Horizontal Curve

Horizontal Curve Formulas

Input Data:

Intersection Angle = o
Degree of Curve = o
P.I. Station =
Results:

Radius = ft
Tangent = ft
Length = ft
External = ft
Long Chord = ft
PC Station =
PT Station =

Horizontal Curve Formulas

Horizontal Curve Picture

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.
2 sin(I/2) 2 cos(I/2)

L.C. = R sin (I/2) D1° = R = 5,729.58 D2° = 5,729.58 D = 5,729.58
2 2 R

M = R [1 - cos(I/2)] = R - R cos(I/2)

 

E + R = sec(I/2)R - M = cos(I/2)
R R
c = 2R sin(d/2) d = kD
100
L.C. = 2R sin(I/2) E = R [sec(I/2) - 1] = R sec(I/2) - R