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

# Overtaking sight distance derivation

Transportation Engineering I · Chapter 3: Geometric Design of Highway

- Asked in: 2080 Chaitra, 6 marks; 2079 Ashwin, 2+6 marks; 2078 Baisakh, 4 marks; 2070 Magh, 8 marks; 2067 Mangsir (old course), 2+6 marks; 2064 Shrawan (old course), 8 marks (asked 6 times)
- Video: [Overtaking Sight Distance: Derivation, Formula, Explained || Transportation Engineering](https://www.youtube.com/watch?v=7UztlCCq4Uc) — OPengineer
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_6/transportation_engineering_i/osd-derive
- Whole chapter: https://www.bctengineer.com/md/semester_6/transportation_engineering_i/chapter-3

## Question

Define overtaking sight distance. List the factors affecting it and derive an expression for overtaking sight distance for two lane two-way roads with neat sketch.

## Short answer

Overtaking Sight Distance (OSD) is the minimum distance for safe overtaking on two-lane roads without colliding with oncoming traffic. Factors: speeds of overtaking, overtaken, and opposing vehicles; spacing; driver reaction time and skill; acceleration; gradient; road width. OSD = d1 + d2 + d3 where d1 = v_b·t (reaction), d2 = v_b·T + 2s (overtaking), d3 = v·T (oncoming), T = √(4s/a), s = 0.7v_b + 6.

## Answer

**Overtaking Sight Distance (OSD)** is the minimum distance open to the vision of the driver of a vehicle intending to overtake a slower vehicle ahead, so that the driver can overtake safely without any risk of collision with a vehicle coming from the opposite direction.

#### Factors affecting OSD
1. Speeds of the overtaking, overtaken and opposing vehicles.
2. Spacing between the vehicles (depends on speed).
3. Skill and reaction time of the driver.
4. Rate of acceleration of the overtaking vehicle.
5. Gradient of the road and the road surface condition.
6. Width of the road (two-lane/multi-lane) and the traffic volume.

#### Derivation (two-lane two-way road)
Let $A$ = overtaking vehicle, $B$ = overtaken vehicle (speed $v_b$ m/s), $C$ = oncoming vehicle; $v$ = design speed of $A$ and $C$ (m/s), $a$ = acceleration of $A$ (m/s²), $t$ = reaction time of the driver of $A$ (2 s).

```text
 A  <-d1->|<-------- d2 -------->|<---- d3 ---->  C
 [A]..[B] |  [A]  ........ [B] [A]|   <- [C]
 start    |  overtaking path      | opposite car
```

**$d_1$ - distance travelled during the reaction time** (A travels at speed $v_b$ behind B):

$$
d_1 = v_b\,t
$$

**$d_2$ - distance during the overtaking operation.** A starts at spacing $s$ behind B and finishes at spacing $s$ ahead of B, so A gains $2s$ on B in time $T$. Relative to B, A starts with zero relative speed and accelerates at $a$:

$$
\begin{aligned}
2s &= \tfrac12 a T^2 \ \Rightarrow\ T = \sqrt{\frac{4s}{a}} \\
d_2 &= v_b\,T + 2s
\end{aligned}
$$

where $s = 0.7v_b + 6$ (m, with $v_b$ in m/s).

**$d_3$ - distance travelled by the oncoming vehicle C** during the overtaking time $T$ (C runs at the design speed $v$):

$$
d_3 = v\,T
$$

#### Total

$$
\boxed{OSD = d_1 + d_2 + d_3 = v_b t + (v_bT + 2s) + vT}
$$

As per IRC, the speed of the overtaken vehicle is taken as $V_b = V - 16$ km/h (i.e. $v_b = v - 4.5$ m/s) when it is not known.

IRC gives about 470 m for $V = 80$ km/h on a two-way road (about 300 m for 60 km/h). On one-way roads $d_3$ is not needed, so $OSD = d_1 + d_2$.

## Check yourself

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

1. OSD is the minimum distance a driver needs to see so that he can:
   A. Stop before an object
   B. Overtake a slow vehicle safely without collision with opposite traffic
   C. Read a sign
   D. Turn at an intersection
   Answer: B. OSD ensures safe overtaking with no risk from the opposing vehicle. (Key point: Definition)

2. OSD on a two-way road is the sum of:
   A. d1 and d2 only
   B. d1, d2 and d3
   C. d2 and d3 only
   D. d1 and d3 only
   Answer: B. OSD = d1 (reaction) + d2 (overtaking) + d3 (oncoming vehicle). (Key point: Components)

3. The overtaking distance d2 is:
   A. v b t
   B. v T
   C. v_b T + 2s
   D. 2 v T
   Answer: C. A gains 2s on B in time T, so d2 = v_b T + 2s. (Key point: d2)

4. d3 is the distance travelled by:
   A. The overtaken vehicle in reaction time
   B. The oncoming vehicle at design speed during overtaking time T
   C. The overtaking vehicle after overtaking
   D. The overtaking vehicle in reaction time
   Answer: B. d3 = v T for the opposite vehicle. (Key point: d3)

## Related in Transportation Engineering I

- [Vertical curve for overtaking sight distance](https://www.bctengineer.com/question.md?key=semester_6%2Ftransportation_engineering_i%3An-81c-vc-overtaking) — Transportation Engineering I, chapter 3
- [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×
- [Overtaking sight distance and zone, 60 kmph](https://www.bctengineer.com/question.md?key=semester_6%2Ftransportation_engineering_i%3An-76b-osd-60) — Transportation Engineering I, chapter 3
- [Overtaking sight distance and zone numerical](https://www.bctengineer.com/question.md?key=semester_6%2Ftransportation_engineering_i%3An-62j-osd-numeric) — Transportation Engineering I, chapter 3
- [Stopping sight distance and derivation](https://www.bctengineer.com/question.md?key=semester_6%2Ftransportation_engineering_i%3Assd-factors-derive) — Transportation Engineering I, chapter 3, asked 6×
- [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

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