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




active travel, injury risk function, Safe System, speed limit, Vision Zero


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.


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Author Biographies

Nils Lubbe, Autoliv Research, Sweden


Nils Lübbe is Director of Research at Autoliv Development AB, Sweden. His academic qualifications include Docent, PhD, and MSc from Chalmers University of Technology, Sweden. He has published over 70 journal and conference papers. His research interests include crash analysis and prevention as well as injury biomechanics on crash data analysis and safety system concepts.

Yi Wu, Autoliv Vehicle Safety System Technical Center, China

Yi Wu is a data scientist at Tesla. Previously, he was a traffic safety research engineer at Autoliv in China. He has a BSc in software engineering from Chongqing University, China and a MSc in business analytics from University of Bath, UK. He is experienced in data analysis and machine learning and has conducted crash data analysis with different databases such as the German In-Depth Accident Study (GIDAS) and the China In-Depths Accident Study (CIDAS).

Hanna Jeppsson, Autoliv Research, Sweden

Hanna Jeppsson is a traffic safety research engineer at Autoliv Development AB, Sweden. She has a BSc from University of Borås, Sweden. Her main research area is crash analysis for vulnerable road users, such as pedestrians and cyclists, but also including new mobility devices such as e-scooters. Hanna is particularly interested in modelling the relation between impact circumstances and injury outcome for these and other road users.


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How to Cite

Lubbe, N., Wu, Y., & Jeppsson, H. (2022). 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. Traffic Safety Research, 2, 000006.