6.2 Transportation: Traffic Engineering & Pavement

Traffic Flow Fundamentals

The three primary traffic variables are flow (q) in vehicles per hour (veh/hr), density (k) in vehicles per mile (veh/mi), and speed (v) in miles per hour (mph). They are tied by the fundamental identity:

• q = k · v

A classic trap: use space-mean speed (harmonic-average travel speed), not time-mean speed, in q = k·v. Time-mean speed is always ≥ space-mean speed.

Greenshields' linear model assumes speed falls linearly with density:

• v = v_f·(1 − k/k_j)

where v_f = free-flow speed and k_j = jam density (density at standstill). Substituting into q = k·v gives a parabola peaking at capacity:

Worked example. With v_f = 60 mph and k_j = 200 veh/mi: q_max = (60·200)/4 = 3000 veh/hr, occurring at v_o = 30 mph and k_o = 100 veh/mi. The headway (s/veh) at any flow is simply 3600/q.

Capacity, Level of Service, and Signals

Capacity is the maximum sustainable hourly flow under prevailing conditions. The Highway Capacity Manual (HCM) defines Level of Service (LOS), a letter grade A (free flow) through F (forced/breakdown flow), keyed to a measure of effectiveness such as density (freeways), delay (intersections), or volume-to-capacity (v/c) ratio. LOS E corresponds to operating at capacity; LOS F means demand exceeds capacity.

Signal timing basics the FE may test:

• Cycle length (C) = total time for one full sequence of phases (s).
• Effective green (g) = green + yellow + all-red minus startup lost time.
• Capacity of a movement = s·(g/C), where s is the saturation flow rate (veh/hr of green).
• Yellow (change) interval: y = t + v/(2a) where t is reaction time; the all-red clears the intersection: ar = (w + L)/v.

The v/c (degree of saturation) ratio drives delay; as v/c approaches 1.0, delay grows sharply. Webster's formula and HCM delay models estimate average control delay per vehicle for LOS at signalized intersections.

Pavement Types and ESALs

Two pavement families appear on the FE:

• Flexible (asphalt concrete) pavements distribute wheel loads through successive layers (surface, base, subbase) onto the subgrade; the surface bends with the layers. Designed by the structural number (SN) method.
• Rigid (Portland cement concrete, PCC) pavements carry load primarily in slab bending, spreading it over a wide area; the slab's flexural strength (modulus of rupture) dominates. Designed by slab thickness.

Traffic loading is normalized to the ESAL — 18,000-lb (18-kip) Equivalent Single Axle Load. Each axle is converted by a Load Equivalency Factor (LEF) that scales roughly with the fourth power of axle load, so heavy trucks dominate damage:

• ESALs = Σ (axle passes × LEF for that axle)

Worked ESAL example. A 36-kip tandem axle has an LEF ≈ 1.38 (from AASHTO tables). 500 passes contribute 500 × 1.38 = 690 ESALs. By contrast, a passenger car (LEF ≈ 0.0001) is negligible — pavement design is driven by trucks.

Traffic safety measures use crash rates: RMVM = (crashes × 100,000,000)/(VMT) per 100 million vehicle-miles, and intersection rate per million entering vehicles.

Volume Factors and a Worked Crash-Rate Example

Demand on a facility is described with several volume terms the FE expects you to use correctly:

• AADT — Annual Average Daily Traffic (veh/day), the yearly mean of daily volumes.
• DHV — Design Hourly Volume, often the 30th-highest hour, estimated as DHV = AADT·K, where K ≈ 0.08–0.12.
• DDHV — Directional Design Hourly Volume = DHV·D, where D is the directional split.
• PHF — Peak Hour Factor = hourly volume / (4 × peak 15-min volume); PHF ≤ 1.0, with lower values indicating sharper peaking.
• Flow rate = peak hourly volume / PHF, used in HCM capacity checks.

Worked crash-rate example. A 5-mile segment carries AADT = 12,000 veh/day and experienced 18 crashes in one year. Annual VMT = 12,000 × 365 × 5 = 21,900,000 vehicle-miles. The rate per hundred million vehicle-miles = (18 × 100,000,000)/21,900,000 = 82.2 crashes/100 MVM. Comparing this to a statewide average for similar roads flags whether the segment is a high-crash location warranting safety improvements.

Worked PHF example. If the peak 15-minute count is 450 vehicles, the hourly volume is at most 4 × 450 = 1800; if the actual hourly count is 1500, PHF = 1500/1800 = 0.83, and the design flow rate = 1500/0.83 = 1807 veh/hr. Using the unadjusted hourly volume instead of the flow rate understates the true peak demand — a frequent error.

Remember the chain of conversions the FE rewards: AADT scales to a design hour (× K), then to one direction (× D), then to a 15-minute flow rate (÷ PHF). Each factor narrows from a yearly average to the actual peak the geometry must serve. Reversing or skipping a factor is the single most common traffic-volume mistake, so write out the units (veh/day → veh/hr → veh/hr per lane) at every step and confirm the result is dimensionally consistent before selecting an answer.