5.3 Transportation Engineering

Geometric Design Drives the Section

Transportation Engineering contributes roughly 8 to 12 questions, most rooted in AASHTO (American Association of State Highway and Transportation Officials) geometric-design relationships found in the NCEES FE Reference Handbook.

Horizontal Curves and Superelevation

A vehicle on a curve is held by side friction and superelevation (banking, e). The minimum-radius relationship is:

R = V² / [ 15 · (e + f) ]

with V in mph, e the superelevation rate (decimal), and f the side-friction factor. Curve geometry uses the degree of curve and these standard elements:

Δ is the central (deflection) angle. The point of curvature (PC) and point of tangency (PT) bound the curve.

Sight Distance

Stopping sight distance (SSD) has two parts — the perception-reaction distance and the braking distance:

SSD = 1.47·V·t + V² / [ 30·( (a/32.2) ± G ) ]

V is in mph, t is perception-reaction time (AASHTO uses 2.5 s), a is deceleration (≈ 11.2 ft/s²), and G is grade (+ uphill, − downhill). Downgrades lengthen SSD because braking is less effective.

Vertical Curves

Vertical curves are parabolas connecting two grades. Let A = |G₂ − G₁| (algebraic grade difference, in percent). For sight-distance-controlled design:

• Crest curve, S < L: L = A·S² / 2158
• Sag curve, S < L (headlight control): L = A·S² / (400 + 3.5·S)

The high or low point occurs where the curve grade equals zero, at station offset x = G₁·L / A from the curve start.

Traffic Flow Fundamentals

The foundational identity is q = k · v, where q is flow (veh/hr), k is density (veh/mi), and v is space-mean speed (mph). The Greenshields model assumes a linear speed-density relationship, giving a parabolic flow-density curve:

• Maximum flow (capacity) occurs at k = k_jam / 2 and v = v_free / 2
• q_max = (k_jam · v_free) / 4

Capacity, Level of Service, and Signal Timing

Level of Service (LOS) grades operating quality A (free flow) through F (breakdown), based on density or delay from the Highway Capacity Manual. For an isolated signal, basic timing uses:

• Cycle length C = sum of phase green + yellow + all-red times
• Capacity of a movement = saturation flow rate × (effective green / cycle) = s · (g/C)

Reference Handbook Tip

Find R = V²/[15(e+f)] and SSD under 'Transportation — Horizontal/Vertical Curves'; the q = kv relationship and Greenshields under 'Traffic Flow.' Confirm whether a problem uses the S < L or S > L curve-length form before substituting.