Polynomial Solutions of Transition Curves

Abstract

The solutions of transition curves presented in this paper are new geometric solutions that can be used in various tasks related to road designing. Their basic advantage is that they form groups of transition curves. This paper is concerned with transition curves with the classical curvature diagram and so-called general transition curves. These can be a valuable alternative for the traditional solutions (first transition curve–circular arc–second transition curve or first transition curve–second transition curve). As a result, they are particularly useful when it comes to solving road design–related tasks, e.g., location of siding within road junctions when there are land limitations or for grade-line setting out through assigned points of set elevations. As for the presented solutions of general transition curves, they add to the range of geometric tools that can be used for road designing in a site plan and a longitudinal profile. The solutions of general transition curves described are well-suited for special areas of road designing, such as forming a completely curvilinear road design. It is equivalent to the solutions presented in the literature called polynomial location.