Alan Wootton 3/12/13
This is what I think Musk's idea is.
There's a pod-car traveling at 408 meters per second, which is mach 1.2 (912 miles per hour). The pod is 5 meters long and 2 meter thick at it's widest point. It has the shape of two cones joined end to end. It's pointed at the front and pointed at the back. It seats 4 humans.
The pod moves down the center of a cylindrical tunnel with a diameter of 3.1 meters. The tunnel is only a tunnel in the sense that it protects the car from the birds and is not necessarily underground. The air in the tunnel is at normal atmospheric pressure. The mass of the tunnel is not more that enough to basically resist the elements and support one car at rest.
There is a mag-lev rail(s) that keeps the pod in the center of the tunnel and also provides propulsion.
Why? How can I have such numbers?
The numbers I present derive from some basic assumptions, plus a special trick. A trick worthy of Elon Musk.
Mach 1.2 = 408 meter/sec. SF to LA, approx 400 miles, in 30 minutes, is faster than sound so I picked mach 1.2. Someone mentioned 900 mph.
I would like to take that trip race car style, reclined, with a small cross-section but I don't think normal people would want that so I looked up the cabin width of a small jet (lear-25) and picked 1.5 meters as a diameter for the pod. Due to the angle of the pod I simplify the math by saying it's 2 meter at the max even though it's more like 4.8 feet above each row of seats.
Let's remember that trains, and the railway system, were designed in a day when engines where huge massive affairs and the tracks had to support a large weight, and so the cars could also be heavy – rolling on steel wheels on heavy steel tracks. In a mag-lev system where the propulsion comes from the track the 'cars' can be any size and don't need to be dragged behind an engine. It's advantageous for the 'track' to only need to support a single, smaller, car.
One can't run a 'car' supersonic. It would give off a wicked shock wave and, more to the point, the shock wave carries away a huge amount of energy. It has to be in a tunnel, but this presents an opportunity. We design the geometry of the podcar, and the tunnel, so that the shock wave from the front of the pod reflects off the tunnel walls and then lands exactly on the back part of the car so that the net result is zero!
I have derived the size of the tunnel from the length and width of the car. There is a question about the angle of the cone on the car. At mach 1.2 it has to be at least 39.8 degrees but that would concentrate the shock wave into compressed wave (there's an infinity in the math) which might blister the paint. The size of the tunnel for that is 2.24 meters. I have backed off from that by a factor of 2, where the half angle of the cone is 22.6 degrees and that works out to a tunnel diameter of 3.18 meters. This shock wave is more spread out.
I don''t know how many g's one can expect from the passengers but the math is relentless. If they can endure 1 g then it takes 42 seconds to get to full speed! This takes more than 17 kilometers. If they will only handle 0.5 g then it takes 19 km, or 43 miles, to get up to speed. For testing one could use a lighter pod at 4 g's and only 2km of track.
The total energy of a 1000kg pod at 408 m/s is 83.2 million joules, and at $0.25 per kilowatt hour that's $5.80. Of course one would get that back at the end point. I have no way to calculate the energy per mile just yet.
I calculate the cost of 400 miles of capacitors to power the thing at $64 million. :-) (looked that up at mouser)
I did this in pencil on 5 sheets of paper and one sleepless night. Most of the math was done two ways but I could still be wrong. There's tons more to figure out but I have a very high paying day job.
Yes, I think it could be done.
No, I am not applying for a patent.
No, I can't estimate how much it would cost just yet.
Yes, one could have a 'double length' pod where the shock wave bounces off the wall, then off the car, then off the wall, and then back on the tapering end.
No, I don't know the losses at any speed.
Yes. I'm sure the pods will still levitate at much slower speeds and the subsonic aerodynamics won't be bad.
No, I have not designed the mag-lev part. Think Halback.
Yes. I could write this all up in code and optimize it 'till the cows come home.
Yes, Mr. Elon Stark Musk. I will build this bad boy for you. Ask me.
Cheers - a