# How to Calculate Superelevation ••• den-belitsky/iStock/GettyImages

Superelevation is the lateral angling of a curved roadway or track to counteract the effects of centripetal force on the vehicle traversing the curve. On roadways, vehicles have a tendency to skid in the direction of the outside of the curve if the lateral force overcomes the resistance to the friction force between the tires and the road. In the case of railroad vehicles, cars have a tendency to tilt toward the outside of the curve. To maintain operational speeds, engineers design roadway and track curves to have a banked surface plane angled toward the inside of the curve so that the vehicle does not have to rely on friction to keep it on the road. Superelevation can be stated as an angle, as a percentage or in the case of rail, a fixed height differential between the high rail and the low rail.

You will need to know the maximum driving speed and the radius of the curve. For example, assume that the maximum driving speed (V) is 80 feet per second, and the radius of the curve (r) is 500 feet.

Take the maximum driving speed in feet per second (meters per second for metric) and square it. Using the example from the previous step, V^2 = (80 ft/sec)^2 = 6,400 ft^2/sec^2.

Divide the square of the speed by the radius of the curve in feet (meters for metric) and the acceleration due to gravity of 32 feet per second squared (9.8 meters per second for metric). The result of this calculation is the superelevation ratio in terms of rise over run. in our example: V^2 / (g --- r) = 6,400 ft^2/sec^2 / (32 ft/sec^2 --- 500 ft) = 0.4

To convert the superelevation ratio into an angle, take the inverse tangent of the ratio. The resultant is the angle of the roadway bank in degrees. Using the previous calculation, tan(&#x398;) = 0.4, so &#x398; = tan^-1(0.4) = 21.8&#xB0;. This is the minimum bank angle to avoid relying on friction to keep the vehicle on the road.

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