edit: Jacques admitted it was an oversight.
Still, it's interesting reading these ideas even if they might not be what Elon is thinking.
That's a very interesting puzzle to me and I think this may be a way in which the patent office could do their reviews: ask a community of smart cookies to come up with what is in the (secret to that point) patent application, the one that gets it right gets a part of the filing fee and the patent is denied, if nobody can crack it in some set time (say 4 weeks) then the patent is granted.
He has said that his system is like a “ground based Concorde”. His specs give you a speed of over 1200 km/h. If you're going 1200 km/h on the ground and aren't in a tube, you've got a problem.
LA is also 17 miles from the coast, so if you're getting from downtown SF to downtown LA in 30 minutes, you've got less than 15 minutes to travel nearly 400 miles underwater in order to leave enough time to even attempt to get to LA under the deadline. You're now travelling at Mach II, almost twice as fast as Musk proposed.
As for oceans, I think the risks are less than you think. A tsunami does great damage when it hits land, but in the open ocean you just bob a few inches. The mechanics behind that are simple - a wave coming in to shore starts to get bigger once the depth of the land is the same as the depth of the wave. Tsunamis are very deep waves.
As for oceans, a Tsunami is still going to put a lot of stress on a 400-mile underwater tunnel. And at the points you get in and out of the tunnel, you're going to be at the shore anyway, where the Tsunami is its strongest. Also boats.
OK, let's discuss Mach 1 without a vacuum. A condition that I had not through, but which actually makes surprising sense as a design limit with the system that I am suggesting.
The Chapman–Jouguet condition says that a supersonic shock wave travels at the speed of sound in the air behind it. The ideal gas law says that this speed is almost entirely determined by temperature, not pressure. If you were to go anywhere above Mach 1, the temperature behind the shock wave gets hotter than room temperature very, very quickly. At Mach 1 exactly you should be able to maintain a thin (~0.2 micrometers is quoted by Wikipedia as the measured value) bow shock.
That shock can trap a huge pressure differential behind it, which could allow an open container to maintain normal air pressure while moving through a much lower density of air. If you are moving below that speed, the pressure differential that you maintain is much less than if you speed it up. Therefore for efficiency you'd want the vehicles to be moving at Mach 1 relative to the gas. Assuming that the gas is dragged along, this would let you actually go slightly faster than Mach 1. But if we assume that we have a lot of tunnel and occasional objects, the air would move much closer to the speed of the tunnel than the objects moving through, and therefore the top speed would be approximately Mach 1.
The exact relationship between the air pressure of the tube and the air pressure behind that flap is very complex. But with the flap design that I suggested, at pressures above 1 atmosphere there would be leakage and an opportunity to remove air. If the pressure fell below 1 atmosphere, that opportunity would disappear. Therefore the flap system that I suggested would do a good job of letting air leak out of the tunnel at about the necessary rate to maintain 1 atmosphere inside of the open containers as the speed of the whole system increases and air leaves the tunnel. (It should not be hard to design ways to bring air into the tunnel...)
This reinforces the point that the tunnel need not be evacuated, and explains why Elon said it would run at the speed that he predicted.
At any rate, the subject of Evacuated Tube Transport Technologies (ET3) tm was disclosed in US patent 5,595,543 in 1999. For the record, Coanda's system was pneumatic (and took alot of power to move the air). Search for "evacuated tube transport" on youtube for an overview. I have not noted any claims for 'hyperloop', that are not exceeded by ET3 (tm). see www.et3.com and www.et3.net
There are already some very long vehicular tunnels at depth (the Chunnel, Seikan Tunnel, etc.). I don't think one atmosphere more or less would be a showstopper.
The Chunnel also cost about $17 billion in today's dollars and is only 31 miles long (including the above-ground parts). I don't think this is a feasible model for long-distance transit, especially when Musk claimed a cost of $6 billion for SF to LA.
With SpaceX Elon has demonstrated an ability to reduce costs by a factor of 10 in large part by eliminating the use of contractors. If you look on the PandoDaily interview, just before the Hyperloop is discussed he was railing on about how inefficient the 405 highway expansion is. I wouldn't be surprised if he thinks that he could save an even bigger factor in that kind of public work than he did with SpaceX.
I'm not saying that he's right. I'm saying that his cost projections are extremely unlikely to start with existing construction projects as a base line.
A tunnel filled with hydrogen has a large surface area for potential leaks.
Suffice it to say, the challenges of an electrically grounded hydrogen tunnel lined with heavyweight materials using modern technologies & sensors are a hell of a lot different than the challenges of an ultra-lightweight, ultra-thin flammable gas bag before the advent of plastics, in an electrical storm.
A tunnel filled with vacuum has it a hundred times worse, because you're dealing with 15PSI trying to get in rather than 0PSI pressure difference diffusing out. We already regularly use larger-molecule methane at thousands of PSI.
Obviously a modern hydrogen tunnel would be much different than a zeppelin, and have different challenges. Still, 400 miles of 10-foot diameter tunnel would have plenty of opportunities for problems (whether it's evacuated or filled with hydrogen or something else). I'm not sure an evacuated tunnel is necessarily worse from a safety standpoint, though. It might be harder to engineer, but the failure mode seems safer. A hydrogen tunnel means that a leak will mix hydrogen with an oxidizer. If it's at 0 PSI, this could mean a leak lets oxygen into the tunnel (either due to high-pressure weather or due to hydrogen rising from the leak, leaving a low-pressure environment in the tunnel). If you wanted to fill a tunnel with hydrogen, I think it would be wise to keep at least a small positive pressure to ensure than any leaks are outward only.
I'm totally unclear why methane stored at thousands of PSI is relevant. Is there some 400-mile long, 10-foot diameter, above-ground methane tunnel I'm not aware of?