Optimization of Vertical Alignment using General Transition Curves

Abstract

The paper presents an original design method of vertical alignment of road routes. It involves the use of the so-called general or universal transition curves. These curves describe the entire curvilinear transition between two straight lines using a single equation. They also have only one curvature extremum, which is of great practical significance. By using general transition curves, it is possible to obtain a completely curvilinear course of vertical alignment ensuring full smoothness at the connection points of each curve. The paper presents a methodology of creating appropriate approximation equations for longitudinal profile points as well as their development using the method of least squares in order to determine the parameters for optimum vertical alignment. The proposed approach reflects the principles of the so-called polynomial routing and makes it possible to create vertical alignment that may be composed of both general transitional curves, as well as straight line sections. Numerical studies of several longitudinal profiles on the site have shown that the proposed approach allows for a better fit to the vertical terrain than traditional design methods of vertical alignment, i.e. using tangent polygon of parabolic arcs.