IA idea · Sport

When should a Formula 1 driver pit? Modelling tyre degradation

AA SLAI SLAA HLAI HL Ambitious Also in: Modelling, Calculus

Research question

Using lap-time data from a real race, can a linear or quadratic model of tyre degradation find the lap on which a one-stop driver should pit to minimise total race time?

Adapt it: change the place, the data or the comparison until the question is yours.

Why it makes a good exploration

Race strategy is mathematics under pressure. Lap times get slower as tyres wear; a pit stop costs about 20 seconds. Modelling the trade-off with real lap data gives an optimisation problem with a clear answer to check against what teams did.

The mathematics you'll need

Regression of lap time against tyre age
Total time as a sum (arithmetic series or integral)
Minimising total time with respect to pit lap
Comparison of one- and two-stop strategies

Course labels show where a technique sits; using maths from outside your course is fine if you explain it clearly and say it is new to you.

Where the data comes from

Download lap times and pit-stop data for a race from the Jolpica-F1 API.

Jolpica-F1 API — Free Formula 1 results, lap times and pit stops from 1950 (the successor to the closed Ergast API).

Cite every source in a footnote where you use it and in your bibliography. Check the licence of any dataset you download.

A possible outline

Clean the data (safety cars, traffic).
Fit degradation models for each tyre compound.
Write total race time as a function of the pit lap.
Optimise and compare with the real strategy.
Reflect on fuel load, track position and safety cars.

Pitfalls that cost marks

Including safety-car laps in the fit.
Ignoring that the car gets lighter as fuel burns.
Overlooking undercut/overcut effects.

Showing personal engagement

Choose a race you watched.
Compare your strategy with the winner's.
Explain a surprising team decision using your model.

See Criterion C: personal engagement for what examiners look for.

Taking it further

Add a fuel-load correction (lap time falls as fuel burns) and re-optimise.

Turn this idea into your IA

Plan this IAOpens the planner with this question, the maths and data sources filled in. Desmos workspacePlot your data, fit models and keep your graphs with your plan. AI feedback on a draftCriterion-by-criterion feedback with evidence from your own text. Coaching, not rewriting. Examiner reviewPete, a practising IA examiner, reads your draft and talks it through with you (€100).