Road curve Road Curve In highways railways or

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

Layout of a Simple 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

Circular Curve Components

Properties of Circular Curves 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 R = 5730 / D (Degree of curvature is not used with metric units because D is defined in terms of feet. )

Properties of Circular Curves Length of Curve • For a given external angle (Δ), the length of curve (L) is directly related to the radius (R) L = (RΔπ) / 180 = RΔ / 57. 3 R = Radius of Circular Curve L = Length of Curvature Δ = Deflection Angle • In other words, the longer the curve, the larger the radius of curvature

Properties of Circular Curves Other Formulas… Tangent: T = R tan(Δ/2) Chord: C = 2 R 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

EX: 1

EX: 2

EX: 3