Superelevation and equilibrium superelevation

Superelevation (cant) is the transverse slope provided at a horizontal curve by raising the outer edge of the pavement above the inner edge, so that a component of the vehicle's weight acts against the centrifugal force.

Equilibrium superelevation is the value of superelevation at which the centrifugal force is completely balanced by the weight component, so that no lateral friction is needed:

$$e = \tan\theta = \frac{v^2}{gR} \qquad\left(= \frac{V^2}{127R}\ \text{with } V \text{ in km/h}\right)$$

Assumptions

1. The vehicle is treated as a point mass moving at a uniform speed $v$.
2. The curve has a constant radius $R$, and the pavement is a plane surface with a uniform slope.
3. Lateral friction is zero (neglected) in the equilibrium condition.
4. The vehicle neither skids nor overturns, and the height of its centre of gravity is not considered in the basic derivation.
5. The superelevation is small, so $\sin\theta \approx \tan\theta$ and $\cos\theta \approx 1$.