220 The UMAP Journal 24.3(2003) The total energy absorbed should equal the performer's initial energy(kinetic and potential) Fda =Uso vso However, the catcher itself cannot exert too large a force or it would be no better than having the performer hit the ground in the first place. We therefore set a maximum force, Fmax. The smaller we make F, the larger(and more expensive) the box catcher has to be. Therefore, to save both money and life, we would like to have F≈(1-6)Fmax, where d is a safety margin(0<8<1) The box catcher a box catcher consists of many corrugated cardboard boxes, stacked in yers, possibly with modifications such as ropes to keep the boxes together or inserted sheets of cardboard to add stability and distribute forces. When the stunt person falls into the box catcher, the impact crushes boxes beneath. As box collapses, not only does the cardboard get torn and crumpled, but the air inside is forced out, providing a force resisting the fall that is significant but not too large. As the performer passes though the layers, each layer takes away some kinetic energy Modeling the Cardboard Box We examine in detail the processes involved when a stunt person vertically impacts a single cardboard box. This analysis allows us to predict the effect of varying box parameters(shape, size, etc. on the amount of energy absorbed by the box Assumptions: Sequence of Events Although the impact involve ly complex interactions--between the performer's posture, the structure of the box, the air inside the box, the support of the box, the angle and location of impact, and other details--modeling thin- shell buckling and turbulent compressible flow is neither cost-effective for a movie production nor practical for a paper of this nature. We therefore assume and describe separately the following sequence of events in the impact 1. A force is applied to the top of the cardboard box220 The UMAP Journal 24.3 (2003) The total energy absorbed should equal the performer’s initial energy (kinetic and potential),
F dz = Us0 + Vs0 . However, the catcher itself cannot exert too large a force or it would be no better than having the performer hit the ground in the first place. We therefore set a maximum force, Fmax. The smaller we make F, the larger (and more expensive) the box catcher has to be. Therefore, to save both money and life, we would like to have F ≈ (1 − δ)Fmax, where δ is a safety margin (0 <δ< 1). The Box Catcher A box catcher consists of many corrugated cardboard boxes, stacked in layers, possibly with modifications such as ropes to keep the boxes together or inserted sheets of cardboard to add stability and distribute forces. When the stunt person falls into the box catcher, the impact crushes boxes beneath. As a box collapses, not only does the cardboard get torn and crumpled, but the air inside is forced out, providing a force resisting the fall that is significant but not too large. As the performer passes though the layers, each layer takes away some kinetic energy. Modeling the Cardboard Box We examine in detail the processes involved when a stunt person vertically impacts a single cardboard box. This analysis allows us to predict the effect of varying box parameters (shape, size, etc.) on the amount of energy absorbed by the box. Assumptions: Sequence of Events Although the impact involves many complex interactions—between the performer’s posture, the structure of the box, the air inside the box, the support of the box, the angle and location of impact, and other details—modeling thin￾shell buckling and turbulent compressible flow is neither cost-effective for a movie production nor practical for a paper of this nature. We therefore assume and describe separately the following sequence of events in the impact. 1. A force is applied to the top of the cardboard box