Introduction to Horizontal Curves

Horizontal Curves
Introduction
Most types of transportation routes, such as highways, railroads, and pipelines, are connected by curves in both horizontal and vertical planes. Horizontal Curves: Curves used in horizontal planes to connect two straight tangent sections. Two types of horizontal cures:
Circular arcs, and Spirals

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Horizontal Curves
Introduction
Simple Curve: A circular arc connecting two tangents. Compound Curve: Two or more circular arcs of different radii tangent to each other. Broken-back Curve: Combination of a short length of tangent connecting two circular arcs that have centers on the same side. Reverse Curve: Two circular arcs tangent to each other, with their centers on opposite side of the alignment.

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Horizontal Curves
Degree of Circular Curve
The rate of curvature of circular curves can be designated either by their radius (100-m curve), or by their degree of curve. The degree of curve: Arc definition: The central angle subtended by a circular arc of 100-ft. Chord definition: The angle at the center of a circular arc subtended by a chord of 100 ft.

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Horizontal Curves
Definitions and Derivation of Circular Curve Formulas
PI: Point of intersection PC: Point of curvature (the beginning of the curve) PT: Point of tangency (the end of the curve) TC: Tangent to curve CT: Curve to tangent R: Curve radius T: Tangent distance (PC-PI or PI-PT) LC: Long chord (PC-PT) Circular curve elements L: Length of the curve (along the curve) E: Length from the PI to the curve midpoint on a radial line. M: Middle ordinate. The radial distance from the midpoint of the long chord to the curves midpoint.
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Horizontal Curves
Definitions and Derivation of Circular Curve Formulas
POC: Any point on