Length Of A Valley Curve Problem and Their Solution - Civil Engineering

Wednesday, 17 April 2019

Length Of A Valley Curve Problem and Their Solution

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[Nv³ /c]1/2
L = 2 [( 0.083⨯23.61³)/0.61]1/2 
L = 2 ⨯ 42.31 = 84.6m
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