Communications - Scientific letters of the University of Zilina X:X | DOI: 10.26552/com.C.2026.038

Construction of Optimal Transition Curves on Railways Based on Curvature

Ahmad Imanov ORCID...*, Isa Khalilov ORCID...
Azerbaijan Technical University, Department of Machine Design and Industrial Technologies, Baku, Azerbaijan

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.

Keywords: curvature, deflection angle, parametric representation, railway, transition curve, optimal design
Grants and funding:

The authors received no financial support for the research, authorship and/or publication of this article.

Conflicts of interest:

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Received: April 6, 2026; Accepted: June 24, 2026; Prepublished online: June 24, 2026 

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