How Many G’s Will the Hyperloop Pull in Its Next Test?

Is Elon Musk crazy or just awesome? This week, the serial CEO (Tesla, SpaceX, Neuralink) posted on Twitter about yet another one of his ventures, the super fast tube-based transportation system called hyperloop.

Is this even possible? Let’s do some quick calculations. First, what is the speed of sound? I am assuming that Elon is referring to the speed of sound at sea level (and not speed of sound in a low pressure tube). In that case, a pretty standard value for the speed of sound would be about 340 m/s (760 mph). And no—there won’t be a sonic boom if the hyperloop reaches this speed, since that won’t be the speed of sound at the low pressure inside of the tube.

This means the hyperloop vehicle has to get up to a speed of 340 m/s and then back to 0 m/s in just 1.2 km, or about three quarters of a mile. If the acceleration for increasing speed has the same magnitude during the slow down phase, then it would reach its maximum speed right in the middle—after 0.6 km.

In order to calculate the required acceleration, let me start with the definition of acceleration in one dimension. It’s basically a measure of how fast the velocity changes. I can write that as: