GATE 2022 CE (CE2) – Question 62
A parabolic vertical crest curve connects two road segments with grades +1.0% and −2.0%. If a 200 m stopping sight distance is needed for a driver at a height of 1.2 m to avoid an obstacle of height 0.15 m, then the minimum curve length should be ______ m. (round off to the nearest integer)
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Correct answer: 273
Explanation
The algebraic grade difference is A=1−(−2)=3%. For a crest curve with S≤L, $L=AS^2/[200(\sqrt{h_1}+\sqrt{h_2})^2]$.
Substitute S=200 m, h₁=1.2 m and h₂=0.15 m to obtain L≈272.91 m. This exceeds S, confirming the chosen case. **Answer: 273 m**.