Madring

the tight line is the one that runs out.

one thumb picks the line, the car holds it and handles its own throttle -- the arc you choose is the speed you are allowed

A tyre has one budget of grip and turning spends it, so the speed a corner allows comes out of its radius: v = sqrt(mu g r). Here the car takes each corner at the speed the road allows and your thumb picks the line; hug the inside and your arc is tighter than that speed can hold, so the front runs out and you go wide. That is the whole reason a racing driver runs wide on entry and wide on exit, and there is no bravery in the equation at all. Turn 12 here, La Monumental, is the same equation with the road tilted: 550 metres of banking at a 24% gradient (13.5 degrees) lets the track itself carry some of the cornering load, so the same radius takes about a third more speed. The circuit is the real one, 5.416 km of it, with the real hills.

Concepts: friction, centripetal-force, radius, banking.

An interactive you play with one thumb, on Wundr.