---
title: "Valley curve 1 in 30 and 1 in 25"
subject: "Transportation Engineering I"
chapter: 3
key: "semester_6/transportation_engineering_i:n-67m-valley-1-30"
source: https://www.bctengineer.com/q/semester_6/transportation_engineering_i/n-67m-valley-1-30
site: BCT Engineering
---

# Valley curve 1 in 30 and 1 in 25

Transportation Engineering I · Chapter 3: Geometric Design of Highway

- Asked in: 2067 Mangsir (old course), 8 marks
- Video: [Length of Valley Curve | Numerical | Transportation Engineering](https://www.youtube.com/watch?v=QFe8Fht6ZuM) — ONLINETYARI CLASSES
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_6/transportation_engineering_i/n-67m-valley-1-30
- Whole chapter: https://www.bctengineer.com/md/semester_6/transportation_engineering_i/chapter-3

## Question

A valley curve divided by a descending gradient of 1 in 30 meeting an ascending gradient of 1 in 25. Design the length of valley curve to fulfil both comfort condition and head light sight distance required for a design speed of 80 Kmph. Assume allowable rate of change of centrifugal acceleration is 0.6 m/sec² and stopping sight distance is 160 m.

## Short answer

Use N=0.07333, V=22.22 m/s, C=0.6, SSD=160 m. Comfort gives 73.2 m; headlight sight distance gives 264.4 m. Adopt the larger value, 265 m.

## Answer

A descending 1 in 30 grade meeting an ascending 1 in 25 grade gives a **valley curve**.

#### Data
$N=\dfrac{1}{30}+\dfrac{1}{25}=0.07333$, $V=80$ km/h $=22.22$ m/s, SSD $S=160$ m (given). The allowable rate of change of centrifugal acceleration is taken as $C=0.6$ m/s³ (the units "m/s²" in the question are read as m/s³). Headlight height 0.75 m, beam angle 1°.

#### (a) Comfort condition

$$
L=2\sqrt{\frac{NV^3}{C}}=2\sqrt{\frac{0.07333(22.22)^3}{0.6}}=73.2\ \text{m}
$$

#### (b) Headlight sight distance
Assuming $L>S$:

$$
L=\frac{NS^2}{2(h+S\tan\alpha)}=\frac{0.07333(160)^2}{1.5+0.035(160)}=264.4\ \text{m}
$$

$L>S$, valid.

#### Design length
The larger value governs.

**Answer:** L = 264 m, adopt **265 m**.

## Check yourself

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

1. How is N found for 1 in 30 descending and 1 in 25 ascending?
   A. N = 1/30 + 1/25 = 0.0733
   B. N = 1/25 - 1/30 = 0.0067
   C. N = 1/30 x 1/25
   D. N = 55
   Answer: A. For a valley curve the grades have opposite signs, so the deviation angle is the sum. (Key point: Valley N)

2. Which formula gives the comfort length?
   A. L = N S^2 / (1.5 + 0.035S)
   B. L = 2 sqrt(N V^3 / C) = 73.2 m
   C. L = N V^2 / C
   D. L = 2 sqrt(C / N V^3)
   Answer: B. The comfort condition limits the rate of change of centrifugal acceleration C (m/s^3). (Key point: Comfort length)

3. The comfort length is 73.2 m and headlight length is 264.4 m. Which is adopted?
   A. 73 m, the smaller
   B. 169 m, the average
   C. 264 m, the larger
   D. 160 m, equal to S
   Answer: C. The longer length satisfies both criteria. (Key point: Design length)

## 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 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
- [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 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
- [Vertical curve for overtaking sight distance](https://www.bctengineer.com/question.md?key=semester_6%2Ftransportation_engineering_i%3An-81c-vc-overtaking) — Transportation Engineering I, chapter 3
- [Stopping sight distance at 50 kmph](https://www.bctengineer.com/question.md?key=semester_6%2Ftransportation_engineering_i%3An-66m-ssd-50) — Transportation Engineering I, chapter 3

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