LENGTH OF VERTICAL CURVE,RATE OF CHANGE IN GRADIENT

RATE OF CHANGE IN GRADIENT

The percentage change in the gradient with respect to length of the curve is called Rate of Change of Gradient. This rate is 0.1 % in 30 meters (100ft) in summit while this rate is 0.05% in 30 meters (100ft) in sag.

LENGTH OF VERTICAL CURVE

The length of vertical curve is set out by the following formula
Length of curve =L= Total change in gradients
                                   Rate of change in gradient
The half of the length of a curve is set out on both sides of the apex point.

• Example

A centre line of a road has +0.75% gradient. At a certain point this gradient changes to -0.55%. If the rate of change o grade at this point is 0.1% to 30 meter length, then calculate the length of vertical curve.

• Solution:

First gradient = +0.75%
Second gradient = -0.55%
Total change is gradient = +0.75-(-0.55) = 1.30%
Length of curve =L= Total change in gradients
                                   Rate of change in gradient
Rate of change in gradient = 1.3/0.1 x 30= 390 m