Modeling of Compound Curves on Railway Lines

This article addresses the issue of designing compound curves, i.e., a geometric system consisting of two (or more) circular arcs of different radii, pointing in the same direction and directly connected to each other. Nowadays, compound curves are mainly used on tram lines; they also occur on railways (e.g., on mountain lines), but new ones are generally no longer being built there. Therefore, in relation to railway lines, the aim is to be able to recreate (i.e., model) the existing geometric layout with compound curves, so that it is then possible to correct this layout. An analytical method for designing track geometric systems was used, adapted to the mobile satellite measurement technique, in which calculations are carried out in the appropriate local Cartesian coordinate system. The basis of this system is the symmetrically arranged adjacent main directions of the route, and the beginning is located at the point of intersection of these directions. A number of detailed issues have been clarified and basic characteristic quantities have been determined, and the computational algorithm described in the paper leads to the solution of the problem in a sequential manner. The obtained possibilities of modeling the compound curves are illustrated by the provided calculation example.