Compound and Reversed Curves

SPONSORED LINKS

Compound Curves

A compound curve consists of two (or more) circular curves between two main tangents joined at point of compound curve (PCC). Curve at PC is designated as 1 (R1, L1, T1, etc) and curve at higher station is designated as 2 (R2, L2, T2, etc).
 

Elements of compound curve

 

Elements of compound curve

  • PC = point of curvature
  • PT = point of tangency
  • PI = point of intersection
  • PCC = point of compound curve
  • T1 = length of tangent of the first curve
  • T2 = length of tangent of the second curve
  • V1 = vertex of the first curve
  • V2 = vertex of the second curve
  • I1 = central angle of the first curve
  • I2 = central angle of the second curve
  • I = angle of intersection = I1 + I2
  • Lc1 = length of first curve
  • Lc2 = length of second curve
  • L1 = length of first chord
  • L2 = length of second chord
  • L = length of long chord from PC to PT
  • T1 + T2 = length of common tangent measured from V1 to V2
  • θ = 180° – I
  • x and y can be found from triangle V1-V2-PI.
  • L can be found from triangle PC-PCC-PT

 

Finding the stationing of PT

Given the stationing of PC
$ \text{Sta PT} = \text{Sta PC} + L_{c1} + L_{c2} $
 

Given the stationing of PI
$ \text{Sta PT} = \text{Sta PI} - x - T_1 + L_{c1} + L_{c2} $

 

Reversed Curve

Reversed curve, though pleasing to the eye, would bring discomfort to motorist running at design speed. The instant change in direction at the PRC brought some safety problems. Despite this fact, reversed curves are being used with great success on park roads, formal paths, waterway channels, and the like.
 

Elements of reversed curve

 

Elements of Reversed Curve

  • PC = point of curvature
  • PT = point of tangency
  • PRC = point of reversed curvature
  • T1 = length of tangent of the first curve
  • T2 = length of tangent of the second curve
  • V1 = vertex of the first curve
  • V2 = vertex of the second curve
  • I1 = central angle of the first curve
  • I2 = central angle of the second curve
  • Lc1 = length of first curve
  • Lc2 = length of second curve
  • L1 = length of first chord
  • L2 = length of second chord
  • T1 + T2 = length of common tangent measured from V1 to V2

 

Finding the stationing of PT

Given the stationing of PC
$ \text{Sta PT} = \text{Sta PC} + L_{c1} + L_{c2} $

Given the stationing of V1
$ \text{Sta PT} = \text{Sta } V_1 - T_1 + L_{c1} + L_{c2} $

 

Reversed Curve for Nonparallel Tangents
 

Example of reversed curve connecting nonparallel tangents

 

Reversed Curve for Parallel Tangents
 

Example of reversed curve connecting parallel tangents

 

Tags: 

SPONSORED LINKS