Motion of Vehicles on Banked Curved Roads

Motion of Vehicles on Banked Curved Roads

• When roads are banked the horizontal component of normal reaction partly balances the outward centrifugal force. The design speed for particular angle of banking is calculated without considering friction.

The F.B.D. of vehicle is shown in Fig. 9.12.1.

• The above equation gives maximum speed to avoid skidding outwards.

• To avoid skidding inwards, the direction of frictional force will be opposite. Hence minimum speed to avoid skidding is,

Solved Examples for Understanding

Example 9.12.1 

The sports car having a mass of 1700 kg is travelling horizontally along a 20° banked track which is circular and has a radius of curvature of 100 m. If the coefficient of static friction between the tyres and road is μs = 0.2, determine the maximum constant speed at which car can travel without sliding up the slope. Neglect the size of car.

Solution: 

From equation (9.12.3), the maximum speed without skidding is

Example 9.12.2 

A highway curve of 250 m radius is banked for a speed of 45 km/h. Determine a) The amount of superelevation if the width of the road is 16 m, and b) The maximum speed for no skidding on the curve if the coefficient of friction is 0.5.

Solution: 

The angle of banking is given by

To avoid skidding, the maximum safe velocity is given by,