---
title: "Setback on six lane highway, 550 m radius"
subject: "Transportation Engineering I"
chapter: 3
key: "semester_6/transportation_engineering_i:n-72a-setback-350"
source: https://www.bctengineer.com/q/semester_6/transportation_engineering_i/n-72a-setback-350
site: BCT Engineering
---

# Setback on six lane highway, 550 m radius

Transportation Engineering I · Chapter 3: Geometric Design of Highway

- Asked in: 2072 Ashwin, 8 marks
- Video: [Setback Distances | Highway Engineering | Lec-5 Part-2 | GATE](https://www.youtube.com/watch?v=QtgXO8_dZ6g) — Unacademy GATE & ESE - Civil & ES
- 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-72a-setback-350
- Whole chapter: https://www.bctengineer.com/md/semester_6/transportation_engineering_i/chapter-3

## Question

A six lane highway has a curve 350 m long and 550 m radius. The stopping sight distance and overtaking sight distance are 200 m and 400 m respectively. Find out the setback distance from the inner edge of the road to the obstruction for both cases.

## Short answer

Path radius for inner lane = 541.25 m. For SSD 200 m (< L) setback from inner edge = 7.46 m. For OSD 400 m (> L) setback = 34.24 m.

## Answer

#### Assumptions
Six-lane undivided carriageway with lane width $w=3.5$ m, $R=550$ m (road centre line), $L=350$ m. The driver follows the centre of the inner (kerb-side) lane, at $n=2(3.5)+1.75=8.75$ m from the centre line, so the path radius is $R_i=550-8.75=541.25$ m. Setback from the inner edge of the road = $m_c-w/2$.

#### Case 1: stopping sight distance S = 200 m ($S<L$)

$$
\frac{\alpha}{2}=\frac{S}{2R_i}=0.18476\ \text{rad},\quad m_c=R_i\left(1-\cos\frac{\alpha}{2}\right)=9.212\ \text{m}
$$

Setback from the inner edge = 9.212 − 1.75 = **7.462 m**.

#### Case 2: overtaking sight distance S = 400 m ($S>L$)

$$
\frac{\alpha}{2}=\frac{L}{2R_i}=0.32333\ \text{rad}
$$


$$
m_c=R_i\left(1-\cos\frac{\alpha}{2}\right)+\frac{S-L}{2}\sin\frac{\alpha}{2}=28.045+25\sin(18.525^\circ)=35.988\ \text{m}
$$

Setback from the inner edge = 35.988 − 1.75 = **34.238 m**.

**Answer:** about **7.46 m** for SSD and **34.24 m** for OSD, measured from the inner edge of the road.

## Check yourself

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

1. What is the sight-line radius on this six-lane highway?
   A. Ri = 550 - 8.75 = 541.25 m, the centre of the inner lane
   B. 550 m
   C. 550 - 1.75 = 548.25 m
   D. 550 + 8.75 m
   Answer: A. The inner lane centre is 2 lanes + half lane = 8.75 m from the centre line. (Key point: Driver path radius)

2. Why is the simple formula m = Ri(1 - cos(α/2)) used for SSD = 200 m?
   A. Because S > L
   B. Because S = 200 m < L = 350 m, the sight line lies fully on the curve
   C. Because the road is six lane
   D. Because the setback is measured from the centre
   Answer: B. m_c = 9.21 m. (Key point: SSD case)

3. For OSD = 400 m, what is α/2 based on?
   A. The sight distance S
   B. The lane width
   C. The curve length L, α/2 = L/(2Ri), since S > L
   D. The radius only
   Answer: C. α/2 = 0.3233 rad; an added term (S-L)/2 sin(α/2) is also used. (Key point: OSD case)

4. How is final setback from the inner edge found?
   A. Add 1.75 m to m_c
   B. Subtract 8.75 m
   C. Use m_c unchanged
   D. Subtract half a lane width (1.75 m) from m_c
   Answer: D. 7.462 m for SSD and 34.238 m for OSD. (Key point: Setback from inner edge)

## Related in Transportation Engineering I

- [Setback on six lane highway, 450 m curve](https://www.bctengineer.com/question.md?key=semester_6%2Ftransportation_engineering_i%3An-73m-setback-six-lane) — Transportation Engineering I, chapter 3
- [Setback on four lane carriageway, 400 m radius](https://www.bctengineer.com/question.md?key=semester_6%2Ftransportation_engineering_i%3An-70bh-setback-four-lane) — Transportation Engineering I, chapter 3
- [Setback on 400 m curve, 1.95 m lane distance](https://www.bctengineer.com/question.md?key=semester_6%2Ftransportation_engineering_i%3An-68m-setback-1-95) — Transportation Engineering I, chapter 3, asked 2×
- [Setback on six lane road, 500 m radius](https://www.bctengineer.com/question.md?key=semester_6%2Ftransportation_engineering_i%3An-65c-setback-500) — Transportation Engineering I, chapter 3
- [Sight distance with obstruction on curve](https://www.bctengineer.com/question.md?key=semester_6%2Ftransportation_engineering_i%3An-78b-sd-obstruction) — Transportation Engineering I, chapter 3
- [Setback on curve 400 m radius, 1.9 m](https://www.bctengineer.com/question.md?key=semester_6%2Ftransportation_engineering_i%3An-78p-setback-400) — Transportation Engineering I, chapter 3, asked 2×

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