Banking of Roads

The term 'banking' refers to the practice of raising the outer edge of curved roads to give an incline in the road so that vehicles have the necessary centrifugal force to turn safely.

Now the question arises, what is centripetal force? As an object travels around a circle, it experiences a push or a pull toward the centre, creating circular or angular motion. In the following sections, we will discuss the angles of banking and the terms used in banking roads.

What is a Banked Turn?

Whenever there is a turn in the road, the outer edge is slightly higher; this is called a banked turn. This is a turn where the vehicle inclines to the inside.

What is Bank Angle?

Bank angle refers to the angle at which the vehicle inclines to the inside. Inclination occurs along the horizontal and longitudinal axes.

Why is Banking necessary?

There is a probability that a vehicle will skid when it turns along a curved road. An inclined turn or a "banked" turn reduces the chance of skidding. A road's outer edge is raised in turn to have an incline, and its outer edge rises above the inner edge. An angle of inclination formed by a surface is known as a banking angle. The normal force acting on a vehicle while moving through a curved road has a horizontal component. This ensures the vehicle has a centripetal force to turn safely. This centripetal force prevents the vehicle from skidding, and roads have a banked turn to provide this centripetal force.

A vehicle's maximum speed is limited for a particular angle of inclination. It is unaffected by the weight of the vehicle. Three factors affect it: the banking angle, the coefficient of friction, and the radius of curvature.

Centripetal Force

Rotating bodies are attracted to the centre of rotation along the radius of a circular path. It is called centripetal force in classical physics. When a body of mass m moves in a circle of radius r, it produces a centripetal force of the following magnitude,
F= mv2/r

The formula for Banking of Road (Without Friction)

The vertical component of the normal force of the road balances the weight of a vehicle when there is no friction. The horizontal component is responsible for generating centripetal force toward the centre of curvature of the road.
In a curved roadway with a banking angle, the normal force N (perpendicular to the road) segregates into two components.

This gives the expression of the maximum velocity of an object to remain in the curved path.
v= √grtanθ
Where
r is the centre of curvature
g is the acceleration due to gravity
θ is the angle of inclination

The formula for the Banking of Roads (with Friction)

Friction force 'f' acts along the inclined plane's inner edge. The friction force above acts in two directions: horizontally along the centre and vertically downward. If the coefficient of Friction is μ, the friction force is related to the normal force as follows:
F= μN

The expression for the maximum speed at which you can remain on the curved road:
v= √gr(tanθ + μ/1- μtanθ)
Where
μ is the coefficient of Friction

Zero Banking Angle

A vehicle has to take a turn on a horizontal surface if the banking angle is zero. Due to its vertical position, the normal force cannot relate to the centripetal force. It is impossible to make a turn when we consider a frictionless surface. In such cases, a body will experience a centripetal force only on rough surfaces. Thus, on a surface with a friction coefficient μ, when the forces in the vertical direction are balanced, the force is
N = mg
The velocity is given by
v= √μgr

Banking and its Importance

• Banking is a technique for providing a vehicle with the centrifugal force necessary to navigate a curved road safely.
• A banked turn helps avoid skidding.
• A banked road prevents overturns and tumbles.

Points to Remember

• A vehicle's maximum possible speed depends on the banking angle. This is because the banking angle must also be significant to turn at high speed. Hence, racing bikes have more inclined angles than regular bikes. This allows for more extreme speeds on the race tracks.
• Turning is impossible on a smooth, flat surface.
• The top speed of an object moving along a curved path is independent of the mass.
• Railway tracks also have banking. Aircraft turn by inclining their wings above their horizontal position.