RACKET FOR PLAYING A GAME WITH A BALL

Abstract: The stiffness of a tennis racket is adjusted so that the first mode of bending of the racket under free-free constraint conditions is between 170 Hz and 250 Hz preferably between 200 Hz and 210 Hz. The second mode of bending under clamped-free constraint conditions is between 215 Hz and 315 Hz and preferably between 230 Hz and 265 Hz.

Description: This invention relates generally to a game racket having a handle portion, a loop-shaped head portion, and a throat portion joining the handle portion and the head portion, the racket having a longitudinal axis which is aligned with the centerline of the handle and a midplane which extends through the longitudinal axis parallel to the plane of the loop-shaped head portion. In such a conventional racket, which is shown by EP-A-0 168 041, the stiffness of the frame and shaft portions are such that when a ball strikes the strung face of the racket, the head frame portion is forced out of the longitudinal axis of the racket. This deflection adversely affects the flight path of the rebounding ball. In any body subjected to an input loading, some complicated vibrational reaction will occur. This complicated deformed shape of the body can be reduced to the sum of an infinitive number of simple vibrational mode shapes with varying amplitudes and frequencies. The specific frequencies, mode shapes, and amplitudes associated with a vibrating body are dependent upon a number of factors. Among these are the stiffness and weight distributions within the body, as well as the level of constraint of the body. Stiffness and distributions may be controlled in two ways. One method would be the use of specialized reinforcement materials in portions of the body, where these materials would have greater strength-to-weight and stiffness-to-weight ratios. Another method of controlling stiffness and wait distributions would be varying the geometry of the cross-section of the body, more specifically using a constant amount of material in the cross-section while varying the area-moment-of-inertia of the section so that the stiffness-to-weight ratio is varied. Increasing stiffness increases the vibrational frequencies and decreases dynamic deformation amplitudes. Increasing weight reduces vibrational frequencies and decrease dynamic deformation amplitudes. Two specific constraint conditions are of interest in this discussion. One extreme, the condition of "free-free" constraint, represents a body vibrating unconstrained in space. This may be approximated in the laboratory by suspending the body by elastic bands and allowing it to vibrate freely. The first two vibrational mode shapes for a simple beam in bending under "free-free" constraint conditions are shown in Figure 10. At the opposite extreme is the "clamped-free" constraint condition, where one end of the body is rigidly clamped in a support fixture while the other end is allowed to vibrate freely. The first three vibrational mode shapes for a simple beam in bending under "clamped-free" constraint conditions are shown in Figure 11. It should be noted that modes 1 and 2 in Figure 10 have approximately the same shapes as modes 2 and 3, respectively, in Figure 11. The addition of a rigid clamp to a body in bending under the "free-free" condition results in the excitation of an additional low frequency mode of vibration (mode 1 in Figure 11). The frequencies of modes 1 and 2 under "free-free" constraint conditions are not the same as the frequencies for the associated mode shapes (modes 2 and 3 respectively) under "clamped-free" conditions. The frequency of a mode shape under one of the constraint conditions can be approximated from the frequency of the mode shape under the other condition using the following relationship: Freq cf = Freq ff X (L ff /L cf )² (Equation 1) with L cf - L ff - L cc where Freq cf = frequency of the mode shape under "clamped-free" conditions Freq ff = frequency of the mode shape under "free-free" conditions L ff = length of the beam under "free-free" conditions L cc = length of the beam held under the clamping fixture L cf = equivalent length of the beam under "clamped-free" conditions. Tennis rackets exhibit vibrational characteristics similar to those described above for simple beams due to ball/racket impacts which occur during play. Laboratory testing was performed on various rackets. Test results indicate that for conventional tennis rackets under "free-free" constraint conditions, the first mode of bending is in the range 100 Hz to 170 Hz. Conventional rackets under "clamped-free" constraint conditions exhibit frequency ranges for the first and second modes of bending between 25 Hz to 50 Hz and 125 Hz to 210 Hz, respectively. US-A-4,664,380 (DE-A-3434898) states that the resonance frequency of the racket described therein under "clamped-free" constraint is from 70 to 200 Hz. Studies have shown that a tennis racket vibrating under "free-free" conditions more closely approximates the behavior of a tennis racket during play than does a racket in the "clamped-free" condition. If "clamped-free" constraint conditions exist during testing, equation 1 must be used to modify the frequency values so that the second mode of bending under "clamped-free" conditions approximates the first mode frequency values for "free-free". It has been observed that for a conventional tennis ball, ball/racket impact times range between 2 and 7 milliseconds, with the average being between 2 and 3 milliseconds. During this period, the head portion of the racket is deflecting back due to the force input from the ball. In a conventional racket, the ball leaves the strings some time between the point of ball/racket impact when the racket begins deforming and shortly after the racket has reached the maximum point of deflection. As a result, the flight path of the shot is affected (see Figure 12) and energy is lost since the racket has not returned to its undeformed position where the rebound angle is zero and the racket head speed is a maximum. The above mentioned EP-A-0168041 does not disclose the frequency of either the first mode of bending under free-free contraint or the frequency of the second mode of bending under clamped-free constraint. Rather, EP-A-0168041 merely describes vibrating an implement with a vibrator to determine the mechanical impedance and varying the structure of the racket so that a primary minimum value of the mechanical impedance falls within a specified range of frequency of from 110 to 500 Hz. There is no disclosure in the document regarding the frequency of the first mode of bending under free-free constraint conditions. US-A-4291574 refers to a frequency F₁ of vibration perpendicular to the racket face with the ends free, and the racket is held at the nodal pivot at the handle end. The maximum frequency disclosed is only 170 Hz. Having regard to that prior art, the inventor set himself the aim of providing a racket of the kind set forth in the opening part of this specification, which shows ameliorated conditions for the ball-striking performance of rackets. These and other objects are achieved in a racket according to the teaching of the independent claim. Other embodiments, are shown in the dependent claims of the invention. If the ball remains on the strings while the racket deflects and does not leave the strings until the racket has returned to the undeformed position, the ball flight path will be unaffected and the accuracy of the shot is improved (see Figure 13). In addition, since the racket head speed is a maximum at this point, greater energy is imparted to the ball, and a more powerful shot results. Changing the deformation period of the tennis ball is not considered a desirable solution to the problem. Therefore, for optimum performance the tennis racket must be designed so that the frequency of the dominant vibrational mode excited in the racket during play is matched with the duration of the ball/racket contact. More specifically, one-half of the period of the first mode of bending for a tennis racket under "free-free" constraint conditions should be equal to the dwell time of the tennis ball on the strings. The first mode of bending under "free-free" constraint conditions is chosen because this is the dominant vibrational mode excited during play. The optimum tennis racket would have a first mode of bending under "free-free" constraint conditions between 170 Hz and 250 Hz since ball/racket impact times of 2 to 3 milliseconds are common. Using equation 1, the frequency range under "clamped-free" conditions, considering a 685.8 mm (27 inch) racket suspended by a rigid support at 76.2 mm (3 inches) on the handle, would be between 215 Hz and 315 Hz for the second mode of bending. One specific embodiment of the racket has a frequency range between 200 Hz and 210 Hz for the first mode of bending under "free-free" constraint conditions, and a frequency between 230 Hz and 265 Hz for the second mode of bending under "clamped-free" conditions. The invention will be explained in conjunction with an illustrative embodiment shown in the accompanying drawing, in which -- Fig. 1 is a top plan view of a tennis racket formed in accordance with the invention. Fig. 2 is a side elevational view of the racket of Fig. 1; Fig. 3 is a top plan view of the frame of the racket of Fig. 1 without the strings and the handle cladding; Fig. 4 is a side elevational view of the racket frame of Fig. 3; Fig. 5 is a sectional view taken along the line 5-5 of Fig. 3; Fig. 6 is a sectional view taken along the line 6-6 of Fig. 3; Fig. 7 is a sectional view taken along the line 7-7 of Fig. 3; Fig. 8 is a sectional view taken along the line 8-8 of Fig. 3; Fig. 9 is a fragmentary perspective view of a portion of the racket frame showing the multiple layers of graphite fibers; Fig. 10 illustrates the first and second modes of bending of a tennis racket in the free-free constraint condition; Fig. 11 illustrates the first, second, and third modes of bending of a tennis racket under clamped-free constraint conditions; Fig. 12 illustrates the deformation of a conventional prior art racket when a conventional tennis ball rebounds from the racket after impact; and Fig. 13 illustrates the deformation of a tennis racket in accordance with the invention when a conventional tennis ball rebounds from the racket after impact. As described previously, it is desirable to adjust the stiffness of a tennis racket so that after a conventional tennis ball impacts the racket, the racket will return to its original undeformed position before the ball leaves the strings of the racket. Under those conditions, the flight path of the ball before and after impact with the racket will be unaffected and the accuracy of the shot will be improved as illustrated in Fig. 13. Further, greater energy is imparted to the rebounding ball, and a more powerful shot results. It is desirable to adjust the stiffness of the tennis racket so that the racket has a first mode of bending under free-free constraint conditions between 170 Hz and 250 Hz. Such a racket would have a second mode of bending under clamped-free constraint conditions between 215 Hz and 315 Hz. Figs. 1-9 illustrate one particular embodiment of a tennis racket 15 which has such frequencies. Referring first to Figs. 1 and 2, the racket 15 includes a frame 17 which has a handle portion 18, a throat portion 19, and a head portion 20. The throat portion 19 includes a pair of frame members 21 and 22 which diverge from the handle portion 18 and merge with the head portion 20. A yoke piece 23 extends between the throat pieces 21 and 22 and forms the bottom of the head portion, which is generally loop-shaped or oval. The tennis racket also includes a plurality of longitudinal strings 24 and cross strings 25 which extend into conventional openings in the head portion 20 and yoke piece 23. A plastic bumper 26 extends around the top of the head portion to protect the head from scuffs and abrasions. The bumper is held in place by the strings, and the bumper also protects the strings from abraiding against the holes in the racket frame. A plastic insert 27 extends between the end of the bumper 26 and the throat portion 19 to protect the strings in the lower portion of the head. The racket also includes a conventional handle cladding 28 and end cap 29 on the handle portion 18. The handle cladding can be formed from a spirally wound strip of leather. Figs. 3 and 4 illustrate the racket frame 17 without the strings and the handle cladding. Referring to Figs. 5-8, each of the frame portions 18-23 is formed from a tubular frame member having a wall thickness of about 1.143 mm to 1.27 mm (0.045 to about 0.050 inch). The tubular frame member is formed from layers of resin-impregnated graphite fibers which are wrapped around an inflatable bladder. As is well known in the art, when the racket frame is placed in a mold, the bladder is inflated to force the layers of graphite fiber against the mold until the resin cures. Fig. 9 illustrates the layers 31-42 of resin-impregnated graphite fibers which are used to form the tubular frame members of the preferred embodiment. Each of the layers 31-42 includes unidirectional graphite fibers which are oriented in the direction indicated by the cross hatching. Layers 31, 32, and 35-42 include graphite fibers having a modulus of elasticity of about 227528.4 x 10⁶ N/m² (33,000,000 pounds per square inch). Layers 33 and 34 include graphite fibers having a modulus of elasticity of about 310266 x 10⁶ N/m² (45,000,000 pounds per square inch). About 10 to 20% of the graphite fibers used in the racket frame have the higher modulus of elasticity, and about 80 to 90% of the graphite fibers have the lower modulus of elasticity. The use of the higher modulus graphite fibers increases the stiffness of the racket without increasing the weight of the racket. The outer layer 43 of the racket frame which is illustrated in Fig. 9 is a layer of paint. Returning to Figs. 3-6, the outer surface of the head is provided with a groove 45 in which the string holes 46 are located. The groove 45 also serves to position the bumper 25 and the insert 26 (Fig. 2). The height of the racket frame is determined with respect to Fig. 4 and measures the dimension of the racket perpendicular to a midplane MP which extends through the longitudinal centerline CL of the handle portion 18. The longitudinal centerline CL also forms the longitudinal axis of the racket in Fig. 3. The strings of the racket lie in the midplane MP, and the bending of the racket which is illustrated in Figs. 10 and 11 occurs in a plane which extends perpendicularly to the midplane. The height of the racket frame in Fig. 4 increases continuously from the dimension A at the top of the head portion of the frame to the dimension B in the throat portion of the frame. The height of the racket decreases continuously from the dimension B to the dimension C at the top of the handle portion 18. The height of the handle portion increases from the dimension C to the dimension D and then remains continuous to the bottom of the handle portion. The maximum height B of the racket frame occurs in the area where the throat members 21 and 22 merge with the head portion 20. Comparing Figs. 3 and 4, the maximum dimension B is generally aligned with the center of the yoke piece 23 where the yoke piece is intersected by the longitudinal centerline CL. Comparing Figs. 6 and 7, the height of the yoke piece 23 is substantially less than the height of the yoke members 21 and 22 and the head portion 20 in the area of the maximum height B. In one specific embodiment of a large head racket, the inside longitudinal dimension E of the head portion was 34.962 cm (13.7647 inches), the inside transverse dimension F of the head portion was 25.797 cm (10.1563 inches), and the overall length L was 68.4784 cm (26.960 inches). The height A at the top of the head portion was 2.7686 cm (1.090 inches), the maximum height B was 3.81 cm (1.500 inches), the height C was 2.54 cm (1.000 inch), and the height D varied depending upon the handle size in accordance with conventional handle dimensions. Referring to Fig. 5, the overall width G of the head portion at the top of head portion was 0.9652 cm (0.380 inch). Referring to Fig. 7, the height H of the yoke piece 23 was 2.7432 cm (1.080 inches), and the width I was 1.016 cm (0.400 inch). The ratio of the maximum height B to the minimum height A of the head portion was 1.5/1.09 or 1.376. The area moment of inertia of the racket at the point on the frame of maximum cross-sectional height was 13.73 cm⁴ (0.33 inch⁴). The frequency of the first mode of bending under free-free constraint conditions was 204 Hz, and the frequency of the second mode of bending under clamped-free conditions was 230 Hz. In one specific embodiment of a midsize racket, the inside longitudinal dimension E of the head portion was 31.8 cm (12.520 inches), the inside transverse dimension F was 23.698 cm (9.330 inches), and the length L was 68.42 cm (26.938 inches). The height A at the top of the head was 2.3368 cm (0.920 inches), the maximum height B was 3.175 cm (1.250 inches), the height C was 2.54 cm (1.000 inch), and the height D varied depending upon the handle size. The width G of the head portion at the top of the head was 1.0287 cm (0.405 inch). The height H of the yoke piece 23 was 2.2987 cm (0.905 inch), and the width I was 1.14224 cm (0.4497 inch). The ratio of the maximum height B to the minimum height A of the head portion was 1.25/0.92 or 1.3587. The frequency of the first mode of bending under free-free conditions was 208 Hz, and the frequency of the second mode of bending under clamped-free conditions was 230 Hz. The shape and dimensions of the racket frame illustrated in Figs. 3-9 provide moments of inertia with respect to the midplane MP such that the racket is stiffer than conventional rackets and has the desired frequency of 170 to 250 Hz for the first mode of bending under free-free constraint or 215 to 315 Hz for the second mode of bending under clamped-free constraint. The ratio of the maximum height B to the minimum height A is desirably about 1.35 to about 1.38. The use of the relatively high modulus graphite fibers in layers 33 and 34 permits the weight of the frame to be reduced sufficiently to accommodate the bumper 26 while maintaining the overall weight of the racket within the normal range. The frame uses about 270 grams of graphite fibers and resin, which can be conventional resin. A large head racket and a midsize racket having specific shape and dimensions are described herein for achieving the desired stiffness and frequency. It will be understood, however, that other shapes and dimensions could be used so long as the resulting stiffness provides the desired frequency. The important objective is to achieve a frequency of the first mode of bending under free-free constraint between 170 Hz and 250 Hz or a frequency of the second mode of bending under clamped-free constraint of between 215 Hz and 315 Hz.

Claims: A game racket (15) having a handle portion (18), a loop-shaped head portion (20), and a throat portion (19) joining the handle portion (18) and the head portion (20), the racket (15) having a longitudinal axis (22) which is aligned with the centerline of the handle and a midplane (MP) which extends through the longitudinal axis parallel ot the plane of the loop-shaped head portion (20), characterized in that the racket (15) has a frequency of the first mode of bending under free-free constraint conditions in a plane which extends perpendicularly to said midplane (MP) within the range of 170 Hz to 250 Hz. Racket of claim 1 in which said frequency is within the range 200 Hz to 210 Hz. Racket of claim 1 in which the racket has a frequency of the second mode of bending under clamped-free constraint conditions in a plane which extends perpendicularly to said midplane (MP) within the range of 215 Hz to 315 Hz. Racket of claim 1 or 3 in which said frequency of the second mode of bending under clamped-free constraint conditions is within the range of 230 Hz to 265 Hz. Racket of at least one of the claims 1 to 4, in which the racket is formed from a tube composed of multiple layers (31-42) of resin-impregnated graphite fibers, the fibers in some of the layers having a modulus of elasticity of about 227528,4 x 10⁶ N/m² (33,000,000 pounds per square inch or psi) and the fibers in other layers having a modulus of elasticity of about 310266 x 10⁶ N/m² (45,000,000 pounds per inch or psi). Racket of at least one of the claims 1 to 5, in which the racket is formed from a tube composed of 12 layers (31-42) of resin-impregnated graphite fibers, the fibers in two of the layers having a modulus of elasticity of about 310266 x 10⁶ N/m² (45,000,000 pounds per square inch or psi) the fibers in other layers having a modulus of elasticity of about 227528,4 x 10⁶ N/m² (33,000,000 pounds per square inch or psi). Racket of claim 5 or 6 in which about 10 to 20 % of the fibers have a modulus of elasticity of about 310266 x 10⁶ N/m² (45,000,000 pounds per square inch or psi) and about 80 to 90 % of the fibers have a modulus of elasticity of about 227528,4 x 10⁶ N/m². Racket of claim 6 or 7, in which the two inner layers (31,32) and 8 outer layers include graphite fibers having a modulus of elasticity of about 227528,4 x 10⁶ N/m² (33,000,000 pounds per sqare inch or psi). Racket of at least one of the claims 1 to 8 in which the tube has a wall thickness of about 1,143 mm to 1,27 mm (0,045 to 0,05 inch). Racket at least one of the claims 1 to 9, in which the throat portion includes a pair of frame members (21,22) which diverge from the handle portion (18) and merge with the head portion (20), the racket (15) including a yoke piece (23), which extends between the diverging frame members (21,22) and forms the bottom of the loop-shaped head portion (20), the height (B) of the racket (15) perpendicular to the midplane (MP) being at a maximum in the diverging frame members (21,22) in the area where the yoke piece (23) merges with the diverging frame members (21,22). Racket of claim 10 in which the ratio of said maximum height (B) of the racket (15) to the height (A) at the top of the head portion (20) is about 1.35 to 1.38. Racket of claim 10 or 11, in which the area moment of Inertia at the point on the frame (17) of maximum cross-sectional height (B) is about 13,73 cm⁴ (0,33 inch ⁴) Racket of claim 10 or 11 in which the height of the racket decreases continuously from said maximum height (B) to the top of the head portion (20) and decreases continuously from said maximum height (B) to the top of said handle portion (18). Racket of claim 1 having a length of about 685.8 mm (27 inches).

Inventors: KARASEK, MARK L
Applicants: WILSON SPORTING GOODS COMPANY
Application year: 1988
Main classification: A63B49
IPC codes: A63B49, A63B59