A General Method for Designing Railway Transition Curve Algebraic Equations

Abstract

As train speed increases, it makes higher demands on track geometry. Whether the type of transition curve is set up rationally or not directly affects the train running stability and comfort of passengers. A general and new method for designing algebraic equations for the characteristics of a railway transition curve is presented. First, according to the given boundary conditions of the transition curve, the equation of curvature with unknown coefficients is given. Second, the unknown coefficients in the curvature equation are determined by the boundary conditions of curvature and the curvature equation is obtained. At last, the equation of the transition curve in Cartesian coordinates can be obtained by double integration of the curvature equation. By taking transition curves which meet different boundary conditions as examples, the application of the proposed method is illustrated in detail. The proposed method is proved to be correct and simple. It is a general method that can be applied for determination of transition curve algebraic equations. And it offers a new design method for high-speed railway transition curves.