Designing the Railway Line Direction Changing Area in Linear and Cartesian Coordinate Systems

Abstract

Due to the development of geodetic measurement techniques, for the basic geometric layout of tracks, i.e. a symmetrical layout consisting of a circular arc and two transition curves of the same type and length, it is possible to unequivocally solve the design problem, using an appropriate mathematical notation. Moreover, when considering railway route designation requirements in the field, it is strongly recommended to determine Cartesian coordinates for points located at fixed distances in a linear system. These issues constitute the main subject of this article. It describes the creation of a route polygon in the national spatial reference system, determination of the route turning angle and determination of the coordinates of the beginning of the local coordinate system in the PL-2000 system. The algorithms for determining the coordinates in the linear and Cartesian coordinate systems are presented, taking into account the individual geometric segments of the route change area separately. The developed design algorithms were used in the presented calculation example. The discussed method allows one to determine the coordinates of the track axis in a sequential manner, in accordance with the requirements of their field application.