Which is following situation created for summit curve ?

Question

Examoogle · Accepted Answer

Option D: All of the above

Explanation & Concepts:
A summit curve (or crest curve) is a vertical curve with convexity upwards. It is formed at the intersection of two gradients whenever the algebraic difference of gradients (deviation angle $N$) results in a crest, causing a peak point. Any condition where the second gradient is steeper downwards (or less steep upwards) than the first gradient forms a summit curve, making all given options valid.

Working Principle: Vertical summit curves are provided at gradient changes to ensure a smooth transition and adequate Sight Distance (Stopping Sight Distance or Overtaking Sight Distance) for drivers. The deviation angle is calculated as $N = n_1 - n_2$, where $n_1$ and $n_2$ are the gradients considering sign convention (+ for upgrade, - for downgrade). A summit curve is formed whenever $N > 0$.

Key Formulas: $N = n_1 - n_2$ — Algebraic difference of gradients (deviation angle); $L = \frac{N S^2}{4.4}$ — Length of summit curve for $L > SSD$ (where $h_1 = 1.2	ext{ m}, h_2 = 0.15	ext{ m}$); $L = 2S - \frac{4.4}{N}$ — Length of summit curve for $L

Key Points: A summit curve is formed when convexity is upward (crest formed).; Deviation angle $N$ must be positive ($N > 0$) for a summit curve.; Square parabola is standardly preferred for summit curves due to simple design and uniform rate of change of grade.; The primary design criteria for summit curves is Sight Distance (SSD and OSD/ISD), whereas headlamp sight distance is critical for valley curves.

Advantages: Provides smooth vertical transition between different grades.; Ensures adequate sight distance for safe stopping and overtaking.; Prevents sudden comfort shocks to vehicle occupants.

Disadvantages: Sight distance is restricted at the peak of the curve due to summit convexity.; Requires significant earthwork cut/fill during construction in hilly terrain.

Applications: Highway vertical alignment design at crests.; Railway track vertical gradient transitions.; Flyover crest transitions.

Additional Info: Option A: $+n_1$ followed by $-n_2 \implies N = (+n_1) - (-n_2) = n_1 + n_2 > 0$ (Summit Curve).. Option B: $+n_1$ followed by $+n_2$ (where $n_1 > n_2$) $\implies N = n_1 - n_2 > 0$ (Summit Curve).. Option C: Level surface ($0$) followed by $-n_2 \implies N = 0 - (-n_2) = n_2 > 0$ (Summit Curve).

Answer: D is correct — All listed gradient combinations yield a positive algebraic difference ($N > 0$), creating convexity upwards which forms a summit curve.

Exam Tip: Remember: Convexity UP = Summit Curve (governed by SSD/OSD); Convexity DOWN = Valley/Sag Curve (governed by Headlamp Sight Distance & Comfort).

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Option A: Upgrade followed by a downgrade

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Option B: Upgrade followed by another upgrade

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Option C: plane surface followed by downgrade

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