The Tyranny of the Rocket Equation
Tsiolkovsky: ΔV = v
e
· ln(m₀/m_f) — exponential physics, brutal consequences
Controls
Delta-V (ΔV):
9.4
km/s
9.4
0
LEO 9.4
Moon 13.4
Mars 21
30
Exhaust velocity (v
e
):
4.4
km/s
4.4
Chemical 2–4
H₂/O₂ 4.4
Nuclear ~8
Mass Ratio
8.47
Payload Fraction
11.8%
Mass Breakdown
Fuel+Structure 88.2%
Payload 11.8%
Toggle Staging
Two-Stage Rocket
(10% structural mass per stage shed)
Stage 1: provides ΔV/2 → ratio₁ =
—
Stage 2: provides ΔV/2 → ratio₂ =
—
Effective payload fraction:
—
Mass Ratio vs ΔV — Exponential Curve