Banked Curve & Banking Angle — equation of the banked angle derivation

Banking Angle — what is the banking angle and why is it important?

When a car travels without skidding around an unbanked curve, the static frictional force between the tires and the road provides the centripetal force. But the wear and tear of tires caused by this friction increases the maintenance cost of the vehicles and increases the risk of sudden accidents at the curved points of the roads.

However, if the curve of a road is banked at an angle relative to the horizontal, much in the same way that a plane is banked while making a turn, the reliance on friction to provide the required centripetal force can be eliminated completely for a given speed. This angle the curve of the road makes here with respect to the horizontal is called banking angle or banked angle.

Banking angle at the curved turns of the roads reduces friction between the tires and the road and this, in turn, reduces maintenance cost and accidents of the vehicles.

Banking angle formula with derivation

Say, a car going around a friction-free banked curve. The radius of the curve is r, where r is measured parallel to the horizontal and not to the slanted surface.

We have to consider the normal force FN that the road applies to the car, the normal force being perpendicular to the road.

Because the roadbed makes an angle θ with respect to the horizontal, the normal force has a component sin θ that points toward the center C of the circle and provides the centripetal force:
……… (1)

[ Read the complete Post with diagrams here: Banking angle physics ]

Different observations related to the Banking angle of the road

[ Read the complete Post with diagrams here: Banking angle observation — physics ]

How do the Banked Curve & Banking Angle help a car? | banking angle formula with derivation

Originally published at on August 9, 2020.

NIT Grad & IT prof. Writes and teaches HS physics. A motivational speaker and an active blogger with multiple niches. With lots of stories to tell.

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