---
title: "Design speed from setback on 650 m curve"
subject: "Transportation Engineering I"
chapter: 3
key: "semester_6/transportation_engineering_i:n-76bh-setback-650"
source: https://www.bctengineer.com/q/semester_6/transportation_engineering_i/n-76bh-setback-650
site: BCT Engineering
---

# Design speed from setback on 650 m curve

Transportation Engineering I · Chapter 3: Geometric Design of Highway

- Asked in: 2076 Bhadra, 8 marks
- Video: [Geometric Design of Highway: Setback Distance](https://www.youtube.com/watch?v=h7xXm2GdcSA) — Sunil Khyaju
- 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-76bh-setback-650
- Whole chapter: https://www.bctengineer.com/md/semester_6/transportation_engineering_i/chapter-3

## Question

A two lane highway has a curve 300 m long, 650 m radius. The setback distance from centre of the carriageway is specified to be 25 m with reference to the intermediate sight distance of the curve. Find the design speed for the curve. Assume coefficient of longitudinal friction as 0.35.

## Short answer

ISD provided = 367.9 m, SSD = 184 m. Solving gives design speed ≈101 km/h.

## Answer

#### Data
$R=650$ m, $L=300$ m, setback $m=25$ m from the centre of the carriageway, sight distance = intermediate sight distance (ISD = 2 × SSD, IRC). The sight line is measured along the road centre line ($n=0$); $t=2.5$ s, $f=0.35$.

#### Step 1: sight distance provided by the setback
Try $S>L$ (usual for a short curve with a large setback):

$$
\frac{\alpha}{2}=\frac{L}{2R}=\frac{300}{2(650)}=0.23077\ \text{rad}=13.222^\circ
$$


$$
m=R\left(1-\cos\frac{\alpha}{2}\right)+\frac{S-L}{2}\sin\frac{\alpha}{2}
$$


$$
25=17.231+\frac{S-300}{2}(0.2287)\Rightarrow S=367.9\ \text{m}
$$

$S>L$, so the case is valid. ISD $=S=367.9$ m.

#### Step 2: SSD and design speed

$$
SSD=\frac{ISD}{2}=184.0\ \text{m}
$$


$$
184.0=0.278V(2.5)+\frac{V^2}{254(0.35)}=0.695V+\frac{V^2}{88.9}
$$

Solving: $V=100.7$ km/h.

**Answer:** design speed for the curve is about **101 km/h**.

## Check yourself

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

1. What sight distance does the problem require on this curve?
   A. Intermediate sight distance, ISD = 2 x SSD
   B. Overtaking sight distance
   C. Stopping sight distance only
   D. Headlight sight distance
   Answer: A. The setback is specified for ISD, so SSD = ISD/2 at the end. (Key point: Required sight distance)

2. Why is the S>L formula used first?
   A. Because S is always greater than R
   B. Because with a large setback on a short 300 m curve the sight line extends beyond the curve
   C. Because the setback is zero
   D. Because S>L is the only valid formula
   Answer: B. The result S = 367.9 m confirms S > L = 300 m. (Key point: Case check)

3. In m = R(1 - cos(α/2)) + ((S-L)/2) sin(α/2), what does the second term represent?
   A. The superelevation effect
   B. The lane width
   C. The extra offset from the straight parts of the sight line beyond the curve ends
   D. The reaction distance
   Answer: C. With 25 = 17.231 + ((S-300)/2)(0.2287), S = 367.9 m. (Key point: Setback equation)

4. After ISD = 367.9 m, how is the design speed found?
   A. V = sqrt(127R f) directly
   B. Set 367.9 = 0.278Vt only
   C. V = ISD/2.5
   D. SSD = ISD/2 = 184 m is set equal to 0.278Vt + V^2/(254f) and solved for V
   Answer: D. Solving 184 = 0.695V + V^2/88.9 gives V about 101 km/h. (Key point: From ISD to speed)

## Related in Transportation Engineering I

- [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 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
- [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 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 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×
- [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

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