Superelevation on Roads: Formula, IRC Design Steps and Example
Superelevation (also called cant or banking) is the transverse slope given to a road on a horizontal curve, raising the outer edge above the inner edge. It counteracts the centrifugal force that pushes vehicles outward, so they can take the curve safely at speed.
The basic formula
For equilibrium of a vehicle on a curve:
e + f = V² / (127 R)
- e = rate of superelevation (ratio, e.g. 0.07 = 7%)
- f = coefficient of lateral friction (IRC takes 0.15)
- V = speed in km/h, R = radius of the curve in metres
(In SI units it is e + f = v²/(gR) with v in m/s; the 127 comes from 3.6² × 9.81.)
IRC limits
| Situation | Maximum superelevation |
|---|---|
| Plain and rolling terrain | 7% |
| Hill roads not bound by snow | 10% |
| Snow-bound hill roads | 7% |
| Urban roads with frequent intersections | 4% |
The minimum superelevation is equal to the camber, so the curve still drains water.
IRC design steps
- Superelevation for 75% of design speed, neglecting friction: e = (0.75V)² / (127 R).
- If this e is less than the maximum, provide it. If it is more, provide the maximum e (for example 7%).
- Check friction at full design speed: f = V² / (127 R) − emax. If f ≤ 0.15, the design is safe.
- If f > 0.15, the speed must be restricted to the allowable speed Va = √[127 R (e + f)] with e = emax and f = 0.15, and speed-limit signs put up — or the radius increased.
Worked example
Design the superelevation for a curve of radius 250 m on a plain-terrain highway with design speed 80 km/h.
- e = (0.75 × 80)² / (127 × 250) = 3600 / 31750 = 0.113 (11.3%)
- This exceeds the 7% limit, so provide e = 0.07
- Check friction: f = 80² / (127 × 250) − 0.07 = 0.202 − 0.07 = 0.132
- 0.132 < 0.15, so the curve is safe at 80 km/h with 7% superelevation
Ruling minimum radius
Turning the formula round gives the smallest radius for a design speed, using the maximum e and f:
Rruling = V² / [127 (e + f)]
For 80 km/h in plain terrain: R = 80² / (127 × 0.22) = 229 m.
How superelevation is introduced
The full superelevation is built up gradually over the transition curve, by one of three methods:
- rotating the pavement about the centre line (most common, least earthwork change),
- rotating about the inner edge (useful for drainage),
- rotating about the outer edge.
Exam tip: The superelevation is designed for 75% of the speed with no friction, but checked at full speed with friction. Questions often give R and V and ask only for the "e for 75% speed" — don't forget to cap it at the IRC maximum.
Frequently asked questions
What is the formula for superelevation?
e + f = V² / (127 R), with V in km/h, R in metres, e as a ratio and f the lateral friction coefficient (0.15 as per IRC).
What is the maximum superelevation as per IRC?
7% for roads in plain and rolling terrain and in snow-bound hill areas, 10% for hill roads not bound by snow, and 4% on urban roads with frequent intersections.
Why is superelevation designed for 75% of the design speed?
So that slow vehicles do not slide inwards on a steeply banked curve; the remaining centrifugal force at full speed is taken by friction.
What is the minimum superelevation?
It should not be less than the camber of the road, so that the curve still drains.
Geometric design, traffic and pavement design are covered chapter by chapter in our Highway Engineering notes.
See the Highway notes ›