**Geometric Design (II) **

**Learning Objectives** • To calculate minimum radius of horizontal curve • To understand design concepts for transition curves and compute min length • To understand the role of SSD in horizontal and vertical design • To define and apply grade considerations • To develop vertical curves (Chapter 6.1 ~ 6.4)

**Horizontal Curve** • Minimum Curve Radius • Curve requiring the most centripetal force for the given speed • Given emax, umax, Vdesign R

**Point of ** Tangency Point of Curvature Horizontal Curve Properties Based on circular curve • R: radius of curve • D: degree of curve • : central angle • T: length of tangent • L: length of curve • LC: long chord • M: middle ordinate dist • E: external dist

**Horizontal Design Iterations** • Design baseline • Curve radius above the minimum • Superelevation and side-friction factor not exceeding the maximum values • Design is revised to consider: cost, environmental impacts, sight distances, aesthetic consequences, etc.

**R** Horizontal Curve Sight Distance • Sight line is a chord of the circular curve • Sight Distance is curve length measured along centerline of inside lane

**Horizontal Curve Sight Distance** Figure 6-10

**Transition Curves** • Gradually changing the curvature from tangents to circular curves Without Transition Curves With Transition Curves

**Transition Curves** • Gradually changing the curvature from tangents to circular curves • Use a spiral curve L: min length of spiral (ft) V: speed (mph) R: curve radius (ft) C: rate of increase of centrifugal accel (ft/sec3), 1~3

**Transitional Curves** • Gradually changing the cross-section of the roadway from normal to superelevated (Figure 6-9) Keep water drainage in mind while considering all of the available cross-section options

**Vertical Alignment** Reduced Speed Increased Speed

**Vertical Alignment** • Grade • measure of inclination or slope, rise over the run • Cars: negotiate 4-5% grades without significant speed reduction • Trucks: significant speed changes • 5% increase on short descending grades • 7% decrease on short ascending grades

**Grade Considerations** • Maximum grade – depends on terrain type, road functional class, and design speed Rural Arterials

**Grade Considerations** • Critical length of grade • Maximum length which a loaded truck can travel without unreasonable speed reduction • Based on accident involvement rates with 10mph speed reduction as threshold

**Grade Considerations** General Design Speed Reduction

**Vertical Curves** • To provide transition between two grades • Consider • Drainage (rainfall) • Driver safety (SSD) • Driver comfort • Use parabolic curves • Crest vs Sag curves

**Vertical Curves**

**Vertical Curves** • Given • G1, G2: initial & final grades in percent • L: curve length (horizontal distance) • Develop the actual shape of the vertical curve point of vertical intersection PVI point of verticaltangency point of vertical curvature G1% G2%

**Vertical Curves** • Define curve so that PVI is at a horizontal distance of L/2 from PVC and PVT • Provides constant rate of change of grade: A G1% G2%

**Example** • G1 = 2% • G2 = -4% • Design speed = 70 mph • Is this a crest or sag curve? • What is A?

**Vertical Curves** • Major control for safe operation is sight distance • MSSD should be provided in all cases (use larger sight distance where economically and physically feasible) • For sag curves, also concerned with driver comfort (large accelerations due to both gravitational and centrifugal forces)

**Crest Vertical Curves** • Critical length of curve, L, is where sight line is tangent to the crest • Assume driver eye height (H1) = 3.5 ft and object height (H2) = 2.0 ft and S=MSSD

**Sag VC - Design Criteria** • Headlight sight distance • Rider comfort • Drainage control • Appearance