**3. Results**

A crash test of Mercedes Benz C300 4Matic AWD from 2013, published by National Highway Tra ffic Safety Administration [20] was used to identify the impact parameters. The car tested was involved in a head-on collision with a rigid barrier (overlap 100%) with the speed of 56.3 km/h. The total mass of the vehicle was 1703 kg, its length: 4.581 m, its width: 1.770 m, its wheel base: 2.760 m, the front axle: 1.549 m and the rear axle: 1.552 m, the height above the ground: 0.552 m, the moments of inertia: roll 605 kgm3, pitch: 2700 kgm3, and yaw: 2771 kgm3. The test was recorded from above and from the right and left sides of the vehicle, as well as from the bottom.

In practice, the experts and assessors have problems obtaining the experimental data to be used in the simulation calculation of a reconstructed road accident. To acquire the data, a research method involving measurements of the vehicle body position during an impact from the crash test film has been proposed. Crash tests are recorded with fast video cameras facilitating the separation of particular frames (images) of the moving vehicle, even every 1 ms. First, the assessor should, of course, establish precise technical data of the vehicle involved in the accident. A precise data determination is very important as, according to the author, it is the assessor's further task to find a crash test of a vehicle with structure similar to the one which was involved in the accident. Only then can they go on to separate all the single images from the video, preferably, every 1 ms. Next, they should adjust the scale of the vehicle images to its vector styling, which is in scale and depicts details of the car body. A division into images (frames) can be performed with programs designed for this kind of film processing, whereas precise scaling is possible with the use of the V-SIM program. For this purpose, a single image needs to be imported to the program, and the size of a vehicle image needs to be matched with its vector styling; those stylings, in turn, are imported from external databases. For the purpose of this study, the styling of the Mercedes available in the AutoView database was used. The vehicle scale tapes can be applied in crash tests, as well as technical data, including the width, length, and the axle base.

According to the research procedure proposed, after scaling, it is necessary to start the analysis with the image depicting the moment of contact consistent with simulation time being *t* = 0 ms. The results of the image scaling at the moment of contact corresponding to the beginning of simulation are presented in Figure 7a. Measuring the vehicle body position changes, it is necessary to consider the vehicle elements which do not undergo deformation in the picture; the analysis accepts the roof edge near the windscreen. No universal rule can be used here due to di fferent kinds of impacts and di fferent zones of body deformation. It is more di fficult to scale the image of the undercarriage, and one must focus on a selected well-visible element. The rear part of the engine supporting frame, close to the gear box, was selected for analysis.

**Figure 7.** Scaled image of the vehicle with a coordinate system connected with the vehicle (**a**) and rigid area preview on its vector styling projection (**b**).

In Figure 7b, a rigid area preview is presented on a projection of a vector styling of a Mercedes. However, in this program, the changes in the vehicle body positions were measured in a system, the center of which is in the middle of the vehicle mass. Axis *x'* of this system is directed in the forward-facing position of the car, axis *y'* runs left clockwise, and axis *z'* runs vertically, upward.

After scaling the images, according to the proposed research procedure, a simulation with default impact parameters, proposed by the V-SIM program, started. The results are presented in Figure 8a–c. After the measurements, an impact simulation was performed for the crash test parameters, and the results are presented in Figure 8d–f.

**Figure 8.** Comparison of car projections with recorded images for default data: *t* = 50 ms (**a**), *t* = 150 ms (**b**), *t* = 300 ms (**c**) and identified data: *t* = 50 ms (**d**), t = 150 ms (**e**), and t = 300 ms (**f**).

A comparison of the simulation results for the program default data with data identified from the crash test shows that the positions of vehicles were similar only in the initial phase. In time *t* = 50 ms, the stylings of the simulated vehicles are similar, and they overlap with the image of the real vehicle at the edge of the roof, near the windscreen (Figure 8a–d). However, over time, an error of the vehicle position develops for the program default data. In time *t* = 150 ms, the vehicle simulated for default data is definitely shifted forward in relation to the actual one; the edges of the roof near the windscreen do not overlap (Figure 8b), whereas, for a vehicle simulated for the data identified, entered into the program, a consistence of the position with the real vehicle was obtained (Figure 8e). In turn, in the case of post-impact movement, the simulated vehicle for default data is moved backward in relation to the real one, after the vehicle rebound from the obstacle, in time *t* = 300 (Figure 8c), and, for a vehicle simulated with the data identified, the consistence of its position with the real vehicle was found (Figure 8f).

It was also observed that during the impact, elements of different stiffness undergo deformation which affects the compression and restitution phases. The scaled images of the vehicle undercarriage were used to analyze the deformation of those elements (Figure 9a–f).

**Figure 9.** Comparison of the vehicle undercarriage projections with recorded images for default data: *t* = 25 ms (**a**), *t* = 61 ms (**b**), *t* = 300 ms (**c**), identified data: *t* = 25 ms (**d**), *t* = 61 ms (**e**), and *t* = 300 ms (**f**).

Initially, in the compression phase in time *t* = 25 ms, while the bumper lining and its cross beam are being deformed, interferences in the impact reconstruction simulation for default parameters are acceptable in comparison with the ones received for the data identified, as shown in Figure 9a,d. The impact consistence for accident reconstruction using the program lasted until time *t* = 50 ms, when the engine support frame and the engine had not been crushed yet. Further, in time *t* = 61 ms, it can be observed that the wheel suspension, engine supporting frame, and engine are crushed; however, the deformations do not increase any more, as shown in Figure 9b,e). The vehicle body stiffening occurred during the impact. The phenomenon is discussed in other studies [21,22], which shows the effect of the engine chamber elements (engine, drive block) on the stiffness and deformation of the vehicle body and discusses the simplifications accepted in linear characteristics of the body deformations during the impact.

The vehicle body zones show a different stiffness, which additionally changes during the impact due contact with those elements, susceptible to deformation, with a barrier. When, after deformation of the bumper lining, the rigid barrier hit the engine supporting frame, the stiffness of the vehicle body increased, which was not precisely reconstructed by the V-SIM program for default parameters. Therefore, in order to reconstruct the collision, it was necessary to identify the crash test parameters and to enter them for simulation. The increase in stiffness in the compression phase facilitated reducing

the error in simulation reconstruction for the compression phase. A change in the restitution coefficient and the body stiffness increase in the restitution phase were due to the program-modeled stiffness increase by a crushed engine with its support frame. However, having entered the task to block the wheels, their braking was reconstructed, which made the vehicle pull back after the impact. A change in the plane of contact force <sup>Δ</sup>*y'* was also entered to ensure a better overlap of the simulated vehicle for crash test images. To show the differences in the course of the impact simulation for other V-SIM default data and identify them following the above methods, a crash test was used to develop a video [23].

The research method presented also facilitates determining the value of the coefficient of unitary body stiffness *k* following the formula below [24]. In that approach, the measure of the body deformation is assumed to be its width, depth, and height. For the case considered, the parameters of the body deformation are presented in Figure 10a,b, whereas, obtained with those parameters, the value of unitary stiffness coefficient k is 564 243 <sup>N</sup>/<sup>m</sup>·<sup>m</sup>2.

$$k = \frac{m \cdot v^2}{w \cdot h \cdot \mathbb{C}^2} \tag{25}$$

where:

*m*—gross vehicle mass,

*v*—velocity of the impact into the barrier, and

*w*, *h*,*C*—width, height, and depth of the vehicle undercarriage deformation.

Table 1 shows default parameters proposed in the V-SIM program and changed according to the data identified from the Mercedes crash test.


**Table 1.** Default and identified parameters.

The stiffness of the car body for compression phase was increased to decrease the depth of the penetration of the barrier into the car body. Right after the compression phase *t* = 70 ms, the car impact speed is already low, so the coefficient of restitution decreased, and stiffness for the restitution phase increased. During the restitution phase, stiffness is high, and some energy is released. In V-SIM, the car body stiffness for the phase of compression and restitution is the same, which is a simplification in the impact model applied. Once the program default parameters were changed into the ones identified in time *t* = 70 ms, the same depth deformation of the vehicle simulated in the top and side projections were also obtained, as compared with the actual car filmed (Figure 10).

The analysis has also demonstrated that for time t = 35 ms the front wheels of the Mercedes were blocked, which can be clearly seen in the crash test recording, showing the vehicle from the left and the right side, which is caused by a progressing deformation of the vehicle front, and the V-SIM program does not reconstruct it for default data. The problem of uncertainty which occurs in car crash reconstruction, with models of the same physical phenomenon providing different results, is described in another study [25,26]. In Reference [27], problems related to various types of car impacts and the impact of road surface condition on the reconstruction of object movement are discussed, while, in Reference [28,29], a discussion of problems of autonomous differential lock in a truck during movement in different terrain conditions is presented.

**Figure 10.** Test and simulation depth of deformations in the final compression phase t = 70 ms, side view (**a**) and top view (**b**).

To illustrate the above differences, time histories of changes: longitudinal component X, transverse component Y, yaw angle Ψ, and impact force F (Figure 11a–d) are presented, as well. In the simulation for default data, the maximum displacement of the vehicle body along X axle occurred in time *t* = 72 ms and was X = 0.767 m, whereas, for identified data, it was lower, X = 0.721 m and occurred earlier, in time *t* = 67 ms (Figure 11a). The differences in the position of simulated vehicles along Y axle were consistent with time t = 34 ms, after which the differences occurred (Figure 11b).

**Figure 11.** Time histories: longitudinal component X (**a**), transverse component Y (**b**), yaw orientation angle Ψ (**c**), and impact force F (**d**) recorded in V-SIM simulations.

The vehicle simulated for default data rotated faster than indicated in the crash test; hence, a correction of the plane of contact force Δy', which is also reflected in the time histories of yaw angle Ψ (Figure 11c).

In the compression phase, impact force F (Figure 11d) in the simulation for the data identified reaches the maximal value 696.86 kN in time t = 68 ms, next—298.62 kN, in time *t* = 71 ms, and further drops down to zero. In turn, for the program default data, impact force F reaches, in the compression phase, a lower value 640.88 kN, and the maximum follows in time *t* = 74 ms, then—144.39 kN in time *t* = 75 ms, and decreases down to zero. The di fferences result from those phenomena related to an increase in the body sti ffness while the engine and the engine supporting frame are being crushed.
