Modelling duration of car-bicycles overtaking manoeuvres on two-lane rural roads using naturalistic data

•Bayesian predictive models for overtaking duration to cyclists were developed.•Car-bicycle overtaking duration affects safety and traffic operation on rural roads.•Road, cyclists, and manoeuvre related factors influence the overtaking duration.•Flying overtaking strategy to cyclists was more prevalent than accelerative.•Overtaking manoeuvres naturalistic data were collected using instrumented bicycles. Nowadays, Spanish two-lane rural roads frequently accommodate sport cyclists. They usually ride on the shoulder or on the right edge of the lane, sharing the infrastructure with motorised vehicles. Due to the speed difference between road users, the most frequent and dangerous interaction is in overtaking manoeuvres. One key factor from a safety and traffic operation point of view is the overtaking duration. The main aim of this paper is to analyse how factors related to the road, the cyclists, and the overtaking manoeuvre influence the duration of overtaking to cyclists on two-lane rural roads. Naturalistic field data were obtained using instrumented bicycles. Seven groups of cyclists, formed by different numbers of cyclists riding in-line and two-abreast, rode along five rural roads with different geometric and traffic characteristics. A total of 1592 flying manoeuvres, in which drivers did not reduce their speed, and 192 accelerative manoeuvres were analysed. The overtaking duration, considering each overtaking strategy, was modelled using Bayesian statistics. Results showed that flying manoeuvres were more prevalent than accelerative. They were performed with higher speeds and lower lateral clearances and, therefore, presented lower overtaking durations. For both overtaking strategies, duration increased on wider roads and with a larger size of the group. The presence of an oncoming vehicle decreased the overtaking duration. However, other factors presented opposite effects on the duration depending on the overtaking strategy. The developed predictive models allow obtaining overtaking durations varying road and cyclist grouping characteristics. Results can be used by road administration to manage and propose some specific countermeasures to integrate the cyclists in a safe and efficient way on two-lane rural roads.