Maths in physics and engineering · Solid · Dissertation

Why rockets have stages: a maths EPQ idea

Why it works as an EPQ

The rocket equation follows from momentum and integration, and its logarithm explains staging clearly.

Scope and difficulty

Solid. Solid. Derive, then compare one-stage and multi-stage designs with your own numbers.

The maths

Builds on these A Level topics: Exponentials and logarithms · Integration · Forces and Newton's laws.

You would learn:

• Momentum and variable mass
• The rocket equation
• Optimising stage masses

Learning maths beyond the course is expected in a maths EPQ, but you must understand and explain everything you use.

One possible plan

1. Derive Δv = vₑ ln(m₀/m₁) from conservation of momentum.
2. Calculate the mass fraction needed for orbit with one stage.
3. Show how staging reduces it.
4. Judge the trade-offs designers face, using published figures.

Pitfalls

• Ignoring gravity and drag losses without saying so.
• Unsourced figures for real rockets.

Where to start reading

• Search for: Tsiolkovsky rocket equation derivation
• Search for: rocket staging mass ratio example

Prefer books, lecture notes, journal articles and official data to a single website, and record every source as you read (how to reference).

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