The Procedure of Identifying the Geometrical Layout of an Exploited Railway Route Based on the Determined Curvature of the Track Axis

Abstract

This paper presents a detailed algorithm for determining the curvature of a track axis with the use of a moving chord method, and then discusses the procedure for identifying the geometric layout of an exploited railway route on the basis of the determined curvature. In the moving chord method, the measured coordinates of the track axis allow one to directly determine the existence of the horizontal curvature without the need for additional measurements. This enables comprehensively identifying the existing geometric elements—straight lines, circular arcs, and transition curves. The conducted activities were illustrated with a calculation example, including a 5.5 km long test section with five areas of directional change. This showed a sequential procedure that led to the solution of the given problem. Based on the curvature diagram, the coordinates of the segmentation points, which define the connections of the existing geometric elements with each other, were determined.

A Method for Determining the Directional Angle of a Railway Route Based on Field Measurements

“…Therefore, the basic problem to solve remains determining the value Θ i of the angle of inclination of the tangent at a given point. For this purpose, a chord of a specific length stretched along the track can be used, as is the case when determining the curvature of the track axis using the moving chord method [ 30 ]. In this method, the basic task of the procedure for determining the curvature at the measurement point—based on the determined Cartesian coordinates—is to determine the values of the angles of inclination of two virtual chords (derived, from this point, forward and backward) to the abscissa of the appropriate rectangular coordinate system.…”

“…The methodology for determining the curvature of the track axis was explained in detail in [ 30 ]. Similarly, the sequence of activities aimed at determining the values of angles and at any measurement point is illustrated in Figure 2 .…”

“…It so happens that the angles of inclination of chords occurring in the discussed method are also used in the method of determining the curvature of the geometric layout of tracks [ 30 ]. The applicable formula for curvature is as follows: …”

“…These measurement data should be the Cartesian coordinates of the track axis, allowing for the visualization of a given railway route and obtaining a general orientation about its course. This article presents a proposed solution to the problem referring to the assumptions made in the new method of determining the curvature of the railway track axis using a moving chord [ 30 ]. To obtain greater transparency of the analysis, we focussed on the situation corresponding to the model geometric layout, determined according to the principles of the analytical design method [ 31 ].…”

“…The basis for identification may be the curvature of the geometric layout; thus, an appropriate method for determining the curvature should be developed. In [ 30 ], a proposal for a new method for determining the curvature of the track axis, named “the moving chord method”, was presented.…”