Horizontal Curves

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Horizontal Curves

• Issue
• Challenges

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Highway Design Example
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Horizontal Curves

• Purpose
• Process
• Types

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Horizontal Curves Simple Curve
Straight road sections
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Horizontal Curves Compound Curve
Straight road sections
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Horizontal Curves Broken Back Curve
Straight road sections
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Horizontal Curves Reverse Curve
Straight road sections
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Horizontal Curves Spiral
Straight road section
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Geometry of Circular Curves

• Notation
• PI
• PC
• PT
• T

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Direction
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Geometry of Circular Curves

• Notation cont.
• R
• LC
• L

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Geometry of Circular Curves

• Notation cont.
• I or ?
• E
• M

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Geometry of Circular Curves

• Notable aspects of circle geometry
• Designation of Horizontal Curves

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Degree of Curvature

• Arc definition (Da)
• Central angle subtended by 100 feet of arc (along
  curve)

• Note 100' ? one full station

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Degree of Curvature cont.

• Chord definition
• Units

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Relationship of Da and R

• Metric equivalents by conversion, e.g.

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Curve Relationships

• Note
• Top five equations can be English or metric units

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Example Curve Calculations

• Given
• Deflection angle at PI (?) 8 24'
• Station of PI 64 27.64
• Da specified as 2 00'
• Compute
• Curve components
• Stations of PC and PT

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Derive Curve Components
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Derive Stations of PC and PT

• Station of PI 64 27.64
• Station of PC Station of PI T
• (64 27.64) (2 10.38) 62 17.08
• Station of PT Station of PC L (distance
  along curve)
• (62 17.08) (4 20.00) 66 17.08

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Selection (Design) of Curve

• Issue
• Design basis

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Layout of Circular Curves

• Issue
• Angle-distance technique
• Note

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Sight Distance on Horizontal Curves

• Issue
• Standards
• Set by American Association of State Highway and
  Transportation Officials (AASHTO)

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Example of Using SSD

• Consider
• Curve with R 1909.86 ft
• Sight obstruction (e.g. building) 12 ft from
  curve (M 12 ft)
• Question
• Recall car going 60 mph needs SSD of 475 ft
• Does curve have enough SSD for a car going 60 mph?

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LC ?
R 1909.86'

• Available sight distance 428' Required SSD60
  475'
• Not enough sight distance for 60 mph
• Post lower speed limit or redesign curve