01 · The equation
Delta-v
Δv = vₑ ln(m₀/m_f). The log is why tanks eat the vehicle. LEO wants about 9.4 km/s including losses — more than the 7.8 you stay up with.
In English
A rocket throws mass backward so the rest goes forward. How much speed you gain is exhaust speed times the log of how much lighter you got. Double the fuel, you do not double the Δv. That log is the whole subject.
- Try this
- Set mass ratio to 3, then 10. Switch Isp from 330 s (kerolox) to 450 s (hydrolox). See whether you clear the LEO bar.
- Keep this
- Δv = vₑ ln(m₀/m_f). Tanks buy less than they appear to.
Lab · the rocket equation
Δv = vₑ ln(m₀/m_f). The log is why tanks eat the vehicle. LEO wants about 9.4 km/s including losses — more than the 7.8 km/s you stay up with.
Mass ratio m₀/m_f = 8.0
Isp
- Exhaust vₑ
- 3.24 km/s
- Δv
- 6.73 km/s
- vs LEO budget
- short 2.7
Tsiolkovsky (1903): Δv = ve ln(m0/mf), ve = Isp g0. The log is why a 90% propellant fraction is ordinary and 95% is heroic.
The 9.4 km/s LEO bar already includes gravity and drag. Hitting 7.8 km/s of orbital speed is not the same as paying the ticket.