Horizontal Curves Circular Curves

Degree of Curvature Terminology Calculations Staking

Transition Spirals Calculations Staking

Circular Curves

Portion of a circle

I – Intersection angle

R

I R - Radius Defines rate of

change

Degree of Curvature D defines Radius Chord Method

R = 50/sin(D/2) Arc Method

(360/D)=100/(2R) R = 5729.578/D

D used to describe curves

Terminology PC: Point of Curvature PC = PI – T

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’

'83.22915.2

578.5729

R

'87.4552

5.22tan38.2291

T

13.94170)87.554()50175( PC

'00.9005.2

5.22100

L

13.94179)009()13.94170( PT

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

'83.2291R

'23.8942

5.22sin)83.2291(2..

CL

'04.442

5.22cos183.2291

M

'90.441

25.22

cos

183.2291

E

Curve Design Select D based on:

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

200,2

,100

DlD

l

)sin(22

sin2 RRc

Curve Staking Example

'86.105)"24'191sin()83.2291(2

"24'191200

)5.2(87.105

00172

00172

c

13.94170,'302 PCD

"24'040200

5.287.5

,'87.500171

l

'87.5)"24'40sin()83.2291(2

,83.2291

c

R

Curve Staking

If chaining along the curve, each station has the same c:

'99.99)'151sin()83.2291(2

'151200

)5.2(100

100

100

c

With the total station, find and c, use stake-out

'34.405)"24'045sin()83.2291(2

"24'045200

)5.2(87.405

00175

00175

c

Computer Example

Moving Up on the CurveSay 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 115’ to sight on

Sta 178+00.