Maths in physics and engineering · Ambitious · Dissertation or artefact

Hanging chains and bridges: a maths EPQ idea

Why it works as an EPQ

Two similar-looking curves with different physics, which you can derive, measure and compare.

Scope and difficulty

Ambitious. Ambitious. The catenary needs a differential equation; photographs of a real chain give data.

The maths

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

You would learn:

• Hyperbolic functions
• Setting up equilibrium differential equations
• Curve fitting

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 the catenary from the forces on a small piece of chain.
2. Derive the parabola for a uniformly loaded suspension bridge.
3. Photograph a hanging chain and fit both curves.
4. Judge when the difference matters in design.

Pitfalls

• Fitting curves without measuring the error.
• Mixing up the load per unit length of chain and of horizontal span.

Where to start reading

• Search for: catenary derivation differential equation
• Search for: suspension bridge parabola uniform load

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

Making something? Read the artefact guide first: an artefact still needs a research-based written report.

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All maths in physics and engineering ideas · all 93 ideas

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