Mathematical Formulations for Impact Modelling

A wide variety of mathematical models have been applied to the study of pedestrian and cyclist impact. Early researchers formulated one-dimensional particle models of the human body to analyze the relationship between impact speed and pedestrian projection distance (e.g. [1], see Chapter 4). Today, finite element models of the human body with many thousands of degrees of freedom1 are used to predict pedestrian injuries [2–4]. However, despite the level of detail in these models, they do not automatically yield meaningful injury predictions (see Chapter 8), and their inherent complexity can mask fundamental insights which a simpler model may emphasise. This raises the important question of the appropriate complexity when formulating a model to analyze a problem. Clearly, a particle model of the human body cannot be used to predict detailed body kinematics, let alone body deformations and injuries, but it is less obvious whether a detailed multi-body or even finite element model is more appropriate to study pedestrian or cyclist projection distances than a simplified particle model. A guiding principle should be that if two models have been validated for a given purpose and yield the same prediction of a response, then the simpler model is better for that application, because additional detail which does not improve a model's predictions serves only to reduce clarity.² Furthermore as models become more complex they usually require more detailed knowledge of the input parameters, and this is frequently a limiting factor.