Smoothed transition curve for railways

Abstract

The work draws attention to the existing situation in the area of transition curves used in the geometric layouts of the railway track. Difficulties in the practical implementation and maintenance of very small horizontal ordinates of the transition curve and the ordinates of the gradient due to cant in the initial section, appearing on smooth transition curves, were indicated. The main reason for this situation was the excessive smoothing of the curvature in their initial section. Employing the method of curvature identification by differential equations, a new form of the curve was obtained, which was referred to as the "smoothed transition curve". A definite advantage of this curve was shown, from the implementation point of view, over representing the smooth transition curves of the Bloss curve. . It seems that it could successfully compete with the commonly used clothoid, to which it is similar in the initial section, while it differs significantly along its further length, especially in the final section, where it provides a gentle entry from the transition curve into a circular arc.