# 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.

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 } (v ^{ 2 } / (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/s ^{ 2 } ) *

- or alternatively in degrees

* Θ _{ degrees } = tan ^{ -1 } (v ^{ 2 } / (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/s ^{ 2 } ))) *

* = 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.

### Road Banked Turn Diagram

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

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