Tsiolkovsky's Rocket Equation

The fundamental equation of spaceflight. It tells you how much velocity change (delta-v) a rocket can achieve based on its fuel and exhaust speed.

Δv = v_e × ln( m₀ / m_f )

Parameters

Exhaust velocity (v_e) 3,000 m/s Wet mass (m₀) — total 100,000 kg Dry mass (m_f) — empty 10,000 kg

Presets

Visualization

Delta-v = 6,908 m/s (6.91 km/s)

What can you do with this delta-v?

The Tyranny of the Rocket Equation

Mass ratio = m₀/m_f = 10.0
Fuel fraction = 90.0%

The logarithm is cruel. To double your delta-v, you need to square your mass ratio. Going from 3 km/s to 6 km/s means going from 63% fuel to 87% fuel. Getting to orbit (9.4 km/s) requires ~90% of a rocket to be fuel.

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