July 28, 2013

Hyperloop lets you travel on a resonant acoustic wave

Elon Musk is a fascinating guy, and his Hyperloop concept equally so. Now that the details have started trickling out, almost in the form of a riddle, I can't help speculating on what it is.

So, in riddle form:
It takes you from LA to SF in 30 minutes,
it leaves when you arrive,
it can store energy over many hours or even days,
it can't crash,
Elon Musk calls it a "Hyperloop" and
it's not an evacuated tunnel. What is it?

The best speculation I've seen so far is Charles Alexander's. My guess is a variation on the same theme: Elon Musk's Hyperloop is a double tunnel connected in a loop, designed to resonate acoustically at a low frequency with "standing waves" traveling around the loop, each wave capable of carrying a small capsule with goods or passengers at almost the speed of sound.

My knowledge of acoustics is far too rudimentary to go into the physics (or even feasibility) of this design, but my gut tells me that it should be possible to generate standing waves even in a very long pipe or tunnel, and it's well known that acoustic waves can be used to exert a force on an object. The video below shows a beautiful example, albeit on a significantly smaller scale.

As the term 'standing waves' implies these are not ideal for travel. But when you connect the ends of the tunnel into a loop you remove the edge conditions on the wave equation and I would not be surprised if there are then solutions with similar energy preserving characteristics as a standing wave, but where the wave fronts instead travel along the tunnel at just about any speed up to the speed of sound. Imagine the droplets in the video being capsules carrying goods and people, and instead of levitating, being pushed through a tube at almost the speed of sound. That's what I think the Hyperloop is.

Again, I haven't made a single calculation to verify this design is even possible. Instead I will prove my case in prose!

It takes you from LA to SF in 30 minutes

This means you must be traveling at about the speed of sound. Let's say 90% of the speed of sound, pushed along by a traveling resonant wave going around the Hyperloop.

(It could be that there's a pure traveling wave solution to the wave equation with favorable energy preservation characteristics. My gut however arrived at this design by first imagining a standing wave and then slowly phase shifting it up to speed, while fulfilling the wave equation. It therefore tells me something weird could happen as velocity approaches the speed of sound.)

It leaves when you arrive

Clearly, if it's a standing wave then you'll have HZ departures a second to choose from. No waiting at the station. Just crawl into a capsule and be catapulted up to speed before entering the Hyperloop.

It can store energy over many hours or even days

This is what gave it all away. Just kidding, but there aren't that many designs that can store energy for a longish time. Here it would take some time to build up the resonant standing wave and that would in effect be a form of energy store. My gut tells me it's not entirely impossible that you could build up wave energy during the day using solar and use it during the night.

But again, I could be completely off; a combination of gut feeling and prosaic elegance is not certain to lead to revolutionary transportation system design.

It can't crash

Steering of course would be trivial. But also, if there was ever a terror attack or something like that the tunnel would be opened up to the outside atmosphere. That would immediately ruin the resonance and all capsules should come to a screeching halt. This sounds remarkably safe for a "train" traveling at near the speed of sound: if there's any problem with the "rails" up ahead the "cars" would be notified at twice the speed of sound, in order of distance to the break, and will automatically lose power.

Elon Musk calls it a "Hyperloop"

Elon Musk is a smart guy, and super logical. I'm willing to bet he would not call it a "loop" if it wasn't, or if that fact was not important to the functioning of the system. This is one of few designs I can think of where the loop property is essential. You can't have a traveling resonant wave without it.

UPDATE 28/7: After the discussion on Hacker News I'd like to clarify that
  1. the reason it might be better to push capsules along with a sort of acoustic propulsion like this is of course that it may require less energy than overcoming the air resistance with some other method of propulsion, and/or be cheaper to build,
  2. using a "rapidly phase shifting standing wave" would avoid having to travelling at exactly the speed of sound (as in Charles' proposal), which my gut tells me would be beneficial because otherwise you'd likely have supersonic airflow somewhere over the craft and that usually ruins efficiency, and finally
  3. the energy economics of a system like this would of course depend heavily on the rate of energy dispersion along the tunnel, which would depend heavily on the stiffness of the tunnel wall (and therefore difficult to calculate), but my gut tells me that low frequency sound e.g. from blasts of various kinds sometimes travel several times around the earth, and that implies that propagation characteristics could be quite good.
I rest my case.

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