---
title: "Summit curve limited to 750 m"
subject: "Transportation Engineering I"
chapter: 3
key: "semester_6/transportation_engineering_i:n-75bh-vc-summit-750"
source: https://www.bctengineer.com/q/semester_6/transportation_engineering_i/n-75bh-vc-summit-750
site: BCT Engineering
---

# Summit curve limited to 750 m

Transportation Engineering I · Chapter 3: Geometric Design of Highway

- Asked in: 2075 Bhadra, 8 marks; 2072 Ashwin, 8 marks (asked 2 times)
- Video: [Design a Summit Curve for Limited Visibility on a Hilly Highway || Transportation Engineering-II](https://www.youtube.com/watch?v=PaDkNBMC3I4) — OPengineer
- 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-75bh-vc-summit-750
- Whole chapter: https://www.bctengineer.com/md/semester_6/transportation_engineering_i/chapter-3

## Question

A vertical summit curve is to be designed when two grades +1/60 (ascending grade of 1 in 60) and -1/45 (descending grade of 1 in 45) meet on a highway. The stopping sight distance and overtaking sight distance required are 210 m and 600 m respectively. But due to site condition, the length of vertical curve has to be restricted to a maximum value of 750 m if possible. Calculate the length of summit curve needed to fulfil the requirements of:
i) Stopping sight distance
ii) Overtaking sight distance or at least intermediate sight distance, and discuss the result.

## Short answer

For SSD of 210 m, required length is 390 m (feasible). OSD of 600 m requires 1458 m, exceeding the 750 m limit. Intermediate sight distance (420 m) can be provided with 715 m length, so adopt 715–750 m and prohibit overtaking.

## Answer

**Given:** $g_1 = +1/60 = +1.667\%$, $g_2 = -1/45 = -2.222\%$; SSD $= 210$ m, OSD $= 600$ m; $L_{max} = 750$ m.

$$
N = \frac{1}{60} + \frac{1}{45} = 0.03889
$$

**Sight line heights (IRC):** eye height $H = 1.2$ m; object height $h = 0.15$ m for SSD and $h = 1.2$ m for OSD and ISD.

#### (i) Stopping sight distance ($S = 210$ m)
Assuming $S < L$:
$$
L = \frac{N S^2}{\left(\sqrt{2H}+\sqrt{2h}\right)^2} = \frac{0.03889\,(210)^2}{(\sqrt{2.4}+\sqrt{0.3})^2} = \frac{1715.0}{4.397} = 390.0\ \text{m}
$$
$S = 210 < 390$, so the assumption holds. **$L = 390$ m < 750 m: OK.**

#### (ii) Overtaking sight distance ($S = 600$ m)
$$
L = \frac{N S^2}{(\sqrt{2.4}+\sqrt{2.4})^2} = \frac{0.03889\,(600)^2}{9.6} = 1458.3\ \text{m}
$$
$S < L$, valid. But **1458 m is more than the limit of 750 m**, so it is not feasible.

**Intermediate sight distance** $= 2\times SSD = 420$ m:
$$
L = \frac{0.03889\,(420)^2}{9.6} = 714.6\ \text{m} \ (< 750\ \text{m})
$$

#### Discussion
| Sight distance | Length required | Within 750 m? |
|---|---|---|
| SSD = 210 m | 390 m | Yes |
| OSD = 600 m | 1458 m | No |
| ISD = 420 m | 715 m | Yes |

A summit curve of 750 m cannot give the full overtaking sight distance; providing OSD would need 1458 m, which is too costly. So adopt **$L \approx 715$-$750$ m**, which gives at least the intermediate sight distance (420 m) and more than the SSD everywhere. Overtaking is then possible only with caution, and "no overtaking" signs and markings are provided on the curve. A length of 750 m gives an ISD of about 430 m.

## Check yourself

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

1. The algebraic difference of grades for +1/60 and -1/45 is
   A. 0.00555
   B. 0.03889
   C. 0.0389 % only
   D. 0.0194
   Answer: B. N = 1/60 + 1/45 = 0.03889. (Key point: Grade difference)

2. Length for SSD = 210 m (H = 1.2 m, h = 0.15 m) is about
   A. 390 m
   B. 750 m
   C. 1458 m
   D. 715 m
   Answer: A. L = N S^2/(sqrt(2H) + sqrt(2h))^2 = 1715/4.397 = 390 m, within 750 m. (Key point: SSD length)

3. What is the length needed for full OSD of 600 m, and is it feasible?
   A. 390 m, feasible
   B. 715 m, feasible
   C. 1458 m, not feasible within 750 m
   D. 750 m, exactly feasible
   Answer: C. L = 0.03889 x 600^2/9.6 = 1458 m, more than the 750 m limit. (Key point: OSD length)

4. What is adopted given the 750 m limit?
   A. Full OSD with 1458 m
   B. ISD = 2 x SSD = 420 m (about 715 m length) with no-overtaking markings
   C. SSD only with 390 m
   D. Remove the curve
   Answer: B. ISD of 420 m needs 715 m, which fits; overtaking is allowed only where clear and signs/markings are provided. (Key point: Compromise)

## Close variants set in other exams

- [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×

## 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
- [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
- [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
- [Vertical curve 35 m headlight and momentum grade](https://www.bctengineer.com/question.md?key=semester_6%2Ftransportation_engineering_i%3An-80c-vc-headlight-35m) — Transportation Engineering I, chapter 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
- [Summit curve +1.5% and -2%](https://www.bctengineer.com/question.md?key=semester_6%2Ftransportation_engineering_i%3An-68bh-summit) — Transportation Engineering I, chapter 3

## Related in other subjects

- [Vertical curve +0.5% and -0.7%, IP RL 350.750](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Avertical-curve-pos05-neg07-ip-500) — Surveying II, chapter 6
- [Road earthwork, grades from 90 m to 210 m (s)](https://www.bctengineer.com/question.md?key=semester_7%2Festimating_and_costing%3Aroad-earthwork-s-grade-90-210) — Estimating and Costing, chapter 6, asked 3×
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