A Solution to Remove Railway Track Discontinuities at Spiral Junctions

To design railway track layouts, engineers use tangent and circle segments. To maintain curvature and bank angle continuities between flat straight lines, with zero curvature, and banked circles, they use spiral segments where curvature and bank angle vary linearly as function of distance. This method meets the behavior of track engineers for which curvature and super-elevation are the main data used to lay the groundwork. However, it demonstrates dynamical drawbacks at both ends of spirals where bank angle and curvature derivatives would be discontinuous. Several unsuccessful attempts have been made to change spirals definition to alleviate this issue. In reality, track engineers smoothen the theoretical layout at the junctions, but there is no analytical definition for that although it is necessary track data at least for simulation codes. Smoothing portions are called ‘doucines’ but the maps of railway lines do not mention these unknown data and railway numerical codes ignore them, thus having to deal with subsequent dynamical perturbations which are avoided by doucines in reality. This paper proposes an analytical definition of practical doucines which does not modify actual theoretical method for designing lines. It also describes a method for programming it in railway codes. It uses trigonometric functions, sine and cosine which are simple to integrate to get at first the track orientation and then the X-Y coordinates of the layout line. In addition to doucine definitions, usable as well in practice as for all multibody codes, the paper shows how it can be implemented into the specific French calculation method, which uses an imaginary space, developed at first for calculating the dynamics of TGV. After modifying the author’s Ocrecym code according to the proposed doucine method, dynamical simulations of a light trailer coach, running over curved lines with and without doucines are presented to demonstrate the effectiveness of proposed solution.