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#1800 by WarpTech on 19 Oct, 2016 01:40
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<snip...>
(**)
Please notice that if Q is a power function of r, there is no power of r that will give (1/Q)dQ/dr larger than 1
Even if Q is an exponential function of r:
Q= Exp[r]
Then dQ/dr=Exp[r]
=Q
Hence if Q= Exp[r]
(1/Q) dQ/dr =1
Therefore, Q would need to have an extremely high nonlinear dependence on r, much higher than a power, and higher than purely exponential to be able to get (1/Q) dQ/dr =Q. Since there is no apparent reason why a cone would give such a phenomenally nonlinear dependence on Q, one concludes, that Todd is correct that his equations likely point to a dependence on Q that maybe flat (for Q=Exp[r]) to inverse to Q (for Q a power function of r). At the extreme, if Q is linearly dependent on r, then (1/Q) dQ/dr =1/Q. So, the likely dependence on Q for Todd's thrust expression can be between flat, independent of Q (for Q=Exp[r]) to inversely proportional to Q (like 1/Q).
According to my model, we want Q to be very high at the small end and low at the big end, in order to push the frustum forward, with the small end leading. Since r is measured from the apex of the cone, AND since I would assume resistance will go up linearly with the diameter of the frustum, which is linear with r. I would expect the relationship to be;
Q ~ 1/r
Then, it gets smaller toward the big end and very large at the small end.
(1/Q) dQ/dr = -(1/r) = -Q.
AND....The thrust is still proportional to Q.
Also, it's been commented that Q is a "constant" of the cavity. Well, we have 2 choices. Either the mode frequency is constant and Q varies, or Q is constant and the mode frequency varies;
Q = (w0*tau)/2
tau is the decay time as a function of r. It will vary depending on the resistance in the circuit, dissipating power. I "know" there is a large probability that tau is changing with r. So which of the two remaining variables will vary, frequency or Q? If we insist that the mode frequency should be constant, then there is only one choice.
Todd -
#1801 by dustinthewind on 19 Oct, 2016 02:11
-
<snip...>
(**)
Please notice that if Q is a power function of r, there is no power of r that will give (1/Q)dQ/dr larger than 1
Even if Q is an exponential function of r:
Q= Exp[r]
Then dQ/dr=Exp[r]
=Q
Hence if Q= Exp[r]
(1/Q) dQ/dr =1
Therefore, Q would need to have an extremely high nonlinear dependence on r, much higher than a power, and higher than purely exponential to be able to get (1/Q) dQ/dr =Q. Since there is no apparent reason why a cone would give such a phenomenally nonlinear dependence on Q, one concludes, that Todd is correct that his equations likely point to a dependence on Q that maybe flat (for Q=Exp[r]) to inverse to Q (for Q a power function of r). At the extreme, if Q is linearly dependent on r, then (1/Q) dQ/dr =1/Q. So, the likely dependence on Q for Todd's thrust expression can be between flat, independent of Q (for Q=Exp[r]) to inversely proportional to Q (like 1/Q).
According to my model, we want Q to be very high at the small end and low at the big end, in order to push the frustum forward, with the small end leading. Since r is measured from the apex of the cone, AND since I would assume resistance will go up linearly with the diameter of the frustum, which is linear with r. I would expect the relationship to be;
Q ~ 1/r
Then, it gets smaller toward the big end and very large at the small end.
(1/Q) dQ/dr = -(1/r) = -Q.
AND....The thrust is still proportional to Q.
Also, it's been commented that Q is a "constant" of the cavity. Well, we have 2 choices. Either the mode frequency is constant and Q varies, or Q is constant and the mode frequency varies;
Q = (w0*tau)/2
tau is the decay time as a function of r. It will vary depending on the resistance in the circuit, dissipating power. I "know" there is a large probability that tau is changing with r. So which of the two remaining variables will vary, frequency or Q? If we insist that the mode frequency should be constant, then there is only one choice.
Todd
I'm just curious, if we consider the small end plus the side walls as facing forward it seems that is more surface area facing forwards than the single back plate facing backwards. That or the front profile has the same area as the back area. Heat radiated though all copper walls seems like more would be radiated forwards than backwards or maybe the same amount. Unless it could be because of the current patterns in the copper. (I'm reminded of the web page that had the modeled modes, energy density and heat patterns in the cavity.)
If more was being radiated forwards could it be a light drag effect, such as you mentioned to me once before when I was investigating near field phased arrays using dielectric's of high index, to get the phased arrays close together. That is light passing through a medium tends to drag it along with it? (placement of superconductive plate at large end?)
Or is it heat radiated backwards, similar to a thermal thrust. (superconductive plate at side walls and small end?)
Or maybe we are talking the transference of energy of light/currents to another medium by way of work. Leading to a thermal gradient? Just trying to get a grip on it. -
#1802 by Rodal on 19 Oct, 2016 03:26
-
<snip...>
(**)
Please notice that if Q is a power function of r, there is no power of r that will give (1/Q)dQ/dr larger than 1
Even if Q is an exponential function of r:
Q= Exp[r]
Then dQ/dr=Exp[r]
=Q
Hence if Q= Exp[r]
(1/Q) dQ/dr =1
Therefore, Q would need to have an extremely high nonlinear dependence on r, much higher than a power, and higher than purely exponential to be able to get (1/Q) dQ/dr =Q. Since there is no apparent reason why a cone would give such a phenomenally nonlinear dependence on Q, one concludes, that Todd is correct that his equations likely point to a dependence on Q that maybe flat (for Q=Exp[r]) to inverse to Q (for Q a power function of r). At the extreme, if Q is linearly dependent on r, then (1/Q) dQ/dr =1/Q. So, the likely dependence on Q for Todd's thrust expression can be between flat, independent of Q (for Q=Exp[r]) to inversely proportional to Q (like 1/Q).
According to my model, we want Q to be very high at the small end and low at the big end, in order to push the frustum forward, with the small end leading. Since r is measured from the apex of the cone, AND since I would assume resistance will go up linearly with the diameter of the frustum, which is linear with r. I would expect the relationship to be;
Q ~ 1/r
Then, it gets smaller toward the big end and very large at the small end.
(1/Q) dQ/dr = -(1/r) = -Q.
AND....The thrust is still proportional to Q.
Also, it's been commented that Q is a "constant" of the cavity. Well, we have 2 choices. Either the mode frequency is constant and Q varies, or Q is constant and the mode frequency varies;
Q = (w0*tau)/2
tau is the decay time as a function of r. It will vary depending on the resistance in the circuit, dissipating power. I "know" there is a large probability that tau is changing with r. So which of the two remaining variables will vary, frequency or Q? If we insist that the mode frequency should be constant, then there is only one choice.
Todd
See: https://forum.nasaspaceflight.com/index.php?topic=39214.msg1474347#msg1474347
for a detailed discussion formally proving that Q is a function of the geometry of the cavity, the material, and the mode shape.
Please notice that Q scales proportional to the square root of the dimensions:
Q ~ Sqrt[L]
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#1803 by WarpTech on 19 Oct, 2016 03:43
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According to my model, we want Q to be very high at the small end and low at the big end, in order to push the frustum forward, with the small end leading. Since r is measured from the apex of the cone, AND since I would assume resistance will go up linearly with the diameter of the frustum, which is linear with r. I would expect the relationship to be;
Q ~ 1/r
Then, it gets smaller toward the big end and very large at the small end.
(1/Q) dQ/dr = -(1/r) = -Q.
AND....The thrust is still proportional to Q.
Also, it's been commented that Q is a "constant" of the cavity. Well, we have 2 choices. Either the mode frequency is constant and Q varies, or Q is constant and the mode frequency varies;
Q = (w0*tau)/2
tau is the decay time as a function of r. It will vary depending on the resistance in the circuit, dissipating power. I "know" there is a large probability that tau is changing with r. So which of the two remaining variables will vary, frequency or Q? If we insist that the mode frequency should be constant, then there is only one choice.
Todd
I'm just curious, if we consider the small end plus the side walls as facing forward it seems that is more surface area facing forwards than the single back plate facing backwards. That or the front profile has the same area as the back area. Heat radiated though all copper walls seems like more would be radiated forwards than backwards or maybe the same amount. Unless it could be because of the current patterns in the copper. (I'm reminded of the web page that had the modeled modes, energy density and heat patterns in the cavity.)
If more was being radiated forwards could it be a light drag effect, such as you mentioned to me once before when I was investigating near field phased arrays using dielectric's of high index, to get the phased arrays close together. That is light passing through a medium tends to drag it along with it? (placement of superconductive plate at large end?)
Or is it heat radiated backwards, similar to a thermal thrust. (superconductive plate at side walls and small end?)
Or maybe we are talking the transference of energy of light/currents to another medium by way of work. Leading to a thermal gradient? Just trying to get a grip on it.
No. Do not think something needs to get outside and interact with something. That is not the case. Momentum does not need to escape to the outside.
Nobody would argue that if I had a mass oscillating on a spring inside the frustum. As the mass oscillates from front to back, the frustum would oscillate the other way, and vise versa. Agreed?
Now, consider the Woodward effect. When the mass moves toward the front, it gains mass, and when it moves toward the back, it loses mass. We've all been thinking in terms of photons, but forget photons. Think about a classical wave in a resonant cavity, where we are constantly adding and subtracting energy at opposite ends.
When the wave moves toward the front, more energy is added by the antenna (which Shawyer has now moved to the small end, where it belongs). When the wave moves toward the back, more energy is lost due to heat dissipation, preferably on the big end plate. Even if the heat doesn't escape the heatsink for hours, it's irrelevant once the energy has left the cavity. It is the oscillation of the energy, combined with high damping (resistance) at one end and high Q and input energy at the other end.
Note: This all came to me as I started typing here... so it's kind of off the cuff, but accurate I think.
Todd
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#1804 by meberbs on 19 Oct, 2016 04:57
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I think we can't expect Shawyer to have solved it all himself. What I get from his explanation is that he expects there to have been a back reaction on something such that the cavity accelerates. The only thing there is, is the light, so it seems he is indicating the light is getting the back reaction. Now this may seem heresy but I think he may be somewhat correct. I will have to try and describe this.
I think most of your post is generally accurate. The problem is that Shawyer tries to claim that the back reaction is the direction the cavity moves in. The reaction is on the EM wave, when it is reflected, which is what I think your post was getting at. His claim is like pointing a laser at a mirror on a spacecraft and he expects the spacecraft to accelerate towards the source of the laser.
...
I agree that we can't necessarily expect Shawyer to come up with a theory for how this works himself, I can't come up with one either. But we could expect him to admit when he doesn't have a working theory and instead say something like what Rodal suggested: "hey it seems to work, but I am not 100% sure why" That is a much better approach than insisting you have a working theory when others point out flaws in your theory. -
#1805 by 1 on 19 Oct, 2016 05:26
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Nobody would argue that if I had a mass oscillating on a spring inside the frustum. As the mass oscillates from front to back, the frustum would oscillate the other way, and vise versa. Agreed?
Be careful when using this as a starting point. The phrase 'the frustum would oscillate' has a built in assumption that forces (read: changes in momentum) from the spring would propagate from their mounting point on one end of the frustum to the opposite end extremely quickly. Generally speaking, this is valid. The speed of propagation (speed of sound) through a solid material is much larger than the instantaneous velocity of any spring I've ever seen.
However, in the case of RF, we must expect the opposite to be true. An EM wave might bounce back and forth many hundreds of thousands of times before any one momentum change can be observed on the frustum as a whole; never mind the fact that most (all?) of the antennas I've seen in the threads so far should be radiating more or less equally in the forward and backwards directions; as we'd expect from a standing wave in a resonant cavity.
Barring any new physics, I believe you're back to radiation pressure: a net outward push in all directions, but no net momentum change. -
#1806 by aero on 19 Oct, 2016 17:17
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Per Dr. Rodal's request, I've made a few meep runs to calculate the energy distribution in a resonant cavity. This may involve several posts, but all are for the same cavity resonating in what is thought to be a TE013 mode at 1996 MHz. First a couple of .gifs, of slices of the cavity in the x and in the y coordinate directions. For this cavity model, the .gif images taken this way are indistinguishable irrespective of the source bandwidth, so only one set is shown. This at a bandwidth of 49 MHz.
The next data set of images plots the cavity energy and meep calculated force in the axial direction. Pardon that the x coordinates are not the same. The energy plot shows each value within the computational lattice from 0 to 155, while the force plot shows 21 force detectors from the cavity big end to small end, with no points outside of the cavity. Again, bandwidth is 49 MHz.
If the bandwidth label confuses, note that BWm=0.025 is the same bandwidth as 49 MHz.
The final set is posted next.
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#1807 by WarpTech on 19 Oct, 2016 17:24
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See: https://forum.nasaspaceflight.com/index.php?topic=39214.msg1474347#msg1474347
for a detailed discussion formally proving that Q is a function of the geometry of the cavity, the material, and the mode shape.
Please notice that Q scales proportional to the square root of the dimensions:
Q ~ Sqrt[L]
Okay, I see that the math does show Q ~ δ and Q ~ 1/δ as valid results, depending on how you write them out.
The confusion stems from one step in your derivation, that is mathematically correct, but the physics may not be a good representation of a cavity with a “constant” mode frequency. You write;
ω = 2 ρ / (μ δ2)
Which implies that the frequency is a “function of the skin depth”. In my mind, that’s looking at the physics upside down. The “skin depth is a function of the frequency”, not the other way around, at least not physically.
If I do not use this to convert frequency to be in terms of skin depth as you did, then your Q ~ δ of the material, just as it is in the reference, for a constant frequency. But I would NOT believe that if the skin depth changes, it will affect the frequency. The frequency depends on the dimensions of the cavity, not the skin depth. So the equation above is mathematically correct, but physically it is an incorrect dependence relationship, that is being put into the equation, resulting in an incorrect interpretation that Q ~ 1/δ, when in fact, Q ~ δ makes a lot more sense physically. Because, as δ "of the material" decreases resistance goes up for the "same frequency", and Q goes down, not the other way around.
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#1808 by aero on 19 Oct, 2016 17:28
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The final data set shows the energy and the meep force within the cavity when resonating at the same 1996 MHz frequency with a narrow bandwidth of 19 MHz, or BWm = 0.010.
I was not surprised to note that the narrow bandwidth stored more energy in the cavity though Q was the same value irrespective of bandwidth. But I was surprised that the force calculated was much lower at the narrow bandwidth than at the wider bandwidth. And no, I didn't get the two curves confused. Perhaps someone can explain that to me but clearly force calculations can not be substituted for energy calculations.
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#1809 by Bob012345 on 19 Oct, 2016 17:45
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Good question and I'll try to answer very simply for basically it's not hard.And you can’t have evanescent waves in a superconductor, right? So maybe that helps explain Shaywer’s superconducting end plate?
No there is a evanescent part of a wave function acting on a superconductive wall.
https://en.wikipedia.org/wiki/London_penetration_depth
You're correct and that may not be a bad thing. http://pubs.acs.org/doi/abs/10.1021/acs.jpclett.6b00119
Where some of my current reading and research is going looking into the drive's ability to decay and extract the build up of energy. Using the energy that exists from the build of a high Q TE013 cavity and then forcibly decaying that energy into decaying evanescent wave actions.
In simple terms I'm thinking of the EMDrive or even the Cannea device as a photon momentum and force extractor using evanescent decaying waves. Evanescent waves that extract forces at levels greater than the standard photon rocket or light sails. The key I believe is evanescent waves which are virtual photons carrying extraordinary momentum and force that that transfer the force and momentum to the EMDrive and then vanish. So it's just not the reflected energy transfer of a bouncing photon and re-transmission of a lower shifted frequency photon, it consists of all the vector functions and extraordinary forces of the photon in a evanescent wave.
My Very Best,
Shell
I'm trying to understand what you were meaning concerning evanescent waves. Were you suggesting a decaying magnetic field outside the device? In simple classical terms, could a decaying or any magnetic field outside the device also interact with currents on the device to provide a net force on the device? And could such a field be created by the device yet also become sufficiently detached such as to be considered a free field in space the device could interact with? In other words, could you have your cake and eat it too?
For this to potentially work and not violate Mother Nature (she abhors being violated) you must think of what processes can permeate the closed cavity and what energies can escape. For if I have a perfectly enclosed box, Mother Nature (Maxwell too) says nothing I do in the box will have an effect outside the box. But it's not a perfect box, is it?
Gravity exists inside and outside the box and can freely be felt inside, as gravity inside can be felt outside. If I took a tinny black hole and put it into the box and you put your hand on the box... you would know it's a black hole you were close too. So this means gravitational effects produced in the box can be seen and acted on outside the box.
Spacetime is inside and outside, somehow warp it inside the box and it's felt outside.
Some particles also share space inside and outside.
Magnetic fields generated in the copper walls from induced flowing currents create small fields outside the box.
Evanescent wave actions can also collapse inside the box past cutoff points and close to the antenna(s) produce energy that could escape.
This very short list of physics and Quantum actions comprise subjects that honestly we know just enough about to get us into trouble.
Gravity
Spacetime
Magnetic Fields
Some Particles
Evanescent Waves (Virtual Particles should be here as well)
Which one do you think is causing this anomaly of thrusts?
Best,
Shell
Here's a nasty thought, only because it puts a huge burden on experimenters and hasn't been controlled for in any experiment I am aware of. One field that CAN somewhat freely transmit from the constraints of the Emdrive frustrum to the "outside world" is the magnetic field. The extensive discussions regarding TE and TM mode shapes may be illustrative, or not?
What if the propagating field within the frustum, alternatively expanding and collapsing, extending and retracting, was generating a "jellyfish" like magnetic field which interacts with the surrounding (earth's) field? Thrust results would be hugely dependant upon the internal frustum mode, the orientation of the frustum to the earth, and the phase of the selected mode. Phase reversal would result in thrust reversal, like the inversion of speech in a single side-band radio when the local oscillator is on the "wrong" side of the DC product. IF this is possible, the Emdrive would be a useful space drive, IF it were immersed in a magnetic field. The weaker the external field, the less effective the thrust.
There would be multiple "anti-Crazy Eddy" points during an Emdrive voyage, where the local magnetic field was nullified due to interaction between external fields. The hypothetical Emdrive "pilot" would have to constantly correct the thrust vector to optimize for the external field environment.
The reason that this effect may be observable with a microwave frustum rather than, say, a conical solenoid, is that the frustum allows control of mode (TE, TM, phase). Optical wavelengths and solenoids do not (easily), so the "effect" hasn't been observed. Just an odd thought.
Correct me if I'm wrong but I think the earths magnetic field has already been eliminated in most experiments. -
#1810 by Rodal on 19 Oct, 2016 18:32
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See: https://forum.nasaspaceflight.com/index.php?topic=39214.msg1474347#msg1474347
for a detailed discussion formally proving that Q is a function of the geometry of the cavity, the material, and the mode shape.
Please notice that Q scales proportional to the square root of the dimensions:
Q ~ Sqrt[L]
Okay, I see that the math does show Q ~ δ and Q ~ 1/δ as valid results, depending on how you write them out.
The confusion stems from one step in your derivation, that is mathematically correct, but the physics may not be a good representation of a cavity with a “constant” mode frequency. You write;
ω = 2 ρ / (μ δ2)
Which implies that the frequency is a “function of the skin depth”. In my mind, that’s looking at the physics upside down. The “skin depth is a function of the frequency”, not the other way around, at least not physically.
If I do not use this to convert frequency to be in terms of skin depth as you did, then your Q ~ δ of the material, just as it is in the reference, for a constant frequency. But I would NOT believe that if the skin depth changes, it will affect the frequency. The frequency depends on the dimensions of the cavity, not the skin depth. So the equation above is mathematically correct, but physically it is an incorrect dependence relationship, that is being put into the equation, resulting in an incorrect interpretation that Q ~ 1/δ, when in fact, Q ~ δ makes a lot more sense physically. Because, as δ "of the material" decreases resistance goes up for the "same frequency", and Q goes down, not the other way around.
Todd, that Q increases with diminishing skin depth, and Q decreases with increasing skin depth, as factor of the Volumetric/Surface energy ratio, is a result well known in all standard treatises, and not a subject for disagreement.
The following result is both mathematically and physically correct:
Q=(2/SkinDepth)(∫Electromagnetic Energy Density dV/ ∫ Electromagnetic Energy Density dA)
Talking about unphysical results: are you seriously proposing now that an electromagnetically resonant cavity has Q diminishing with diminishing skin depth, when keeping constant (∫Electromagnetic Energy Density dV/ ∫ Electromagnetic Energy Density dA) ?
Besides a number of standard treatises (Collin, etc.) this dependence of Q with skin depth has been verified here numerically by painstaking work by me and X_Ray:
https://forum.nasaspaceflight.com/index.php?topic=39214.msg1474351#msg1474351
https://forum.nasaspaceflight.com/index.php?topic=39214.msg1476683#msg1476683
https://forum.nasaspaceflight.com/index.php?topic=39214.msg1476704#msg1476704
https://forum.nasaspaceflight.com/index.php?topic=39214.msg1476709#msg1476709
and other posts.
Please go over this physics carefully and consult a number of references.... One can write different expression as a function of skin depth depending on what variables one uses to factor. What I wrote is correct, both mathematically and physically.
I highly recommend to you this book edited by Kip Thorne:
Systems with small dissipation
Braginsky, Mitrofanov and Panov
which deals with the relationship of Q and skin depth in detail (Eq. 6-11 page 51, 65, 67). This book was also recommended by Notsosureofit.
You can get it used in good conditions for $15
https://www.amazon.com/Systems-Small-Dissipation-V-Braginsky/dp/0226070735/ref=sr_1_1?ie=UTF8&qid=1476902948&sr=8-1&keywords=Systems+with+small+dissipation++Braginsky%2C+Mitrofanov+and+Panov&tag=mit-tb-20
EDIT: 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 -
#1811 by Tellmeagain on 19 Oct, 2016 18:44
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Here's a nasty thought, only because it puts a huge burden on experimenters and hasn't been controlled for in any experiment I am aware of. One field that CAN somewhat freely transmit from the constraints of the Emdrive frustrum to the "outside world" is the magnetic field. The extensive discussions regarding TE and TM mode shapes may be illustrative, or not?
What if the propagating field within the frustum, alternatively expanding and collapsing, extending and retracting, was generating a "jellyfish" like magnetic field which interacts with the surrounding (earth's) field? Thrust results would be hugely dependant upon the internal frustum mode, the orientation of the frustum to the earth, and the phase of the selected mode. Phase reversal would result in thrust reversal, like the inversion of speech in a single side-band radio when the local oscillator is on the "wrong" side of the DC product. IF this is possible, the Emdrive would be a useful space drive, IF it were immersed in a magnetic field. The weaker the external field, the less effective the thrust.
There would be multiple "anti-Crazy Eddy" points during an Emdrive voyage, where the local magnetic field was nullified due to interaction between external fields. The hypothetical Emdrive "pilot" would have to constantly correct the thrust vector to optimize for the external field environment.
The reason that this effect may be observable with a microwave frustum rather than, say, a conical solenoid, is that the frustum allows control of mode (TE, TM, phase). Optical wavelengths and solenoids do not (easily), so the "effect" hasn't been observed. Just an odd thought.
Correct me if I'm wrong but I think the earths magnetic field has already been eliminated in most experiments.
Your solid belief in EmDrive seems from insufficient information. In fact non EmDrive experiments so far eliminated earth magnet field. Worse, EW 2014 paper added on top of the Earth magnetic field their own strong rare earth magnetic field from the damper. Their coming 2016 paper likely still has a damper, just this time partially enclosed with shielding, but that shielding is insufficient (this was shown in my experiment with alike damper). -
#1812 by Rodal on 19 Oct, 2016 19:43
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The final data set shows the energy and the meep force within the cavity when resonating at the same 1996 MHz frequency with a narrow bandwidth of 19 MHz, or BWm = 0.010.
I was not surprised to note that the narrow bandwidth stored more energy in the cavity though Q was the same value irrespective of bandwidth. But I was surprised that the force calculated was much lower at the narrow bandwidth than at the wider bandwidth. And no, I didn't get the two curves confused. Perhaps someone can explain that to me but clearly force calculations can not be substituted for energy calculations.
The force you are calculating using Meep cannot, as presently calculated, result in any thrust. As I understand it, what you refer to as a force is just the integration of a component of Maxwell's stress tensor. The force you are calculating is self-balanced in the equations of motion. The equations built-in in Meep satisfy conservation of energy and conservation of momentum and, as I understand your post (please correct me if this is incorrect) there is nothing that you have included in the analysis to "open" the system: no general relativity is included, or other external fields. Hence I am not clear as to what expectations did you have on this force calculation when you write <<But I was surprised that the force calculated was much lower at the narrow bandwidth than at the wider bandwidth>>. For example, for equilibrium considerations, there is also a force, as part of equilibrium, due to the time derivative of the Poynting vector that you have to consider in the analysis. The Poynting vector is not constant with time in your Meep calculation. You are calculating a solution in the transient regime.
Haus and Penfield (MIT Radiation Lab) wrote some time ago that there was not much physical significance to a component of the Maxwell stress tensor in a transient problem where the derivative of the Poynting vector is not zero... -
#1813 by WarpTech on 19 Oct, 2016 20:25
-
See: https://forum.nasaspaceflight.com/index.php?topic=39214.msg1474347#msg1474347
for a detailed discussion formally proving that Q is a function of the geometry of the cavity, the material, and the mode shape.
Please notice that Q scales proportional to the square root of the dimensions:
Q ~ Sqrt[L]
Okay, I see that the math does show Q ~ δ and Q ~ 1/δ as valid results, depending on how you write them out.
The confusion stems from one step in your derivation, that is mathematically correct, but the physics may not be a good representation of a cavity with a “constant” mode frequency. You write;
ω = 2 ρ / (μ δ2)
Which implies that the frequency is a “function of the skin depth”. In my mind, that’s looking at the physics upside down. The “skin depth is a function of the frequency”, not the other way around, at least not physically.
If I do not use this to convert frequency to be in terms of skin depth as you did, then your Q ~ δ of the material, just as it is in the reference, for a constant frequency. But I would NOT believe that if the skin depth changes, it will affect the frequency. The frequency depends on the dimensions of the cavity, not the skin depth. So the equation above is mathematically correct, but physically it is an incorrect dependence relationship, that is being put into the equation, resulting in an incorrect interpretation that Q ~ 1/δ, when in fact, Q ~ δ makes a lot more sense physically. Because, as δ "of the material" decreases resistance goes up for the "same frequency", and Q goes down, not the other way around.
Todd, that Q increases with diminishing skin depth, and Q decreases with increasing skin depth, as factor of the Volumetric/Surface energy ratio, is a result well known in all standard treatises, and not a subject for disagreement.
The following result is both mathematically and physically correct:
Q=(2/SkinDepth)(∫Electromagnetic Energy Density dV/ ∫ Electromagnetic Energy Density dA)
Talking about unphysical results: are you seriously proposing now that an electromagnetically resonant cavity has Q diminishing with diminishing skin depth, when keeping constant (∫Electromagnetic Energy Density dV/ ∫ Electromagnetic Energy Density dA) ?
Besides a number of standard treatises (Collin, etc.) this dependence of Q with skin depth has been verified here numerically by painstaking work by me and X_Ray:
https://forum.nasaspaceflight.com/index.php?topic=39214.msg1474351#msg1474351
https://forum.nasaspaceflight.com/index.php?topic=39214.msg1476683#msg1476683
https://forum.nasaspaceflight.com/index.php?topic=39214.msg1476704#msg1476704
https://forum.nasaspaceflight.com/index.php?topic=39214.msg1476709#msg1476709
and other posts.
Please go over this physics carefully and consult a number of references.... One can write different expression as a function of skin depth depending on what variables one uses to factor. What I wrote is correct, both mathematically and physically.
I highly recommend to you this book edited by Kip Thorne:
Systems with small dissipation
Braginsky, Mitrofanov and Panov
which deals with the relationship of Q and skin depth in detail (Eq. 6-11 page 51, 65, 67). This book was also recommended by Notsosureofit.
You can get it used in good conditions for $15
https://www.amazon.com/Systems-Small-Dissipation-V-Braginsky/dp/0226070735/ref=sr_1_1?ie=UTF8&qid=1476902948&sr=8-1&keywords=Systems+with+small+dissipation++Braginsky%2C+Mitrofanov+and+Panov&tag=mit-tb-20
EDIT: 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
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, and a higher permeability material will help.
Consider these equations at constant frequency and constant dimensions. What two variables do we have left to play with, in terms of materials?
Edit: I see how it will scale as sqrt(R), I am holding R and w constant to see how to enhance existing designs.
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#1814 by Rodal on 19 Oct, 2016 20:39
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...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 precise to 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
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#1815 by RERT on 19 Oct, 2016 21:20
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QuoteQuote
1. The vacuum is not immutable
......
2. It is like a frictionless fluid which has both a local mass density and velocity field
3. Its mass density is almost entirely uniform, because non-uniformity dissipates very quickly
4. Consequently the net gravitational effect of the vacuum on any object is almost entirely nil, and the mass of the vacuum is undetectable in the lab.
5. The EMdrive works by transferring momentum to the vacuum, creating a 'flow' of massive vacuum.
6. However, the vacuum is special: we cannot detect motion through the vacuum. Once it is moving, it has 'dark momentum' - actually I quite like that name. 'dark momentum' is inherent in 'dark matter' after all...
7. Similarly, variations in the local mass-density of the vacuum on astronomical scales might account for 'dark matter'.
8. The EMdrive is propellant-less much like an Ocean Liner: it finds its reaction mass in its path. It is indeed not a rocket.
9. Gradients in the local velocity field of the vacuum caused by the EMdrive might cause local gravitational effects, which would be expected to dissipate quickly, much like the wake of a ship. However, a ship is not limited in its thrust to power ratio by the energy to momentum ratio of the waves which dissipate its wake. Nature takes as long as it needs to do that.
It doesn't matter about how the Emdrive works, but it matters much about CoE.
It may conduce to an infinite generation of energy if Quantum Vacuum auto-restores. It depends on how this auto-restoration works.
If we compare the Quantum vacuum to the sea, when a propeller is used to accelerate a ship, the momentum of the generated currents is not kept a long time, but it means that the entire sea gained a very little momentum. Would it be the same here ? does the entire quantuum vacuum got a very little dark momentum ?
Hadn't thought of that, but yes. The 'wake' begins as a local disturbance, which propagates to infinity and dissipates. There is an assumption of CoM, so the vacuum in the rest of the universe eventually acquires a momentum in the opposite direction.QuoteI think that it is important about a theory to know if it breaks CoM or CoE in our 3D+time universe. I do not tell that it is a nullification argument, but that the consequences of any theory about CoE and CoM needs to be clear.
I'm implicitly assuming CoE. The only 'odd' thing is that the 'aether' experiments founding relativity show that motion of any material vacuum is undetectable. So, any momentum and energy transferred to the vacuum will appear to have vanished. Conversely, one can 'explain' apparent breakage of CoE/CoM as transfers to/from the vacuum.
Consider for a minute why I considered a massive vacuum was appealing in the first place. For a massive object, E/p ~ (1/2 m v^2)/mv ~v can be as small as you like. The EMdrive experiments seem to require E/P<<c. In fact, we could say E/P ~1 for the high force systems postulated. So v~1.
But for a 'Jet Ski' model of the EMDrive, the momentum transfer to a massive vacuum would be around
F=(mass/sec)*v = ρAv*v where ρ is the density of the medium, A is the cross-sectional area of the plume.
For a DIY EMdrive, A~0.1, F~0.2 and so we can deduce ρ = 2 kg/m^3
So if you think that density of the vacuum of that level is possible, the idea might work. To me it seems high, and is actually about 18*10^25 larger than the cosmological estimate from Wiki. I guess you can find comfort in the fact that it is below the quantum vacuum energy density estimate, but it is fairly cold comfort....QuoteNow that I hope having at least a little understood this theory, what would make the local mass-density heterogenous ?
The obvious answer is galactic EM-fields. If the EM fields in the EM drive can manipulate the vacuum, why not natural EM fields? It's worth noting that the EM field has an outrageously special position in space-time and causality, so why not expect the EM field to be coupled to the flow of space... -
#1816 by rq3 on 19 Oct, 2016 21:25
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Quote
Here's a nasty thought, only because it puts a huge burden on experimenters and hasn't been controlled for in any experiment I am aware of. One field that CAN somewhat freely transmit from the constraints of the Emdrive frustrum to the "outside world" is the magnetic field. The extensive discussions regarding TE and TM mode shapes may be illustrative, or not?
What if the propagating field within the frustum, alternatively expanding and collapsing, extending and retracting, was generating a "jellyfish" like magnetic field which interacts with the surrounding (earth's) field? Thrust results would be hugely dependant upon the internal frustum mode, the orientation of the frustum to the earth, and the phase of the selected mode. Phase reversal would result in thrust reversal, like the inversion of speech in a single side-band radio when the local oscillator is on the "wrong" side of the DC product. IF this is possible, the Emdrive would be a useful space drive, IF it were immersed in a magnetic field. The weaker the external field, the less effective the thrust.
There would be multiple "anti-Crazy Eddy" points during an Emdrive voyage, where the local magnetic field was nullified due to interaction between external fields. The hypothetical Emdrive "pilot" would have to constantly correct the thrust vector to optimize for the external field environment.
The reason that this effect may be observable with a microwave frustum rather than, say, a conical solenoid, is that the frustum allows control of mode (TE, TM, phase). Optical wavelengths and solenoids do not (easily), so the "effect" hasn't been observed. Just an odd thought.QuoteCorrect me if I'm wrong but I think the earths magnetic field has already been eliminated in most experiments.
If so, I haven't seen the results. Several experimenters have oriented their Emdrive at various angles to the local magnetic field, and obtained varying "thrust" results. As far as I know, no experimenter has built the necessarily large Helmholts coils to NULLIFY the external magnetic field in the volume that the Emdrive is occupying. This would be a required experiment to prove that the Emdrive is NOT interacting with any external magnetic fields. All we know at this point is that it does, but not how or why, nor if the interaction is responsible for the "thrust". Such an interaction would not necessarily be a bad thing, but it certainly hasn't been objectively quantified.
I suppose that waiting for the construction of an Emdrive that actually produces unequivocal thrust would be a first step, before complicating the issue further than it is. -
#1817 by PNeilson on 19 Oct, 2016 21:53
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The use of Q in the equations has bothered me since the beginning.
Lots of undefined assumptions in Q.
If you could get rid of Q in the equations, I sort of think the CoE arguments will fall by the wayside.
Infinite Q is simply unphysical. Sure makes for lots of over unity CoE arguments around here though. -
#1818 by WarpTech on 19 Oct, 2016 22:08
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...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 precise to 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.
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#1819 by OnlyMe on 19 Oct, 2016 22:34
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No. Do not think something needs to get outside and interact with something. That is not the case. Momentum does not need to escape to the outside.
Nobody would argue that if I had a mass oscillating on a spring inside the frustum. As the mass oscillates from front to back, the frustum would oscillate the other way, and vise versa. Agreed?
Now, consider the Woodward effect. When the mass moves toward the front, it gains mass, and when it moves toward the back, it loses mass. We've all been thinking in terms of photons, but forget photons. Think about a classical wave in a resonant cavity, where we are constantly adding and subtracting energy at opposite ends.
When the wave moves toward the front, more energy is added by the antenna (which Shawyer has now moved to the small end, where it belongs). When the wave moves toward the back, more energy is lost due to heat dissipation, preferably on the big end plate. Even if the heat doesn't escape the heatsink for hours, it's irrelevant once the energy has left the cavity. It is the oscillation of the energy, combined with high damping (resistance) at one end and high Q and input energy at the other end.
Note: This all came to me as I started typing here... so it's kind of off the cuff, but accurate I think.
Todd
First, if the frustum moves momentum does get to the outside. It just maybe did not begin from the outside.
The trivial comment above aside, after reading your above post and a couple of the responses, an idea occurred to me that may be worth closer examination, than I am currently able to give...
Before I start, what I understand of the practical design of an EMDrive and EM mode simulations (which is imperfect at best) all comes from the discussions here. Keeping this in mind...
What occurred to me is that under most circumstances direct interaction between the resonant microwaves inside a frustum with the frustum walls should end in a transfer of energy in the form of heat. But the way that transfer occurs may not be completely symmetrical, especially when considering how the EM mode and different materials affect the process.
To keep things as simple as possible, consider a shortened frustum side wall (which I believe you suggested at one point), a superconducting large end plate as indicated in Shawyer's latest patent and a TE213 mode shape (hope I got that right)....
Am I correct in my understanding that the skin depth of the super conducting plate is less than the copper or even silver plated copper of the frustum as a whole, and that the TE213 mode shape focuses a higher intensity resonant EM field at or near the small end plate? If so...
It would seem that one could look at the EM field inside the frustum almost as if it were a an oscillating EM field, similar in some respects to SeeShell's mention of evanescent waves, except without the virtual particles and asymmetrically filling the frustum interior. The oscillating field doing work on the atoms of the frustum walls proportional to the local field intensity/density. Essentially pushing and pulling on atoms to perhaps the skin depth of the involved wall material. Over most of the interior surface the interaction between the walls and the lower or weaker field density would very rapidly be randomized as heat. However, at the small end or wherever the intensity of the resonant EM field is high the atoms would be pushed and pulled relative to the plane of the involved surface, vibrating in resonance with the field.., and it is here where the thought occurred to me that as an EM field pulls an atom toward the interior of the frustum the transfer of momentum/force to the underlying atoms would be limited by the strength of the atomic/molecular bonding between the atoms and the strength/intensity of the EM field, while when pushed toward the surface there might be a small increase in the transferred kinetic energy associated with the atoms actually impacting one another. The net force or momentum would be perpendicular to and toward the involved surface and as it moves beyond the skin depth rapidly randomized as heat. However, there might be a small net force perpendicular to and toward the surface. In this case the small end plate.
If this makes any sense, the reduced skin depth of the superconducting large end plate might reduce the effect at the large end and it might explain why results involving the TM212 mode where the field intensity is more centrally located in the frustum (again hope I got that right), where it's interaction with the sidewalls would result in a smaller net thrust toward the small end, dependent on the angle of the sidewalls.
There would be no CoM/CoE issue here, but the drive's efficiency, if c is a true universal limit, might be velocity dependent... and there would also be a need to control the absolute field strength inside the frustum, to avoid degrading the frustum walls to rapidly. Essential a strong field might just pull atoms off of the walls.
