---
title: "Summit curve +1.5% and -2%"
subject: "Transportation Engineering I"
chapter: 3
key: "semester_6/transportation_engineering_i:n-68bh-summit"
source: https://www.bctengineer.com/q/semester_6/transportation_engineering_i/n-68bh-summit
site: BCT Engineering
---

# Summit curve +1.5% and -2%

Transportation Engineering I · Chapter 3: Geometric Design of Highway

- Asked in: 2068 Bhadra (old course), 8 marks
- 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-68bh-summit
- Whole chapter: https://www.bctengineer.com/md/semester_6/transportation_engineering_i/chapter-3

## Question

A summit curve is to be provided at the intersection of two gradients +1.5% and -2%. What is length required (i) For stopping sight distance of 200 m (ii) For overtaking sight distance of 600 m? What is the vertical distance between the point of vertical intersection and curve in either case?

## Short answer

For N = 0.035, SSD 200 m gives L = NS^2/4.4 = 318 m, vertical offset at PVI E = NL/8 = 1.39 m. OSD 600 m gives L = NS^2/9.6 = 1313 m, E = 5.74 m.

## Answer

$g_1=+1.5\%,\ g_2=-2\%$, so $N=0.015+0.02=0.035$ (summit curve). Eye height 1.2 m, object height 0.15 m for SSD and 1.2 m for OSD (IRC/NRS 2070).

#### (i) SSD = 200 m
Assuming $L>S$:

$$
L=\frac{NS^2}{4.4}=\frac{0.035(200)^2}{4.4}=318.2\ \text{m}
$$

Since $L>S$, it is valid. **L = 318 m (say 320 m)**.

#### (ii) OSD = 600 m
Here $h_1=h_2=1.2$ m:

$$
L=\frac{NS^2}{9.6}=\frac{0.035(600)^2}{9.6}=1312.5\ \text{m}
$$

**L = 1313 m** ($>S$, valid).

#### Vertical distance between PVI and curve
For a parabolic curve the offset at the PVI is $E=\dfrac{NL}{8}$.
- (i) $E=\dfrac{0.035(318.2)}{8}=\mathbf{1.392}$ m
- (ii) $E=\dfrac{0.035(1312.5)}{8}=\mathbf{5.742}$ m

**Answer:** (i) L = 318 m, E = 1.39 m; (ii) L = 1313 m, E = 5.74 m.

## Check yourself

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

1. Which formula gives L for SSD (L > S) with h1 = 1.2 m and h2 = 0.15 m?
   A. L = N S^2 / 9.6
   B. L = N S^2 / 4.4
   C. L = N S / 4.4
   D. L = 2S - 4.4/N
   Answer: B. With the IRC heights for SSD, the constant is 4.4: L = 0.035(200)^2/4.4 = 318 m. (Key point: Length for SSD)

2. Why does the OSD case use 9.6 instead of 4.4?
   A. OSD uses a lower eye height
   B. OSD uses a valley curve formula
   C. The object height is 1.2 m (not 0.15 m), giving L = N S^2 / 9.6
   D. The gradients are doubled for OSD
   Answer: C. With h1 = h2 = 1.2 m the constant becomes 9.6, giving 1312.5 m. (Key point: Length for OSD)

3. Which expression gives the vertical distance between PVI and the curve?
   A. E = N L / 8
   B. E = N L / 2
   C. E = N L^2 / 8
   D. E = L / 8N
   Answer: A. For a parabola the mid offset below the PVI is NL/8: 1.39 m and 5.74 m. (Key point: Vertical distance)

## Related in Transportation Engineering I

- [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
- [Vertical curve with intermediate sight distance](https://www.bctengineer.com/question.md?key=semester_6%2Ftransportation_engineering_i%3An-81a-vc-intermediate) — Transportation Engineering I, chapter 3
- [Summit curve limited to 750 m](https://www.bctengineer.com/question.md?key=semester_6%2Ftransportation_engineering_i%3An-75bh-vc-summit-750) — Transportation Engineering I, chapter 3, asked 3×
- [Summit curve +4% and -4%, limited to 800 m](https://www.bctengineer.com/question.md?key=semester_6%2Ftransportation_engineering_i%3An-71m-summit-800) — Transportation Engineering I, chapter 3, asked 3×
- [Overtaking sight distance and zone numerical](https://www.bctengineer.com/question.md?key=semester_6%2Ftransportation_engineering_i%3An-62j-osd-numeric) — Transportation Engineering I, chapter 3
- [Overtaking sight distance and zone, 60 kmph](https://www.bctengineer.com/question.md?key=semester_6%2Ftransportation_engineering_i%3An-76b-osd-60) — Transportation Engineering I, chapter 3

## Related in other subjects

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- [Vertical curve table, -4.5% and +3.5%, 200 m](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Avertical-curve-table-neg45-pos35-200m) — Surveying II, chapter 6
- [Three-point problem: A 800 m N, C 600 m E (600, 200, 500)](https://www.bctengineer.com/question.md?key=semester_3%2Fengineering_geology_i%3Athreepoint-problem-a-800-m) — Engineering Geology I, chapter 5, asked 4×
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