Elements of Horizontal Curve

Fig shows main elements of a horizontal curve

PC = Point of curvature. It is the beginning of curve.

PT = Point of tangency. It is the end of curve.

PI = Point of intersection of the tangents.

T = Length of tangent from PC to PI and from PI to PT. It is known as sub-tangent.

R = Radius of simple curve, or simply radius.

L = Length of chord from PC to PT. Point Q as shown in the figure is the midpoint of L.

Lc = Length of curve from PC to PT. Point M as shown in the figure is the midpoint of Lc.

E = External distance. It is the nearest distance from PI to the curve. From the above figure, point M is the midpoint of the curve and E is the distance from PI to M.

m = Middle ordinate. It is the distance from the midpoint of the curve to the midpoint of the chord. From the figure above, m is the distance MQ.

I = Deflection angle (also called angle of intersection and central angle). It is the angle of intersection of the tangents. The angle subtended by PC and PT at O is also equal to I, where O is the center of the circular curve from the above figure.

x = offset distance from tangent to any point in the curve; note that x is perpendicular to T.

θ = offset angle subtended at PC between PI and any point in the curve

D = Degree of curve. It is the central angle subtended by a length of curve equal to one station. In English system, one station is equal to 100 ft and in SI, one station is equal to 20 m.

Sub chord = chord distance between two adjacent full stations.