U.S. patent application number 10/029469 was filed with the patent office on 2002-05-09 for tennis racquet.
Invention is credited to McCutchen, Wilmot H..
Application Number | 20020055403 10/029469 |
Document ID | / |
Family ID | 23589071 |
Filed Date | 2002-05-09 |
United States Patent
Application |
20020055403 |
Kind Code |
A1 |
McCutchen, Wilmot H. |
May 9, 2002 |
Tennis racquet
Abstract
A tennis racquet having a bipolar weighting system, comprising a
headweight and a tailweight, is shown to outperform all racquets
known to prior art. The racquet is very head-light (15 points) and
has a high swingweight (350), while it weighs under 400 grams. A
series of high-bounce plastic string pads serves to improve
stringbed life and bounce.
Inventors: |
McCutchen, Wilmot H.;
(Orinda, CA) |
Correspondence
Address: |
Wilmot H. McCutchen
P.O. Box 689
Orinda
CA
94563
US
|
Family ID: |
23589071 |
Appl. No.: |
10/029469 |
Filed: |
December 18, 2001 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
|
|
10029469 |
Dec 18, 2001 |
|
|
|
09401748 |
Sep 23, 1999 |
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Current U.S.
Class: |
473/524 |
Current CPC
Class: |
A63B 60/54 20151001;
A63B 2049/0212 20151001; A63B 60/002 20200801; A63B 2049/0207
20151001; A63B 60/02 20151001; A63B 49/022 20151001 |
Class at
Publication: |
473/524 |
International
Class: |
A63B 049/00; A63B
049/02 |
Claims
I claim:
1. A safe and efficient tennis racquet having a bipolar weighting
system, the racquet comprising the combination of: a length less
than 73.7 cm; a mass less than 400 grams; and a mass distribution
such that the balance of the racquet is at least 15 points
head-light, and the swingweight of the racquet about an axis 10 cm
from its handle end is at least 350 kg.cm.sup.2.
2. The tennis racquet of claim 1, comprising a headweight and a
tailweight.
3. The tennis racquet of claim 2, wherein the headweight comprises
a slick grommet strip.
4. The tennis racquet of claim 2, wherein the headweight comprises
a series of string pads.
5. The tennis racquet of claim 4, wherein the string pads are of
high-bounce plastic.
6. The tennis racquet of claim 4, wherein the string pads are of
low-bounce plastic.
7. The tennis racquet of claim 2, wherein the tailweight is a slug
within a matrix of low-bounce material, the tailweight being
disposed within the handle of the racquet.
7. An improved tennis racquet, wherein the improvement comprises a
series of string pads, the string pads being disposed between the
racquet head and the strings and firmly engaging the strings.
8. The improved tennis racquet of claim 7, wherein the string pads
are of high-bounce plastic material.
9. The improved tennis racquet of claim 7, wherein the string pads
are of low-bounce plastic material.
10. An improved tennis racquet, the improvement comprising a
headweight and a tailweight which serve to clamp the free ends of
the racquet and thus reduce its resonant frequency.
11. The improved tennis racquet of claim 10, the racquet comprising
the combination of: a length less than 73.7 cm; a mass less than
400 grams; and a mass distribution such that the balance of the
racquet is at least 15 points head-light, and the swingweight of
the racquet about an axis 10 cm from its handle end is at least 350
kg.cm.sup.2.
12. The tennis racquet of claim 10, wherein the headweight
comprises a slick grommet strip.
13. The tennis racquet of claim 10, wherein the headweight
comprises a series of string pads.
14. The tennis racquet of claim 13, wherein the string pads are of
high-bounce plastic.
15. The tennis racquet of claim 13, wherein the string pads are of
low-bounce plastic.
16. The tennis racquet of claim 10, wherein the tailweight is a
slug within a matrix of low-bounce material, the tailweight being
disposed within the handle of the racquet.
Description
[0001] This application is a continuation in part of Ser. No.
09/401,748, filed Sep. 23, 1999.
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 1/8 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.cm.sup.2. 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.cm.sup.2, 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.cm.sup.2)
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.cm.sup.2 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/s.sup.2
[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: Mr.sup.2/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.cm.sup.2 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: Mr.sup.2/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.cm.sup.2 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.cm.sup.2.
[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.cm.sup.2. 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.TM.) 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 s.sub.1=0; outgoing ball speed
s.sub.2=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 (s.sub.1 and s.sub.2) (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 209.sup.th 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.
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