# Modeling Head-On Collisions: The Problem of Identifying Collision Parameters
## 1 Introduction  
One of the crucial problems accompanying the automotive sector development are road accidents resulting in human and material loss. Such events involve material loss and a loss of life. In 2018, in Poland, as many as 31,674 road accidents were reported, in which 2862 people were killed and 37,359 were injured. However, in the corresponding period, the total of 436,414 road collisions resulted only in material loss. The events classified as collisions of vehicles in motion, which accounted for 53.8% of all the accidents, were found to be most common. As many as 44.3% of all the people were killed in car crashes, and 58.6% were injured. There were 3104 head-on collisions, resulting in 510 deaths and 4676 people suffering injuries. In Poland, the death rate for every 100 accidents was found to be the highest in all the European Union member states in 2017 (8.6). The country which came right after Poland is Greece, with the rate of 6.7, whereas Germany had the lowest rate, at 1.1 [1], which suggests that Poland faces a serious road traffic safety problem to be urgently addressed. Next to the human loss, one must also remove the material damage, repair the vehicles damaged in road accidents and collisions. Usually, only accidents involving material losses of road accidents and collisions are considered, whereas insurance companies are involved in compensation of both material and human loss related to the outcomes of accidents delayed in time. As such, they do not focus only on road accidents but also on road collisions and the subsequent costs of repairs. The costs of spare parts, painting, and man-hours for the post-accident vehicle repair are calculated from the car damage analysis. In Europe, the USA, and Canada one must follow the requirements providing for the impacts of cars with a rigid barrier. Another study [2] discusses the vehicle superstructure designing method to developthe guidelines for the application of bumper beams and impact energy absorbers. The study also covered the head-on collision with rigid barriers. The low-speed collision requirements by the Insurance Institute for Highway Safety (IIHS) and Dunner tests, considered in this study, are demonstrated in Figure 1.  
For insurance companies, prior to the payment of damages for the car to be repaired, it is also very important to determine whether they are liable for damages or not. For that reason, in the process of insurance claim settlement, insurance companies usually use professional assessments provided by experts ordered by courts and public prosecutors to establish liability for the consequences of road accidents. Currently, the assessors use simulation programs to reconstruct road accidents, so manual calculations are hardly used. Adequate simulation results are of key importance as using incorrect simulation results leads to inadequate decisions in terms of liability for damages, which also triggers some legal effects for the parties to a car repair damages court case. The highest calculation accuracy is provided by programs with finite elements method modeling; the FEM convention, e.g., Abaqus, and LS-Dyna. Another study [3] uses LS-Dyna program for researching the vehicle structure stiffening elements during head-on collision. The test involved a Sport Utility Vehicle (SUV), very popular in China. The vehicle Finite Element (FE) model was initially validated against a full-frontal rigid barrier impact test by National Crash Analysis Center (NCAC). The study included also a head-on collision with a rigid barrier. A satisfactory compliance of the test and simulation deformations for each such collision was found (Figure 2). Figure 1: Requirements for low-speed collisions by the Insurance Institute for Highway Safety (IIHS) and Dunner tests. Figure 2: Deformations of the car in test and simulation. Other authors [4] report on using LS-Dyna program for the vehicle front protection system (VFPS).