Transportation highways horizontal curve

Determine the geometric properties of a horizontal curve based on the provided values of intersection angle, degree of curve, and point of intersection. Horizontal curves on roads facilitate smooth transitions between tangent sections, enabling vehicles to navigate turns gradually and safely.Degree of Curve

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$R = \frac{5729.58}{D}$
$T = R \cdot \tan\left(\frac{A}{2}\right)$
$L = 100 \cdot \left(\frac{A}{D}\right)$
$LC = 2 \cdot R \cdot \sin\left(\frac{A}{2}\right)$
$E = R \left(\frac{1}{\cos\left(\frac{A}{2}\right)} - 1\right)$
$M = R \left(1 - \cos\left(\frac{A}{2}\right)\right)$
$PC = \pi - T$
$PT = PC + L$

The variables used in the formulas are:

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
A = 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

Each formula calculates a specific geometric property based on the given values of D, A, and R.