224 The UMAP Journal 24.3 (2003) while the energy loss of the stunt person is from deceleration and falling: dt msu du dos dve t gus (5) Combining(3-5), substituting for ua, and rearranging, we obtain (6) Stage 4: Box Is Flattened Once the cardboard box is fully compressed and all the air is pushed out we assume that the box no longer has any effect on the stunt person. ummar In stages 1 and 4, the box is essentially inert--little energy goes into it Therefore in our mathematical description, we ignore these and concentrate on stages 2 and 3. Stage 2 occurs in the top AH of box deformation, while stage 3 occurs in the remainder of the deformation. Combining (1)and( 6), we get 2ms△HY ,|z|<|△Hi; 1 0A 2ma2-9,||21△H, where z is measured from the top of the box Modeling the Box Catcher Cardboard Properties We assume that each cardboard box is made of corrugated cardboard with uniform physical properties, using the data shown in Table 2 Table 2 Properties of corrugated cardboard [ Bever 1986 Property Symbol Value Tensile strength Ts 12.2MP Thickness 5 mm Youngs modulus 1.3 GPa224 The UMAP Journal 24.3 (2003) while the energy loss of the stunt person is from deceleration and falling: dUs dt + dVs dt = msus dus dt + msgus. (5) Combining (3–5), substituting for ua, and rearranging, we obtain dus dt = 1 2 ρA ms u2 s α2 − g. (6) Stage 4: Box Is Flattened Once the cardboard box is fully compressed and all the air is pushed out, we assume that the box no longer has any effect on the stunt person. Summary In stages 1 and 4, the box is essentially inert—little energy goes into it. Therefore in our mathematical description, we ignore these and concentrate on stages 2 and 3. Stage 2 occurs in the top ∆H of box deformation, while stage 3 occurs in the remainder of the deformation. Combining (1) and (6), we get dus dt =    1 2ms∆H T2 S Y V, |z| < |∆H|; 1 2 ρA ms u2 s α2 − g, |z|≥|∆H|, (7) where z is measured from the top of the box. Modeling the Box Catcher Cardboard Properties We assume that each cardboard box is made of corrugated cardboard with uniform physical properties, using the data shown in Table 2. Table 2. Properties of corrugated cardboard [Bever 1986]. Property Symbol Value Tensile strength TS 12.2 MPa Thickness τ 5 mm Young’s modulus Y 1.3 GPa