Transportation Engineering for the FE Exam
Transportation engineering covers the planning, design, operation, and maintenance of transportation systems. On the FE Civil exam, this topic includes highway geometric design, traffic engineering, and pavement design. These concepts are practical and formula-driven, making them very scoreable with proper preparation.
Horizontal Curves
Horizontal curves connect straight road sections (tangents) and allow vehicles to change direction safely. A simple circular curve is defined by its radius R or degree of curve D.
Key Horizontal Curve Elements
- Radius (R): The radius of the circular arc.
- Degree of curve (D): The angle subtended by a 100-foot arc. D = 5729.58 / R (for arc definition).
- Tangent length (T): T = R * tan(delta/2), where delta is the deflection angle (the angle between the two tangents).
- Curve length (L): L = R * delta (in radians), or L = 100 * delta / D (in degrees).
- External distance (E): E = R * [1/cos(delta/2) - 1].
- Middle ordinate (M): M = R * [1 - cos(delta/2)].
Superelevation
Superelevation (banking) helps vehicles safely navigate horizontal curves. The design equation relates speed, radius, superelevation rate, and side friction:
e + f = V^2 / (g * R)
Where e is the superelevation rate, f is the side friction factor, V is the design speed, g is gravitational acceleration, and R is the curve radius.
Stopping Sight Distance
Stopping sight distance (SSD) is the minimum distance a driver needs to see an obstacle and stop safely:
SSD = reaction distance + braking distance = V * t + V^2 / (2 * g * (f +/- G))
Where t is the perception-reaction time (typically 2.5 seconds), f is the coefficient of friction, and G is the grade (positive for uphill, negative for downhill).
Vertical Curves
Vertical curves are parabolic curves that connect road sections with different grades. Two types:
- Crest curves: Convex curves where the road goes over a hill. Design controlled by headlight sight distance.
- Sag curves: Concave curves where the road goes through a valley. Design controlled by headlight illumination distance.
Key vertical curve properties:
- L: Length of the vertical curve
- A: Algebraic difference in grades: A = |g1 - g2| (expressed as a percentage)
- K: K = L / A. The K-value represents the horizontal distance needed for a 1% change in grade. Design tables give minimum K-values for different design speeds.
Traffic Flow Theory
Traffic flow is described by three fundamental variables:
- Flow (q): The number of vehicles passing a point per unit time (vehicles/hour).
- Density (k): The number of vehicles per unit length of road (vehicles/mile).
- Speed (u): The average speed of vehicles (miles/hour).
The fundamental relationship: q = k * u (flow equals density times speed).
Level of Service (LOS)
Level of service rates the quality of traffic flow from A (free flow) to F (breakdown):
- LOS A: Free flow, no delays
- LOS B: Reasonably free flow
- LOS C: Stable flow, acceptable delays
- LOS D: Approaching unstable flow
- LOS E: Unstable flow, at capacity
- LOS F: Breakdown, stop-and-go traffic
Traffic Signal Timing
Basic signal timing concepts include:
- Cycle length (C): Total time for all phases of the signal, typically 60 to 120 seconds.
- Green time (g): The effective green time for a phase.
- Yellow interval: Typically 3 to 5 seconds.
- All-red interval: Clears the intersection between conflicting phases.
- Capacity per lane: c = s * g/C, where s is the saturation flow rate (typically 1,800 to 1,900 vehicles per hour of green per lane).
Pavement Design Basics
- Flexible pavements: Asphalt surface over granular base layers. Design considers traffic loading, soil support (CBR or resilient modulus), and environmental factors.
- Rigid pavements: Portland cement concrete slabs. Design considers slab thickness, joint spacing, and load transfer.
- ESAL (Equivalent Single Axle Load): Converts different axle loads to a common reference (18,000 lb single axle) for design purposes.
Transportation engineering problems on the FE exam are highly formulaic. Know where the formulas are in the reference handbook, practice applying them, and these become reliable points.