--- title: "Intersection control methods; Webster signal 400/300 PCU" subject: "Transportation Engineering II" chapter: 1 key: "semester_7/transportation_engineering_ii:intersection-control-methods-webster-400-300" source: https://www.bctengineer.com/q/semester_7/transportation_engineering_ii/intersection-control-methods-webster-400-300 site: BCT Engineering --- # Intersection control methods; Webster signal 400/300 PCU Transportation Engineering II · Chapter 1: Traffic Engineering - Asked in: 2066 Bhadra, 2+6 marks - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_7/transportation_engineering_ii/intersection-control-methods-webster-400-300 - Whole chapter: https://www.bctengineer.com/md/semester_7/transportation_engineering_ii/chapter-1 ## Question What are different methods of traffic control at an intersection? The average normal flow of traffic on cross roads A and B during design period are 400 and 300 PCU per hour; the saturation flow values on these roads are estimated as 1450 and 1150 PCU per hour respectively. The all-red time required for pedestrian crossing is 12 sec. Design two phase traffic signal by Webster's method. ## Short answer Methods include signs, channelization, roundabouts, signals, and grade separation. For flows 400 and 300 PCU/h, saturations 1450 and 1150 PCU/h, all-red 12 s, Webster gives optimum cycle 65 s with phase greens 25 s and 24 s and 2 s amber each. ## Answer #### Methods of traffic control at an intersection 1. **Uncontrolled (priority by rules):** drivers give way to the vehicle on the right or on the main road; suitable for very low volume. 2. **Traffic signs and markings:** STOP and GIVE WAY signs, with stop lines; the minor road gives way to the major road (IRC:67, IRC:35). 3. **Channelisation:** islands and markings guide the movements (IRC:SP:41). 4. **Rotary (roundabout):** one-way circulation, no signals (IRC:65). 5. **Traffic signals:** fixed-time, vehicle-actuated or area-coordinated (IRC:93). 6. **Police control** by hand signals at peak times or special events. 7. **Grade separation:** flyover, underpass or interchange for very high volume. #### Design of a two-phase signal by Webster's method Data: roads A and B carry 400 and 300 PCU/h; saturation flows 1450 and 1150 PCU/h; all-red time for pedestrians $R$ = 12 s per cycle. #### Step 1: Flow ratios Flow ratio $y = q/s$ for each approach; the larger value in a phase is the critical one. | Phase | Approach | q | s | y = q/s | |---|---|---|---|---| | Phase 1 | Road A | 400 | 1450 | 0.276 | | Phase 2 | Road B | 300 | 1150 | 0.261 | $$ Y = 0.276 + 0.261 = 0.537 $$ #### Step 2: Lost time An amber of 2 s per phase is assumed and taken as the lost time of that phase; the all-red time $R$ = 12 s is also lost. $$ L = 2 + 2 + 12 = 16.0\ \text{s} $$ #### Step 3: Optimum cycle time (Webster) $$ C_0 = \frac{1.5L + 5}{1 - Y} = \frac{1.5(16.0) + 5}{1 - 0.537} = 62.6\ \text{s} $$ Adopt **C = 65 s**. #### Step 4: Green times Total effective green $= C - L = 65 - 16.0 = 49.0$ s, divided in proportion to $y$: $$ g_{1} = \frac{y_1}{Y}(C-L) = \frac{0.276}{0.537}(49.0) = 25.2\ \text{s} $$ $$ g_{2} = \frac{y_2}{Y}(C-L) = \frac{0.261}{0.537}(49.0) = 23.8\ \text{s} $$ Because the whole amber is counted as lost time, the displayed green equals the effective green (so that $\sum G + \sum I + R = C$): | Phase | Effective g (s) | Green G (s) | Amber (s) | |---|---|---|---| | Phase 1 | 25.2 | 25 | 2 | | Phase 2 | 23.8 | 24 | 2 | Check: 25 + 2 + 24 + 2 + 12 = 65 s. #### Phase diagram ```text | P1 green 25 | A2| P2 green 24 | A2| R 12 | ``` ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. In Webster's method, what is the flow ratio y of an approach and how is Y obtained here? A. y = s/q; Y is the larger of the two B. y = q/s; Y is the sum of the critical y values of the phases (0.276 + 0.261 = 0.537) C. y = q x s; Y is the average of the phases D. y = q/s; Y is the difference of the two phases Answer: B. y = q/s for each phase's critical approach, and Y is their sum, 0.537. (Key point: Flow ratio and critical value) 2. How was the total lost time L = 16 s obtained? A. 2 s lost per phase for two phases plus 12 s all-red for pedestrians B. 12 s per phase for two phases C. Only the 12 s all-red time D. 2 s amber only, no all-red Answer: A. L = (0+2) + (0+2) + 12 = 16 s, i.e. 2 s per phase plus the 12 s pedestrian all-red. (Key point: Lost time) 3. Which formula gives Webster's optimum cycle time? A. C0 = (1.5L + 5)/(1 - Y) B. C0 = (L + 5)/(1 + Y) C. C0 = 1.5L/Y D. C0 = (1.5L - 5)/Y Answer: A. Webster's formula is C0 = (1.5L + 5)/(1 - Y), giving 62.6 s here, adopted as 65 s. (Key point: Optimum cycle time) 4. How is the effective green (C - L = 49 s) divided between phases? A. Equally between phases B. In proportion to the flow ratios y/Y C. In proportion to saturation flows only D. All to the road with the higher volume Answer: B. g = (y/Y)(C - L), giving about 25.2 s for Road A and 23.8 s for Road B. (Key point: Green time split) 5. Which method of intersection control is suitable for very high volume and removes crossing conflicts? A. Police control B. Channelisation C. Grade separation D. Uncontrolled give-way rule Answer: C. Flyovers, underpasses or interchanges are used for very high volumes because they remove crossing at the same level. (Key point: Control methods) ## Close variants set in other exams - [Webster signal: roads H and F, 3 s and 4 s headways](https://www.bctengineer.com/question.md?key=semester_7%2Ftransportation_engineering_ii%3Awebster-two-phase-h-f-400) — Transportation Engineering II, chapter 1, asked 2× ## Related in Transportation Engineering II - [Two-phase signal: 400 and 250 PCU/hr, 7 m roads](https://www.bctengineer.com/question.md?key=semester_7%2Ftransportation_engineering_ii%3Awebster-two-phase-400-250-width) — Transportation Engineering II, chapter 1 - [Webster signal: 450 and 350 PCU/hr, all-red 15 s](https://www.bctengineer.com/question.md?key=semester_7%2Ftransportation_engineering_ii%3Awebster-two-phase-450-350-pcu) — Transportation Engineering II, chapter 1 - [Webster two-phase signal with saturation headways](https://www.bctengineer.com/question.md?key=semester_7%2Ftransportation_engineering_ii%3Awebster-two-phase-four-legged-table) — Transportation Engineering II, chapter 1 - [Signal design: roads X 15 m and Y 10.5 m](https://www.bctengineer.com/question.md?key=semester_7%2Ftransportation_engineering_ii%3Asignal-design-roads-x-15m-y) — Transportation Engineering II, chapter 1 - [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× - [Signal timing: roads A 15 m and B 7 m](https://www.bctengineer.com/question.md?key=semester_7%2Ftransportation_engineering_ii%3Asignal-pedestrian-road-a-15m-7m) — Transportation Engineering II, chapter 1