A STUDY OF SOFTBALL PLAYER SWING SPEED * LLOYD SMITH Shool of Mehanal and Materals Engneerng Washngton State Unversty E-mal: lvsmth@wsu.edu JEFF BROKER Department of Bology Unversty of Colorado, Colorado Sprngs E-mal: jbroker@us.edu ALAN NATHAN Department of Physs Unversty of Illnos at Urbana-Champagn E-mal: a-nathan@uu.edu A feld study was onduted to measure the effet of a bat s weght and mass moment of nerta (MOI) on the swng speed. The study nvolved 16 amateur slow-pth softball players of two skll levels and two groups of bats. One bat group had a onstant MOI, but varyng weght, whle the other group had onstant weght, but varyng MOI. Players were assgned to ether the onstant MOI or onstant weght group of bats and asked to swng at pthed softballs, usng eah of the fve bats n that group ten tmes. Bat moton was reorded usng hgh speed vdeo for eah swng. The results from the batters were ombned by normalzng eah swng speed to the respetve batter s average. The swng speed of the onstant MOI bats was observed to be nearly ndependent of the bat weght, whle the swng speed of the onstant weght bats showed a strong dependene on MOI. The dependene of swng speed on bat weght and MOI was smlar for the two player skll levels onsdered. The bat s enter of rotaton durng the nstant of mpat wth the ball was found to roughly orrespond to the loaton of the enter of the batter s wrsts. The results of ths study wll be used to develop test methods to orrelate bat performane. 1. Introduton In order to properly haraterze the httng performane of a baseball or softball bat, t s neessary to have some understandng of how fast the bat an be swung. For example, f two bats perform dentally n a laboratory test at a fxed relatve ball-bat speed, the bat that an be swung faster wll lkely perform better n the feld. Indeed, that s the urrent state of affars wth the Natonal Collegate Athlet Assoaton, whh has regulated that hollow alumnum baseball bats perform essentally dentally to wood bats n fxed-speed laboratory tests. Nevertheless, t s generally pereved that alumnum bats * Ths work was supported by the Amateur Softball Assoaton.
outperform wood bats n the feld beause the alumnum bats an be swung faster. Unfortunately, t s very dffult to model the swng of a bat n order to predt how swng speed s affeted by the nertal propertes of the bat, suh as ts mass or mass moment of nerta (MOI). Moreover, there have been very few systemat studes of bat speed n the sentf lterature, refletng the fat that bat speed s dffult to measure and an depend on ondtons not easly ontrolled or even quantfed. Despte these dffultes, prevous studes [1-4] have shown a qualtatve dependene of bat speed on nertal propertes. Unfortunately, beause of the dffulty n dong suh measurements and due to the seleton of bats used n these studes, the dependenes are usually not quantfed nor are the effets of mass and MOI separately determned. The lak of suh quanttatve results provded the prme motvaton for the urrent study, the results of whh wll mprove the way laboratory bat performane measures aount for a bat s mass propertes. 2. Feld Study The urrent study onsdered the effets that weght and MOI have on the swng speed of a softball bat. To ths end, 20 alumnum bats of the same model were weghted to study the effet of weght and MOI ndependently. Ten bats had the same weght but dfferent MOI, whle the remanng 10 bats had the same MOI but dfferent weght. The weght and MOI were nreased n fve nrements, as shown n Fgure 1, where MOI s referened to a pont 6 nhes from the knob to the barrel end of the bat. The study was onduted at the 2002 Natonal Softball Champonshp Tournament n Montgomery Alabama. Eght level A and sx level D male rghthanded players, known to be good htters, were nvted to partpate n the study before tournament play began. Eah player was assgned to the group of onstant weght or onstant MOI bats and asked to swng all fve bats n that group n random order. To redue fatgue effets, the batters worked n pars, alternatng after swngng eah bat ten tmes. Eah batter was allowed a few prate swngs before httng wth a new bat. 12000 11000 Bat Group MOI Effet WeghtEffet The bat speed was measured usng a hgh-speed vdeo system as depted n Fgure 2. A hgh-speed vdeo amera was plaed on a truss dretly over the batter. The amera reorded the player moton at 1000 frames per seond usng a shutter Bat MOI (oz n 2 ) 10000 9000 8000 7000 6000 24 26 28 30 32 Bat weght (oz) Fgure 1. Weght and MOI of the 20 bats
speed of 1/4000 seond and a resoluton of 1024 by 512. The amera was mounted 150 nhes above the ground and had a horzontal feld of vew of 142 by 71 nhes. Two addtonal vdeo ameras were plaed behnd the batter to provde a redundant reord of the vertal tp loaton of the bat as well as the orentaton of the bat wth respet to the horzontal plane. The vdeo ameras were albrated wth sales that were plaed horzontally on the ground and vertally next to home plate. To aommodate automat vdeo trakng from the overhead amera, eah bat had markers plaed at 12, 22, and 32 nhes from the knob at four loatons rumferentally around the bat. A redundant measure of bat speed was provded usng refletve tape on the bat and a lght trap that was plaed next to home plate. Four radar guns (one behnd home plate and three n the outfeld) were used as seondary measures of the batted ball speed. 3. Data Reduton The hgh-speed vdeo data were redued usng ommeral vdeo edtng software (Image Express Motontrak) whh provded the loaton and veloty of the ball and eah marker on the bat as a funton of tme wth respet to the fxed albraton sales. The bat-ball mpat typally ourred 40 nhes above the ground and up to 30 nhes n front of the plate. The orreted loatons for eah marker were found by solvng the followng smultaneously equatons for the orreted loatons. H z = (1) x xv H z y = y v (2) x xs + l z = ( zv h) d ( ) + h l sn θ (3) where x, y, and z denote the oordnates of the marker, the subsrpt or v denotes the orreted or vdeo loaton, respetvely, the supersrpt denotes the marker number, H and l are as depted n Fgure 2, and θ s the out-of-plane bat angle found from the low speed vdeo amera. Wth the orreted marker loatons, the veloty omponents, v, of eah marker were orreted and hgh speed vdeo amera reords player moton H 10 n. l Lght trap z h low speed vdeo amera reords vertal tp loaton and bat angle durng mpat Fgure 2. Shemat of vdeo system used to determne the bat speed.
expressed wth respet to the bat n the radal, r, and tangental, t, dretons aordng to H z [ ( ) ( )] v = v v t x os α avg y sn α (4) avg H z [ ( ) ( )] v = v + v r x sn αavg y os α avg (5) where α avg s the average n-plane orentaton of the bat, obtaned from the angle between the markers, as j x x α = j Tan 1 j y y (6) The oordnates of the bat s enter of rotaton, wth respet to the knob end of the bat, were found from v a = 10 + (34 d ) 1 v v + (7) v r t = ( d aavg ) v 34 (8) where a s the dstane from the knob of the bat along ts long axs, t s the transverse dstane from ths axs, and 34 and 10 represent the bat length and marker spang, respetvely. The dstane along the bat from the ball to the outer most marker, d b, was found from db = h b snαb (9) where 4. Verfaton ( ) 2 x x + ( y y ) 2 hb = b b (10) b y y α = b Tan 1 +θ b x x (11) After the data were redued, they were heked to ensure ther auray. The average marker spang from the hgh speed vdeo was wthn 0.03 nhes of the nomnal 10 nh spang. The marker spang durng 15% of the swngs was more than 0.5 nhes from ths value. Ths erroneous measurement exeeds the resoluton of the amera (0.14 nhes) and was attrbuted to non-level swngs, mpat ourrng outsde the feld of vew, or hangng lghtng ondtons as the test progressed. The vertal loaton was adjusted for these swngs to brng the marker spang wthn 0.25 nhes of the nomnal value. Wth ths orreton, 70% of the swngs had a marker spang wthn 0.25 nhes of the nomnal value.
The dstane from the pther to home plate (50 ft) and lmts on the pthed ball ar (6 to 12 ft) allow an deal pth speed to be found usng projetle moton. For a ball that begns ts trajetory at 2 ft from the ground, the n-plane omponent of the pth speed s between 22 and 34 mph. The average pth speed from the hgh speed vdeo was found to be 23 mph. The swng speed from the hgh speed vdeo was found to be, on average, 18% hgher than that found usng the statonary lght trap. The unfavorable lghtng ondtons only allowed a omparson of 30% of the swngs wth the lght trap. (The large amount of ambent lght redued the ablty of the lght trap to observe the refletve tape on the bat.) The ball-bat mpat normally ourred n front of the plate, sometmes as muh as three feet, resultng n a lower measured bat speed from the lght trap. On average the hgh speed vdeo reported a batted ball speed that was 8% hgher than that found usng radar guns. The dsrepany was attrbuted to the onedmensonal speed measurement obtaned from the radar gun, n omparson to the two-dmensonal hgh speed vdeo. Batted ball speeds are more dffult to measure aurately wth a radar gun than pth speed due to the unertanty regardng the ht ball dreton. 5. Results and Dsusson The speed for eah swng was normalzed to the average speed of the respetve player. Ths allowed omparson between players ndependent of ther skll level. The normalzed swng speed of the bats wth onstant MOI s presented n Fgure 3. The swng speed appears nearly ndependent of bat mass. The normalzed swng speed of the bats wth onstant mass, presented n Fgure 4, shows a strong dependene on bat MOI, where t saled aordng to ω ω = ( I I ) n (12) where n=¼, and I=9000 oz n 2. The dependene of bat MOI on swng speed vared among the players (0.08<n<0.37), but no onsstent orrelaton of n wth player skll level was observed. The average swng speed (at 6 nhes from the end of the bat) of the A and D level players was found to be 89 and 81 mph, respetvely. These speeds are hgher than have been observed n baseball [3]. The hgher speeds may be attrbuted to the nreased player preparaton and response tme assoated wth a slower pth. The nstantaneous enter of rotaton of the bat durng mpat wth the ball was found to le near the enter of the player s wrsts. The average loaton from ths study was found to be 2.6 nhes from the knob (toward the batter) and 2.7 nhes behnd the bat (toward the ather). As mght be expeted,
there was substantal satter n the enter of rotaton of the swngs. The majorty appeared evenly dstrbuted wthn a 4 nh radus of ths loaton. 6. Summary A feld study was onduted to determne the effet of bat mass and MOI on the swng speed of softball bats. A two-dmensonal hgh speed vdeo system was used to measure swng speed, pth speed, ht ball speed, and bat enter of rotaton. The system appears to have aptured the desred parameters of the bat and ball moton. The bat speed was shown to have an observable dependene on bat MOI, whle the effet of bat mass was not apparent. Results of ths work wll be used to mprove test methods to determne bat performane. 7. Referenes [1] S. Plagenhoef, Patterns of Human Moton, Prente-Hall, New Jersey (1971). [2] G. S. Flesg, N. Zheng, D. Stodden, and J. R. Andrews. Sports Engneerng, 5:1-8 (2002). [3] J. J. Crso, R. M. Greenwald, L. H. Penna, and K.R. Saul, The Engneerng of Sport, Blakwell Sene, A. J. Sub and S. J. Haake, eds. 193-200 (2000). [4] K. Koeng, T. Hanngan, N. Davs, M. Hllhouse, L, Spener, NCAA Researh Program on Bat and Ball Performane, Fnal Report, Provdene, RI, 88-100 (1997). Normalzed bat speed 1.10 1.05 1.00 0.95 Data Normalzed bat speed 1.10 1.05 1.00 0.95 Data n= 1/4 0.90 24 26 28 30 32 Bat weght (oz) Fgure 3. Normalzed bat swng speed (6 nhes from the tp) as a funton of bat mass for bats wth onstant MOI. 0.90 6000 7000 8000 9000 10000 11000 12000 Bat MOI (oz n 2 ) Fgure 4. Normalzed swng speed as a (6 nhes from the tp) funton of bat MOI for bats wth onstant mass.