CA1318696C

CA1318696C - Tennis racket

Info

Publication number: CA1318696C
Application number: CA000547074A
Authority: CA
Inventors: Mark L. Karasek
Original assignee: Wilson Sporting Goods Co
Current assignee: Wilson Sporting Goods Co
Priority date: 1987-08-04
Filing date: 1987-09-16
Publication date: 1993-06-01
Anticipated expiration: 2010-06-01
Also published as: FI874269L; ZA878042B; ES2008281A6; KR890003419A; KR910009207B1; EP0317711A2; JP2507397Y2; AU608254B2; ATE83163T1; AU8012587A; JPS6437967A; DK169163B1; IN170468B; GB2208356B; DE3876605T2; EP0317711A3; FI874269A0; EP0317711B1; ES2037158T3; GR3007278T3

Abstract

TENNIS RACKET

Abstract of the Disclosure The stiffness of a tennis racket is adjusted so that the first mode of bonding of the racket under free-free constraint conditions is between 170 HZ and 250 HZ and 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

sackground This invention relates generally to a racket for playing a game with a ball of limited reQiliency, such as a tennis racket.
In a conventional tenni3 racket, the~stiffness of the frame and shaft portions are sUCh that when a ball strike3 the strung face of the racket, the head frame portion i9 forced out of the longitudinal axi3 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. ThlQ complicated deformed shape of the body can be reduced to the sum of an infinite number of simple vibrational mode ~hapes 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 weight 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 weight distributions would be varying the geometry of the cross-section of the body, more specifically using a constant a~ount 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 decrease~ dynamic deformation amplitudes. IncreaSing weight reduces vibrational frequencies and decreases dynamic deformation amplitudes.
Two specific constraint conditions are of interest in this discussion. One extreme, the condition of ~free-free~

131$~
constraint~ represents a body vibrating unconstrained in space, ThiS may be approximated in the laboratory by suspending the body by ela~tic band8 and allowing it to vibrate freely. The first two vibrational mode shapes for a simple beam in bending under ~free-free~ con8traint conditions are shown in Pigure 10.
At the oppo~ite extreme i~ the ~clamped-free~ constraint condition, where one end of the body i~ rigidly clamped in a support fixture while the other end is allowed to vibrate freely. The fir~t three vibrational mode shapes for a simple beam in bending under ~clamped-free~ con5traint conditions are shown in Figure 11. It should be noted that modes 1 and 2 in Figure 10 have approximately the same ~hapes as modes 2 and 3, re-qpectively, in Figure 11. The addition of a rigid clamp to a body in bending under the ~free-free~ condition result~ 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 frequencie~ for the as~ociated mode shapes (mode~ 2 and 3 respectively) under ~clamped-free~ conditions. The frequency of a mode shape under one of the constraint condition~ can be approximated from the frequency of the mode shape under the other condition using the following relationship:
Freqcf - Freqff X (Lff/LCf)2 (Equation 1) with Lcf - Lff - Lcc where Freqcf = frequency of the mode shape under ~clamped-free~ conditions Freqff = requency of the mode shape under Rfree-free- conditions Lff = length of the beam under ~free-free~
conditions LCC = length of the beam held under the clamping fixture Lcf = equivalent length of the beam under ~clamped-free~ condition~.

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TenniS racket~ exhibit vibrational characteristic~
similar to those described above for imple beams due to ball/racket impact8 which occur during play. Laboratory te ting was performed on variou8 racketsO Test result~ indicate that for conventional tennis rackets under ~free-free~ constraint condition~, the first mode of bending i8 in the range 100 Hz to 170 Hz. conventional racketq under clamped-free~ constraint condition~ exhibit frequency ranges for the first and second mode~ of bending between 25 ~z to 50 Hz and 125 HZ to 210 HZ, respectively. U.S. Patent No. 4,664,380 (German laid-open DE-OS
3434898) states that the reYonance frequency of the racket described therein under ~clamped-free~ con3traint i-~ 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 value~ 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 convenional racket, the ball leave 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.

~ 3 ~
Summary of the Invention If the ball remains on the strings while the racket deflects and doe3 not leave the string~ until the racket haQ
returned to the undeformed position, the ball flight path will be unaffected and the accuracy of the shot is improved Isee Figure 13). In addition, ~ince the racket head speed i~ a maximum at thi~ point, greater energy i5 imparted to the ball, and a more powerful shot results. Changing the deformation period of the tenni9 ball is not considered a desirable solution to the problem. Therefore, for optimum performance the tennis racket must be deqigned 80 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 condition~ should be equal to the dwell time of the tennis ball on the strings. The first mode of bending under ~free-free~ constraint conditionq is chosen because this is the dominant vibrational mode excited during play.
The optimum tenniq 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 l, the frequency range under ~clamped-free~ conditions, considering a 27 inch racket suspended by a rigid support at 3 inches on the handle, would be between 21S 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-freeU conditions.

~3~8g9,~3 Descriptlon of the Drawin~
The invention will be explained in conjunction with an illu~trative embodiment shown in the accompanying drawing, in which -Fi9. 1 i9 a top plan view of a tenni~ racket formed inaccordance with the invention.
Pig. 2 i a -Qide elevational view of the racket of Fig.
1 , Fig. 3 i a top plan view of the frame of the racket of Fig. 1 without the strings and the handle claddingt Fig. 4 is a side elevational view of the racket frame of Fig. 3 t Fig. 5 is a sectional view taken along the line 5-S of Fig. 3t Fig. 6 is a sectional view taken along the line 6-6 of Fig. 3 t 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 fir~t, second, and third modes of bending of a tennis racket under clamped-free constraint conditionS t ~ ig. 12 illustratec 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~

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De~criPtion of Specific Embodiment Aa described previou~ly, it is desirable to adju~t the stiffness of a tennis racket so that after a conventional tennis ball impact~ the racket, the racket will return to it~ original undeformed position before the ball leaves the strings of the racket. Under thoqe condition8, the flight path of the ball before and after impact with the racket will be unaffected and the accuracy of the -~hot will be improved as illustrated in Fig.
13. Further, greater energy i3 imparted to the rebounding ball, and a more powerful shot results.
It is desirable to ad~ust the stiffnes3 of the tenniq racket so that the racket has a fir~t mode of bending under free-free con~traint 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 fir-ct 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-qhaped 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 abracions. 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.

1318g9~
~ he 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 string8 and the handle cladding.
Referring to ~igs. 5-8, each of the frame portionY 18-23 is formed from a tubular frame member having a wall thickness of about 0.045 to about 0.050 inch. The tubular frame member i3 formed from layers of resin-impregnated graphite fibers which are wrapped around an inflatable bladder. As is well known in the ar~, 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 fiber~ having a modulus of elasticity of about 33,000,000. Layers 33 and 34 include graphite fibers having a modulus of elasticity of about 45,000,000. 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 increaseQ 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).

13~iS~ 3 The height of the racket frame i~ determined with respect to Fig. 4 and measure8 the dimension of the racket perpendicUlar to a midplane MP which extend3 through the ongitudinaI centerline cL of the handle portion 18. The longitudinal centerline CL al~o ~orms the longitudinal axi~ of the racket in Pig. ~. The ~tring3 of the racket lie in the midplane MP, and the bending of the racket which i~ illu~trated in Fig9. 10 ànd 11 occurs in a plane which extends perpendicularly to the midplane.
The height o~ the racket frame in Fig. ~ increaseq 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 decreaseq continuously from the dimension B to the dimenqion 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 maximu~ dimension B iq 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 13.7647 inches, the inside transverse dimension F of the head portion was 10.1563 inches, and the overall length L was 26.960 inches. The height A at the top of the head portion was 1.090 inches, the maximum height B was 1.500 inches, the height C was 1.000 inch, and the height D varied depending upon the handle size in accordance with conventional handle dimensions. Referring to ~L31~$~
Fig. 5, the overall width G Of the head portion at the top of head portion was 0.380 inch. Referring to Pig. 7, the height ~
of the yoke piece 23 was 1.080 inches, and the width I was 0.~00 inch. The ratio of the maximum height B to the minimum height A
of the head portion wa8 1.5/1.09 or 1.376.
The area moment of inertia of the racket at the point on the fram~ of maximum cros~-sectional height wa3 0.33 inch4. The frequency of the first mode of bending under freé-free constraint conditions wa~ 204 Hz, and the frequency of the second mode of bending under clamped-free conditions wa~ 230 ~z.
In one specific embodiment of a midsize racket, the inside longitudinal dimenqion E of the head portion was 12.520 inche~, the in~ide tran~verse dimension F wa~ 9.3~0 inches, and the length L was 26.938 inches. The height A at the top of the head wa~ 0.920 inches the maximum height B wa-q 1.250 inches, the height C was 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 0.405 inch. The height H of the yoke piece 23 was 0.905 inch, and the width I was 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 ~requency of 170 to 250 Hz ~or 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.

~3~9~
The use of the relatively high modulu~ graphite fiber~
in layer~ 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 use~ about 270 gram8 of graphite fiber-R 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 under tood, however, that other ~hapes and dimensions could be used ~o long as the resulting 3tiffness provide~ the desired frequency. The important ob~ective i~ 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.
While in the foregoing specification detailed descriptions of specific embodiments of the invention were set forth for the purpose of illustration, it will be understood that many of the details herein given may be varied considerably by tho2e skllled in the àrt without departing from the spirit and scope of the invention.

Claims

THE EMBODIMENTS OF THE INVENTION IN WHICH AN EXCLUSIVE PROPERTY OR
PRIVILEGE IS CLAIMED ARE DEFINED AS FOLLOWS:

1. A tennis 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, the racket having a frequency of the first mode of,bending under free-free constraint conditions in a plane which extends perpendicularly to said midplane within the range of 170 Hz to 250 Hz.

2. The racket of claim 1 in which said frequency is within the range of 200 HZ to 210 HZ.

3. The 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 within the range of 215 HZ to 315 Hz.

4. The racket of claim 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.

5. The racket of claim 1 in which the racket is formed from a tube composed of multiple layers of resin-impregnated graphite fibers, the fibers in some of the layers having a modulus of elasticity of about 33,000,000 and the fibers in other layers having a modulus of elasticity of about 45,000,000.

6. The racket of claim 5 in which about 10 to 20% of the fibers have a modulus of elasticity of about 45,000,000 and about 80 to 90% of the fibers have a modulus of elasticity of about 33,000,000.

7. The racket of claim 1 in which the racket is formed from a tube composed of 12 layers of resin-impregnated graphite fibers, the fibers in two of the layers having a modulus of elasticity of about 45,000,000, the fibers in other layers having a modulus of elasticity of about 33,000,000.

8. The racket of claim 1 in which the throat portion includes a pair of frame members which diverge from the handle portion and merge with the head portion, the racket including a yoke piece which extends between the diverging frame members and forms the bottom of the loop-shaped head portion, the height of the racket perpendicular to the midplane being at a maximum in the diverging frame members in the area where the yoke piece merges with the diverging frame members.

9. The racket of claim 8 in which the ratio of said maximum height of the racket to the height at the top of the head portion is about 1.35 to 1.38.

10. The racket of claim 8 in which the height of the racket decreases continuously from said maximum height to the top of the head portion and decreases continuously from said maximum height to the top of said handle portion.

11. A tennis 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, the racket having a frequency of the second mode of bending under clamped-free constraint conditions in a plane which extends perpendicularly to said midplane within the range of 215 Hz to 315 Hz.

12. The racket of claim 11 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.

13. 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, the racket having a length of about 27 inches and having a frequency of the first mode of bending under free-free constraint conditions in a plane which extends perpendicularly to said midplane within the range of 170 Hz to 250 Hz.

14. The racket of claim 1 in which said frequency is within the range of 200 Hz to 210 Hz.