Vertical Alignment of Highways - IES Previous Year Questions
11.  A descending gradient of 4% meets an ascending gradient of 1 in 40 where a valley curve of length 200 m is to be formed. What will be the distance of the lowest point on the valley curve from its first tangent point ?
[IES 2015]
- 111 m
- 125 m
- 118 m
- 100 m
Answer: Option A
Explanation:
N1 = - 0.04, N2 = 1/40 = 0.025
Total deviation angle, N = | N1 - N2 | = |-0.04 - 0.025| = 0.065
Length of valley curve, L = 200 m
The distance of lowest point on the valley curve from its first tangent point is,
x = L x (N1/2N)½
⇒ x = 200 x {0.04 / (2 x 0.065)}½
⇒ x = 110. 94 m
Explanation:
N1 = - 0.04, N2 = 1/40 = 0.025
Total deviation angle, N = | N1 - N2 | = |-0.04 - 0.025| = 0.065
Length of valley curve, L = 200 m
The distance of lowest point on the valley curve from its first tangent point is,
x = L x (N1/2N)½
⇒ x = 200 x {0.04 / (2 x 0.065)}½
⇒ x = 110. 94 m