily, it seems they excited a TM mode of the cylinder. The TM mode concentrates the E field on the end plates and the H field on the side walls. The E field does not cause nearly as much (if any) power dissipation. It is the H field can cause power dissipation, and dissipation on the side walls of a cylinder will have a symmetrical effect. In order to have power dissipation, the material must have some conductivity. The resistivity of HDPE is too high, so there is very little power dissipation there. Instead, I think it's practically invisible to the MW's.
If they construct a cylinder where one end is copper and the other end is steel, they might see a different result.

http://forum.nasaspaceflight.com/index.php?topic=41475.0
I formally challenge the EM drive to a race. CID on one torsion balance and the EM on another and you can only use 12V @ 3 amps. Lets see which one makes a rotation first.
....
Sincerely,
Harry Sprainto have any relevance whatsoever to the subject of this thread (space flight applications) the contest should be performed in a vacuum chamber under at least 10^(-6) Torr, and the drives should be powered by a battery , self-integrated in the same body being accelerated.
No power cords allowed, as:
*Prof. Juan Yang defenestrated all her prior tests by performing tests with a battery showing that in her previous tests the power cords suffered thermal expansion as a result of getting hot, which produced the anomalous force artifact. Yang reported no thrust when taking into account the relative error of her experiments.
*Samsonov is the only "citizen-scientist" that to this date has reported EM Drive tests performed with a battery.
Samsonov reported no thrust when taking into account the relative error of his experiments.
Are you suggesting that all reported results without internal batteries are spurious effects, Shawyer, Fetta, everyone building devices here?
Take the exact same vehicle, put it in deep space and turn on the EmDrive, which immediately accelerates the 1,000kg mass at 1g for as long as the power is on.
No, this high Q is NOT QLoaded it's QUnloaded=Q0!
This is not an accelerator cavity with a big hole in the middle so particles can be accelerated through the hole by the massive E field. The only losses are the eddy current heating and the momentum xfer to the accelerating mass.
It is loaded Q as the momentum loss from the EmWave is another loss factor to the cavity that drains stored cavity energy faster than just eddy current heating losses. The force curves published in the patent application are the result of the lost cavity energy and so they are in fact the loaded Q fill and decay time for the cavity with 5x TC being 1~ sec and 1x TC being ~0.2 sec.
From that you can calc the cavities effective loaded Q as the forces were generated.
Ql = 2 Pi Freq Tc. Assuming 2.45GHz excitement, the loaded Q is approx 3x10^9.If you eliminate R in the resonant circuit (superconductive resonator) there is still Rs, this is the source resistance. It can't be ignored, its part of the circuit.
EDIT
I am sure we discussed this in the past. If my memory serves you has agreed with this at that time.
The antenna defines a specific coupling factor between the inner and the outer circuit. The same antenna what is used to couple the RF-energy into the cavity is able to couple the energy out, back into the source with the same effectivity. This is basic microwave 101 knowlage.
,,,I just read the paper on the cylindrical cavity with HDPE dielectric, and the results were "inconclusive", not "null". They did measure thrust, but the results were in either direction. ...
Argumentative.
Zellerium himself reported his own experiments here:
http://emdrive.wiki/Experimental_Results
and he reported them very clearly as zero thrust.
As documented at NSF in several of his posts, Zellerium reported this at http://emdrive.wiki/Experimental_Results after much thought and deliberation.
...Another thing I've been looking at is, that with a TM mode, the current flows along the length of the cavity, and resistance will go "UP" at the small end where the width of the conductor is narrower. With a TE mode, the current flows around the circumference of the cavity,...

...Another thing I've been looking at is, that with a TM mode, the current flows along the length of the cavity, and resistance will go "UP" at the small end where the width of the conductor is narrower. With a TE mode, the current flows around the circumference of the cavity,...?
There are no currents on the surfaces of a perfect metal conductor in a TE mode in an electromagnetically resonant cavity. The boundary condition is that any electrical component parallel to a perfect electrical conductor is zero.
http://www.antenna-theory.com/tutorial/electromagnetics/electric-field-boundary-conditions.php
For an imperfect conductor, the magnitude of such currents is extremely small (see Jackson).
Currents, heating and Q factors...
...The Ampère-Maxwell Law then tells us that the current enclosed by the loop, running through the wall perpendicular to the loop, will be proportional to the magnetic field just inside the cavity.
...In the TE modes, the currents run around the axis.
...That is odd because I thought there were currents even for a superconductor. ...
:...Well take for instance, "TE012 square of norm of magnetic field.png" at this link: http://forum.nasaspaceflight.com/index.php?topic=36313.msg1352878#msg1352878 where the square of the magnetic field should be from currents moving in a circle at the base. Edit: Well, half from the light and the other half from the currents....
, and I know what is being plotted and what BC are satisfied in my solution !...
http://gregegan.customer.netspace.net.au/SCIENCE/Cavity/Cavity.html#CURRENTSQuoteCurrents, heating and Q factors...
...The Ampère-Maxwell Law then tells us that the current enclosed by the loop, running through the wall perpendicular to the loop, will be proportional to the magnetic field just inside the cavity.
...In the TE modes, the currents run around the axis.
So far, we have treated the cavity walls as being made of a perfect conductor. In reality, of course, this will not be true, and the currents induced in the walls by the electromagnetic field will meet resistance
For an imperfect conductor, the magnitude of such currents is extremely small (see Jackson).
TE modes
For the TE modes there is no electric field at the wall
. ...That's my story and I'm satisfied with it. I prefer to work with magnetic fields, which should cause a much larger power dissipation, due to higher current flow.
are satisfied with it.
...
http://gregegan.customer.netspace.net.au/SCIENCE/Cavity/Cavity.html#CURRENTSQuoteCurrents, heating and Q factors...
...The Ampère-Maxwell Law then tells us that the current enclosed by the loop, running through the wall perpendicular to the loop, will be proportional to the magnetic field just inside the cavity.
...In the TE modes, the currents run around the axis.Greg Egan states clearly, in the section titled "Currents, heating and Q factors...", at the outset:Quote from: Greg EganSo far, we have treated the cavity walls as being made of a perfect conductor. In reality, of course, this will not be true, and the currents induced in the walls by the electromagnetic field will meet resistance
which is in agreement with my statement, and with Jackson:Quote from: RodalFor an imperfect conductor, the magnitude of such currents is extremely small (see Jackson).
From the same reference: http://gregegan.customer.netspace.net.au/SCIENCE/Cavity/Cavity.htmlQuote from: Greg EganTE modes
For the TE modes there is no electric field at the wall
which is exactly what I stated.
I carefully stated "perfect conductor" in my statements. I never commingled perfect conductor with superconductor. i never commingled perfect conductor with imperfect conductor. I was careful to make separate statements about them.
So far, we have treated the cavity walls as being made of a perfect conductor. In reality, of course, this will not be true, and the currents induced in the walls by the electromagnetic field will meet resistance, and dissipate energy as heat. If this rate of loss is not too great, and the energy in the cavity is constantly being replenished by a source of microwaves at the resonant frequency, then it’s reasonable to assume that the field geometry will closely resemble that of the lossless mode.
...
The resistance of a given area of the wall will be constant, so the power dissipated as heat per unit area will be proportional to the square of the current, and hence proportional to the square of the magnetic field strength at the wall.
When the temperature of the material is decreased pass the critical temperature the resistance of the material abruptly drops to zero.
...
What is the difference between Superconductor and Perfect Conductor?
• Superconductivity is a phenomenon occurring in real life, while perfect conductivity is an assumption made to ease the calculations.
• Perfect Conductors can have any temperature, but superconductors only exist below the critical temperature of the material.
...Another thing I've been looking at is, that with a TM mode, the current flows along the length of the cavity, and resistance will go "UP" at the small end where the width of the conductor is narrower. With a TE mode, the current flows around the circumference of the cavity,...?
There are no currents on the surfaces of a perfect metal conductor in a TE mode in an electromagnetically resonant cavity. The boundary condition is that any electrical component parallel to a perfect electrical conductor is zero.
http://www.antenna-theory.com/tutorial/electromagnetics/electric-field-boundary-conditions.php
For an imperfect conductor, the magnitude of such currents is extremely small (see Jackson).
.I am not sure I am understanding what the important difference is beyond this.
I had difficulty finding the quote from Jackson at that particular link.
[The H2 field will cause currents to flow in the skin depth, that's what prevents the field from passing through the copper. If there were no current induced in the copper, the magnetic field would escape to the outside....
[The H2 field will cause currents to flow in the skin depth, that's what prevents the field from passing through the copper. If there were no current induced in the copper, the magnetic field would escape to the outside....I carefully separated my statements between BC for perfect conductor and imperfect conductor.
You are stating << If there were no current induced in the copper,>> which means that you either failed to read my statements or you are commingling one with another.
You are commingling the two, and moreover not addressing the numerical magnitude of the currents, since I stated that in an imperfect conductor like copper the currents in TE modes are very small, and you make no numerical statement whatsoever.
So far, we have treated the cavity walls as being made of a perfect conductor. In reality, of course, this will not be true, and the currents induced in the walls by the electromagnetic field will meet resistance, and dissipate energy as heat. If this rate of loss is not too great, and the energy in the cavity is constantly being replenished by a source of microwaves at the resonant frequency, then it’s reasonable to assume that the field geometry will closely resemble that of the lossless mode.
...
The resistance of a given area of the wall will be constant, so the power dissipated as heat per unit area will be proportional to the square of the current, and hence proportional to the square of the magnetic field strength at the wall.
...
There are no currents on the surfaces of a perfect metal conductor in a TE mode in an electromagnetically resonant cavity.
...
For an imperfect conductor, the magnitude of such currents is extremely small (see Jackson).
[The H2 field will cause currents to flow in the skin depth, that's what prevents the field from passing through the copper. If there were no current induced in the copper, the magnetic field would escape to the outside....I carefully separated my statements between BC for perfect conductor and imperfect conductor.
You are stating << If there were no current induced in the copper,>> which means that you either failed to read my statements or you are confusing one with another.
You are commingling the two, and moreover not addressing the numerical magnitude of the currents, since I stated that in an imperfect conductor like copper the currents in TE modes are very small, and you make no numerical statement whatsoever.
I was trying to help by looking for a mathematical solution to the boundary condition problem for your equations.
If you are not going to use perfect conductor BC's to solve your equations, please show me your mathematical solution using BC's for imperfect conductors, using your equations.
...
But if very little current is induced in a restive conductor (bottom quote) then that would imply no current is induced in a perfect conductor, right? Is it that the current is zero so zero energy is dissipated through the walls, or is it the resistance is zero so zero energy is dissipated through the walls. Or is it the very little as a relative term that is throwing me off.
...