【正文】 , 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”。 c. distance between the pivot and the centerofmass d ( the distance between Block 2 and Block 3 in Fig. 43)。s left hand. Fig45. Second bending mode 2 (670 Hz) The figures show the two bending modes of a freely supported baseball bat. The handle end of the bat is at the right, and the barrel end is at the left. The numbers on the axis represent inches (this data is for a 30 inch Little League wood baseball bat). These figures were obtained from a modal analysis experiment. In this opinion we prefer to follow the convention used by Rod Cross[2] who defines the sweet zone as Team 8038 Page 11 of 20 the region located between the nodes of the first and second modes of vibration (between about 47 inches from the barrel end of a 30inch Little League bat). Fig. 46 The figure of “Sweet Zone 2” The solving time in accordance with the searching times and backtrack times. It is objective to consider the two indices together. Optimization Model Based on TOPSIS Method Table42 swing period T bat mass M bat length S CM position d coefficient of restitution BBCOR initial velocity inv swing speed batv ball massballm wood bat (ash) cm Adopting the parameters in the above table and based on the quantitative regions in sweet zone 1 and 2 in , the following can be drawn:[2] Sweet zone 1 is ),( LL = ),50( cmcm Sweet zone 2 is ),( *2*1 LL = ),( cmcm As shown in Fig 43, define the position of Block 2 which is the pivot as the origin of the number axis, and x as a random point on the number axis. 1) Optimization modeling[2] The TOPSIS method is a technique for order preference by similarity to ideal solution whose basic idea is to transform the integrated optimal region problem into seeking the difference among evaluation objects—“distance”. That is, to determine the most ideal position and the acceptable most unsatisfactory position according to certain principals, and then calculate the distance between each evaluation object and Team 8038 Page 12 of 20 the most ideal position and the distance between each evaluation object and the acceptable most unsatisfactory position. Finally, the “sweet zone” can be drawn by an integrated parison. Step 1 : Standardization of the extent value Standardization is performed via range transformation, minmaxmin* xx xxx ??? , *x is a dimensionless quantity， and ]1,0[*?x ),(}, a x {}, i n { m a xm i n*2m a x*1m i n xxxLLxLLx ??? 。 2) When mass M and the location of centerof mass CM changes, batI changes, which is the dominant factor deciding the swing speed. Analysis of corked bat and wood bat [5][6] Table 43 swing period T bat mass M Bat length S CM position d coefficient of restitution BBCOR initial velocity inv swing speed batv ball massballm wood cm cork cm The hitting effect reflects by above physical parameters: Apply these values in formula (411) and (413) 1) Calculate respectively： smBBS /)1( ? smBBS /)2( ? Thus )2()1( BBSBBS ? . )1(BBS represents the maximum battedballspeed of a corked bat, and )2(BBS represents the maximum battedballspeed of a wood bat. Team 8038 Page 16 of 20 Conclusion: when the swing speed ( batv ) and the initial velocity of the ball ( inv ) remain the same, the initial velocity of the wood bat is higher than the corked bat. That is to say that the corked bat does not enhance the “sweet spot” effect. Hence, it is not the reason why Major League Baseball prohibits “corking”. But the change of the momentofinertia caused by the material can explain the prohibit. 2) Calculation of the momentofinertia of two different bats: 2*142)1( cmgI bat ? , 2* 59)2( cmgI bat ? Thus )2()1( batbat II ? . )1(batI is the momentofinertia of the corked bat, and )2(batI is the momentofinertia of the wood bat. Conclusion: the mass and the momentofinertia of the bat reduces after corking, so then swing speed gets faster, which means the professional players are able to watch the ball travel an additional 56 feet before having to mit to a swing. It makes the game unfair to increase the hitting accuracy by corking the bat. Reas。 Step 3: Calculating the distance The Euclidean distance of the positive ideal position is: ? ?? ?? )( ** xxd The Euclidean distance of the negative ideal position is: ? ?? ?? )( ** xxd Step 4: Seeking the integrated optimal region The integrated evaluation index of the evaluation object is: ????? dd db… …………………………（ 45） 2) Optimization positioning Considering bat material physical attributes of normal wood, when the period is sT ? and the vibration frequency is 520?f HZ, the ideal “sweet zone” extent can be drawn as ? ?cmcm 0 4 , . As this consequence showed, the “sweet spot” cannot be at the end the bat. This conclusion can also be verified by the model for problem II. Verifying the “sweet spot” is not at the end of the bat 1) Analyzed from the hitting effect According to Formula 411 and Table 42, the maximum battedballspeed of Team 8038 Page 13 of