The Latest Research Findings on Vehicle Stiffness Coefficients

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Energy cannot be destroyed, only converted from one form to another. During a crash, the kinetic energy from a moving vehicle is converted into crush damage. When reconstructionists need to assess the severity of a crash, one of the tools at their disposal is the crush analysis method, which measures the amount of crush damage (permanent deformation) to the vehicle. Using “vehicle stiffness coefficients” in their calculations, experts are able to give more accurate answers regarding vehicle speed and speed change.

Figure 1 - A vehicle crushing during a crash test (Source: NHTSA).
Figure 1 - A vehicle crushing during a crash test (Source: NHTSA).

Stiffness Coefficients—What Do They Mean?

Vehicles of different size, weight, manufacturing year, and origin vary in how much they deform or “crush” when involved in a crash because they differ in stiffness. Cars crush like a spring in a can. The crush analysis method requires the crash reconstructionist to calculate two stiffness variables for the vehicle involved. The following values required for the crush analysis method can be calculated for specific vehicles using the data obtained from crash tests:

  • The “A” crush stiffness coefficient represents the beginning of the damage threshold, i.e. the maximum force (per unit of width) that can be sustained without producing any permanent crush.
  • The “B” crush stiffness coefficient represents the relatively linear relationship between the force and the amount of permanent crush. In other words, it is the ratio of the force per unit width (of the contact area) to the crush depth.

The A and B crush stiffness coefficients are then used along with the crush measurements of the vehicle(s) to calculate the speed changes experienced by the vehicle(s), which is a measure of the severity of the collision. These speed changes are correspondingly used to compute the impact speeds of the vehicle(s).

Stiffness Variables Depend on the Vehicle Generation, Make, and Model – but What Are the General Trends?

The front end of vehicles, in general, have become stiffer over the years; however, the general trend also appears to be currently stabilizing.

Stiffness coefficients did not significantly increase in the 1970s or the early 1980s. In fact, they declined slightly. From 1985 to 2004, stiffness coefficients nearly doubled, corresponding well with the development and implementation of government regulations regarding vehicle safety, as well as advancements in crashworthiness and automotive engineering. After 2004, stiffness coefficients continued to increase, but at a lower rate. Manufacturers were shifting their focus to other ways of improving occupant compartment crash worthiness and supplemental safety restraints (such as multiple airbags and rollover safety).

In general, the stiffest vehicles are SUVs, followed by vans, then pickups, and, finally, sedans. European vehicles were found to be slightly stiffer than American and Japanese/Korean vehicles.

Conclusion: Why Do Stiffness Trends Matter?

While reconstructionists will generally calculate or otherwise attempt to obtain the stiffness coefficients for the exact vehicle year, make, and model involved, sometimes there is no specific crash test data available for that vehicle. Additionally, sometimes little is known about one of the involved vehicles (such as in a hit and run). In these situations, it is useful for reconstructionists to have trends (and average A and B crush stiffness coefficients) to rely on in their calculations.


We would like to thank Sam Kodsi, B.Eng., P.Eng., Sarah Selesnic, Shady Attalla, P.Eng., CFEI, and Avery Chakravarty for providing insight and expertise that greatly assisted this research.

More About J.S. Held’s Contributors

Sam Kodsi is a Consulting Forensic Engineer in J.S. Held's Accident Reconstruction Practice. Mr. Kodsi has been active in automotive engineering safety since 1995 and has specialized in Accident Reconstruction since 1997. He has been involved in more than 5,000 technical investigations and has been the lead engineer in more than 4,000 reconstructions involving motor vehicle collisions and other personal injury incidents. Mr. Kodsi has been involved in peer-reviewed research and testing and has qualified to provide expert evidence in the Ontario Court of Justice, Superior Court of Justice and in Arbitrations in the following areas: accident reconstruction (dynamics & speeds), biomechanics, mechanical failures, collision consistency, and driver perception and response.

Sam can be reached at [email protected] or +1 416 977 0009.

Shady Attalla is a Vice President of Engineering in J.S. Held's Accident Reconstruction Practice. He has been an active member of the accident reconstruction industry since 2008. Mr. Attalla has been involved in more than 1200 technical investigations and has been the lead engineer in more than 700 technical investigations involving automobiles, pedestrians, cyclists, motorcycles, and mechanical failures. His specialty areas are driver and pedestrian behaviour, damage consistency analysis, and investigations of material failures. Mr. Attalla is a published author and has qualified to provide expert evidence in the Ontario Court of Justice.

Shady can be reached at [email protected] or +1 416 977 0009.

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This publication is for educational and general information purposes only. It may contain errors and is provided as is. It is not intended as specific advice, legal, or otherwise. Opinions and views are not necessarily those of J.S. Held or its affiliates and it should not be presumed that J.S. Held subscribes to any particular method, interpretation, or analysis merely because it appears in this publication. We disclaim any representation and/or warranty regarding the accuracy, timeliness, quality, or applicability of any of the contents. You should not act, or fail to act, in reliance on this publication and we disclaim all liability in respect to such actions or failure to act. We assume no responsibility for information contained in this publication and disclaim all liability and damages in respect to such information. This publication is not a substitute for competent legal advice. The content herein may be updated or otherwise modified without notice.

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