Design of curvilinear sections in vertical alignment of roads and railways using general transition curves

Creation of road and railway routes in general and also design of vertical alignment in particular constitute an significant engineering problem. The vertical alignment of roads, and especially of railways, is of great importance for passenger comfort under high-speed driving conditions. This requires alignment smoothness to a greater extent. In practice, the dominant tendency is to consider vertical arcs as parabolic curves (quadratic or cubic). Other solutions have been also proposed and analyzed in the literature, thus providing an alternative approach to traditional methods. This paper describes a design method of vertical arcs using the so-called general transition curves. These curves describe the entire curvilinear transition between two straight lines using a single equation, and the curvature at the contact points with the straight lines is zero, which is of great practical significance in the light of vehicle motion dynamics. As a result, relevant research shows that general transition curves, compared to other curves, provide a more favorable distribution of lateral changes of acceleration. The paper deals not only with appropriate design procedures of a general nature, but also specific procedures of fitting vertical arcs to preset points. The methods for designing vertical arcs constitute a useful extension of available methods, and offer a valuable tool for engineers and designers of road and railway routes.