CA1140608A - Tennis racket - Google Patents
Tennis racketInfo
- Publication number
- CA1140608A CA1140608A CA000357071A CA357071A CA1140608A CA 1140608 A CA1140608 A CA 1140608A CA 000357071 A CA000357071 A CA 000357071A CA 357071 A CA357071 A CA 357071A CA 1140608 A CA1140608 A CA 1140608A
- Authority
- CA
- Canada
- Prior art keywords
- racket
- weights
- ball
- head
- tennis
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Expired
Links
Classifications
-
- A—HUMAN NECESSITIES
- A63—SPORTS; GAMES; AMUSEMENTS
- A63B—APPARATUS FOR PHYSICAL TRAINING, GYMNASTICS, SWIMMING, CLIMBING, OR FENCING; BALL GAMES; TRAINING EQUIPMENT
- A63B60/00—Details or accessories of golf clubs, bats, rackets or the like
- A63B60/54—Details or accessories of golf clubs, bats, rackets or the like with means for damping vibrations
Landscapes
- Health & Medical Sciences (AREA)
- General Health & Medical Sciences (AREA)
- Physical Education & Sports Medicine (AREA)
- Golf Clubs (AREA)
- Vibration Prevention Devices (AREA)
- Vibration Dampers (AREA)
Abstract
TENNIS RACKET
ABSTRACT:
A tennis racket comprises dynamic weights (6) distributed symmetrically relative to the longitudinal axis of the racket between the throat and the transverse axis of the head and suspended by arcuate straps (7) glued to the racket frame (2), the weights being displaceable in a direction perpendicular to the plane of the stringed area (3). The combination of weights and straps is adapted for having an intrinsic vibration frequency about 1.4 to 2 times the fundamental vibration frequency of the racket, such that when the weights are vibrated at their intrinsic frequency (by a ball striking the racket), the vibration of the racket is damped by energy transfer to the weights, and yet energy is also returned to the racket as a reaction in the direction of the ball's flight before -the ball leaves the racket. The angular stability of the racket is improved over either fixed weights or dynamic weights having frequencies outside the critical range.
ABSTRACT:
A tennis racket comprises dynamic weights (6) distributed symmetrically relative to the longitudinal axis of the racket between the throat and the transverse axis of the head and suspended by arcuate straps (7) glued to the racket frame (2), the weights being displaceable in a direction perpendicular to the plane of the stringed area (3). The combination of weights and straps is adapted for having an intrinsic vibration frequency about 1.4 to 2 times the fundamental vibration frequency of the racket, such that when the weights are vibrated at their intrinsic frequency (by a ball striking the racket), the vibration of the racket is damped by energy transfer to the weights, and yet energy is also returned to the racket as a reaction in the direction of the ball's flight before -the ball leaves the racket. The angular stability of the racket is improved over either fixed weights or dynamic weights having frequencies outside the critical range.
Description
:~L4U6~8 DESCRIPTION:
_NNIS RACKET
Technical Field The present in~ention concerns a tennis racket having an increased moment of inertia around the racket handle axis and improved means S for damping the vibration of the racket caused by off-center impact.
Background Art __ __ Various methods have been proposed to improve ball control on tennis rackets. Generally, 10 the ob~e~t of the methods is to increase the effective hitting area of the head (sweet spot or center of percussion). Thus, U.S. Patent 3,99~,756 discloses a tennis racket, the construction of which is adapted to increase the string area, thus 15 giving a high restitution coefficient.
Another method having -the same kind of object is disclosed in U.S. Patent 3,801,099 (Lair) which concerns a tennis racket with a low weight to stiffness ratio and the head frame of 20 which is shaped in order that the longer axis of the head ellipse is perpendicular to the handle axis; this arrangement increases the moment of inertia around the racket handle axis.
U.S. Patent 3,907,292 concerns a tennis 25 racket the rim and the handle of which are surrounded by a tubular organ containing a series of fly-weights which normally rest in the throat portions of the tube due to the action of helical springs. Under use, the weights move toward the 30 head of the racket because of the centrifugal ~4~
force resulting from the racket swinging motion during play and increase the "sweet spot" of the stringed area; this also ensures a better bouncing control on the ball and an increased hitting 5 power.
U.S. Patent 3,941,380 (Lacoste) discloses a tennis racket in which the head oscillations are damped by means of a secondary oscillator working along the handle axis thereof at vibration antinodes.
10 Since the oscillating bodies are located on the longitudinal axis of the racket, they do not affect the center of percussion and do not reduce the torque around the axis which results from an off-centered impact.
lS U.S. Patent 4,057,250 (Kuban) discloses means to generate a reactive orce for diminishing the bouncing of the racket after ball impact. For achieving this, masses producing the force must be able to move as freely as possible and, in this 20 connection, the masses can even consist o~
loose metal shot. Thus, the device is not a secondary oscillator. The effect is distinguishable from the present invention slnce the increase of the moment of inertia of the racket in Kuban will 25 only take place when the body has reached the end of its free elastic displacement which may be too late after the impact for being effectîve to increase the center of percussion. Moreover no damping of vibration is contemplated by an oscillator.
Another reference, French Patent 2,387,670, concerns a golf club, the head of which is provided with balancing weights which can vibrate in a direction perpendicular to the longitudinal axis of said head. This oscillating motion ensures 35 that the orientation of the head is maintained 6~3 during the interval starting ~rom the moment the ball is hi~ ~y the head to the moment it loses contact therewith after being hit. The balancing ~eights increase the moment of inertia of the club S in relationship to the hitting point of the head. Thus, these weights have first a static effect because they increase the club iner~ia and, second, they have a dynamic effect because they move in a direction perpendicular to the hitting 10 plane of the head. Such displacements generate moments of inertia around the striking point which are substantially equal and enable the head to stay properly oriented after striking the ball, this action being effective for the full distance lS where the head and the ball stay in contact.
Disclosure of the Invention ~ he object of the present invention is to increase the moment of inertia and the area of the "sweet spot" or center of percussion both 20 iongitudinally and transversely on a tennis racket to increase a players chance of striking the center, and at the same time to ensure the damping of the oscillation of the racket when the ball is nevertheless struck off-center.
~S It is also an object to provide a tennis r~cket with improved angular stability over standard xackets, or those with static weights, on off-centered impacts.
It is further an object to temporarily 30 store some of the impact (vibrational) ener~y of the racket transferred from -the impacting ball in oscillating weights whereb~ to attenuate racke~
vib~ation but to also return at least a portion of such energy to the racket, -and subsequently the )61~
ball, before the ball leaves the racXet.
The invention provides a tennis racket having moveable or dynamic weights attached to the rlm of the racket's head on both sides relative to 5 the handle of the racket between the racket throat and the transverse axis of the head. The position of these weights increases the moment of inertia around both the longitudinal and transverse axes of the racket effectively enlarging the sweet 10 spot or center of percussion in all directions.
The moveable weights are coupled to said rim by elastic means whereby they can oscillate in a direction substantially perpendicular to the plane of the racket head with an intrinsic frequency 15 1.4-2 times that of the fundamental frequency of oscillation of the racket itself. ~his arrangement provides an unique weighting system chosen in a manner such that when the system consisting of the moveable weights and the elastic means is 20 driven into vibration at the frequency 1.4-2 times that of the racket, the weights complete the first half of their cycle and apparently restore energy to the racket before the ball leaves the racket.
Moreover, the moveable weights with this critical 25 frequency improve the angular stability of the racket over fixed weights or dynamic weights without the critical frequency.
Brief Description of the Drawing Figure 1 is a view partially in perspecti~e 30 of one embodiment of the invention using weights held in moveable straps.
Figure 2 is a diagram showing the damping effect of a two-section osclllator chain which we believe may help explain the invention.
,.
. . . . .. . ..
Figure 3 is a comparatiVe diagxam of the vibration in two rackets of the same type, one of which is provided with the moveable weights accordlng to the invention.
Figure 4 is a perspective view o an alternative configuration of the present invention.
Figure 5 is a perspective view at a greater scale of the weight system of Figure ~.
Figure 6 is a graph showing the improvement 10 in angular stability due to moveable weights-having the cri-tical intrinsic fre~uency range.
Best Mode of Carr in Out the Invention Y g Figure 1 shows a conventional tennis racket 1 comprising the head 2, the strings 3 15 attached to the head 2 and two side members 4 and 5 forming the throat of the racket connecting the head to the handle (not pictured). The longitudinal and transverse axes are along lines 20Q and 20t respectively. The racket comprises six moveable 20 weights 6, consisting in this example of small cylinders of about 3g each, which are coupled to the head 2 by means of straps 7. The straps 7 consist of energy absorbent polyure-thane or equivalent elastomer, 1 mm thick, glued at the top o~ the 25 arcuate section of each strap on the underside thereof to the frame. These straps 7 constitute elastic means for allowing movement of the weights generally perpendicular to the plane of the xacket head. The system composed of the straps 30 and the moveable weights has an intrinsic oscillatory fxequency and constit~tes, with the racket itself, a two-section oscillator chain, each oscillator starting to vibrate with its own independent o~cillating frequency whenever a ball impacts the .
~:~4~6~3 racket strings 3. The straps and/or the weights are made of energy absorbent materials wh~ch may a~d the damping of the racket vibration in aAdition to the attenuating effect of the oscillator chain.
The moveable weights have multiple ef~ects. The first erfect of the weights 6 is to increase the moment of lnertia of the racket around both the longitudinal and transverse axes of the racket and to increase the angular stability 10 to an off-centered impact of a ball on the racket.
Static weights would have a similar effect in increasing the effective size of -the center of percussion, popularly known as the "sweet spot" of the racket, bUt the moveable weights, with the 15 ~rltical fre~uency, improve the angular stability over static weights as shown in Figure 6. The ordinate of the graph in Figure 6 is the ratio of the angular rotation for moveable weights over that ~or static weights. The abscissa shows the 20 xatio of the intrinsic frequency of the weight system to the fundamental frequency of the racket.
This analytical curve shows that over the frequency range of about 1.3-2 and also above 2.7, the angular stability is up to about 3% better wi,th 25 moveable weights than fixed weights. We believe that between 1.3 and 1.4 and above 2.7 the angular stability is improved, but these ranges are not ideal based on the o-ther properties discussed later.
In practice, it is naturally advisable -that the additional weights be as light as possible relative to the racket so as not to impose an additional burden on the player. For example, it is preferred that the weights make a total o~
35 about 20 g.
~, 6~18 The location of the weigh~s ~ust also be optimized in connection with the center ~f gravity and the moment of inertia of the rac~et.
Placement of the weights as far as possible away 5 from the longitudinal axis would maximize the moment of inertia but would require a laryer compensating weigh-t in the handle to retain the center of gravity at about point C in Figure 1, thereby increasing the total weight of ~he 10 racket. Placement nearest the throat would require minimal compensating weight but would not have much effect on the sweet spot in the transverse directions. A compromise is preferably struck, according to the invention, by symme-trically 15 locating the weights on the rim at angles between abou~ 30 and 70 degrees from the longitudinal axis on both sides thereof between the transverse axis and the throat. This position also has the advantage that the sweet s~ot of the racket is 20 elongated in both the longitudinal and the transverse directions of the racket thereby increasing the possibility of a good return of a tennis ball.
The second and third effects of the 25 weights are to damp racket vibration after impact and to restore a small but significant portion of the impact energy to the racket while the ball is still in contact. The reason for the energy restoration is complicated and not 30 casily explained. However, accordiny to one theory, which we believe may be used to analyze the situation, the absolute values of the amplitudes Al and A2 related to a two-section oscillator chain system, as proposed for the present case, 35 are related to the impact excitation frequency .
. . _ . . . __ _ _ _. . . ~ , = , . .. _ n as schematically represented on the diayram o~
Figure 2. The magnitudes of the amplitudes A
and A2 correlate with the amplitudes of the ~ibration of the racket and of the displacement 5 of the weights 6, respectively. It can be shown that, on the abscissa, the zero position of the unction Al(n2) is satisfied when:
~ = C2 1/2 (1) in which c2 is the spring constant of the elastic 10 means 7 for suspending the weights 6 and m2 is the mass of the weights ~. Thus, in principle, if the excitation has a frequency Q equal to the intrinsic vibration frequency of the c2, m2 system, then ml which constitutes the mass of 15 the racket stays at rest. Although this would be ideal for reducing vibration, it would not help angular stability and energy restoration.
However, using this equation, it is also possible to select the appropriate spring constant of the ~0 suspendin~ means 7 of the moveable weights 6 such that the individual frequency of said weights corresponds to that multiple of the frequency of the first mode of intrinsic vibration of -the racket taken alone which optimizes the ~5 vibration attenuation with the angular stability and other desired properties.
As an example of a calculation of the necessary spring constant using this theory, the oscillation period Tl of the racket was measured 30 by means of a strain gauge placed on a sample racket and was found to be 0.01 sec.
Therefore fl = T ~ 100 Hz and 1,..
.. ,. . .~ ... .. ....
~060~
g wl = 628.3 sec~l We have calculated that in order to temporarily store impact energy in the suspended masses and to then res-tore a portion of the 5 impact energy to the racket before the ball leaves, it will be necessary to have the elastically suspended masses located on the opposite side of the racket relative to the ball at ,he moment the ball leaves the racket. We have found that 10 this requires tha~ the frequency, ~2~ of the weight system be related to the first mode of the racket fre~uency, ~1~ such that:
1.4w1 ~ ~2 ~ 2 ~1 (2) Using equations (1) and (2) for a 3 15 ~ram (weight), the spring constant c2 must be between about 235 g(force)/mm and 485 g(~orce)/mm to ensure damping and restoration of energy to the racket prior to the impacting ball leaving the racket. The energy restored by two weight 20 systems each consistlng of 3 three-gram weights secured by three straps having spring constants in the range calculated above and ~eighing a total of one gram (therefore 2 ten gram weight systems~, would be on ~he order of 25 ~%, a seemingly small yet significant gain.
~ eights 6 and straps 7 having the properties determined above were divided into two groups, each group of three weights being located symmetrically on one side of the longitu~inal 30 axis of the racket such as shown in Figure 1, at an angle of about 45 to the longitudinal axis.
Various experiments and measurements have been performed on this racket. Firstly, comparative .
.
-- 10 ~
measurements have been effected on t~o identical rackets, one of them being provided Wi~h the added weights of the invention, the other bein~
unmo~ified. Vibra-tion damping coefficients on 5 bo-th rackets were measured. Figure 3 represents two dlagrams, "a" and "b", of the damping of the vibrations, curve "a" corresponding to the control racket without ,he weights and curve "b"
corresponding to the racket equipped with two 10 groups of ten gram weights (three 3g weights ~eld by a lg strap). It can be seen that the damping xate of "b" is much faster than "a" as impact energy is transmitted to the moveable weights and the energy absorbing materials and 15 then has been partially restored to the racket on the first cycle of the weights.
Thereafter, playing trials were carried out by several tennis players who generally noted that racket "b" provided a better control 20 of the ball especially in the case of overspin or sliced balls, i.e. when the surface of the racket is at a non~orthogonal angle with the path of the incoming ball.
Since the reports of the players were 25 possibly subjective and did not provide quantitative results and definite explanation in connection with the practical behavior of the modified racket, laboratory experiments were performed.
For such experiments, the racket was attached to 30 a~ bench support so as to provide a certain de~ree of elastic rotational freedom around the handle axis. This was intended to simulate the rotational allowance of a racket when handled by ~ playex in actual play and its resistance to 35 the torque produced by the`impact of the ball.
Balls were projected horizontally on the racket by means o~ a tube operated b~ a spring. The movements of the racket and ball were recorded with a very high-sp~ed camera and the pictures 5 showed that the contact time of 'he ball and the racket of the invention was about 20% greater than ~ith the control racket. Further, it was fou~d that the half period of vibration of the added weights, which corresponds to their return 10 to their initial position, corresponds to about 60-70% of the contact time of the ball and the racket during the impact. Consequently, we have found that, as the weights move to the opposite slde of the racket relative to the ball, energy lS temporarily stored in the moving weights is restored to the racket when the ball is still ~ouching the strings. And the contact time is increased leading to better ball control.
Moreover, after impact, the inventive weight 20 system attenuates the vibration better than fixed wei~Jhts and only slightly less effectively than moveable weights having frequencies equal to the fundamental mode of vibration of the racket.
The increase of the time of contact bet~een the strings and the ball provides a better control of the overspin or cut shots and reduces the slipping of the ball when it leaves the racket. This is actually an essential 30 condition for an accurate control of -the force and rotation imparted to the ball and of the direction of its path. Neither flxed weights nor moveable weights havin~ frequencies outside the critica~ range combine this increased contact 35 time with improved anyular stability and vlbratlon .. .. , ., ... , ~ .. . .
)6~8 at~enuation.
I-t is not altogetner clear why ~etter vibration attenuation and the restoration of some impact energy is obtained while the ball is 5 still in contact with the racket. However, one theory which may explain our observations is as follows. Tests show that the fundamental racket ~Tibration is best attenuated with dynamic masses having the same frequency as the racket fundamental 10 frequency. This would be the case after the ball leaves the racket. But we believe that during the ball contact, which only lasts for about the first half period of the racket vibration, ~he funda~ental mode of vibration may not be lS established and that the vibration zone during ``
wave expansion is smaller than the entire length of the racket, therefore, momentarily establishing random higher frequencies than the fundamental.
This means that efficient attenuation may then 20 be obtained during the time of ball contact with dynamic masses having a higher frequency than the racket fundamental frequency.
~ e have found experimentally that a frequency between 1.4 and 2 times higher is such 25 a condition which yields the improved performance.
~oreover, the random higher frequency vibration~
may be responsible for forcing the ball off the racket too early and therefore the attenuation thereof may explain the increased contact time 30 with the inVention. Of course, after the ball leaves, the attenuation is not as good as it ~ould be with less stiff attachment of the weights, but the improved ball control appears to be worth the sacrifice. However, regardless 35 of the reason we have observed that the properties -- , .
V6~
of the racket discussed above are improved with dynamic masses having the sti~fer attachment.
The modification shown in Figure 4 and Figure 5 illustrates a racket embodiment according S to -the invention in which the weights and the suspending elastic means are incorporated ~Yithin the frame of the head. Suitable adsorbent materials can be used in their construction.
This frame, which is somewhat enl~rged to acco~odate 10 the weights and springs, comprises three tubular housings 8 the axis of which are perpendicular to the plane of the head. The stringing holes 9 are distributed in this area of the frame between the housings 8. Each housing 8 is lS adaptèd for accommodating one oE the weights, which are in the form of small cylinders 10, for example weighing 3g, and having each an annular groove lOa in their side wall. The cylindrical weights 10 are mounted axially within a helical 20 spring 11, the end winding of which is crimped around the groove lOa and the first winding of which is set to a general base plate 12 by means of two strips 13 stamped in said plate 12. The assembly of -the three weights 10 and the springs 25 11 is assembled by putting each weight into its tubular housing 8/ the base plate being inserted in a hollow area (not visible) located r~ at one end of said housings 8. Another identical plate (not shown) is inserted in another similar 30 hollow area 14 of the other side of said housings. In this modification, the presence o~
the added weights assembly is hardly visible from the outside except for the slight widening of the frame side where the housings 8 are 35 incoxporated; thus, the racket of this modification is hardly ~istinguishable from an unmodified racket. ~eight of the cylinders and stiffness of the springs are selected ~s in the case of the straps discussed above. Total added weight 5 of about 20 g~ams is preferred. The important feature, however, is the frequency of the added mass/spring assembly.
It shoula be no-ted that the cost of such a racket is not much over -that of an ordinary 10 racket since there are only 11 additional parts on each side relative to the handle:
three tubes, three weights, three springs and two plates. The installation of these parts can be achieved easily and can be aaapted to partially 15 automatic manufacturing techniques.
, ,, , , ~, .... .. . . .. .
_NNIS RACKET
Technical Field The present in~ention concerns a tennis racket having an increased moment of inertia around the racket handle axis and improved means S for damping the vibration of the racket caused by off-center impact.
Background Art __ __ Various methods have been proposed to improve ball control on tennis rackets. Generally, 10 the ob~e~t of the methods is to increase the effective hitting area of the head (sweet spot or center of percussion). Thus, U.S. Patent 3,99~,756 discloses a tennis racket, the construction of which is adapted to increase the string area, thus 15 giving a high restitution coefficient.
Another method having -the same kind of object is disclosed in U.S. Patent 3,801,099 (Lair) which concerns a tennis racket with a low weight to stiffness ratio and the head frame of 20 which is shaped in order that the longer axis of the head ellipse is perpendicular to the handle axis; this arrangement increases the moment of inertia around the racket handle axis.
U.S. Patent 3,907,292 concerns a tennis 25 racket the rim and the handle of which are surrounded by a tubular organ containing a series of fly-weights which normally rest in the throat portions of the tube due to the action of helical springs. Under use, the weights move toward the 30 head of the racket because of the centrifugal ~4~
force resulting from the racket swinging motion during play and increase the "sweet spot" of the stringed area; this also ensures a better bouncing control on the ball and an increased hitting 5 power.
U.S. Patent 3,941,380 (Lacoste) discloses a tennis racket in which the head oscillations are damped by means of a secondary oscillator working along the handle axis thereof at vibration antinodes.
10 Since the oscillating bodies are located on the longitudinal axis of the racket, they do not affect the center of percussion and do not reduce the torque around the axis which results from an off-centered impact.
lS U.S. Patent 4,057,250 (Kuban) discloses means to generate a reactive orce for diminishing the bouncing of the racket after ball impact. For achieving this, masses producing the force must be able to move as freely as possible and, in this 20 connection, the masses can even consist o~
loose metal shot. Thus, the device is not a secondary oscillator. The effect is distinguishable from the present invention slnce the increase of the moment of inertia of the racket in Kuban will 25 only take place when the body has reached the end of its free elastic displacement which may be too late after the impact for being effectîve to increase the center of percussion. Moreover no damping of vibration is contemplated by an oscillator.
Another reference, French Patent 2,387,670, concerns a golf club, the head of which is provided with balancing weights which can vibrate in a direction perpendicular to the longitudinal axis of said head. This oscillating motion ensures 35 that the orientation of the head is maintained 6~3 during the interval starting ~rom the moment the ball is hi~ ~y the head to the moment it loses contact therewith after being hit. The balancing ~eights increase the moment of inertia of the club S in relationship to the hitting point of the head. Thus, these weights have first a static effect because they increase the club iner~ia and, second, they have a dynamic effect because they move in a direction perpendicular to the hitting 10 plane of the head. Such displacements generate moments of inertia around the striking point which are substantially equal and enable the head to stay properly oriented after striking the ball, this action being effective for the full distance lS where the head and the ball stay in contact.
Disclosure of the Invention ~ he object of the present invention is to increase the moment of inertia and the area of the "sweet spot" or center of percussion both 20 iongitudinally and transversely on a tennis racket to increase a players chance of striking the center, and at the same time to ensure the damping of the oscillation of the racket when the ball is nevertheless struck off-center.
~S It is also an object to provide a tennis r~cket with improved angular stability over standard xackets, or those with static weights, on off-centered impacts.
It is further an object to temporarily 30 store some of the impact (vibrational) ener~y of the racket transferred from -the impacting ball in oscillating weights whereb~ to attenuate racke~
vib~ation but to also return at least a portion of such energy to the racket, -and subsequently the )61~
ball, before the ball leaves the racXet.
The invention provides a tennis racket having moveable or dynamic weights attached to the rlm of the racket's head on both sides relative to 5 the handle of the racket between the racket throat and the transverse axis of the head. The position of these weights increases the moment of inertia around both the longitudinal and transverse axes of the racket effectively enlarging the sweet 10 spot or center of percussion in all directions.
The moveable weights are coupled to said rim by elastic means whereby they can oscillate in a direction substantially perpendicular to the plane of the racket head with an intrinsic frequency 15 1.4-2 times that of the fundamental frequency of oscillation of the racket itself. ~his arrangement provides an unique weighting system chosen in a manner such that when the system consisting of the moveable weights and the elastic means is 20 driven into vibration at the frequency 1.4-2 times that of the racket, the weights complete the first half of their cycle and apparently restore energy to the racket before the ball leaves the racket.
Moreover, the moveable weights with this critical 25 frequency improve the angular stability of the racket over fixed weights or dynamic weights without the critical frequency.
Brief Description of the Drawing Figure 1 is a view partially in perspecti~e 30 of one embodiment of the invention using weights held in moveable straps.
Figure 2 is a diagram showing the damping effect of a two-section osclllator chain which we believe may help explain the invention.
,.
. . . . .. . ..
Figure 3 is a comparatiVe diagxam of the vibration in two rackets of the same type, one of which is provided with the moveable weights accordlng to the invention.
Figure 4 is a perspective view o an alternative configuration of the present invention.
Figure 5 is a perspective view at a greater scale of the weight system of Figure ~.
Figure 6 is a graph showing the improvement 10 in angular stability due to moveable weights-having the cri-tical intrinsic fre~uency range.
Best Mode of Carr in Out the Invention Y g Figure 1 shows a conventional tennis racket 1 comprising the head 2, the strings 3 15 attached to the head 2 and two side members 4 and 5 forming the throat of the racket connecting the head to the handle (not pictured). The longitudinal and transverse axes are along lines 20Q and 20t respectively. The racket comprises six moveable 20 weights 6, consisting in this example of small cylinders of about 3g each, which are coupled to the head 2 by means of straps 7. The straps 7 consist of energy absorbent polyure-thane or equivalent elastomer, 1 mm thick, glued at the top o~ the 25 arcuate section of each strap on the underside thereof to the frame. These straps 7 constitute elastic means for allowing movement of the weights generally perpendicular to the plane of the xacket head. The system composed of the straps 30 and the moveable weights has an intrinsic oscillatory fxequency and constit~tes, with the racket itself, a two-section oscillator chain, each oscillator starting to vibrate with its own independent o~cillating frequency whenever a ball impacts the .
~:~4~6~3 racket strings 3. The straps and/or the weights are made of energy absorbent materials wh~ch may a~d the damping of the racket vibration in aAdition to the attenuating effect of the oscillator chain.
The moveable weights have multiple ef~ects. The first erfect of the weights 6 is to increase the moment of lnertia of the racket around both the longitudinal and transverse axes of the racket and to increase the angular stability 10 to an off-centered impact of a ball on the racket.
Static weights would have a similar effect in increasing the effective size of -the center of percussion, popularly known as the "sweet spot" of the racket, bUt the moveable weights, with the 15 ~rltical fre~uency, improve the angular stability over static weights as shown in Figure 6. The ordinate of the graph in Figure 6 is the ratio of the angular rotation for moveable weights over that ~or static weights. The abscissa shows the 20 xatio of the intrinsic frequency of the weight system to the fundamental frequency of the racket.
This analytical curve shows that over the frequency range of about 1.3-2 and also above 2.7, the angular stability is up to about 3% better wi,th 25 moveable weights than fixed weights. We believe that between 1.3 and 1.4 and above 2.7 the angular stability is improved, but these ranges are not ideal based on the o-ther properties discussed later.
In practice, it is naturally advisable -that the additional weights be as light as possible relative to the racket so as not to impose an additional burden on the player. For example, it is preferred that the weights make a total o~
35 about 20 g.
~, 6~18 The location of the weigh~s ~ust also be optimized in connection with the center ~f gravity and the moment of inertia of the rac~et.
Placement of the weights as far as possible away 5 from the longitudinal axis would maximize the moment of inertia but would require a laryer compensating weigh-t in the handle to retain the center of gravity at about point C in Figure 1, thereby increasing the total weight of ~he 10 racket. Placement nearest the throat would require minimal compensating weight but would not have much effect on the sweet spot in the transverse directions. A compromise is preferably struck, according to the invention, by symme-trically 15 locating the weights on the rim at angles between abou~ 30 and 70 degrees from the longitudinal axis on both sides thereof between the transverse axis and the throat. This position also has the advantage that the sweet s~ot of the racket is 20 elongated in both the longitudinal and the transverse directions of the racket thereby increasing the possibility of a good return of a tennis ball.
The second and third effects of the 25 weights are to damp racket vibration after impact and to restore a small but significant portion of the impact energy to the racket while the ball is still in contact. The reason for the energy restoration is complicated and not 30 casily explained. However, accordiny to one theory, which we believe may be used to analyze the situation, the absolute values of the amplitudes Al and A2 related to a two-section oscillator chain system, as proposed for the present case, 35 are related to the impact excitation frequency .
. . _ . . . __ _ _ _. . . ~ , = , . .. _ n as schematically represented on the diayram o~
Figure 2. The magnitudes of the amplitudes A
and A2 correlate with the amplitudes of the ~ibration of the racket and of the displacement 5 of the weights 6, respectively. It can be shown that, on the abscissa, the zero position of the unction Al(n2) is satisfied when:
~ = C2 1/2 (1) in which c2 is the spring constant of the elastic 10 means 7 for suspending the weights 6 and m2 is the mass of the weights ~. Thus, in principle, if the excitation has a frequency Q equal to the intrinsic vibration frequency of the c2, m2 system, then ml which constitutes the mass of 15 the racket stays at rest. Although this would be ideal for reducing vibration, it would not help angular stability and energy restoration.
However, using this equation, it is also possible to select the appropriate spring constant of the ~0 suspendin~ means 7 of the moveable weights 6 such that the individual frequency of said weights corresponds to that multiple of the frequency of the first mode of intrinsic vibration of -the racket taken alone which optimizes the ~5 vibration attenuation with the angular stability and other desired properties.
As an example of a calculation of the necessary spring constant using this theory, the oscillation period Tl of the racket was measured 30 by means of a strain gauge placed on a sample racket and was found to be 0.01 sec.
Therefore fl = T ~ 100 Hz and 1,..
.. ,. . .~ ... .. ....
~060~
g wl = 628.3 sec~l We have calculated that in order to temporarily store impact energy in the suspended masses and to then res-tore a portion of the 5 impact energy to the racket before the ball leaves, it will be necessary to have the elastically suspended masses located on the opposite side of the racket relative to the ball at ,he moment the ball leaves the racket. We have found that 10 this requires tha~ the frequency, ~2~ of the weight system be related to the first mode of the racket fre~uency, ~1~ such that:
1.4w1 ~ ~2 ~ 2 ~1 (2) Using equations (1) and (2) for a 3 15 ~ram (weight), the spring constant c2 must be between about 235 g(force)/mm and 485 g(~orce)/mm to ensure damping and restoration of energy to the racket prior to the impacting ball leaving the racket. The energy restored by two weight 20 systems each consistlng of 3 three-gram weights secured by three straps having spring constants in the range calculated above and ~eighing a total of one gram (therefore 2 ten gram weight systems~, would be on ~he order of 25 ~%, a seemingly small yet significant gain.
~ eights 6 and straps 7 having the properties determined above were divided into two groups, each group of three weights being located symmetrically on one side of the longitu~inal 30 axis of the racket such as shown in Figure 1, at an angle of about 45 to the longitudinal axis.
Various experiments and measurements have been performed on this racket. Firstly, comparative .
.
-- 10 ~
measurements have been effected on t~o identical rackets, one of them being provided Wi~h the added weights of the invention, the other bein~
unmo~ified. Vibra-tion damping coefficients on 5 bo-th rackets were measured. Figure 3 represents two dlagrams, "a" and "b", of the damping of the vibrations, curve "a" corresponding to the control racket without ,he weights and curve "b"
corresponding to the racket equipped with two 10 groups of ten gram weights (three 3g weights ~eld by a lg strap). It can be seen that the damping xate of "b" is much faster than "a" as impact energy is transmitted to the moveable weights and the energy absorbing materials and 15 then has been partially restored to the racket on the first cycle of the weights.
Thereafter, playing trials were carried out by several tennis players who generally noted that racket "b" provided a better control 20 of the ball especially in the case of overspin or sliced balls, i.e. when the surface of the racket is at a non~orthogonal angle with the path of the incoming ball.
Since the reports of the players were 25 possibly subjective and did not provide quantitative results and definite explanation in connection with the practical behavior of the modified racket, laboratory experiments were performed.
For such experiments, the racket was attached to 30 a~ bench support so as to provide a certain de~ree of elastic rotational freedom around the handle axis. This was intended to simulate the rotational allowance of a racket when handled by ~ playex in actual play and its resistance to 35 the torque produced by the`impact of the ball.
Balls were projected horizontally on the racket by means o~ a tube operated b~ a spring. The movements of the racket and ball were recorded with a very high-sp~ed camera and the pictures 5 showed that the contact time of 'he ball and the racket of the invention was about 20% greater than ~ith the control racket. Further, it was fou~d that the half period of vibration of the added weights, which corresponds to their return 10 to their initial position, corresponds to about 60-70% of the contact time of the ball and the racket during the impact. Consequently, we have found that, as the weights move to the opposite slde of the racket relative to the ball, energy lS temporarily stored in the moving weights is restored to the racket when the ball is still ~ouching the strings. And the contact time is increased leading to better ball control.
Moreover, after impact, the inventive weight 20 system attenuates the vibration better than fixed wei~Jhts and only slightly less effectively than moveable weights having frequencies equal to the fundamental mode of vibration of the racket.
The increase of the time of contact bet~een the strings and the ball provides a better control of the overspin or cut shots and reduces the slipping of the ball when it leaves the racket. This is actually an essential 30 condition for an accurate control of -the force and rotation imparted to the ball and of the direction of its path. Neither flxed weights nor moveable weights havin~ frequencies outside the critica~ range combine this increased contact 35 time with improved anyular stability and vlbratlon .. .. , ., ... , ~ .. . .
)6~8 at~enuation.
I-t is not altogetner clear why ~etter vibration attenuation and the restoration of some impact energy is obtained while the ball is 5 still in contact with the racket. However, one theory which may explain our observations is as follows. Tests show that the fundamental racket ~Tibration is best attenuated with dynamic masses having the same frequency as the racket fundamental 10 frequency. This would be the case after the ball leaves the racket. But we believe that during the ball contact, which only lasts for about the first half period of the racket vibration, ~he funda~ental mode of vibration may not be lS established and that the vibration zone during ``
wave expansion is smaller than the entire length of the racket, therefore, momentarily establishing random higher frequencies than the fundamental.
This means that efficient attenuation may then 20 be obtained during the time of ball contact with dynamic masses having a higher frequency than the racket fundamental frequency.
~ e have found experimentally that a frequency between 1.4 and 2 times higher is such 25 a condition which yields the improved performance.
~oreover, the random higher frequency vibration~
may be responsible for forcing the ball off the racket too early and therefore the attenuation thereof may explain the increased contact time 30 with the inVention. Of course, after the ball leaves, the attenuation is not as good as it ~ould be with less stiff attachment of the weights, but the improved ball control appears to be worth the sacrifice. However, regardless 35 of the reason we have observed that the properties -- , .
V6~
of the racket discussed above are improved with dynamic masses having the sti~fer attachment.
The modification shown in Figure 4 and Figure 5 illustrates a racket embodiment according S to -the invention in which the weights and the suspending elastic means are incorporated ~Yithin the frame of the head. Suitable adsorbent materials can be used in their construction.
This frame, which is somewhat enl~rged to acco~odate 10 the weights and springs, comprises three tubular housings 8 the axis of which are perpendicular to the plane of the head. The stringing holes 9 are distributed in this area of the frame between the housings 8. Each housing 8 is lS adaptèd for accommodating one oE the weights, which are in the form of small cylinders 10, for example weighing 3g, and having each an annular groove lOa in their side wall. The cylindrical weights 10 are mounted axially within a helical 20 spring 11, the end winding of which is crimped around the groove lOa and the first winding of which is set to a general base plate 12 by means of two strips 13 stamped in said plate 12. The assembly of -the three weights 10 and the springs 25 11 is assembled by putting each weight into its tubular housing 8/ the base plate being inserted in a hollow area (not visible) located r~ at one end of said housings 8. Another identical plate (not shown) is inserted in another similar 30 hollow area 14 of the other side of said housings. In this modification, the presence o~
the added weights assembly is hardly visible from the outside except for the slight widening of the frame side where the housings 8 are 35 incoxporated; thus, the racket of this modification is hardly ~istinguishable from an unmodified racket. ~eight of the cylinders and stiffness of the springs are selected ~s in the case of the straps discussed above. Total added weight 5 of about 20 g~ams is preferred. The important feature, however, is the frequency of the added mass/spring assembly.
It shoula be no-ted that the cost of such a racket is not much over -that of an ordinary 10 racket since there are only 11 additional parts on each side relative to the handle:
three tubes, three weights, three springs and two plates. The installation of these parts can be achieved easily and can be aaapted to partially 15 automatic manufacturing techniques.
, ,, , , ~, .... .. . . .. .
Claims (5)
1. An improved tennis racket comprising a frame head, a throat, a handle and strings across the frame head and including weights on the frame head for expanding the center of percussion in the plane of the strings and for initially absorbing ball impact energy and thereby damping impact vibrations on the racket but then restoring at least a portion of the absorbed impact energy to the racket while the ball is still contacting the strings characterized in that the weights are coupled to the racket frame head by elastic means at locations on both sides of the longitudinal axis of the frame head between the racket throat and the transverse axis of the head, said elastic means having properties such that the weights oscillate in a direction substantially perpendicular to the plane of the strings with an intrinsic frequency of about 1.4-2 times that of the first mode of vibration of the racket.
2. The tennis racket of claim 1 wherein the weights are coupled at positions which are symmetric with respect to the longitudinal axis.
3. The tennis racket of claim 2 wherein the total weights on each side of the longitudinal axis are equal in magnitude.
4. The tennis racket of claim 1 characterized in that the head comprises guide holes through the frame head perpendicular to the plane of the strings and wherein the elastic means are springs and the springs and weights are housed within the guide holes.
5. The tennis racket of claim 1 characterized in that the elastic means are straps.
Applications Claiming Priority (2)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| US6105279A | 1979-07-26 | 1979-07-26 | |
| US061,052 | 1979-07-26 |
Publications (1)
| Publication Number | Publication Date |
|---|---|
| CA1140608A true CA1140608A (en) | 1983-02-01 |
Family
ID=22033325
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CA000357071A Expired CA1140608A (en) | 1979-07-26 | 1980-07-25 | Tennis racket |
Country Status (6)
| Country | Link |
|---|---|
| EP (1) | EP0032506B1 (en) |
| JP (1) | JPS56500955A (en) |
| CA (1) | CA1140608A (en) |
| DE (1) | DE3067259D1 (en) |
| IE (1) | IE49957B1 (en) |
| WO (1) | WO1981000214A1 (en) |
Families Citing this family (9)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| EP0166561B1 (en) * | 1984-06-22 | 1988-08-24 | Dunlop Limited | Games racket |
| US5098098A (en) * | 1988-07-07 | 1992-03-24 | Petralia John W | Shock and vibration absorbant sports racket |
| US5039097A (en) * | 1990-04-12 | 1991-08-13 | Bartlett William L | Snap-on weight for a tennis racket |
| WO1995004575A1 (en) * | 1993-08-05 | 1995-02-16 | Kenneth Godfrey Degaris | Counterweight balancing system for games racquets |
| US5599018A (en) * | 1994-03-31 | 1997-02-04 | Radel; Harry | Strung racket |
| FR2751235B1 (en) * | 1996-05-07 | 1998-10-09 | Bianchi Jean Claude | ANTI-VIBRATION DEVICE FOR BALL GAME RACKET FRAME |
| GB2334894A (en) * | 1998-03-04 | 1999-09-08 | Dunlop Slazenger Group Ltd | Mounting weights on games rackets |
| JP4615674B2 (en) * | 2000-05-29 | 2011-01-19 | Ｓｒｉスポーツ株式会社 | Racket frame |
| EP2036594A1 (en) * | 2007-09-12 | 2009-03-18 | Yuan Min An Enterprise Co., Ltd. | Multifunction racket |
Family Cites Families (9)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US1526734A (en) * | 1923-04-04 | 1925-02-17 | Frederick B Andrews | Tennis racket |
| US2823037A (en) * | 1956-02-16 | 1958-02-11 | Ferte Louis G La | Vibratory impulse generator for golf club |
| US3801099A (en) * | 1971-06-23 | 1974-04-02 | J Lair | Tennis racquet |
| US3907292A (en) * | 1972-02-05 | 1975-09-23 | James P Moreland | Dynamically variable tennis racket |
| US3941380A (en) * | 1972-07-31 | 1976-03-02 | Patentex S.A. | Tennis rackets and similar implements with vibration damper |
| US4057250A (en) * | 1975-09-05 | 1977-11-08 | Kuban William G | Tennis racket construction |
| DE2554267A1 (en) * | 1975-12-03 | 1977-06-16 | Kuebler & Co | STICK FOR TENNIS O.DGL. GAMES |
| FR2352220A1 (en) * | 1976-05-21 | 1977-12-16 | Malnar Leon | Vibration damping for tennis rackets - uses hollow frame filled with natural or synthetic shock absorbent |
| JPS53131133A (en) * | 1977-04-21 | 1978-11-15 | Zenzou Yamamoto | Golf club |
-
1980
- 1980-07-23 JP JP50193180A patent/JPS56500955A/ja active Pending
- 1980-07-23 WO PCT/US1980/000943 patent/WO1981000214A1/en active IP Right Grant
- 1980-07-23 DE DE8080901593T patent/DE3067259D1/en not_active Expired
- 1980-07-24 IE IE1541/80A patent/IE49957B1/en unknown
- 1980-07-25 CA CA000357071A patent/CA1140608A/en not_active Expired
-
1981
- 1981-02-09 EP EP80901593A patent/EP0032506B1/en not_active Expired
Also Published As
| Publication number | Publication date |
|---|---|
| IE801541L (en) | 1981-01-26 |
| DE3067259D1 (en) | 1984-05-03 |
| EP0032506B1 (en) | 1984-03-28 |
| IE49957B1 (en) | 1986-01-22 |
| JPS56500955A (en) | 1981-07-16 |
| EP0032506A4 (en) | 1982-05-26 |
| WO1981000214A1 (en) | 1981-02-05 |
| EP0032506A1 (en) | 1981-07-29 |
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| Date | Code | Title | Description |
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| MKEX | Expiry |