The important requirement of a vertical curve is that they should provide a constant rate of change of grade.
Therefore if y = f (x), be the general equation of a curve, for a vertical curve it is required to have
This requirement is fulfilled by parabolic curve.
Morever, parabolic curve further fulfills the requirements of a vertical curve in the following ways:
- It is flatter at the top and hence provides a longer sight distance. Greater the sight distance, lesser is the possibility of any accident.
- Rate of change of grade is uniform throughout and hence produces best riding qualities.
- It is simple in computation and setting works.
Thus, a parabolic curve is most commonly used as a vertical curve.
Elevation of points to set out a vertical parabolic curves is computed by using (1) equation of the parabola directly or by using, (2) geometric properties of the parabola (to calculate vertical offsets from the tangent).