Determination of Track Axis Coordinates in the Analytical Method of Designing Railway Route Geometry

Abstract

The article presents the final version of the analytical method for designing railway route geometry, in which individual elements of geometric system (straight sections, circular arcs and transition curves) are described using mathematical equations. The design of the route change section is carried out in an appropriate local Cartesian coordinate system, the basis of which is the symmetrically arranged adjacent main directions. The described method is adapted to the technique of mobile satellite measurements, which provide, in a very short time, a huge number of track axis coordinates, incomparable to traditional geodetic measurements. By locating the origin of the local coordinate system at the intersection point of the main directions of the route, the basis for a universal design variant was created. This variant includes both symmetrical cases and asymmetrical ones resulting from different types and lengths of transition curves. Two situations that may arise when using the local coordinate system were considered, related to the position of the designed geometric system to the main point of the route. A number of specific issues were also clarified. After determining the basic characteristic values, the computational algorithm described in the work leads to solving the problem in a sequential way, much more convenient than before. The obtained possibilities are illustrated by two computational examples.