Identification of Transition Curves in Vehicular Roads and Railways

In the paper attention is focused on the necessity to systematize the procedure for determining the shape of transition curves used in vehicular roads and railway routes. There has been presented a universal method of identifying curvature in transition curves by using differential equations. Curvature equations for such known forms of transition curves as clothoid, quartic parabola, the Bloss curve, cosinusoid and sinusoid, have been worked out and by the use these equations it was possible to determine some appropriate Cartesian coordinates. In addition some approximate solutions obtained in consequence of making certain simplifying assumptions orientated mainly towards railway routes, have been provided. Notice has been taken of limitations occurring in the application of smooth transition curves in railway systems, which can be caused by very small values of the horizontal ordinates in the initial region. This problem has provided an inspiration for finding a new family of the so-called parametric transition curves, being more advantageous not only over the clothoid but also over cubic parabola as far as dynamics is concerned.