I was looking into the practicality of rail-gun technology to achieve orbital launches (As promoted by the answers at What is the possibility of a railgun assisted orbital launch? ), but found that the heat generated at 3000 meters per second (About 3 miles/sec) would be insane. The downstream calculation for launch vehicle of less than 10000 kg with a diameter of about 2 feet (.6 m), and a drag coefficient of .25, would be a power loss of 1.28 GW, with a specific heat change of 8000 degrees celsius over 6 seconds (The bottom 18 miles of the atmosphere at 3 miles/sec). Just 3000 m/s would suggest it'd burn up due to the atmospheric drag. The lighter you are, the more temperature will increase at this speed and cross-sectional area.
So this begs the question, what is the fastest speed that can be attained from a railgun launcher without "burning up" like a comet travelling at 25 km / sec. I'm suspecting this might be the real limit to using railguns to achieve the necessary escape velocity of 11 km/s to reach geostationary orbit. I'm speculating a hybrid approach of using railguns at lower speeds (2km/s to achieve 100-150 mile height) and rocket for the rest of the way to geostationary orbit might be advantageous, but not sure if the benefits are significant enough compared to regular rockets.
There may be certain technologies that enable higher atmospheric travel speeds, but it's mostly speculative. Advanced futuristic "heat shields" may enable higher orbital launch speeds from railgun technology. Advanced enough technology might enable the 11 km/sec required for earth's escape velocity, but that's probably some highly advanced technology.
Existing navy railguns can achieve 2 km/s, which could probably reach launch heights of 100-200 miles.
