Solved Example & Practice Problems: Motion of Vehicles on Banked Curved Roads

Motion of Vehicles on Banked Curved Roads

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,

Examples for Practice

Q.1

A curved road is to be banked for a speed of 50 km/h. If the radius of the curved road is 200 m, determine the angle of banking. If the width of the road is 10 m, determine the superelevation. 

[Ans. : 5.615°, 0.98 m]

Q.2

A curved section of road has radius 100 m and is to be banked for a speed of 40 km/h. Determine the angle of banking. If coefficient of friction is 0.3, what is the safe velocity without skidding on the banked road?

[Ans. : 7.173°, 75 km/h]