I decided to have a look at what Karman did in his calculations to find the edge of outer space. I used the equation for lift L=1/2 rho.S.v^2.C(L) were rho is air density, S is the wing area, v is speed and C(L) is the lift coefficient. Karman used the Bell X-2 so I got data from here. I got the air density vs altitude from here and speed of sound vs altitude from here.
I simplified it by assuming half full fuel tank for mass. I have no idea about lift coefficient so I fixed it by noting that the plane reached Mach 3 at about 20000m. That needs C(L) = 0.1. However, C(L) is probably not constant throughout. The aim was that v calculated is the speed needed to achieve aerodynamic lift. Karman then factored in whether or not the aircraft was overheating. For me, this was just an exercise to start to play with the numbers. If it is anything near valid, the speeds become phenomenal.
