Elements of a horizontal curve

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ELEMENTS OF A HORIZONTAL CURVE

The elements of a circular curve are shown in figure 11-3. Each element is designated and explained as follows:

PI POINT OF INTERSECTION. The point of intersection is the point where the back and for-ward tangents intersect. Sometimes, the point of intersection is designated as V (vertex).

I INTERSECTING ANGLE. The intersecting angle is the deflection angle at the PI. Its value is either computed from the preliminary traverse angles or measured in the field.

A CENTRAL ANGLE. The central angle is the angle formed by two radii drawn from the

Figure 11-2.—Horizontal curves.

Figure 11-3.—Elements of a horizontal curve.

center of the circle (O) to the PC and PT. The value of the central angle is equal to the I angle. Some authorities call both the intersecting angle and central angle either I or A.

R    RADIUS. The radius of the circle of which the curve is an arc, or segment. The radius is always perpendicular to back and forward tangents.

PC    POINT OF CURVATURE. The point of curva-ture is the point on the back tangent where the circular curve begins. It is sometimes designated as BC (beginning of curve) or TC (tangent to curve).

PT    POINT OF TANGENCY, The point of tangency is the point on the forward tangent where the curve ends. It is sometimes designated as EC (end of curve) or CT (curve to tangent).

POC    POINT OF CURVE. The point of curve is any point along the curve.

LENGTH OF CURVE. The length of curve is the distance from the PC to the PT, measured along the curve.

T    TANGENT DISTANCE. The tangent distance is the distance along the tangents from the PI to the PC or the PT. These distances are equal on a simple curve.

LC    LONG CHORD. The long chord is the straight-line distance from the PC to the PT. Other types of chords are designated as follows:

C The full-chord distance between adja-cent stations (full, half, quarter, or one-tenth stations) along a curve.

c] The subchord distance between the PC and the first station on the curve.

c? The subchord distance between the last station on the curve and the PT.

E    EXTERNAL DISTANCE. The external distance (also called the external secant) is the distance from the PI to the midpoint of the curve. The external distance bisects the interior angle at the PI.

M    MIDDLE ORDINATE. The middle ordinate is the distance from the midpoint of the curve to the midpoint of the long chord. The extension of the middle ordinate bisects the central angle.

D    DEGREE OF CURVE. The degree of curve defines the sharpness or flatness of the curve.