1. Horizontal Curves Circular Curves Transition Spirals
Degree of Curvature
Terminology
Calculations
Staking
Transition Spirals

2. Circular Curves I – Intersection angle Portion of a circle R - Radius
Defines rate of change I R

3. Degree of Curvature D defines Radius Chord Method Arc Method
R = 50/sin(D/2)
Arc Method
(360/D)=100/(2R)
R = /D
D used to describe curves

4. Terminology PC: Point of Curvature PC = PI – T PT: Point of Tangency
PI = Point of Intersection
T = Tangent
PT: Point of Tangency
PT = PC + L
L = Length

5. Curve Calculations L = 100I/D T = R·tan(I/2) L.C. = 2R·sin(I/2)
E = R(1/cos(I/2)-1)
M = R(1-cos(I/2))

6. Curve Calc’s - Example
Given: D = 2°30’

7. Curve Calc’s - Example
Given: D = 2°30’

8. Curve Design Select D based on: Determine stationing for PC and PT
Highway design limitations
Minimum values for E or M
Determine stationing for PC and PT
R = /D
T = R tan(I/2)
PC = PI –T
L = 100(I/D)
PT = PC + L

9. Curve Design Example Given: I = 74°30’ PI at Sta 256+32.00
Design requires D < 5°
E must be > 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 can’t see past Sta 177+00.
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