16-Civ-B10 Traffic Engineering · December 2017
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
Paper format. National Examinations, December 2017 — 16-Civ-B10 Traffic Engineering, 3-hour duration, OPEN BOOK (any non-communicating calculator permitted). Seven questions of equal value (20 marks each); the paper requires five solutions and marks only the first five as they appear in the answer book. Because the set is a study resource, all seven questions are solved here. The paper's own Note 1 invites a clear statement of any assumptions made and Note 2 permits any required-but-not-given data to be assumed; every assumption used below is stated explicitly where it is introduced.
Reference texts.
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.
A protected phase is an interval in the signal cycle during which a movement receives an exclusive right-of-way indication — conventionally a green arrow — so that no conflicting movement may legally proceed. For left turns the question is not whether to protect but when in the cycle to place the protection relative to the adjacent through movement, and that placement is the difference between leading and lagging.
A leading protected phase serves the left turn before the through movement on the same approach: the cycle opens with a green arrow for the left turn while the opposing through traffic is held on red, and only when the left-turn arrow terminates does the through green begin. Its advantages are that drivers expect it (it is by far the more common arrangement in Canadian practice), the left-turn bay is emptied at the start of the phase when the queue is longest, and the movement is clearly separated from the opposing through platoon. Its principal drawback is the yellow trap risk it creates if the opposing left turn is permitted while the subject left turn still shows a permissive indication.
A lagging protected phase serves the left turn after the through movement: both through movements run first, and the left-turn arrow is displayed at the end of the phase after the opposing through movement has been terminated. Lagging protection is used to favour progression along an arterial — the through band can be released without interruption and the left turns are cleaned up at the tail of the phase — and it permits a lead–lag arrangement in which one direction leads and the other lags, which is a powerful tool for time–space band optimisation on a coordinated corridor. Its weaknesses are driver unfamiliarity, higher exposure to the yellow trap when the opposing direction is permissive rather than protected, and left-turn queues that must wait through the whole through interval, which lengthens the storage bay required.
Both are averages of vehicle speeds over a traffic stream, but they average different populations and therefore answer different questions. Time mean speed is the arithmetic mean of the spot speeds of vehicles passing a point on the roadway during a stated interval,
and it is what a radar gun or a single inductive-loop pair measures. Space mean speed is the average speed of the vehicles occupying a length of roadway at an instant; operationally it is the harmonic mean of the individual speeds, equivalently the length of the study section divided by the mean travel time,
The two are related by the identity
in which $\sigma_s^{2}$ is the variance of the speeds about the space mean speed. Because a variance cannot be negative, time mean speed is always greater than or equal to space mean speed, with equality only when every vehicle travels at the same speed; the faster vehicles are over-represented in a point sample because more of them cross the detector per unit time. For a stream with $u_s = 50$ km/h and $\sigma_s^{2} = 25$ (km/h)$^2$, for example, $u_t = 50 + 25/50 = 50.5$ km/h.
The distinction is not academic. The fundamental relation of traffic flow, $q = u\,k$, holds only for space mean speed, so travel-time studies, density estimates and level-of-service determinations must use SMS. Time mean speed is the correct statistic for enforcement, for spot-speed distributions and for the 85th-percentile speed used to set posted limits.
A circular (simple) curve is a horizontal alignment element of constant radius $R$ joining two tangents. Its curvature, $1/R$, is uniform along the whole arc, which means it jumps discontinuously from zero on the tangent to $1/R$ at the point of curvature. The unbalanced lateral acceleration a vehicle experiences therefore appears instantaneously, and the superelevation must be developed on the tangent approaches rather than within the curve.
A spiral (transition) curve is an element whose radius varies continuously from infinity at the tangent end to the radius of the circular curve at its other end — in North American practice the clothoid, in which curvature increases linearly with arc length. Inserting a spiral between the tangent and the circular arc gives a natural path for the steering input, allows the superelevation runoff and any pavement widening to be developed inside the transition rather than on the tangent, improves the appearance of the alignment, and removes the abrupt onset of lateral acceleration.
Practically, spirals matter most where the radius is small relative to the design speed. Both the TAC Geometric Design Guide for Canadian Roads and the AASHTO Green Book express the criterion through the rate of change of lateral acceleration — roughly $C \le 0.6$ m/s$^3$ — so that spirals are required on sharp curves at high design speed and become unnecessary on flat curves where the driver's own natural spiral path can be accommodated within the lane width. Spirals also complicate staking and add two more alignment points (TS, SC, CS, ST rather than PC, PT), which is the main argument for the simple circular curve where a transition is not needed.
A high-occupancy vehicle (HOV) lane is a lane reserved, either continuously or during stated hours, for vehicles carrying at least a specified number of occupants — typically 2+ or 3+ — together with buses and, in most Canadian jurisdictions, motorcycles, emergency vehicles and taxis. HOV lanes are a demand-side, person-throughput measure: they do not add vehicular capacity so much as reallocate it to the vehicles that move the most people, and they buy that reallocation with a travel-time advantage that makes ridesharing and transit attractive.
They may be implemented as a concurrent-flow lane separated by a painted buffer (the usual treatment on Ontario's Highway 403/404 and British Columbia's Highway 1), as a barrier-separated or reversible facility, or as a queue-jump/bypass lane at a ramp meter or an intersection. The performance argument is straightforward: a general-purpose lane carrying 2000 veh/h at an average occupancy of 1.15 moves about 2300 persons per hour, whereas an HOV lane carrying 1200 veh/h at an occupancy of 2.5 plus a few buses can exceed 3000 persons per hour. The operational risks are under-use (an HOV lane that looks empty invites political pressure and violation), the speed differential and weaving conflicts at the buffer openings, and the need for real enforcement. Occupancy thresholds, hours of operation and enforcement level are therefore the three design variables that decide whether an HOV lane succeeds.
Pedestrian clearance time is the interval provided at a signalised crossing, beginning at the end of the WALK indication, during which a pedestrian who stepped off the curb at the very end of WALK can complete the crossing before conflicting vehicular traffic is released. It is displayed as the flashing DON'T WALK (or flashing hand) indication and is timed from the walking-speed requirement
where $L_c$ is the crossing length and $S_p$ the assumed walking speed. MUTCDC and the HCM take $S_p = 1.2$ m/s for the general population, reduced to about 1.0 m/s where older pedestrians, school children or persons with disabilities are prevalent. For the 20 m carriageway of Questions 3 and 4, $\text{PCT} = 20/1.2 = 16.7$ s.
Pedestrian clearance time must be distinguished from the total pedestrian interval, which is the WALK time plus the clearance time; the WALK time is the perception–reaction and start-up allowance (a minimum of about 3–7 s, and longer where volumes are high enough that a platoon cannot all step off at once). It must also be distinguished from the vehicular change and clearance intervals (yellow plus all-red), which serve a different population. The consequence for signal design is that the pedestrian requirement can govern the cycle length — which is exactly what happens in Question 3 — because the clearance time is a fixed number of seconds that must fit inside a green whose length is only a fraction of the cycle.
