Maths in physics and engineering · Solid · Dissertation

The limit on wind turbine power: a maths EPQ idea

Why it works as an EPQ

The Betz limit, 16/27 of the wind's power, follows from an optimisation you can do with A Level calculus.

Scope and difficulty

Solid. Solid. The derivation plus a comparison with published turbine data.

The maths

Builds on these A Level topics: Differentiation · Algebra and functions.

You would learn:

• Momentum and energy in a flow
• Optimising a cubic
• Power coefficients

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

One possible plan

1. Find the power in the wind through an area.
2. Derive the Betz limit by optimising the slowdown factor.
3. Compare with published turbine power curves.
4. Judge why real turbines fall short.

Pitfalls

• Confusing power and energy.
• Turbine data with no source.

Where to start reading

• Search for: Betz limit derivation
• Search for: wind turbine power curve data

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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All maths in physics and engineering ideas · all 93 ideas

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