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 Geometric Design: Theory and Concepts

 
Minimum Radius Calculations

Calculating the minimum radius for a horizontal curve is based on three factors: the design speed, the superelevation, and the side-friction factor (see superelevation and sidefriction factor modules). The minimum radius serves not only as a constraint on the geometric design of the roadway, but also as a starting point from which a more refined curve design can be produced.

For a given speed, the curve with the smallest radius is also the curve that requires the most centripetal force. The maximum achievable centripetal force is obtained when the superelevation rate of the road is at its maximum practical value, and the side-friction factor is at its maximum value as well. Any increase in the radius of the curve beyond this minimum radius will allow you to reduce the side-friction factor, the superelevation rate, or both.

Using the equations for circular motion, friction, and inclined plane relationships, the following equation has been derived.

Rmin = V2/(127(emax/100+fmax))

Where:
Rmin = Minimum radius of the curve (m)
V = Design velocity of the vehicles (km/h)
emax = Maximum superelevation rate as a percent
fmax = Maximum side-friction factor

This equation allows the engineer to calculate the minimum radius for a horizontal curve based on the design speed, the superelevation rate, and the side friction factor.