B. Vertical Curves

1. Nomenclature

A vertical curve is used to provide a smooth transition between two different grade lines, Figure B-1.



Figure B-1
Adding a Vertical Curve


The parts of the curve, Figure B-2, are:

Figure B-2
Curve Parts


PVI Point of Vertical Intersection (aka PI)
BVC Begin Vertical Curve (aka, BC, PVC, PC)
EVC End Vertical Curve (aka EC, PVT, PT)
L Curve Length


Distances, including the curve length, are horizontal, not along the grade lines or curve.

An equal tangent vertical curve is used. This places BVC and EVC equidistant from the PVI, Figure B-3.

Figure B-3
Equal Tangent Vertical Curve


The curve is tangent to the grade lines at both ends to provide a smooth transition between the grade lines and curve.

The stations and elevations of the BVC and EVC are determined from Equations B-1, -2, -3, and -4.

BVC EVC sta   BVC EVC elev
Equations B-1 and B-2        Equations B-3 and B-4


Because grade ratio and percent differ by a factor of 100 as do distances in feet or stations, care must be taken to use the correct form of each in Equations B-1 through  B-4. If g is in %, then L must be in stations, if g is a ratio, then L is in feet.