Definition of horizontal curves:
Properties of horizontal curves:
Formula of horizontal curves:
Where:
= Degree of curve [angle subtended by a 30.5-m (100 ft) arc along the horizontal curve.
Horizontal Curves are one of the two important transition elements in geometric design for highways (along with Vertical Curves). A horizontal curve provides a transition between two tangent strips of roadway, allowing a vehicle to negotiate a turn at a gradual rate rather than a sharp cut.
The design of the curve is dependent on the intended design speed for the roadway, as well as other factors including drainage and friction. These curves are semicircles as to provide the driver with a constant turning rate with radii determined by the laws of physics surrounding centripetal force.
Properties of horizontal curves:
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 centripetal force, which is an external force required to keep the vehicle on a curved path. For any given velocity, the centripetal force would need 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 could serve as a countering force, but it generally would provide very little resistance. Thus, the vehicle would have to make a very wide circle in order to negotiate a turn. Given that road designs usually encounter very narrow design areas, such wide turns are generally discouraged.
Formula of horizontal curves:
The allowable radius R for a horizontal curve can then be determined by knowing the intended design velocity V, the coefficient of friction, and the allowed super elevation on the curve.
With this radius, practitioners can determine the degree of curve to see if it falls within acceptable standards. Degree of curve, D_{a}, can be computed through the following formula, which is given in Metric.
Where:
= Degree of curve [angle subtended by a 30.5-m (100 ft) arc along the horizontal curve.
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