# Compound and Reversed Simple Curves

## 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 (*R*_{1}, *L*_{1}, *T*_{1}, etc) and curve at *PT* is designated as 2 (*R*_{2}, *L*_{2}, *T*_{2}, etc).

**Elements of compound curve**

*PC*= point of curvature*PT*= point of tangency*PI*= point of intersection*PCC*= point of compound curve*T*_{1}= length of tangent of the first curve*T*_{2}= length of tangent of the second curve*V*_{1}= vertex of the first curve*V*_{2}= vertex of the second curve*I*_{1}= central angle of the first curve*I*_{2}= central angle of the second curve*I*= angle of intersection =*I*_{1}+*I*_{2}*L*_{c1}= length of first curve*L*_{c2}= length of second curve*L*_{1}= length of first chord*L*_{2}= length of second chord*L*= length of long chord from*PC*to*PT**T*_{1}+*T*_{2}= length of common tangent measured from*V*_{1}to*V*_{2}*θ*= 180° -*I**x*and*y*can be found from triangle*V*_{1}-*V*_{2}-*PI*.*L*can be found from triangle*PC-PCC-PT*

**Finding the stationing of PT**

*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**

*PC*= point of curvature*PT*= point of tangency*PRC*= point of reversed curvature*T*_{1}= length of tangent of the first curve*T*_{2}= length of tangent of the second curve*V*_{1}= vertex of the first curve*V*_{2}= vertex of the second curve*I*_{1}= central angle of the first curve*I*_{2}= central angle of the second curve*L*_{c1}= length of first curve*L*_{c2}= length of second curve*L*_{1}= length of first chord*L*_{2}= length of second chord*T*_{1}+*T*_{2}= length of common tangent measured from*V*_{1}to*V*_{2}

**Finding the stationing of PT**

*PC*

$\text{Sta PT} = \text{Sta PC} + L_{c1} + L_{c2}$

Given the stationing of *V*_{1}

$\text{Sta PT} = \text{Sta } V_1 - T_1 + L_{c1} + L_{c2}$

**Reversed Curve for Nonparallel Tangents**

The following figure is an example reversed curves of unequal radii connecting non-parallel tangents.

**Reversed Curve for Parallel Tangents**

The figure below is an example of reversed curves of unequal radii connecting two parallel roads.