Highway and Traffic Engineering: Transport Infrastructure Engineering

Course Information and Time Schedule

Course Code: ECHTE4A
Subject: Highway and Traffic Engineering
Lecturer: Mr SC Khoza
Focus Area: Transport Infrastructure Engineering - Unit 4
Semester: 1st Semester - 2026
Department: Civil Engineering Department
Schedule: - Tuesday: $17h30 \text{ – } 19h30$ (Online lecture) - Wednesday: $17h30 \text{ – } 19h30$ (Online lecture) - Monday: $13h00 \text{ – } 15h00$ (Consultation)

Manuals and Reading Materials

SANRAL Geometric Design Guidelines (2003): Pretoria, South Africa.
Banks, James H.: Introduction to Transportation Engineering (2002), McGraw-Hill, New York, 2nd Edition, ISBN 007-124034-9 – Chapter 4.

Introduction to Road Design

Definition: Road design is the art of creating a 3D structure that should ideally be: - Safe - Efficient - Functional - Economical - Aesthetically pleasing
Designer Limitations: - Vehicle characteristics - Driver performance

Design Controls

Primary Controls: - Human factors - Speed - Design Vehicle - Sight distance - Environmental factors - Traffic characteristics - Road classification
Road Traffic System Components: - Human (Road user) - Vehicle (Motorized and Non-motorized) - Road Infrastructure

Human Factors in Design

Drivers: - Driving Tasks: Navigation, guidance, and control. - Potential Problems: Insufficient inputs, strange inputs, and long reaction times. - Expectancy: Performance is influenced by what the driver expects to see. - Reaction: The physical and mental response to road conditions.
Other Road Users: Includes pedestrians and cyclists.

Speed Classifications and Definitions

Significance: Drivers aim to minimize travel time; speed is critical in route selection.
Influencing Factors: Driver capability/culture/behavior, vehicle operating capabilities, physical road characteristics, surrounding environment, weather, traffic presence, and posted speed limits.
Types of Speeds: - Desired Speed: The speed a driver wishes to travel based on motivation and comfort. - Design Speed: The speed selected as a safe basis to establish geometric design elements (e.g., curves). It must be logical relative to topography, anticipated operating speed, land use, and functional road classification. - Operating Speed: Observed speeds during free-flow conditions (generally lower than desired speed due to non-ideal conditions). - Running Speed: The average speed maintained over a route while the vehicle is in motion. The difference between running and design speed is affected by traffic volume. - Posted Speed: A speed limit set for safe operations and traffic regulation, not necessarily the geometric design limit.

Design Vehicle

Physical Characteristics: Define various geometric design elements.
Vehicle Types defined in the Road Traffic Act: - Passenger cars and minibuses (kombis). - Standard single unit buses. - Articulated buses ("Bus Train"). - Two-axle trucks (with or without trailers). - Three and four-axle vehicles. - Three, four, and five-axle articulated trucks. - Five and six-axle articulated trucks. - Multi-vehicle combinations.
Selection Criteria: - Cross-section elements: Determined by Bus and Heavy vehicles. - Horizontal & vertical alignment: Typically determined by the passenger car. - Major intersections (Arterial/Commercial): Must accommodate semi-trailers (occasional encroachment on lanes is allowed, but never on sidewalks). - Truck route intersections: Largest possible semi-trailer combinations. - Major haulage routes: Tractor-trailer combinations.
Manoeuvrability: A function of overall size, length, width, height, and mass. Roadways must handle the maximum legal vehicle size.

Vehicle Characteristics and Minimum Turning Radii

Design Dimensions: Affect visibility, cornering, and braking.
Table 3.3: Minimum Turning Radii: - Passenger Car (P): $6,8\,m$ - Single unit truck (SU): $10,0\,m$ - Bus (B): $11,5\,m$ - Semi-trailer (WB-15): $11,0\,m$

Sight Distance and Visibility

Adequate Sight Distance Types: - Passing sight distance: Required for two-lane roads. - Intersection sight distance: Allows minor-road drivers to evaluate safe entry into traffic. - Decision sight distance: Required to detect unexpected hazards and respond to road markings. - Headlight sight distance: Typically applied to sag vertical curves. - Centre line barrier sight distance.
Determinants: Based on a direct line of sight between the driver's eye and an object.
Eye Heights (Design Vehicle Dependent): - Passenger car: $1.05\,m$ - Truck: $1.8\,m$ - Semi-trailer combination: $1.9\,\text{m – } 2.4\,m$

Object Height Design Domains

Table 3.4: Object Height Applicability: - $0,00\,m$ : Risk of road washouts. - $0,15\,m$ : Pavement markings in critical locations; risk of fallen trees/rocks; fallen person; vehicle tail or brake light. - $0,60\,m$ : Risk of fallen person; log or construction debris from truck. - $1,30\,m$ : Passing sight distance (top of car); intersection sight distance.

Stopping Sight Distance (SSD)

Definition: Sum of brake reaction distance and stopping distance.
Parameters: - Reaction time: $2.5\,s$ - Assumed deceleration: $3.0\,m/s^2$
Formula: - $SSD = R \times v + \frac{v^2}{2(d + G \times g)}$ - where $v$ is initial speed ( $m/s$ ), $R$ is driver reaction time ( $s$ ), $d$ is longitudinal deceleration rate ( $m/s^2$ ), $G$ is grade (decimal), and $g$ is gravity ( $9.8\,m/s^2$ ).
Table 3.5: Recommended SSD for Design: - $30\,km/h$ : $35\,m$ - $60\,km/h$ : $90\,m$ - $100\,km/h$ : $200\,m$ - $120\,km/h$ : $270\,m$

Passing Sight Distance (PSD)

Table 3.6: Passing Sight Distance Requirements: - $60\,km/h$ : Absolute Min $410\,m$ ; Desirable Min $450\,m$ - $100\,km/h$ : Absolute Min $680\,m$ ; Desirable Min $900\,m$ - $120\,km/h$ : Absolute Min $800\,m$ ; Desirable Min $1100\,m$

Road Classification and Hierarchy

Purpose: Subdividing networks into groups with similar characteristics for logical planning and geometric design control.
Criteria: - Functional Classification: Role in the network. - Administrative Classification: National, Provincial, Local authority. - Design Type Classification: Based on traffic usage.
Functional Classes (SANRAL): - Class 1: Principal route network of National routes. - Class 1a: Similar to Class 1, but not National routes. - Class 2: Other main avenues of communication (arterial nature). - Class 3: All other surfaced roads under a road authority. - Class 4: All gravel roads under a road authority. - Class 5: Special purpose roads (strategic, defense, social).

Design Philosophy and Techniques

Levels of Design: 1. Geometric planning. 2. Detailed design (focused on operational safety).
Holistic Philosophy: Reducing the probability of failure and minimizing the consequences of failures that occur.
Key Tools and Techniques: - Flexibility in highway design: Resolve issues by using design standards adaptively, lowering design speed, or maintaining existing geometry. - Interactive Highway Safety Design Model (IHSDM): Modules include Crash Prediction, Design Consistency, Driver/Vehicle, Intersection Diagnostic Review, Policy Review, and Traffic Analysis. - Design Domain Concept: Recognizes a range of values (between absolute upper/lower limits and practical limits) rather than a single value. It balances safety, operation, and cost. - Safety Audits: Systematic evaluation of road safety. - Economic Analysis: Balancing mobility benefits against construction, maintenance, and environmental costs. - Value Engineering: Finding the best functional balance between cost, performance, and reliability.

Road Safety Audits (RSA)

RSA Manual (South Africa): Consists of Part A (Introduction), Part B (Conducting), and Part C (Legal environment).
Contributing Factors to Road Trauma: - Human Behavior: $75\text{--}90\%$ - Road Environment: $5\text{--}10\%$ - Vehicle: $5\text{--}20\%$
Objectives: Minimize crash severity/risk, reduce remedial measures after opening, reduce life-cycle costs, and maintain safety awareness during design.
SANRAL Principles: Medians, grade separation, smooth roads, proper signing, and high design standards.

Traffic Control and Conflict Points

Intersection Types and Safety: - Without Signal/Intersection: $16$ vehicle/pedestrian conflict points. - Roundabout: $8$ vehicle/pedestrian conflict points.

Principles of Highway Alignment

3D coordinates ( $x, y, z$ ): Usually reduced to two 2D components. - Horizontal Alignment: Plan view ( $x, z$ ). - Vertical Alignment: Profile view ( $x, y$ ).
Distance Measurement: Measures in "stations" ( $1\,\text{station} = 1000\,m$ ). Example: $1500\,m$ from origin is station $1 + 500$ .
Elevations: Vertical axis ( $y$ ) measured above a reference level (e.g., sea level).

Vertical Alignment: Grades

Convention: Rising gradient is positive ( $+\%$ ); descending is negative ( $-\%$ ).
Table 4.11: Maximum Gradients (%): - $60\,km/h$ : Flat ( $6$ ), Rolling ( $7$ ), Mountainous ( $8$ ). - $100\,km/h$ : Flat ( $4$ ), Rolling ( $5$ ), Mountainous ( $6$ ). - $120\,km/h$ : Flat ( $3$ ), Rolling ( $4$ ), Mountainous ( $5$ ).

Vertical Curves: Fundamentals

Symmetric Parabolic Curves: Rate of change of grade is constant.
Key Terms: - BVC (PVC): Beginning of vertical curve. - EVC (PVT): End of vertical curve. - PVI (PI): Point of vertical intersection. - $G_1$ : Initial tangent grade (%). - $G_2$ : Final tangent grade (%). - $A$ : Absolute difference in grades ( $|G_2 - G_1|$ ). - $L$ : Length of curve ( $m$ ).
Equations: - General parabolic form: $y = ax^2 + bx + c$ - $a = \frac{G_2 - G_1}{2L}$ - $b = G_1$ - $c = \text{Elevation of BVC}$
Offsets: - Vertical offset at distance $x$ from BVC: $Y = \frac{Ax^2}{200L}$ - Middle Ordinate ( $Y_m$ ) at $P_I$ : $Y_m = \frac{AL}{800}$ - Offset at end of curve ( $Y_f$ ): $Y_f = \frac{AL}{200}$

K-values and Vertical Curvature

K-value: The horizontal distance required for a $1\%$ change in slope. - $K = \frac{L}{A}$
High/Low Point Location: $x_{hl} = K \times |G_1|$ (Distance from BVC).
K-Values for Crest Curves (Table 4.12): - $100\,km/h$ ( $SSD=200\,m$ ): $K = 100$ (for $0,15\,m$ object). - $120\,km/h$ ( $SSD=270\,m$ ): $K = 180$ (for $0,15\,m$ object).

Vertical Curve Examples

Example 1: - Input: $L = 490\,m$ , BVC at $3+700$ and $460\,m$ . $G_1 = -3.5\%$ , $G_2 = +6.5\%$ . - Solutions: - PI Stationing: $(3 + 700) + \frac{490}{2} = 3 + 945$ - PI Elevation: $460 - (0.035 \times 245) = 451.425\,m$ - EVC Stationing: $3+700 + 490 = 4 + 190$ - Lowest Point Distance ( $x$ ): $x = 171.569\,m$ from BVC. - Lowest Point Station: $3+871.568$ - Lowest Point Elevation: $457\,m$
Example 2 (Crest Curve): - Input: $L = 150\,m$ , PI at $10+360$ and $400\,m$ . $G_1 = +4\%$ , $G_2 = -2.5\%$ . - Solutions: - BVC Station: $10 + 285$ , Elevation: $397\,m$ - High Point Distance ( $x$ ): $92.166\,m$ from BVC. - High Point Elevation: $398.843\,m$

Sag Vertical Curve Controls

Controls: Headlight sight distance (nighttime), rider comfort (vertical acceleration limit of $0.05g \text{ to } 0.10g$ ), drainage (0,5\% < g\% < 5\%), and appearance.
Formula for $L_{min}$ (Headlight $\beta = 1^\circ$ , $H = 0.6\,m$ ): - For $S < L$ : $L_{min} = \frac{A \times SSD^2}{120 + 3.5 \times SSD}$ - For $S > L$ : $L_{min} = 2 \times SSD - \frac{120 + 3.5 \times SSD}{A}$

Horizontal Alignment and Curves

Components: Tangents (straight sections), circular curves, and transition (spiral) curves.
Curve Types: - Simple: Circle segment of radius $R$ . - Reverse: Two simple curves turning in opposite directions with common tangent. - Compound: Successive curves turning in the same direction.
Elements of Circular Curve: - Tangent Length ( $T$ ): $T = R \tan\left(\frac{\Delta}{2}\right)$ - Length of Curve ( $L$ ): $L = \frac{\pi}{180} R \Delta$ - Middle Ordinate ( $M$ ): $M = R \times \left(1 - \cos\left(\frac{\Delta}{2}\right)\right)$ - External Distance ( $E$ ): $E = R \times \left(\frac{1}{\cos(\Delta/2)} - 1\right)$
SSD and Horizontal Design: - Sight obstruction clear distance ( $M_s$ ): - $M_s = R_v \times \left[1 - \cos\left(\frac{90 \times SSD}{\pi \times R_v}\right)\right]$

Horizontal Alignment Examples

Example 3: - Input: $R = 610\,m$ , $T = 120\,m$ , PI at $3+140$ . - Solution: $\Delta = 22.26^\circ$ , $L = 237.0\,m$ . TC Station: $3+020$ . CT Station: $3+257$ .
Example 4: - Input: $R = 610\,m$ , lanes $3.6\,m$ , design speed $100\,km/h$ ( $SSD = 200\,m$ ). - Solution: $R_v = 608.2\,m$ (critical lane). $M_s = 8.2\,m$ from center of lane. Clear distance from inner lane edge: $8.2 - 1.8 = 6.4\,m$ .

Superelevation and Vehicle Dynamics

Purpose: Counteract centripetal acceleration using road inclination ( $e = \tan(\alpha)$ ).
Basic Formula: - $R_{min} = \frac{V^2}{127(e_{max} + f_{max})}$ - where $V$ is design speed ( $km/h$ ), $e$ is superelevation rate, and $f$ is side friction coefficient.
SANRAL Side Friction: $f = 0.21 - 0.001 \times V$
Table 4.1: Minimum Radii (m) for $e_{max} = 10\%$ : - $60\,km/h$ : $110\,m$ - $100\,km/h$ : $360\,m$ - $120\,km/h$ : $600\,m$
Design Domain for $e_{max}$ : - Rural Roads: $8\% \text{ to } 10\%$ - High-speed Urban: $6\% \text{ to } 8\%$ - Minor Urban: $4\% \text{ to } 6\%$

Superelevation Development and Runoff

Components: - Tangent Runoff: Rotating from normal camber ( $-2.5\%$ ) to level ( $0\%$ ). - Superelevation Runoff: Rotating from level ( $0\%$ ) to max superelevation ( $e$ ).
Location Distribution: On circular curves, runoff occurs $60\%$ on the tangent and $40\%$ within the curve.
Maximum Relative Gradients (Table 4.7): - $80\,km/h$ : $0.56\%$ - $100\,km/h$ : $0.48\%$ - $120\,km/h$ : $0.40\%$
Example 6: - Input: $V = 80\,km/h$ , lane $3.6\,m$ , camber $2.5\%$ , $e = 4\%$ , slope $1:200$ . - Solution: - Tangent runoff length: $3.6 \times 0.025 \times 200 = 18\,m$ - Superelevation runoff length: $3.6 \times 0.04 \times 200 = 28.8\,m$

Cross-Section Design Elements

Basic Elements: Road reserve, road prism, roadbed, roadway (carriageway), median, shoulders (inner/outer), verges, shoulder breakpoint, and traveled way.
Auxiliary Lanes: - Climbing Lanes: Warranted if truck speed drops by > 20\,km/h. Locations: do not hide terminals in curves; use decisions sight distance ( $300\,m$ terminal suggested). - Passing Lanes. - HOV Lanes.
Width Selection Factors: - Lane Width: Traffic volume, vehicle dimensions, speed-volume combination. - Shoulder Width: Space for stationary vehicles and incident avoidance, driver comfort, increased sight distance.

Coordination of Alignment

Principle: Horizontal and vertical alignments must coincide in scale to avoid optical illusions or unsafe conditions.
Optical Illusions: - Crest curves make horizontal curves look larger. - Sag curves make horizontal curves look sharper. - Avoid local dips on long grades to maintain a uniform alignment.