Beginner — Highway Geometric Design
Start here if you are new to transportation engineering.
Design Controls and Standards
Highway geometric design follows standards established by AASHTO's "Green Book" (A Policy on Geometric Design of Highways and Streets). The design process begins with selecting a design speed — the maximum safe speed that can be maintained over a specified highway section. Design speed governs horizontal curvature, sight distance, superelevation, and vertical curve lengths. Higher design speeds (80-120 km/h for freeways) require larger radii and longer sight distances than lower speeds (30-60 km/h for local roads).
Design vehicles are the critical vehicle types that influence geometric design — the passenger car (P), single-unit truck (SU), and various semitrailer combinations (WB-15, WB-20). Each design vehicle has specified dimensions (length, width, turning radius, and off-tracking characteristics) that determine minimum curve radii and lane widths at intersections. The stopping sight distance (SSD) is the sum of brake reaction distance (d₁ = 0.278 V t_r) and braking distance (d₂ = V²/(254(f ± G))), where V is speed (km/h), t_r is perception-reaction time (typically 2.5 seconds), f is friction coefficient, and G is grade.
Horizontal Alignment Design
Horizontal alignment consists of tangents connected by circular curves, often with spiral transitions. The minimum radius for a horizontal curve is R_min = V²/(127(e + f_max)), where e is superelevation rate (typically 4-10%) and f_max is the side friction factor. Superelevation (banking) counteracts centrifugal force on vehicles — the AASHTO method distributes the centrifugal force between friction and superelevation. Maximum superelevation rates are limited by climate: 8-10% for dry climates, 6-8% for wet climates, and 4-6% for snow/ice regions.
Circular curve elements include radius (R), deflection angle (Δ), tangent length (T = R tan(Δ/2)), curve length (L = π R Δ/180), external distance (E = R sec(Δ/2) - R), and middle ordinate (M = R(1 - cos(Δ/2))). Spiral transitions (clothoids) provide a gradual change in curvature between tangent and circular curve, improving driver comfort and safety. The spiral length is typically based on the rate of superelevation runoff. Stationing along the alignment is measured continuously, with points of curvature (PC), point of tangency (PT), and spiral-curve-spiral (SCS) transitions identified. Use the Horizontal Curve Calculator for curve geometry.
Vertical Alignment Design
Vertical alignment (the highway profile) consists of straight grade lines connected by parabolic vertical curves. Grades are expressed as percentages — positive for upgrades, negative for downgrades. Maximum grades depend on design speed and terrain: 3-5% for freeways (120 km/h), 5-8% for arterials (70 km/h), and 8-12% for local roads (30 km/h). Critical length of grade is the maximum length of a specific upgrade before truck speeds drop below a threshold (typically 15 km/h below average running speed).
Crest vertical curves provide stopping sight distance over the crest of a hill. The required curve length depends on the algebraic grade difference (A = |G₁ - G₂|) and the design SSD. When S < L: L = A S²/658. When S > L: L = 2S - 658/A. Sag vertical curves are designed for headlight sight distance (S < L: L = A S²/(120 + 3.5S)) and comfort (centrifugal acceleration limit). The K-value (L/A) method simplifies design — K values for each design speed are tabulated in AASHTO. The point of vertical intersection (PVI), vertical curve (PVC), and point of vertical tangent (PVT) define the curve geometry. Use the Vertical Curve Calculator for profile design.
Intermediate — Pavement Design and Traffic Engineering
Build on fundamentals with pavement and traffic analysis.
Flexible and Rigid Pavement Design
Pavement design provides a structural layer system that distributes traffic loads to the subgrade without excessive stresses. Flexible pavements (asphalt) consist of an asphalt concrete surface course, base course, and subbase course over the prepared subgrade. The AASHTO 1993 empirical design method uses the structural number (SN = a₁D₁ + a₂D₂m₂ + a₃D₃m₃) to characterize pavement strength, where a_i are layer coefficients (0.30-0.44 for asphalt, 0.10-0.14 for granular base), D_i are thicknesses, and m_i are drainage coefficients.
Rigid pavements (Portland cement concrete) use a concrete slab with doweled or tied joints. The AASHTO design equation relates slab thickness to traffic loads (ESALs), concrete flexural strength (MR), modulus of subgrade reaction (k), load transfer coefficient (J), and drainage coefficient (C_d). Joint spacing (typically 4.5-6.0 m for plain concrete) controls cracking from temperature and moisture stresses. Dowel bars transfer load across transverse joints. The Mechanistic-Empirical Pavement Design Guide (MEPDG / Pavement ME) is the current state-of-practice, using mechanistic response models calibrated to observed pavement performance.
Traffic Flow Theory and Capacity Analysis
Traffic flow theory describes the relationship between flow rate (Q, vehicles per hour), density (K, vehicles per km), and speed (V, km/h): Q = K × V. The fundamental diagram shows that flow increases with density up to a maximum capacity (Q_max), then decreases as congestion sets in. Free-flow speed (V_f) is the speed at zero density; jam density (K_j) is the density at zero flow. The Greenshields model assumes a linear speed-density relationship: V = V_f (1 - K/K_j).
Highway capacity per the Highway Capacity Manual (HCM) depends on free-flow speed, lane width, lateral clearance, and number of lanes. A basic freeway segment at 120 km/h free-flow speed has a capacity of approximately 2400 passenger cars per hour per lane (pc/h/ln). Level of service (LOS) classifies traffic conditions from A (free flow) to F (breakdown/congested), based on density thresholds. Adjustment factors for heavy vehicles (f_HV), driver population, and road conditions convert mixed traffic to equivalent passenger car units (PCU). Use the Traffic Flow Calculator for capacity analysis.
Intersection Design and Signal Control
Intersections are the most critical points in the roadway network — over 40% of traffic crashes occur at intersections. At-grade intersection types include three-leg (T/Y), four-leg (cross), multi-leg, and roundabouts. Intersection design considers turning radii (based on design vehicle off-tracking), channelization (left-turn bays, right-turn lanes), sight distance (intersection sight distance ISD), and pedestrian facilities. Left-turn lanes (deceleration and storage lengths) significantly improve capacity and safety.
Traffic signal control allocates right-of-way to conflicting movements. Key parameters: cycle length (C, typically 60-180 seconds), green time (G), yellow change interval (Y), and all-red clearance interval (AR). The Webster method optimizes cycle length for minimum delay: C_opt = (1.5L + 5)/(1 - ΣY_i), where L is total lost time per cycle and Y_i are critical flow ratios. The saturation flow rate (typically 1800-1900 veh/h/lane) and critical lane volume determine phase timing. Actuated signals use detectors to adjust timing based on real-time demand. Signal coordination on arterials (green wave) uses offset timing to provide continuous progression in the peak direction at the design speed.
Advanced — Transportation Planning, Safety, and Multimodal Systems
For senior students and practicing engineers.
Transportation Planning and Demand Modeling
Transportation planning forecasts future travel demand and evaluates infrastructure needs. The four-step transportation demand model is the standard approach: trip generation (how many trips begin/end in each zone, based on land use and socioeconomic data), trip distribution (where trips go, using gravity model or Fratar method), mode choice (which mode — car, transit, bike, walk — based on utility functions), and traffic assignment (which routes, using user equilibrium or system optimum assignment).
The gravity model for trip distribution: T_ij = P_i (A_j F_ij K_ij) / Σ_j (A_j F_ij K_ij), where T_ij is trips from zone i to zone j, P_i is productions at i, A_j is attractions at j, and F_ij is a friction factor (function of travel time or cost). Traffic assignment uses Wardrop's principles — user equilibrium (no driver can reduce their travel time by switching routes) and system optimum (total system travel time is minimized). Dynamic traffic assignment extends the model for time-varying conditions. Transportation modeling software (CUBE, VISUM, Emme, TransCAD) implements these methods for regional planning studies.
Highway Safety and Crash Analysis
Highway safety analysis aims to identify hazardous locations and evaluate countermeasures. Crash frequency (crashes per year), crash rate (crashes per million vehicle-miles), and severity distribution (fatal, injury, property damage only) are basic measures. The Highway Safety Manual (HSM) provides predictive methods using safety performance functions (SPFs): N_predicted = N_spf × CMF_1 × CMF_2 × ... × CMF_n, where N_spf is the base predicted crash frequency and CMFs are crash modification factors for site-specific conditions.
Crash modification factors (CMFs) quantify the safety effectiveness of countermeasures — adding a left-turn lane (CMF = 0.65), converting an intersection to a roundabout (CMF = 0.30-0.50), improving lighting (CMF = 0.70), and widening shoulders (CMF = 0.80-0.95). Network screening identifies sites with potential for safety improvement (PSI) using methods like sliding window, empirical Bayes, and full Bayes. Road safety audits (RSA) are systematic reviews of the safety performance of a roadway project from planning through operation.
Multimodal Transportation: Transit, Bicycle, and Pedestrian
Complete streets accommodate all users — pedestrians, cyclists, transit riders, and motorists. Pedestrian facility design follows AASHTO's Guide for the Planning, Design, and Operation of Pedestrian Facilities. Minimum sidewalk width is 1.5 m (two-way), with wider sidewalks in high-pedestrian areas. Crosswalk markings, pedestrian signal heads, accessible pedestrian signals (APS), and curb ramps (ADA compliance) are required at intersections. The level of service for pedestrians depends on sidewalk width, separation from traffic, and crossing delays.
Bicycle facility types include bike lanes (on-street, striped), cycle tracks (separated from traffic), shared lane markings (sharrows), and shared-use paths (off-street). The AASHTO Guide for the Development of Bicycle Facilities provides design criteria: bike lane width (1.5-1.8 m), minimum sight distance, intersection treatment, and signing. Transit facility design includes bus stops (far-side, near-side, mid-block), bus rapid transit (BRT) stations with level boarding and signal priority, and rail transit stations with platform heights matching vehicle floor height. Transit capacity and quality of service manual (TCQSM) provides analysis methods for bus and rail systems.
Practice Exercises
Exercise 1: Horizontal Curve Design
A highway with a design speed of 100 km/h requires a horizontal curve with a deflection angle of 30°. The maximum superelevation rate is 8% and the side friction factor is 0.12. Calculate the minimum radius, tangent length, curve length, and external distance. Determine the station of PT if the PC is at station 1+250. Use the Horizontal Curve Calculator to verify.
Exercise 2: Vertical Curve Design
A crest vertical curve connects a +3.5% grade to a -2.5% grade. The design speed is 90 km/h with a required stopping sight distance of 160 m. Determine the minimum curve length using both S < L and S > L conditions. Compute the elevation at the PVC and at 20 m intervals along the curve if the PVI elevation is 125.50 m at station 4+000.
Exercise 3: Traffic Signal Timing
A four-leg intersection has critical lane volumes of 420 veh/h (EB), 380 veh/h (WB), 310 veh/h (NB), and 290 veh/h (SB). The saturation flow rate is 1900 veh/h per lane, the lost time per phase is 4 seconds, and the total lost time per cycle is 16 seconds. Using the Webster method, determine the optimum cycle length and split the green times among phases. Assume 2 seconds for yellow change intervals.
Exercise 4: Flexible Pavement Design
Design a flexible pavement for a highway with a design ESAL of 8.5 million over 20 years. The subgrade CBR is 6, the asphalt concrete modulus is 350,000 psi (MR), and the granular base modulus is 30,000 psi. Using the AASHTO 1993 method with a reliability of 90%, overall standard deviation of 0.45, and terminal serviceability index of 2.5, determine the required structural number (SN) and layer thicknesses.
Related Calculators
Horizontal Curve Calculator
Compute horizontal curve geometry elements.
Vertical Curve Calculator
Design crest and sag vertical curves.
Traffic Flow Calculator
Analyze traffic flow, density, and level of service.
Earthwork Cut-Fill Calculator
Calculate roadway earthwork volumes.
Mass Haul Calculator
Optimize earthwork haul for highway projects.
Live and Dead Load Calculator
Estimate highway bridge loads.
Proctor Compaction Calculator
Analyze subgrade compaction test results.
Survey Area Calculator
Compute land areas for highway right-of-way.
References
- AASHTO. A Policy on Geometric Design of Highways and Streets (Green Book). 7th ed., 2018.
- AASHTO. Mechanistic-Empirical Pavement Design Guide (MEPDG). 2nd ed., 2015.
- TRB. Highway Capacity Manual (HCM). 7th ed., Transportation Research Board, 2022.
- AASHTO. Highway Safety Manual. 1st ed., 2010 (with 2014 supplement).
- Mannering, F.L. and Washburn, S.S. Principles of Highway Engineering and Traffic Analysis. 7th ed., Wiley, 2019.
- Garber, N.J. and Hoel, L.A. Traffic and Highway Engineering. 5th ed., Cengage, 2014.
- ITE. Traffic Engineering Handbook. 7th ed., Institute of Transportation Engineers, 2016.
- Civil Engineering Handbook — Highway Engineering chapter.
- Engineering Formula Library — Curve geometry and traffic flow formulas.
- Engineering Standards Reference — AASHTO LRFD bridge provisions.
- Engineering Glossary — Definitions of transportation engineering terms.