Development of a Methodology for the Geometric Parameterization of Three-Dimensional Tracks

The definition of railway, tramway or roller coaster tracks requires the accurate description of their geometries, which is usually done with the parameterisation of the track ceterline. Furthermore, the definition of a reference plane where the rails sit is required. In this paper, a methodology for the accurate description of the track centerline geometry, in the framework of multibody dynamics, is presented. Three different parameterisation schemes, using cubic splines, Akima splines and shape preserving splines, are proposed. Since the track is time invariant, a pre-processor is used to define its spatial geometry. In order to achieve computational efficiency, the pre-processor generates, in a tabular manner and as a function of the track length, all the position data and other quantities required for the dynamic analysis of rail guided vehicles. The advantages and drawbacks of the proposed methodology are discussed, emphasizing the influence of the type of parametric curves used to construct the track model. The discussion is supported through the application of the formulation to the dynamic analysis of a roller coaster model with complex spatial track geometry. Special emphasis is given to the calculation of the reaction forces imposed on the roller coaster structure by the running vehicles.