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

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

Degree of Curvature D defines Radius Chord Method Arc Method R = 50/sin(D/2) Arc Method (360/D)=100/(2R) R = 5729.578/D D used to describe curves

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

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))

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

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

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 = 5729.58/D T = R tan(I/2) PC = PI –T L = 100(I/D) PT = PC + L

Curve Design Example Given: I = 74°30’ PI at Sta 256+32.00 Design requires D < 5° E must be > 315’

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

Curve Staking Example

Curve Staking If chaining along the curve, each station has the same c: With the total station, find  and c, use stake-out

Computer Example

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 178+00.