PE Exam Exam > PE Exam Notes > Civil Engineering (PE Civil) > Cheatsheet: Highway Design
Cheatsheet: Highway Design
1. Design Vehicles and Vehicle Characteristics
1.1 Design Vehicle Classifications
| Vehicle Type | Key Dimensions and Characteristics |
|---|---|
| Passenger Car (P) | Length: 19 ft, Width: 7 ft; minimum design vehicle |
| Single Unit Truck (SU) | Length: 30 ft, Width: 8 ft; typical delivery truck |
| Intermediate Semitrailer (WB-40) | Wheelbase: 40 ft, Overall Length: 45 ft |
| Interstate Semitrailer (WB-62) | Wheelbase: 62 ft, Overall Length: 68.5 ft; most common design vehicle |
| Interstate Semitrailer (WB-67) | Wheelbase: 67 ft, Overall Length: 73.5 ft; larger design vehicle |
| Bus (BUS-40, BUS-45) | Length: 40-45 ft, Width: 8.5 ft; transit and intercity |
1.2 Vehicle Performance Characteristics
| Characteristic | Value/Description |
|---|---|
| Eye Height (passenger car) | 3.5 ft above roadway |
| Eye Height (truck) | 7.6 ft above roadway |
| Object Height (stopping sight) | 2.0 ft above roadway |
| Perception-Reaction Time | 2.5 seconds for design |
| Deceleration Rate | 11.2 ft/s² (3.4 m/s²) on level roadway |
2. Horizontal Alignment
2.1 Circular Curves
| Parameter | Formula/Definition |
|---|---|
| Degree of Curve (D) | D = 5729.58/R (arc definition); angle subtended by 100 ft arc |
| Radius (R) | R = 5729.58/D (in feet) |
| Tangent Length (T) | T = R × tan(Δ/2), where Δ = deflection angle |
| Length of Curve (L) | L = (100 × Δ)/D or L = R × Δ (Δ in radians) |
| External Distance (E) | E = R × [sec(Δ/2) - 1] |
| Middle Ordinate (M) | M = R × [1 - cos(Δ/2)] |
| Chord Length (C) | C = 2R × sin(Δ/2) |
2.2 Superelevation
| Parameter | Value/Formula |
|---|---|
| Basic Formula | e + f = V²/(15R), where e = superelevation rate, f = side friction factor |
| Maximum Superelevation | e_max = 0.04 to 0.12 (4% to 12%); commonly 0.06 or 0.08 |
| Minimum Radius | R_min = V²/[15(e_max + f_max)] |
| Normal Crown (NC) | -0.02 (-2%); negative superelevation |
| Superelevation Runoff | Distance to transition from normal crown to full superelevation |
2.2.1 Maximum Side Friction Factors (f_max)
- 15 mph: f = 0.17
- 20 mph: f = 0.17
- 25 mph: f = 0.16
- 30 mph: f = 0.15
- 35 mph: f = 0.14
- 40 mph: f = 0.14
- 45 mph: f = 0.13
- 50 mph: f = 0.12
- 55 mph: f = 0.11
- 60 mph: f = 0.10
- 65 mph: f = 0.09
- 70 mph: f = 0.09
- 75 mph: f = 0.08
- 80 mph: f = 0.08
2.3 Spirals (Transition Curves)
| Parameter | Formula/Description |
|---|---|
| Spiral Length (L_s) | L_s = 3.15V³/(RC), where C = rate of increase of centripetal acceleration |
| Minimum Spiral Length | L_s(min) = 2V for superelevation transition (V in mph, L_s in feet) |
| Spiral Angle (θ_s) | θ_s = L_s/(2R) (radians) |
| Offset Distance (p) | p = L_s²/(24R) |
3. Vertical Alignment
3.1 Vertical Curves - General
| Parameter | Formula/Definition |
|---|---|
| Rate of Change (K) | K = L/A, where L = curve length (ft), A = algebraic grade difference (%) |
| Curve Length (L) | L = KA, where A = |G₁ - G₂| (absolute difference) |
| Elevation at Point | y = (Ax²)/(200L), where x = distance from BVC |
| High/Low Point Location | x = -LG₁/A (from BVC) |
3.2 Crest Vertical Curves
| Condition | Design Formula (K) |
|---|---|
| Stopping Sight (S <> | K = AS²/(100[√(2h₁) + √(2h₂)]²), where h₁ = 3.5 ft, h₂ = 2.0 ft |
| Stopping Sight (S < l)=""> | K = S²/2158 or L = AS²/2158 |
| Stopping Sight (S > L) | L = 2S - 2158/A |
| Passing Sight (S <> | K = S²/2800, where h₁ = h₂ = 3.5 ft |
| Passing Sight (S > L) | L = 2S - 2800/A |
3.3 Sag Vertical Curves
| Condition | Design Formula (K) |
|---|---|
| Stopping Sight (S <> | K = AS²/(200[H + S×tan(β)]), where H = headlight height = 2.0 ft, β = 1° |
| Stopping Sight (S < l)=""> | K = S²/(400 + 3.5S) or L = AS²/(400 + 3.5S) |
| Stopping Sight (S > L) | L = 2S - (400 + 3.5S)/A |
| Comfort Control (S <> | K = AV²/46.5 |
| Appearance Control | K ≥ 100 for design speeds ≥ 50 mph |
4. Sight Distance
4.1 Stopping Sight Distance (SSD)
| Parameter | Formula/Value |
|---|---|
| SSD Formula | SSD = 1.47Vt + V²/(30[a/32.2 ± G]), where V in mph, t = 2.5 sec, a = 11.2 ft/s² |
| SSD Simplified (Level) | SSD = 1.47Vt + V²/30(f + G), where f = 0.348 for level grade |
| SSD (Most Common) | SSD = 1.47V(2.5) + V²/(30 × 0.348) = 3.675V + 0.0955V² |
4.1.1 Minimum SSD Values by Speed
- 15 mph: 80 ft
- 20 mph: 115 ft
- 25 mph: 155 ft
- 30 mph: 200 ft
- 35 mph: 250 ft
- 40 mph: 305 ft
- 45 mph: 360 ft
- 50 mph: 425 ft
- 55 mph: 495 ft
- 60 mph: 570 ft
- 65 mph: 645 ft
- 70 mph: 730 ft
- 75 mph: 820 ft
- 80 mph: 910 ft
4.2 Passing Sight Distance (PSD)
| Design Speed | Minimum PSD |
|---|---|
| 20 mph | 400 ft |
| 25 mph | 450 ft |
| 30 mph | 500 ft |
| 35 mph | 550 ft |
| 40 mph | 600 ft |
| 45 mph | 700 ft |
| 50 mph | 800 ft |
| 55 mph | 900 ft |
| 60 mph | 1000 ft |
| 65 mph | 1100 ft |
| 70 mph | 1200 ft |
4.3 Decision Sight Distance (DSD)
- Used for complex locations requiring additional driver decision time
- Values range from 1.5 to 2.5 times SSD depending on design speed and avoidance maneuver
- Applied at interchanges, lane drops, toll plazas, and areas with complex information
5. Cross-Section Elements
5.1 Lane Widths
| Facility Type | Lane Width |
|---|---|
| Freeway/Interstate | 12 ft (standard) |
| Arterial/Highway | 10-12 ft (12 ft preferred for speeds > 45 mph) |
| Local/Residential | 9-11 ft acceptable for low speeds and volumes |
5.2 Shoulder Widths
| Facility Type | Right Shoulder |
|---|---|
| Interstate (Rural) | 10-12 ft (paved) |
| Interstate (Urban) | 10 ft (paved) minimum |
| Arterial (Rural) | 6-8 ft minimum |
| Arterial (Urban) | 4-8 ft |
| Left Shoulder (Multilane) | 4-8 ft (narrower than right) |
5.3 Median Widths
- Interstate: 36-80 ft (varies by terrain and cost)
- Minimum desirable: 46 ft (allows recovery area)
- Absolute minimum: 22 ft (barrier required)
- Painted median: 4 ft minimum (low-speed facilities)
5.4 Pavement Cross Slope
| Surface Type | Cross Slope Range |
|---|---|
| Portland Cement Concrete | 1.5% to 2.0% |
| Asphalt Concrete | 1.5% to 2.0% |
| Gravel/Stabilized | 2.0% to 3.0% |
5.5 Clear Zones
| Design Speed | Clear Zone Width (Flat Slopes) |
|---|---|
| 40 mph | 12-16 ft |
| 50 mph | 16-20 ft |
| 60 mph | 20-26 ft |
| 70 mph | 26-30 ft |
- Clear zone varies with traffic volume, side slope, and horizontal curvature
- Measured from edge of traveled way
6. Grades and Grade Controls
6.1 Maximum Grades
| Design Speed | Rural/Level Terrain |
|---|---|
| 20 mph | 11% |
| 30 mph | 10% |
| 40 mph | 9% |
| 50 mph | 7% |
| 60 mph | 6% |
| 70 mph | 5% |
| 80 mph | 4% |
- Interstate maximum: 5% (rural), 4% (urban), 6% (mountainous terrain)
- Urban areas: 1-2% steeper grades acceptable
6.2 Minimum Grades
- Minimum grade with curbs: 0.5%
- Without curbs: 0.3% (may use 0% in well-draining areas)
- Applied for adequate drainage
6.3 Critical Length of Grade
| Parameter | Description |
|---|---|
| Definition | Maximum length of upgrade on which a truck can operate without speed reduction > 10 mph |
| Application | Used to determine need for climbing lanes |
| Typical Values | 300-2000 ft depending on grade percentage and terrain |
7. Intersections and Interchanges
7.1 Intersection Sight Distance
| Type | Formula/Description |
|---|---|
| Approach Sight Triangle | Clear sight area needed for driver to perceive and react to conflicts |
| Departure Sight Triangle | ISD = 1.47V_major × t_gap, where t_gap = 7.5 sec for passenger car from stop |
| Eye Height | 3.5 ft for decision point |
| Object Height | 3.5 ft for approaching vehicle |
7.2 Turning Radii
| Design Vehicle | Minimum Centerline Radius |
|---|---|
| Passenger Car (P) | 45 ft |
| Single Unit Truck (SU) | 60 ft |
| WB-40 | 90 ft |
| WB-62 | 120 ft |
| WB-67 | 140 ft |
7.3 Acceleration and Deceleration Lanes
| Lane Type | Length Components |
|---|---|
| Acceleration Lane | L = speed change length + taper; depends on design speed and grade |
| Deceleration Lane | L = maneuver distance (2-3 sec) + speed change length + taper |
| Taper Rate | 50:1 to 70:1 (ft of taper per ft of lane width) for high-speed facilities |
7.4 Ramp Design Speeds
- Loop ramps: 25-30 mph
- Directional ramps: 40-55 mph (70-80% of highway design speed)
- Semi-directional ramps: 35-45 mph
- Diagonal ramps: 35-50 mph
8. Roadside Design
8.1 Side Slopes
| Slope Ratio | Description/Application |
|---|---|
| 4:1 or flatter | Recoverable; vehicle can safely return to roadway |
| 4:1 to 3:1 | Non-recoverable but traversable; reduce crash severity |
| 3:1 to 2:1 | Critical slope; marginal traversability |
| Steeper than 2:1 | Non-traversable; barrier required if within clear zone |
8.2 Guardrail Placement
- Required when fixed object or non-traversable slope within clear zone
- Minimum offset from edge of travel lane: 2-4 ft (face of rail)
- Length of need (LON): extends beyond hazard with approach and departure tapers
- End treatment: requires crashworthy terminal (energy absorbing)
8.3 Barrier Warrant Criteria
- Embankment height > 10 ft with slope steeper than 3:1
- Fixed objects closer than 1/2 clear zone width
- Bridge protection: rail required at edges
- Median barrier: ADT > 20,000 with median < 30="" ft="" or="" steep="" median="">
9. Parking Geometry
9.1 Parking Stall Dimensions
| Angle | Stall Width × Depth |
|---|---|
| Parallel | 8 ft × 22 ft (minimum) |
| 45° | 8.5 ft × 17.5 ft |
| 60° | 8.5 ft × 18 ft |
| 90° (Perpendicular) | 9 ft × 18 ft (standard) |
9.2 Aisle Widths (Two-Way Operation)
| Parking Angle | Minimum Aisle Width |
|---|---|
| 45° | 13 ft |
| 60° | 18 ft |
| 90° | 24 ft |
- One-way aisles: reduce by 3-5 ft
- Accessible parking: 8 ft stall + 5 ft access aisle (van: 11 ft stall + 5 ft aisle)
10. Design Speed Relationships
10.1 Design Speed Selection
| Functional Class | Design Speed Range |
|---|---|
| Interstate/Freeway (Rural) | 70-80 mph |
| Interstate/Freeway (Urban) | 50-70 mph |
| Arterial (Rural) | 50-70 mph |
| Arterial (Urban) | 40-55 mph |
| Collector (Rural) | 40-60 mph |
| Collector (Urban) | 30-45 mph |
| Local | 20-35 mph |
10.2 Design Consistency
- Operating speed should not exceed design speed by more than 5 mph
- Avoid abrupt changes in horizontal/vertical alignment requiring large speed reductions
- Coordinate horizontal and vertical curves to avoid driver surprise
- Horizontal curve radius and vertical curve K-value should match design speed
11. Drainage Considerations
11.1 Gutter Flow Capacity
| Parameter | Formula/Value |
|---|---|
| Manning's Equation | Q = (1.486/n)AR^(2/3)S^(1/2) |
| Gutter n-value | 0.013-0.016 for concrete, asphalt |
| Maximum Spread | 6-8 ft on streets; 10-12 ft on highways with curbs |
11.2 Inlet Spacing
- Function of gutter flow capacity, longitudinal slope, and cross slope
- Inlets required at sag vertical curves to capture all flow
- Bypass flow from upstream inlets added to next downstream inlet
12. Earthwork and Mass Diagram
12.1 Volume Calculations
| Method | Formula |
|---|---|
| Average End Area | V = (A₁ + A₂)/2 × L |
| Prismoidal | V = L/6(A₁ + 4A_m + A₂) |
12.2 Shrinkage and Swell Factors
| Material | Factor |
|---|---|
| Bank to Loose | 1.25-1.40 (swell) |
| Bank to Compacted | 0.90-1.00 (shrinkage) |
| Rock | 1.50-1.70 (swell) |
12.3 Mass Diagram Properties
- Ordinate = cumulative algebraic sum of cut (+) and fill (-) volumes
- Ascending line = cut section; descending line = fill section
- Horizontal line intersection = balance point (cut volume = fill volume)
- Peak or valley = transition from cut to fill or fill to cut
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Apr 20, 2026
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