Thinking Outside the box 253 The edge crush test(ECT) value of a gauge of cardboard is the force per unit length that must be applied along the edge before the edge breaks. We make extensive use of the concept of such a value; however, the actual numbers given for gauges of cardboard apply to ideal situations that would not be replicated in the cases that we are considering [Boxland Online 19991 The flatwise compression test(FCT) value of a gauge of cardboard is the pressure that must be applied to collapse it. It does not directly correlate to the stress placed on boxes in practice and therefore is not used as an industr standard [Pflug et al. 2000 The bursting strength of a gauge of cardboard is the amount of air pressure required to break a sample. Because our model is concerned mainly with the strength of a box edge, but the bursting strength more accurately the strength of a face, we do not make use of it [Boxland Online 1999] The stacking weight of a box is the weight that can be applied uniformly to the top of a box without crushing it. In general, the stacking weight of a box is smaller than the ECT or bursting strength, because it takes into account the structural weaknesses of the particular box. We derive most of our numerical values for box strength from manufacturers specified stacking weights[ Bankers Box 2003] Assumptions The force exerted on every layer beneath the top platform is horizontally uniform The force that the motorcycle exerts on the top platform is concentrated where the wheels touch. Ideally, however, this top platform is perfectly flat and rigid so it distributes the force evenly to all lower layers. We approach this ideal by adding additional flats to the top platform The stacking weight of a box is proportional to its perimeter and inversely propor- tional to its height. This assumption is physically reasonable, because weight on a box is supported by the edges and because the material in a taller box This claim can be verified from data Clean Sweep Supply 2002 Orter box on average is farther from the box's points of stability than in a sh Nearly all of the work done to crush a box is used to initially damage its structural integrity. After the structure of a box is damaged, the remaining compression follows much more easily; indeed, we suppose it to be negligible. We denote by d the distance through which this initial work is done and assume for simplicity that the work is done uniformly throughout d. Through rough experiments performed in our workroom, we find that d a 0.03 m. W assume that this value is constant but also discuss the effect of making it function of the size of box and of the speed of the crushing objectThinking Outside the Box 253 • The edge crush test (ECT) value of a gauge of cardboard is the force per unit length that must be applied along the edge before the edge breaks. We make extensive use of the concept of such a value; however, the actual numbers given for gauges of cardboard apply to ideal situations that would not be replicated in the cases that we are considering [Boxland Online 1999]. • The flatwise compression test (FCT) value of a gauge of cardboard is the pressure that must be applied to collapse it. It does not directly correlate to the stress placed on boxes in practice and therefore is not used as an industry standard [Pflug et al. 2000]. • The bursting strength of a gauge of cardboard is the amount of air pressure required to break a sample. Because our model is concerned mainly with the strength of a box edge, but the bursting strength more accurately measures the strength of a face, we do not make use of it [Boxland Online 1999]. • The stacking weight of a box is the weight that can be applied uniformly to the top of a box without crushing it. In general, the stacking weight of a box is smaller than the ECT or bursting strength, because it takes into account the structural weaknesses of the particular box. We derive most of our numerical values for box strength from manufacturers’ specified stacking weights [Bankers Box 2003]. Assumptions • The force exerted on every layer beneath the top platform is horizontally uniform. The force that the motorcycle exerts on the top platform is concentrated where the wheels touch. Ideally, however, this top platform is perfectly flat and rigid, so it distributes the force evenly to all lower layers. We approach this ideal by adding additional flats to the top platform. • The stacking weight of a box is proportional to its perimeter and inversely propor￾tional to its height. This assumption is physically reasonable, because weight on a box is supported by the edges and because the material in a taller box on average is farther from the box’s points of stability than in a shorter box. This claim can be verified from data [Clean Sweep Supply 2002]. • Nearly all of the work done to crush a box is used to initially damage its structural integrity. After the structure of a box is damaged, the remaining compression follows much more easily; indeed, we suppose it to be negligible. We denote by d the distance through which this initial work is done and assume for simplicity that the work is done uniformly throughout d. Through rough experiments performed in our workroom, we find that d ≈ 0.03 m. We assume that this value is constant but also discuss the effect of making it a function of the size of box and of the speed of the crushing object