My first assumption is that for the same air density, the friction is
directly proportional to the speed of the aircraft.

Nope. To oversimplify, it goes as the cube at subsonic speeds. Once supersonic other terms enter the equation. So at Mach 10 the scramjet would
have to exert more than 1000 times the thrust as for Mach 1 at the same altitude. And a scramjet can't run from a standing stop.

Jose
--
Freedom. It seemed like a good idea at the time.
for Email, make the obvious change in the address.