Tennis racquet

FIELD OF THE INVENTION

[0002] This invention relates to tennis racquets, to means for reducing the resonant frequency of tennis racquets, to means for improving the coefficient of restitution of tennis racquet stringbeds, and to means for preventing string breakage.

BACKGROUND—PRIOR ART

[0003] U.S. Pat. No. 5,058,902 (1991) to McCutchen describes a 568 gram racquet having a distal handle end weight of 200 grams for the purpose of raising the center of percussion and achieving a balance approximately 30 points head-light. U.S. Pat. No. 5,605,327 (1996) to McCutchen describes a butt cap for adding a particulate handle end weight.

[0004] The term “head-light” is used in tennis to describe a racquet having a balance point closer to the butt end than to the tip, i.e. below instead of above the midpoint of the racquet's length. “Head-heavy” means balanced more toward the racquet head, like a hammer. A “point” is a measuring unit of ⅛ inch (3.175 mm). Racquets are described as being a certain number of points head-light or head-heavy, thus giving the relative location of the balance point, or mass center, with respect to the midpoint of the racquet's length.

[0005] “Swingweight” is the tennis term for the moment of inertia, or rotational inertia, of a racquet about a standard axis of rotation in the handle. The industry standard measuring device, the Babolat Racquet Diagnostic Center, measures swingweight about an axis of rotation 10 cm from the butt end of the racquet. The unit of measurement for swingweight is kg.cm2. Where swingweight is given herein, the axis is 10 cm from the butt end of the racquet, unless otherwise stated.

[0006] Tennis racquets are roughly classified in two groups: game improvement racquets and players' racquets. The classification is based on their weight and balance. Game improvement racquets are head-heavy and light, generally below 300 grams in mass. Players' racquets are head-light and heavy, in excess of 300 grams. Swingweight of players' racquets is, as a rule, less than the swingweight of game improvement racquets, because, as a rule but not always, head-light balance correlates with low swingweight. The measuring unit for swingweight, kg.cm2, explains the correlation: the distance unit is squared so the location of mass is more important than its amount, and therefore a light racquet may have a high swingweight if its balance is head-heavy. But head-light balance does not necessarily imply low swingweight.

[0007] High swingweight allows for a slow swing to produce high racquet angular momentum upon impact with the ball. However, high swingweight requires more effort to produce a required swing speed, or angular velocity. Opinions differ among skilled players, with some—e.g. Thomas Muster—preferring high swingweight (400 in Muster's case) and others—e.g. Sergei Bruguera—preferring low swingweight (307 in Bruguera's case).

[0008] Apart from its implications for swingweight, head-heavy balance is not good, because the racquet has a high first moment and is therefore hard to hold up. Also, with a head-heavy balance the resultant Torque (force twisting the racquet backward) and Shock (change in racquet internal energy, which produces frame vibration) from impact are greater. With the mass center far from the player's hand, more effort (Work) is required to swing it around in order that the racquet head has sufficient velocity to produce a desired ball speed. The benefit of head-light balance for swing speed, however, is not absolute, because a high racquet head velocity with a low swingweight will not produce high angular momentum. A proper mix of head-light balance and high swingweight is necessary for low Work.

[0009] Of commercially available racquets, the most extreme head-light balance is the Wilson ProStaff 6.1 110 Stretch at 14.4 points. Its swingweight is 321. Of head-light racquets, the highest swingweight is the Cayman Energizer II at 395, and its balance is 5 points head-light. Heretofore, an extreme (i.e. in excess of 15 points) head-light balance and a high (i.e. in excess of 350) swingweight were mutually exclusive objects, because in adding mass to the head to increase swingweight, the balance became more head-heavy.

[0010] The combination of an extreme head-light balance (in excess of 15 points) and high swingweight (in excess of 350 kg.cm2) is desirable because of the separate recognized advantages of high swingweight and head-light balance, and also because the combination of these two attributes gives enhanced performance according to the evaluation criteria whose formulas appear in FIG. 5 and which are described below. In a racquet weighing less than 400 grams, and less than 29 inches long, the combination of extreme head-light balance and high swingweight is unknown in prior art.

[0011] Evaluation criteria for racquets include the following:

[0012] 1. Sweet Spot (center of percussion) distance from the racquet tip. The closer to the tip the sweet spot is, the less is the racquet's impulse due to impact. The formula for finding the sweet spot is

q=I/Mr

[0013] q=distance in cm from axis of rotation to center of percussion

[0014] I=swingweight in kg.cm2 about axis of rotation

[0015] M=racquet mass in kg

[0016] r=distance in cm from axis of rotation to mass center, or balance point

[0017] 2. Moment (first moment). Moment is the downward twisting force at the player's hand as he holds the racquet parallel to the ground. Low Moment is desirable because the player finds the racquet easier to hold up, so it feels lighter and is more maneuverable to position for volleys and returns. The formula for finding moment is:

Moment in Newton.meters=Mrg/100

[0018] M=racquet mass in kg

[0019] r=distance in cm from axis of rotation to mass center, or balance point

[0020] g=gravitational constant, 9.81 m/s2

[0021] 3. Torque. Torque is the twisting force backward resulting from impact with the ball. The resultant torque about the axis of rotation (at the hand) from impact should be minimized to reduce the risk of tennis elbow. The critical ratio for determining Torque is: Mr2/I (M=racquet mass in kg; r=distance in cm from axis of rotation to mass center, or balance point; and I=swingweight in kg.cm2 of the racquet about the axis of rotation). From the formula for sweet spot above, it can be seen that this ratio is r/q. So a high sweet spot together with a head-light balance means low Torque.

[0022] 4. Impulse Reaction. The other resultant force at the player's hand due to impact of the racquet head with the ball is Impulse Reaction. This is a translational force at the axis of rotation. The direction of this force is indicated by its sign: a push is positive, and a pull is negative. If the sweet spot is closer to the tip than is the center of the strings, the Impulse Reaction will be a push when the impact is at the center of the strings. If the sweet spot is farther away from the tip than is the center of the strings, Impulse Reaction will be a pull.

[0023] 5. Shock. By the term Shock is meant the change in internal energy of the racquet which results from impact. The internal energy load on the racquet from impact, which expresses itself as frame vibration, should be minimized. As with Torque, the critical ratio for Shock is: Mr2/I (M=racquet mass in kg; r=distance in cm from axis of rotation to mass center, or balance point; and I=swingweight in kg.cm2 of the racquet about the axis of rotation).

[0024] 6. Work. Work is the player effort required to produce the racquet kinetic energy necessary to produce a required ball speed. Work should be minimized so that the player gets more ball speed from a given effort.

[0025] 7. Shoulder Pull. The rotation of the racquet about the shoulder produces a centripetal force called Shoulder Pull, which should be minimized.

[0026] 8. Shoulder Crunch. As the racquet swings, its centripetal force (Shoulder Pull) is in equilibrium with its centrifugal force. Impact with the ball reduces suddenly the centrifugal force of the racquet, but the shoulder muscles keep pulling as if the full centripetal force were still present. Effectively, this is a muscle spasm. This imbalance, known as Shoulder Crunch, should be minimized for player safety.

[0027] 9. Elbow Crunch. At the elbow, the resultant imbalance of centripetal and centrifugal forces due to impact is known as Elbow Crunch.

[0028] 10. Impact Impulse. When the racquet strikes the ball, an impulse occurs because of the change in racquet momentum.

[0029] A clamping effect on the free end of a vibrating rigid body is known to result from adding weight to the free end. See H. Brody, “The Physics of Tennis III: The BallRacket Interaction,” 65 Am. J. Phys. (October 1997). The effect of a handle clamp is to decrease resonant frequency, the effect on resonant frequency of a player's grip being roughly equivalent to 40 grams of handle weight. Also, according to Professor Brody's data (FIG. 1 on p. 982), for impacts near the tip, a clamped head should give higher ball rebound velocity than an unclamped head. In his experiment, the head clamp was a vise, not a weight.

[0030] Lead tape on the racquet head has been used for many years, particularly by players who rely on big serves. The advantage of such head-weighting may be the combination of higher swingweight and tip clamping.

[0031] Adding to the dwell time of the ball on the strings has been accomplished by means of rockers and rollers at the string holes, which serve to distribute string stress over more string length. An alternative approach, offered in the Volkl Catapult line, is a flexing ridge between the middle cross strings and the frame, which ridge depresses and then springs back so as to give the strings a boost.

SUMMARY OF THE PRESENT INVENTION

[0032] A tennis racquet having the combination of a swingweight in excess of 350, a weight less than 400 grams, and a balance 15 or more points head-light, is safer to play with and more efficient than all racquets known to prior art, according to the evaluation criteria set forth here. This desirable mix of specifications is obtained through a bipolar weighting system, with the racquet's mass concentrated at its two ends by means of a tailweight and a headweight. The preferred embodiment is a tennis racquet 28 inches (71 cm) long, having a total mass of 395 grams, a balance 22 points head-light, and a swingweight of 390. Alternative 1 is a 28 inch (71 cm) long racquet having a mass of 325 grams, a balance 15 points head-light, and a swingweight of 350. Alternative 2 is a 27 inch (68.6 cm) long racquet having a mass of 350 grams, a balance 16 points headlight, and a swingweight of 350. Each of these embodiments of the present invention outperforms all prior art.

[0033] The bipolar weighting system serves to clamp the free ends of the so as to reduce the resonant frequency of frame vibration and to give greater rebound velocity for impacts near the tip.

[0034] In the embodiment of an internal handle tailweight, frame vibration is transduced into internal energy of the matix, thus damping frame vibration.

[0035] In the embodiment of a slick grommet strip, the headweight serves to distribute string stress over more string length and prevent breakage by allowing the strings to slip easily through the string holes on impact. In the embodiment of a high-bounce plastic, the headweight serves to give a boost to the strings as it performs the same function as the slick grommet strip. And in the embodiment of a low-bounce plastic, the headweight serves to damp string vibration.

OBJECTS AND ADVANTAGES OF THE PRESENT INVENTION

[0036] It is an object of the present invention to provide a tennis racquet having lower Torque, Shock, Work, Shoulder Pull, Shoulder Crunch, Elbow Crunch, and Impact Force than any other racquet known to prior art. The advantage of such a racquet is that risk of player injury is reduced while performance is enhanced.

[0037] It is also an object of the present invention to provide means for reducing the resonant frequency of racquet frame vibration. The headweight and tailweight are tantamount to a clamp on the free ends, which serves to reduces the racquet's resonant frequency.

[0038] It is also an object of the present invention to provide means for damping frame vibration. A tailweight in a matrix of low coefficient of restitution urethane foam or other low-bounce material, disposed at the handle end, transduces frame vibration to internal energy of said material and serves to aid in damping frame vibration, while the tailweight lowers its frequency.

[0039] It is also an object of the present invention to provide means for increasing the rebound ball speed for impacts near the tip. The headweight, particularly in its embodiment with high-bounce plastic, accomplishes this object by acting as a clamp.

[0040] It is also an object of the present invention to provide means for decreasing string breakage. The headweight in its embodiment with a slick grommet strip allows the strings to slip easily through the string holes and to distribute string stress over a longer string length. The headweight in its embodiment as a high-bounce, low durometer plastic, serves to distribute string stress over a longer string length by deforming while maintaining contact with the strings on impact, thus effectively performing the same function as the slick grommet strip. Additionally, the high-bounce plastic boosts the recovery of the strings and gives the stringbed more bounce.

[0041] It is also an object of the present invention to provide means for damping string vibration. The headweight in its embodiment as a low-bounce plastic string pad serves to absorb string vibration.

SUMMARY OF THE DRAWINGS

[0042]
FIG. 1 shows the preferred embodiment of the present invention, a tennis racquet having a headweight and a tailweight and having a mass less than 400 grams and a mass distribution such that its balance is in excess of 15 points head-light while its swingweight is in excess of 350 kg.cm2.

[0043]
FIG. 2 is a detail of an alternative embodiment of the racquet handle end, showing a tailweight in excess of 50 grams in a damping matrix within the handle.

[0044]
FIG. 3 shows a table giving the measurements of the preferred embodiment and Alternatives 1 and 2, as compared to the prior art racquets.

[0045]
FIG. 4 is a table showing the performance of the preferred embodiment and Alternatives 1 and 2 as compared to the best racquets known to prior art.

[0046]
FIG. 5 is a table of the formulas used to determine the performance of the preferred embodiment, Alternatives 1 and 2, and 276 racquets known to prior art.

[0047]
FIG. 6 shows a detail of the headweight of the preferred embodiment, a series of high-bounce plastic string pads along the tip.

DETAILED DESCRIPTION OF THE DRAWINGS.

[0048]
FIG. 1 shows the preferred embodiment, a tennis racquet having a bipolar weighting system according to the present invention. The tennis racquet comprises a frame (1), the frame being a molded composite comprising a head (2), the head comprising a tip (3), and a handle (4), the handle comprising a handle end or butt (5). The head comprises a string bed of strings that go through holes around the head. Perpendicularly through the handle and parallel to the plane defined by the head (2) is an axis of rotation (a-a), about which the racquet is rotated in a stroke. This axis (a-a) is located 5 cm from the butt, approximately where it would be on a serve, and this common axis is used to compare the preferred embodiment, Alternatives 1 and 2, and prior art. A parallel axis (b-b) is 10 cm from the butt, and it is this axis that is used for swingweight measurements on the Babolat Racquet Diagnostic Center, presently the industry standard measuring device. Halfway along the racquet's length of 28 inches, or 71 cm, is a midpoint (6). The racquet has a mass center (7) at which it balances evenly, said mass center in the preferred embodiment being 22 points, i.e. 2.75 inches, or 7 cm, toward the butt (5) from the midpoint (6).

[0049] The total mass of the racquet, including strings and grip, is 395 grams. The swingweight of the racquet about the parallel axis of rotation (b-b) is 390 kg.cm2. The foregoing measurements, as well as the measurements for Alternatives 1 and 2 and the prior art racquets used in the comparison shown in FIG. 4, are for racquets that are strung and gripped. Said measurements are achieved by a bipolar weighting system, comprising a tailweight (8), and a headweight (7), the headweight and tailweight being mass elements attached to the racquet frame. Preferably, the headweight is at the tip, and the tailweight is at the butt, located such that a player's hand gripping the racquet for a groundstroke will be between the tailweight and the headweight.

[0050] The headweight (7) serves to increase swingweight and to clamp the racquet head so as to improve rebound ball speed and reduce resonant frequency of the frame. Preferably, the headweight is in the form of a series of string pads as shown in detail in FIG. 6. Alternatively, the headweight is in the form of a slick grommet strip, comprising metal coated with PTFE (Teflon™) The slick grommet strip allows the strings to slide easily through the string holes on impact, thus distributing string stress over a longer string length and reducing the chance of string breakage. The slick grommet strip is of the same shape as grommet strips known to the art.

[0051] An alternative embodiment of the same shape is Alternative 1, a 28 inch (71 cm) long racquet having a mass of 325 grams, a balance 15 points head-light, and a swingweight of 350. Another alternative embodiment, Alternative 2, is a 27 inch (68.6 cm) long racquet having a mass of 350 grams, a balance 16 points head-light, and a swingweight of 350. The total mass for each is less than 400. As these alternative embodiments look the same, except for length, as the preferred embodiment, there is no need to draw them separately.

[0052]
FIG. 2 shows a detail of an alternative embodiment of a damping tailweight (8) for the racquet described in FIG. 1. The tailweight comprises a slug (10), preferably in excess of 50 grams within a matrix (9) of material having a low coefficient of restitution. By the term low coefficient of restitution is meant a low to non-existent bounce when the material is dropped onto a hard surface, such as for example one would see upon dropping a lump of damp clay. The matrix (9) is preferably urethane foam having a low coefficient of restitution. Other materials of similar low bounce, such as clay, could be also used. The tailweight (8) is disposed within the handle and attached thereto. A butt cap (not shown), of the type known to prior art, covers the handle end, and a grip (not shown) of the type known to prior art, covers the handle. The tailweight (8) adds to the swingweight and counterbalances the mass of the racquet head, such that the swingweight of the racquet is at least 350, and the balance of the racquet is at least 15 points head-light. In play, the tailweight would not move longitudinally sufficient to change the swingweight of the racquet materially.

[0053]
FIG. 3 shows the measurements of the preferred embodiment, Alternatives 1 and 2, and a Wilson Sledge Hammer 3.8 MP PH (the racquet known to prior art to have a center of percussion closest to its tip). Also shown are the average measurements for 276 racquets known to prior art.

[0054]
FIG. 4 shows the results of applying the formulas in FIG. 5 to the measurements in FIG. 3 to compare the preferred embodiment and Alternatives 1 and 2 with prior art. All racquets were evaluated under the following stipulations: axis of rotation 5 cm from butt; incoming ball speed s1=0; outgoing ball speed s2=49.17 m/s (110 mph serve); coefficient of restitution of the ball/racquet system c=0.85; dwell time t of ball on racquet strings=0.004 s; ball mass b=57 grams. The measured swingweight about the 10 cm axis (b-b) was converted to the swingweight about the 5 cm axis I using the Parallel Axis Theorem. These results demonstrate a clear superiority of the present invention to prior art and prove that the present invention is not an obvious improvement to be expected from the routine experimentation of uninstructed artisans. The performance difference is a quantum leap, far superior to all prior art under the objective performance criteria.

[0055]
FIG. 5 gives the formulas used to obtain the results shown in FIG. 4, based on the measurements shown in FIG. 3. To enable racquet comparisons to be made objectively, the ball speeds before and after impact (s1 and s2) (0 and 49.17 m/s respectively), the coefficient of restitution (c) (=0.85), the duration of impact (t) (=0.004 s), the ball mass (b) (57 grams), the axis of rotation (=5 cm from butt), and the impact point distance from tip (=16 cm) were stipulated to be the same for all racquets, and the racquet measurements were converted to values for the variables M, r, d, and I.

[0056]
FIG. 6 shows a detail of the headweight in its embodiment as a series of string pads on the outside of the racquet head. A string pad (11) is disposed between the string holes (12) such that a racquet string (13) passing through the holes firmly engages the string pad and presses the string pad against the racquet head. Preferably, the string pad is made of a high-bounce plastic, e.g. urethane, of a durometer hardness in the Shore A range. By the term high-bounce is meant high coefficient of restitution, like the high bouncing balls seen in novelty shops. Alternatively, the string pad could be made of low-bounce (low coefficient of restitution) material such as urethane or leather. The advantage of using high-bounce plastic is that its bounce is added to the strings in their recovery, so as to boost the bounce of the string bed, and its deformation serves to take some load off the strings on impact and to distribute string stress over longer string length. The advantage of low-bounce material is that string vibration is damped.

OPERATION, RAMIFICATIONS, AND SCOPE

[0057] A racquet having a very head-light balance together with a high swingweight is a significant improvement in reducing risk of player injuries and improving performance, as the comparisons in FIG. 4 show.

[0058] The combination of head-light balance and high swingweight is desirable because of the effect of this combination in raising the location of the center of percussion, according to the formula:

q=I/Mr

[0059] q=distance in cm from axis of rotation to center of percussion

[0060] I=swingweight in kg.cm2 about axis of rotation

[0061] M=mass in kg

[0062] r=distance in cm from axis of rotation to mass center, or balance point

[0063] It can be seen that increasing I (higher swingweight) and reducing r (more headlight balance) will increase q. This places the center of percussion close to the tip (1).

[0064] The highest sweet spot known to prior art is the Wilson Sledge Hammer 3.8 MP PH which is 15.7 cm from the tip when the axis of rotation is 5 cm from the butt. Measuring the distance of the sweet spot (center of percussion) from the tip is preferable to measuring its absolute distance from the hand because this way the differences in racquet length are accounted for. The Wilson Sledge Hammer 3.8 MP is 15 points head-heavy, with a swingweight of 353, and a mass of only 269 grams. The preferred embodiment of the present invention (395 grams, balance 22 points head-light, and swingweight 390) has its sweet spot at 15.3 cm from the tip. Although the prior art and the preferred embodiment are arguably close as to their result in raising the sweet spot, the approaches used to achieve this result are radically different. The Wilson racquet is very head-heavy (as the name Sledge Hammer would imply) while the preferred embodiment is very head-light. Under all other performance criteria, as shown in FIG. 4, the preferred embodiment is clearly superior to all prior art racquets, including said Wilson model. Elbow Crunch is only 118.67 Newtons, much less than the 154.54 of the th Wilson (which placed 209th out of 279 racquets under this criterion—very inferior), a 23% superiority in performance for the preferred embodiment. For Work, the superiority is 36% over the Wilson Sledge Hammer 3.8 MP PH, and for Shock, 35%.

[0065] On all other evaluation criteria except Moment, the preferred embodiment outperformed the best racquets known to prior art, see FIG. 4. A racquet having a mass of 325 grams, a length of 28 inches (71 cm), a balance 15 points head-light, and a swingweight of 350 (Alternative 1) would also be superior to prior art, as shown by FIG. 4. Alternative 2, a racquet having a mass of 350 grams, a length of 27 inches (68.6 cm), a balance 16 points head-light, and a swingweight of 350 would also outperform all prior art, as shown by FIG. 4. Its sweet spot would be the highest of all.

[0066] The tailweight reduces the racquet's resonant frequency by acting as a clamp on the handle. The tailweight also serves to damp frame vibration by transducing the frame internal energy into internal energy of the matrix. The slug oscillating inside the matrix gives up its kinetic energy to the matrix, where it becomes internal energy.

[0067] The headweight also serves to reduce resonant frequency by acting as a clamp on the racquet's other free end. The headweight increases swingweight. In its embodiment as a slick grommet strip, the headweight allows for the strings to slide easily through the string holes in the racquet head, thus distributing string stress over a longer string length and reducing the chance of string breakage. In its embodiment as a series of string pads of high-bounce plastic, the same advantages as the slick grommet strip are obtained, with the additional advantage of a boost in stringbed bounce.

[0068] The bipolar weighting system disclosed in the present invention has not only the benefit of outstanding performance under the objective performance criteria, but also of providing the collateral benefit of clamping the free ends so as to reduce the resonant frequency of frame vibration.

[0069] Those skilled in the art of tennis racquets will readily see that the teachings of the present invention may readily be extended to racquet designs other than those shown in the preferred embodiment and Alternatives 1 and 2. The specifications for these embodiments are given for illustration purposes and to prove the superiority of the present invention to prior art, and should not be read as in any way abridging or limiting the scope of the claims.

	Number	Date	Country
Parent	09401748	Sep 1999	US
Child	10029469	Dec 2001	US

Tennis racquet

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