254 The UMAP Journal 24.3(2003) Figure 2. Tire before and after landing, acting as a shock absorber When the motorcycle lands, we ignore the effects of any shock absorbers and assume that the motorcyclist does not shift position to cushion the fall. This is a worst case scenario. To calculate how much force the tires experience per unit area, we consider a standard 19-inch tire of height 90 mm and width 120 mm [Kawasaki 2002]. It compresses no less than 50 mm(Figure 2). A simple geometry calculation then tells us that the surface area of the tire touching the platform is approximately 3000 mm. We assume that the force exerted on the motorcycle on landing is uniformly distributed over this area The pressure required to compress a stack of cardboard flats completely is the sun of the pressures required to compress each individual flat In a uniformly layered stack of boxes, each layer collapses completely before the layer beneath it begins to collapse. This is probably an oversimplification; however, it is reasonable to suppose that the motorcycle is falling nearly as fast as the force that it is transmitting The motorcyclist can easily land a jump 0. 25 m high The model Crushing an Individual Box For a cardboard box of height h, width w, and length l, by the assumptions ade above the stacking weight s is S(h, l, w) k(l+w) where k is a constant(with units of force) Once a box is compressed by a small amount, its spine breaks and very little additional force is required to flatten it. Thus most of the force that the box exerts on the bike is done over the distance d h, and we assume that the work is done uniformly over this distance; this work is W=(force)(distance) k(l +w)d254 The UMAP Journal 24.3 (2003) Figure 2. Tire before and after landing, acting as a shock absorber. • When the motorcycle lands, we ignore the effects of any shock absorbers and assume that the motorcyclist does not shift position to cushion the fall. This is a worst￾case scenario. To calculate how much force the tires experience per unit area, we consider a standard 19-inch tire of height 90 mm and width 120 mm [Kawasaki 2002]. It compresses no less than 50 mm (Figure 2). A simple geometry calculation then tells us that the surface area of the tire touching the platform is approximately 3000 mm2. We assume that the force exerted on the motorcycle on landing is uniformly distributed over this area. • The pressure required to compress a stack of cardboard flats completely is the sum of the pressures required to compress each individual flat. • In a uniformly layered stack of boxes, each layer collapses completely before the layer beneath it begins to collapse. This is probably an oversimplification; however, it is reasonable to suppose that the motorcycle is falling nearly as fast as the force that it is transmitting. • The motorcyclist can easily land a jump 0.25 m high. The Model Crushing an Individual Box For a cardboard box of height h, width w, and length l, by the assumptions made above, the stacking weight S is S(h, l, w) = k(l + w) h , where k is a constant (with units of force). Once a box is compressed by a small amount, its spine breaks and very little additional force is required to flatten it. Thus, most of the force that the box exerts on the bike is done over the distance d h, and we assume that the work is done uniformly over this distance; this work is W = (force)(distance) = k(l + w)d h .