CURVES

SIMPLE CURVES Horizontal Curve

Circular Curves TYPES OF CURVES: Simple Curve Compound Curve Reverse Curve spiral R R R R Easement or Transitional Curve spiral

Definitions “Degree of Curve” Central angle subtended by a circular ARC of 100 ft (highways) 100 ft R R D/100’ = 360/ 2p r = full circle angle / circumference PI PC PI = Point of Intersection PC = Point of Curvature PT = Point of Tangency L = Length of Curve L PT

Formulae T = R Tan I/2 L = 100 I0/D0 = R I rads LC = 2 R Sin I/2 LC = Long Chord M = Middle Ordinate E = External Distance T = Tangent Distance I = Intersection Angle T E T L M PC PT LC R T = R Tan I/2 R I/2 L = 100 I0/D0 = R I rads I LC = 2 R Sin I/2 R/ (R+E) = Cos I/2 => E = R [(1/Cos (I/2)) - 1] (R - M)/R = Cos I/2 => M = R [1 - (Cos (I/2)]

Stationing (usually every 100 feet) PC 4+86.75 4+00.00 0+00.00 1+00.00 2+00.00 3+00.00 5+00.00 T PI L 6+00.00 7+00.00 PC sta = PI sta – T PT sta = PC sta + L PT 7+27.87 8+00.00 9+00.00 10+00.00 11+00.00

Curve Layout Need to stake at “full stations” (XX+00.00) Set up on PC, backsight PI, turn deflection angle (d), measure chord distance (c) PI d PC chord