Closed form implementation of an N-point unequally spaced approximation of vehicle shortening applied to various force-shortening models

Force-shortening models have been ubiquitously utilized for the quantification of dissipated energy for motor vehicles involved in real world collisions. Inherent in the use of force-shortening models is the necessity for modeling of the shortening geometry. The methodologies presented in the subject study increase the utility of force-shortening models beyond the traditional three, four or six-point equally spaced approximations and the recently published N-point equally spaced approximation of a continuum motor vehicle shortening profile. Closed form solutions for the four most commonly utilized force-shortening models incorporating an N-point unequally spaced linearly interpolated model of the shortening geometry are provided. The specific solutions for the three, four and six point models are also presented.