When the California “high speed” rail was approved, I was quite disappointed, as I know many others were too. How could it be that the home of Silicon Valley and JPL – doing incredible things like indexing all the world’s knowledge and putting rovers on Mars – would build a bullet train that is both one of the most expensive per mile and one of the slowest in the world? Note, I am hedging my statement slightly by saying “one of”. The head of the California high speed rail project called me to complain that it wasn’t the very slowest bullet train nor the very most expensive per mile.

The underlying motive for a statewide mass transit system is a good one. It would be great to have an alternative to flying or driving, but obviously only if it is actually better than flying or driving. The train in question would be both slower, more expensive to operate (if unsubsidized) and less safe by two orders of magnitude than flying, so why would anyone use it?

If we are to make a massive investment in a new transportation system, then the return should by rights be equally massive. Compared to the alternatives, it should ideally be:
◾ Safer
◾ Faster
◾ Lower cost
◾ More convenient
◾ Immune to weather
◾ Sustainably self-powering
◾ Resistant to Earthquakes
◾ Not disruptive to those along the route

Is there truly a new mode of transport – a fifth mode after planes, trains, cars and boats – that meets those criteria and is practical to implement? Many ideas for a system with most of those properties have been proposed and should be acknowledged, reaching as far back as Robert Goddard’s to proposals in recent decades by the Rand Corporation and ET3.

Unfortunately, none of these have panned out. As things stand today, there is not even a short distance demonstration system operating in test pilot mode anywhere in the world, let alone something that is robust enough for public transit. They all possess, it would seem, one or more fatal flaws that prevent them from coming to fruition.

Constraining the Problem

The Hyperloop (or something similar) is, in my opinion, the right solution for the specific case of high traffic city pairs that are less than about 1500 km or 900 miles apart. Around that inflection point, I suspect that supersonic air travel ends up being faster and cheaper. With a high enough altitude and the right geometry, the sonic boom noise on the ground would be no louder than current airliners, so that isn’t a showstopper. Also, a quiet supersonic plane immediately solves every long distance city pair without the need for a vast new worldwide infrastructure.

However, for a sub several hundred mile journey, having a supersonic plane is rather pointless, as you would spend almost all your time slowly ascending and descending and very little time at cruise speed. In order to go fast, you need to be at high altitude where the air density drops exponentially, as air at sea level becomes as thick as molasses (not literally, but you get the picture) as you approach sonic velocity.

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 wherestandard commercial pumps could easily overcome an air leak and the transport pods could handle variable air density would be inherently robust. Unfortunately, this means that there is a non-trivial amount of air in the tube and leads us straight into another problem.

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 or 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.

Making the Economics Work

The pods and linear motors are relatively minor expenses compared to the tube itself – several hundred million dollars at most, compared with several billion dollars for the tube. Even several billion is a low number when compared with several tens of billion proposed for the track of the California rail project. The key advantages of a tube vs. a railway track are that it can be built above the ground on pylons and it can be built in prefabricated sections that are dropped in place and joined with an orbital seam welder. By building it on pylons, you can almost entirely avoid the need to buy land by following alongside the mostly very straight California Interstate 5 highway, with only minor deviations when the highway makes a sharp turn.

Even when the Hyperloop path deviates from the highway, it will cause minimal disruption to farmland roughly comparable to a tree or telephone pole, which farmers deal with all the time. A ground based high speed rail system by comparison needs up to a 100 ft wide swath of dedicated land to build up foundations for both directions, forcing people to travel for several miles just
to get to the other side of their property. It is also noisy, with nothing to contain the sound, and needs unsightly protective fencing to prevent animals, people or vehicles from getting on to the track. Risk of derailment is also not to be taken lightly, as demonstrated by several recent fatal train accidents.

Earthquakes and Expansion Joints

A ground based high speed rail system is susceptible to Earthquakes and needs frequent expansion joints to deal with thermal expansion/contraction and subtle, large scale land movement.

By building a system on pylons, where the tube is not rigidly fixed at any point, you can dramatically mitigate Earthquake risk and avoid the need for expansion joints. Tucked away inside each pylon, you could place two adjustable lateral (XY) dampers and one vertical (Z) damper.

These would absorb the small length changes between pylons due to thermal changes, as well as long form subtle height changes. As land slowly settles to a new position over time, the damper neutral position can be adjusted accordingly. A telescoping tube, similar to the boxy ones used to access airplanes at airports would be needed at the end stations to address the cumulative length change of the tube.

Can it Really be Self-Powering?

For the full explanation, please see the technical section, but the short answer is that by placing solar panels on top of the tube, the Hyperloop can generate far in excess of the energy needed to operate. This takes into account storing enough energy in battery packs to operate at night and for periods of extended cloudy weather. The energy could also be stored in the form of compressed air that then runs an electric fan in reverse to generate energy, as demonstrated by LightSail.