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Due to environmental problems, number of small vehicles with fuel efficiency increases. Since the small vehicles have small deformation space, it is difficult for them to achieve good crashworthiness at a frontal impact accident. Small deformation space usually yields high vehicle deceleration to absorb kinetic energy of the vehicle. The high vehicle deceleration may produce high occupant deceleration and lead to high occupant injury value. For example, North America, Japan and Europe specify head and chest injury value at vehicle's frontal collision. Those injury values tend to be improved if vehicle deceleration decreases. Deceleration of small vehicle with a little deformation space must be adjusted in order to prevent increase of the occupant injury value. A vehicle deceleration is expressed by 9, 18 or 36 discrete variables. A vehicle, an occupant and restraint systems such as seat belts are modeled by masses and a spring to simulate a frontal collision.

With the surge of environmental problems, the number of small vehicles with lower energy consumption is increasing. For such a vehicle, difficulty of achieving crashworthiness exists since it has smaller deformation space in a frontal impact accident. Smaller deformation space needs high vehicle deceleration for absorbing kinetic energy of the vehicle.The high vehicle deceleration in the event of a frontal collision may produce high occupant deceleration, resulting high chances of an occupant injury value. In this study, over 138 types of vehicle decelerations expressed by three variables in a frontal collision were examined in order to reduce occupant decelerations. Solving differential equations, following results were obtained (1) The minimum value of the maximum occupant deceleration exists.