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#1480 by meberbs on 12 Sep, 2019 19:16
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No no, we do not want to violate the law of conservation of momentum. We just want to calculate the manifestations of the Doppler effect at different points of the rocket, and then, already think about what to do next.
You aren't proposing interactions with anything else, therefore anything better than a photon rocket breaks conservation of momentum.What is it? I hit Emdrive with a hammer or thermally processed it, and is there a very real moment in time when at its different ends, for a very short time, but the photon pressure changed very, very much? With the accumulation of the effect due to the quality factor of the resonator?
This does not matter, go do the math, the effects cancel out and you are still left with a photon rocket. Resonators are not magical devices, if a resonator is moving at constant velocity, a Doppler shift on one side is cancelled out by the opposite Doppler shift on the other end, and things do not accumulate the way you wish. -
#1481 by Alex_O on 12 Sep, 2019 19:29
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UPD
I will add a little drama.
On the trolley stands Emdrive turned on, and he remains at rest. Since the total (large value) radiation pressure on its walls is zero. This thing is created by electromagnetic forces, and there may even be manifestations of wake acceleration (ponderomotive forces).
Known ideas of particle accelerators to huge energies due to wake acceleration.
Then the wizard came and hit Emdrive with a light hammer. The cart rolled along the rails at a low speed. And suddenly, we saw that the total radiation pressure inside the resonator suddenly became different from zero !!!.
And the difference in pressure strongly depends on the quality factor of the resonator. Yes, it was for a split second. So what? Our Intuition expects an increase in effect like an avalanche when the trolley continues to move. The creative thought of an engineer will immediately think - how to enhance the effect.
And you know what? I would like to draw a plot of forces right away. Force vector. I know where the force vector ends (on the inner surface of the resonator), but I do not know where the beginning of the vector is. What if the beginning of the vector lies outside the cavity? This may mean that for some nanosecond, a still unknown external force acted on the resonator Emdrive. -
#1482 by meberbs on 12 Sep, 2019 19:40
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Then the wizard came and hit Emdrive with a light hammer. The cart rolled along the rails at a low speed. And suddenly, we saw that the total radiation pressure inside the resonator suddenly became different from zero !!!.
Because the wizard actually used a magic wand to turn off the laws of physics? What you describe simply has no basis in reality, the radiation pressure would not disappear magically.And the difference in pressure strongly depends on the quality factor of the resonator. Yes, it was for a split second. So what? Our Intuition expects an increase in effect like an avalanche when the trolley continues to move.
Your intuition is wrong. There is no effect that has been described that could feed itself. As I already explained, the only case where a closed cavity does not have net 0 force due to radiation pressure is when there is an externally applied acceleration, and it is always in the opposite direction of the acceleration. Since it is opposed to the acceleration, it is completely nonsensical to claim that it can cause itself.The creative thought of an engineer will immediately think - how to enhance the effect.
Not when there is no effect to enhance.
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#1483 by Alex_O on 12 Sep, 2019 19:48
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No no, we do not want to violate the law of conservation of momentum. We just want to calculate the manifestations of the Doppler effect at different points of the rocket, and then, already think about what to do next.
You aren't proposing interactions with anything else, therefore anything better than a photon rocket breaks conservation of momentum.What is it? I hit Emdrive with a hammer or thermally processed it, and is there a very real moment in time when at its different ends, for a very short time, but the photon pressure changed very, very much? With the accumulation of the effect due to the quality factor of the resonator?
This does not matter, go do the math, the effects cancel out and you are still left with a photon rocket. Resonators are not magical devices, if a resonator is moving at constant velocity, a Doppler shift on one side is cancelled out by the opposite Doppler shift on the other end, and things do not accumulate the way you wish.
Sorry, we are not studying inertial reference systems. We were told that in order to initialize the thrust of the emdrive rocket, we need to tell the emdrive initial for a short moment of time acceleration. We do not have uniform movement, in principle.
It seems to me that I have proved that in a non-inertial reference system, in a closed, closed EM resonator system, one can find short time intervals when the total effect of radiation pressure on the inner surface, due to the Doppler effect, can be non-zero !. -
#1484 by meberbs on 12 Sep, 2019 19:58
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Sorry, we are not studying inertial reference systems. We were told that in order to initialize the thrust of the emdrive rocket, we need to tell the emdrive initial for a short moment of time acceleration. We do not have uniform movement, in principle.
My statements are not dependent on that.It seems to me that I have proved that in a non-inertial reference system, in a closed, closed EM resonator system, one can find short time intervals when the total effect of radiation pressure on the inner surface, due to the Doppler effect, can be non-zero !.
You have proven nothing. I previously explained that there will be a (small) radiation pressure difference between the 2 ends of the cavity, in the opposite direction of externally applied acceleration, for as long as there is an externally applied acceleration and no longer. This produces exactly no useful effects. -
#1485 by Bob012345 on 12 Sep, 2019 20:04
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No no, we do not want to violate the law of conservation of momentum. We just want to calculate the manifestations of the Doppler effect at different points of the rocket, and then, already think about what to do next.
You aren't proposing interactions with anything else, therefore anything better than a photon rocket breaks conservation of momentum.
While I very much want to violate conservation of momentum but sadly, I can't...
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#1486 by Alex_O on 12 Sep, 2019 20:21
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Sorry, we are not studying inertial reference systems. We were told that in order to initialize the thrust of the emdrive rocket, we need to tell the emdrive initial for a short moment of time acceleration. We do not have uniform movement, in principle.
My statements are not dependent on that.It seems to me that I have proved that in a non-inertial reference system, in a closed, closed EM resonator system, one can find short time intervals when the total effect of radiation pressure on the inner surface, due to the Doppler effect, can be non-zero !.
You have proven nothing. I previously explained that there will be a (small) radiation pressure difference between the 2 ends of the cavity, in the opposite direction of externally applied acceleration, for as long as there is an externally applied acceleration and no longer. This produces exactly no useful effects.
Well, we agreed that at the ends of the resonator, within a very short period of time, the radiation pressure forces due to Doppler can change?
Moreover, the process looks like inconsistent, at different times, the pressure at the ends does not change synchronously, but with a delay?
Then slice, mentally, make a resonator from thin, flexible walls, and let it oscillate along the axis - like a corrugated siphon! We mentally reinforced the deformation of the resonator body, due to greater flexibility. And immediately enhanced the effect of Doppler.
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#1487 by Alex_O on 12 Sep, 2019 20:40
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Sorry, we are not studying inertial reference systems. We were told that in order to initialize the thrust of the emdrive rocket, we need to tell the emdrive initial for a short moment of time acceleration. We do not have uniform movement, in principle.
My statements are not dependent on that.It seems to me that I have proved that in a non-inertial reference system, in a closed, closed EM resonator system, one can find short time intervals when the total effect of radiation pressure on the inner surface, due to the Doppler effect, can be non-zero !.
You have proven nothing. I previously explained that there will be a (small) radiation pressure difference between the 2 ends of the cavity, in the opposite direction of externally applied acceleration, for as long as there is an externally applied acceleration and no longer. This produces exactly no useful effects.
SavePoint 0
You forgot that there are two options. external force - hammer blow, and thermal deformation due to the work of internal forces. And there and there is room for Doppler. For, an example of a worm. The worm, in zero gravity, in a vacuum, compresses, unclenches its body due to internal energy, which is an resonator resonator. And catches the buzz from the gradients of radiation pressure at the ends. -
#1488 by meberbs on 12 Sep, 2019 20:49
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Well, we agreed that at the ends of the resonator, within a very short period of time, the radiation pressure forces due to Doppler can change?
Why do you keep bringing up a "short period of time"? A continuous acceleration works just fine for creating a difference in radiation pressure and is easier to do the math on. (Of course the difference is useless because it just opposes the external acceleration, but the same is true if the external acceleration comes from a short hammer blow.)Moreover, the process looks like inconsistent, at different times, the pressure at the ends does not change synchronously, but with a delay?
Continuous acceleration works just as well if not better, you are just over-complicating things, but if you want to do the math for this case, go ahead and do it, you will find that this does not create a useful force, since that would violate conservation of momentum. (I'd do the math for you, but typing it all out is tedious, and based on your responses so far you would just ignore the results anyway.)Then slice, mentally, make a resonator from thin, flexible walls, and let it oscillate along the axis - like a corrugated siphon! We mentally reinforced the deformation of the resonator body, due to greater flexibility. And immediately enhanced the effect of Doppler.
Again, conservation of momentum works, you aren't enhancing anything here. You haven't done any of the math for the last 2 or 3 steps, and are well past the point of handwaving.You forgot that there are two options. external force - hammer blow, and thermal deformation due to the work of internal forces. And there and there is room for Doppler. For, an example of a worm. The worm, in zero gravity, in a vacuum, compresses, unclenches its body due to internal energy, which is an resonator resonator. And catches the buzz from the gradients of radiation pressure at the ends.
I didn't forget the options you listed, but neither of them are useful in any way, shape or form. You have not proven anything about either case, just made unfounded assumptions of magical behaviors. If you ever did the actual math you would see that none of this would produce a useful net force. Midway through this post you now start talking complete gibberish, worms are in no way relevant. -
#1489 by Alex_O on 13 Sep, 2019 11:01
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Well, we agreed that at the ends of the resonator, within a very short period of time, the radiation pressure forces due to Doppler can change?
Why do you keep bringing up a "short period of time"? A continuous acceleration works just fine for creating a difference in radiation pressure and is easier to do the math on. (Of course the difference is useless because it just opposes the external acceleration, but the same is true if the external acceleration comes from a short hammer blow.)Moreover, the process looks like inconsistent, at different times, the pressure at the ends does not change synchronously, but with a delay?
Continuous acceleration works just as well if not better, you are just over-complicating things, but if you want to do the math for this case, go ahead and do it, you will find that this does not create a useful force, since that would violate conservation of momentum. (I'd do the math for you, but typing it all out is tedious, and based on your responses so far you would just ignore the results anyway.)Then slice, mentally, make a resonator from thin, flexible walls, and let it oscillate along the axis - like a corrugated siphon! We mentally reinforced the deformation of the resonator body, due to greater flexibility. And immediately enhanced the effect of Doppler.
Again, conservation of momentum works, you aren't enhancing anything here. You haven't done any of the math for the last 2 or 3 steps, and are well past the point of handwaving.You forgot that there are two options. external force - hammer blow, and thermal deformation due to the work of internal forces. And there and there is room for Doppler. For, an example of a worm. The worm, in zero gravity, in a vacuum, compresses, unclenches its body due to internal energy, which is an resonator resonator. And catches the buzz from the gradients of radiation pressure at the ends.
I didn't forget the options you listed, but neither of them are useful in any way, shape or form. You have not proven anything about either case, just made unfounded assumptions of magical behaviors. If you ever did the actual math you would see that none of this would produce a useful net force. Midway through this post you now start talking complete gibberish, worms are in no way relevant.
Thank you dear meberbs for a very useful conversation, I will be three days without the Internet, allow me to agree:
1. Emdrive stands on an ideal trolley or balancer.
2. Turn on the RF power.
3. Significant radiation force acts on the cavity walls, but the drive remains motionless. Since according to the law of conservation of momentum, the sum of the forces of radiation pressure on the internal surfaces of the resonator - the sum of the force is zero.
4. There are no external forces (no magic hammer).
5. Due to internal forces, the resonator body experiences thermal expansion. At the same time, over a short time interval, using a fast camera, it is observed that different parts of the resonator perform accelerated movement at different speeds. Within the flexible (elastic) properties of a copper substance.
6. The value of the time interval is selected within the time limit for the propagation of mechanical (sound waves) in the resonator body, that is, about 3570 m / s, which gives an interval of about 10 μs.
7. Thus, I described the initial boundary conditions. For the sake of simplicity of modeling, I chose such a regime of thermal loads when the small bottom remains motionless, and the large bottom moves rapidly - towards the small bottom, at a speed of 3570 m / s, during a small time interval = 10 μs. (or 1 μs, not important).
8. Earlier, we agreed that the force of radiation pressure on the large bottom in this case will differ by dp due to the Doppler effect.
9. Since the small bottom is motionless, the radiation force on it will not change.
10. I conclude that in the indicated small time interval, in comparison with point 3, a “strange” new, unbalanced force will appear in the resonator. Since the sum of radiation pressure forces in this case will differ by a "derivative" from dp.
11. Since the photon gas (I use this term for brevity) is somehow significantly different from the properties of any gas or liquid, I believe that from the side of the photon gas - at this point in time, a new, unbalanced force will act on the large bottom of the resonator and if the overall drive is granted freedom of movement, this force will force the drive to make a small movement with acceleration. Accurate scales will measure the thrust of an emdrive rocket. The thrust vector may have a direction towards the large bottom.
12. Thus, we see that in a small time interval, the EM field that is inside the resonator cavity can cause the cavity to move in space.
I wanted to prove just that. Q.E.D.
13. Clarification, the effect will manifest itself obviously in a shorter time interval when the reflected (but already changed by the Doppler) photons have not yet reached the small bottom. That is, the time interval is about 10-9 seconds.
14. That is, a photon gas creates a pulse force, with a pulse duration of about 10-9 seconds.
15. But since photons can be reflected many times between the large and small bottoms in the interval of 10 μs, the result of the pulse force should be summed up the work of the pulse force in the interval of 10 μs.
16. Thermal loads will cause the movement of the center of mass. This will mask the effect; a resonator with high quality factor is required for detection.
17. To clarify the pressure force on the small bottom, when more “violet” photons “arrive” on the small bottom (for the first time), which are already modified in frequency by the Doppler effect on the large bottom - at the initial moment of the time interval from 10-9 seconds. Obviously, the pressure force on the small bottom will also be increased. But since the area of the small and large bottoms is very different, this will not be able to destroy the effect of rocket thrust on the big bottom due to the Doppler effect.
18. Clarify the likelihood that the side walls of the resonator, due to the curved surface of the large bottom — that there are such photons in the total photon flux — never act on the side walls.
Thank. R.S. Sorry, I was in a hurry yesterday and could make messages with physics errors. And I could not answer your questions well during the conversation. (my wife swore at me very much that I should go to sleep
. I also spend time on Google translating from Russian into English and correcting translation errors.
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#1490 by meberbs on 13 Sep, 2019 14:14
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Thank you dear meberbs for a very useful conversation, I will be three days without the Internet, allow me to agree:
Agree would imply that you are agreeing with previous statements I made, but several of your points contradict things I have said. I appreciate you breaking things down step by step like this, it makes it easier to show exactly where you make incorrect assumptions.5. Due to internal forces, the resonator body experiences thermal expansion. At the same time, over a short time interval, using a fast camera, it is observed that different parts of the resonator perform accelerated movement at different speeds. Within the flexible (elastic) properties of a copper substance.
Thermal expansion actually happens on a relatively slow time scale of seconds, because it takes time for the metal to heat up.7. Thus, I described the initial boundary conditions. For the sake of simplicity of modeling, I chose such a regime of thermal loads when the small bottom remains motionless, and the large bottom moves rapidly - towards the small bottom, at a speed of 3570 m / s, during a small time interval = 10 μs. (or 1 μs, not important).
The motion of the large end will be much slower than 3570 m/s, otherwise you exceeded the mechanical limits of the object, and it breaks into pieces. The exact velocity is not relevant, but lets go with 10 m/s for convenience.8. Earlier, we agreed that the force of radiation pressure on the large bottom in this case will differ by dp due to the Doppler effect.
Not quite, this only looks at one side of what is happening. While there would be increased radiation pressure on the large end since it is moving towards the EM waves, the resulting EM waves would be Doppler shifted to a higher frequency. That means that on their next reflection from the small end, they will increase the radiation pressure on the small end by the same amount, but obviously in the opposite direction. This is still balanced, and the only thing this accomplishes is moving momentum from the large end to the small end through the EM waves at the speed of light, rather than mechanically through the side walls at the speed of sound.9. Since the small bottom is motionless, the radiation force on it will not change.
Again, no, because the EMwaves hitting it have increased in momentum after being reflected off the large end.10. I conclude that in the indicated small time interval, in comparison with point 3, a “strange” new, unbalanced force will appear in the resonator. Since the sum of radiation pressure forces in this case will differ by a "derivative" from dp.
You conclude wrong. Your conclusion breaks conservation of momentum by claiming an unbalanced force. As I stated before , if you conclude that conservation of momentum is broken it means you made a mistake somewhere. In this case your mistake is what I just pointed out above.11. Since the photon gas (I use this term for brevity) is somehow significantly different from the properties of any gas or liquid, I believe that from the side of the photon gas - at this point in time, a new, unbalanced force will act on the large bottom of the resonator and if the overall drive is granted freedom of movement, this force will force the drive to make a small movement with acceleration. Accurate scales will measure the thrust of an emdrive rocket. The thrust vector may have a direction towards the large bottom.
Several problems with your statements here:
-There actually is a small amount of transfer of momentum, from the walls to the EM waves, but it is much smaller than implied by your incorrect bullet points above. It is easier to explain where this small force comes from in a continuous acceleration than in your example.
-A scale does not fit in with the design of the experiment described. What you actually could do is see the final velocity of the cavity which would be slower (compared to a cavity that was not filled with RF) by an amount to small to have any hope of actually measuring. The difference is solely because of the additional mass the cavity has due to the photons' energy and E=mc^2.
-The direction towards the large end is the opposite of the supposed effect based on experiments (though the best experiments show no measurable effect.)12. Thus, we see that in a small time interval, the EM field that is inside the resonator cavity can cause the cavity to move in space.
No, the EM waves apply a force that resists the motion induced by the externally applied force. The same would happen if you placed a small ball inside the cavity. The total mass of the cavity including the ball would increase, so the total increase in velocity would be smaller for the same momentum transfer.13. Clarification, the effect will manifest itself obviously in a shorter time interval when the reflected (but already changed by the Doppler) photons have not yet reached the small bottom. That is, the time interval is about 10-9 seconds.
Now you are getting to assumptions that actually lead towards the correct answer.14. That is, a photon gas creates a pulse force, with a pulse duration of about 10-9 seconds.
The first problem is that after the 1 ns for the Doppler shifted waves to get from one end of the cavity to the other, the forces are balanced. The total radiation pressure is continuously increasing, but there is no longer a difference between the ends. The next problem is that under the assumptions of the situation you set up, the cavity deformed over that time period. Over a comparable time period, the cavity will un-derform, so what effects do actually accumulate over the time period get undone while the deformation is being reversed. A very careful analysis would should just a very slight bit of extra momentum (directed towards the small end) stored in the EM waves when all is done.
15. But since photons can be reflected many times between the large and small bottoms in the interval of 10 μs, the result of the pulse force should be summed up the work of the pulse force in the interval of 10 μs.16. Thermal loads will cause the movement of the center of mass. This will mask the effect; a resonator with high quality factor is required for detection.
Thermal loads will NOT cause movement of the center of mass for an emDrive sitting on a cart. center of mass shifts due to thermal loads are an error source in experiments such as torsional pendulums where it causes things to no longer be balanced from deformation, or other situations such as where one end is resting on a scale, so only the other end is free to move.17. To clarify the pressure force on the small bottom, when more “violet” photons “arrive” on the small bottom (for the first time), which are already modified in frequency by the Doppler effect on the large bottom - at the initial moment of the time interval from 10-9 seconds. Obviously, the pressure force on the small bottom will also be increased. But since the area of the small and large bottoms is very different, this will not be able to destroy the effect of rocket thrust on the big bottom due to the Doppler effect.
Normally in an emDrive shaped cavity, there is less force on the small end, because some of the reflection happens on the side walls. Your logic here is just a complete failure, because if there was no force on the sidewalls because of some special setup (say you just run this with 2 relatively large mirrors (one bigger than the other for no real reason) and a concentrated laser) you would just be implying that the pressure (force per area) is higher on the "smaller" end so that the force is the same.18. Clarify the likelihood that the side walls of the resonator, due to the curved surface of the large bottom — that there are such photons in the total photon flux — never act on the side walls.
Likelihood of that is zero for an RF resonator. And if you came up with some setup where that was true, it would just mean that there is more pressure on the smaller end than the larger end, so that the forces balance.
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#1491 by Alex_O on 13 Sep, 2019 16:36
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Thank you, I'm on my way to the slow Internet, I agree on all points of your comments and see how to improve the model. figuratively, it is necessary to consider photons. 1 photon flew out of the antenna. He flew to a large bottom that had already begun the movement. Through him a second, he will fly to a small bottom. It seems my model starts here, the difference in pressure on the big bottom before and after the Doppler effect begins. I'll clarify everything on Monday, unless of course I see a still good idea for physics.
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#1492 by RyanC on 13 Sep, 2019 20:23
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Wouldn't it be quicker to build a Starlink sized EM drive demonstrator unit and have it tossed from a F9 during a regular Starlink mission to actually flight test a EM drive in space?
It sounds like the kind of crazy thing Musk would do; especially since the other 59 satellites (or so) in a Starlink mission would pay for the one off crazy experiment. -
#1493 by RotoSequence on 13 Sep, 2019 21:51
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Wouldn't it be quicker to build a Starlink sized EM drive demonstrator unit and have it tossed from a F9 during a regular Starlink mission to actually flight test a EM drive in space?
It sounds like the kind of crazy thing Musk would do; especially since the other 59 satellites (or so) in a Starlink mission would pay for the one off crazy experiment.
I don't think any propellant-less thruster scheme has enough potential left in the tank for SpaceX to dedicate their engineers' time towards trying it. -
#1494 by Monomorphic on 14 Sep, 2019 00:57
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Wouldn't it be quicker to build a Starlink sized EM drive demonstrator unit and have it tossed from a F9 during a regular Starlink mission to actually flight test a EM drive in space?
No, it would not be quicker. There is a tremendous amount of work involved in designing, fabricating, launching and precise tracking of an Emdrive propelled microsat.
Solar power, batteries, communications, and everything else necessary is far more effort than simply building one on the ground and testing it rigorously with known methods.
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#1495 by dustinthewind on 14 Sep, 2019 04:59
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Wouldn't it be quicker to build a Starlink sized EM drive demonstrator unit and have it tossed from a F9 during a regular Starlink mission to actually flight test a EM drive in space?
It sounds like the kind of crazy thing Musk would do; especially since the other 59 satellites (or so) in a Starlink mission would pay for the one off crazy experiment.
Some of them were proposed to work. Others didn't seem to work. Whose would you toss out the airlock? Question is what would make them work if they work in the first place. If we had ones that really worked then Investigate those to see why they work. What if they need air to work? Maybe air to make a sort of cold plasma. Toss them in a vacuum and maybe they stop working.
Other sources were possible thermal hydrodynamic propulsion via heating of air around the cavity. Magnetic torque with the Earth's magnetic field. Thermal baloon lift are all false signal sources that one has to weed through If one could be made to provide a signal above the noise floor or above other possible non-usedul thrust sources, it might help narrow things down but what is really wanted is a physical mechanism for propellantless thrust. You can't maximize something you don't understand. -
#1496 by mwvp on 15 Sep, 2019 02:53
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To ALL. Is there anyone with experience in calculating radiation pressure taking into account the doppler effect?
FYI...
"Cavity Optomechanics"
https://arxiv.org/abs/1303.0733
see fig. 14 pg 20. Consider that a hollow metallic frustrum will have inductive losses that are greater for lower frequencies than higher ones, especially when detuned. So that red-shifted energy will exhaust through a nozzle after delivering momentum to the frustrum. The cavity is anisotropically open to red-shifted energy.
You made a good point about high Q cavities. I don't see how much energy, more than a few milliwatts could be supplied to a superconducting cavity before the field strength would exceed vacuum-breakdown, then arcing and failure. Might make for a milli-newton thruster but not hover-car.
Also, since the cavity is full of radiation-pressure and can detune megahertz/micrometers, nonlinear instabilities would require some clever active measures. Just like the fusion folks have to deal with.
More interesting math can be found in http://onlyspacetime.com/OnlySpacetime.pdf at the end of chapter 1. I reference other works in my earlier posts, such as:
Bradshaw on dispersion in: http://arxiv.org/abs/1005.5467v1
https://forum.nasaspaceflight.com/index.php?topic=41732.msg1674886#msg1674886
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#1497 by Alex_O on 17 Sep, 2019 07:02
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Hello mwvp!...
To ALL. Is there anyone with experience in calculating radiation pressure taking into account the doppler effect?
FYI...
"Cavity Optomechanics"
https://arxiv.org/abs/1303.0733
see fig. 14 pg 20. Consider that a hollow metallic frustrum will have inductive losses that are greater for lower frequencies than higher ones, especially when detuned. So that red-shifted energy will exhaust through a nozzle after delivering momentum to the frustrum. The cavity is anisotropically open to red-shifted energy.
You made a good point about high Q cavities. I don't see how much energy, more than a few milliwatts could be supplied to a superconducting cavity before the field strength would exceed vacuum-breakdown, then arcing and failure. Might make for a milli-newton thruster but not hover-car.
Also, since the cavity is full of radiation-pressure and can detune megahertz/micrometers, nonlinear instabilities would require some clever active measures. Just like the fusion folks have to deal with.
More interesting math can be found in http://onlyspacetime.com/OnlySpacetime.pdf at the end of chapter 1. I reference other works in my earlier posts, such as:
Bradshaw on dispersion in: http://arxiv.org/abs/1005.5467v1
https://forum.nasaspaceflight.com/index.php?topic=41732.msg1674886#msg1674886
Thanks for the nice link. I read the article and noted that the authors did a good job of generalizing. I noticed that examples of mechanical oscillators with a GHz frequency are being discussed. It inspired me a little. I will continue to study the materials on your links, thanks again. In a post below I will try to show a small result of inspiration
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#1498 by Alex_O on 17 Sep, 2019 07:08
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Thank you dear meberbs for a very useful conversation, I will be three days without the Internet, allow me to agree:
Agree would imply that you are agreeing with previous statements I made, but several of your points contradict things I have said. I appreciate you breaking things down step by step like this, it makes it easier to show exactly where you make incorrect assumptions.
..13. Clarification, the effect will manifest itself obviously in a shorter time interval when the reflected (but already changed by the Doppler) photons have not yet reached the small bottom. That is, the time interval is about 10-9 seconds.
Now you are getting to assumptions that actually lead towards the correct answer.
...18. Clarify the likelihood that the side walls of the resonator, due to the curved surface of the large bottom — that there are such photons in the total photon flux — never act on the side walls.
Likelihood of that is zero for an RF resonator. And if you came up with some setup where that was true, it would just mean that there is more pressure on the smaller end than the larger end, so that the forces balance.
Hello dear meberbs, please look at the new model?
I changed the model, used a cylindrical microwave cavity and installed artificial muscles on the outer surface of the cavity. Now the walls of the cavity can make small, independent movements to the right and left due to the operation of the drive according to an arbitrary algorithm. In this way, I built an example of a small worm. The worm compresses, unclenches the muscles, and controls the movement of the end walls of the resonator. In this case, the end walls can move relative to the side wall of the cavity independently.
I also launched a single (for example) microwave photon into the resonator and tuned the cavity to some resonance, I got a microwave cavity with a Q factor.
First I turned on the RF power and waited a bit. Then, he allowed the worm to squeeze / unclench its muscles. I mentally observed changes in the momentum on the walls of the cavity and the microwave photon with an interval of time of the order of 1 nanosecond. I recorded the results of the observations in a table.
I don’t know how it is right, if there is an error in the statement of the problem and the observation method, but it seems to me that I see that in this cavity the radiation pressure on the end walls is always different.
Then I go further in my mind and want to see how my worm is trying to use the difference in radiation pressure on the end walls to move in a given direction.
It seems to me that such an algorithm can be universal for the motion of a spaceship, for example, on the end walls, instead of radiation pressure, it is possible to create dynamic Casimir forces. And using fast switching, "crawl through the vacuum." It's like a submarine of Dr. Harold G. White of EW, but she does not swim, she crawls.
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#1499 by rq3 on 17 Sep, 2019 14:24
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Hello dear meberbs, please look at the new model?
I changed the model, used a cylindrical microwave cavity and installed artificial muscles on the outer surface of the cavity. Now the walls of the cavity can make small, independent movements to the right and left due to the operation of the drive according to an arbitrary algorithm. In this way, I built an example of a small worm. The worm compresses, unclenches the muscles, and controls the movement of the end walls of the resonator. In this case, the end walls can move relative to the side wall of the cavity independently.
I also launched a single (for example) microwave photon into the resonator and tuned the cavity to some resonance, I got a microwave cavity with a Q factor.
First I turned on the RF power and waited a bit. Then, he allowed the worm to squeeze / unclench its muscles. I mentally observed changes in the momentum on the walls of the cavity and the microwave photon with an interval of time of the order of 1 nanosecond. I recorded the results of the observations in a table.
I don’t know how it is right, if there is an error in the statement of the problem and the observation method, but it seems to me that I see that in this cavity the radiation pressure on the end walls is always different.
Then I go further in my mind and want to see how my worm is trying to use the difference in radiation pressure on the end walls to move in a given direction.
It seems to me that such an algorithm can be universal for the motion of a spaceship, for example, on the end walls, instead of radiation pressure, it is possible to create dynamic Casimir forces. And using fast switching, "crawl through the vacuum." It's like a submarine of Dr. Harold G. White of EW, but she does not swim, she crawls.
Aha! The old "swimming in vacuum" trick!
https://dspace.mit.edu/handle/1721.1/6706
. I also spend time on Google translating from Russian into English and correcting translation errors.