Analysis of Moving Chord Inclination Angles when Determining Curvature of Track Axis

Abstract

The analysis presented in the paper explains computational issues related to the use of a new method of determining the curvature of the track axis – the so-called moving chord method. It indicates the versatility of this method – it may be used both in a horizontal and vertical plane. It also draws attention to its very high precision, as evidenced by the exemplary geometric cases under consideration. The focus here is on the computational foundations of the discussed method regarding the angles of inclination of the moving chord. It was found that for a circular arc in the horizontal plane, the inclination angles of the moving chord depend on the track turning angle, while the difference in inclination angles depends only on the radius of the arc. In the case of a circular arc in the vertical plane, the moving chord inclination angles are much smaller than in the horizontal plane, which is connected with the range of the applied radii of the arcs. As in the horizontal plane, the radius of the vertical curve is the only factor that determines the discrepancy in the inclination angles of the moving chord.