Banking of Road Formula

The phenomena in which the edges of the curved roads are raised above the inner edge to provide the necessary centripetal force to the vehicles so that they take a safe turn. The various terminologies used in the case of banking of roads are:

  • Banked Turn – It is defined as the turn or change of direction in which the vehicle inclines towards inside.
  • Bank Angle – The angle at which the vehicle is inclined is defined as the bank angle.

In the next section, let us look at the formula for the angle of banking.

Angle of Banking Formula

The velocity of a vehicle on a curved banked road

\(v=\sqrt{\frac{(rg(tan\Theta+\mu_s))}{1-\mu_S\,tan\theta}}\)

For a given pair of roads, and tyre \(\mu_s=tan\lambda\), where \(\lambda\) is the angle of friction, the velocity of a vehicle on a curved banked road is

\(v=\sqrt{rg\,tan(\Theta+\lambda)}\)

The safe velocity on an unbanked road is given by the expression

\(v_{max}=\sqrt{\mu\times r\times g}\)

The expression for the angle of banking of road is given by

\(\Theta=\tan^{-1}\frac{v^2}{rg}\)

The expression for the safe velocity on the banked road is given by

\(v_{max}=\sqrt{rg\,\tan\Theta}\)

The expression for the angle of banking

\(\Theta=\tan^{-1}\frac{v^2}{rg}\)

Roads are most often banked for the average speed of vehicles passing over them. Nevertheless, if the speed of a vehicle is lesser or more than this, the self-adjusting state friction will operate between tyre and road and vehicle will not skid.

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Practise This Question

Mass of two spheres is in the ratio 8:1. Assuming that both of them have the same density, find the ratio of their radii.

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