Spiral Curve | Transition CurveSpirals 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.

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 = Spiral angle from tangent to any point on the spiral s= 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 curveFormulas for Spiral CurvesDistance along tangent to any point on the spiral:

At L = Ls, Y = Yc, thus,

Offset distance from tangent to any point on the spiral:

At L = Ls, X = Xc, thus,

Length of throw:

Spiral angle from tangent to any point on the spiral (in radian):

At L = Ls,=s, thus,

Deflection angle from TS to any point on the spiral:

At L = Ls, i = is, thus,

This angle is proportional to the square of its distance

Tangent distance:

Angle of intersection of simple curve:

External distance:

Degree of spiral curve: