Fifteen lessons, in the order the ideas depend on each other. The physics a race engineer actually uses is a small set - Newton's laws, friction, energy, a little heat, and reading a graph - and after these the learning comes from data, not sheets. Pace: one lesson per race weekend or practice day, so each sheet's "go measure it" problem gets measured.
Lessons 1-8 use only measured numbers. Lessons 9-11 and 14-15 are built on a lap model of our kart (traces marked synthetic on every page): what the physics predicts a lap looks like, tuned to nothing but the real 58.33 s best. Lesson 12 is built on the official timing from the first race. Three checkpoints (corner weights, the pyrometer, the data logger) upgrade earlier sheets when they arrive: the answers get truer as the season goes, and the day the logger goes on, the gap between the model traces and the real ones becomes the lesson.
Foundations: mechanics, no calculus
- Units, and the check that catches wrong reasoning. A quantity is a number and a unit; make the units cancel or the reasoning is wrong. Mars Climate Orbiter, the Gimli Glider, the Paris kilogram.
- Gearing. Gears don't make power: a taller ratio trades push for top speed in the same proportion. The only engine lever the rules leave you, and why a draft can't help you past the limiter.
- Weight transfer. A kart has no differential, so it turns by lifting the inside rear. Transfer = g x weight x height / track. Every setup lever is a way to change how much weight moves.
- Tires. Grip rises with load but less than proportionally, so moving weight always costs grip. Heat: the pressure gauge is a thermometer, and the pyrometer (a probe thermometer for tire rubber) reads inside, middle and outside to say what the tire is doing across its width.
- Braking and corner entry. Braking moves weight forward off the axle that has the only brake. Why the rear steps out on entry, and what the driver can do about it before anyone touches the kart.
- Energy. Kinetic energy goes as speed squared: 10% more corner speed is 21% more energy. Where lap time actually lives (the slow corners) and why the straight matters less than it feels.
- The friction circle. A tire has one budget for braking, cornering and accelerating, spent together. Trail braking (still on the brake as you turn in) is spending it well. The driving lesson, in physics clothes.
- Front geometry. Caster, camber, toe, Ackermann (the inside front steering more than the outside), front width: what each does to weight transfer and patch shape. Caster is how the inside rear finishes lifting after transfer has done what it can.
Data: on the model now, on the logger later
- Reading a trace. Speed against distance; rpm; throttle and brake. Slope of speed is acceleration, area under speed is distance - the two ideas of calculus, met as the shape of a graph before anyone says the word.
- Comparing two laps. The delta-time trace (the gap between two laps, plotted around the track) and segment times. Where the four tenths to the leaders live, corner by corner.
- Heat and the engine. Cylinder-head temperature, the limiter, why the engine fades hot, and why a night race is a different air density and a different engine.
- Statistics for the stopwatch. Lap-time scatter; why one fast lap proves less than five consistent ones; accuracy versus repeatability, made general. Written by the analytics side.
Depth: if the driver wants it
- The chassis as a spring. Flex, the torsion bar, why a stiffer frame lifts the inside rear more, and the lever arms the simple transfer formula leaves out.
- Aerodynamics at 55 mph. Drag, and the draft in numbers.
- A lap-time model. The friction circle plus the engine curve, integrated around the track: what a setup change is worth before you try it.