Banked Turn

For a vehicle moving in a circle - like a train or a car in a curve - the wheels on the vehicle produces a centripetal acceleration toward the center of the circle. The road or track experiences a centrifugal thrust that tries to move the road or track outwards.

• Centripetal and Centrifugal Force - Acceleration

The outwards thrust can be reduced by inclining the outside of the track. The inclined angle - or banked angle - is the angle at which a vehicle is inclined about its longitudinal axis with respect to its path.

The banked angle can be calculated in radians as

Θ_rad = tan^-1(v² / (r a_g ))                        (1)

where

Θ_rad = banked angle (rad)

v = velocity (m/s)

r = radius of the curve (m)

a_g = acceleration of gravity (9.91 m/s²)

- or alternatively in degrees

Θ_degrees = tan^-1(v² / (r a_g )) (360 / 2 π)                     (1b)

Example - A Train on a Railway Track in a Curve with Radius 1000 m with Speed 70 km/h

The required banked angle to avoid the centrifugal force can be calculated:

Θ = tan^-1(((70 km/h) ( 1000 m/km) / (3600 s/h))²/ ((1000 m) (9.81 m/s²)))

= 0.0385 rad

= (0.0385 rad) (360 / 2 π)

= 2.2^o

Banked Turn Calculator

This calculator can be used to calculate the centripetal acceleration of the car and the banked angle.

Velocity - (m/s)

Curve Radius (m)

• Load Calculator!

• Acceleration Unit Converter

Road Banked Turn Diagram

The diagram below indicates velocity vs. curve radius and required banked turn to compensate centrifugal forces.