Modeling of Reverse Curves on a Railway Line Using the Analytical Design Method

This study discusses the issue of designing reverse curves, i.e. a geometric system consisting of two circular arcs (usually with different radii), directed in opposite directions and directly connected to each other. The design is performed in an appropriate local Cartesian coordinate system. The origin of this system is located at the point of intersection of adjacent main directions of the route. Unlike other geometric situations, reverse curves have three main directions, which significantly complicate the design process. The initial values of the radii of the reverse arcs must correspond to the existing system of main directions. The introduction of transition curves causes these radii to decrease; their values are determined iteratively. A set of formulas for creating a geometric system of reverse curves is presented. These formulas were used in the calculation example. A graph of the horizontal curvature of the track axis and a method for determining the possible train speed, both without the use of cant on an arc and with the use of cant, are shown. The presented procedure is universal and can be applied to other geometric situations involving the design of reverse curves. It is also necessary to emphasize the practical usefulness of the discussed method not only in the design process, but also to pay attention to the cognitive value of the article.