How the rocket equation works
The Tsiolkovsky rocket equation gives the velocity change a stage can deliver from its exhaust velocity and the ratio of its mass before and after the burn. In a multi-stage vehicle each stage carries everything above it, so the payload and upper stages count as part of the lower stage's mass.
- Stage delta-v:
Δv = Isp·g₀·ln(m₀/m_f), withg₀ = 9.80665 m/s² m₀= stage propellant + stage dry mass + everything abovem_f= stage dry mass + everything above
Worked example: two-stage launcher
A first stage with 395.7 t of propellant, 25.6 t dry mass and an average Isp of 300 s, topped by a second stage with 92.7 t of propellant, 3.9 t dry mass and 348 s Isp, delivers about 4.0 km/s and 6.1 km/s respectively to a 15 t payload: about 10.05 km/s in total, above the roughly 9.4 km/s typically needed for low Earth orbit including losses.
Good to know
- Mission totals include gravity and drag losses, which vary with the vehicle and trajectory.
- Pro adds burn times, thrust-to-weight at each ignition, and the margin against LEO, GTO and trans-lunar targets.