Geometric approach to define a railway plan model

Abstract

The construction of new railway lines is based on the railway plan. There are various ways to draw up a railway plan. The basis of all railway plans is a scheme of geometric point locations, the projection of the center of gravity of the carriage is on a horizontal plane and consists of a single flat line. The railway plan consists of linear and curved parts connecting straight sections. However, the curves determining the position of the rails of the railway track in the curved part will be spatial. To extinguish the centrifugal force arising in the curved part of the road, an external rail rises. In this case, the elevated curve representing the outer rail becomes spatial. Therefore, in the work, it is proposed to draw up a plan of a railway track as two curves, one of which is flat, and the other depicts an external spatial rail. In this case, the distance between the ends of the rectilinear parts and the angle between the rectilinear parts are selected as the main parameters. In the work, for the simplest case, when both linear parts belong to the same horizontal plane, it is proved that the curved part is a spatial curve. The curvature of the required curve was determined and a dynamic system was constructed, the solution of which would be a curve that satisfied the technical conditions presented for the railway route. This dynamic system is proposed as a mathematical model of the railway route. In the rectilinear parts, the railway plan is straight on a horizontal plane. The curve of the road should be spatial.