Naick, P. and Carnago, K., "Theoretical Relationship of HIC d to Crush Space for FMVSS-201 Head Impact Tests, and the Effective Use of FEA in Predicting HIC for Design, Verification and Optimization of Countermeasures," SAE Technical Paper 982349, 1998, https://doi.org/10.4271/982349.
FMVSS 201 requires the HIC_d, calculated from the integration of the time vs. acceleration pulse, in a 14.4 ± 0.5 mph test with a 10 lbs free-motion headform, to be below 1000. To achieve this, the headform should be decelerated through a specified distance. The aim is to derive a theoretical relationship between the HIC_d and the stopping distance, such that for a given baseline HIC_d, the minimum additional crush-space needed to meet the requirements can be quickly determined. Other investigators have derived this relationship assuming a simplified, triangular wave function for the pulse. This study incorporates a more practical haversine wave function, and further develops it to include both positively and negatively skewed haversine wave forms. This represents the complete range of actual tests, with varying waveform efficiencies. The curves, which represent the relationship between HIC_d and stopping distance, for three different efficiencies, are derived and are shown in comparison to the theoretical best. Discussion includes a practical guide for using these curves in determining additional crush space. Appropriate countermeasures which best utilize this crush distance can then be designed and optimized using Finite Element Analysis. Also discussed is the use of Finite Element Analysis to predict baseline HIC_d values before building prototypes, and performing design iterations to optimize the countermeasures for reducing intrusion into the passenger cabin, compliance, material, feasibility, and cost.