The deviation angle for one-lane roundabouts: A general mathematical formulation and application

Properly designed roundabouts may lead to safety improvements based on both reducing approaching speeds and controlling traffic. Measurements of deflection of vehicle trajectories are commonly used to estimate roundabout speed control. One of these measurements is the deviation angle, which is mentioned in both the Italian and Swiss road standards and, in specific conditions, can be more effective than other methods. This article presents a general mathematical formulation for linking several geometric parameters with the deviation angle in different rural and urban one-lane roundabout configurations, which is currently missing in the literature. For urban roundabouts, refuge islands for pedestrians and cyclists were considered. Based on the proposed formulation, a sensitivity analysis of the influential geometric parameters was conducted. Results suggest that an insufficient deflection of trajectories (deviation angle less than 45°) is always present for roundabouts with inscribed circle diameter less than 25 m; for urban roundabouts with refuge islands for pedestrians and cyclists having inscribed circle diameter less than 34 m and orthogonal legs; and for roundabouts with angles between opposite legs smaller than 140°. The main parameters which are responsible for a decrease in the deviation angle are: a decrease in the inscribed circle diameter; a decrease in the angle between opposite legs; and an increase in the width of the circulatory lane. Some optimized procedures for roundabout design, the generalized application of the deviation angle method and alternative speed control measures in cases of small deviation angles are discussed.