Definition and formula of Superelevation and Angle of Inclination in Roadway and Highway (or railway).

Whenever a roadway (or railway) is laid on a curved path, then its outer edge is always made higher than the inner edge, to keep the vehicle in equilibrium while in motion. The amount by which the outer edge is raised, is known as cant or superelevation. In case of roadways, the process of providing superelevation is known as banking of the road. The general practice, to define the superelevation in roadways, is to mention the angle of inclination (also called angle of banking) Of the road surface, such that

where

v = Velocity of the vehicle, and

r = Radius of circular path.

In case of railways, the general practice to define the superelevation, is to mention the difference of levels between the two rails. In such a case, superelevation is given by

where  G = Gauge of the track.

Notes:

1. When a vehicle is moving on a level circular path, then the maximum velocity of the vehicle, in order to avoid overturning is given by

and in order to avoid skidding,

where   

h = Height of C.G. of the vehicle from the ground level,

2a = Distance between the outer and inner wheel, and

μ = Coefficient of friction between the wheels of the vehicle and the ground.

2. When a vehicle moves on a level circular path, the reaction at the inner wheel

and reaction at the outer wheel

where  m = Mass of the vehicle in kg.