1. CURVES

2. SIMPLE CURVES
Horizontal Curve

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

4. 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

5. 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)]

6. Stationing (usually every 100 feet)PC T PI L
PC sta = PI sta – T
PT sta = PC sta + L PT

7. 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