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.


Download data is not yet available.

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.


AAAM (2016) The Abbreviated Injury Scale. Association for the Advancement of Automotive Medicine. 2015 revision:

Academic Expert Group (2019) Saving Lives Beyond 2020. Swedish Transport Administration. TRV 2019:209:

Bahouth, G., J. Graygo, K. Digges, C. Schulman, P. Baur (2014) The Benefits and Tradeoffs for Varied High-Severity Injury Risk Thresholds for Advanced Automatic Crash Notification Systems. Traffic Injury Prevention 15 (Supplement 1), 134-140. DOI:

Bahrololoom, S., W. Young, D. Logan (2020) Modelling injury severity of bicyclists in bicycle-car crashes at intersections. Accident Analysis & Prevention 144, 105597. DOI:

Bareiss, M., H. C. Gabler (2020) Estimating near side crash injury risk in best performing passenger vehicles in the United States. Accident Analysis & Prevention 138, 105434. DOI:

BMDV (2021) Germany 2030 - a cycling nation. National Cycling Plan 3.0. Federal Ministry for Digital and Transport:

Davis, A. L., D. Obree (2020) Equality of restraint: Reframing road safety through the ethics of private motorised transport. Journal of Transport & Health 19, 100970. DOI:

Davis, G. A. (2001) Relating Severity of Pedestrian Injury to Impact Speed in Vehicle-Pedestrian Crashes: Simple Threshold Model. Transportation Research Record 1773 (1), 108-113. DOI:

Destatis (2019) Verkehrsunfälle. Statistisches Bundesamt. Fachserie 8 Reihe 7:

Ding, C., M. Rizzi, J. Strandroth, U. Sander, N. Lubbe (2019) Motorcyclist injury risk as a function of real-life crash speed and other contributing factors. Accident Analysis & Prevention 123, 374-386. DOI:

Doecke, S. D., M. R. J. Baldock, C. N. Kloeden, J. K. Dutschke (2020) Impact speed and the risk of serious injury in vehicle crashes. Accident Analysis & Prevention 144, 105629. DOI:

Dozza, M., R. Schindler, G. Bianchi-Piccinini, J. Karlsson (2016) How do drivers overtake cyclists? Accident Analysis & Prevention 88, 29-36. DOI:

EC (2018) Annual Accident Report. European Commission, Directorate General for Transport

ECMT (2004) National Policies to Promote Cycling. European Conference of Ministers of Transport:

ETSC (2020) How safe is walking and cycling in Europe? European Transport Safety Council. PIN Flash Report 38:

Eugensson, A., J. Ivarsson, A. Lie, C. Tingvall (2011) Cars are Driven on Roads, Join Visions and Modern Technologies Stress the Need for Co-operation. 22nd International Technical Conference on the Enhanced Safety of Vehicles (ESV), Washington DC, USA

Forman, J., G. S. Poplin, C. G. Shaw, T. L. McMurry, K. Schmidt, J. Ash, C. Sunnevang (2019) Automobile injury trends in the contemporary fleet: Belted occupants in frontal collisions. Traffic Injury Prevention 20 (6), 607-612. DOI:

Forman, J. L., T. L. McMurry (2018) Nonlinear models of injury risk and implications in intervention targeting for thoracic injury mitigation. Traffic Injury Prevention 19 (sup2), S103-S108. DOI:

Gabauer, D. J., H. C. Gabler (2006) Comparison of delta-v and occupant impact velocity crash severity metrics using event data recorders. Annual proceedings/association for the advancement of automotive medicine:

Götschi, T., J. Garrard, B. Giles-Corti (2015) Cycling as a Part of Daily Life: A Review of Health Perspectives. Transport Reviews 36 (1), 45-71. DOI:

Hautzinger, H., M. Pfeiffer, J. Schmidt (2004) Expansion of GIDAS Sample Data to the Regional Level. Proceedings of Expert Symposium on Accident Research

He, H., Y. Ma (Eds.) (2013) Imbalanced learning: foundations, algorithms, and applications. John Wiley & Sons. ISBN 978-1-118-07462-6 DOI:

Hu, J., K. D. Klinich (2015) Toward designing pedestrian-friendly vehicles. International Journal of Vehicle Safety 8 (1), 22. DOI:

Hussain, Q., H. Feng, R. Grzebieta, T. Brijs, J. Olivier (2019) The relationship between impact speed and the probability of pedestrian fatality during a vehicle-pedestrian crash: A systematic review and meta-analysis. Accident Analysis & Prevention 129, 241-249. DOI:

Isaksson-Hellman, I., J. Werneke (2017) Detailed description of bicycle and passenger car collisions based on insurance claims. Safety Science 92, 330-337. DOI:

ISO (2020) Road vehicles—Traffic accident analysis— Part 1: Vocabulary. International Organization for Standardization. 12353-1:2020:

ITF/OECD (2008) Towards Zero. Ambitious road safety targets and the Safe System approach. International Transport Forum:

ITF/OECD (2018) Road Safety Annual Report 2018. International Transport Forum:

ITF/OECD (2019) Road Safety in European Cities: Performance Indicators and Governance Solutions. International Transport Forum Policy Papers:

Jacobsen, P. L., F. Racioppi, H. Rutter (2009) Who owns the roads? How motorised traffic discourages walking and bicycling. Injury Prevention 15 (6), 369-373. DOI:

Jeppsson, H., N. Lubbe (2020) Simulating Automated Emergency Braking with and without Torricelli Vacuum Emergency Braking for cyclists: Effect of brake deceleration and sensor field-of-view on accidents, injuries and fatalities. Accident Analysis & Prevention 142, 105538. DOI:

Jurewicz, C., A. Sobhani, J. Woolley, J. Dutschke, B. Corben (2016) Exploration of Vehicle Impact Speed – Injury Severity Relationships for Application in Safer Road Design. Transportation Research Procedia 14, 4247-4256. DOI:

Kleinbaum, D. G., K. Dietz, M. Gail, M. Klein, M. Klein (2002) Logistic Regression. Springer-Verlag

Kullgren, A., A. Axelsson, H. Stigson, A. Ydenius (2019) Developments in Car Crash Safety and Comparisons Between Results From Euro NCAP Tests and Real-World Crashes. 26th International Technical Conference on the Enhanced Safety of Vehicles (ESV), Eindhoven, Netherlands:

Larsson, P., S. W. A. Dekker, C. Tingvall (2010) The need for a systems theory approach to road safety. Safety Science 48 (9), 1167-1174. DOI:

Liers, H. (2018) Traffic Accident Research in Germany and the German In-Depth Accident Study (GIDAS). ACMA-SIAM-VDA Conference On Safer & Sustainable Road Transportation, New Delhi, India:

NHTSA (2020) Overview of Motor Vehicle Crashes in 2019. National Highway Traffic Safety Administation's National Center for Statistics and Analysis. DOT HS 813 060:

Niebuhr, T., M. Junge (2017) Detection of the toughest: Pedestrian injury risk as a smooth function of age. Traffic Injury Prevention 18 (5), 537-543. DOI:

Niewöhner, W., F. Roth, J. Gwehenberger, C. Gruber, M. Kuehn, R. Sferco, C.-H. Pastor, U. Nagel, M. Stanzel (2011) Proposal for a Test Procedure of Assistance Systems Regarding Preventive Pedestrian Protection. 22nd International Technical Conference on the Enhanced Safety of Vehicles (ESV), Washington, DC, USA

Nilsson, P., H. Stigson, M. Ohlin, J. Strandroth (2017) Modelling the effect on injuries and fatalities when changing mode of transport from car to bicycle. Accident Analysis & Prevention 100, 30-36. DOI:

Nishimoto, T., K. Mukaigawa, S. Tominaga, T. Kiuchi (2015) Development of AACN algorithm for pedestrian and cyclist. Transactions of Society of Automotive Engineers of Japan 46 (6), 1123-1129.

Otte, D., C. Krettek, H. Brunner, H. Zwipp (2003) Scientific approach and methodology of a new in-depth investigation study in Germany called GIDAS. 18th International Technical Conference on the Enhanced Safety of Vehicles (ESV), Nagoya, Japan

Pfeiffer, M., J. Schmidt (2006) Statistical and methodological foundations of the GIDAS accident survey system. Expert Symposium on Accident Research (ESAR), Hannover, Germany:

Pucher, J., R. Buehler (2010) Walking and Cycling for Healthy Cities. Built Environment 36 (4), 391-414. DOI:

Rosén, E. (2013) Autonomous emergency braking for vulnerable road users. International Research Council on the Biomechanics of Injury (IROCBI) Conference, Gothenburg, Sweden:

Rosén, E., U. Sander (2009) Pedestrian fatality risk as a function of car impact speed. Accident Analysis & Prevention 41 (3), 536-542. DOI:

Rosén, E., U. Sander (2010) Influence of impact speed estimation errors on pedestrian fatality risk curves. Expert Symposium on Accident Research (ESAR), Hannover, Germany:

Rosén, E., H. Stigson, U. Sander (2011) Literature review of pedestrian fatality risk as a function of car impact speed. Accident Analysis & Prevention 43 (1), 25-33. DOI:

Schmitt, K.-U., P. F. Niederer, D. S. Cronin, B. Morrison Iii, M. H. Muser, F. Walz (2019) Trauma Biomechanics: An Introduction to Injury Biomechanics. Springer. ISBN 978-3-030-11659-0. DOI:

Schramm, S. (2011) Methode zur Berechnung der Feldeffektivität integraler Fußgängerschutzsysteme. PhD thesis. Technical University Munich:

Spitzhüttl, D. I. F., D. I. H. Liers (2016) Methodik zur Erstellung von Verletzungsrisikofunktionen aus Realunfalldaten

Stigson, H., A. Kullgren, E. Rosén (2012) Injury risk functions in frontal impacts using data from crash pulse recorders. Annals of Advances in Automotive Medicine/Annual Scientific Conference:

Strandroth, J., S. Sternlund, A. Lie, C. Tingvall, M. Rizzi, A. Kullgren, M. Ohlin, R. Fredriksson (2014) Correlation Between Euro NCAP Pedestrian Test Results and Injury Severity in Injury Crashes with Pedestrians and Bicyclists in Sweden. 58th Stapp Car Crash Conferences. DOI:

Tarriere, C. (1995) Children are not miniature adults. International Research Council on the Biomechanics of Injury (IRCOBI), Brunnen, Switzerland:

Tight, M., M. Page, A. Wolinski, R. Dixey (1998) Casualty reduction or danger reduction: conflicting approaches or means to achieve the same ends? Transport Policy 5 (3), 185-192. DOI:

Trafikverket (2016) Trafikverkets årsredovisning 2016. Swedish Transport Administration. 2017:095:

Wisch, M., M. Lerner, J. Kovaceva, A. Bálint, I. Gohl, A. Schneider, J. Juhasz, M. Lindman (2017a) Car-to-cyclist crashes in Europe and derivation of use cases as basis for test scenarios of next generation advanced driver assistance systems – Results from PROSPECT. 25th International Technical Conference on the Enhanced Safety of Vehicles (ESV), Detroit, USA:

Wisch, M., M. Lerner, E. Vukovic, D. Hynd, A. Fiorentino, A. Fornells (2017b) Injury Patterns of Older Car Occupants, Older Pedestrians or Cyclists in Road Traffic Crashes with Passenger Cars in Europe – Results from SENIORS. International Research Council on Biomechanics of Injury (IRCOBI) Conference, Antwerp, Belgium:




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.