A banked turn is a turn or change of direction in which the vehicle banks or inclines, usually towards the inside of the 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.
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
Θrad = tan-1(v2 / (r ag)) (1)
Θrad = banked angle (rad)
v = velocity (m/s)
r = radius of the curve (m)
ag = acceleration of gravity (9.91 m/s2)
- or alternatively in degrees
Θdegrees = tan-1(v2 / (r ag)) (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)
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)
Road Banked Turn Diagram
The diagram below indicates velocity vs. curve radius and required banked turn to compensate centrifugal forces.