Safe speeds: fatality and injury risks of pedestrians, cyclists, motorcyclists, and car drivers impacting the front of another passenger car as a function of closing speed and age

As crash speed increases, so does the probability of injury. The vulnerability of different road users varies greatly, in part due to differences in their protective equipment. Therefore, for the same speed, their injury probabilities are different. The objective of this study is to define injury risk curves, mathematical relations between closing speed (the relative speed between two crash partners) and injury outcome, for different road users. These risk curves can be used to rank road user vulnerability and define safe speeds, i.e. speeds not exceeding tolerable injury probabilities. Crashes involving pedestrians, cyclists, motorcyclists, and car drivers impacting the front of another passenger car (i.e. frontal impacts from the other car’s perspective) were extracted from the German in-depth accident study (GIDAS). The injuries were modelled as a function of closing speed and road user age using a weighted binary logistic regression. In accordance with the Abbreviated Injury Scale 2015 revision, three injury severities were modelled: at-least-moderate injury severities, at-least-serious injury severities, and fatal injuries. The constructed risk curves predicted injury outcomes with an average Area under the Curve ranging from 0.66 to 0.94 in cross-validation. A 10% risk of sustaining at-least-serious injuries corresponds to a closing speed of 29 km/h for pedestrians, 44 km/h for cyclists, 48 km/h for motorcyclists, and 112 km/h for car drivers. If a 10% risk of serious injury is acceptable, the closing speeds can be translated into safe speed limits of 25 km/h for cars with pedestrian encounters; 20 to 25 km/h for cyclists, motorcyclists, and cars when they encounter each other; and 55 km/h for cars in head-on impacts. These safe speeds align with current speed limits of 20 to 30 km/h in urban centers but bring into question the current practices of much higher speed limits on rural roads shared by bicycles, motorcycles, and cars. However, safe speed limits could be increased (maintaining a 10% serious injury risk) if road users have more protective equipment and Automated Emergency Braking reliably reduces impact speeds in all crash types.