CIRCULAR HORIZONTAL CURVES - CPP

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CIRCULAR HORIZONTAL CURVES

BC =Beginning of Curve PC = Point of Curve

TC = Tangent to Curve

EC = End of Curve PT = Point of Tangent CT = Curve to Tangent

Most curve problems are calculated from field measurements ( and chainage), and from the design parameter, radius of curve( R). R is dependent on the design speed and . All other curve components can be computed.

GEOMETRY OF CURVE

In triangle BC, O, PI In triangle BC, O, B

T/R = tan (/2) Tangent T = Rtan (/2)

(1/2C)/R =sin (/2) Chord C = 2Rsin(/2)

OB/R = cos (/2) OB = Rcos (/2)

OB = R - M

R - M = Rcos (/2) Mid ordinate (M) M = R{1-cos (/2)}

In triangle BC, O, PI Distance O to PI = R +E R/(R+E) = cos (/2)

E = R { [1/(cos (/2))] - 1} External Distance E = R{sec (/2)) - 1}

LENGTH OF CURVE

(L/2R) = (/360) Length of Curve L = 2R(/360) DEGREE OF CURVE (D) Highway Definition The Central Angle subtended by a 100' arc Railroad Definition The Central Angle subtended by a 100' chord Consider the figure above.

D/360 = 100/ (2R) D = 5729.58/R

And L/100 = /D L=100/D

STATIONING The distance along a route in highway surveying is represented by stationing. Stationing is expressed in units of 100 feet, OR units of 1000 feet. For example, a point 626.57 feet along the route is expressed as:

6 + 26.57 in the 100 foot system and 0+626.57 in the thousand foot system

Example

= 16o 38' R = 1000' PI at 6+26.57 Calculate the stationing of BC, and EC, and find M (mid-ordinate), C (chord) and E (external) T = R tan (/2) = 1000 tan 8o 19' = 146.18 ft L = 2R /360 = (2)1000(16.6333/360)

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