Rose, N. and Carter, N., "Further Assessment of the Uncertainty of CRASH3 ΔV and Energy Loss Calculations," SAE Technical Paper 2014-01-0477, 2014, doi:10.4271/2014-01-0477.
In a 2012 paper, Brach, Brach, and Louderback (BBL) investigated the uncertainty that arises in calculating the change in velocity and crush energy with the use of the CRASH3 equations (2012-01-0608). They concluded that the uncertainty in these values caused by variations in the stiffness coefficients significantly outweighed the uncertainty caused by variations in the crush measurements.This paper presents a revised analysis of the data that BBL analyzed and further assesses the level of uncertainty that arises in CRASH3 calculations. While the findings of this study do not invalidate BBL's ultimate conclusion, the methodology utilized in this paper incorporated two changes to BBL's methodology. First, in analyzing the crash test data for several vehicles, a systematic error that is sometimes present in the reported crush measurements was accounted for and corrected. This systematic error arises when a vehicle's plastic bumper fascia rebounds more than the underlying structure, creating an air gap and causing the reported crush measurements both to underestimate the actual deformation and to exhibit more scatter than they otherwise would. This scatter translates into uncertainty in the stiffness coefficients.Second, linear regression was used to obtain the stiffness coefficients and to quantify their uncertainty. Instead of using linear regression, BBL assumed the same damage onset speed (b0) for each crash test. In essence, this means that BBL assumed a value for one of the stiffness coefficients, with the only variability in that coefficient coming from the differences in vehicle weights from test to test. The methodology employed in this paper eliminated the need to assume a damage onset speed.