Geometric Design (II)
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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

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Geometric Design (II)

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Geometric design ii

Geometric Design (II)


Learning objectives

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

Horizontal Curve

  • Minimum Curve Radius

    • Curve requiring the most centripetal force for the given speed

    • Given emax, umax, Vdesign

R


Horizontal curve properties

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

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

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 distance1

Horizontal Curve Sight Distance

Figure 6-10


Transition curves

Transition Curves

  • Gradually changing the curvature from tangents to circular curves

Without Transition Curves

With Transition Curves


Transition curves1

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

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

Vertical Alignment

Reduced Speed

Increased Speed


Vertical alignment1

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

Grade Considerations

  • Maximum grade – depends on terrain type, road functional class, and design speed

Rural Arterials


Grade considerations1

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 considerations2

Grade Considerations

General Design Speed Reduction


Vertical curves

Vertical Curves

  • To provide transition between two grades

  • Consider

    • Drainage (rainfall)

    • Driver safety (SSD)

    • Driver comfort

  • Use parabolic curves

  • Crest vs Sag curves


Vertical curves1

Vertical Curves


Vertical curves2

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 curves3

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

Example

  • G1 = 2%

  • G2 = -4%

  • Design speed = 70 mph

  • Is this a crest or sag curve?

  • What is A?


Vertical curves4

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

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

Sag VC - Design Criteria

  • Headlight sight distance

  • Rider comfort

  • Drainage control

  • Appearance


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