Horizontal Curves

1
Horizontal Curves

• Circular Curves
• Degree of Curvature
• Terminology
• Calculations
• Staking
• Transition Spirals
• Calculations
• Staking

2
Circular Curves

• I Intersection angle

• Portion of a circle

• R - Radius
• Defines rate of change

R
3
Degree of Curvature

• D defines Radius
• Chord Method
• R 50/sin(D/2)
• Arc Method
• (360/D)100/(2?R)
• R 5729.578/D
• D used to describe curves

4
Terminology

• PC Point of Curvature
• PC PI T
• PI Point of Intersection
• T Tangent
• PT Point of Tangency
• PT PC L
• L Length

5
Curve Calculations

• L 100I/D
• T Rtan(I/2)
• L.C. 2Rsin(I/2)
• E R(1/cos(I/2)-1)
• M R(1-cos(I/2))

6
Curve Calcs - Example

• Given D 230

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Curve Calcs - Example

• Given D 230

8
Curve Design

• Select D based on
• Highway design limitations
• Minimum values for E or M
• Determine stationing for PC and PT
• R 5729.58/D
• T R tan(I/2)
• PC PI T
• L 100(I/D)
• PT PC L

9
Curve Design Example

• Given
• I 7430
• PI at Sta 25632.00
• Design requires D lt 5
• E must be gt 315

10
Curve Staking

• Deflection Angles
• Transit at PC, sight PI
• Turn angle ? to sight on Pt along curve
• Angle enclosed ?
• Length from PC to Pt l
• Chord from PC to point c

11
Curve Staking Example
12
Curve Staking
If chaining along the curve, each station has the
same c
With the total station, find ? and c, use
stake-out
13
Computer Example
14
Moving Up on the Curve

• Say you cant see past Sta 17700.
• Move transit to that Sta,sight back on PC.
• Plunge scope, turn 7? 34 24 to sight on a
  tangent line.
• Turn 1?15 to sight on Sta 17800.