4. Theoretical and Application Aspects of Determining the Curvature of the Railway Track Axis by the Moving Chord Method

The paper concerns a new approach to the problem of identifying the measured railway route. It presents the general characteristics of the currently used ways of identifying the track axis, which consist of generating an optimized geometrical layout in the tested area by minimizing the occurring deviations of this layout from the measurement points. The proposed new approach uses the obtained measurement data to determine the existing curvature of the geometric layout. The theoretical basics of the proposed new method of determining the curvature of the railway track axis (the so-called moving chord method) have been presented, including the corresponding computational algorithm. As it turns out, the scope of applicability of this method is limited, but it corresponds to the conditions on railway roads. In a number of earlier works, its high efficiency was demonstrated, now the issue of explaining the influence of deviations from the model (theoretical) shape of the track on the obtained curvature values, occurring in the real (i.e., in operation) railway track, has been addressed. Since the moving chord method uses the determined Cartesian coordinates of the track axis, deviations from the model shape are the result not only of the existing track deformations, but—mainly—of the measurement error. The analysis shows that the poorer quality of the measurement data, characterized by a higher value of the maximum error, causes greater disturbances in the curvature diagram determined by the moving chord method. However, these disturbances can be significantly reduced by appropriately increasing the chord lengths used. At the end, the direction of future research to the development of the discussed method of determining the curvature of the railway track is indicated.