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August 12, 2013

Elon Musk Hyperloop all the technical details of the Alpha design of the fifth mode of transportation that solves the Kantrowitz limit

The Hyperloop design is trying to achieve the following objectives. (57 page pdf)

The tesla motors pdf copy could get overloaded. Here is the pdf on Spacex

* Safer
* Faster
* Lower cost
* More convenient
* Immune to weather
* Sustainably self-powering
* Resistant to Earthquakes
* Not disruptive to those along the route

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 are a 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

1) where you go slowly
2) 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.


Existing conventional modes of transportation of people consists of four unique types: rail, road, water, and air. These modes of transport tend to be either relatively slow (i.e., road and water), expensive (i.e., air), or a combination of relatively slow and expensive (i.e., rail). Hyperloop is a new mode of transport that seeks to change this paradigm by being both fast and inexpensive for people and goods. Hyperloop is also unique in that it is an open des ign concept , similar to Linux. Feedback is desired from the community that can help advance the Hyperloop design and bring it from concept to reality. Hyperloop consists of a low pressure tube with capsules that are transported at both low and high speeds throughout the length of the tube. The capsules are supported on a cushion of air, featuring pressurized air and aerodynamic lift. The capsules are accelerated via a magnetic linear accelerator affixed at various stations on the low pressure tube with rotors contained in each capsule. Passengers may enter and exit Hyperloop at stations located either at the ends of the tube, or branches along the tube length.

In this study, the initial route, preliminary design, and logistics of the Hyperloop transportation system have been derived. The system consists of capsules that travel between Los Angeles, California and San Francisco, California. The total trip time is approximately half an hour, with capsules departing as often as every 30 seconds from each terminal and carrying 28 people each. This gives a total of 7.4 million people each way that can be transported each year on Hyperloop. The total cost of Hyperloop in this analysis is under $6 billion USD. Amortizing this capital cost over 20 years and adding daily operational costs gives a total of about $20USD (in current year dollars) plus operating costs per one- way ticket on the passenger Hyperloop.

Useful feedback is welcomed on aspects of the Hyperloop design. E-mail feedback to hyperloop@spacex.com or hyperloop@teslamotors.com .

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