---
title: "Signal timing: roads H 12 m and F 9.6 m"
subject: "Transportation Engineering II"
chapter: 1
key: "semester_7/transportation_engineering_ii:signal-pedestrian-road-h-12m-f"
source: https://www.bctengineer.com/q/semester_7/transportation_engineering_ii/signal-pedestrian-road-h-12m-f
site: BCT Engineering
---

# Signal timing: roads H 12 m and F 9.6 m

Transportation Engineering II · Chapter 1: Traffic Engineering

- Asked in: 2070 Chaitra, 8 marks
- Video: [Design of Two Phase Traffic Signal Using Webster's Traffic Signal Design Method| Solved Problem](https://www.youtube.com/watch?v=HyIFzbsYXe0) — Master Civil Engineering
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_7/transportation_engineering_ii/signal-pedestrian-road-h-12m-f
- Whole chapter: https://www.bctengineer.com/md/semester_7/transportation_engineering_ii/chapter-1

## Question

An isolated signal with pedestrians indication is to be installed on a right angled intersection with road H of 12 m wide and road F of 9.6 m wide. The heaviest volume per hour for each lane of H and F are 475 and 325 respectively. The approach speeds are 60 and 45 kmph for road H and road F respectively. Design the timings of traffic and pedestrian signals. Assume amber times for road H and road F as 5 and 4 secs respectively.

## Short answer

Using Webster’s method with given ambers, pedestrian crossing times (H: 15 s, F: 13 s), and saturation flow 1800 PCU/h/lane, cycle length 45 s. Road H: green 21 s, amber 5 s; Road F: green 15 s, amber 4 s. Pedestrian WALK 5 s plus clearance for each phase.

## Answer

Isolated two-phase signal with pedestrian indications for road H (12 m) and road F (9.6 m). The ambers are given (5 s and 4 s), so the approach speeds are not needed for them.

Design basis (IRC:93-1985, *Guidelines on Design and Installation of Road Traffic Signals*, with Webster's method): two-phase signal, Phase 1 = road H moves, Phase 2 = road F moves. Pedestrians cross a road while the traffic on the cross road has green. Assumed (not given): saturation flow 1800 PCU/h per lane, start-up lost time 2 s per phase, pedestrian walking speed 1.2 m/s and initial walk (pedestrian start-up) time 5 s.

#### Step 1: Amber (change) time

Amber times are given: road H = 5 s, road F = 4 s.

#### Step 2: Pedestrian crossing time

Time to cross = initial walk + width / walking speed:

$$
\begin{aligned} t_{p,H} &= 5 + \frac{12}{1.2} = 15.0\ \text{s}\\ t_{p,F} &= 5 + \frac{9.6}{1.2} = 13.0\ \text{s} \end{aligned}
$$

Pedestrians crossing road H walk during Phase 2, so Phase 2 green must be at least 15.0 s. Pedestrians crossing road F walk during Phase 1, so Phase 1 green must be at least 13.0 s.

#### Step 3: Webster cycle time from traffic

$$
\begin{aligned} y_H &= \frac{475}{1800} = 0.264, \quad y_F = \frac{325}{1800} = 0.181, \quad Y = 0.444\\ L &= (2+5) + (2+4) = 13\ \text{s}\\ C_0 &= \frac{1.5L+5}{1-Y} = \frac{1.5(13)+5}{1-0.444} = 44.1\ \text{s} \end{aligned}
$$

$$
\begin{aligned} g_H &= \frac{0.264}{0.444}(31.1) = 18.5\ \text{s}, \quad G_H = g_H + 2 = 20.5\ \text{s}\\ g_F &= \frac{0.181}{0.444}(31.1) = 12.6\ \text{s}, \quad G_F = g_F + 2 = 14.6\ \text{s} \end{aligned}
$$

#### Step 4: Check against pedestrian needs

| Phase | Green from traffic (s) | Pedestrian minimum (s) | Adopted green (s) |
|---|---|---|---|
| 1 (road H) | 20.5 | 13.0 | 21 |
| 2 (road F) | 14.6 | 15.0 | 15 |

Adopted cycle length $C = 21 + 5 + 15 + 4 = 45$ s.

#### Final timings

| Signal | Phase 1: road H | Phase 2: road F |
|---|---|---|
| Vehicle green | 21 s | 15 s |
| Vehicle amber | 5 s | 4 s |
| Vehicle red | 19 s | 26 s |

Pedestrian signals: pedestrians crossing road F get WALK for 5 s then flashing (clearance) for 8 s during Phase 1 (total 13 s of 21 s green); pedestrians crossing road H get WALK for 5 s then flashing for 10 s during Phase 2 (total 15 s of 15 s green). All pedestrian indications show DON'T WALK (red man) while their cross traffic moves.

#### Phase diagram

```text
Cycle = 45 s
Road H: [GREEN 21][A 5][  RED 19  ]
Road F: [ RED 26 ][GREEN 15][A 4]
Ped crossing F: [WALK+FLASH 21][DON'T WALK 24]
Ped crossing H: [DON'T WALK 26][WALK+FLASH 15][DW]
```

## Check yourself

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

1. What is the crossing time for the 12 m road H (5 s initial walk, 1.2 m/s)?
   A. 10.0 s
   B. 13.0 s
   C. 15.0 s
   D. 17.0 s
   Answer: C. t = 5 + 12/1.2 = 15.0 s. (Key point: Pedestrian crossing time)

2. Which green must be at least 13.0 s (the crossing time of road F)?
   A. Phase 1 (road H green)
   B. Phase 2 (road F green)
   C. The amber of road F
   D. Total cycle
   Answer: A. Road F pedestrians cross while road H has green, so Phase 1 must be at least 13.0 s. (Key point: Phase for pedestrian minimum)

3. Why is Phase 2 green adopted as 15 s and not 14.6 s?
   A. Webster's formula gives 15 s exactly
   B. Pedestrians crossing road H need at least 15.0 s
   C. Amber of road H is 5 s
   D. Saturation flow is 1800
   Answer: B. The pedestrian minimum of 15.0 s exceeds the traffic green of 14.6 s, so it governs. (Key point: Pedestrian governs Phase 2)

4. What is the adopted cycle with greens 21 s and 15 s and ambers 5 s and 4 s?
   A. 44.1 s
   B. 41 s
   C. 45 s
   D. 50 s
   Answer: C. C = 21 + 5 + 15 + 4 = 45 s. (Key point: Cycle length)

## Close variants set in other exams

- [Signal timing: roads A 18 m and B 12 m](https://www.bctengineer.com/question.md?key=semester_7%2Ftransportation_engineering_ii%3Asignal-pedestrian-road-a-18m-b) — Transportation Engineering II, chapter 1, asked 2×
- [Signal timing: roads A 15 m and B 12 m](https://www.bctengineer.com/question.md?key=semester_7%2Ftransportation_engineering_ii%3Asignal-pedestrian-road-a-15m-b) — Transportation Engineering II, chapter 1, asked 2×

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