space shuttle

In class today I did the rocket, the calculation of the trajectory of a device that is propelled by a continuous stream of momentum-carrying propellant. It accelerates as it sheds mass, and the final velocity is related to the initial velocity by a logarithm of the mass ratio (initial to final). I then worked out how big the Space Shuttle's fuel tanks need to be—relative to the orbiter—to get the orbiter to orbit, assuming that the propellant is expelled at around the speed of sound. Insane! It turns out that the space shuttle boosters expel propellant at around 4000 m/s, far, far higher than the speed of sound. If I know anything about hydrodynamics, this is non-trivial. Kudos to those NASA engineers.