1. Nomenclature

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

 vcurv01

vcurv02

Figure B-1
Adding a Vertical Curve

 

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

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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.

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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 Equationa B-1 and B-2:

BVC EVC sta   BVC EVC elev
Equation B-1        Equation B-2

 

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 and B-2. If g is in %, then L must be in stations, if g is a ratio, then L is in feet.