**1. Introduction**

Over a billion people live with some form of disability, which represents 15% of the world's population [1]. Between 110–190 million adults have very significant difficulties in functioning. Rate of disability is increasing. According to [2], approximately 2% of road accidents in Spain result in moderate, serious or total disability. The authors of [2] point out that the acquisition of a disability is associated with a reduced ability to work, greater functional dependence, greater need for assistance, and the need for family support.

Technological and medical developments make it possible to extend and improve quality of life. A grea<sup>t</sup> deal of attention has been paid in recent years to activating older people and people with disabilities (DP—disabled persons). Researchers from all over the world carry out research related to different aspects of DPs' lives, looking, for example, at how they spend their leisure time [3], how well the infrastructure fits their needs [4–6], or their preferences when making choices [7]. These people in many cases possess valuable skills. Understanding the specific requirements of this social group allows the development of technical solutions that remove barriers that prevent them from active functioning, socially and professionally. This will enable the public to benefit from these skills.

Among the many factors influencing the professional and social activation of people with disabilities, aspects related to the mobility of DPs and the adaptation of existing systems of transportation to the needs of older and disabled people are often mentioned [5,8]. While in large cities, DPs can count on public transport adapted to their needs, in smaller towns and villages DPs are practically dependent on having individual means of transport or on third parties to provide them. One possible solution of this problem is the individual adaptation of a car to the needs of the particular person with disabilities [9]. However, it should be considered to ensure that any structural changes made do not result in reduced road safety, other people, and disabled driver.

Among many causes of road accidents, the human factor is indicated as one of the main ones [10]. It is difficult to eliminate all the imperfections and limitations of the physical driver, but thanks to technological developments, the driver has more and more systems to support his actions. Among these are constantly developed active safety systems. Their use, combined with appropriate training of drivers to operate them, can significantly reduce the number of road accidents [11,12].

New solutions for use in the automotive industry must be tested in accordance with product standards. The most extensive testing applies to new vehicles, as each must pass very stringent tests before it can be put into road traffic. Of course, cars on the market have varying levels of safety (depending, among other things, on the number of active driver assistance systems), but any new car that does not meet the minimum requirements cannot be put on the road. Another point worth noting is that new cars are designed with the average consumer in mind, and tests are carried out for the chosen body configuration and weight of the occupants. Therefore, modification of the vehicle by changing the steering equipment or adjusting the car for a person with a physique significantly different from the one assumed during design, requires additional tests [13].

There are now very many methods in use for analysing dangerous situations that may occur on the road. Experimental research is undoubtedly the most important of these. Their disadvantage is the very high unit cost of each test and restrictions on carrying out certain measurements. Therefore, a very popular method of verifying the operation of technical objects is the numerical analysis [14–18]. Testing in virtual space allows for evaluating the structure in a short period of time in order to check the compliance with many standards [19,20], and for predicting the structure's behaviour in different load scenarios. The lack of the need to physically build new prototypes and prepare experimental research also allows for significant financial savings. An additional advantage of computer simulations is the possibility to record more data than in the case of experimental studies [21].

Many different numerical tools are currently available for analyzing dangerous traffic situations [22]. One of the fastest are calculations using analytical formulae that take into account, among other things, the velocity, weight and stiffness of vehicles [23–25]. They allow many scenarios to be analyzed in a very short time and, when supplemented with a reliable vehicle database, make it possible to assess a real accident. An additional advantage of analytical methods is the possibility of transferring the loads acting on the driver to 3D models and further local analysis of his behavior.

Another fast and accurate method based on Reduced Order Dynamic Model [26], in which discretization of vehicle's perimeter takes place only in a 2D environment. It reduces the number of equation and thus reduce time calculation.

Analytical and 2D models do not allow an accurate analysis of driver behavior. Therefore, if the aim of the study is to determine e.g., injuries to the driver, methods based on multibody analyzes [19] or FEM are used [27]. The big disadvantage of these methods is the long calculation time. To reduce it, it is possible to use different strategies. One of them is an approach in which a global collision is analyzed using analytical or 2D models and the results are transferred to 3D models and further analysis of only a selected area. A second solution is to use multi-stage analyses, in which selected aspects of a hazardous road event are investigated independently.

### **2. Materials and Methods**

### *2.1. Numerical Research Strategy*

The main objective of this article is to examine the impact of the change in the position of the driver's mass, caused by various types of disabilities or the use of specialist equipment, on the driver's biomechanical parameters. Additional objectives are to show how to model selected elements of car safety systems and to draw attention to possible changes in the driver's biomechanics related to the adaptation of the car to the needs of the disabled.

This article is a continuation and development of models described in the work [28]. The paper uses a three-stage scheme of numerical tests (Figure 1), in which the first stage is to carry out an analysis of the frontal impact of the validated full car model [28]. Based on these analyses, the change of velocity of the vehicle interior, which is used in the third stage, is determined. The second stage involves subsidence a dummy on the seat while resting its limbs on the floor, the steering wheel or a special handle mounted on the steering wheel and the manual gas and brake control unit. The subsidence is a very important process. It involves the dummy falling under the gravity load on the interior elements of the vehicle. This deforms the structure of e.g., the seat and causes forces between them, which are transferred to the third stage. The magnitude of these forces directly affects the magnitude of the friction forces and thus the behaviour of the dummy during the impact.

**Figure 1.** Numerical research strategy [28].

For numerical simulations carried out using the LS-Dyna system, two approaches to the realisation of this stage are popular. The former involves positioning the dummy in a roughly approximate position, positioning the belts and performing dynamic relaxation [18,29]. The advantage of this approach is its low numerical cost and rather low level of complexity. During the analysis, additional damping is added, which facilitates and shortens the subsidence process (oscillations of the manikin's position are dampened much faster). The dynamic relaxation is performed immediately before the actual numerical analysis, and the analysis time after the relaxation is 0.0 s, so there is no need to define appropriate shifts in numerical procedures defined later. Strains and deformations from dynamic relaxation are transferred automatically to the target analysis.

The second approach involves carrying out a full analysis of the subsidence process of the dummy (using an explicit or implicit time integration) [30,31]. In such analysis the dummy, under the influence of gravity, falls on the interior elements of the vehicle. The result is a file containing, for the time corresponding (termination time), the state of deformation, stresses and forces acting between the individual elements. Starting the collision analysis requires a full restart, which includes the procedure of loading the state from the end of the subsidence analysis (as an external file with the option stress initialisation), changing the initial (boundary change, etc.), boundary and inducement conditions by defining appropriate cards (preparing a new model file).

A simpler and less demanding method in terms of computer power is one that uses dynamic relaxation. However, it is limited by the problems with the safety belt retractor. During dynamic relaxation it is performed to a limited extent, which may result in a lack of adequate belt tension at the beginning of the final crash analysis. Therefore, the authors decided on an approach involving the performance of a full subsidence analysis using explicit time integration (stage 2 in Figure 1).

### *2.2. Numerical Model Description*

In the numerical models developed by the authors, grea<sup>t</sup> emphasis has been placed on considering key elements of safety systems that can influence the behaviour of the driver's body during a frontal collision, while at the same time applying simplifications that do not significantly affect his behaviour. Therefore, on the basis of previously conducted research, it was decided to model only a section of the vehicle and give it the properties of a rigid body [28]. Deformable seat, steering wheel handle, airbag and seat belts were modelled inside the vehicle [28] (Figure 2).

**Figure 2.** Numerical model used in simulations.

The seat belts were modelled on the basis of previously conducted experimental research [18,28,29]. Their arrangemen<sup>t</sup> was carried out using the seatbelt fitting procedure, available in the LS-Prepost pre-processor. Belts were modelled as 2D elements (for parts where their contact with the dummy is important) and as 1D elements for parts near attachment points (Figure 3). The lower belt is rigidly attached to the vehicle body on the right-hand side of the driver and to the ear connected to the seat base on the right. The function of the ear is performed by a special seatbelt slipring numerical element [30,31], thanks to which the shortening of one 1D element can be transformed into an extension of the other 1D element. The relation between the displacements of the ends of the two connected belts (Figure 3) is described using the following equation:

$$\mathbf{x}\_1 = \mathbf{x}\_2 + \Delta \mathbf{l}\_1 + \Delta \mathbf{l}\_2 \tag{1}$$

$$
\Delta \mathbf{l}\_1 = (\mathbf{F}\_1 \cdot \mathbf{l}\_1) / (\mathbf{A}\_1 \cdot \mathbf{E}\_1) \tag{2}
$$

$$
\Delta \mathbf{l}\_2 = (\mathbf{F}\_2 \cdot \mathbf{l}\_2) / (\mathbf{A}\_2 \cdot \mathbf{E}\_2) \tag{3}
$$

$$\mathbf{x}\_1 = \mathbf{x}\_2 + (\mathbf{F}\_1 \cdot \mathbf{l}\_1) / (\mathbf{A}\_1 \cdot \mathbf{E}\_1) + (\mathbf{F}\_2 \cdot \mathbf{l}\_2) / (\mathbf{A}\_2 \cdot \mathbf{E}\_2) \tag{4}$$

$$\mathbf{F\_1 = F\_2 + F\_3 = F\_2 + F\_1 \cdot \mu = F\_2 / (1 - \mu)}\tag{5}$$

where: x1, x2—displacement of the ends of 1D seat belts elements, Δl1, Δl1—elongation and shortening of connected elements, F1, F2—tensioning force, A1, A2—cross section of elements, E1, E2—Young modulus of elements, Ft—friction force in slipring, μ—coefficient of friction.

**Figure 3.** Numerical model of seatbelts.

If both belts (bottom and top) are made of the same material, the final formula is as follows.

$$\mathbf{x}\_{1} = \mathbf{x}\_{2} + \left( (\mathbf{F}\_{2}/(1-\mu)) \cdot \mathbf{l}\_{1} + \mathbf{F}\_{2} \cdot \mathbf{l}\_{2} \right) / \ (\mathbf{A} \cdot \mathbf{E}) = \mathbf{x}\_{2} + (\mathbf{F}\_{2} \cdot (\mathbf{l}\_{1}/(1-\mu) + \mathbf{l}\_{2})) / \ (\mathbf{A} \cdot \mathbf{E}) \tag{6}$$

Thanks to the use of this type of numerical element, the "shortening" of the lower belt can be turned into the "lengthening" of the upper belt, i.e., it is possible to implement the rewinding of the belt through the assembly eye. In the developed numerical models, the upper belt starts and ends with the slipring elements. In the upper attachment, the belt changes direction and is connected to the attachment point in the lower part of the vehicle body, in which the elements representing the pretensioner and retractor are modelled. When modelling seat belts, the position of the attachment points should not be changed in relation to the points in the actual car, as this changes the length of the belt, which in turn affects its global deformation under the influence of force.

In numerical models, the pretensioner has been modelled using the SEATBELT\_ RETRACTOR [30,31] type element that generates constant belt tension up to the pullout force limit above which the retractor locks. The retractor is also locked when the pretensioner (SEATBELT\_PRETENSIONER [30,31]) is activated, which retracts the belt until it reaches the user-defined belt tension limit. In these cases, the belt was activated by an acceleration sensor (SEATBELT\_SENSOR) which registers the front acceleration of the vehicle. When the acceleration of 25.0 m/s<sup>2</sup> was exceeded, the sensor activated the pretensioner. The retractor and the pretensioner operate numerically similarly to the rewinder, with the difference that the shortening of the belt is not converted into the lengthening of another belt but is recorded as the retracted length of the belt.

## *2.3. Analysed Cases*

During the research, three main groups of drivers were analysed: without disabilities (RD-reference driver), with disabilities requiring the use of a special steering wheel handle (H—group, HB—handle basic) and with a steering wheel handle and a manual gas and brake control unit (C—group, CB—control unit basic) (Figure 4). The use of specialist equipment may be required by various disabilities, such as paralysis or lack of a limb. Therefore, the HB and CB dummies have been modified so that it is possible to perform

analyses for limbless dummies (Figure 5). The limb amputation, when compared to the paralysis, from the frontal impact analysis point of view primarily changes the position of the body's centre of gravity and reduces the areas of contact between the body and the vehicle interior. Figures 4 and 5 show the changes in the driver's mass (dm) and centre of gravity position for each of the analysed cases in the global coordinate system (dx, dy, dz).

**Figure 4.** First stage of dummy model modifications.

**Figure 5.** Second stage of dummy model modifications.

An individual subsidence analysis was conducted for each of the cases studied, preceded by positioning the dummy in an estimated target position. In each group, the initial setting was identical, so that only the impact of amputation of a given limb was examined.
