Banking of the roads

 

Roads are banked as sometime the friction in the roads is not sufficient enough to provide the necessary inward centripetal force for the circular turning of the vehicle. The phenomenon of raising outer edge of the curved road above the inner edge is to provide necessary centripetal force to the vehicles to take a safer turn and the curved road is called Banking of Roads.

If the bank angle is zero, the surface is flat and the normal force is vertically upward. The only force keeping the vehicle turning on its path is friction, or traction. This must be large enough to provide the centripetal force, a relationship which can be expressed as an inequality, assuming the car is driving in a circle of radius r:

\mu mg>{mv^{2} \over r}.

The expression on the right hand side is the centripetal acceleration multiplied by mass, the force required to turn the vehicle. The left hand side is the maximum frictional force, which equals the coefficient of friction μ multiplied by the normal force. Rearranging the maximum cornering speed is

v<{\sqrt {r\mu g}}.

Note that μ can be the coefficient for static or dynamic friction. In the latter case, where the vehicle is skidding around a bend, the friction is at its limit and the inequalities becomes equations. This also ignores effects such as downforce which can increase the normal force and cornering speed.

When vehicles go through turnings, they travel along a nearly circular arc. There must be some force which will produce the required acceleration. If the vehicle goes in a horizontal circular path, this resultant force is also horizontal. A vehicle of mass M moving at a speed v is making a turn on the circular path of radius r. The external forces acting on the vehicle are (i) weight Mg (ii) Normal contact force (iii) friction f. Friction is not always reliable at circular turns if high speeds and sharp turns are involved. To avoid dependence on friction, the roads are banked at the turn so that the outer part of the road is somewhat lifted up as compared to the inner part.

 

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