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## PowerPoint Slideshow about ' Geometric Design (II) ' - dakota-gregory

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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

Tangency

Point of

Curvature

Horizontal Curve PropertiesBased 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.

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

- 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

- 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

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