How to Calculate Banking Angle of Road

What is Banking Angle?

At the turning of the road you might have observed that the inner side of the road (or the side of the road which forms the inside of the turning arc) has the lower height than the other side of the road. As a result, at the turning, the surface of the road is not flat; it is inclined towards the centre of the turning of the road.

Banking Angle of Road

 

Such inclination at the turning is called the banking of roads and the angle of inclination of the road at turning is called the banking angle of the road.

 

Why We Need Banking?

Well, in short, due to the centrifugal force. To explain it further, say, we have a road turning with turning radius R and the turning doesn’t have the banking or inclination.

Let’s assume further that a car is passing the turning with a velocity of V and the coefficient of friction between the car tire and road is μ.

At the turning, with the absence of the banking, the centrifugal force developed in the vehicle need to be entirely balanced by the frictional force between the car wheels and road.

Road without banking

 

Frictional force>=Centrifugal force

μ*M*g =>(M*V2)/R

or, V <= √(μ*R*g)………………eq.1

Where,

M – Mass of the car

g – Acceleration due to the gravity

From the above eq.1, you can see that, for the turning of the road without banking, the speed of the car cannot be more than √(μ*R*g).

So, in order to facilitate the driving at higher speed (higher than the value of √μ*R*g) at the turning banking of the road is required.  

How to Calculate the Banking Angle of the Road

In case of baking of the road in the turning, the centrifugal force is balanced by the component of the reaction force. See the below force balance diagram for the banking of road:

Calculation of Road Banking Angle

 

R1*Cosθ=M*g………………………………….eq.2

R1*Sinθ=Centrifugal force= (M*V2)/R………………eq.3

 

By dividing the eq.3 to eq.2,

Tanθ=(V2)/(R*g)……………………….eq.4

 

So, with the banking at the road turning by increasing the banking angle the higher velocity of the passing car can be achieved safely.

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