The Study of Geometry of the Selected Transition Curves in the Design of Circular Roads

Abstract

Transition curves connecting straight sections with circular curves and vice versa are present on all types of roads. They are designed to smooth the transition from rectilinear to circular motion. In numerous instances, they are hardly noticeable by road use. Although adequately selected, they increase the safety and comfort of driving. The research aimed to investigate the effectiveness of three most popular curves, in the design of road routes: clothoid, a parabola of the 3rd-degree and Bernoulli lemniscate. Starting from the permissible values of the increment of centripetal acceleration on the transition curves, the minimum lengths of the transition curves for the assumed speeds of the wheeled vehicle were determined. Then, based on the formulas of individual curves, their lengths were calculated, depending on the design speed and the radius of the circular arc. As a result of the research, the differences between the individual curves were obtained. Finally, it was found that due to the unconstrained movement of the vehicle on the road, all curves could be used as transition curves. By slightly adjusting their lengths, we can achieve the appropriate value of the increment of centripetal acceleration. The legitimacy of using different curves as transition curves lies primarily in their different geometric appearance. The choice of the curve to be used is based primarily on the terrain conditions and the type of the planned section of the route (serpentines, turnouts, etc.).

Keywords

• transition curve
• clothoid
• 3rd-degree parabola
• bernoulli lemniscate
• incremental centripetal acceleration