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Sports Engineering ISSN 1340-8763 The Japan Society of Mechanical Engineers Vol.15, No.2 December 2004 URL http://www.jsme.or.jp/English Sports Engineering Base Ball and Golfball Aerodynamics A mysterious flight trajectory of a rugby ball Taketo Mizota, Kazuya Seo Fukuoka Institute of Technology, Associate Professor Intelligent Mechanical Engineering Faculty of Education, Yamagata University Introduction Abstract: 3-dimentional-trajectory analysis of baseball and golf ball is conduct- The aerodynamic characteristics of a rugby ball as well as its unpredict- ed. These balls flight with various flight conditions of ball speed, revo- able flight trajectory are described. It is found that the side force is in- lution speed and direction of fluenced by the four corners of the ball. The simulated flight trajectory its axes. We can observe of the ball with lower spin these features with TV im- rate fluctuates in the lateral ages or flight experiments. direction. Aerodynamic forces acting Introduction on the balls under individual There is an unpredictable flight conditions are meas- flight trajectory of a rugby ured by precise wind tunnel ball during flight. This tra- experiment. The kinematics jectory is seen with a non- equations are estimated by U ↑ → ← spinning (or slower Continued on page 2 Continued on page 4 The swimming style and fluid dynamics of A current of product development for swimming competitive swimsuits Shinichiro Ito Hideki Takagi Assistant Professor, Department of Mechanical Engineering, Associate professor, Institute of School of System Engineering, Health & Sport Sciences, University National Defense Academy of Tsukuba Advancing movement of an animal in water can be roughly divided Introduction into two categories, locomotion of the maximal efficiency (the minimal Humans have long dream of being able to swim like fish, despite the energy consumption mode) fact that we are not physically well suited to swimming. When a human for an usual motion and swims, the around the body Catch that of the maximal speed undergoes a transition to (the maximal thrust mode) turbulent flow, and drag Pull for an urgent evacuation or dramatically increases. For a predatory action instinc- instance, Reynolds number Finish tively. Human's instinctive during human-swimming motion of the maximal reaches a range of 2.5*106 speed might have been al- to 3.5*106, then the flow tered by intelligence in the around the body changes (a) S-Shaped pull (b) I-Shaped pull swimming history. from the laminar Continued on page 6 Continued on page 8 JSME NEWS Base Ball and Golfball Aerodynamics Taketo Mizota Fukuoka Institute of Technology, Intelligent Mechanical Engineering Continued from page 1 numerically under the initial conditions The aerodynamic cause of rolling spin knuckle ball is and the aerodynamic forces of ball flight. These results are con- simpler, as explained as follows. The ball rotates around firmed by outdoor or wind tunnel experiments. These analyses are an axes toward forward direction (X-direction) with large traditional or typical research method, but there is a science. When side force vector. The vector raises horizontal (Z-direc- we can find the various flight equations, we feel as to find up new tion) component and perpendicular (Y-direction) one. The living thing. horizontal one becomes a force cause of ball shake. This force is one cycle change with ball one round, so up to 4 Aerodynamic characteristics of sports balls1) round spin per second is available to make the ball with Sports ball is 3-D body. Reynolds number is ranging ～ knuckle change. 105～. These balls flight under lower speed of critical Re We succeed in the formulation of these flutter phenom- number of smooth sphere. But, the transition of surface ena, and well coincidences are reported with the shaking boundary layer occurs by the influence of surface rough- amplitude of the ball by this theoretical result and the flut- ness of ball seams or dimples. More over, the ball rotates. ter experiments with wind tunnel. The lift force acts on the backspin forward ball by Magnus Under these theoretical explanations, we made a shoot- effects. Index of the degree of the magnitude of aerody- ing machine of the knuckle ball. We could observe 3-D namic force, which is available to make ball erratic move- trajectory pass of the ball thrown from this machine using mant is expressed so called Mass ratio= (Ball mass) / (Air video camera system. In Fig.1, one example of flight pass mass of ball volume). Most heavy ball with less influence are shown as a top view. All balls have same initial shoot- of aerodynamic force is a cannonball, the sensitive ball to ing condition, but non-same-trajectory ball had observed. air force may be a beach volleyball. The knuckle ball is one of the flutters. Thanks to a conver- sation with Tim Wakefield6). Erratic behavior of baseball Forkball7) Knuckle ball2),3),4) Every time, good fork balls are utilized alternatively This changing ball is special characteristics by thrown with good straight balls. The good straight ball has a hori- with almost zero spinning ball. Various strange changes of zontal backspin axes, which makes upward Magnus force more than 40 cm shaking amplitudes, sudden drop and as same magnitude of ball weight. The straight ball sometimes floating ball as if in the non-gravity space are thrown by one of the most excellent pitcher in Japan, observed during ball flight of 18.44m between pitcher's named Matsuzaka, falls down only 3 or 4 cm during plate and home base. 18.44m, so it looks like a rising ball. There are two kinds of Knuckle ball with spinning axes. The other hand, the spinning axes of good forkball has One is side spin knuckle ball with vertical axes with speed oriented to vertical direction and side spinning with 10～ of about 80 Km/h. The other is rolling spin axes with hori- 20rps. No lift force acts on the ball, so as to fall about 70 zontal axes toward home base and speed of about 110 cm naturally with gravity force. Throwing form of the Km/h. Tim Wakefield, measure leaguer, Boston Redsox had maneuvered the sidespin knuckleball in his earlier ages, but recently he has been throwing rolling spin knuckleball. The aerodynamic reason of sidespin knuckle ball is 0.5 explained as follows. Turbulent boundary layer on one side by a ball seam roughness → retrogression of separa- tion line toward ball rear surface → wake shift the other 0 side with this phenomenon → circulatory flow around ball → side force as same magnitude of drag force → change the relative position of seam with small spin by aerody- Z-position (m) -0.5 namic torque5) → reverse side force → shaking ball with alternative side force. The side forces change four times 01020 with the ball one round, so more than 0.8 round/sec, less Ｘ-position (m ) amplitude of the flight ball results in far to the outfield of Fig.1 Knuckle ball trajectory (Top view observation: baseball park by a batter. non-ball trajectory with same pass) 2 Vol.15, No.2 December 2004 observe that golf ball fright is toward right and left detach- ing from its initial pass. The cause of this phenomenon had been explained as ball side spin concepts during these 100 years. Recently, Mizota and Naruo9) had succeeded in the for- mulation of 3-D trajectory of golf ball under the inclina- tion of ball back spin axes, and conducted out door flight experiments to clarify the effects of natural wind by atmospheric boundary layer Conclusion remarks Fig.2 Vertical slider pitched by Matsuzaka, Seibu Lions, In this short article, we suggest that there are many sci- observed from catcher, U=136 Km/h, 42.5rps, entific un-explored subjects in sports ball aerodynamics. 1/90sec picture. Numerical analysis by computer is powerful weapons to approach in the problem but wind tunnel experiments are pitcher is same as in the case of straight ball pitching. more reliable tool. Until the half way of this ball fright, its trajectory is almost same pass of straight ball, so batter can not recog- Reference nize straight or fork ball. Some time we watch on TV that １）R.D. Mehta: Aerodynamics of Sports Ball, Ann. Rev. batter swings one bound ball just front area at home base. Fluid Mech., Vol.17, pp.151-189, 1989. ２）R.G. Watts and E. Sawyer: Aerodynamics of knuck- Longitudinal slider by Matsuzaka8） leball, Am. J. Phys. Vol. 43, No.11, pp961～963, This changing ball had been much focused by many 1975. persons after that Matsuzaka became active in the Japan- ３）Taketo Mizota, Hiroyuki Kuba and Atsushi Okajima; ese professional baseball. Lundy Johnson, Diamond Erratic Behavior of Knuckleball (1) Quasi-steady Backs, also has same nice slider ball. The changing fea- Flutter Analysis and Experiment, J. of Wind Engi- ture is same as the fork ball, fall. Matsuzaka pitches this neering, , No.62, pp.3-13, January 1995 near around 140Km/h, so we call this as high speed slider. ４）Taketo Mizota, Hiroyuki Kuba and Atsushi Okajima; Fig.2 is high speed slider pitched by Matsuzaka pho- Erratic Behavior of Knuckleball, (2) Wake Field and tographed from catcher side. The ball seam appears in Aerodynamic Forces, J. of Wind Engineering, No.62, every frame as rotating U-type symbol. This means that pp.15-21, January 1995 the spinning axes direction of the high speed slider by ５）R. Weaver: Comment on "Aerodynamics of knuckle- Matsuzaka oriented to ball forward one. This ball kine- ball", Am. J. Phys. Vol.44, No.12, p1251, 1976 matical conditions result in non-lift and non-side force on ６）Get more winning game, Wakefield, J.
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