---
title: "Stopping sight distance and derivation"
subject: "Transportation Engineering I"
chapter: 3
key: "semester_6/transportation_engineering_i:ssd-factors-derive"
source: https://www.bctengineer.com/q/semester_6/transportation_engineering_i/ssd-factors-derive
site: BCT Engineering
---

# Stopping sight distance and derivation

Transportation Engineering I · Chapter 3: Geometric Design of Highway

- Asked in: 2075 Bhadra, 8 marks; 2075 Baisakh, 8 marks; 2072 Magh, 8 marks; 2071 Magh, 8 marks; 2068 Bhadra (old course); 2065 Chaitra (old course), 2+6 marks (asked 6 times)
- Video: [Stopping Sight Distance - Highway Geometric Design - Transportation Engineering 1](https://www.youtube.com/watch?v=MdnOFeSCbSk) — Ekeeda
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_6/transportation_engineering_i/ssd-factors-derive
- Whole chapter: https://www.bctengineer.com/md/semester_6/transportation_engineering_i/chapter-3

## Question

Define stopping sight distance. Explain the factors affecting stopping sight distance and derive an expression for it (at level road).

## Short answer

Stopping Sight Distance (SSD) is the minimum distance a driver needs to see an object and stop safely. It equals lag distance (vt) plus braking distance (v²/2gf). Factors: vehicle speed, driver reaction time (2.5s), friction coefficient (0.35-0.40), gradient, brake efficiency, and visibility. Expression: SSD = 0.278Vt + V²/(254f) for level roads.

## Answer

**Stopping Sight Distance (SSD)** is the minimum distance ahead along the road that a driver must be able to see an object (height 0.15 m) on the carriageway so that the vehicle running at the design speed can be stopped safely before reaching it. It is the sum of the lag distance and the braking distance.

#### Factors affecting SSD
1. **Speed of the vehicle** (increases SSD as $V^2$).
2. **Total reaction time** of the driver (PIEV, 2.5 s as per IRC/NRS).
3. **Coefficient of longitudinal friction $f$** between tyre and pavement (0.35-0.40; depends on surface, tyre and weather).
4. **Gradient** of the road (down-grade increases SSD).
5. **Brake efficiency** and tyre condition; weight of the vehicle.
6. **Visibility conditions** such as night, fog, and the height of eye and object.

#### Derivation (level road)
Let $v$ = speed (m/s), $t$ = reaction time (s), $f$ = coefficient of friction, $l$ = lag distance, $l_b$ = braking distance.

**Lag distance** (vehicle moves at constant speed during reaction time):

$$
l = v\,t
$$

**Braking distance:** work done by friction = loss of kinetic energy

$$
\begin{aligned} f\,W\,l_b &= \frac{1}{2}\frac{W}{g}v^2 \\ l_b &= \frac{v^2}{2gf} \end{aligned}
$$

Therefore

$$
SSD = v\,t + \frac{v^2}{2gf}
$$

In terms of $V$ (km/h): $v = 0.278V$

$$
\boxed{SSD = 0.278\,V\,t + \frac{V^2}{254\,f}}
$$

For a gradient $n\%$ the braking term becomes $\dfrac{V^2}{254(f \pm 0.01n)}$ (+ upgrade, - downgrade).

Example: $V = 60$ km/h, $t = 2.5$ s, $f = 0.35$: $SSD = 41.7 + 40.5 = 82.2$ m.

## Check yourself

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

1. SSD is the sum of:
   A. Lag distance and braking distance
   B. Braking distance and overtaking
   C. Reaction time and gradient
   D. Lag distance and headway
   Answer: A. SSD = vt + v^2/(2gf). (Key point: SSD components)

2. Braking distance on a level road is:
   A. v t
   B. v^2 / (2 g f)
   C. v / (g f)
   D. 2 g f / v^2
   Answer: B. Friction work f W lb equals kinetic energy W v^2/(2g), so lb = v^2/(2gf). (Key point: Braking distance)

3. Which factor increases SSD?
   A. Higher friction coefficient
   B. Shorter reaction time
   C. Up-gradient
   D. Higher speed (SSD increases with V^2) and down-grade
   Answer: D. Higher speed and downgrade lengthen the braking distance. (Key point: Factors)

4. With V = 60 km/h, t = 2.5 s, f = 0.35, SSD =
   A. 41.7 + 40.5 = 82.2 m
   B. 41.7 + 20.2 = 61.9 m
   C. 100 m
   D. 30 m
   Answer: A. 0.278x60x2.5 = 41.7 and 3600/(254x0.35) = 40.5, total 82.2 m. (Key point: Numerical check)

## Related in Transportation Engineering I

- [Factors affecting stopping sight distance](https://www.bctengineer.com/question.md?key=semester_6%2Ftransportation_engineering_i%3Assd-factors-only) — Transportation Engineering I, chapter 3, asked 3×
- [Stopping distance and stopping sight distance](https://www.bctengineer.com/question.md?key=semester_6%2Ftransportation_engineering_i%3Astopping-distance-relation) — Transportation Engineering I, chapter 3, asked 3×
- [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
- [Overtaking sight distance derivation](https://www.bctengineer.com/question.md?key=semester_6%2Ftransportation_engineering_i%3Aosd-derive) — Transportation Engineering I, chapter 3, asked 6×
- [Percent grade from stopping distance difference](https://www.bctengineer.com/question.md?key=semester_6%2Ftransportation_engineering_i%3An-71bh-grade-ssd) — 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

## Related in other subjects

- [Stopping distance and brake energy](https://www.bctengineer.com/question.md?key=semester_5%2Fautomotive_technology%3Abraking-distance-energy-numerical) — Automotive Technology, chapter 7
- [Correlation vs regression; stopping distance line](https://www.bctengineer.com/question.md?key=semester_5%2Fprobability_and_statistics%3Acorrelation-regression-plot-stopping-distance) — Probability and Statistics, chapter 5