Road curve

Road Curve In highways, railways, or canals the curve are provided for smooth or gradual change in direction due the nature of terrain, cultural features, or other unavoidable reasons

Road Curve In highway practice, it is recommended to provide curves on straight route to break the monotony in driving on long straight route to avoid accidents. The vertical curves are used to provide a smooth change in direction taking place in the vertical plane due to change of grade.

Horizontal Alignment Tangents Curves

Tangents & Curves Tangent Curve Tangent to Circular Curve Tangent to Spiral Curve to Circular Curve

ELEMENTS OF A HORIZONTAL CURVE R = Radius of Circular Curve BC = Beginning of Curve (or PC = Point of Curvature) EC = End of Curve (or PT = Point of Tangency) PI = Point of Intersection T = Tangent Length (T = PI – BC = EC - PI) L = Length of Curvature (L = EC – BC) M = Middle Ordinate E = External Distance C = Chord Length Δ = Deflection Angle

ELEMENTS OF A HORIZONTAL CURVE POC = POINT OF CURVE. The point of curve is any point along the curve. LC = LONG CHORD. The long chord is the straight-line distance from the PC= to the PT. Other types of chords are designated as follows: C=The full-chord distance between adjacent stations (full, half, quarter, or onetenth stations) along a curve.

ELEMENTS OF A HORIZONTAL CURVE C1 = The subchord distance between the PC and the first station on the curve. C2 = The subchord distance between the last station on the curve and the PT.

Degree of Curvature Traditionally, the “steepness” of the curvature is defined by either the radius (R) or the degree of curvature (D) Degree of curvature = angle subtended by an arc of length 100 feet or meter

Degree of Curvature (arc definition) Traditionally, the “steepness” of the curvature is defined by either the radius (R) or the degree of curvature (D) Degree of curvature = angle subtended by an arc of length 100 feet or meter

Degree of Curvature (chord definition) This definition states that the degree of curve is the central angle formed by two radii drawn from the center of the circle to the ends of a chord 100 feet (or 100 meters) long. Notice that in both the arc definition and the chord definition, the radius of curvature is inversely proportional to the degree of curvature.

Length of Curve For a given external angle (Δ), the length of curve (L) is directly related to the radius (R)

Properties of Circular Curves Other Formulas… Tangent: T = R tan(Δ/2) Chord: C = 2R sin(Δ/2) Mid Ordinate: M = R – R cos(Δ/2) External Distance: E = R sec(Δ/2) - R Sec: secant exact opposite of cos

Circular Curve Geometry

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