# Banked Turn

## 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)

where

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) (360 / 2 π)

= 2.2o

### Banked Turn Calculator

Velocity - (m/s)

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

## Related Topics

• Dynamics - Motion - velocity and acceleration, forces and torques

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