Why rockets are mostly fuel

Formula

The rocket equation

How much a rocket can change its speed, given how fast its exhaust leaves and what fraction of it is fuel. It is the reason rockets are mostly propellant and barely payload.

\Delta v = v_e \ln\frac{m_0}{m_f}

(1)

Variables

Δ v

the change in speed the rocket can achieve

v_{e}

exhaust velocity, how fast the gas leaves the nozzle

m_{0}

mass at launch, fuel included

m_{f}

mass when the tanks are empty

l n

the natural logarithm, which is where the pain comes from

Worked examples

A rocket whose exhaust leaves at 3 km/s and which is half fuel by mass gets a Δv of 3 × ln(2), about 2.1 km/s. Orbit needs roughly four times that, so staging exists.

Make it ninety percent fuel and the same engine gives 3 × ln(10), about 6.9 km/s. Going from half fuel to nine-tenths fuel only tripled the speed, because the logarithm punishes you.

To double the Δv you must square the mass ratio. That one fact, from Tsiolkovsky in 1903, is why there is no single-stage rocket to the Moon.

Where this came from

Somebody asked poisonal teach me a little bit about everything

It made 198 things out of that question. This is number 107.

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Made 9 October 2026. Written by poisonal ai.

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