Key passages from Elon Musk’s promised reveal about the Hyperloop, his idea for a clean, high-speed fifth mode of transport:

“So What is Hyperloop Anyway?

Short of figuring out real teleportation, which would of course be awesome (someone please do this), the only option for super fast travel is to build a tube over or under the ground that contains a special environment. This is where things get tricky.

At one extreme of the potential solutions is some enlarged version of the old pneumatic tubes used to send mail and packages within and between buildings.

You could, in principle, use very powerful fans to push air at high speed through a tube and propel people-sized pods all the way from LA to San Francisco. However, the friction of a 350 mile long column of air moving at anywhere near sonic velocity against the inside of the tube is so stupendously high that this is impossible for all practical purposes.

Another extreme is the approach, advocated by Rand and ET3, of drawing a hard or near hard vacuum in the tube and then using an electromagnetic suspension. The problem with this approach is that it is incredibly hard to maintain a near vacuum in a room, let alone 700 miles (round trip) of large tube with dozens of station gateways and thousands of pods entering and exiting every day. All it takes is one leaky seal or a small crack somewhere in the hundreds of miles of tube and the whole system stops working.

However, a low pressure (vs. almost no pressure) system set to a level where standard commercial pumps could easily overcome an air leak and the transport pods could handle variable air density would be inherently robust.

Overcoming the Kantrowitz Limit

Whenever you have a capsule or pod (I am using the words interchangeably) moving at high speed through a tube containing air, there is a minimum tube to pod area ratio below which you will choke the flow. What this means is that if  the walls of the tube and the capsule are too close together, the capsule will behave like a syringe and eventually be forced to push the entire column of air in the system. Not good.

Nature’s top speed law for a given tube to pod area ratio is known as the Kantrowitz limit. This is highly problematic, as it forces you to either go slowly r have a super huge diameter tube. Interestingly, there are usually two solutions to the Kantrowitz limit – one where you go slowly and one where you go really, really fast.

The latter solution sounds mighty appealing at first, until you realize that going several thousand miles per hour means that you can’t tolerate even wide turns without painful g loads. For a journey from San Francisco to LA, you will also experience a rather intense speed up and slow down. And, when you get right down to it, going through transonic buffet in a tube is just fundamentally a dodgy prospect.

Both for trip comfort and safety, it would be best to travel at high subsonic speeds for a 350 mile journey. For much longer journeys, such as LA to NY, it would be worth exploring super high speeds and this is probably technically
feasible, but, as mentioned above, I believe the economics would probably favor a supersonic plane.

The approach that I believe would overcome the Kantrowitz limit is to mount an electric compressor fan on the nose of the pod that actively transfers high pressure air from the front to the rear of the vessel. This is like having a pump
in the head of the syringe actively relieving pressure.

It would also simultaneously solve another problem, which is how to create a low friction suspension system when traveling at over 700 mph. Wheels don’t work very well at that sort of speed, but a cushion of air does. Air bearings,
which use the same basic principle as an air hockey table, have been demonstrated to work at speeds of Mach 1.1 with very low friction. In this case, however, it is the pod that is producing the air cushion, rather than the tube, as it is important to make the tube as low cost and simple as possible. That then begs the next question of whether a battery can store enough energy to power a fan for the length of the journey with room to spare. Based on our calculations, this is no problem, so long as the energy used to accelerate the pod is not drawn from the battery pack.

This is where the external linear electric motor comes in, which is simply a round induction motor (like the one in the Tesla Model S) rolled flat. This would accelerate the pod to high subsonic velocity and provide a periodic reboost roughly every 70 miles. The linear electric motor is needed for as little as ~1% of the tube length, so is not particularly costly.”