---
title: "Setback on six lane road, 500 m radius"
subject: "Transportation Engineering I"
chapter: 3
key: "semester_6/transportation_engineering_i:n-65c-setback-500"
source: https://www.bctengineer.com/q/semester_6/transportation_engineering_i/n-65c-setback-500
site: BCT Engineering
---

# Setback on six lane road, 500 m radius

Transportation Engineering I · Chapter 3: Geometric Design of Highway

- Asked in: 2065 Chaitra (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-65c-setback-500
- Whole chapter: https://www.bctengineer.com/md/semester_6/transportation_engineering_i/chapter-3

## Question

Calculate the minimum setback from centre line of road for a curve of radius 500 m for a six lane road to ensure safe visibility. The stopping sight distance is 200 m, lane width is 3.5 m and the curve length is 100 m and no extra width is to be provided.

## Short answer

Inner lane radius is 491.25 m and S=200 m exceeds L=100 m. Using the S>L formula with α/2=5.832°, minimum setback from the centre line is 16.37 m.

## Answer

#### Assumptions
Six-lane undivided carriageway, lane width $w=3.5$ m, $R=500$ m (road centre line), $L=100$ m, SSD $S=200$ m. No extra widening. The sight line is along the centre of the inner (kerb-side) lane, at $n=2(3.5)+1.75=8.75$ m from the centre line, so its radius is $R_i=500-8.75=491.25$ m.

#### Check S against L
$S=200$ m is greater than $L=100$ m, so the sight line extends beyond the curve along the straight tangent and the angle is based on the curve length:

$$
\frac{\alpha}{2}=\frac{L}{2R_i}=\frac{100}{2(491.25)}=0.10178\ \text{rad}=5.832^\circ
$$

#### Setback from the centre line

$$
m=R-(R-n)\cos\frac{\alpha}{2}+\frac{S-L}{2}\sin\frac{\alpha}{2}
$$


$$
m=11.292+50\sin(5.832^\circ)=16.373\ \text{m}
$$

(Clearance from the centre of the inner lane is $m_c=7.623$ m; the road edge is $3\times3.5=10.5$ m from the centre line.)

**Answer:** minimum setback from the centre line $\approx$ **16.37 m**.

## Check yourself

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

1. For a six-lane road, what is n and R_i?
   A. n = 2(3.5) + 1.75 = 8.75 m, R_i = 491.25 m
   B. n = 3.5 m, R_i = 496.5 m
   C. n = 10.5 m, R_i = 489.5 m
   D. n = 1.75 m, R_i = 498.25 m
   Answer: A. The sight line is along the centre of the kerb-side lane, 8.75 m from the centre line. (Key point: Sight-line offset)

2. S = 200 m and L = 100 m. How is the half-angle found?
   A. Use S: alpha/2 = S / (2 R_i)
   B. Use L: alpha/2 = L / (2 R_i), since S > L
   C. Use S - L
   D. Use R only, ignoring n
   Answer: B. When S > L the sight line extends onto the tangent, so alpha depends on the curve length. (Key point: S vs L)

3. Which expression gives the setback?
   A. m = R - (R - n)cos(alpha/2) only
   B. m = (S - L) sin(alpha)
   C. m = R - (R - n)cos(alpha/2) + (S - L)/2 sin(alpha/2)
   D. m = R(1 - cos alpha)
   Answer: C. The tangent portion beyond the curve adds (S-L)/2 sin(alpha/2): total 16.37 m. (Key point: Setback formula)

## 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 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 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×
- [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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