AU608254B2

AU608254B2 - Tennis racquet

Info

Publication number: AU608254B2
Application number: AU80125/87A
Authority: AU
Inventors: Mark L. Karasek
Original assignee: Wilson Sporting Goods Co
Current assignee: Wilson Sporting Goods Co
Priority date: 1987-08-04
Filing date: 1987-10-26
Publication date: 1991-03-28
Anticipated expiration: 2007-10-26
Also published as: KR910009207B1; NO173686C; FI874269A; GB8720149D0; ES2037158T3; JPH0591726U; DE3876605D1; EP0317711A3; NZ222358A; EP0317711B1; KR890003419A; FI89334C; DE3826545A1; NO874084D0; ZA878042B; DK510887D0; GR3007278T3; DK169163B1; JPS6437967A; IN170468B

Description

-N Form Australia PATENTS ACT 1952 COMPLETE SPECIFICATION

(ORIGINAL)

FOR OFFICE kIlSE Short Title: Int. CI: IThis document contains thd' amten~lfts MO~de under Section 49 andis crefor Application Number; Lodged: ICbmplete Specification-Lodged: J: Accepted: Lapsed: Published: 'riority: *Related Art; S4jame of Applicant: SAddress of Applicant: Actual Inventor: TO BE COMPLETED BY APPLICANT WILSON SPORTING GOODS CO.

2233 West Street, River Grove, IT, 602.71, U.S.A.

MARK L. KARASEK Address for Service-, CAILLINAN AND ASSOCIATES, Patent Attorneys, of 48-50 Bridge Road, Richmond, State of Victoria, Australia.

Complete Specification for the Invention entitled:- ITENNIXS RACQUET" The following statement Is a full descriptioni of this Invention, including the best method of performing It known to me:- Note., The description Is to bo typed In eoubl spacing, pica typo face, In on area not exceeding 260 mm In depth and 160 mm In Width, on tough WNW(t paper of good quality and It Is to be Inserted Inside this form.

.i .I This invention relates particularly, but not exclusively, to a racquet for playing a game with a ball of limited resiliency, such as a tennis racquet.

S In a conventional tennis racquet, the stiffness of the frame and shaft portions are such that when a ball strikes the strung face of the racquet, the head frame portion is forced out of the longitudinal axis of *0 the racquet. This deflection adversely affects the flight path cf the rebounding ball.

o 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 infinite 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.

Stifr"ess 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 strengthto-weight and stiffness-to-weight ratios. Another method of controlling stiffness and weight distributions vwould be varying the geometry of the cross-section of the body, more specifically using a "onstant amount of material in the cross-section while varying the area-moment-of-inertia 2 -lr I 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 decreases dynamic deformation amplitudes.

Two specific constraint conditions are of interest in this discussion. One extreme, the condition of "free-free" constraint, represents a body T? vibrating unconstrained in space. This may be approximated in the laboratory by suspending the body .9 *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 At the opposite extreme is the "clamped- 0 free" constraint condition, where one end of the body is rigidly clamped in a support fixture while the other e* 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).

3

-J

i 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 I relationship: Freq f Freqff X (Lff/Lcf) (Equation 1) with Lcf Lff Lc f f c where Freqcf frequency of the mode shape under S"clamped-free" conditions Freqf frequency of the mode shape under "free-free" conditions Lff length of the beam under "freefree" conditions L length of the beam held under the cc S. clamping fixture L equivalent length of the beam #cf under "clamped-free" conditions.

Tennis racquets exhibit vibrational characteristics similar to those described above for simple beams due to ball/racquet impacts which occur during play. Laboratory testing was performed on various racquets. Test results indicate that for conventional tennis racquets under "free-free" constraint conditions, the first mode of bending is in the range from 100 Hz to 170 Hz. Conventional racquets under -4 "clamped-free" constraint conditions exhibit frequency ranges for the first and second modes of bending between 25 Hz to 50 Hz and from 125 Hz to 210 Hz, respectively. U.S. Patent No. 4,664,380 (German laid-open DE-OS 3434898) states that the resonance freqency of the racquet described therein under "clampedfree" constraint is from 70 to 200 Hz.

i. Studies have shown that a tennis racquet vibrating under "free-free" conditions more closely approximates the bahaviour of a tennis racquet during play than does a racquet 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".

4* It has been observed that for a conventional a a S tennis ball, ball/racquet 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 sacquet is deflecting back due to the force input from the ball. In a conventional racquet, the ball leaves the strings some time between the point of ball/racquet impact when the racquet begins deforming and shortly after the racquet 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 racquet has not returned to its undeformed position where i the rebound ang a maximum.

le is zero and the racquet head speed is

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9.

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S.

9 9 Sl 0' If the ball remains on the strings while the racquet deflects and does not leave the strings until the racquet 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, S since the racquet 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 S to the problem. Therefore, for 94pe f performance the tennis racquet must be designed so that the frequency of the dominant vibrational mode excited in the racquet during play is matched with the duration of the ball/ racquet contact. More specifically, one-half of the I period of the first mode of bending for a tennis racquet under "free-free" constraint conditions should be equal to S 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 racquet would have a first mode of bending under "free-free" constraint conditions between 170 Hz and 250 Hz since ball/racquet impact times of from 2 to 3 milliseconds are common.

Using equation 1, the frequency range i ndir "clamped-free" conditions, considering a 27 inch racquet suspended by a 6 r- I- 1 rigid support at 3 inches on the handle, would be between 215 Hz and 315 Hz for the second mode of bending. Once specific embodiment of the racquet 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 th second mode of bending under "clamped-free" conditions.

In accordance with a first aspect of the present invention there is provided a tennis racquet having a handle portion, a loop-shaped head portion, and a throat portion joining the handle portion and the bead portion, the racquet having a longitudinal axis which is aligned with the centerline of the handle and *1 a midplane which extends through the longitudinal axis parallel to the plane of the loop-shaped head portion, the racquet having a frequency of the first mode of bending under free-free constraint conditions in a place which extends perpendicularly to said midplane within the range of form 170 Hz to 250 Hz and S a frequency of the second mode of bending under clamped-free constraint conditions in a plane which extends perpendicularly to said midplane within the

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range of from 215 Hz to 315 Hz.

0)*S In accordance with a second aspect of the present invention there is provided a tennis racquet having a handle portion, a loop-shaped head portion, and a throat portion joining the handle portion and the head portion, the racquet 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 racquet having a frequency of the first mode of -7i -1 I i, i bending under clamped-free constraint conditions in a plane which extends perpendicularly to said midplane within the range of from 215 Hz to 315 Hz.

In accordance with a further aspect of the present invention there is provided a game racquet having a handle portion, a loop-shaped head portion, and a throat portion joining the handle portion and the head portion, the racquet 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 racquet having a length of about 27 incbhs 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 from 170 Hz to 250 Hz.

t 7a r j I L r.ln~- extends perpendicularly t llpane within the M s>->ff«-rr F -nm c 1 P !z +o 3-15 H z se I-e s o so *:so 0: 9 .5.9 :*Is

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*9 5 9 Y C I. order that the invention may be more clearly understood and put into practical effect there shall now be described in detail a preferred construction of a tennis racquet in accordance with the invention.

The description is given by way of non-limitative example only and is with reference to the accompanying drawings, wherein: Fig. 1 is a top plan view of a tennis racquet formed in accordance with the invention; Fig. 2 is a side elevational view of the racquet of Fig. 1; Fig. 3 is a Fig.

Fig. 4 is a Fig.

Fig. 5 is a Fig.

Fig. 6 is a Fig.

Fig. 7 is a Fig.

Fig. 8 is a Fig.

Fig. 9 is a top plan view of the frame of the racquet of 1 withqot the strings and the handle cladding; side elevational view of the racquet frame of 3; sectional view taken along the line 5-5 of 3; sectional view taken along the line 6-6 of 3; sectional view taken along the line 7-7 of 3; sectional view taken along the line 8-8 of 3; fragmentary perspective view of a portion of the racquet frame showing the multiple layers of graphite fibers; 8 i i i i Lj I _1 111.11 1 _I Fig. 10 illustrates the first and second modes of bending of a tennis racquet in the free-free constraint condition; Fig. 11 illustrates the first, second, and third modes of bending of a tennis racquet under clampedfree constraint conditions; Fig. 12 illustrates the deformation of a conventional 'f prior art racquet when a conventional tennis ball rebounds from the racquet after impact; and Fig. 13 illustrates the deformation of a tennis racquet *eo* in accordance with the invention when a conventional tennis ball rebounds from the racquet after impact.

e.

As described previously, it is desirable to adjust the stiffness of a tennis racquet so that after a conventional tennis ball impacts the racquet, the racquet will return to its original undeformed position S before the ball leaves the strings of the racquet. Under those conditions, the flight path of the ball before and after impact with the racquet 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.

Xt is desirable to adjust the stiffness of the tennis racquet so that the racquet has a first mode of bending under free-free constraint conditions between 170 Hz and 250 Hz. Such a racquet would have a second mode of bending under clamped-free constraint conditions 9 I i ;L'I between 215 Hz and 315 Hz. Figs. 1-9 illustrate one particular embodiment of a tennis racquet 15 which has such frequencies.

Referring first to Figs. 1 and 2, the racquet 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 4: 22 which diverge from the handle portion 18 and merge with the head portion 20. A yoke piece 23 extends S 49 lD between the throat pieces 21 and 22 and forms the bottom of the head portion, which is generally loop-shaped or oval.

The tennis racquet also includes a plurality of longitudinal strings 24 and cross strings 25 which extend into conventional openings in the head portion and yoke piece 23. A plastics material bumper 26 extends around the top of the head portion to protect the head S, from scuffs and abrasions. The bumper i, held in place r by the strings, and the bumper also protects the strings S 4 from abrading against the holes in the racquet frame.

A plastics material 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 racquet 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.

10 Figs. 3 and 4 illustrate the racquet 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 from 0.045 to 0.050 inch. The tubular frame member is formed from layers of resinimpregnated graphite fibers which are wrapped around an inflatable bladder. As is well known in the art, when the racquet frame is placed in a mold, the bladder is "Too: inflated to force the layers of graphite fiber against *foe O the mold until the resin cures.

Fig. 9 illustrates the layers 31-42 of resinimpregnated graphite fibers which are used to form the

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0 t* I 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

S

the cross hatching. Layera 31, 32, and 35-42 include graphite fibers having a modulus of elasticity of about 3' 33,000,Q000 Layers 33 and 34 include graphite fibers having a modulus of elasticity of about 45 000 000 Frow to 20% of the graphite fibers used in the raequet frame have the higher modulus of elasticity, and from 80 to of the graphite fibers have the lower modulus of elaaticity.

The use of the higher modulus graphite fibers increasoe the stiffness of th racGquet without increasing the weight of the racquet, The outer layer 43 of the racquot frame which is illustrated in 9 i a iayer of paiP m 11 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 racquet frame is determined with respect to Fig. 4 and measures the dimension of the racquet perpendicular to a midplane MP which extends through the longitudinal centerline CL of tie handle portion 18. The longitudinal centerline CL 0 so IS0 also forms the longitudinal axis of the racquet in Fig, 3. The strings of the racquet lie in the midplane MP, Sqo.

and the bending of the racquet whichis illustrated in Figs. 10 and 11 occurs in a plane which extends perpendicularly to the midplane.

0 046 *The height of the racquet frame in Fig. 4 increases continuously from the dimension A at the top *40 of the head portion of the frame to the dimension B in thP throat portion of the frame. The height of the racquet •3 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 racquet 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 th yoke piece is intersected 12

I

by the longitudinal centerline CL. Comparing Figs. 6 and 7, the height of the yoke piece 23 l& substantially less than the height of the yoke members 21 and 22 and the hezd portion 20 in the area of the maximum height B.

In one specific embodiment of a large head racquet, 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 4.

the head portion was 1.090 inches, the maximum height B *o.e was 1.500 inches, the height C was 1.000 inch, and the 9 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 *i5 top of head portion was 0.380 inch. Referring to Fig. 7, the height H of the yoke piece 23 was 1.080 inches, and the width I was 0.400 inch. The ratio of the maximum height B 9 to the minimum height A of the head portion was 1.5/1.09 or 1,376.

The area moment of inertia of the racquet at the point on the frame of maximum cross-sectional height was 0.33 inch 4 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 racquet, the inside longitudinal dimension E of the head portion was 12.520 inches, the inside transverse dimension F was 9.330 inches, and the length T, was 26.938 inches.

13 The height A at the top of the head was 0.920 inches the maximum height B was 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 S, A of the head portion was 1.25/0.92 or 1.3587.

The frequency of the first mode of bending 1, 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 racquet frame illustrated in Figs. 3-9 provide moments of inertia with respect to the midplane MP such that the racquet is stiffer than conventional racquets and has the desired frequency of from 170 to 250 Hz for the first mode of bending under free-free constraint or from 215 to 315 Hei V 0 0 for the second mode of bending under clamped-free constraint. The ratio of the maximum height B to the minimum height A is desirably from 1.35 to 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 racquet within the normal range. The frame uses about 270 grams of graphite fibers and resin, which can be conventional resin.

14 i' ~-~il A large head racquet and a midsize racquet havifg 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 *1 under clamped-free constraint of between 215 Hz and 315 Hz.

*0 While in the foregoing specification detailed descriptions of specific embodiments of the invention were set forth for the purpose of illustration, e a *r3 it will be understood that many of the details herein S0,o* given may be varied considerably by those skilled in the art without departing from the spirit and scope of the invention.

4 15

Claims

1. A tennis racquet having a handle portion, a loop-shaped head portion, and a throat portion joining the handle portion and the head portion, the racquet 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 racquet 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 from 170 Hz to 250 Hz and So a frequency of the second mode of bending under clamped-free constraint S"t0* conditions in a plane which extends perpendicularly to said midplane within the range of from 215 Hz to 315 Hz.

2. The racquet as claimed in claim 1, in which said frequency of said first S mode of bending is within the range of from9 2Hz to 210 Hz.

3. The racquet as claimed in claim 1 or claim 2, in which said frequency of the second mode of bending under clamped-free constraint conditions is within the range of from 230 Hz to 265 Hz. Sb'' S

4. The racquet as claimed in any one of claims 1 to 3, in which the racquet 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 psi and the fibers in other layers having a modulus of elasticity of about 45,000,000 psi.

The racquet as claimed in claim 4, iz which from 10 to 20% of the fibers have a modulus of elasticity of about 45,000,000 psi and from 80 to 90% of the -16- :i fibers have a modulus of elasticity of about 33,000,000 psi.

6. The racquet as claimed in claim 4 or claim 5, in which the racquet 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 psi, the fibers in other layers having a modulus of elasticity of about 33,000,000 psi.

7. The racquet as claimed in any one of the preceding claims, in which the throat portion includes a pair of frame members which diverge from the handle portion and merge with the head portion, the racquet including a yoke piece which S extends between the diverging frame members and forms the bottom of the loop- shaped head portion, the height of the racquet 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.

8. The racquet as claimed in claim 7, in which the ratio of said maximum height of the racquet to the'height at the top of the head portion is from 1.35 to 1il 1.38. 0

9. The racquet as claimed in Claim 7 or Claim 8, in which the height of the !I S racquet decreases continuously from said position of maximum height to the top 4 of the head portion and decreases continuously from said position of maximum height to the top of said handle portion.

10. A tennis racquet having a handle portion, a loop-shaped head portion, and a throat portion joining the handle portion and the head portion, the racquet 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 I -17- loop-shaped head portion, the racquet 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 from 215 Hz to 315 Hz.

11. The racquet as claimed in Claim 10, in which said frequency of the second mode of bending under clamped-free constraint conditions is within the range of from 230 Hz to 265 Hz.

12. A game racquet having a handle portion, a loop-shaped head portion, and a throat portion joining the handle portion and the head portion, the racquet 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 racquet having a length of about 27 inches and having a frequency of the first mode of bending under free-free constraint S conditions in a plane which extends perpendicularly to said midplane within the range of from 170 Hz to 250 Hz.

13. The racquet as claimed in Claim 12, in which said frequency is within the range of from 200 Hz to 210 Hz. *0.

14. A racquet, substantially as described herein with reference to Figs. 1 to 11 and 13 of the accompanying drawings. DATED this 14th day of November, 1990 WILSON SPORTING GOODS CO. By their Patent Attorneys: CALLINAN LAWRIE -18- A"