Question

A valley curve is formed by a descending gradient of 1 in 30 meeting an ascending gradient of 1 in 25. What will be the length of valley curve to fulfil both comfort and head light sight distance requirement for a design speed of 25 m/s.
$[\text{Given:}C=0.6m/s^3]$

• A. 251.5 m
• B. None of these
• C. 87.4 m
• D. 153. 50 m

Answer 1

The correct option is A 251.5 m

$N=\frac{1}{30}+\frac{1}{25}=\frac{55}{750}$

$\text{Comfort condition}$
$L{C}_1=2\sqrt{\frac{N{v}^3}{C}}$
$L{C}_1=2\sqrt{\frac{\frac{55}{750}\times (25{)}^3}{0.6}}=87.40m$

$\text{Headlight sight distance}$
$L{C}_2=\frac{N{S}^2}{2(h_1+Stan\beta )}=\frac{N{S}^2}{(1.5+0.035S)}$
$S=SSD=v.t+\frac{v^2}{2gf}$
$=25\times 2.5+\frac{{25}^2}{2\times 9.81\times 0.35}$
$SSD=153.51m$

$L{C}_2=\frac{\frac{55}{750}\times {153.51}^2}{(1.5+0.035\times 153.51)}$
$=251.44m$

Hence, the length of the valley curve
= 251. 44 m