Relative to the frame of reference, it seems to me the sparse particles would be travelling closer to the speed of the craft than the dense particles.
The "density front" travels at exactly the speed of sound, but it consists of nearly static particles (not static from the frame of reference, from the frame of reference they are moving backward at nearly the speed of sound), these static particles are the relevant V.
The sparse particles just in front of the dense ones are accelerating to get more sparse. From the perspective of the reference frame, they are therefore moving 'backward' at slightly less than the speed of sound, making there relative velocity closer to that of the reference frame. So lower density and lower velocity. and that doesn't even account for additional compression which I don't even know enough to do armchair reasoning on.
So, I'm the farthest thing from an expert, but this is why it doesn't seem to make sense to me.
In all seriousness though I'm going through your post to see if you've found a gaping problem =). I don't think there can be different density velocity ratios at any point of displacement in the wave's reference frame because the same net number of particles has to pass through each point or you start making a permanent buildup on one side or the other of that point, which you can't do because in the reference frame of the still air that point is moving at the speed of sound.
A moving point passes by the same number of unique particles at the speed of sound as it would if it were going the speed of turtle (if you ignore thermal dispersion).
"the same net number of particles has to pass through each point"
Agreed: the corollary to the "the sparse particles just in front of the dense ones" is the "sparse ones just behind the next wave of dense ones", which are, in fact, decelerating, or moving backward even closer to the speed of sound than the dense ones relative to the reference frame. So individual particles oscillate back and forth, but net effect is no movement (to the reference frame of the average speed of the particles, which is a third reference frame :-) )
Surely that animation exaggerates how little net molecule displacement occurs. I'm not sure what would cause many of the molecules to reverse direction while in the low-pressure part of the wave.
The pressure (also density) maximum is the velocity maximum.
Shouldn't you put the front of the craft at the pressure minimum and the back of the craft at the pressure maximum? Then the wave would be pushing you along.
The wave won't push you along at the speed of sound; at any point on the wave from the wave's reference frame (the speed of sound) there is a net flow of particles heading the opposite direction, unless your amplitude gets so high that average particle velocity in some places starts to exceed the speed of sound, in which case you don't have a sound wave anymore I don't think.
The difference between the dense particles just behind the craft with maximal drag and sparse particles just in front, means a pressure differential pushing the vehicle forward
The guy launches rockets and builds electric sports cars ... I tend to think he has a plan. Allowing the speculation to persist might improve that plan but I suspect it was viable on it's own (and perhaps the waiting period was simply to allow some small scale testing to occur).
To be honest that is what my money was originally on.. that or this just being some sort of self-constructed mythology for himself, sort of like free wirelessly transmitted power was for Tesla perhaps (though more 'intentionally' and less 'mistakenly/delusionally').
As time goes on he keeps getting more and more specific with his deadline for going public though. First it was "eventually", then it was "sometime after Tesla is profitable", then it was "sometime later this year", now we've actually got a date to look forward to. I now think that he actually is thinking of something.
You know... this remark got me thinking, and it turns we've been here before as a society, with remarkably similar technology (superficially, at least) and technologists hyping it up a little. Look up Beach Pneumatic Transit - the first New York City subway, in a tube, powered by compressed air. Which is kind of cool: http://en.wikipedia.org/wiki/Beach_Pneumatic_Transit
"A tube, a car, a revolving fan! Little more is required. The ponderous locomotive, with its various appurtenances, is dispensed with, and the light aerial fluid that we breathe is the substituted motor!" -- http://www.columbia.edu/~brennan/beach/chapter2.html
Trains in tubes and promises of dramatic changes in the way people think of transportation! People thought they would be building tubes all over the countryside to move trains around... and then they went and invented the electric-multiple-unit subway train which took off instead. :P
Somewhere, someone is reading this over a data connection going over some fiber that has been pulled through an old unused pneumatic tube mail system that was installed in a subway tunnel.
Or even if he does have a design planned, he might consider "creating other usable designs" as a deliberate side effect of stirring up speculation. He seems to be motivated by saving the world in general more than personally making a lot of money.
All this speculation reminds me of the hype surrounding the Segway launch. I recall it being being touted as a game-changer, a revolution in transportation that would change the way cities were built...
[The Segway] will be to the car what the car was to the horse and buggy (Dean Kamen)[1]
John Doerr, predicted Segway would rack up $1 billion in sales faster than any company in history [1]
The Segway was demonstrably inferior to commonplace alternatives on simple metrics alone: speed, capacity, cost, safety, comfort.
It was only hyped because it was "cool".
If the hyperloop, however it works, can duplicate the capabilities of a high speed rail system in terms of passenger throughput, speed, and waiting time and do so safely at much lower cost then even if was the uncoolest thing in the world it would still be of immense practical benefit.
> The Segway was demonstrably inferior to commonplace alternatives on simple metrics alone: speed, capacity, cost, safety, comfort.
Metrics are like statistics, in that they can also mislead. It's really about the experience in specific contexts.
> It was only hyped because it was "cool".
Actually, it failed because it just looked dorky. (Which Steve Jobs predicted in his secret meeting with Dean Kamen.) Good tech badly marketed sometimes still doesn't sell.
The Segway hype was so generic it could have been anything: it didn't offer any concrete metric to justify it.
A system allowing to travel LA to SF in 30 minutes, without the hassle involved with air travel, WOULD be revolutionary, regardless of how good or bad is the marketing department of its company.
No one predicted this would be the problem, and indeed most people still haven't come to Graham's conclusion. In that sense, concrete metrics are irrelevant. The hyperloop is just as likely a priori to have some sort of similar fatal flaw. This is the problem with getting too excited about any new particular device; there's too much that can go wrong between zero and revolutionary.
The author appears to have confused group velocity (the speed of the wave) with particle velocity (the speed of the air molecules). This is a very basic notion of how waves work -- the waves move, not the medium.
In this case, the wave (and the vehicle) would be moving at the speed of sound, but the air particles they hit wouldn't. They're basically still stationary. There is no magical force to bring them up to the speed of sound before they hit the vehicle. Hence, the drag is not reduced.
I'm a physicist, but by no means an expert on sound. There are more details on how sound actually works on this page: http://mysite.du.edu/~jcalvert/waves/soundwav.htm. A relevant quote: "v [the particle velocity] is much less than the phase [wave] velocity of sound" (note: phase and group velocity are equal for sound in air).
You read it wrong; at no point were any particles in the wave assumed to be going the speed of sound; that's why when you look from the vehicles reference you see a standing wave but at every point on it particles are still flowing towards the vehicle. The picture says it is in a sound-speed reference frame, but it probably confused you if you didn't read that.
At no point is the air doing anything but apply drag to the vehicle's movement; there is just a sweet spot to minimize drag, but it isn't minimized to zero.
Read through this thread a bit and you'll see me talking about the exact same difference of propagation of a disturbance vs displacement/velocity of individual particles...
Just some info: Transonic/supersonic and near-speed-of-sound aerodynamics differ from traditional low velocity aerodynamics (I think the threshold is approximately 0.25Vs, so up to 1/4 of the speed of sound, I am a bit rusty on that). After that point you can't ignore compressibility phenomena, meaning that the density is no longer a constant, but also becomes a variable. You may be able to reduce drag by going very high in the atmosphere where the air is very thin (10^-6). Speed of sound also is an equation of the density and the temperature.
This is an intriguing proposal, but one that I think it ultimately flawed. Once a wave is strong enough for there be to appreciable density differences (NOT the usual case for sound waves), the usual wave equation for sound does not apply [1]. In the case of such "Very Strong Sound Waves", you have a non-linear wave equation and thus the shape of your wave is no longer fixed as it moves. Eventually, you end up with shock wave, where the front of your wave is a discontinuity.
Why is this problematic? Well, once you have a shock wave (e.g., a wave crashing on the beach), the physics gets a lot more complicated. You are basically riding an explosion in a tube.
At this point, it no longer safe to me to neglect factors like dissipation. Your shock wave is going to heat up the air and eventually fizzle out. If you want to keep it going, you'll need to be continually supplying tremendous amounts of energy at exactly the right time along your tube. You'll also have to be continually cooling or cycling the air to relieve the waste energy.
To me, it seems a lot simpler and more reliable (not to mention safer) to simply evacuate your tube, which, I believe, is the original hyperloop idea.
That's a great link.. should help see how far this could be practically taken.
When the wave is very strong the heat generated by compression isn't dissipated adiabatically the wave starts losing energy to waste heat; if you increase the wavelength you again move back to the adiabatic regime. How far can you take it? I don't know, I'd like to see some numbers and that's probably what I'd work on next if I keep looking into this.. probably won't until after Elon's announcement.
For extreme cases of high-amplitude waves where the particle velocity itself is getting close to the speed of sound, I definitely don't know what all happens, but somewhere in the write-up or comments here I at least had going that far as a bound on how far you could push things before you didn't really even have sound waves anymore.
"To me, it seems a lot simpler and more reliable (not to mention safer) to simply evacuate your tube, which, I believe, is the original hyperloop idea."
Musk has said on the record that it's not an evacuated tube.
Presumably the pressure wave is maintained by a continuous array of big-ass subwoofers along the whole length of the tube - If this is the case, then keeping the noise pollution down will be a bit of a challenge - unless some sort of active-noise cancellation technology is used for the outside.
Hmmm... This should not be too tricky, since you are generating the original signal yourself, but if one of the exterior noise-cancellation speakers breaks down - it's gonna be LOUD.
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The "density front" travels at exactly the speed of sound, but it consists of nearly static particles (not static from the frame of reference, from the frame of reference they are moving backward at nearly the speed of sound), these static particles are the relevant V.
The sparse particles just in front of the dense ones are accelerating to get more sparse. From the perspective of the reference frame, they are therefore moving 'backward' at slightly less than the speed of sound, making there relative velocity closer to that of the reference frame. So lower density and lower velocity. and that doesn't even account for additional compression which I don't even know enough to do armchair reasoning on.
So, I'm the farthest thing from an expert, but this is why it doesn't seem to make sense to me.
http://www.acs.psu.edu/drussell/Demos/waves/Lwave-v8.gif
In all seriousness though I'm going through your post to see if you've found a gaping problem =). I don't think there can be different density velocity ratios at any point of displacement in the wave's reference frame because the same net number of particles has to pass through each point or you start making a permanent buildup on one side or the other of that point, which you can't do because in the reference frame of the still air that point is moving at the speed of sound.
A moving point passes by the same number of unique particles at the speed of sound as it would if it were going the speed of turtle (if you ignore thermal dispersion).
Agreed: the corollary to the "the sparse particles just in front of the dense ones" is the "sparse ones just behind the next wave of dense ones", which are, in fact, decelerating, or moving backward even closer to the speed of sound than the dense ones relative to the reference frame. So individual particles oscillate back and forth, but net effect is no movement (to the reference frame of the average speed of the particles, which is a third reference frame :-) )
Deleted Comment
Shouldn't you put the front of the craft at the pressure minimum and the back of the craft at the pressure maximum? Then the wave would be pushing you along.
The difference between the dense particles just behind the craft with maximal drag and sparse particles just in front, means a pressure differential pushing the vehicle forward
As time goes on he keeps getting more and more specific with his deadline for going public though. First it was "eventually", then it was "sometime after Tesla is profitable", then it was "sometime later this year", now we've actually got a date to look forward to. I now think that he actually is thinking of something.
"A tube, a car, a revolving fan! Little more is required. The ponderous locomotive, with its various appurtenances, is dispensed with, and the light aerial fluid that we breathe is the substituted motor!" -- http://www.columbia.edu/~brennan/beach/chapter2.html
Trains in tubes and promises of dramatic changes in the way people think of transportation! People thought they would be building tubes all over the countryside to move trains around... and then they went and invented the electric-multiple-unit subway train which took off instead. :P
Better luck this time?
[The Segway] will be to the car what the car was to the horse and buggy (Dean Kamen)[1]
John Doerr, predicted Segway would rack up $1 billion in sales faster than any company in history [1]
Let's hope the Hyperloop fares better.
[1] http://www.wired.com/wired/archive/11.03/segway.html
It was only hyped because it was "cool".
If the hyperloop, however it works, can duplicate the capabilities of a high speed rail system in terms of passenger throughput, speed, and waiting time and do so safely at much lower cost then even if was the uncoolest thing in the world it would still be of immense practical benefit.
Metrics are like statistics, in that they can also mislead. It's really about the experience in specific contexts.
> It was only hyped because it was "cool".
Actually, it failed because it just looked dorky. (Which Steve Jobs predicted in his secret meeting with Dean Kamen.) Good tech badly marketed sometimes still doesn't sell.
A system allowing to travel LA to SF in 30 minutes, without the hassle involved with air travel, WOULD be revolutionary, regardless of how good or bad is the marketing department of its company.
http://www.paulgraham.com/segway.html
No one predicted this would be the problem, and indeed most people still haven't come to Graham's conclusion. In that sense, concrete metrics are irrelevant. The hyperloop is just as likely a priori to have some sort of similar fatal flaw. This is the problem with getting too excited about any new particular device; there's too much that can go wrong between zero and revolutionary.
In this case, the wave (and the vehicle) would be moving at the speed of sound, but the air particles they hit wouldn't. They're basically still stationary. There is no magical force to bring them up to the speed of sound before they hit the vehicle. Hence, the drag is not reduced.
I'm a physicist, but by no means an expert on sound. There are more details on how sound actually works on this page: http://mysite.du.edu/~jcalvert/waves/soundwav.htm. A relevant quote: "v [the particle velocity] is much less than the phase [wave] velocity of sound" (note: phase and group velocity are equal for sound in air).
Edit: This criticism is not right; see below.
At no point is the air doing anything but apply drag to the vehicle's movement; there is just a sweet spot to minimize drag, but it isn't minimized to zero.
Read through this thread a bit and you'll see me talking about the exact same difference of propagation of a disturbance vs displacement/velocity of individual particles...
Deleted Comment
Why is this problematic? Well, once you have a shock wave (e.g., a wave crashing on the beach), the physics gets a lot more complicated. You are basically riding an explosion in a tube.
At this point, it no longer safe to me to neglect factors like dissipation. Your shock wave is going to heat up the air and eventually fizzle out. If you want to keep it going, you'll need to be continually supplying tremendous amounts of energy at exactly the right time along your tube. You'll also have to be continually cooling or cycling the air to relieve the waste energy.
To me, it seems a lot simpler and more reliable (not to mention safer) to simply evacuate your tube, which, I believe, is the original hyperloop idea.
[1] http://mysite.du.edu/~jcalvert/waves/soundwav.htm#H
When the wave is very strong the heat generated by compression isn't dissipated adiabatically the wave starts losing energy to waste heat; if you increase the wavelength you again move back to the adiabatic regime. How far can you take it? I don't know, I'd like to see some numbers and that's probably what I'd work on next if I keep looking into this.. probably won't until after Elon's announcement.
For extreme cases of high-amplitude waves where the particle velocity itself is getting close to the speed of sound, I definitely don't know what all happens, but somewhere in the write-up or comments here I at least had going that far as a bound on how far you could push things before you didn't really even have sound waves anymore.
Musk has said on the record that it's not an evacuated tube.
Hmmm... This should not be too tricky, since you are generating the original signal yourself, but if one of the exterior noise-cancellation speakers breaks down - it's gonna be LOUD.