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The "materials science" problem I call out is in the tube's lateral thermal expansion.I admire your method of argumentation.
The comment I replied to said nothing at all about thermal expansion. Your original comment, which I wasn't replying to, was mostly strange references to pressure ratios, and a single line about thermal problems, with no numbers cited. In that comment you did link to the Space Power Facility... as an argument against Hyperloop One! You did something similar downthread: https://news.ycombinator.com/item?id=15459777 But by asserting that you addressed the problem in your original comment, you make the person you're arguing with look like a bully, without having to actually address their points. Very efficient.
>The best solution I've come up with for that is to take a regenerative rocket engine [1] and make it a tube. Pumping fluid in spirals along kilometers of a vacuum tube isn't easy, but it isn't as hard as trying to invent a material that won't deform when the top gets hotter than the bottom, or the east side gets hotter than the west.
Using the phrase "regenerative cooling" in this context is another headscratcher. Regenerative cooling in rocketry is running propellant through channels in the nozzle, then either dumping it overboard, using it to power a gas generator, or burning it in the rocket. It's a great way to get rid of megawatts of heat.
None of these things would be useful for a hyperloop tube? You don't want to run kerosene/liquid oxygen/hydrazine/whatever through a cooling jacket then dump it on the ground, you don't need a gas generator for anything, and there's no way to feed the heated propellant to the actual hyperloop car. And if you could, you wouldn't want to, since if you combusted it in the car it would just dump the exhaust in the tube, killing the vacuum.
Presumably active cooling of a hyperloop tube would use a closed refrigerant cycle, which has little to do with regenerative cooling, besides the idea of cooling channels.
Talking about regenerative cooling in this context isn't wrong, exactly, it just betrays a rather shallow understanding of the problem at hand, as seen in your first comment.