An Analytical Study on Headform Impact Protection Space for a Rigid Target

This paper examines the theoretical worst case of normal headform impact on an infinitely rigid surface with the help of a dynamic spring-mass model. It is pointed out that the current approach is not an actual representation of any vehicle upper interior but is useful in gaining insight into the headform impact phenomenon and determining how to further enhance design. After considering force-deflection characteristics of a variety of commonly used headform impact protection countermeasures, a mathematical model is set up with spring properties that approximate those of physical countermeasures. Closed-form solutions are derived for various dynamic elasto-plastic phases including elastic unloading and contact. A parametric study is then carried out with HIC(d) as the dependent variable, and spring stiffness, yield force and spring length (representing countermeasure crush space) as the design variables. Through analysis performed in this study, it will be shown that no matter how efficient a countermeasure may be in terms of energy absorption, a crush space of about 30 mm to cover an infinitely rigid surface is generally required for attaining HIC(d) levels below 1000 at an impact velocity of 15 mph. It is pointed out that in an actual vehicle environment, a crush space of less than 30 mm may suffice due to structural compliance of vehicle targets. The approach detailed here can be extended to this latter case of headform impact targets with finite stiffness and yield characteristics.