Transportation Engineering
Transportation engineering designs the geometry of roads and analyzes the traffic that uses them. The PE tests horizontal and vertical curves, sight distance, the fundamental traffic-flow relationships, signal timing, and pavement basics, following AASHTO geometric design and the Highway Capacity Manual. Geometry and traffic flow together make up most of the questions.
Horizontal Curves
A circular horizontal curve is defined by its radius R and central (intersection) angle Δ. The degree of curve by the arc definition is D = 5,729.58/R, so a larger radius gives a flatter, smaller-degree curve. The standard curve elements all key off R and Δ: tangent length T = R·tan(Δ/2), curve length L = R·Δ (Δ in radians) or 100·Δ/D, external distance E = R·(sec(Δ/2) - 1), and middle ordinate M = R·(1 - cos(Δ/2)). Sight distance around a curve depends on the middle ordinate to a lateral obstruction. Superelevation (banking) tilts the pavement so that a component of the vehicle's weight, together with side friction, supplies the centripetal force; the design relation is R_min = V^2/[g·(e + f)], or in US units R_min = V^2/[15·(e + f)] with V in mph. Spiral (transition) curves ease a driver from the tangent into the circular curve by gradually introducing curvature and superelevation, and a reverse curve joins two curves that bend in opposite directions.
Vertical Curves
Vertical curves are parabolas connecting two grades that differ by an algebraic amount A = |g_2 - g_1| (in percent). The rate of vertical curvature K = L/A is the horizontal distance needed to change grade by 1% and is the value checked against sight-distance tables. On a symmetric parabolic curve, the offset from the tangent is proportional to the square of the distance from the curve's start (BVC), and the high or low point falls where the grade line is horizontal, at a distance x = g_1·L/A from the BVC. Crest curves are limited by stopping sight distance over the hump; sag curves are governed by headlight sight distance at night (and by comfort and drainage). Elevations along the curve come from y = y_BVC + g_1·x + (A/(2L))·x^2 with consistent sign conventions.
Sight Distance and Vehicle Dynamics
Stopping sight distance (SSD) is the sum of two parts: the brake-reaction distance a driver covers while perceiving and reacting, d_1 = 1.47·V·t (V in mph, t in seconds), and the braking distance d_2 = V^2/[30·(f ± G)], where G is the grade (add for upgrade, subtract for downgrade — a downgrade lengthens the stop). AASHTO's standard perception-reaction time for SSD design is 2.5 seconds. Passing sight distance on a two-lane road is much longer than SSD because it must cover the whole overtaking maneuver. Basic kinematics also appear directly: uniform acceleration a = Δv/Δt, braking distance from v^2 = 2·a·d, and speed-from-skid-marks estimates using v = sqrt(2·g·f·d). Grade resistance — the downslope pull on a vehicle — is simply the weight times the grade, W·G.
Traffic Flow Fundamentals
The three traffic-stream variables are tied by one identity: flow = density × speed, q = k·v, with q in veh/hr, k in veh/mi, and v the space-mean speed. Average spacing is 5,280/k (ft per vehicle) and average time headway is 3,600/q (seconds per vehicle). Greenshields' linear model assumes speed falls linearly with density from free-flow speed v_f at zero density to zero speed at jam density k_j; maximum flow (capacity) occurs at half the free-flow speed and half the jam density. At jam density the road is stopped: speed and flow are both zero. The peak-hour factor PHF = hourly volume/(4 × peak 15-min count) measures how concentrated demand is within the hour, and the design hour volume is derived from AADT using the K-factor (DHV = AADT × K) and directional split D.
Capacity, Level of Service, and Signal Timing
Level of service (LOS) grades operating quality from A (free flow) to F (breakdown, demand exceeds capacity) based primarily on measures like density or delay for the facility type. Heavy vehicles are folded into capacity analysis through passenger-car equivalents, which inflate a truck's effect on an upgrade. For signals, the cycle length must absorb lost time — total lost time is the sum of the per-phase lost times — and a movement's capacity is its saturation flow rate times the effective green ratio, c = s·(g/C). The degree of saturation (v/c ratio) drives delay: as v/c approaches 1.0, delay grows sharply toward infinity in Webster-type models. Deterministic queuing gives the buildup when arrivals exceed a bottleneck's service rate: queue = (arrival - service) × time.
Pavement and Design Standards
Pavements are flexible (asphalt, which distributes load through granular layers and flexes) or rigid (concrete slabs, which spread load by beam action through the slab). Traffic damage is highly load-sensitive: by the AASHTO fourth-power law, doubling an axle load multiplies pavement damage by roughly 2^4 = 16, so a few heavy trucks dominate design. The flexible-pavement structural number SN = Σ a_i·D_i sums each layer's coefficient times its thickness (with drainage factors), and subgrade support is characterized by the California Bearing Ratio (CBR). Asphalt binders are graded by the Superpave PG system (PG 64-22 = performs to 64 °C high and -22 °C low), and mix stability is checked by the Marshall test. Traffic-control-device and signal-warrant standards in the US are set by the MUTCD.
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