Transition Curve with Smoothed Curvature at its Ends for Railway Roads

In the paper, in view of a railway ballasted track, a new concept of transition curve of linear form of curvature along its length and smoothed extreme regions is presented. For this purpose use has been made of an original, universal method for identifying transition curves by means of differential equations. Some general curvature equations for three regions investigated have been determined to be followed by appropriate parametric formulae. The possibility of determining the rectangular coordinates by numerical integration has been indicated. Taking into consideration the criterion of practical execution, and on account of very small horizontal ordinates in the initial region, a suggestion is made to reduce the length of the extreme regions and for such a case some particular theoretical relations have been worked out.