CURVE RANGING

1. SPIRAL CURVE

1.1. Spirals are used to overcome the abrupt change in curvature and superelevation that occurs between tangent and circular curve. The spiral curve is used to gradually change the curvature and superelevation of the road, thus called transition curve.

1.2. Elements of Spiral Curve TS = Tangent to spiral SC = Spiral to curve CS = Curve to spiral ST = Spiral to tangent LT = Long tangent ST = Short tangent R = Radius of simple curve Ts = Spiral tangent distance Tc = Circular curve tangent L = Length of spiral from TS to any point along the spiral Ls = Length of spiral PI = Point of intersection I = Angle of intersection Ic = Angle of intersection of the simple curve p = Length of throw or the distance from tangent that the circular curve has been offset X = Offset distance (right angle distance) from tangent to any point on the spiral Xc = Offset distance (right angle distance) from tangent to SC Y = Distance along tangent to any point on the spiral Yc = Distance along tangent from TS to point at right angle to SC Es = External distance of the simple curve θ = Spiral angle from tangent to any point on the spiral θs = Spiral angle from tangent to SC i = Deflection angle from TS to any point on the spiral, it is proportional to the square of its distance is = Deflection angle from TS to SC D = Degree of spiral curve at any point Dc = Degree of simple curve

1.3. formula of spiral curve

2. SIMPLE CURVE

2.1. Terminologies in Simple Curve PC = Point of curvature. It is the beginning of curve. PT = Point of tangency. It is the end of curve. PI = Point of intersection of the tangents. Also called vertex T = Length of tangent from PC to PI and from PI to PT. It is known as subtangent. R = Radius of simple curve, or simply radius. L = Length of chord from PC to PT. Point Q as shown below is the midpoint of L. Lc = Length of curve from PC to PT. Point M in the the figure is the midpoint of Lc. E = External distance, the nearest distance from PI to the curve. m = Middle ordinate, the distance from midpoint of curve to midpoint of chord. I = Deflection angle (also called angle of intersection and central angle). It is the angle of intersection of the tangents. The angle subtended by PC and PT at O is also equal to I, where O is the center of the circular curve from the above figure. x = offset distance from tangent to the curve. Note: x is perpendicular to T. θ = offset angle subtended at PC between PI and any point in the curve D = Degree of curve. It is the central angle subtended by a length of curve equal to one station. In English system, one station is equal to 100 ft and in SI, one station is equal to 20 m. Sub chord = chord distance between two adjacent full stations.

2.2. Formulas for simple curve