## Length Of A Valley Curve Problem and Their Solution

Calculate the length of a valley curve when ascending, descending gradient and design speed is given:

### Mathematical Problem

A valley curve is formed by a **descending gradient of 1/20** meets with an **ascending gradient of 1/30. Design speed 85 km/h** allowable rate of change of centrifugal acceleration **is 0.61 m/s³**. Find the length of valley curve for comfort.

### Mathematical Solution

Given,

c = 0.61 m/s³

Design speed(v) = 85km/h = 23.61m/s

Now,

N = [(-1/20) – (1/30)] = 0.083

**Length of Valley Curve**

L = 2[Nv* ^{3}* / c]

^{1/2}L = 2 [( 0.083⨯23.61* ^{3}*) / 0.61]

^{1/2 }L = 2 ⨯ 42.31 = 84.6m

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