 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 $$\begin{array}{l}v=\sqrt{\frac{(rg(tan\Theta+\mu_s))}{1-\mu_S\,tan\theta}}\end{array}$$ For a given pair of roads, and tyre $$\begin{array}{l}\mu_s=tan\lambda\end{array}$$, where $$\begin{array}{l}\lambda\end{array}$$ is the angle of friction, the velocity of a vehicle on a curved banked road is $$\begin{array}{l}v=\sqrt{rg\,tan(\Theta+\lambda)}\end{array}$$ The safe velocity on an unbanked road is given by the expression $$\begin{array}{l}v_{max}=\sqrt{\mu\times r\times g}\end{array}$$ The expression for the angle of banking of road is given by $$\begin{array}{l}\Theta=\tan^{-1}\frac{v^2}{rg}\end{array}$$ The expression for the safe velocity on the banked road is given by $$\begin{array}{l}v_{max}=\sqrt{rg\,\tan\Theta}\end{array}$$ Centripetal Force F = mv2/r = mω2r

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.

Stay tuned with BYJU’S for more such interesting articles. Also, register to “BYJU’S – The Learning App” for loads of interactive, engaging Physics-related videos and an unlimited academic assist.