Hi, aerospace engineer here. As far as benefits go it depends.
If we assume the tube is constant volume and constant temperature. The ideal gas law says that in this case, the pressure would change proportionally with density. So if you lower the pressure by 50% the density should lower by about 50%.
Drag force is also proportional to density. So a 50% decrease in density will result in a 50% decrease in drag. This is true for subsonic speeds. The speed of sound is 343 m/s or 770 mph.
Drag also has a square relationship with velocity. So drag gets extremely high when there is an increase in velocity.
If we take the speed of the shinkansen(90 m/s or 200mph) as a baseline and lower the pressure by half. The new speed the Hyperloop would be able to travel with the new speed is 127m/s or 284 mph. That is faster 40% for the same amount the trains will have to work, but to build all of that infrastructure, spend all the money creating a lower pressure environment and maintain that pressure for thousands of miles is just not worth it. The vacuum tube is just not practical to make.
Edit: If you maintain a reduced pressure and increase speeds about 30% of the speed of sound, the subsonic equations I used start to be less accurate. But in that case drag increases dramatically in transonic and supersonic regimes.
This is the kind of actual discussion that I hope for in these discussions. While many people focus on the dangers of the vacuum tube proposed for the Hyperloop infrastructure, I always wondered about the benefits. It's not like putting a train in a vacuum will suddenly make it go infinitely fast.
So, the question is how much faster would it go? Once you have that number, you can adjust the car vs plane vs train chart that CityNerd showed off. All it would do is deepen and lengthen the railed transit curve some amount. It would potentially increase the distance two cities could be and still provide a benefit over airplane travel. It's just a question of how many city pairs it would help to include as a rail option.
Going from 200 mph to 284 mph won't make that much of a difference. Yes, it'll open up more city pairs for high speed rail, but when comparing those benefits against the cost of the massive tube construction it's not going to seriously pencil out as a net benefit.
Here's the video where CityNerd lays out their reasoning and charts a rough model of where high speed rail is going to be a more reasonable choice for travel based on the distance needed to go: https://youtu.be/pwgZfZxzuQU?t=477
@azimir @Erismi14 I'd be interested in seeing "the cost of building a massive tube" compared to "the cost of building a massive highway".
DOTs across the country have been using phony math to justify ludicrously expensive highway projects for decades -- given a train in a tube would be higher speed and higher throughout, I feel like using their same logic we'd see huge "economic benefits" from connecting two new business centers with a transport mode that allows workers to work in-transit.
I think if we had an economy already built around these tubes it would be much cheaper, but I think that it would still be similar if not more in price as the building of highways.
It is not as easy as building a "bigger oil pipeline and running trains through it. The train moving at high speeds will need a complex and robust system that is continuous inside and outside the tube. The tube will also need ground foundation to handle those forces.
Curves and elevation changes will need to happen at even flatter grades than highways. The higher speeds mean higher acceleration around curves or up inclines. The less sharp turns means more of a reliance on raised structures and tunneling. Good luck on convincing thousands of farmers to put a tube through their property
Maintenance. A highway with a crack in it still works. A highway with a pothole in it still works. Maintenance on that pothole costs $10k USD and the highway is still usable through maintenance. Hyperloop maintenance would not be as cheap, the tube would be shut down before and during maintenance due to repressuring. The tube would need to be vacuumed again.
I'm sure there are other things undiscovered that would be costs as well.
I think the Hyperloop is a cool and shiny idea. In the US I would much prefer reliable and cheap, normal speed rail first, then highspeed, then Hyperloop if we ever get there. I don't think we should be able to eat our pudding before we eat our meat if that makes sense.
Add to that that the Hyperloop is incompatible with regular rail.
If you build a highspeed rail connection between two cities, you can start by just building highspeed tracks on the straight, empty areas of the connection where you get the biggest benefits, while letting the train run on regular rails in between. So while building the track, the travel time will be gradually reduced as more and more of the track is completed. In the cities themselves, the train can use regular tracks (since highspeed travel probably won't be a thing there anyway due to space restrictions), and it can also use the regular railway stations. This allows you to directly connect the rail service to other trains without having to build separate stations with potential shuttle services in between.
I think if they are doing a vacuum tube, they should get as close to a vacuum as possible.
I think if the USA is going to spend trillions on rail infrastructure, I think we should start with doubling or tripling the amount of trains on Amtrak first. It's not as sexy as the Hyperloop, but it would get people riding trains more often
