How to find out length of vertical curve ?

Question

Examoogle · Accepted Answer

Option B: A total change of grade / rate of change of grade

Explanation & Concepts:
The length of a vertical curve ($L$) is defined as the horizontal distance over which the change of grade takes place. It is directly calculated as the ratio of the total change of grade ($N$) to the allowable rate of change of grade ($r$).

Working Principle: When two different gradients meet, a vertical curve is provided to ensure smooth vehicular movement, adequate sight distance, and passenger comfort. The curve transitions the grade at a constant rate ($r$), meaning the total elevation/slope change ($N = |g_1 - g_2|$) divided by the rate of change per unit distance gives the total length of the curve.

Key Formulas: $L = \frac{N}{r}$ — Length of vertical curve; $N = |g_1 - g_2|$ — Total change of grade (algebraic difference between slopes $g_1$ and $g_2$)

Key Points: Parabolic curves are universally preferred for vertical curves in highways due to their constant rate of change of grade.; The total change of grade $N$ is the algebraic difference between the incoming grade ($g_1$) and outgoing grade ($g_2$).; The rate of change of grade $r$ is determined based on driver comfort and safety criteria.

Advantages: Ensures smooth transition between two intersecting gradients.; Provides adequate sight distance (SSD and OSD) for safe vehicle operation.

Disadvantages: Inadequate design length can lead to sudden uncomfortable acceleration or sight distance restrictions.

Applications: Summit curves (crest curves) connecting upgrade to downgrade or flatter upgrade.; Valley curves (sag curves) connecting downgrade to upgrade or flatter downgrade.

Additional Info: Standard IRC allowable rate of change of grade for summit curves generally varies between 0.1% per 30m to 0.2% per 30m depending on design speed.. Option A and Option D incorrectly place the rate of change of grade or change of grade in the wrong ratio positions.

Answer: B is correct — Length of a vertical curve is given by the ratio of total change of grade to the rate of change of grade.

Exam Tip: For summit curves, always check whether the required length $L$ based on sight distance ($S$) satisfies $L > S$ or $L

Examoogle · Answer

Option A: Change of grade / rate of change of grade

Examoogle · Answer

Option C: Rate of change of grade / total change of grade

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Option D: Rate of change of grade / change of grade

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