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Transfer or response equations are important as they provide relationships between the responses of different surrogates under matched, or nearly identical loading conditions. In the present study, transfer equations for different body regions were developed via mathematical modeling. Specifically, validated finite element models of the age-dependent Ford human body models (FHBM) and the mid-sized male Hybrid III (HIII50) were used to generate a set of matched cases (i.e., 192 frontal sled impact cases involving different restraints, impact speeds, severities, and FHBM age). For each impact, two restraint systems were evaluated: a standard three-point belt with and without a single-stage inflator airbag. Regression analyses were subsequently performed on the resulting FHBM- and HIII50-based responses. This approach was used to develop transfer equations for seven body regions: the head, neck, chest, pelvis, femur, tibia, and foot.

In the 1999 Supplemental Notice for Proposed Rulemaking (SNPRM) for Advanced Airbags, the National Highway Traffic Safety Administration (NHTSA) sought comments on the maximum speed at which the high-speed, unbelted occupant test suite will be conducted, i.e., 48 kph vs. 40 kph. To help address this question, an analysis of constraints was performed via extensive mathematical modeling of a theoretical restraint system. First, math models (correlated with several existing physical tests) were used to predict the occupant responses associated with 336 different theoretical dual-stage driver airbag designs subjected to six specific Regulated and non-Regulated tests.

A theoretical, mathematical, risk assessment procedure was developed to estimate the fraction of drivers that incurred head and thoracic AIS3+ injuries in full-engagement frontal crashes. The estimates were based on numerical simulations of various real-world events, including variations of crash severity, crash speed, level of restraint, and occupant size. The procedure consisted of four steps: (1) conduct the simulations of the numerous events, (2) use biomechanical equations to transform the occupant responses into AIS3+ risks for each event, (3) weight the maximum risk for each event by its real-world event frequency, and (4) sum the weighted risks. To validate the risk assessment procedure, numerous steps were taken. First, a passenger car was identified to represent average field performance.

An age-dependent, serious-to-fatal (AIS3+), thoracic risk curve was derived and evaluated for frontal impacts. The study consisted of four parts. In Part 1, two datasets of post mortem human subjects (PMHS) were generated for statistical and sensitivity analyses. In Part 2, logistic regression analyses were conducted. For each dataset, two statistical methods were applied: (1) a conventional maximum likelihood method, and (2) a modified maximum likelihood method. Therefore, four statistical models were derived — one for each dataset/statistical method combination. For all of the resulting statistical models (risk curves), the linear combination of maximum normalized sternum deflection and age of the PMHS was identified as a feasible predictor of AIS3+ thoracic injury probability. In Part 3, the PMHS-based risk curves were transformed into test-dummy-based risk curves. In Part 4, validation studies were conducted for each risk curve.

A new inflator specification, the “inflator thrust variable,” was developed to better explain measured mid-sized male, instrumented test dummy responses in the chest-on-module test condition. Specifically, controlled laboratory experiments were conducted with non-production, driver airbag modules with inflators of various outputs and gas constituents in an effort to assess their effects on a pertinent occupant response. Regression analyses showed that the inflator thrust variable is a better predictor of the observed variation in peak viscous criterion responses than either peak tank pressure or the related pressure rise rate when inflators of differing gas composition were compared.