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# Parabolic Curves

Parabolic curves find there usage when we have to connect sections of highways or railroads of differing gradient. The use of a parabolic curve provides a gradual change in direction along the curve.

where
PVC= point of vertical curvature, beginning of curve
PVI= point of vertical intersection of grades on either side of curve
PVT= point of vertical tangency, end of curve
G1= grade at beginning of curve, ft/ft (m/m)
G2= grade at end of curve, ft/ft (m/m)
L=length of curve, ft (m)
R =rate of change of grade, ft/ft2 (m/m2)
V =elevation of PVI, ft (m)

Eo= elevation of PVC, ft (m)
Et= elevation of PVT, ft (m)
x =distance of any point on the curve from the
PVC, ft (m)
Ex= elevation of point x distant from PVC, ft (m)
xs= distance from PVC to lowest point on a
sag curve or highest point on a summit curve, ft (m)
Es= elevation of lowest point on a sag curve or highest point on a summit curve, ft (m)

Equations of Parabolic Curves

R=(G2-G1)/L

Eo=V-LG1/2

Ex=Eo+G1x +Rx2/2

xs1/R

Eso-G12/2R

For xs>L:The curve has no high or low point

### Kanwarjot Singh

Kanwarjot Singh is the founder of Civil Engineering Portal, a leading civil engineering website which has been awarded as the best online publication by CIDC. He did his BE civil from Thapar University, Patiala and has been working on this website with his team of Civil Engineers.

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