268 The UMAP Journal 24.3 (2003) To illustrate the process of collision with just one layer separately, we sup pose that the mutual effect of the stunt person and the box-pile is motion with a constant acceleration. During that, the stunt person plus motorcycle is sup- ported by a constant vertical force F--that is, we treat f as the average force during the whole process It can be proved that although the stunt person strikes the boxes of different layers at different initial velocities, the work consumed to fall through each box is the same(Appendix A). The number of layers L of the box-pile is determined by the formula Work×L where L is the smallest integer that satisfies this inequality. Strength and weaknesses This model is simple and efficient. However, we have ignored the detailed process and substituted constant work, though in fact the force changes with Realistic mechanical Model First we study the empirical deformed load curve of the cushion system 2000 g the boxes'deformation under a static load(Figure 2)[Yan and Yuan Deforation Figure 2. Deformation curve The compression process is divided into three phases, as shown in the figure Oa phase: Elastic deformation, according to Hooke law AB Phase: Plastic deformation. The compression grows more slowly and reaches the maximum BC phase: Crush-down deformation: After compression reaches the maxi- mum the rate of deformation starts to fall. The unrecoverable deformation goes on IncreasIng
268 The UMAP Journal 24.3 (2003) To illustrate the process of collision with just one layer separately, we suppose that the mutual effect of the stunt person and the box-pile is motion with a constant acceleration. During that, the stunt person plus motorcycle is supported by a constant vertical force F— that is, we treat F as the average force during the whole process. It can be proved that although the stunt person strikes the boxes of different layers at different initial velocities, the work consumed to fall through each box is the same (Appendix A). The number of layers L of the box-pile is determined by the formula Work × L − mgh ≥ 1 2mv2 0 − 1 2mv2 safe, where L is the smallest integer that satisfies this inequality. Strength and Weaknesses This model is simple and efficient. However, we have ignored the detailed process and substituted constant work, though in fact the force changes with time. Realistic Mechanical Model First we study the empirical deformed load curve of the cushion system, showing the boxes’ deformation under a static load (Figure 2) [Yan and Yuan 2000]. Figure 2. Deformation curve. The compression process is divided into three phases, as shown in the figure: • OA phase: Elastic deformation, according to Hooke Law. • AB phase: Plastic deformation. The compression grows more slowly and reaches the maximum. • BC phase: Crush-down deformation: After compression reaches the maximum, the rate of deformation starts to fall. The unrecoverable deformation goes on increasing
You Too Can Be james Bond 269 According to the Kellicut formula [Yan and Yuan 2000; Zhao et al. the com pressive strength of a box is d P=P Z/4 ZJ where P is the compressive strength of the box, Pr is the comprehensive annular compressive strength of the paper, d is the corrugation constant Z is the circumference of the top surface, and J is the box shape coefficient For the stunt person plus motorcycle, the maximum supporting force from the box is nearly 2/3 F0=D=P2)2J1p=b2-5, where b is a constant concerning the properties of paper We assimilate the static loading process to the dynamical process of getting impacted and obtain the following buffering force and its deformation graph gure Fo F ≤x≤b; h The model describes the mechanical capability of the box and offers an ap propriate curve of the relationship between buffering power and deformation We can measure the energy consumed by the crushing of boxes. One limitation is the Kellicut formula, which applies only to certain kinds of cardboard boxes Error may also occur in replacing the dynamical process with a static process Ideal air box model We consider the depleting energy consumed by the resistance of air in the process of compression. We divide the process into two phases Phase 1: Assume that the cardboard is closed(gas can' t escape). The pressure in the box rises from standard atmospheric pressure Po to Pt=k po(k atmo- sheres)at time t when the box ruptures. We consider that the impact is so
You Too Can Be James Bond 269 According to the Kellicut formula [Yan and Yuan 2000; Zhao et al.], the compressive strength of a box is P = Px dx2 Z/4 1/3 ZJ, where P is the compressive strength of the box, Px is the comprehensive annular compressive strength of the paper, dx2 is the corrugation constant, Z is the circumference of the top surface, and J is the box shape coefficient. For the stunt person plus motorcycle, the maximum supporting force from the box is nearly F0 = P s (Z/4)2 = Px dx2 Z/4 2/3 ZJ s (Z/4)2 = bZ−5/3s, where b is a constant concerning the properties of paper. We assimilate the static loading process to the dynamical process of getting impacted and obtain the following buffering force and its deformation graph (Figure 3). F = F0 a x, x ≥ a; F0, a ≤ x ≤ b; F0 exp −a(x − b) h , x ≥ b. The model describes the mechanical capability of the box and offers an appropriate curve of the relationship between buffering power and deformation. We can measure the energy consumed by the crushing of boxes. One limitation is the Kellicut formula, which applies only to certain kinds of cardboard boxes. Error may also occur in replacing the dynamical process with a static process. Ideal Air Box Model We consider the depleting energy consumed by the resistance of air in the process of compression. We divide the process into two phases: Phase 1: Assume that the cardboard is closed (gas can’t escape). The pressure in the box rises from standard atmospheric pressure P0 to Pt = kP0 (k atmospheres) at time t when the box ruptures. We consider that the impact is so