Non-linear method of determining vehicle pre-crash speed based on tensor B-spline products with probabilistic weights - Intermediate Car Class

Mateusz Krukowski; Przemysław Kubiak; Adam Mrowicki; Krzysztof Siczek; Jacek Gralewski

doi:10.1016/j.forsciint.2018.10.011

Non-linear method of determining vehicle pre-crash speed based on tensor B-spline products with probabilistic weights - Intermediate Car Class

Forensic Sci Int. 2018 Dec:293:7-16. doi: 10.1016/j.forsciint.2018.10.011. Epub 2018 Oct 24.

Authors

Mateusz Krukowski¹, Przemysław Kubiak², Adam Mrowicki³, Krzysztof Siczek³, Jacek Gralewski⁴

Affiliations

¹ Institute of Mathematics, Lodz University of Technology, Lodz, Poland.
² Department of Vehicles and Fundamentals of Machine Design, Lodz University of Technology, Lodz, Poland. Electronic address: przemyslaw.kubiak@p.lodz.pl.
³ Department of Vehicles and Fundamentals of Machine Design, Lodz University of Technology, Lodz, Poland.
⁴ Institute of Social Sciences and Management of Technologies, Lodz University of Technology, Lodz, Poland.

PMID: 30391668
DOI: 10.1016/j.forsciint.2018.10.011

Abstract

In the following study we consider the Intermediate Car Class. We apply a novel non-linear method, where the work W of car deformation is defined as an algebraic function of deformation ratio C_s. We use the data from the NHTSA (National Highway Traffic Safety Administration) database comprising numerous frontal crash tests. On the basis of this database, we determine the mathematical model parameters. In the so-called energetic approach, collisions are treated as non-elastic. The velocity threshold that defines the elastic collision was set to be 11km/h. Such an approach, which greatly simplifies our considerations, determines the linear dependence of energy lost during deformation on deformation coefficient C_s. The coefficient Cs is calculated as a weighted mean value of deformation points C₁-C₆. In this paper, the authors suggest a more precise non-linear method in order to determine the work of deformation.

Keywords: Car accidents; Car crash reconstruction; Crash test; Equivalent energy speed; Tensor product system.