Exploring benefits of using blending splines as transition curves

Abstract

Track geometry is a fundamental subject in railway construction. With the demand for increased capacity in terms of load and speed, the need for suitable transitions between consecutive track sections is highly relevant. Properly constructed transition curves lead to improved travel comfort, increased safety, and reduced wear. The well known clothoid curve is widely used as a transition curve; however, the linear curvature is not sufficiently smooth to meet the requirements for railways carrying high speed trains or heavy hauls. Blending spline curves are flexible spline constructions possessing favourable smoothness properties at the end points, which makes them considerable for use as transition curves. This paper demonstrates some selected blending splines applied as transition curves between two existing circular arc segments selected from the Ofotbanen railway. The main results in this paper are related to the smoothness at the end points and the behaviour of the curvature of the curves, where the new transition curves were shown to be smoother than the original clothoid. Another new result is the observation that the proposed method allows for the improvement of existing railways without forcing extensive changes to the original track. Some representative examples are included to highlight the flexibility of this first instance of blending splines as transition curves.