Transportation Learning HubTransportation Learning Hub · PE Civil Transportation · Area 7 of 10
Traffic Signals — PE Civil Transportation
Signals are applied kinematics and judgement: how long each movement needs to stop, clear and cross — and whether a junction should be signalised at all. The calculations are short; the marks are in setting them up with the right speed, the right width and the right pedestrian.
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Change and clearance intervals
When a phase ends, two intervals protect the transition. The yellow change interval is derived from braking kinematics: a driver who cannot stop comfortably should be able to proceed, and a driver who can stop must be able to — the interval covers perception–reaction plus comfortable braking time, and on a grade the braking term is adjusted for the slope (a downgrade lengthens it). Calculated values are rounded up for design. The all-red clearance interval then holds every approach at red while the last vehicle crosses the conflict area: junction width plus one vehicle length, at the approach speed.
\[Y = t + \frac{v}{2a} \qquad \text{AR} = \frac{W + L}{v}\]
| Y, AR | yellow change interval and all-red clearance interval, s |
|---|---|
| t | perception–reaction time, s (given) |
| v | approach speed, ft/s — convert from mph before substituting |
| a | comfortable deceleration, ft/s² (given) |
| W, L | junction (conflict-area) width and vehicle length, ft (given) |
The form comes from distance: during the interval a driver travels the reaction distance \(v\,t\) plus the braking distance \(v^{2}/(2a)\); dividing that total distance by the approach speed \(v\) gives \(t + v/(2a)\). Keep speeds in ft/s throughout — mph is the planted unit error.
Worked example Yellow and all-red intervals
Given: An approach speed of 44 ft/s on a level grade, perception–reaction time \(t = 1.0\) s and deceleration \(a = 10\ \text{ft/s}^{2}\) (both given). The junction width is 60 ft and the design vehicle length is 20 ft. Find the yellow change interval and the all-red clearance interval.
Solution:
- Yellow: \(Y = 1.0 + \dfrac{44}{2 \times 10} = 1.0 + 2.2 = 3.2\) s — in design this is rounded up to the next setting increment.
- All-red: \(\text{AR} = \dfrac{60 + 20}{44} = \dfrac{80}{44} = 1.82\) s \(\approx 1.8\) s.
Answer: \(Y = 3.2\) s (round up in design); all-red \(\approx 1.8\) s.
Phasing and pedestrian timing
A phase is a set of movements given right of way together; a cycle is one complete sequence of phases, and each movement's capacity scales with the share of the cycle it is effectively green. Phasing questions turn on conflicts: protected phases separate conflicting movements in time, permissive phases make drivers judge gaps, and pedestrian phases must fit inside the parallel vehicle phase or be given their own. Pedestrian timing has two parts — a walk interval that lets pedestrians establish themselves in the crossing, then a clearance (flashing don't walk) interval long enough to finish crossing at the design walking speed. Near rail lines, preemption overrides the normal sequence: the signal must clear the tracks before a train arrives, which can truncate or extend phases regardless of traffic demand.
\[\text{Pedestrian clearance} = \frac{\text{crossing distance}}{\text{walking speed}}\]
| Crossing distance | kerb-to-kerb width of the road being crossed, ft (given) |
|---|---|
| Walking speed | design walking speed, ft/s (given in the stem) |
| Preemption | railroad (or emergency-vehicle) override of normal phasing; track clearance takes priority |
Worked example Pedestrian clearance time
Given: A crossing is 56 ft wide and the design walking speed given is 3.5 ft/s. Find the pedestrian clearance time.
Solution:
- Clearance \(= \dfrac{56}{3.5} = 16.0\) s.
- This is the flashing don't walk period; the walk interval that precedes it is additional.
Answer: Pedestrian clearance \(= 16.0\) s.
Warrants and signal design
A signal is a treatment to be justified, not a default. Warrant analysis compares measured conditions — traffic volumes by hour, pedestrian demand, school crossings, crash experience, network factors — against the warrant criteria in the MUTCD framework: meeting a warrant means a signal may be justified, and engineering judgement still decides, because an unwarranted signal can add delay and rear-end crashes. Signal design then covers the hardware and layout that deliver the timing: signal faces and their placement so drivers see the indication intended for them, detection that calls and extends phases where demand varies, and controller operation (fixed-time, actuated, coordinated along a corridor). Exam questions in this subtopic are mostly conceptual — know what each warrant family measures, what detection does, and why visibility and placement rules exist.
Warrant met \(\neq\) signal required — a warrant is a threshold for study and justification, not an instruction
Design chain: demand \(\rightarrow\) phasing \(\rightarrow\) timing \(\rightarrow\) faces, placement and detection to deliver it
If a question asks whether a signal must be installed because a warrant is satisfied, the careful answer is no — satisfaction triggers justification and judgement, and the disbenefits of an unnecessary signal are part of that judgement.