Superelevation on horizontal curves, with the IRC method

A vehicle on a curve needs a force towards the centre. Friction between tyres and road provides some of it; banking the road, called superelevation, provides the rest.

The basic relation

e + f = V²127 R

e is the superelevation (rise per unit width), f the lateral friction coefficient, V the speed in km/h and R the radius in metres.

IRC takes the maximum lateral friction f = 0.15.

IRC limits on e

Terrain	emax
Plain and rolling	7%
Hill roads, snow-bound	7%
Hill roads, not snow-bound	10%
Urban roads with frequent junctions	4%

Minimum e is the camber, so the curve still drains.

IRC design steps

1. Find e for 75% of the design speed with no friction, so slow vehicles don't slide inward:

e = (0.75 V)²127 R = V²225 R

2. If e is more than e_max, use e_max.
3. Check friction at the full design speed:

f = V²127 R − e_max

If f is 0.15 or less, the design is safe. If not, lower the speed limit on that curve or increase the radius.

Worked example

V = 80 km/h, R = 250 m, plain terrain.

e = 80²225 × 250 = 0.114

That exceeds 0.07, so take e = 0.07.

f = 80²127 × 250 − 0.07 = 0.132

Since 0.132 is less than 0.15, the curve is safe at 80 km/h with 7% superelevation.

Ruling minimum radius

R_ruling = V²127 (e + f) = 80²127 × 0.22 = 229 m

Our road curves tool works out superelevation, extra widening and transition length step by step.