*4 Department of Mechanical Engineering, Saitama Institute of Technology, 1690, Okabe, Saitama, , Japan

Transcription

1 19 CNo (26-6) *1 *2, * Mechanism of Racket Spin Performance in Tennis (Spin Performance Improvement by Lubrication of String Intersections with Super High Speed Video Analysis) Yoshihiko KAWAZOE *4, Kenji OKIMOTO and Keiko OKIMOTO *4 Department of Mechanical Engineering, Saitama Institute of Technology, 169, Okabe, Saitama, , Japan Players often say that some strings provide a better grip and more spin than others, but ball spin did not depend on string type, gauge or tension in the past laboratory experiment. There was no research work on the spin to uncover what is really happening during actual tennis impact owing to difficult experiment. This paper made clear the mechanism of top spin and its improvement by lubrication of strings according to the high speed video analysis. It also provided the more detailed explanations of spin behavior by comparison between a lubricant string racket and a famous 'Spaghetti string racket' which was banned in 1978 by the International Tennis Federation since it used plastic spaghetti tubing over the strings to reduce friction resulting in the excessive spin on the ball. As the main strings stretch and slide side ways more, the ball is given more spin due to restoring force parallel to the string face when the main strings spring back and the ball is released from the strings. Furthermore, it showed that the more spin results in the reduction of shock vibrations of the wrist joint during impact. Key Words : Sport Engineering, Tennis Racket, Impact, Ball Spin, Strings, High Speed Video Analysis, Tennis Elbow, Shock Vibrations 1. ( 1 ) ( 2 ) ( 3 ) * * kawazoe@sit.ac.jp ( 4 ), ( 5 ) ( 1 ) ( 4 ) ( 5 )

2 ITF 1977 ( 6 ),( 7 ) 1978 ITF12(a) ( 6 ), ( 7 ) 1 1, 1 (a) (b) 1(c)(d) 34 ms 1(e)(f) 2 (a) From the side (b) From backside Fig.2 High speed video for impact topspin analysis. (a) fl (b) f3l (c) f5l (d) f7l (e) f9l (f) f11l Fig.1 Oblique view of topspin impact ( trial T2) of a tester in this experiment A 3A 6A 76A 86A 98A 17A 127A 147A 167A 187A 27A 227A Fig.3 Side angle views of topspin impact (trial 25) of a tester with frames per 1-4 s. Pre-impact: AL76A, contact: 86A17A, post-impact: 127A 197

3 2(a) 2(b) 2.1(b) 23 % (c) 23 7 nn 3 % 3 16 % 6 % 1, 3. 2 I 4 B = ( 2 / 3 ) R B m B = cm 2 g D 2 R B 6.7 cm m B 57.7 gtrial 25 (a) (b) VB 24.2 m / s 246 rpm, 5 lbs 3 hrs/day (a) (b) MEAN, F T, MEAN F T, MEAN d t / ( R B T C ) 7.9 N 4(a) 3.4 ms 4(b) 4.1 ms Trial 13F T, MEAN 5.3 N 4. (1) (a) 5 4(b) 8 (2) 5(b) F ( t ) = F m a x s i n ( t / T c ) ( t T c ) (1) 5(c) 1.7 ms S ( f ) =2 F m a x T c c o s ( f T c )/ [1 - (2 f T c ) 2 ] (2) j i k X i j k 5(d) 4.1 ms ) f 4(a) X i j k = r i j k S j ( f k ) (3) 3 5(c) 6 i j k r i k T c ( 8 ) - ( 12 ) 9 1 ( 12 )- (15) 11 ( 13 )- (15) 3, 4, 5 (a) 198

4 (T45_f179_L) Start contact. ms (T56_f142_L4) Start contact. ms (T45_f185_L).6 ms (T56_f148_L4).6 ms (T45_f19_L) 1.1 ms (T56_ f153_l4) 1.1 ms (T45_f196 _L) 1.7 ms (T56_ f159_l4) 1.7 ms (T45_f2_L) 2.1 ms (T56_ f163_l4) 2.1 ms (T45_f24_L) 2.5 ms (T56_f167_L4) 2.5 ms (T45_f29) 3. ms (T56_f172_L4) 3. ms (T45_f211) 3.2 ms (T56_f174_L4) 3.2 ms (T45_f213_L) End contact 3.4 ms (a) Without strings lubrication (trial T45) (T56_f176_L4) 3.4 ms (T56_f18_L4) 3.8 ms (T56_f183_L4) End contact: 4.1 ms (b) With strings lubrication (trial 56) Fig.4 Effect of strings lubrication on the ball spin behaviors (impact views from back side direction with frames per 1-4 s). (a) Without strings lubrication (b) With strings lubrication 199

5 (a) (T56 f ) Before impact (b) (T56_f142_L4) Start contact. ms (c) (T56_ f159_l4) 1.7 ms after contact (d) (T56_f183_L4) End contact: 4.1 ms after contact Fig.5 Ball spin behavior and mechanism of spin rate increase by lubrication of string intersections. Main strings stretch and slide side ways and spring back when the ball is released from the strings. (Impact views from back side direction). [rpm] [ms] [m/s] (a) Ball spin rate (b) Contact time TC (c) Post-impact ball velocity VB Fig.6 Typical Example of Effect of strings intersections lubrication on the ball spin rate and contact time [rpm] [ms] [m/s] (a) Ball spin rate (b) Contact time TC (c) Post-impact ball velocity VB Fig.7 Effect of string intersections lubrication on the ball spin performance (Average and standard error)

6 (a) Contact time TC = 2.6 ms (Flat drive without lubrication) Fig.8 Calculated shock shapes when a ball strikes the center on the string face of the racket at a velocity of (a) 2 m/s and (b) 3 m/s, respectively. 9 B 111 (a) 3 m/s (b), (c) f ( t ) d t F MEAN T C 2F MAX T C / m B V B V B (b), (c) (a) Fig.9 Geometry of Racket MP-1. (b) Contact time TC = 3.4 ms (Top spin without lubrication) (c) Contact time TC = 4.1 ms (Top spin with lubrication) Fig.11 Calculated effect of contact time on the wrist joint shock vibrations. Impact velocity: 3 m/s, hitting location: top side 95 mm from the tip of racket (B in Fig.9). (a) Contact time TC = 2.6 ms (Flat drive without lubrication) (b) Contact time TC = 3.4 ms (Top spin without lubrication) (c) Contact time TC = 4.1 ms (Top spin with lubrication) Fig.1 Calculated effect of contact time on the racket vibration. Impact velocity: 3 m/s, hitting location: top side 95 mm from the tip of racket (B in Fig.9) ( 3 ) 12(a),(b) 16 Goodwill, S & Haake, S. 12(c)

7 ( 6 ), ( 7 ) 4 lbs 7 lbs ( 7 ) X K G K B K GB K G 14 ( 8 ) - ( 12 ) 15 2 m/s ( 2 ), ( 3 ) 7. (a) Illustration of a 'Spaghetti' strung racket. (b) Picture of a 'Spaghetti' strung racket. (c) Fig.12 Comparison of the spin generated by rackets conventionally strung using natural gut and synthetic gut, and those strung using 'Spaghetti' stringing system (reprinted by permission of Goodwill, S. & Haake, S. ( 7 ) ).

8 Fig.13 Stiffness vs. deformation of a ball, strings, and a composed ball/string system assuming that a ball deforms only at the side in contact with the strings ( 1 ) ( 2 ). m K GB C GB M r Fig.14 Impact model of a ball-strings system. Low tension High tension V B Low V B High (a) (b) Fig.15 Stiffness of the string bed vs. impact velocity relative to the string tension as a parameter. 8. (1) (2) (3) (4) (5) (6) 12 Dr. Haake, S. Dr. Goodwill, S International Sports Engineering Association 16 (C) (1) Lindsey, C., Racquet Tech, the United States Racquet Stringers Association), October 23, p.2. (2) Kawazoe, Y., Theoretical and Applied Mechanics, Vol.43, (1994), pp (3) Kawazoe, Y., Tanahashi, R. and Casolo, F., Tennis Science & Technology 2, pp (23). ITF. (4) Cross, R., Sport Engineering, (23) 6, (5) Goodwill, S & Haake, S., The engineering of Sport 5, Vol.2, pp.3-9. International Sports Engineering Association (ISEA) (24) (6) ITF, (7) Goodwill, S & Haake, S., The engineering of Sport 4, pp Blackwell Science, (22) Oxford. (8) Kawazoe, Y., Theoretical and Applied Mechanics, Vol.41 (1992), pp (9) Kawazoe, Y., Theoretical and Applied Mechanics, Vol.42, (1993), pp (1) Kawazoe, Y., Theoretical and Applied Mechanics Japan, Vol.51, (22), pp (11) Kawazoe, Y., The engineering of Sport 5, Vol.2, pp ISEA, (24) (12) Kawazoe, Y.,Theoretical and Applied Mechanics, 46, (1997). (13) Kawazoe, Y., Theoretical and Applied Mechanics, Vol.49, (2), pp (14) Kawazoe, Y., Tomosue, R., Yoshinari, K. and Casolo, F., Tennis Science & Technology 2, (23). International Tennis Federation (ITF). (15) Kawazoe, Y., Casolo, F., Tomosue, R. & Yoshinari, K., The engineering of Sport 5, 1, (24), International Sports Engineering Association (ISEA)