HEAD, CHEST AND FEMUR INJURY IN TEENAGE

PEDESTRIAN – SUV CRASH;

INFLUENCE OF THE VEHICLE MASS

1.INTRODUCTION

Many works are found in literature on the impact between vehicle and teenager [1] [2] or adult pedestrian [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14], also numerous works study the impact between the vehicle and the adult cyclist [15] [16] [17] [18] [19] [20] [21] or both cyclist and pedestrian [17] [22] [23] [24] [25] [26] [27], more recently also the papers on the accident vehicle - teenage cyclist are found in literature [28] [29] [30] [31] [32] [33]. The necessity of study on this field has been highlighted by Neilson, [35] who concluded that the opportunity exists to introduce measures for the protection of pedestrians and the legs of motorcyclists, and to include the latest advances in the protection of car occupants. Overall, the need is seen to develop vehicle safety measures rapidly to permit the introduction of environmental restrictions on vehicle fuel consumption and design without cancelling the advances being made in casualty reduction. In [21] Authors indicate that car-mounted countermeasures designed to mitigate pedestrian injury have the potential to be effective even for bicyclists. In general the rules indicate the characteristics of the dummies for crash evaluation [36] [37] [38] [39], or the shape of the impactor s for the head and legs injury evaluation [40] [41] [42]. Multibody technique is the applied method for numerical simulation; the most widely used programs are MADYMO, Aprosys, PC Crash, while Simpack is used in [12] and Sim Wise is effectively used in this paper using the indirect approach. The influence of the front of the vehicle in the injury of the cyclist or pedestrian is a topic that is frequently found in the literature only in recent times. The work [43] examines the influence of the vehicle frontal part in general, while the works [8] [21] [26] also address the crash between SUV vehicle against cyclist or pedestrian, but other papers on Pick up – cyclist impact are not found, over the paper [44]. This extends the results already achieved in the papers [28] [29] [33] where the injuries caused by the energy impact of a teenage cyclist with a sedan car are taken into account and analyzed. Analogous crash is studied in case of SUV [31] [32] instead than a normal sedan, in order to fill the gap in literature: references are found only to an adult or to a child, in many cases without taking into account the type of vehicle. Paper [45] studied the impact of a passenger vehicle with a P6 dummy. In [46] [47], Authors investigate the deploying time (or response time) of an active hood lift system (AHLS) of a passenger vehicle activated by gunpowder actuator, while in [48] four vehicle types, including large and compact passenger cars, minivans and light trucks, are simulated according to their frequency of involvement in real world accidents. The influences of various vehicle front shape and compliance parameters are analyzed and the possible countermeasures on basis of vehicle front design, to mitigate the injury severity of the pedestrians, are discussed. The paper [49] studies the collision of the pedestrian with four different vehicle types; Authors conclude that the vehicle impact velocity and vehicle front-end shape are two dominant factors influencing the pedestrian kinematics and injury severity. Vehicle designs consisting of a short front-end and a wide windshield area can protect pedestrians from fatalities. The paper [50] shows the influence of numerous parameter of the vehicle front shape. Also in [51] Authors conclude that bonnet leading edge has to be located at a height of 0.74 m from ground and giving other measures; in effects a few high value is found in the paper [52] considering the cyclist impact only. The paper [53] reports the reconstruction of real accidents and techniques for the analysis of the results. The Monte Carlo technique is applied by Wood et al. [9] to determine the impact speed, and the results were compared with actual cases. In the paper [52] the chest speed data of the previous simulations are analyzed in order to quantify the influence of the front part of the vehicle on the injury of the cyclist. The result is obtained using all the crash data and a theoretical approach is given for the study of vehicle crash, with very good results. Theoretical approach allows understanding the influence of the vehicle mass; a criterion is given to determine the best value of some parameters on the vehicle front part. Other papers, except [34] [54], are not found in literature on these scopes. A particular attention is put the bumper in the frontal shape, because it influences the injury to the femur and legs, but also to chest and head. Paper [7] shows the development of a front bumper system. This work extends the obtained results in previous paper [1] [3]. The paper [3] shows the crash pedestrian-vehicle, while the paper [1] shows the results of the crash teenage pedestrian-vehicle, evaluating the damages to the head and the thorax; in this paper a direct comparison is executed using a SUV vehicle instead than a

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sedan, analyzing the damage to the head and the thorax, but also the damages to the femur, using the force injury criteria. 2. Implementation of the teenage pedestrian anthropomorphic model and of SUV virtual model. Pedestrian anthropomorphic model is the same used in previous simulations, as the adult pedestrian, as the teenage cyclist. The simulation technique is the same, by then plentifully tested with numerous simulations in SimWise room. The vehicle is a SUV, but the manufacturer is different than the model in the paper [31] [32]; the information on the characteristic data are given by the manufacturer; the vehicle mass is 2270 kg. This type of SUV is chosen for its characteristics, and to verify if the front shape is really advantageous for the damage of the head and of thorax, as the results of the paper [52] shows for a similar vehicle. Sketchup software is used to obtain the CAD model; it is imported in SimWise attributing the correct value to all the essential parameters. Figure 1 shows the vehicle in SimWise room, figure 2 shows the particular of the vehicle front shape. Three parameters only are chosen like fundamental for the impact fatality, respect to other works in literature; in this phase of the study this choice limits the number of possible combinations.

Figure 1 SUV in SimWise room

Figure 2- Parameters of geometric variation and particular of the front shape.

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2. Biomechanics of the impacts and femur injury criteria.

Biomechanics [55] [56] [57] is the discipline applying the mechanics principles to the living organisms; it allows the description of the several body parts movements and the evaluation of the forces acting on these parts. It is involved in the forecast and the prevention of the injury of the human body allowing the development of the vehicle safety; it needs study models to evaluate the injury gravity. Thus branch of the biomechanics is the starting point of the passive safety. The previous researches showed that in many cases the injury gravity is traceable to the accelerations produced by the crash. The injury scale AIS and the parameters used by the rules for the injury to the head and the thorax are described in the previous works [1]. In general HIC is the parameter used for the head injury and 3 ms criterion for the thorax or TTI for the thorax in frontal impact condition. The injuries to the legs constitute the most frequent trauma in the pedestrian, cyclist and motorcyclist crash. Femur is interested in 19% of road crash and the displacement of the fragments depends on the collision intensity and on the media crushed against the femur. Usually the trauma is revealed for the kinetic energy effect, emphasized by the instinctive muscular contraction. Acceptance levels are inserted in the final relation of EEVC WG10 [36], on the base of biomechanics study and accident reconstructions, proposing the following limits for all the test method regarding the inferior legs:

• Foot/knee • Knee: maximum lateral bend angle 15°; • Knee: maximum displacement 6 mm; • Tibia: maximum lateral acceleration 150 g.

• thigh • Maximum immediate sum of the femur forces 4 kN; • Maximum bending moment in the femur 220 Nm.

Criterion used in this paper is the immediate sum of the forces on the femur, since it is most compatible with the adopted simulation software. In this case the different kinds of femur injury are distributed in an AIS scale shown in table 1. 3. Simulation of teenage pedestrian-vehicle crash Objective of the research is the calculation of HIC, TTI values and the contact force on the femur, when the teenager is found in lateral or frontal position respect to the vehicle; the application of 3ms criterion for the evaluation of the thorax injury when the teenage is found in frontal position. The principal conditions constituting the dynamics of the teenage pedestrian – vehicle impact are reconstructed by using SimWise, fixing the principal conditions and parameters required by the protocol EEVC-17. The more general condition considers the pedestrian in perpendicular direction to the longitudinal axis of the road with an orthogonal speed respect to the vehicle coming up, and negligible respect to the vehicle speed. Simulations are executed considering the teenager in two different positions:

• The pedestrian is motionless on the roadway, with the side towards the vehicle coming up. • The pedestrian is found against the vehicle, on one’s feet and motionless. This condition covers

approximately the 30% of cases of accidents.

Table 1 – AIS values of femur injury.

AIS Description

1 Contusion to the soft tissue 2 Knee dislocation, tendons laceration, bones fractures, pelvis fracture 3 Femur fracture, pelvis fracture and aperture, knee break 4 Knee amputation, pelvis complete aperture 5 Bones crushing, vascular break.

The action of the car brakes, which involves a decrease in vehicle speed, does not seem really benefiting for the bump evolves. In fact, by decreasing the speed, the impact on pedestrians are certainly smaller, it is good to reflect on the fact that, given the time of perception and reaction of the driver and those of their vehicle, the slowing of the vehicle is often very poor. Assumed already elapsed the time of physic-mechanical delays, while considering a good braking ability of the vehicle capable of imposing a deceleration of 0.6 g (at the limit of breakage of the grip conditions in the case of asphalt), the braking action occurs the most of the time when the impact has already taken place or is happening.

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The simulations are executed in a standard way at speeds 20, 30, 40 e 50 km/h; a simulation at 10 km/h is executed for the femur only. Measured parameters during the simulations are:

1. Acceleration in the head center; 2. Acceleration in the thorax gravity center; 3. Acceleration of 4th rib and 12th vertebra; 4. Contact force on the femur; 5. Maximum speed of the head and the thorax;

An example of the accelerations trend of thorax and head versus the time is shown in the figures 3. Figure 4 shows the trajectory of the pedestrian in the crash at 20 km/h, he is put in front to the vehicle, that is in braking. The forward projection of the pedestrian can be noted. One can note the phase of loading on the bonnet and a gradual release on the ground. Figure 5 shows the simulation at constant speed 50 km/h, with the pedestrian side against the vehicle. One can note the phase of loading on the bonnet and the subsequent vault; that is typical of high speed accident.

Figure 3- Lateral impact at V=30 km/h in braking

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Figure 4 Frontal Impact at 20Km/h in braking

Figure 5 Lateral impact at constant speed 50 km/h

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(a) (b)

(b) (d)

Figure 6 Correlation HIC-AIS; a) side in braking; b) side at constant speed.

c) frontal in braking; d) frontal at constant speed

a)

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b) c)

Figure 7

a)Comparison of sedan and SUV mean values with the literature data; b) obtained results in

pedestrian frontal position; c) obtained results in pedestrian lateral position

Table 2 HIC values, percentage of fatality and comparison with sedan [1]

Pos. Speed

[km/h] Conditions

Amax head

[g] HIC AIS

fatality

[%]

HIC

Difference

sedan-

SUV [%]

Side

20

braking

24.15 28.55 1 0 -81 30 47.32 180.98 1 0-5 -69 40 72.32 538.72 2 5-10 -52 50 108.19 1246.26 3 40-45 -24 20

constant

31.31 46.20 1 0 -51 30 57.61 297.88 1 0-5 -55 40 86.30 849.87 2 10-15 -25 50 114.73 1386.53 4 45-50 -7

Front

20

braking

38.96 124.57 1 0 -47 30 77.95 485.81 1 0-5 -18 40 100.89 943.92 3 20-25 -6 50 104.90 1622.55 4 70 -9 20

constant

44.47 141.21 1 0 -46 30 77.30 524.48 2 0-5 -35 40 120.34 1442.48 4 55-60 18 50 119.28 1992.48 6 90 19

20 Mean values for the four positions and conditions

85.1325 30 372.2875 40 943.7475 50 1561.955

4. Results Analysis

4.1 HIC calculation Simulations furnish a great quantity of results. Table 2 shows the results synthesis, HIC values calculated with a base of 36 ms, following the rules. The fatality percentage of the event is determined correlating HIC data obtained by the simulations with the injury scale AIS. Figure 6 shows HIC – AIS correlation for the four conditions of impact. Fatality percentage is reported in table 2. From the qualitative point of view, the time-acceleration diagrams (figure 3) are very similar to those obtained with the sedan, even if the acceleration values and the times are different. HIC values can be compared with those obtained by other researchers. In particular, 188 pedestrian accidents, selected from

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several databases, were studied by Yang et al. [12] the accidents were reconstructed by MADYMO. The researchers distinguished between adults and children, without taking into account other factors such as the compliance and the shape of the bonnet, the relative position and the pedestrian speed, the braking, by relating the HIC value to the impact velocity. These results were statistically interpolated by curves of the second order. The equation for children is:

HIC = 0.2169v2 + 46.141v – 1046.2, R2 = 0:974 (1) the independent variable v is the impact speed in [km/h] and R2 is the variance. A ‘child’ is an individual having a lower age than that of a teenager (i.e. less than 13). Figure 7 a) shows the comparison of the HIC value among the relationship (1), the mean data obtained for the sedan in paper [1], the mean data obtained for the SUV in this work, the data obtained for the SUV and medium sedan by Han et al. [49] and the data obtained in [14] for a child against Skoda Fabia vehicle. In paper [49] four different types of vehicle are investigated by FEM simulations, using a human model of 50th percentile and another with 1.65 m of height and mass 60 kg. Figure 7 b shows the comparison between SUV values and sedan values obtained in [1] considering only the condition of the pedestrian frontal position, in braking and at constant speed. One can note that the condition of braking is less dangerous for the pedestrian and that the SUV gives lower values of HIC for the frontal shape. Only the results of the SUV and sedan with the 60 kg dummy are used for the comparison in the figure 7 c); the dummy is found in a lateral position respect to the vehicle. One can note the SUV data of this work are a few lower than the data obtained for the sedan, and this depends on the fact that the SUV frontal shape sets the injuries to the chest and head. This circumstance was noted also for the teenage cyclist in the paper [52], also if the SUV has a different manufacturer. The data of the paper [49] confirms this evaluation also if the dummy have a greater mass (difference 15 kg) and a greater height than the teenager dummy. The difference of the HIC values can be attributed to this circumstance and to the fact that the vehicles have different mass and different front shape. The previous observations are confirmed, with the difference that the advantage of the braking is not so marked as in the case of frontal position. However the lateral position is less dangerous than the frontal in all the circumstances. One can note that the frontal shape has a very great importance in the injury to pedestrian head (or chest). In the work on the cyclist [52] the fundamental parameters are individuated like: angle bonnet, height bonnet and height bumper; figure 2 shows these parameters and their value for the SUV of this work. The table 3 compares the values with the sedan in [1].

Table 2 Characteristic frontal dimensions of sedan and SUV vehicle.

vehicle Bonnet height

[mm]

Bumper height

[mm]

Bonnet angle

[degrees] Mass [kg]

sedan 847 390 20 968 SUV 945 550 15 2270

4.2 TTI calculation Following the rules, TTI (Thoracic Trauma Index), is calculated by means of the relationship: TTI= 1,4 AGE+0,5 (RIBy + T12y) M/Mstd (2) Where AGE is the teenager age (equal to 15 years), his mass is 45 kg, Mstd is the standard mass equal to 75 kg, RIBy [g] represents the maximum of the absolute value of the lateral acceleration of the fourth or eighth rib, on the side where it is affected; T12y [g] indicates the absolute value of the maximum lateral acceleration of the 12th thoracic vertebra; both are expressed as multiple of gravity acceleration. Some modifications are reported to the anthropomorphic model to measure the last two quantities. These modifications are listed and described in the details in the paper [1]; this allows the insertion of virtual accelerometers obtaining the acceleration values of the 4th rib and 12th vertebra. TTI is used only in the case of side impact, so that only the cases of lateral impact at constant speed and in braking are examined. Table 3 shows the values of the maximum acceleration on the 4th rib and on 12th vertebra in both the cases. In general the vehicle braking increases the time of the peak acceleration, but this consideration has not great influence in TTI case, since this method analyzes the accelerations, but does not their duration in the time.

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TTI values can be compared with other data in literature [1], where the teenage – vehicle impact is examined by the software Visual Nastran 4D; the vehicle is a medium sedan. Table 4 shows TTI values calculated by relationship 2, the comparison with sedan results and the percentage difference.

Table 3 – maximum accelerations for TTI evaluation (side position against SUV)

Speed

[km/h] Conditions Acc. 4th rib [g] Acc 12th vertebra [g]

20

braking

12.83 13 30 41.26 7.40 40 65.84 21.13 50 104.78 71.14 20

constant speed

13.38 14.94 30 31.97 12.48 40 23.69 62.04 50 86.85 71.14

Table 4 –TTI values and comparison

Speed

[km/h] Condit.

TTI SUV

[g]

TTI sedan

[g]

Difference

[%]

20 Constant

speed

29.50 35,50 -17% 30 34.34 41,00 -16% 40 46.72 61,70 -24% 50 72.32 118,00 -39% 20

braking

28.76 31,50 -9% 30 35.60 40,40 -12% 40 47.10 63,00 -25% 50 73.78 102,00 -28%

A further comparison of TTI values can be executed with available data in literature. The papers [13] [14] contain the analysis of impact vehicle-pedestrian; the simulations are executed by means of the software SIMPACK and MAYDMO respectively. MADYMO simulations are executed using Skoda Fabia vehicle against an adult or child pedestrian; values at speed 10 km/h are also calculated. The results for the child are shown in fig. 8, with the teenager results in table 4. SIMPACK results are not used because they are referred to an adult. The figure 8 shows that the thorax injury has not important differences between the condition of constant speed and braking, differently from the head. Moreover the modifications on the dummy are essential and functional. Also in the thorax case the vehicle SUV furnishes a lower injury than the sedan of paper [1] and the sedan in paper [14]. Variation is very strong at 40 km/h, but also in this case the difference depends on the contact point and the shape of the front vehicle, and to the different mass. Other results are very near one another. 4.2 TTI-AIS correlation A correlation scale exists between TTI value and the AIS code. Figure 9 shows the trend; one can note the lack of values referred to AIS1+ and AIS2+, because surely for such injury indices there is no probability of death. Considering the values in Table 4 for SUV vehicle, there are not injuries that provoke the death for speed between 20 and 50 km/h, in fact such values are found in a range between AIS1+ e AIS2+, where the injuries to the skeleton and soft tissues are rather limited. Like paper [1] shows, the sedan at speed 50 km/h has the probability of injury AIS3+, or pulmonary contusion and multiple fractures to the skeleton; the probability is 40% - 42% in the case of constant speed; it is 10% about in the case of braking; 4.3 Chest injury by 3 ms criterion Rules prescribe the use of 3ms criterion in the case of frontal impact. The gravity centre of the chest and of the head have not endure greater acceleration that 60 g and 80 g respectively for a greater time than 3 ms. A virtual accelerometer is inserted in the chest gravity centre. It allows obtaining the results at constant speed and in braking that table 5 shows. The last column shows the corresponding probability AIS4+ that is calculated by the following relationship:

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Figure 8 – TTI values for the different simulations (child and teenager)

Figure 9, Correlation TTI – AIS

Prob (AIS4+) = 1/(1+exp (4,3425-0,0630 * gt) 3) And is equal to 36% for gt= 60 g. The teenager chest endures very high accelerations in the case of frontal impact. This phenomenon is due to the greater ability of bend that the trunk has in the direct contact between the chest and the bonnet; it does not occur in the case of lateral impact since the first contact with the bonnet occurs by the shoulder.

Table 5 – 3 ms criterion results (frontal impact against SUV)

Speed

[km/h] Conditions 3ms [g] Prob. (AIS 4+)

20

braking

29.75 7% 30 54.62 28% 40 80.40 67% 50 109.58 92% 20

Constant speed

39.50 13% 30 61.72 38% 40 127.21 97% 50 140.89 98%

4.4. Femur injury evaluation Method used in this paper is the evaluation of the contact maximum force; to do it some changes are made to the anthropomorphic model. The collision force during the crash is distributed in the contact time and is presented as a bell curve with a big peak. The force-time curve calculation is difficult since requires the analysis of the structural deformation during the crash. The area subtended by this curve is named collision impulse; the collision maximum force depends on the peak amplitude. Given that SimWise simulates the bodies motion in the hypothesis of perfect stiffness, the collision may be considered almost immediate.

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SimWise offers the possibility to choice two different contact models. The default model is named "Impulse/Momentum". During the simulations campaign, problems are found regarding the measurement of the impulse due to uncertain of the contact point position in the femur, since the vehicle front shows several unevenness; such problem is resolved inserting in the dummy two bodies having rectangular shape, connected to the thigh and knee by the constraint “rigid joint”, having small thickness and sufficient size to cover the space where the contact occurs presumably; moreover they are link to a temporal constraint that undoes the use and the functionality as soon as the contact impulse occurs. In this way the impact dynamics is not modified. Figure 10 a) shows the positioning of such elements, while figure 10 b) shows their separation.

a) b)

Figure 10 a) Insertion of the bodies (in red) in the model and b) their separation after the collision

4.4.1 Simulations results Impulse values and the relative duration are obtained by the method of “contact impulse” for both the conditions of frontal impact and side impact. Relative data to both the femurs are measured for the frontal impact, while only the relative data to the femur subjected to the impact are measured in the side impact condition. Fig. 11 a) shows the graphs in the frontal impact condition for the constant speed 50 km/h. Figure 11 b) shows the graph in the side impact condition at constant speed 30 km/h.

a)

b)

Figure 11 a) impulse in the frontal impact at constant speed 50 km/h

b) impulse in the side impact at constant speed 30 km/h

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Tables 6 and 7 show the results for all the simulations. Since the force is the derivative of the impulse, the force value is obtained dividing the impulse maximum value by the elapsed time between zero and maximum.

Table 6 – results in the case of frontal impact against the SUV

speed

[km/h]

Right Femur Left Femur Force [kN] Force [kN] Discrepancy

by right

femur force

[%]

Impulse

[kg m/s]

Time

[ms]

Impulse

[kg m/s]

Time

[ms] right left

Experimental

values by [45]

and [59]

10 2.48 2.00 1.06 2.00 1.24 0.50 0.877 39 20 5.16 2.00 2.85 2.00 2.58 1.40 2.497 2 30 7.55 2.00 16.90 6.00 3.77 2.81 3.41 7 40 12.20 2.00 14.80 4.00 6.10 3.70 5.5 12 50 24.70 4.00 28.00 6.00 9.10 4.66

Table 7 results in the case of side impact against the SUV

speed

[km/h]

Right Femur

Force

[kN] Impulse

[kg m/s]

Time

[ms]

10 2.92 2.00 1.46 20 10.20 4.00 2.55 30 4.70 4.00 3.67 40 25.30 4.00 6.32 50 35.90 4.00 8.97

One can note that the right femur is most damaged in all the simulations; it depends on the fact that the dummy is not in a perfectly centered position, so that the right femur endures a greater force. Instead in the lateral impact the extrapolation data are referred to the femur that goes in contact with the vehicle. For this reason there is very low difference in the data on the right femur. Values of the contact force on the femur may be compared with similar data available in literature. Paper [45] contains the impact analysis vehicle – pedestrian, execute by a dummy P6 (m 1.17, 22 kg) in frontal position respect to the vehicle, with adequate instrumentation for the impact force evaluation at speed 10-20-30 km/h; the datum at 40 km/h is obtained by the reference [59]; the values are shown in table 6, and figure 12 shows the visual comparison; one can note the very good concordance between the data. The last column of table 6 shows the discrepancy in percentage. This comparison shows that the approximation and the modifications on the dummy for the femur contact force calculation are indispensable and functional, and they do not distort the result. The discrepancy are acceptable at all the speeds, Authors did not found data for the speed 50 km/h.

Figure 12 Contact force on the femur versus the time

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Figure 13 Contact force – AIS correlation in the frontal impact

Table 8 probability of AIS2+ injury

Right femur in frontal position Right femur in side position

Speed [km/h] AIS 2+ [%] Speed [km/h] AIS2+ [%]

10 0 10 0 20 0 20 0 30 2 30 2 40 31 40 34 50 93 50 91

4.4.2 Contact force-AIS Correlation A correlation scale exists between the femur force value and the corresponding AIS code. Figure 13 shows the trend; by making reference to the code AIS 2+ corresponding to the femur fracture, or the pelvis fracture or the knee break with its ligaments [49]. Table 8 summarizes the probability that the pedestrian endures an AIS2+ code versus the variation of speed and position. The risk of femur break increases with the speed and assumes considerable value at the speed 40 and 50 km/h, in accordance with the literature data. 5. Impact points localization Fig. 14 show the bonnet areas most involved in the head impact with the vehicle frontal part. The vehicle marking for the areas WAD is done following the EURONCAP rules. In particular the impact points to the several indicated speeds are shown; one can read:

• in read, the impact points for the frontal impact with vehicle at constant speed; • in green, the impact points for the frontal impact with vehicle in braking;

Figure 14 Frontal impact, contact points vehicle-head

The speeds [km/h] are marked

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Table 9 – Speed values obtained by the simulations

Vehicle

Speed

[km/h]

Pos.

SUV Sedan [1]

Chest

speed

[m/s]

Normalized

chest speed

Chest

speed

[m/s]

Normalized

chest speed

20 F 8.43 1.5174 9.74 1.7532 30 F 12.165 1.4598 13.26 1.5912 40 F 15.06 1.3554 15.07 1.3563 50 F 17.64 1.27008 18.5 1.332 20 S 9.99 1.7982 7.09 1.2762 30 S 12.57 1.5084 12.34 1.4808 40 S 16.73 1.5057 15.16 1.3644 50 S 17.38 1.25136 18.14 1.2427

Table 10 – slowing down and vehicle normalized speed

Vehicle

speed

[km/h]

Pos.

SUV Sedan [1]

Post impact

vehicle

speed [m/s]

slowing

[km/h]

Norm. post

impact

speed

Post impact

vehicle

speed [m/s]

slowing

[km/h]

Norm. post

impact

speed

20 F 5.427 0.4628 0.97686 5.11 1.604 0.9198 30 F 8.155 0.642 0.9786 7.89 1.596 0.9468 40 F 10.906 0.7384 0.98154 10.55 2.02 0.9495 50 F 13.665 0.806 0.98388 13.26 2.264 0.95472 20 S 5.374 0.6536 0.96732 5.26 1.064 0.9468 30 S 8.143 0.6852 0.97716 7.98 1.272 0.9576 40 S 10.858 0.9112 0.97722 10.56 1.984 0.9504 50 S 13.671 0.7844 0.984312 13.39 1.796 0.96408

Impact points dispersion is localized in both the cases in the zone between WAD 1000 and WAD 1500; the impacts at 20 and 30 km/h are found near to WAD 1000, instead the others are found versus WAD 1500. In general the greater acceleration peaks correspond to an impact against a more rigid part of the vehicle front. The impact points position is different in the case of SUV or the sedan. In the SUV case all the contact points fall WAD 1000 and WAD 1500. In the sedan case, the teenage pedestrian head hits the superior part of the bonnet always in the zone between WAD 1000 and WAD 1500, but the impact points at 40 km/h are found near to the windscreen, while the head hit the windscreen at 50 km/h. These differences are due to the different frontal part of the vehicle and to the height of the parts respect to the pedestrian. 6. A new theoretical approach on pedestrian-vehicle impact

Obtained data are analyzed by means of the theoretical results given by the momentum conservation and kinetic energy conservation, both can be considered suitable by making the hypothesis of elastic collision. Used parameters are:

• gravity center speed of the head; • gravity center speed of the chest;

the values of the gravity center speed should be used in a more correct way, instead of the chest, but the difference is very little. Table 9 shows the maximum speed data for both the vehicles. The normalized speed is obtained dividing the chest speed by the vehicle speed in coherent unities. Table 10 shows the vehicle speed after: the small slowing is due to the loss of a small part of vehicle kinetic energy is transferred to the pedestrian; normalized speed as the above. Slowing down of the sedan is greater than those of SUV; it is due to the mass difference between the vehicles. Paper [52] shows the theoretical approach for the determination of the speed after the collision, and it is summarized here. Indicating by x the motion direction and by y and z the other two spatial directions, V is the vehicle initial impact speed that has a known value, while the final values Vc (of the pedestrian) and Vv (of the vehicle) are unknown. In general the six components of the speed are different by zero in the final instant. Momentum conservation is:

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( )

zvvzcc

yvvycc

xvvxcc

VmVm

VmVm

VVmVm

−=

−=

−−=

(4)

Squaring the relationships (4) and summing, remembering that is:

222

222

zvyvxvv

zcycxcc

VVVV

VVVV

++=

++= (5)

the following relationship is obtained:

( )VVVVmVm xvvvcc 222222 −+= (6)

another equation can be obtained applying the energy conservation principle. One has:

( )222

2

1

2

1VVmVm vvcc −−= (7)

The energy conservation principle is written neglecting other forms of energy. Introducing the vehicle normalized speed X and pedestrian normalized speed Y of the above and the direction cosine β = Vvv/Vv, relationships (6) and (7) become:

( )XXmYm vc β212222 −+= (8)

( )122 −−= XmYm vc (9)

Relationships (8) and (9) form a system of two equations in three unknowns X, Y and β. The system can be resolved in a conditioned way by making use of Lagrange multipliers λ [58], the solution is:,

2

2

1 2

v

c

cv

v

cv

cv

m

m

mm

mY

mm

mmX −±=

+±=

+

−±= β (10)

some particular cases are indicated in [52]. β and X have the same sign, while the case Y<0 has not interest in the examined case. The solution has to be reconsidered in the case mc> mv, but this case is not interesting for this work purpose. However the mathematical development is studied and verified for the case of vehicle – cyclist crash, but its application can be larger. In general relationships (4) allow the reconstruction of the speed of both the body, if the motion is supposed in plane x-z. Substantially the procedure allows calculating the results so that the solutions of the system constituted by (8) and (9) are real and agreeing. By the geometrical view point [58] the condition is obtained that the curves represented by the above relationships are tangent in the point having the coordinates (X,Y). The third relationship (10) shows that the speed of the cyclist (or pedestrian) can be greater than the vehicle impact speed, since the normalized speed tends to 1.41 if mc<< mv. However the vehicle mass effect is greater as soon as the impact speed V increases. Tables 9 and 10 show the normalized impact speed for sedan [1] and SUV. One can note that the normalized speed X assumes always values a few lower than 1, so that the small reduction of speed may not be neglected, and that the cyclist speed after the impact is greater than the vehicle impact speed. The normalized speed Y assumes values between 1,2 and 2 about, against the theoretical value 1.41 above indicated. This is due to non-fully elastic collision, and to the fact that the energy conservation (7) does not take in account other energy forms. Table 11 shows the mass and β value for both the vehicles.

Table 11, masses and directional cosine.

Mass [kg] β

pedestrian 45 Sedan [1] 968 0.9989188

SUV 2270 0.9998034 β values are very near to one, given that the vehicle mass is very greater that pedestrian one, but one has to highlight that whatever rounding up distorts the result. Figure 15 shows the comparison between the simulations results for theoretical ones. Values of the vehicle normalized speed are reported in abscissa and values of the chest normalized speed are reported in ordinates. Of course the values in the braking are not taken in account, because the slowing is due also to the braking. The relationships (8) and (9) are tangent one another, while the values obtained by the numerical simulations are shown in superposition. The obtained values are in very good agreement with theoretical ones. The figure shows that:

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• All the simulation data, in the analyzed impact conditions, are very near to the optimum condition obtained in the previous.

• Pedestrian speed at the end of the contact is very greater than the speed of the vehicle coming up (until two times).

• SUV has the best behavior, between the two examined vehicles, since the values are very near to the optimal condition.

Figure 15 – Comparison between numerical and theoretical values

sedan on the left and SUV on the right

Table 12: masses and directional cosine

mass [kg] β cyclist 45 sedan 968 0.998919 SUV 2900 0.99988

Pick Up 3085 0.999894 The following procedure is useful to eliminate the mass influence as far as possible: relationships (10) allow the following coordinate transform:

cv

cv

cv

v

mm

mmXX

mm

mYY

+

−=

+= '

2' (11)

In this way the tangency point of the previous has coordinates (X’=1, Y’=1) for whatever vehicle. Substituting (11) in relationship (9), the derivative in the point (1, 1) is:

( )

c

cv

m

mma

dX

dY

21,1

'

' −−== (12)

The tangent equation at both the kinetic and momentum curves in the point (1,1) can be constructed; the following relationship is obtained:

)1'(1' −+= XaY (13) Paper [52] shows the results of analogous simulations in the impact teenage cyclist-vehicle. Table 12 shows the mass and the directional cosines, with analogous observation on β calculation. The tangents are drawn in figure 19; their slope a is strongly dependent on the vehicle mass. All the coordinates of the vehicles and for the different positions are converted by using the relationships (11). The corresponding points are shown in the same figure 16. The simulation results are thickened around the point (1,1) and are positioned along the tangent line of the above. The figure confirms the excellent concordance of the theoretical result with the numerical simulation. Results obtained in this work cannot be considered definitive; best results can be obtained by increasing the number of examined vehicles, and also considering the offset of impact in the lateral crash. They may be used as the starting data for the mathematical procedures that can lead to improve the result. Theory set in this paper shows an excellent validity in the case of teenage pedestrian or cyclist crash, and can found application in other impact conditions.

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Figure 16 – Comparison among the different simulation for teenage pedestrian and cyclist impact

7. Conclusions

The objective of this work is the evaluation of the injury to the teenage pedestrian during the impact with a SUV, analyzing the possible dynamics of impact and giving a contribute to the improvement of safety conditions. Comparison with other experimental or numerical data in literature does possible a series of considerations: the pedestrian height, the shape of the vehicle frontal part, the vehicle minimum height from the ground, the height of the bumper, the bonnet inclination and the vehicle mass are extremely important factors for the impact fatality. The data obtained in the paper [1] in the impact with a sedan, the teenager limits the contact points of the head to the bonnet or the lower part of the windscreen, and instead the teenager limits the head contact points to the bonnet lower part only in the impact with a SUV. It is an advantage since the bonnet has certainly a greater inclination respect to the windscreen and less stiff structure, so that the teenager has less probability to endure a fatal impact. SUV frontal part has a no much acute trend, moreover has a more large and high vertical profile respect to the sedan, with some asperity. This does not limit the contact point concentration during the impact (very dangerous conditions for the legs), in spite of the pedestrian rotation on the bonnet, improving the speeds and accelerations. In fact the parameters (HIC, TTI, 3ms) have values with negative deviation. The analysis confirms that the frontal position results more dangerous than the lateral one, because the contact of the head and the chest occurs on the bonnet directly, while the pedestrian in side position contact the bonnet with the shoulder; this limits the injuries to the fatal parts, besides the injury to the femur does not endure great variation. Multibody model has a series of advantages. For example the designers of a vehicle manufacturer house have the possibility to execute the simulations when the prototype exists like CAD model only, so that one may study the vehicle aggressiveness, to get through the mandatory homologation tests versus the pedestrian, avoiding the FEM mesh. The designers can make the more opportune esthetic functional changes, testing the vehicle in a more fast and economic way. The same can be told for the dummy: during the simulations campaign, problems are found regarding the measurement of TTI, this was resolved inserting virtual accelerometers to obtain the acceleration values of the 4th rib and 12th vertebra. Other problems is found on the measurement of the contact force of the legs with the bumper, given that the precise positioning of the contact point can change for the pedestrian height and the bumper position. Such problem is resolved inserting in the dummy two bodies having rectangular shape, connected to the thigh and knee, having sufficient size to cover the space where the contact occurs presumably. This allows the force accurate measurement and the evaluation of the leg injury in an accurate way. The results of the simulations are compared with an original theoretical procedure based on the application of momentum and energy conservation principle. The results show that the system vehicle – teenage pedestrian assumes naturally a condition of optimum that can be calculated with simplicity. The analysis of chest and head speeds indicates that the pedestrian (or cyclist) assumes a speed that can be very greater than that of the vehicle coming up; this endures a vehicle slowing that cannot be neglected for the study of the

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crash phenomenon. Moreover the theoretical study shows that the vehicle speed has a small component along the orthogonal plane to the motion, due to a value of the directional cosine a few lower than 1. The same theoretical procedure shows that the vehicle mass has a non negligible importance and that the collision with the pedestrian endures a slowing due to fact that a part of the kinetic energy is transferred to pedestrian, this slowing increases with the reduction of the vehicle mass; other works on this scope are not found in literature, except paper [52]. Trough the simulations the effectiveness of active and passive devices can be tested; for example to evaluate the performances of soft bumpers, or the bonnet angle, that is the only device of active protection till now implemented. At last system applications can be in the study of accident dynamics in forensic room.

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