GATE 2026 CE (CE2) – Question 61
A vertical curve is formed by a descending gradient of 1 in 40 meeting an ascending gradient of 1 in 50. Consider the following:
Stopping Sight Distance (SSD) = 90 m
Height of headlight of a vehicle above the road surface = 0.75 m
Headlight beam angle with respect to the longitudinal axis of the vehicle = 1.2°
Based on the sight distance criteria, the design length (in m) of the vertical curve is __________ (*rounded off to the nearest integer*).
Practise this question in The GATE Grind →
Show answer and explanation
Correct answer: 63
Explanation
A descending grade meeting an ascending grade makes a valley curve, designed for headlight sight distance. The deviation angle is $N = \frac{1}{40} + \frac{1}{50} = 0.045$. First try $L > S$: $L = \frac{NS^2}{2h + 2S\tan\alpha} = \frac{0.045 \times 90^2}{1.5 + 180\tan 1.2^\circ} = \frac{364.5}{5.27} = 69.2$ m. That is less than $S = 90$ m, so the assumption fails. For $L < S$, $L = 2S - \frac{2h + 2S\tan\alpha}{N} = 180 - \frac{5.27}{0.045} = 62.9$ m, which is less than $S$ as required. The design length is 63 m.