The Hyperloop (or something similar) is, in my opinion, the right solution for the specific case of high traffic city pairs that are less than about 1500 km or 900 miles apart. Around that inflection point, I suspect that supersonic air travel ends up being faster and cheaper. With a high enough altitude and the right geometry, the sonic boom noise on the ground would be no louder than current airliners, so that isn’t a showstopper. Also, a quiet supersonic plane immediately solves every long distance city pair without the need for a vast new worldwide infrastructure.
However, for a sub several hundred mile journey, having a supersonic plane is rather pointless, as you would spend almost all your time slowly ascending and descending and very little time at cruise speed. In order to go fast, you need to be at high altitude where the air density drops exponentially, as air at sea level becomes as thick as molasses (not literally, but you get the picture) as you approach sonic velocity.
WHAT IS HYPERLOOP?
Short of figuring out real teleportation, which would of course be awesome, the only option for super fast travel is to build a tube over or under the ground that contains a special environment.
At one extreme of the potential solutions is some enlarged version of the old pneumatic tubes used to send mail and packages within and between buildings. You could, in principle, use very powerful fans to push air at high speed through a tube and propel people-sized pods all the way from LA to San Francisco. However, the friction of a 350 mile long column of air moving at anywhere near sonic velocity against the inside of the tube is so stupendously high that this is impossible for all practical purposes.
Another extreme is the approach, advocated by Rand and ET3, of drawing a hard or near hard vacuum in the tube and then using an electromagnetic suspension. The problem with this approach is that it is incredibly hard to maintain a near vacuum in a room, let alone 700 miles (round trip) of large tube with dozens of station gateways and thousands of pods entering and exiting every day. All it takes is one leaky seal or a small crack somewhere in the hundreds of miles of tube and the whole system stops working.
However, a low pressure (vs. almost no pressure) system set to a level where standard commercial pumps could easily overcome an air leak and the transport pods could handle variable air density would be inherently robust. Unfortunately, this means that there is a non-trivial amount of air in the tube and leads us straight into another problem.
The interior of the capsule is specifically designed with passenger safety and comfort in mind. The seats conform well to the body to maintain comfort during the high speed accelerations experienced during travel. Beautiful landscape will be displayed in the cabin and each passenger will have access their own personal entertainment system.
The Hyperloop passenger capsule (Figure 8 and Figure 9) overall interior weight is expected to be near 5,500 lb (2,500 kg) including the seats, restraint systems, interior and door panels, luggage compartments, and entertainment.
The geometry of the tube depends on the choice of either the passenger version of Hyperloop or the passenger plus vehicles version of Hyperloop.
In either case, if the speed of the air passing through the gaps accelerates to supersonic velocities, then shock waves form. These waves limit how much air can actually get out of the way of the capsule, building up a column of air in front of its nose and increasing drag until the air pressure builds up significantly in front of the capsule. With the increased drag and additional mass of air to push, the power requirements for the capsule increase significantly. It is therefore very important to avoid shock wave formation around the capsule by careful selection of the capsule/tube area ratio. This ensures sufficient mass air flow around and through the capsule at all operating speeds. Any air that cannot pass around the annulus between the capsule and tube is bypassed using the onboard compressor in each capsule.