GATE 2023 CE (CE1) – Question 21
$G_1$ and $G_2$ are the slopes of the approach and departure grades of a vertical curve, respectively.
Given $|G_1| < |G_2|$ and $|G_1| \neq |G_2| \neq 0$
Statement 1: +$G_1$ followed by +$G_2$ results in a sag vertical curve.
Statement 2: −$G_1$ followed by −$G_2$ results in a sag vertical curve.
Statement 3: +$G_1$ followed by −$G_2$ results in a crest vertical curve.
Which option amongst the following is true?
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Correct answer: (A) Statement 1 and Statement 3 are correct; Statement 2 is wrong
Explanation
A vertical curve is a sag when the grade increases algebraically along the road (the curve is concave up). For +G₁ then +G₂ with $G_2 > G_1$ the grade increases: a sag (1 true). For −G₁ then −G₂ with $|G_2| > |G_1|$ the grade becomes more negative, so it decreases: a crest, not a sag (2 false). +G₁ followed by −G₂ is a decreasing grade, a crest (3 true).