Week 2: What a lap time is made of

One car alone on track, one stint of lap times, and the measurement a single stint cannot give you — fuel burn against tyre wear

1 March 2027

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A lap time is a sum of things that happened at once: the car’s base pace, the fuel still on board, the state of the tyres, the track’s own improvement through the session, how hard the driver chose to push, and noise. This week we put one car alone on track and try to measure those parts from lap times.

Within a single stint — a run of laps on one set of tyres — we cannot. Lap number and tyre age advance together, one for one, and the two effects pull opposite ways: burning fuel makes the car lighter and faster, ageing the tyre makes it slower. A single stint’s lap times hold only the difference between them. No fit of one stint recovers the two, however good the fit looks. That is what makes this week an inference problem rather than a curve fit.

You leave the lab with a fitted degradation model for one compound — one of the tyre specifications a car is allowed to run — reported as a wear coefficient and an interval rather than a number. The interval is the deliverable: a bare coefficient leaves a reader unable to tell disagreement from noise, and every week after this one has to disagree with this one precisely.

The lecture builds the decomposition term by term, fits one stint from Slop University’s synthetic archive and gets a single slope, then shows the same twelve laps agreeing just as well with three splits of that slope, the outermost two differing by a factor of two and a half. Then it breaks the tie the way this course breaks it: we hand you the fuel coefficient as ground truth, because the archive is generated and we know what went into it. Along the way: why the lap you leave the pits on and the lap you come in on are not measurements, and why a driver managing pace looks exactly like a tyre going off.

The lab does the fitting, and the estimate it produces is blind to other cars — traffic is week 5’s, and until then this is a time trial.

Assignment 1 rests on estimates like this one, and on the uncertainty you declared alongside them. This week is where the first one is made.