Horizontal Curve - Degree of curve

Description

Aside from momentum, when a vehicle makes a turn, two forces are acting upon it. The first is gravity, which pulls the vehicle toward the ground. The second is centrifugal force, for which its opposite, centripetal acceleration is required to keep the vehicle on a curved path. For any given velocity, the centripetal force needs to be greater for a tighter turn (one with a smaller radius) than a broader one (one with a larger radius). On a level surface, side friction fs serves as a countering force to the centrifugal force, but it generally provides very little resistance/force. Thus, a vehicle has to make a very wide circle in order to make a turn on the level.

Given that road designs usually are limited by very narrow design areas, wide turns are generally discouraged. To deal with this issue, designers of horizontal curves incorporate roads that are tilted at a slight angle. This tilt is defined as superelevation, or e {\displaystyle e} e, which is the amount of rise seen on an angled cross-section of a road given a certain run, otherwise known as slope. The presence of superelevation on a curve allows some of the centripetal force to be countered by the ground, thus allowing the turn to be executed at a faster rate than would be allowed on a flat surface. Superelevation also plays another important role by aiding in drainage during precipitation events, as water runs off the road rather than collecting on it. Generally, superelevation is limited to being less than 14 percent, as engineers need to account for stopped vehicles on the curve, where centripetal force is not present.

The allowable radius for a horizontal curve can then be determined by knowing the intended design velocity, the coefficient of friction, and the allowed superelevation on the curve. With this radius, practitioners can determine the degree of curve to see if it falls within acceptable standards.

Where degree of curvature is based on 100 units of arc length.

Related formulas

Variables

Dadegree of curve (100 units of arc length) (dimensionless)
Rallowable radius for a horizontal curve (percent) (dimensionless)