Introduction |
To negotiate a change in gradient smoothly and to provide vision over the crest of a hill far enough ahead for safe driving, a curve in a vertical plane, gets introduced in the adjacent segments of differing grades. Depending on the magnitude and sign of the gradients at the intersection points, vertical curves fundamentally are of two types: summit or convexity upward and sag/valley or convexity downward. Figure 40.1 illustrates crest or summit and valley vertical curves. Point A is the beginning of the vertical curve labeled BVC or PVC, V is the P.I. or P.V.I. the intersection of the tangents, and B is the end of the vertical curve labeled EVC or PVT. The two grades in the direction of stationing along tangent AV and VB expressed in percent are G1 and G2 respectively. The length of the curve AB is designated L and is measured horizontally. When the tangent rises in the direction of stationing, the grade is positive, and when the tangent slopes downward, the grade is negative. Design of vertical curves is a function of the difference in grade of the intersecting tangents, stopping or passing sight distance, which in turn are functions of vehicle design speed and height of the driver's eye above the roadway, and drainage. In addition to these factors, design of a sag vertical curve also depends on headlight beam distance, rider comfort, and appearance. Details governing the design of vertical curve are beyond the scope of this course. |