---
title: "Design controls for valley curves"
subject: "Transportation Engineering I"
chapter: 3
key: "semester_6/transportation_engineering_i:valley-design-controls"
source: https://www.bctengineer.com/q/semester_6/transportation_engineering_i/valley-design-controls
site: BCT Engineering
---

# Design controls for valley curves

Transportation Engineering I · Chapter 3: Geometric Design of Highway

- Asked in: 2066 Magh (old course), 8 marks
- Video: [Design of Summit and Valley Curves | Highways | Transportation](https://www.youtube.com/watch?v=15ObNn0M72A) — APSEd
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_6/transportation_engineering_i/valley-design-controls
- Whole chapter: https://www.bctengineer.com/md/semester_6/transportation_engineering_i/chapter-3

## Question

What are the basic design controls for valley curves? How is the length of valley curve calculated from different criteria?

## Short answer

Valley curve design controls are comfort (rate of change of centrifugal acceleration ≤ 0.6 m/s³), headlight sight distance at night, overhead clearance (min 5.0 m per IRC), appearance and drainage, and stopping sight distance. Length is calculated from comfort (L = 2√(Nv³/C)), headlight sight distance (different formulas for S<L and S>L), and overhead clearance (L = NS²/[8(Hc - (h1+h2)/2)] for S<L). The maximum of these lengths is adopted.

## Answer

A valley (sag) curve is a vertical curve with the centre of curvature above the road, formed where a downgrade meets an upgrade (or a lesser downgrade). A parabola is generally used.

#### Basic design controls
1. **Comfort:** the centrifugal acceleration due to the vertical curvature adds to the weight; its rate of change must be limited (0.6 m/s³) to avoid jerk.
2. **Headlight sight distance at night:** the beam must light up the road ahead for at least the stopping distance (in day time there is no obstruction to vision).
3. **Overhead clearance** under bridges and structures (flyovers) - minimum 5.0 m headroom (as per IRC) with the sight line below the structure.
4. **Appearance and drainage:** the curve should look smooth, and the lowest point needs special drainage (inlets and drains), the gradient near it should not be flat.
5. **Safety and stopping distance:** SSD must be available.

#### Length of valley curve
$N$ = algebraic difference of grades (ratio), $v$ = speed in m/s.

**1. Comfort criterion** ($C = 0.6$ m/s³):
$$
L = 2\sqrt{\frac{N\,v^3}{C}}
$$

**2. Headlight sight distance criterion** ($h = 0.75$ m, beam angle $\alpha = 1^\circ$):
- If $S < L$: $\ L = \dfrac{N S^2}{2\,(h + S\tan\alpha)}$
- If $S > L$: $\ L = 2S - \dfrac{2\,(h + S\tan\alpha)}{N}$

**3. Overhead clearance criterion** (under a structure with clearance $H_c$, driver's eye height $h_1$ and object height $h_2$), for $S<L$: $L = \dfrac{N S^2}{8\,\left(H_c - \tfrac{h_1+h_2}{2}\right)}$.

The **longest** of these values is adopted for design.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. A valley curve is a vertical curve that
   A. has its centre of curvature below the road, at a summit
   B. has its centre of curvature above the road, where a downgrade meets an upgrade
   C. is always circular and never parabolic
   D. joins two upgrades only
   Answer: B. A valley (sag) curve forms where a downgrade meets an upgrade or lesser downgrade; a parabola is generally used. (Key point: Shape of valley curve)

2. Why is headlight sight distance a design control for valley curves?
   A. Because at night the headlight beam must light up the road ahead for at least the stopping distance
   B. Because the sun glare is worst in valleys
   C. Because day-time vision is obstructed by the curve
   D. Because headlights reduce drainage
   Answer: A. In daytime nothing obstructs vision on a valley curve, so night headlight range governs. (Key point: Headlight sight distance control)

3. The comfort criterion for valley curves is based on
   A. the weight of the vehicle
   B. limiting the rate of change of centrifugal acceleration (C = 0.6 m/s^3)
   C. the width of shoulders
   D. the eye height of the driver
   Answer: B. Vertical curvature adds to the weight; its rate of change is limited to avoid jerk. (Key point: Comfort criterion)

4. Which formula gives the comfort length of a valley curve?
   A. L = N v^2/C
   B. L = 2 sqrt(N v^3 / C)
   C. L = N S^2/9.6
   D. L = 2S - 9.6/N
   Answer: B. L = 2 sqrt(N v^3/C), with C = 0.6 m/s^3 and v in m/s. (Key point: Comfort length formula)

5. Which value of valley curve length is adopted for design?
   A. The shortest of the criteria
   B. The average of the criteria
   C. The comfort value always
   D. The longest of the criteria
   Answer: D. The longest value satisfies all the criteria. (Key point: Which length to adopt)

## Related in Transportation Engineering I

- [Valley curve design, 100 kmph, 1 in 40](https://www.bctengineer.com/question.md?key=semester_6%2Ftransportation_engineering_i%3An-valley-100-312) — Transportation Engineering I, chapter 3, asked 2×
- [Valley curve design, 80 kmph, 1 in 40](https://www.bctengineer.com/question.md?key=semester_6%2Ftransportation_engineering_i%3An-76b-valley-80) — Transportation Engineering I, chapter 3
- [Length of transition curve (criteria)](https://www.bctengineer.com/question.md?key=semester_6%2Ftransportation_engineering_i%3Atc-length-methods) — Transportation Engineering I, chapter 3, asked 8×
- [Valley curve 1/35 and 1/45, 80 kmph](https://www.bctengineer.com/question.md?key=semester_6%2Ftransportation_engineering_i%3An-70bh-valley-1-35) — Transportation Engineering I, chapter 3
- [Valley curve 1 in 30 and 1 in 25](https://www.bctengineer.com/question.md?key=semester_6%2Ftransportation_engineering_i%3An-67m-valley-1-30) — Transportation Engineering I, chapter 3
- [Valley curve 2.5% and 3.5%, 80 kmph](https://www.bctengineer.com/question.md?key=semester_6%2Ftransportation_engineering_i%3An-63k-valley-80) — Transportation Engineering I, chapter 3

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