The length (L) of the vertical curve is measured from the point of commencement of the curve to the end point where it again meets the straightIn other words, it is the distance between the two points of tangency.
Thus the length L of the vertical curve is equal to the algebraic difference of the two gradients divided by the rate of change of grade. Thus,
If G1 is the % gradient before the intersection point.
G2 is the % gradient after the intersection point and
r is the rate of change of gradient,
the Length of the vertical curve
The length of the curve actually provided is generally taken equal to the nearest full chain of 20 m. One half of the total length is provided on either side of the summit or sag. In the case of highways, the sight distance should also be considered while deciding the length of the curve.
(a) Summit curve
(b) Valley curve
Figure 40.1 Types of Vertical curves