Construction of Optimal Transition Curves on Railways Based on Curvature
Construction of Optimal Transition Curves on Railways Based on Curvature

Summary/Abstract: Parametric transition curves designed to guarantee a smooth transition from tangent (straight) tracks to circular segments in the horizontal-plane projection of a railway track alignment. A rigorous theoretical framework was developed to express the functional dependence of curvature, deflection angle, and Cartesian coordinates on the curve's arc length. To validate the theoretical derivations, a detailed computational experiment was performed, fully confirming their correctness and accuracy. Furthermore, a methodology for constructing coordinate tables as a function of arc length - highly valuable for practical railway design and field layout - is provided. A robust mathematical apparatus for the curvature-based design of railway transition curves is established. The results demonstrate that the coordinates of the circular arc center were optimized and refined to the required level of precision.

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