The ideal angle of banking provided on the curves of the roads depends on: 

Explanation:

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 the case of roadways, the process of providing superelevation is known as banking of the roads. The general practice, to define the superelevation in roadways, is to mention the angle of inclination (also called the angle of banking) of the road surface, such that

\(\tan {\rm{\theta }} = \frac{{{{\rm{v}}^2}}}{{{\rm{gr}}}}\)

Where v = Velocity of the vehicle, r = Radius of the circular path.

Additional Information  

In the 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

\({S} = \frac{{{\rm{G}}{{\rm{v}}^2}}}{{{\rm{gr}}}}\)

Where G = gauge of the track.

Note:

(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

\({{\rm{v}}_{{\rm{max}}}} = \sqrt {\frac{{gra}}{h}} \)

and in order to avoid skidding

\({{\rm{v}}_{{\rm{max}}}} = \sqrt {μ gr} \)

Where h = Height of center of gravity 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, g = acceleration due to gravity.

(2) When a vehicle moves on a level circular path, the reaction (R_in) at the inner wheel is given by

\({{\rm{R}}_{{\rm{in}}}} = \frac{{mg}}{2}\left( {1 - \frac{{{v^2}h}}{{gra}}} \right)\)

and reaction (R_ot) at the outer wheel

\({{\rm{R}}_{{\rm{ot}}}} = \frac{{mg}}{2}\left( {1\; + \;\frac{{{v^2}h}}{{gra}}} \right)\)

Where m = Mass of the vehicle in kg.