Revisiting the thermal expansion problem... The most severe unaddressed issue in the proposed design is that there would be far too much friction and/or tension for the entire 600km tube to expand and contract passively without buckling.
There are two basic approaches to solving this, as I see it. First would be to put expansion joints at regular intervals along the line. This is obviously complicated by the fact that the tube must remain almost perfectly straight and still maintain a vacuum, but there are reasonably straightforward designs that should work. For instance, the tube could be "cut" in a triangle-wave zigzag pattern, with the "teeth" perhaps a few centimeters wide and a meter long. Even with a half-meter longitudinal gap, the capsule's 1.5-meter-long skis would be well-supported at all times while crossing this zigzag gap. An accordion-like steel "bellows" could be welded to the outside of the pipe across the cut, which could flexibly expand and contract while maintaining a vacuum inside. Outside the tube, straight rail mechanisms could ensure that the two sides of the cut stay perfectly aligned. Additional supports could prevent the bellows from collapsing inwards under vacuum pressure. These expansion joints would have to be placed about every mile or so along the tube, and probably calibrated to close completely shut at a temperature of around 150 °F or so. For each mile-long welded section, the tube would then have to be fixed to the central pylon, and glide longitudinally over the neighboring ones. This could create tension problems especially for non-horizontal sections of the tube, which will require expansion joints at more frequent intervals. (Though inside the tunnels, thermal expansion is minimized.)
The second solution would be to still weld the entire tube together seamlessly as in the alpha proposal, but actively move the tube longitudinally to compensate for the thermal expansion/contraction. This would have to be done continuously and actively, though it could be done with backup battery power and significant redundancy. (Several pylons in a row could fail without compromising the system.) Worst-case, consider the Grapevine section of the tube, where there is a net elevation gain of 700 meters over 80km. At sundown, this entire section of the tube (15,000 metric tons) needs to move "uphill" at roughly a 1° angle, at about 5mm per second, to compensate for thermal contraction. In a frictionless environment, this only takes about 7 kilowatts of power to achieve (total!), which is surprisingly little. In reality, friction will be by far the dominating factor; the bearings on the pylons must have enough friction to prevent unpowered non-horizontal sections of the tube from collapsing under tension like a Chinese finger puzzle. (or other areas warping under compression, like a wet piece of bucatini squished in at both ends.)
I don't see a clear winner between these two approaches, but the second seems much simpler and cheaper from an engineering perspective. The downside is that in case of ongoing systemwide power failure, your entire hyperloop is pretty much toast. (A
Carrington Event could potentially cause this, if the state power grid were shut down for weeks or months. Another reason to make the system self-sufficient with solar!)
Ok, I've rambled on enough. Thoughts from the gallery?
