The paper presents an analytical method of identifying the curvature of the turnout diverging track consisting of sections of varying curvature. Both linear and nonlinear (polynomial) curvatures of the turnout diverging track are identified and evaluated in the paper. The presented method is a universal one; it enables to assume curvature values at the beginning and end point of the geometrical layout of the turnout. The results of dynamics analysis show that widely used in railway practice, clothoid sections with nonzero curvatures at the beginning and end points of the turnout lead to increased dynamic interactions in the track-vehicle system. The turnout with nonlinear curvature reaching zero values at the extreme points of the geometrical layout is indicated in the paper as the most favourable, taking into account dynamic interactions occurring in the track-vehicle system.

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The paper presents an analysis of the elongation of transition curves in relation to railway track alignment correction and modernisation. The analysis is based on numerical computations for a wide range of parameters describing a typical railway geometrical layout with transition curves. The differences between the horizontal ordinates of the existing layout and the layout with the elongated transition curves are evaluated and assessed. The analytical model comprises formulated appropriate theoretical dependencies for each characteristic zone of the layout. The impacts of a circular arc radius and a route intersection angle on the elongation process are considered. Based on the theoretical assumptions, an effective numerical algorithm for comparative analysis of the transition curves’ elongation variants is developed. The value of a new circular arc radius is determined in an optimisation process. For this purpose, the indicators for process evaluation and the constraints determining the feasibility of the design variants are defined.

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