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This paper presents an energy relationship between vehicle impact pulses and restraint systems and applies the relationship to formulations of response factors for linear and nonlinear restraints. It also applies the relationship to derive optimal impact pulses that minimize occupant response for linear and nonlinear restraints. The relationship offers a new viewpoint to impact pulse optimization and simplifies the process mathematically. In addition, the effects of different vehicle impact pulses on the occupant responses with nonlinear restraints are studied. Finally, concepts of equivalent pulses and equal intensity pulses are presented for nonlinear restraints.

A simple spring-mass model of the impact response of the side impact dummy (SID) is established. The spring and mass constants of the model are established through system identification methodology based on data from impact tests. The tests are performed in laboratory with hydraulically driven impactors impacting the chest and pelvis of the SID. The input data to the model consist of measured contact force or impactor velocity time histories, and the output data are accelerations on the rib, spine, and pelvis of the SID. The established model appears to predict the test results with reasonable accuracy. The main purpose of this study, however, is to use this simple model to carry out parametric studies of the response of the dummy with changing impact parameters, the result of which would be useful in understanding vehicle crash tests using the SID.