Vertical Curve Calculation

The vertical point of curvature (PVC) and the vertical point of tangency (PVT) are located a horizontal distance of L/2 from the PVI. The PVC is generally designated as the origin for the curve and is located on the approaching roadway segment. The PVT serves as the end of the vertical curve and is located at the point where the vertical curve connects with the departing roadway segment. In other words, the PVC and PVT are the points along the roadway where the vertical curve begins and ends.

After located the PVI, PVC, and PVT, you are ready to develop the shape of your curve. The equation that calculates the elevation at every point along an equaltangent parabolic vertical curve is shown below.

 

Vertical Curve - PVC, PVC & PVI calculation:

 

                The general form of the parabolic equation, as applied to vertical curves, is

                               

                               

                Where,

                                y = roadway elevation at distance x from the beginning of the vertical curve in ft (m)

                                x = distance from the beginning of the vertical curve in stations or ft (m)

                                c = elevation of the point of vertical curvature (PVC) in ft (m),

                                = initial roadway grade in percent, it is as referred as the initial tangent grade

                               = final roadway (tangent) grade in percent.