Mathematical Model of Vehicle Safety Deformation Under Impact—Design for Safety

Abstract

Under impact, when the velocity is reduced from its initial value vo to zero over a very short period of time, the deceleration a and its rate of increase ȧ (the principal parameters determining the survival of the occupants) are dictated by the length x of the vehicle deformation and by its dynamic process. The model equation suggested by the author is a = Ktn with 0 < n < 1. The constants K and n depend on the design of the vehicle and on deformation conditions. Alternative mathematical expressions of safety deformation requirements are considered with a view to improved design in the future and to speed restrictions on designs currently in use. Analysis of the formula reveals the conflict between the requirements for low a and ȧ, as well as the problem of high initial ȧ. An acceptable compromise can be recommended. Using suitable n values, a more satisfactory dynamic process can be achieved and the time of deformation tt can be increased considerably at a given length xt . The optimal value for n seems to be around 1/4 . The concepts of deformation coefficient and deformation factor are included in the discussion.