Horizontal Curve Formulas
D = Degree of Curve, Arc Definition
1° = 1 Degree of Curve
2° = 2 Degrees of Curve
P.C. = Point of Curve
P.T. = Point of Tangent
P.I. = Point of Intersection
I = Intersection Angle, Angle between two tangents
L = Length of Curve, from P.C. to P.T.
T = Tangent Distance
E = External Distance
R = Radius
L.C. = Length of Long Chord
M = Length of Middle Ordinate
c = Length of Sub-Chord
k = Length of Arc for Sub-Chord
d = Angle of Sub-Chord
R = | L.C. | | T = R tan(I/2) = | L.C.
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2 sin(I/2) | 2 cos(I/2)
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L.C. | = R sin (I/2) | | D1° = R = 5,729.58 | | D2° = | 5,729.58 | | D = | 5,729.58
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2 | 2 | R
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M = R [1 - cos(I/2)] = R - R cos(I/2)
E + R | = sec(I/2) | | R - M | = cos(I/2)
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R | R
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c = 2R sin(d/2) | | d = | kD
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100
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L.C. = 2R sin(I/2) | | E = R [sec(I/2) - 1] = R sec(I/2) - R
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