Curvature and Radius of Curvature

Curvature and Radius of Curvature in xy-Plane | Derivation of Formula | Differential Calculus

Curvature (symbol, $\kappa$) is the mathematical expression of how much a curve actually curved. It is the measure of the average change in direction of the curve per unit of arc. Imagine a particle to move along the circle from point 1 to point 2, the higher the number of $\kappa$, the more quickly the particle changes in direction. This quick change in direction is apparent in smaller circles.

Circle of Curvature


Spiral Curve

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.

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