Horizontal Curves n Circular Curves n n n

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

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

Degree of Curvature n n D defines Radius Chord Method n n Arc Method n n n R = 50/sin(D/2) (360/D)=100/(2 R) R = 5729. 578/D D used to describe curves

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

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

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

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

Curve Design n Select D based on: n n n Highway design limitations Minimum values for E or M Determine stationing for PC and PT n n n R = 5729. 58/D T = R tan(I/2) PC = PI –T L = 100(I/D) PT = PC + L

Curve Design Example n Given: n n I = 74° 30’ PI at Sta 256+32. 00 Design requires D < 5° E must be > 315’

Curve Staking n Deflection Angles n n n 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. n Move transit to that Sta, sight back on PC. n Plunge scope, turn 7 34’ 24” to sight on a tangent line. n Turn 1 15’ to sight on Sta 178+00.