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 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 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
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 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.
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.
What I remember from physics class makes me think this isn't viable.
If you have sound moving through the tube, you have energy pushing the sound. Either you have to keep the whole tube 'humming' or you have to send people off in a blast wave. With the humming idea, you might be able to create vacuums that travel around the tube at the speed of sound (sound works by changing the density of air, oscillating from high pressure to low pressure), and then you can move vehicles around the tube at the speed of sound with very little drag.
So then you need some way to keep the vehicles floating, and you need to get them to the speed of sound in the first place (rail gun?). I'm going to pretend that we have a cheap way to do both of those things.
So, how expensive would it be to keep 100s of miles of hyperloop humming with a sound powerful enough to create vacuums large enough to fit transportation units in? Even if you are only using cars large enough to hold 1 person and a suitcase, you are going to need a lot of energy powering the sound waves throughout the tube.
You might be able to do some acoustics-like engineering to keep the sound loud at little energy cost, but I don't think that solar power above the tunnel is going to be enough. Using this model, Musk would need a handful of technological advances up his sleeve.
So I think the big 'secret' that makes a hyperloop viable is not this one. Then again, with the Tesla and his space adventures, he has had to deal with at least a handful of difficult obstacles. So maybe he is expecting to develop multiple technologies to make this viable.
Seriously? Compared to that design evacuating the tunnel would make a lot of sense, as would going a lot slower than the speed of sound.
Now when Elon says it's not an evacuated tunnel, and also (indirectly) that you'll be traveling more or less exactly at the speed of sound, I'm leaning quite heavily towards the OP.
Someone should build a prototype of such a tube and see if it's efficient. The mystery around Hyperloop generates a lot of ideas that should be tested. Railroad infrastructures are ageing, maybe some tuberoads can replace them.
I remember doing the math in my undergraduate physics studies. Air molecules actually do not move very far when a vibration (ie. sounds) goes through them. Amazingly, high frequency sounds move air back and forth only a few angstroms.
I can't find a link describing the calculation. This link talks about how the change in pressure is equivalent to "140 molecules for every million molecules"
http://www.silcom.com/~aludwig/musicand.htm
So there is no way you are going to create a bubble of vacuum!
Not trying to create a bubble of vacuum (though that was my old idea =).. then I realized what you lost gained by low density you paid for in high velocity).
Also, the idea here isn't involving high frequency sound.
I think the best you could do would be to stay near the trailing end of the pressure wave. This would be where the air was moving (slightly) in the same direction as your travel. You would also travel through the lowest density.
But I suspect you'd always be better off by simply evacuating the tube as much as possible.
Or possibly there is a medium other than air being considered, one in which the speed of sound was much lower at a given density. Perhaps interesting things could happen if the working fluid was a refrigerant and the sound wave was intense enough to induce a phase change cycle.
I'm confused by this... If the air molecules are staying roughly still, but the density of the air surrounding the vehicle rises by a factor of n, isn't the vehicle colliding with n times as many particles as it would have otherwise? How is this more efficient?
Is the velocity in the drag equation relative to the vehicle, or to a stationary frame of reference?
Edit: Or is the point that the velocity of the air particles within the density peak is at its maximal forward-traveling rate before they start to loop back around and form their ellipse?
I'm starting to think Elon has absolutely nothing planned, and just wanted to see what everyone thought he was doing, to help bring about all these awesome ideas for high speed travel :)
I think the problem with that idea is you have to keep the superconductor very cold, which might be too expensive for large objects that need to levitate for 30 minutes.
Sorry, let me clarify your statement: You spent 4 hours in the airport (or getting there, parking, getting sodomized by security) and 1 hour flying. Then another 30-60 minutes disembarking. So you spent around 6 hours in transit from SF to LA.
6 hours compared to 30 minutes (or more likely, 1.5 hours including the necessary boarding / unboarding) is a VAST difference.
Sound: a vacuum and a high pressure alternating ... Using wind would be far cheaper and better I think :-)
I mean really really low sound frequencies are the same anyway. (As far as my physics go)
[+] [-] jasallen|12 years ago|reply
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.
[+] [-] cma|12 years ago|reply
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).
[+] [-] unknown|12 years ago|reply
[deleted]
[+] [-] hotpockets|12 years ago|reply
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.
[+] [-] redwood|12 years ago|reply
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
[+] [-] geon|12 years ago|reply
[+] [-] smoyer|12 years ago|reply
[+] [-] jlgreco|12 years ago|reply
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.
[+] [-] fennecfoxen|12 years ago|reply
"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?
[+] [-] JulianMorrison|12 years ago|reply
[+] [-] Lambdanaut|12 years ago|reply
[+] [-] ddeck|12 years ago|reply
[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
[+] [-] InclinedPlane|12 years ago|reply
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.
[+] [-] Kurtz79|12 years ago|reply
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.
[+] [-] shoyer|12 years ago|reply
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.
[+] [-] cma|12 years ago|reply
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...
[+] [-] gpsarakis|12 years ago|reply
[+] [-] shoyer|12 years ago|reply
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
[+] [-] cma|12 years ago|reply
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.
[+] [-] aidenn0|12 years ago|reply
Musk has said on the record that it's not an evacuated tube.
[+] [-] whiddershins|12 years ago|reply
[+] [-] cma|12 years ago|reply
[+] [-] w_t_payne|12 years ago|reply
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.
[+] [-] redwood|12 years ago|reply
[+] [-] benjamincburns|12 years ago|reply
[+] [-] joshontheweb|12 years ago|reply
[+] [-] hotpockets|12 years ago|reply
[+] [-] Taek|12 years ago|reply
If you have sound moving through the tube, you have energy pushing the sound. Either you have to keep the whole tube 'humming' or you have to send people off in a blast wave. With the humming idea, you might be able to create vacuums that travel around the tube at the speed of sound (sound works by changing the density of air, oscillating from high pressure to low pressure), and then you can move vehicles around the tube at the speed of sound with very little drag.
So then you need some way to keep the vehicles floating, and you need to get them to the speed of sound in the first place (rail gun?). I'm going to pretend that we have a cheap way to do both of those things.
So, how expensive would it be to keep 100s of miles of hyperloop humming with a sound powerful enough to create vacuums large enough to fit transportation units in? Even if you are only using cars large enough to hold 1 person and a suitcase, you are going to need a lot of energy powering the sound waves throughout the tube.
You might be able to do some acoustics-like engineering to keep the sound loud at little energy cost, but I don't think that solar power above the tunnel is going to be enough. Using this model, Musk would need a handful of technological advances up his sleeve.
So I think the big 'secret' that makes a hyperloop viable is not this one. Then again, with the Tesla and his space adventures, he has had to deal with at least a handful of difficult obstacles. So maybe he is expecting to develop multiple technologies to make this viable.
[+] [-] beambot|12 years ago|reply
[+] [-] bjornsing|12 years ago|reply
Now when Elon says it's not an evacuated tunnel, and also (indirectly) that you'll be traveling more or less exactly at the speed of sound, I'm leaning quite heavily towards the OP.
[+] [-] bencollier49|12 years ago|reply
[+] [-] rorrr2|12 years ago|reply
Riding the pressure peak at exactly the speed of sound makes a lot more sense.
[+] [-] antninja|12 years ago|reply
[+] [-] throwmeaway33|12 years ago|reply
I can't find a link describing the calculation. This link talks about how the change in pressure is equivalent to "140 molecules for every million molecules" http://www.silcom.com/~aludwig/musicand.htm
So there is no way you are going to create a bubble of vacuum!
[+] [-] geon|12 years ago|reply
And you don't want low pressure, but high, so the air speed is low. Drag is proportional to the density, but proportional to the square of the speed.
[+] [-] cma|12 years ago|reply
Also, the idea here isn't involving high frequency sound.
[+] [-] hotpockets|12 years ago|reply
[+] [-] marshray|12 years ago|reply
But I suspect you'd always be better off by simply evacuating the tube as much as possible.
Or possibly there is a medium other than air being considered, one in which the speed of sound was much lower at a given density. Perhaps interesting things could happen if the working fluid was a refrigerant and the sound wave was intense enough to induce a phase change cycle.
[+] [-] benjamincburns|12 years ago|reply
Is the velocity in the drag equation relative to the vehicle, or to a stationary frame of reference?
Edit: Or is the point that the velocity of the air particles within the density peak is at its maximal forward-traveling rate before they start to loop back around and form their ellipse?
[+] [-] icegreentea|12 years ago|reply
[+] [-] Aaronneyer|12 years ago|reply
[+] [-] opminion|12 years ago|reply
[+] [-] stcredzero|12 years ago|reply
[+] [-] acd|12 years ago|reply
[+] [-] Taek|12 years ago|reply
[+] [-] jjindev|12 years ago|reply
In that context, I don't really see a transformational improvement going from one 1 hour to 0.5 hours.
[+] [-] nakedrobot2|12 years ago|reply
6 hours compared to 30 minutes (or more likely, 1.5 hours including the necessary boarding / unboarding) is a VAST difference.
[+] [-] jeffasinger|12 years ago|reply
[+] [-] Qantourisc|12 years ago|reply
[+] [-] unknown|12 years ago|reply
[deleted]