Saturday, December 11, 2021

Is the Hyperloop just Hype?

[This is a transcript of the video embedded below. Some of the explanations may not make sense without the animations in the video.]

A few weeks ago I talked about hypersonic flight and why that doesn’t make sense to me. A lot of you asked what’s with Elon Musk’s hyperloop. Does it make any more sense to push high speed trains through vacuum tubes? Can we maybe replace flights with hyperloops? And what’s a hyperloop in the first place? That’s what we’ll talk about today.

As I told you in my previous video, several companies have serious plans to build airplanes that fly more than five times the speed of sound. But physics gets in the way. At such high speed, air resistance rises rapidly. Even if you manage to prevent the plane from melting or simply falling into pieces, you still need a lot of fuel to counter the pressure of the atmosphere. You could instead try flying so high up that the atmosphere is incredibly thin. But you have to get there in the first place, and that too consumes a lot of fuel.

So why don’t we instead build airtight tubes, pump as much air out of them as possible, and then accelerate passenger capsules inside until they exceed the speed of sound? That’s the idea of the “hyperloop” which Elon Musk would like to see become reality. He is a busy man, however, so he made his take on the idea available open source and hopes someone else does it.

The idea of transporting things by pushing them through tubes isn’t exactly new. It’s been used since the eighteenth century to transport small goods and mail. You still find those tube systems today in old office buildings or in hospitals.

In 1908, Joseph Stoetzel, an inventor from Chicago sent his own child through such a tube to prove it was safe. Yeah I’m not sure what ethics committees would say about that today.

The idea to create vacuum in a tube and put a train inside is also not new. It was proposed already in 1904 by the engineer and physicist Robert Goddard, who called it the “vactrain”.

The quality of a vacuum can be measured either in pressure or in percent. A zero percent vacuum is no vacuum, so just standard atmospheric pressure. A one hundred percent vacuum would be no air at all. An interest group in Switzerland has outlined a plan to build a network of high speed trains that would use tunnels with a 93 percent vacuum in which trains could reach about 430 kilometers per hour. That’s about 270 miles per hour if you’re American or about one point four times 10 to the 9 hands per fortnight if you’re British.

It doesn’t look like the Swiss plan has much of a chance to become reality, but about 10 years ago Elon Musk put forward his plan for the hyperloop. Its first version should reach about 790 miles per hour, which is just barely above the speed of sound. But you should think of it as a proof of concept. If it works for reaching the speed of sound, you can probably go above that too. Once you’ve removed the air, speed is really far less of a problem.

Hyperloop is not the name of a company, but the name for the conceptual idea, so there are now a number of different companies trying to turn the idea into reality. The first test for the hyperloop with passengers took place last year with technology from the company Virgin Hyperloop. But there are other companies working on it too, for example Hyperloop Transportation Technologies which is based in California, or TransPod which is based in Canada.

Why the thing’s called the hyperloop to begin with is somewhat of a mystery, probably not because it’s hype going around in a loop. More likely because it should one day reach hypersonic speeds and go in a loop, maybe around the entire planet. Who knows.

Elon did his first research on the hyperloop using a well-known rich-man’s recipe: let others do the job for free. From 2015 to 2019 Musk’s company Space X sponsored a competition in which teams presented their prototypes to be tested in a one kilometer tube. All competitions were won by the Technical University of Munich, and their design served as the base for further developments.

So what are the details of the hyperloop? In 2013 Elon Musk published a white paper called “Hyperloop Alpha” in which he proposed that the capsules would carry 28 passengers each through a 99.9 percent vacuum, that’s about 100 Pascal, and they would be levitated by air-cushions. The idea was that you suck in the remaining air in the tunnel from the front of the capsule and blow it out at the bottom.

This sounds good at first, but that’s where the technical problems begin. If you crunch the numbers, then the gap which the air-cushion creates between the bottom of the capsule and the tube is about one millimeter. This means if there’s any bump or wiggle or two people stand up to go to the loo at the same time, the thing’s going to run into the ground. That’s not good. This is why the companies working on the hyperloop have abandoned the air cushion idea and instead go for magnetic levitation. The best way to achieve the strong fields necessary for magnetic levitation is to use superconducting magnets.

The downside is that they need to be cooled with expensive cryogenic systems, but magnetic levitation can create a gap of about ten centimeters between the passenger capsule and the tunnel which should be enough to comfortably float over all bumps and wiggles.

But there are lots of other technical problems to solve and they’re all interconnected. This figure from Virgin Hyperloop explains it all in one simple diagram. Just in case that didn’t explain it, let me mention some of the biggest problems.

First, you need to maintain the vacuum in the tube, possibly over hundreds of kilometers, and the tube needs to have exits, both regular ones at the stations and emergency exits in between. If you put the tube in a tunnel, you have to cope with geological stress. But putting the tube on pillars over ground has its own problems.

A group of researchers from the UK showed last year that at such high speeds as the hyperloop is supposed to go, the risk of resonance catastrophes significantly increases. In a nutshell this means that the pillars would have to be much stronger than usual and have extra vibration dampers.

The other problem with putting the tube over ground is that temperature changes will create stress on the tube by expansion and contraction. That’s a bigger problem than you may expect because the vacuum slows down the equilibration of temperature changes in the tube. Since temperature changes tend to be larger over ground, digging a tunnel seems the way to go. Unfortunately, digging tunnels is really expensive, so there’s a lot of upfront investment.

This brings me to the second problem. To keep costs low you want to keep the tunnel small, but if the space between the capsule and the tunnel wall is too small you can’t reach high speeds despite near vacuum.

The issue is that even though the air pressure is so low, there’s still air in that tunnel which needs to go around the capsule. If the air can’t go around the capsule, it’ll be pushed ahead of the capsule, limiting its speed. This is known as the Kantrowitz limit. Exactly when this happens is difficult to calculate because the capsules trigger acoustic waves that go back and forth through the tunnels.

The third problem is that you don’t want the passengers to stick flat to the walls each time the capsule changes direction. But the forces coming from the change of direction increase with the square of the velocity. They also go down inversely with the increase of the radius of curvature though. The radius of curvature is loosely speaking the radius of a circle you can match to a stretch of a curve, in this case to a stretch of the hyperloop track. To keep the acceleration inside the capsule manageable, if you double the speed you have to increase the radius of curvature by four. This means basically that the hyperloop has to go in almost perfectly straight lines, or slow down dramatically to change direction.

And this brings me to the fourth problem. The thing shakes, it shakes a lot, and it’s not clear how to solve the problem. Take a look to the footage of the Virgin Hyperloop test and pay attention to the vibration.

It’s noticeable, but you may say it’s not too bad. Then again, they reached a velocity of merely 100 miles per hour. Passengers may be willing to accept the risk of dying from leaks in a capsule surrounded by near vacuum. But only as long as they’re comfortable before they die. I don’t think they’ll accept having their teeth shook out along the way.

So the hyperloop is without doubt facing a lot of engineering challenges that will take time to sort out. However, I don’t really see a physical obstacle to making the hyperloop economically viable in the long run. Also, in the short run it doesn’t even have to be profitable. Some governments may want to build one just to show off their technological capital. Indeed, small scale hyperloops are planned for the near future in China, Abu Dhabi and India, though none of those will reach the speed of sound, and they’re basically just magnetically levitated trains in tubes.

What do governments think? In 2017, the Science Advisory Council of the Department of Transport in the UK looked at Musk’s 2013 white paper. They concluded that “because of the scale of the technical challenges involved, an operational Hyperloop system is likely to be at least a couple of decades away.” A few months ago they reasserted this position and stated that they still favor high speed rail. To me this assessment sounds reasonable for the time being.

In summary, the hyperloop isn’t just hype, it may one day become a real alternative to airplanes. But it’s probably not going to happen in the next two decades.

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