Question 1 of 7: Definitions and Discussion

Question 1: Definitions and Discussion (20 marks — 5 each)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

Given. Four traffic-engineering terms, 5 marks each. Two of them (peak hour factor, PIEV) carry a defining relation that should be written out and exercised on a short illustration; two of them (phase types, count types) are compared concepts best settled by saying exactly what is different about them and when each is the right choice.

Find. For each term: a one-sentence definition, the governing relation where one exists, and a short discussion of what the term is used for in Canadian practice.

Approach. Define each term, give its relation or its discriminating feature, then state the design decision it drives.

1. Part (a) — Peak hour factor. The peak hour factor is the ratio of the whole-hour volume to the flow rate during the busiest short interval within that hour, conventionally 15 minutes: $$\mathrm{PHF} = \frac{V_{60}}{4\,V_{15}}$$ where $V_{60}$ is the hourly volume and $V_{15}$ the count in the peak 15-minute period. It is therefore a measure of how evenly demand is spread inside the hour, not of how heavy demand is. Its value lies between 0.25 (all of the hour's traffic in one quarter) and 1.00 (perfectly uniform flow); urban approaches typically return 0.85–0.95 and rural ones 0.88–0.98.
2. Worked illustration. Take four consecutive 15-minute counts on one approach of 305, 348, 402 and 331 veh. The hourly volume is $V_{60} = 305 + 348 + 402 + 331 = 1386$ veh, and the peak rate of flow is $4 \times 402 = 1608$ veh/h, so $$\mathrm{PHF} = \frac{1386}{1608} = \boxed{0.862}$$ The engineering point is what follows: capacity analysis is done at the peak rate, 1608 veh/h, not at the 1386 veh/h that a one-hour count would report. Dividing the design volume by the PHF is how the HCM converts an hourly volume to the equivalent flow rate, and skipping that step under-designs every approach by 5–15 per cent.
3. Part (b) — Protected vs permissive phase. A protected phase gives a movement the exclusive right of way: the conflicting movements are held on red, so the driver needs no gap and the movement discharges at close to the ideal saturation flow. The usual display is a green arrow. A permissive (permitted) phase gives the movement a circular green shared with the conflicting movement, so a left-turning driver must yield and complete the turn in gaps in the opposing through stream; its saturation flow is therefore much lower and is modelled by a left-turn adjustment factor.
4. Discussion of (b). Protection buys safety and capacity per lane, but it costs a phase: each extra phase adds its own intergreen to the lost time and lengthens the cycle, which raises delay for every other movement and lengthens pedestrian waits. Canadian practice (MUTCDC, and the warrants in most provincial signal manuals) reaches for protected phasing when the left-turn volume, the opposing through volume, the number of opposing lanes, the approach speed or the collision history make gap acceptance unreliable; a protected–permissive combination captures both by running the arrow first and then allowing permitted turns for the rest of the green.
5. Part (c) — Cordon vs screenline counts. A cordon count stations counters on every road, transit route and walkway that crosses a closed boundary drawn around an area — a downtown, a campus, a port — and records volumes in both directions. Accumulating the inbound minus outbound totals over the day gives the number of vehicles or people inside the cordon at any hour, which is what parking supply, transit demand and area-wide travel-demand management are sized on. A screenline count stations counters along an imaginary open line, most often following a natural or built barrier such as a river, a rail corridor or an escarpment, and records the volumes crossing it.
6. Discussion of (c). The screenline total is the single most valuable calibration statistic for a travel-demand model: every trip assigned across that line must sum to the observed crossing volume, so a screenline is how a modeller proves an assignment is not merely plausible. The distinction is therefore one of purpose as well as geometry — a cordon answers “how much travel is in this area?”, a screenline answers “how much travel crosses this line?”. Neither substitutes for the other, and both are normally run as classified counts so that trucks and buses can be converted to passenger-car units.
7. Part (d) — PIEV. PIEV is the four-stage model of the driver's reaction interval: Perception (the stimulus reaches the eye), Intellection (it is identified and understood), Evaluation (a course of action is chosen) and Volition (the muscular act of braking or steering begins). The sum of the four is the perception–reaction time, and AASHTO adopts $t = 2.5$ s for design — a value near the 90th percentile of observed times, deliberately longer than the 0.6–1.5 s a prepared driver needs.
8. Discussion of (d). PIEV matters because during the whole interval the vehicle does not slow at all; it covers $$d_1 = 0.278\,V\,t$$ which at $V = 90$ km/h is $0.278 \times 90 \times 2.5 = 62.6$ m — the very number in the “brake reaction distance” column of the AASHTO table printed on page 4 of this paper. That distance is added to the braking distance to form stopping sight distance, so every sight-distance, crest-curve and signal-clearance calculation in this exam inherits the PIEV assumption. Where the decision is more complex than “stop” — a lane drop, a toll plaza, an unexpected exit — the Intellection and Evaluation stages lengthen and design switches to decision sight distance, which uses reaction times of 3–9.1 s.