GATE 2024 CE (CE2) – Question 63
A vertical summit curve on a freight corridor is formed at the intersection of two gradients, +3.0% and −5.0%. Assume the following:
Only large-sized trucks are allowed on this corridor
Design speed = 80 kmph
Eye height of truck drivers above the road surface = 2.30 m
Height of object above the road surface for which trucks need to stop = 0.35 m
Total reaction time of the truck drivers = 2.0 s
Coefficient of longitudinal friction of the road = 0.36
Stopping sight distance gets compensated on the gradient
The design length of the summit curve (in meters) to accommodate the stopping sight distance is __________ (rounded off to 2 decimal places).
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Show answer and explanation
Correct answer: 117.11 to 118.29
Explanation
The speed is $v = \frac{80}{3.6} = 22.22$ m/s. The stopping sight distance is $S = vt + \frac{v^2}{2gf} = 22.22 \times 2 + \frac{22.22^2}{2 \times 9.81 \times 0.36} = 44.44 + 69.92 = 114.36$ m. The algebraic difference of the grades is $N = 0.03 + 0.05 = 0.08$. For a summit curve with $S < L$, $L = \frac{NS^2}{2\left(\sqrt{H} + \sqrt{h}\right)^2} = \frac{0.08 \times 114.36^2}{2(\sqrt{2.30} + \sqrt{0.35})^2} = \frac{1046.2}{8.889} = 117.70$ m. This is more than $S$, so the assumption $S < L$ holds.