Superelevation Rate for a Horizontal Curve

A vehicle rounding a curve needs a sideways force, and it gets it from two places: the component of its own weight down a banked surface, and friction between tyre and road. The design equation simply says the two together must supply v²/(gR). Highway agencies cap e at 4 % where snow and ice are common (a stalled truck must not slide sideways off a banked curve) and up to 12 % on high-speed rural roads; the friction factor f is taken not from the tyre's real capability but from what a driver will tolerate before feeling uncomfortable, sliding from 0.17 at 30 mph down to about 0.08 at 80 mph.

The familiar shortcuts are this same equation with gravity folded into the units. With V in mph and R in feet, v²/(gR) becomes V²/(15R); with V in km/h and R in metres it becomes V²/(127R), since 3.6² × 9.807 = 127. A worked example: 60 mph on a 1,500 ft radius with f = 0.12 needs e = 100(3600/(15 × 1500) − 0.12) = 4.0 %. The trap is entering the speed in the wrong unit: the term is quadratic, so a 10 % speed error becomes a 21 % error in the required bank.