In this problem, three forces are applied:
- Thrust T = n×fc×g×Isp/2, where n is the total number of RCS, fc their fuel consumption and Isp their specific impulse.
- Weight W = m×g, where g is local gravity, which can be calculated with the formula g=µ/(R+h)^2, R being the radius of Earth, and h altitude.
- Drag Q=1/2×ρ×v^2, with ρ the local atmosphere density (you have ρ=ρ0×exp(-c×h)), and v speed of the ship.
Notice that because of the fuel consumption the ship mass is variable and is given by:
m=m0×(1-n×fc×t/2).
Then, the Newton law allows us to write:
ΣF = m×a
Which gives the final equation:
a = n×fc×g×Isp/(2×m0×(1-n×fc×t/2)) - g - 1/2×ρ0×exp(-c×h)×v^2/(m0×(1-n×fc×t/2))
The resolution of this equation shows that under certain conditions a is positive, and then the ship can fly.
Hey, you wanted a scientific explanation right?
Scientist:
1. RCS glitch
2. Aero glitch
3. RCS has highest TWR of all engines in game, but worse efficiency. It will fly, but not for long.
Yeah... That too.