**4. Discussion**

The main objective of the study is to examine the effect of the change in driver's centre of gravity due to various disabilities and the change in the points of support of the body due to the use of additional equipment on the driver's behaviour during a frontal collision. Due to the inability to carry out such studies through experimental tests, it was decided to employ a research methodology based on numerical analyses using the finite element method, with an explicit integration step. Thanks to FE studies, it was possible, among other things, to consider (in a virtual environment) the vulnerabilities of the car's interior structures, crucial from the point of view of the driver's behaviour, and of the dummy itself. A common approach to analyses of this type is to isolate a single phenomenon (with all the key elements) from the global system and to conduct studies on the influence of single parameters on the course of this phenomenon [19,21,32–34]. For frontal crash analyses aimed at assessing the driver's safety, this is most often a restriction of the numerical model to the area around the driver and modelling selected safety components such as seat belts [19,34] or an airbag. In this study the best possible reproduction of real objects and phenomena was sought, therefore a grea<sup>t</sup> deal of emphasis was placed on the use of the full characteristics of the car body delay during the collision, considering the deformation of the seat under the influence of the weight of the dummy, the friction between them, and the representation of the full operation of the seat belt system and the airbag. This was made possible by dividing the whole frontal impact into three phases—frontal impact of the car with a rigid barrier, subsidence of the dummy under the influence of gravity and the numerical analysis of the behaviour of the dummy inside an isolated part of the vehicle.

The authors were not able to carry out a validation test for the developed numerical models. Instead, the global model is built from smaller numerical models validated in independent tests [18,29]. In this study, a commercially approved numerical model of the dummy [35], an approved car model [36] and constitutive models of seat belts were used.

Frontal collisions, both full cars and selected vehicle parts, are very well documented in the literature. Nevertheless, the authors did not find any studies on the safety of disabled persons in the literature, so it is difficult to relate the results to other works.

In personal cars, the forces exerted on the body of a non-disabled driver during a frontal collision are asymmetrical. Excluding the asymmetrical positioning of the steering wheel in relation to the torso in many cars, asymmetry is mainly caused by the position of the legs and the operation of the seat belts. In the case of cars with automatic transmission, the right leg is usually set straight ahead or more inwards on the brake pedal during a

collision. The left leg rests on a footrest that in many cars is positioned to the left and is closer to the seat than the fully depressed brake pedal. Seat belts, on the other hand, restrict the movement of the left arm, which naturally causes the rotation of the driver's shoulders visible in Figure 11. This rotation increases until the torso rests on the airbag and the driver rebounds from it. From now on, the arms start to rotate in the opposite direction. The lower limbs mentioned previously also play a major role in the first stage of the collision, as the driver moves longitudinally to the seat and hits the space under the steering wheel with his knees. This is considered by vehicle designers at the development stage.

The introduction of additional equipment on the steering wheel or the amputation of the driver's limb affects the process described above. When analysing the position of the dummy at the moment of maximum longitudinal displacement relative to the seat (Figure 7) it can be seen that the use of additional equipment on the steering wheel or between the seats affects the position of the driver's body immediately before the collision. The stiffness of these elements is so low that it does not generate significant movement resistance for the driver. The limb amputation, however, changes the number of support points of the driver, both immediately before the collision and during the loss of his kinetic energy. In addition, if one of the lower limbs is amputated, the latter is automatically more likely to suffer an injury as it will hit the components under the steering wheel with more force.

The changes in the position of the centre of gravity, as shown in Figures 4 and 5, clearly indicate that the sole use of a disabled person's equipment has a slight effect on the change in the driver's centre of gravity. Amputation, in turn, results in a significant reduction in the weight of the entire driver and thus in a significant shift in the driver's centre of gravity. On the one hand, the reduction in the driver's weight means less kinetic energy to reduce, on the other hand, a change in body position affects the operation of safety systems.

Figure 8 shows the lateral displacement of the driver's H-point, which shows that the use of a steering wheel handle or additional Hand Control Unit results in no return to the initial position of the driver's pelvis after a rebound from the airbag. This is particularly evident at time t = 0.43 s when the driver hits the seat's backrest. This is a very negative phenomenon, as it can result in missing the headrest and suffering a serious neck injury. This effect is even stronger in the case of amputation of any of the limbs (Figures 9 and 10).

However, the use of additional equipment does not have a significant influence on the rotation of the arms (Figure 11). The amputation, especially of the left leg, both legs or right hand, does influence the rotation (Figures 12 and 13). In the case of the amputation of the right hand, the mass that causes the rotation by its inertia decreases significantly and thus the rotation diminishes. A similar diminished rotation in the initial phase of movement can be observed in the case of the amputation of the left leg or both legs. This is because the left leg rests on a footrest that is closer to the seat than the brake pedal pressed to the end. In the event of a collision, the leg pushes against its entire surface, while the right leg slides on the brake pedal. Thus, in the case of drivers without disabilities, the left leg increases the rotation, and in the case of a disabled driver, the lack of the limb reduces the rotation.

Lack of support for the left leg means that the belts and the airbag must carry more load (Figures 15 and 16), which may result in increased chest injuries. The analyses carried out showed that the other factors examined did not have a significant impact on the course of force between the dummy and the belts. The modifications made also had no significant impact on HICs.

To sum up, the contribution of this paper is to present a three-stage scheme for conducting numerical analyses of the behaviour of people inside a car during a crash. The article justifies the importance of each of the stages and the use of the results of each of them in the analysis of the entire phenomenon. The paper also presents a method of seat belts modelling aimed at a faithful representation of their actual operation. Describes an approach using a combination of 2D elements (in area of contact with the driver) and 1D elements (which enable the operation of the retractor, pretensioner and slipring). A detailed diagram of the operation of the slipring elements is also presented. Based on the modelling

performed, the paper presents the original results of analyses of the effect of changes in the position of the driver's centre of gravity caused by additional equipment for disabled people and amputations of the limbs on his behaviour during a frontal collision. Based on the results, it can be concluded that it is appropriate to carry out research aimed at assessing the safety of drivers using vehicles adapted to the needs of disabled people. The position of the driver immediately before the collision and the number of support points of the body affects his interaction with the safety systems and may affect his injuries.

Further work will be aimed at studying the impact of prostheses on the safety of a disabled driver.

**Author Contributions:** Conceptualization, K.S. and J.M.; methodology, K.S. and J.M.; software, K.S.; validation, K.S. and J.M.; formal analysis, K.S.; investigation, K.S.; resources, K.S.; data curation, K.S.; writing—original draft preparation, K.S.; writing—review and editing, K.S. and J.M.; visualization, K.S.; supervision, J.M.; project administration, K.S.; funding acquisition, J.M. All authors have read and agreed to the published version of the manuscript.

**Funding:** The article was written as part of the implementation of the university research gran<sup>t</sup> supported by Military University of Technology (No. UGB 22-748/2020).

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Conflicts of Interest:** The authors declare no conflict of interest.
