---
title: "Setback on six lane highway, 450 m curve"
subject: "Transportation Engineering I"
chapter: 3
key: "semester_6/transportation_engineering_i:n-73m-setback-six-lane"
source: https://www.bctengineer.com/q/semester_6/transportation_engineering_i/n-73m-setback-six-lane
site: BCT Engineering
---

# Setback on six lane highway, 450 m curve

Transportation Engineering I · Chapter 3: Geometric Design of Highway

- Asked in: 2073 Magh, 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-73m-setback-six-lane
- Whole chapter: https://www.bctengineer.com/md/semester_6/transportation_engineering_i/chapter-3

## Question

There is a horizontal curve with radius of 450 m and length 220 m on the six lane Koteshwor-Suryabinayak highway. Compute the setback distance required from the edge of the inner lane of the highway so as to provide (i) stopping sight distance of 100 m and (ii) safe overtaking sight distance of 310 m.

## Short answer

Driver path radius from inner lane centre is 441.25 m. For SSD 100 m (< L) setback from inner edge = 1.08 m. For OSD 310 m (> L) setback = 22.99 m.

## Answer

#### Assumptions
Six-lane undivided carriageway, lane width $w=3.5$ m (NRS 2070 / IRC), $R=450$ m to the road centre line, $L=220$ m. The driver keeps to the centre of the innermost (kerb-side) lane, which is $n=2(3.5)+1.75=8.75$ m from the centre line. The path radius is $R_i=450-8.75=441.25$ m. The clearance from the lane centre to the obstruction line is $m_c$; the setback from the inner edge of the lane is $m_c-w/2=m_c-1.75$ m.

#### (i) Stopping sight distance S = 100 m ($S<L$)

$$
\frac{\alpha}{2}=\frac{S}{2R_i}=\frac{100}{2(441.25)}=0.11331\ \text{rad}
$$


$$
m_c=R_i\left(1-\cos\frac{\alpha}{2}\right)=2.830\ \text{m}\ \Rightarrow\ \text{setback}=2.830-1.75=1.080\ \text{m}
$$

#### (ii) Overtaking sight distance S = 310 m ($S>L$)

$$
\frac{\alpha}{2}=\frac{L}{2R_i}=\frac{220}{2(441.25)}=0.24929\ \text{rad}
$$


$$
m_c=R_i\left(1-\cos\frac{\alpha}{2}\right)+\frac{S-L}{2}\sin\frac{\alpha}{2}=13.640+45\sin(14.283^\circ)=24.742\ \text{m}
$$

Setback from the lane edge = 24.742 − 1.75 = 22.992 m.

**Answer:** setback from the edge of the inner lane = **1.08 m** for SSD = 100 m and **22.99 m** for OSD = 310 m.

## Check yourself

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

1. On a six-lane road, where is the driver assumed to be?
   A. At the centre of the innermost lane, 2(3.5)+1.75 = 8.75 m from the centre line
   B. On the road centre line
   C. At the edge of the pavement
   D. 1.75 m from the centre line
   Answer: A. That gives path radius Ri = 450 - 8.75 = 441.25 m. (Key point: Driver path)

2. For SSD = 100 m (S<L), which expression is used?
   A. m_c = Ri(1 - cos(L/(2Ri))) + (S-L)/2 sin
   B. m_c = Ri(1 - cos(S/(2Ri)))
   C. m_c = S^2/R
   D. m_c = Ri cos(S/Ri)
   Answer: B. m_c = 2.83 m from the lane centre. (Key point: SSD case)

3. How is setback from the lane edge obtained from m_c?
   A. Add half the lane width
   B. Subtract the whole lane width 3.5
   C. Subtract half the lane width: m = m_c - 1.75
   D. m_c itself
   Answer: C. m_c is measured from the lane centre; the edge is 1.75 m nearer to the obstruction. (Key point: Converting to edge setback)

4. Why is the extra term (S-L)/2 sin(α/2) added for OSD = 310 m?
   A. Because OSD uses a different radius
   B. Because friction is higher
   C. Because L is longer than S
   D. Because S > L = 220 m so part of the sight line lies along the tangents
   Answer: D. m_c = 13.64 + 45 sin(14.283°) = 24.74 m, setback 22.99 m. (Key point: OSD case)

## Related in Transportation Engineering I

- [Setback on six lane highway, 550 m radius](https://www.bctengineer.com/question.md?key=semester_6%2Ftransportation_engineering_i%3An-72a-setback-350) — 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
- [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×
- [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 rural highway, 80 kmph](https://www.bctengineer.com/question.md?key=semester_6%2Ftransportation_engineering_i%3An-71m-setback-80) — Transportation Engineering I, chapter 3

## Related in other subjects

- [Highway circular curve, apex distance 15.876 m](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Ahighway-curve-apex-distance-tangential-angle) — Surveying II, chapter 6