Vertical Curve

Vertical Curve Formulas

Input Data:

Incoming Grade = %
Outgoing Grade = %
Curve Length = ft
P.V.I. Station =
P.V.I. Elevation = ft
Results:

Tangent Offset at PVI = ft
Rate of Grade Change = %/Sta
PVC Station =
PVC Elevation = ft
PVT Station =
PVT Elevation = ft
x Distance = ft
y Distance = ft
y Elevation = ft
y Station =

VERTICAL CURVE FORMULAS

vertical curve picture

 

L = Length of Curve g2 = Grade of Forward Tangent
PVC = Point of Vertical Curvature a = Parabola Constant
PVI = Point of Vertical Intersection y = Tangent Offset
PVT = Point of Vertical Tangency E = Tangent Offset at PVI
g1 = Grade of Back Tangent r = Rate of Change of Grade

 

y = ax2a = g2 - g1
2 L

E = a (L/2)2

r = g2 - g1
L

Tangent Elevation = YPVC + g1x

Grade Elevation = YPVC + g1x + ax2