# 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 .

## Related Topics

### • Dynamics

Motion - velocity and acceleration, forces and torque.

## Related Documents

### Acceleration of Gravity and Newton's Second Law

Acceleration of gravity and Newton's Second Law - SI and Imperial units.

### Acceleration Units Converter

Converting between units of acceleration.

### Centripetal and Centrifugal Acceleration Force

Forces due to circular motion and centripetal / centrifugal acceleration.

### Formulas of Motion - Linear and Circular

Linear and angular (rotation) acceleration, velocity, speed and distance.

### Vehicles Traffic Flow and Density

Traffic flow and density as used in highway design.