A causal model of crash test pulses: effect of impact speed on deformation and other variables

Abstract

Consider crash tests in which a car strikes a solid block. Suppose there is a particular differential equation (that includes a term in deformation to the power n) relating acceleration at any instant to deformation and velocity at that moment. If that is the case, the dependencies on impact speed of maximum acceleration, duration of impact and deformation are interconnected: the relationships are power functions, and the exponents are all determined by the exponent n in the differential equation. Data from both tests and real crashes suggest that n is about 0.5 for front wheel drive cars.