🏎️ Banking of Roads

📖 The Physics

Why are highway bends and race tracks tilted? On a flat road, only friction can turn a car around a bend — and friction can run out. If the road is banked (tilted inward), the normal force N leans inward, and its horizontal part can supply the needed centripetal force all by itself.

Balancing the horizontal (N·sinθ = mv²/r) and vertical (N·cosθ = mg) equations gives the one ideal angle for a given speed and radius.

Match the banking angle to the ideal value and no friction is needed at all. Notice the angle doesn't depend on the car's mass. Go faster than the safe speed and the car tends to slide up and out; slower and it slips down and in — which is why race tracks and highway ramps are banked for their design speed.