Simple, as well as more sophisticated empirical airbag models have been developed since the early seventies. By discretization of the fabric skin of the airbag in finite elements, phenomena like the inertia effects due to the motion of the different parts of the fabric, bag slap, and pressure forces on penetrating objects are accounted for, also during the deployment phase of the airbag.
In most cases relatively simple thermodynamics, i.e. a lumped parameter approach, can be used. For an out-of-position occupant however a complication can arise if the gas jet coming out of the inflator is directed towards the occupant. A relatively simple analytical model to account for the gas jet effects in combination with a lumped parameter approach is implemented in the MADYMO finite element module.
A model validation using a pendulum test with a passenger side airbag shows a good agreement between the measured and calculated results, only when the gas jet effects are included in the analysis.