Influence of bumper design on pedestrian injuries.

Soica, Adrian ; Taruelscu, Stelian ; Luca, Dana Motoc 等

1. INTRODUCTION

Traffic safety as well as the possibility to reduce the social costs of rehabilitation and the seriousness of injuries suffered by pedestrians present a particular complexity, being necessary to take a close approach to these issues.

In order to carry out developments concerning the traffic safety at low costs, there occurs the necessity to prioritize the interventions on the basis of "costs--advantages" analyses, by introducing the criterion of efficiency when drawing up working programs.

The general desire is to diminish the seriousness of injuries by improving the frontal structures of motor vehicles. From a certain speed the aim of reducing the number of injuries is limited; yet, at speeds below about 40 km/h it is likely to significantly reduce the levels of injuries caused to pedestrians involved in frontal impacts with motor vehicles.

The impact velocity and the vehicle's frontal structures, including the geometry and the rigidity proved to be important factors to cause trauma.

Most of the fatal injuries among pedestrians are caused by head injuries. The major causes of serious head injuries are the bonnet and the A pillars. The modern vehicles have rigid components under the bonnet, with spaces even smaller than 20 mm. Thus, the deformation that is likely to occur is too small to allow the absorption of necessary energy. Theoretically, there is required a distance of about 55 mm at an impact with a velocity of 40 km/h in order to maintain the HIC value below 1 000 for an adult head.

The impact velocity has also a major influence upon the resulted trauma. The pedestrians hit with velocities reaching 25 km/h usually suffers minor injuries. More than 95% of the accidents involving pedestrians are produced at impact velocities below 40 km/h.

2. MATHEMATICAL MODEL OF IMPACT

The hereby paper analyses the impact between the vehicle and pedestrian, the vehicle being in constructive configuration with double bumper. The second bumper is considered to be placed under the first one and a little withdrawn backwards.

The bumpers positioning heights will be varied, and the velocities imprinted at the pedestrian thorax and head will be calculated. For simplification there is considered:

* The pedestrian as mono-mass, of constant height and mass throughout the several simulations;

* The impact model is bidimensional;

* The impact upon the pedestrians' legs will be produced simultaneously by the two bumpers;

* The impact force will be distributed in two points corresponding to the bumpers' heights and it will vary on the upper and lower bumper, but the sum of the two values will be the same for each simulation. Practically, this is translated through a similar impact velocity for each simulation.

* The pedestrian is motionless in both longitudinal and transversal direction;

* The vehicle's running system does not manifest through the occurrence of pitching motions and, therefore, the height of impact points upon the leg will not vary within one simulation.

Therefore, it is considered that the pedestrian is an adult having the mass of 73 kg and the height of 1,78 m. The pedestrian centre of mass is considered to be at 0,57 from his height. Due to the fact that the most serious injuries suffered by the pedestrian are head and thorax injuries and considering the regulations in force, these injuries are measured at the level of the pedestrian's head centre of mass (HIC), pedestrian's thorax centre of mass (TTI), the paper considered a height of 1,71 m for the coordinate of the head centre of mass and of 1,135 m for the coordinate of the thorax centre of mass (Rau, 2000).

[FIGURE 1 OMITTED]

According to the figure 1 the coordinates of the pedestrian centre of gravity are as follows:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1)

Following the successive derivations and transformations there is obtained the vector of the pedestrian translation and rotation accelerations

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (2)

where [A] stands for the pedestrian's angular acceleration coefficients matrix;

[B] stands for the pedestrian's square angular acceleration coefficients matrix;

{a} stands for the vector of the body translation and rotation accelerations.

That can be more simply written under the form:

[M] x {a} = {Q} (3)

where: [M] stands for the matrix of both the mass and pedestrian's inertia moment;

[Q] stands for the matrix of the forces actuating upon the pedestrian;

Aiming at finding out the unknown out of the equations (2) and (3) by multiplying at the left with [[A].sup.T] there will be obtained

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (5)

Where

{[Q.sub.ext]}= [[A].sup.T] x {Q} (6)

The relation (5) represents the simplified form of the differential equation in the unknown [alpha] = [alpha](t). By replacing it in the relation (1) the coordinates of the pedestrian's body centre of mass can be found out.

The vehicle is considered to be equipped with a bumper the impact points of which will vary on height within the ranges limit 0,5-0,6 m for the upper bumper and 0,3 - 0,4 m for the lower one. The impact force added to the two impact forces is of 6 kN for each simulation. The bonnet's frontal edge is situated at the constant height "h" during the simulations. The contact point between the bonnet's edge and the pedestrian's leg is considered to be a cylindrical articulation around which the pedestrian will pivot after the impact.

3. IMPACT SIMULATION

In order to answer the proposed problem a MathCad application was conceived to resolve the system by using the Runge Kutta method with the rkfixed function.

[FIGURE 2 OMITTED]

[FIGURE 3 OMITTED]

The thorax and head velocity are obtained on the basis of the rotation angle of the body, generated by the impact force, trough replacement and particularization in relation (1).

4. CONCLUSIONS

The impact force was distributed on the two bumpers, the secondary bumper on a lower position and a little withdrawn backwards, actuating with lower or at most equal forces to the one on the main bumper. The length of impact was of maximum 0,19 seconds. The simulations enabled us to obtain the body's angles of rotation at the end of the impact, the maximum velocities of the thorax centre of mass and the maximum velocities of the pedestrian's head centre of mass. The data analysis leads to the following results:

* The rotation angles, respectively the lowest impact velocities of the pedestrian's thorax and head are obtained when the primary bumper takes a high percentage of the total impact force;

* The lowest impact velocities of both thorax and head are obtained by locating the bumpers at the highest possible height from the ground, the bonnet's edge remaining at the same standard height;

* The bigger the distance between the bumpers' impact points the higher the velocity the thorax and the head hit the vehicle with;

* The velocity the pedestrian's thorax hit the vehicle with rages from 5,42 to 6,4 m/s at a total impact force of 6 kN;

* The velocity the pedestrian's head hit the vehicle with rages from 14,9 to 12,6 m/s at a total impact force of 6 kN;

As further developments, from design and manufacturing point of view can be conceive a complex bumper with higher rigidity, provided with a special structure for pedestrian protection, doubled with a secondary deformable bumper mounted under the main bumper. The structure can be designed to avoid "tibia pulling" under the front-end of the vehicle that seriously injure the ankle.

5. REFERENCES

Kuhnel, A. (1980). Der fahrzeug fussganger unfall und seine rekonstruktion dissertation, TU-Berlin

Rau, H.; Otte D.; Schulz B. (2000). Vehicle-pedestrian collisions at high speed. Dummy results al 70-90 Kph., Verkehrsunfall und Fahrzeugtechnik, 12/2000

Soica, A.; Florea, D. (2000). Aspects of human body modelling with application on car crash tests, Conference "Prevention of traffic accidents on roads 2000", Novi Sad, Yugoslavia

Soica, A.; Lache, S. (2007). Theoretical and Experimental Approaches to Motor Vehicle--Pedestrian Collision, 3rd WSEAS International Conference on APPLIED and THEORETICAL MECHANICS--MECHANICS '07, Tenerife, Canary Islands, Spain, December 14-16, 2007, ISSN 1790-2769, pp 264-270

Tanase, Gh. (2003). Theoretical and experimental research regarding the front-end vehicle design optimization, PhD Thesis. Transilvania University of Brasov