Basic Variants of the Analytical Method of Designing Track Geometric Layouts

The article presents (and extends) the basic assumptions of the analytical method for designing track geometric layouts. The individual elements of the layout (straight sections, circular arcs and transition curves) are described using mathematical equations and connected with each other while maintaining the condition of tangent compliance. The method covers various design cases: a symmetrical case, with transition curves of the same type and the same length, an asymmetrical case, resulting from different types and lengths of transition curves, as well as methods of designing compound and reverse curves. The work presents a detailed design procedure for the typical, most common case in which the transition curves are symmetrical in relation to the circular arc. Two basic variants differing in the location of the local coordinate system are considered. In the standard (universal) variant, the location of the beginning of the system in the PL-2000 system is not known and is determined only in the final phase of the procedure. Due to this, some interpretation problems may arise. In the case of a symmetrical geometric layout, these difficulties can be avoided thanks to the introduced modification consisting of locating the origin of the local coordinate system at the intersection of two main directions of the route. The article presents computational algorithms for both discussed variants. The benefits of the introduced modification are illustrated by the presented computational examples.