What is grip?
Grip is how hard the tyres can push sideways on the road before they slide. Sticky, warm tyres on a dry road grip a lot. Cold tyres or a wet road grip much less.
Grip is friction. The biggest sideways force a tyre can make is the friction coefficient times the force pressing it into the road:F_max = μ × NA heavier push down (bigger N) means more grip. Rubber also needs to be in its temperature window to reach its best μ.
Peak lateral force is roughly μ·Fz, but μ falls slightly as load rises (load sensitivity), so doubling the load gives a bit less than double the grip. This lab uses μeff = μ₀·(1 − 0.06·(Fz/mg − 1)) and a Gaussian temperature window for each compound.μ_eff = μ₀ · f(T) · (1 − 0.06(Fz/mg − 1))
Why do corners need grip?
To go round a bend, something has to keep pulling the car towards the middle of the corner. That pull comes from the tyres. Faster or tighter corners need a bigger pull.
Moving in a circle needs a centripetal force towards the centre:F = m v² / rDouble the speed and you need four times the force. If the tyres can't supply it, the car slides wide.
Setting m·v²/r = μ(mg + ½ρCLA·v²) and solving gives the limit speed:v² = μ g r / (1 − μ ρ C_L A r / 2m)When the denominator reaches zero, downforce grows as fast as the demand, so in theory there is no speed limit for that radius. Real cars hit power and drag limits first.
The friction circle
A tyre has one "budget" of grip. If you use some for braking, there's less left for turning. That's why drivers brake in a straight line first.
Plot sideways g and braking g on one chart. The tyre's limit is (roughly) a circle. Combined demand is √(g_lat² + g_brake²) ≤ g_availableTry the braking in the corner slider and watch the dot move.
Real tyres trace a friction ellipse, and peak forces happen at a slip angle or slip ratio, not at a hard cut-off. "Trail braking" deliberately uses the combined region to rotate the car on entry.
Why downforce matters
Wings push the car into the ground, like an upside-down aeroplane wing. That squashes the tyres into the road so they grip more, especially at high speed.
Downforce adds to weight in the normal force: N = m g + ½ ρ C_L A v²At low speed it barely matters; at high speed it can be more than the car's weight. Try it in Augmenta Downforce.
Because downforce scales with v² just like the centripetal demand, aero grip is worth most in high-speed corners: the ratio of aero to mechanical grip rises with radius. Notice how the two curves diverge on the chart above.