【正文】 8038 Page 3 of 20 Contents Summary .......................................................................................................................... 1 Contents ........................................................................................................................... 3 of the Problem .............................................................................................. 4 of the Problem ................................................................................................... 4 Analysis of Problem I............................................................................................. 4 Analysis of Problem II............................................................................................ 5 Analysis of Problem III .......................................................................................... 5 Assumptions and Symbols ...................................................................................... 6 Model Assumptions ............................................................................................... 6 Symbols ............................................................................................................... 6 and Solution..................................................................................................... 6 Modeling and Solution to Problem I......................................................................... 6 Model Preparation........................................................................................ 6 Solutions to the two “sweet spot” regions ........................................................ 8 Optimization Model Based on TOPSIS Method ..............................................11 Verifying the “sweet spot” is not at the end of the bat ..................................... 12 Modeling and Solution to Problem II...................................................................... 13 Model Preparation...................................................................................... 13 Controlling variable method analysis ............................................................ 14 Analysis of corked bat and wood bat [5][6] ...................................................... 15 Reason for prohibiting corking[4] ............................................................... 16 Modeling and Solution to Problem III .................................................................... 17 Analysis of metal bat and wood bat [8][9] ........................................................ 17 Reason for prohibiting the metal bat [4] ......................................................... 18 and Weaknesses of the Model ........................................................................... 19 ............................................................................................................ 19 Weaknesses......................................................................................................... 19 ................................................................................................................... 20 Team 8038 Page 4 of 20 of the Problem Explain the “sweet spot” on a baseball bat. Every hitter knows that there is a spot on the fat part of a baseball bat where maximum power is transferred to the ball when hit. Why isn’t this spot at the end of the bat? A simple explanation based on torque might seem to identify the end of the bat as the sweet spot, but this is known to be empirically incorrect. Develop a model that helps explain this empirical finding. Some players believe that “corking” a bat (hollowing out a cylinder in the head of the bat and filling it with cork or rubber, then replacing a wood cap) enhances the “sweet spot” effect. Augment your model to confirm or deny this effect. Does this explain why Major League Baseball prohibits “corking”? Does the material out of which the bat is constructed matter? That is, does this model predict different behavior for wood (usually ash) or metal (usually aluminum) bats? Is this why Major League Baseball prohibits metal bats? of the Problem Analysis of Problem I First explain the “sweet spot” on a baseball bat, and then develop a model that helps explain why this spot isn’t at the end of the bat.[1] There are a multitude of definitions of the sweet spot: 1) the location which produces least vibrational sensation (sting) in the batter39。 then, develop a model to predict different behavior for wood or metal bats to find out the reason why Major League Baseball prohibits metal bats?[1][4] The mass (M) and the center of mass (CM) of the bat are different because of the material out of which the bat is constructed. The changes of the location of COP and moment of inertia ( batI ) could be inferred.[2][3] Above physical attributes influence not only the swing speed of the player (the less the moment of inertia batI is, the faster the swing speed is) but also the sweet spot effect of the ball which can be reflected by the maximum batted ball speed (BBS). The BBS of different material can be got by analyzing the material parameters that affect the moment of inertia. Then, it can be proved that the hitting effects of different bat material are different. Team 8038 Page 6 of 20 Assumptions and Symbols Model Assumptions 1) The collision discussed in this paper refers to the vertical collision on the “sweet spot”。s left hand. Fig45. Second bending mode 2 (670 Hz) The figures show the