Safe landings 227 Thus, we could write a routine that would integrate the equations of motion of the stunt person falling through each level of boxes and for each layer use the e incon ning velocity to calculate the optimal dimensions for the next layer of boxes. This would yield a box-catcher structure that would safely stop the stunt person in the fewest levels of boxes, minimizing the cost of the box catcher. General solutions The most difficult aspect of finding a general solution is the need to know the speed of the stunt person at impact, which depends on the height of the box catcher. Given sufficient computing time, we could solve the equations with condition that the height above the ground at impact is the height of the box catcher. However, this is unnecessary for a paper of this scope Instead we use the model to shed light on the qualitative aspects of building a box catcher. Equation (10)tells us that for higher speeds of thestunt person, we need taller boxes ( larger e )to keep the force on the stunt person at its maximum llowable level. This means that it is necessary to place the tallest boxes at the top of the stack, followed by shorter ones, for both cost effectiveness and safety. Inspecting (11) shows that the optimal width of the box is inversely proportional to the height (w x (-). Thus, the box catcher should have the thinnest boxes on top and the widest ones on the bottom It follows that the optimal box catcher has short, wide boxes at the bottom and tall, narrow boxes at the te Furthermore, the equations of motion(8)contain u- in the air expulsion stage but no velocity-dependent term in the buckling stage. Hence, for high impact speeds, air expulsion provides the dominant deceleration, while for smaller impacts, box buckling is the more important stage Results Motorcycle stunt A stunt person on a motorcycle is preparing to jump over an elephant for the filming of a blockbuster movie. What should be going through a stunt coordinator's mind? The average height of an African elephant is 4m; the mass of a top-of-the- line motorcycle is 230 kg Encyclopedia Britannica Online 2003] We assume that the stunt person clears the elephant by about 2 m, so the impact velocity is 8 m/s. Choosing the parameters (=3 m and w =2m,a 3 m-tall homogeneous box catcher stops the stunt person and motorcycle after they fall about 2.33 m(Figure 1)Safe Landings 227 Thus, we could write a routine that would integrate the equations of motion of the stunt person falling through each level of boxes and for each layer use the incoming velocity to calculate the optimal dimensions for the next layer of boxes. This would yield a box-catcher structure that would safely stop the stunt person in the fewest levels of boxes, minimizing the cost of the box catcher. General Solutions The most difficult aspect of finding a general solution is the need to know the speed of the stunt person at impact, which depends on the height of the box catcher. Given sufficient computing time, we could solve the equations with condition that the height above the ground at impact is the height of the box catcher. However, this is unnecessary for a paper of this scope. Instead, we use the model to shed light on the qualitative aspects of building a box catcher. Equation(10)tells us that for higher speeds of the stunt person, we need taller boxes (larger ) to keep the force on the stunt person at its maximum allowable level. This means that it is necessary to place the tallest boxes at the top of the stack, followed by shorter ones, for both cost effectiveness and safety. Inspecting (11) shows that the optimal width of the box is inversely proportional to the height (w ∝ −2). Thus, the box catcher should have the thinnest boxes on top and the widest ones on the bottom. It follows that the optimal box catcher has short, wide boxes at the bottom and tall, narrow boxes at the top. Furthermore, the equations of motion (8) contain u2 in the air expulsion stage but no velocity-dependent term in the buckling stage. Hence, for high impact speeds, air expulsion provides the dominant deceleration, while for smaller impacts, box buckling is the more important stage. Results Motorcycle Stunt A stunt person on a motorcycle is preparing to jump over an elephant for the filming of a blockbuster movie. What should be going through a stunt coordinator’s mind? The average height of an African elephant is 4 m; the mass of a top-of-the￾line motorcycle is 230 kg [Encyclopedia Britannica Online 2003]. We assume that the stunt person clears the elephant by about 2 m, so the impact velocity is 8 m/s. Choosing the parameters  = 1 3 m and w = 1 2 m, a 3 m-tall homogeneous box catcher stops the stunt person and motorcycle after they fall about 2.33 m (Figure 1)