U.S. patent number RE31,419 [Application Number 06/229,776] was granted by the patent office on 1983-10-18 for tennis racket.
Invention is credited to Jack L. Frolow.
United States Patent |
RE31,419 |
Frolow |
October 18, 1983 |
Tennis racket
Abstract
A tennis racket is provided having the same swing weight as
rackets of the prior art, but having a significant reduction in the
weight, and a significant increase in the distance of the center of
percussion and in the distance of the center of gravity from the
end of the handle. A significant reduction in the deflection and
vibration of the racket caused by the impact of the ball is
provided. The tendency of the racket to turn in the players hand
when a ball hits the racket off of the longitudinal axis of the
racket, is reduced. These improvements are accomplished by
controlling the distribution of material and the cross-sectional
shape along the length, width, and depth of the racket, and by the
utilization of materials having a high stiffness and strength per
unit weight. Methods are provided to measure the swing weight of
the racket about selected axes and to measure the flexibility and
vibratory characteristics of the racket.
Inventors: |
Frolow; Jack L. (Long Branch,
NJ) |
Family
ID: |
26923600 |
Appl.
No.: |
06/229,776 |
Filed: |
January 28, 1981 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
Issue Date |
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Reissue of: |
646848 |
Jan 5, 1976 |
04165071 |
Aug 21, 1979 |
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Current U.S.
Class: |
473/522 |
Current CPC
Class: |
A63B
49/00 (20130101); A63B 49/02 (20130101); A63B
60/48 (20151001); A63B 60/50 (20151001); A63B
60/002 (20200801) |
Current International
Class: |
A63B
49/02 (20060101); A63B 49/00 (20060101); A63B
59/00 (20060101); A63B 049/02 () |
Field of
Search: |
;273/73R,73C,73D,73F,73G,73H,73J,75,165,DIG.7,DIG.23 |
References Cited
[Referenced By]
U.S. Patent Documents
Foreign Patent Documents
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605166 |
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Nov 1934 |
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DE2 |
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2417439 |
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Oct 1975 |
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DE |
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800262 |
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Apr 1936 |
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FR |
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1495578 |
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Aug 1967 |
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FR |
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8112 of |
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1884 |
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GB |
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14147 of |
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1885 |
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GB |
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15670 of |
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1886 |
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GB |
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107660 |
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Jul 1917 |
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GB |
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201245 |
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Jul 1923 |
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GB |
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267837 |
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Mar 1927 |
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GB |
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284754 |
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Feb 1928 |
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GB |
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327796 |
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Apr 1930 |
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GB |
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420966 |
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Dec 1934 |
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GB |
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482164 |
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Mar 1938 |
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GB |
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547946 |
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Sep 1942 |
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GB |
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1223834 |
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Mar 1971 |
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GB |
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1278474 |
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Jun 1972 |
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GB |
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Other References
"The Sporting Goods Dealer"; May 1974; pp. 126, 128. .
"The Sporting Goods Dealer"; May 1975; p. 156..
|
Primary Examiner: Oechsle; Anton O.
Claims
I claim:
1. A complete tennis racket comprising at least a frame having a
head portion supporting a string netting in a plane, and a handle
portion having a grip portion suitably adapted for the hand to
grip; said netting having a length along the longitudinal axis of
said frame greater than 9 inches and a width along an axis
perpendicular to said longitudinal axis greater than 7.5 inches;
said racket having a weight W in ounces; a center of percussion
located at a distance Cp in inches from the end of the grip
portion, when tested in accordance with test 4 of FIG. 40 herein
before defined, said center of percussion taken about a pivot
located at the end of the grip portion, said pivot having an axis
perpendicular to the longitudinal axis of said frame and parallel
to the plane of said string netting; said racket having a length L
in inches from the end of the grip portion to the end of the head
portion; said racket having a center of gravity located a distance
C.sub.g in inches from the end of the grip portion; said racket
having a first moment of inertia I.sub.s in ounce inches squared
about said pivot and I.sub.s is directly proportional to the
product of C.sub.p, C.sub.g, W given by the formula I.sub.s
=(C.sub.p)(C.sub.g)(W); said racket characterized in that the
magnitude of Cp divided by the magnitude of L given by the formula
C.sub.p /L is greater than 0.71; and the magnitude of the weight W
is less than 10.7 ounces.
2. A racket as in claim 1 wherein the said length L is greater than
25.5 inches.
3. A racket as in claim 2; and the said magnitude of the moment of
inertia I.sub.s is greater than 2500 ounce inches squared and less
than 3450 ounce inches squared.
4. A tennis racket as in claim 2; and said racket having a weight
and stiffness distribution providing for the nodal pivot closest to
the grip portion end to be located at a distance N in inches from
the said end of the grip portion, when tested in accordance with
test 15 of FIG. 40 herein before defined; said racket characterized
in that the magnitude of said distance N divided by the magnitude
of the said distance L; given by the formula .[.N.]. N/L is greater
than 0.28.
5. A racket as in claim 2, and said racket having a weight and
stiffness distribution providing for a frequency of vibration
greater than 140 cycles per second when tested in accordance with
test 13 of FIG. 40 herein before defined.
6. A tennis racket as in claim 5 wherein the said frequency of
vibration is greater than 150 cycles per second.
7. A tennis racket as in claim 2; and said racket having a weight
and stiffness distribution providing for a frequency of vibration
greater than 175 cycles per second when tested in accordance with
test 16 of FIG. 40 herein before defined.
8. A tennis racket as in claim 2; and said racket having a weight
and stiffness distribution providing a frequency of vibration
greater than 34 cycles per second when tested in accordance with
test 18 of FIG. 40 herein before defined.
9. A tennis racket as in claim 2; and said racket having a weight
and stiffness distribution providing a frequency of vibration
greater than 40 cycles per second when tested in accordance with
test 20 of FIG. 40 herein before defined.
10. A tennis racket as in claim 2; and said racket having a weight
and stiffness distribution providing a frequency of vibration
greater than 90 cycles per second when tested in accordance with
test 22 of FIG. 40 herein before defined.
11. A tennis racket as in claim 2; and said racket having a center
of the said string netting, located at a distance C.sub.f in inches
from the end of the grip portion; providing for the difference in
the magnitude of the said distance C.sub.f and the said distance
C.sub.p divided by the distance C.sub.p given by the formula
(C.sub.f -C.sub.p)/C.sub.p to be less than 0.12.
12. A tennis racket as in claim 2; and said racket having a weight
distribution providing a second moment of inertia I.sub.a in ounce
inches squared about a longitudinal axis running from the center of
the head portion end to the center of the grip portion end; said
racket further characterized in that the magnitude of the moment of
inertia I.sub.a divided by the magnitude of the said moment of
inertia I.sub.s given by the formula I.sub.a /I.sub.s is greater
than 0.020.
13. A tennis racket as in claim 2; wherein the said frame is made
of metal having a modulus of elasticity in tension E in pounds per
square inch, and a density d in pounds per cubic inch, and the
ratio of .[.e/d.]. .Iadd.E/d .Iaddend.is less than
110.times.10.sup.6.
14. A tennis racket as in claim 2; wherein the said frame utilizes
a composite of fibers and resin, and further the magnitude of the
said weight W is less than 10.0 ounces.
15. A tennis racket as in claim 2 wherein the magnitude of W is
less than 10.0 ounces.
16. A tennis racket as in claim 1 comprising a .[.fame.].
.Iadd.frame .Iaddend.member being an elongated strip of material
shaped to form a head portion, a throat portion and a pair of
spaced substantially parallel sides into a shaft portion; said head
portion curved to inclose a space suitable for supporting a string
netting, said strip adapted to support said string netting; and a
tubular grip member of thin wall material shaped for the hand to
grip fastened to the ends of the spaced sides of the shaft portion
of said frame member; and throat members being two sheets of thin
wall material, each sheet having a top edge portion a bottom edge
portion connected with side edge portions; said sheets having the
side edge portions fastened to the said strip of material at the
throat portion of said frame member.
17. A tennis racket as in claim 16, wherein the elongated strip of
said frame is curved to inclose a space substantially wider at the
head portion end that at the throat portion.
18. A racket as in claim 1 and said racket having a weight and
stiffness distribution providing for a frequency of vibration
greater than 90 cycles per second when tested in accordance with
test 13 of FIG. 40 herein before defined.
19. A racket as in claim 1 and said racket having a weight and
stiffness distribution providing for a frequency of vibration f in
cycles per second when tested in accordance with test 13 of FIG. 40
herein before defined, and said racket further characterized in
that the product of the said length L squared and the said
frequency f given by the expression L.sup.2 f is greater than
65,000.
20. A racket as in claim 19 wherein the said length L is greater
than 23 inches.
21. A tennis racket as in claim 1 comprising a unitary frame formed
by a resin reinforced fiber material having a head portion, a
throat portion, and a shaft portion; said head portion inclosing a
space suitable to support a string netting in a plane, said head
portion having two arms of hollow crossection approaching the
throat portion, said two arms of said head portion merging into the
throat portion; said throat portion having a hollow crossection
having upper and lower throat walls substantially parallel to the
plane of said string netting connected by two throat side walls,
said throat portion merging with the shaft portion; said shaft
portion having upper and lower shaft walls substantially parallel
to the plane of said string netting connected by two shaft side
walls, said shaft portion merging with the grip portion; said grip
portion having a hollow cross section having a thin wall, said grip
portion formed suitably for the hand to grip.
22. A tennis racket as in claim 1 having a hollow metal frame of
two part shell construction comprising substantially outer and
inner shells each having an open side and two opposing sides
connected by a central wall, the outer shell receiving the inner
shell in an inverted position therein, said opposing sides of the
outer shell adjacent to the opposing sides of the inner shell;
means for fastening said sides of the outer shell to the adjacent
side of the inner shell; said frame having a head portion capable
of supporting a string netting in a plane, a throat portion, a
shaft portion and a grip portion.
23. A complete tennis racket comprising at least a frame having a
head portion supporting a string netting in a plane, and a handle
portion having a grip portion suitably adapted for the hand to
grip, said netting having a length along the longitudinal axis of
said frame greater than 9 inches and a width along an axis
perpendicular to said axis greater than 7.5 inches; said racket
having a weight W in ounces; a center of percussion located at a
distance C.sub.p in inches from the end of the grip portion, when
tested in accordance with test 4 of FIG. 40 herein before defined,
said center of percussion taken about a pivot located at the end of
the grip portion, said pivot having an axis perpendicular to the
longitudinal axis of said racket and parallel to the plane of said
string netting; said racket having a length L in inches from the
end of the grip portion to the end of the head portion; said racket
having a center of gravity located at a distance C.sub.g in inches
from the end of the grip portion; said racket having a first moment
of inertia I.sub.s in ounce inches squared about said pivot, and
I.sub.s is directly proportional to the product of C.sub.p,
C.sub.g, W, given by the formula I=(C.sub.p)(C.sub.g)(W); said
racket characterized in that the magnitude of C.sub.p is greater
than 18.75 inches, and the weight W is less than 10.7 ounces.
24. A racket as in claim 23; and the said magnitude of I.sub.s is
greater than 2500 ounce inches squared and less than 3500 ounce
inches squared.
25. A tennis racket as in claim 23; and said racket having a weight
and stiffness distribution providing for the nodal pivot closest to
the grip portion end to be located at a distance N in inches from
the end of the grip portion, when tested in accordance with test 15
of FIG. 40 herein before defined; said racket characterized in that
the magnitude of the said distance N is greater than 7.5
inches.
26. A tennis racket as in claim 23; and said racket having a weight
and stiffness distribution providing a frequency of vibration
greater than 140 cycles per second when tested in accordance with
test 13 of FIG. 40 herein before defined.
27. A tennis racket as in claim 26 wherein the said frequency of
vibration is greater than 150 cycles per second.
28. A racket as in claim 26; and said racket having said distance
C.sub.p greater than 19.3 inches.
29. A tennis racket as in claim 23; and said racket having a weight
and stiffness distribution providing a frequency of vibration
greater than 175 cycles per second when tested in accordance with
test 16 of FIG. 40 herein before defined.
30. A tennis racket as in claim 23; and said racket having a weight
and stiffness distribution providing a frequency of vibration
greater than 34 cycles per second when tested in accordance with
test 18 of FIG. 40 herein before defined.
31. A tennis racket as in claim 23; and said racket having a weight
and stiffness distribution providing a frequency of vibration
greater than 40 cycles per second when tested in accordance with
test 20 of FIG. 40 herein before defined.
32. A tennis racket as in claim 23; and said racket having a weight
stiffness distribution providing a frequency of vibration greater
than 90 cycles per second when tested in accordance with test 22 of
FIG. 40 herein before defined.
33. A tennis racket as in claim 23; and said racket having a center
of said string netting located a distance C.sub.f in inches from
the end of the grip portion; said racket further characterised in
that the difference in the magnitude of the said distance C.sub.f
and the said distance C.sub.p divided by the said distance C.sub.p
given by the formula C.sub.f -C.sub.p /C.sub.p is less than
0.12.
34. A tennis racket as in claim 23; and said racket having a weight
distribution providing a second moment of inertia I.sub.a in ounce
inches squared about a longitudinal axis running from the center of
the grip portion end to the center of the head portion end; said
racket further characterized in that the magnitude of the moment of
inertia I.sub.a divided by the magnitude of the said moment of
inertia I.sub.s given by the formula I.sub.a /I.sub.s is greater
than 0.020.
35. A tennis racket as in claim 23; wherein the said frame is made
of metal having a modulus of elasticity in tension E in pounds per
square inch and a density d in pounds per cubic inch, and the ratio
of E/d is less than 110.times.10.sup.6.
36. A tennis racket as in claim 23; wherein the said frame utilizes
a composite of fibers and resin; and further the magnitude of the
weight W is less than 10.0 ounces.
37. A tennis racket as in claim 23; and said head portion being an
elongated strip having a center portion and two adjacent end
portions curved to inclose said string netting; said handle portion
being a thin wall tube having located at a first end said grip
portion suitably formed for the hand to grip, and said tube
gradually formed along the length toward a second end portion into
a crossectional shape having an upper wall and a lower wall located
at a substantial distance from a plane bisecting said tube
lengthwise and said plane being parallel to the plane of said
string netting; said second end portion of said tube being fastened
to said head portion.
38. A tennis racket as in claim 23 wherein the magnitude of W is
less than 10.0 ounces.
39. A tennis racket as in claim 23 wherein the distance C.sub.p is
greater than 19.5 inches.
40. A tennis racket as in claim 23, and having a displacement less
than 0.008 inches for D.sub.1 when tested as indicated in test 14
of FIG. 40 herein before defined.
41. A racket as in claim 23 and said racket having a weight and
stiffness distribution providing for a frequency of vibration
greater than 90 cycles per second when tested in accordance with
test 13 of FIG. 40 herein before defined.
42. A complete tennis racket comprising at least a frame having a
head portion supporting a string netting in a plane, and a grip
portion suitably adapted for the hand to grip; said racket having a
weight and stiffness distribution providing for the nodal pivot
closest to the grip portion end being located at a distance N
inches from the said end of the grip portion, when tested in
accordance with test 15 of FIG. 40 herein before defined; said
racket characterized in that the magnitude of the said distance N
is greater than 7.5 inches.
43. A tennis racket as in claim 42; and said racket having a center
of gravity located at a distance C.sub.g from the end of the grip
portion; and said racket having a length L from the end of the grip
portion to the end of the head portion; said racket further
characterized in that the magnitude of the said distance C.sub.g
divided by the magnitude of the said distance L given by the
formula C.sub.g /L is greater than 0.56.
44. A tennis racket as in claim 42 wherein the said distance N is
greater than 8.0 inches.
45. A complete tennis racket comprising at least a frame having a
head portion supporting a string netting in a plane, and a grip
portion suitably adapted for the hand to grip; said racket having a
weight and stiffness distribution providing for the nodal pivot
closest to the grip portion end being located at a distance N from
the said end of the grip portion, when tested in accordance with
test 15 of FIG. 40 herein before defined; said racket having a
length L from the end of the grip portion to the end of the head
portion; said racket characterized in that the magnitude of the
said distance N divided by the said distance L given by the formula
N/L is greater than 0.28.
46. A tennis racket as in claim 45; and said racket having a center
of gravity located at a distance C.sub.g from the end of the grip
portion; and said racket having a length L from the end at the grip
portion to the end of the head portion; said racket further
characterized in that the magnitude of the said distance C.sub.g
divided by the magnitude of the said distance L given by the
formula C.sub.g /L is greater than 0.56.
47. A tennis racket as in claim 45; and said racket having a center
of percussion located a distance C.sub.p in inches from the end of
the grip portion when tested in accordance with test 4 of FIG. 40
herein before defined; said center of percussion taken about a
pivot located at the end of the grip portion, said pivot having an
axis perpendicular to the longitudinal axis of said frame and
parallel to a plane containing the surface of the frame; said
racket having a center of gravity located at a distance C.sub.g in
inches from the end of the grip portion; said racket further
characterized in that the magnitude of the said distance C.sub.g
divided by the magnitude of the said distance C.sub.p given by the
formula C.sub.g /C.sub.p is greater than 0.80.
48. A tennis racket as in claim 45 wherein the said ratio N/L is
greater than 0.31.
49. A tennis racket as in claim 45; and said racket having a center
of percussion located at a distance C.sub.p in inches from the end
of the grip portion, when tested in accordance with test 4 of FIG.
40 herein before defined, said center of percussion taken about a
pivot located at the end of the grip portion, said pivot having an
axis perpendicular to the longitudinal axis of said frame and
parallel to the plane of said string netting; said racket
characterized in that the magnitude of C.sub.p divided by the
magnitude of the said distance L, given by the formula C.sub.p /L
is greater than 0.71.
50. A tennis racket as in claim 45; and said racket having a
unitary frame member formed of a resin reinforced fiber material;
and said racket having a center of percussion located at a distance
C.sub.p in inches from the end of the grip portion, when tested in
accordance with test 4 of FIG. 40 herein before defined, said
center of percussion taken about a pivot located at the end of the
grip portion, said pivot having an axis per perpendicular to the
longitudinal axis of said frame and parallel to the plane of said
string netting; said racket characterized in that the magnitude of
C.sub.p divided by the magnitude of the said distace L given by the
formula C.sub.p /L is greater than 0.71.
51. A complete tennis racket comprising at least a frame including
a head portion supporting a string netting, and a grip portion
suitably adapted for the hand to grip; said racket having a weight
and stiffness distribution providing a frequency of vibration f in
cycles per second when tested in accordance with test 13 of FIG. 40
herein before defined; and said racket having a length L in inches
from the end of the grip portion to the end of the head portion;
said racket characterized in that the magnitude of f is greater
than 150 cycles per second, and the magnitude of L is greater than
25.5 inches.
52. A tennis racket as in claim 51; and said racket having a center
of gravity located at a distance C.sub.g from the end of the grip
portion; said racket further characterized in that the magnitude of
the said distance C.sub.g divided by the magnitude of the said
distance L given by the formula C.sub.g /L is greater than
0.56.
53. A tennis racket as in claim 51; and said racket having a center
of percussion located at a distance C.sub.p in inches from the end
of the grip portion, when tested in accordance with test b 4 of
FIG. 40 herein before defined; said center of percussion taken
about a pivot located at the end of the grip portion, said pivot
having an axis perpendicular to the longitudinal axis of the racket
and parallel to a plane containing the surface of the frame; said
racket having a center of gravity located at a distance C.sub.g in
inches from the end of the grip portion; said racket further
characterized in that the magnitude of the said distance C.sub.g
divided by the magnitude of the said distance C.sub.p given by the
formula C.sub.g /C.sub.p is greater than 0.80.
54. A tennis racket as in claim 51 wherein the said frequency of
vibration is greater than 155 cycles per second.
55. A tennis racket as in claim 54; and said racket having a
unitary frame member formed of a resin reinforced fiber
material.
56. A tennis racket as in claim 51 wherein the said frame is made
of a material having a modulus of elasticity in tension E in pounds
per square inch and a density d in pounds per cubic inch, and the
ratio of E/d is less than 110.times.10.sup.6.
57. A tennis racket as in claim 51 comprising a frame member made
of an elongated strip of material shaped to form a head portion, a
throat portion and a pair of spaced substantially parallel sides
into a shaft portion; said head portion curved to inclose a space
suitable for supporting a string netting, said strip adapted to
support said string netting; a tubular grip member of thin wall
material shaped for the hand to grip fastened to the ends of the
spaced sides of the shaft portion of said frame member; throat
members being two sheets of thin wall material, each sheet having a
top edge portion, a bottom edge portion connected with side edge
portions; said sheets having the side edge portions fastened to the
strip of material at the throat portion of said frame member.
58. A tennis racket as in claim 57 wherein the strip of material
comprising said frame has a crossection having tubular edge
portions joined by a central web portion; material suitable for
moving freely within the tubular edge portions; means for
entrapping at will said material suitable for moving freely, in
sections of the tubular edge portions of said strip; and means for
releasing at will said material entrapped, thereby changing the
moment of inertia of said frame member about a first axis running
from the center of the head portion to the center of the grip
member end, and the moment of inertia about a second axis through
the end of the grip member perpendicular to the said first axis and
parallel to a plane containing the surface of said frame.
59. A tennis racket as in claim 51; and said racket having a center
of percussion located at a distance C.sub.p in inches from the end
of the grip portion, when tested in accordance with test 4 of FIG.
40 herein before defined, said center of percussion taken about a
pivot located at the end of the grip portion, said pivot having an
axis perpendicular to the longitudinal axis of said frame and
parallel to the plane of the said string netting; said racket
characterized in that the magnitude of C.sub.p divided by the
magnitude of the said length L, given by the formula C.sub.p /L is
greater than 0.71.
60. A tennis racket as in claim 51; and said racket having a weight
and stiffness distribution providing for the nodal pivot closest to
the grip portion end being located at a distance N from the said
end of the grip portion, when tested in accordance with test 15 of
FIG. 40 herein before defined; said racket characterized in that
the magnitude of the said distance N divided by the said length L
given by the formula N/L is greater than 0.28.
61. A tennis racket as in claim 51; and said racket having a
unitary frame member formed of a resin reinforced fiber material;
and said racket having a center of percussion located at a distance
C.sub.p in inches from the end of the grip portion, when tested in
accordance with test 4 of FIG. 40 herein before defined, said
center of percussion taken about a pivot located at the end of the
grip portion, said pivot having an axis perpendicular to the
longitudinal axis of said frame and parallel to the plane of said
string netting; said racket characterized in that the magnitude of
C.sub.p divided by the said length L, given by the formula C.sub.p
/L is greater than 0.71.
62. A complete tennis racket comprising at least a metal frame
having a head portion supporting a string netting, and a grip
portion suitably adapted for the hand to grip; said racket having a
weight and stiffness distribution providing a frequency of
vibration f in cycles per second when tested in accordance with
test 16 of FIG. 40 herein before defined; and said racket having a
length L in inches from the end of the grip portion to the end of
the head portion; said racket characterized in that the magnitude
of f is greater than 175 cycles per second, and the magnitude of L
is greater than 25.5 inches.
63. A complete tennis racket comprising at least a frame having a
head portion supporting a string netting, and a grip portion
suitably adapted for the hand to grip; said racket with said frame
supporting a string netting having a weight W in ounces, and a
center of gravity located at a distance C.sub.g in inches from the
end of the grip portion, said racket having a length L in inches
from the end of the grip portion to the end of the head portion;
said racket characterized in that the magnitude of the said
distance C.sub.g divided by the said length L given by the formula
C.sub.g /L is greater than 0.56; and said racket has a weight W
less than 10.7 ounces; and the ratio of W/L is less than 0.4.
64. A complete tennis racket comprising at least a frame having a
head portion supporting a string netting and a grip portion
suitably adapted for hand to grip; said racket having a weight
distribution providing a first moment of inertia I.sub.s in ounce
inches squared about a pivot located at the end of the grip
portion, said pivot having an axis perpendicular to the
longitudinal axis of said racket running from the center of the
head portion end to the center of the grip portion end, and
parallel to the plane of said string netting, and a second moment
of inertia I.sub.a in ounce inches squared about said longitudinal
axis; and said racket having a center of gravity located at a
distance C.sub.g from the end of the grip portion; and said racket
having a length L from the end of the grip portion to the end of
the head portion; said racket characterized in that the magnitude
of the said distance C.sub.g divided by the magnitude of the said
distance L given by the formula C.sub.g /L is greater than 0.56;
and the magnitude of the moment of inertia I.sub.a divided by the
magnitude of the said moment of inertia I.sub.s given by the
formula I.sub.a /I.sub.s is greater than .[.0.20..]. .Iadd.0.020.
.Iaddend.
65. A complete tennis racket comprising at least a frame having a
head portion supporting a string netting, and a grip portion
suitably adapted for the hand to grip; said racket having a weight
W in ounces, a center of percussion located a distance C.sub.p in
inches from the end of the grip portion, when tested in accordance
with test 4 of FIG. 40 herein before defined, said center of
percussion taken about a pivot located at the end of the grip
portion, said pivot having an axis perpendicular to the
longitudinal axis of said frame and parallel to a plane containing
the surface of the frame; said racket having a length L in inches
from the end of the grip portion to the end of the head portion;
said racket having a center of gravity located at a distance
C.sub.g in inches from the end of the grip portion; said racket
characterized in that the magnitude of the said distance C.sub.g
divided by the magnitude of the said distance C.sub.g given by the
formula C.sub.g /C.sub.p is greater than 0.80 and the magnitude of
the weight W is less than 10.7 ounces.
66. A racket as in claim 65 and said racket having a weight and
stiffness distribution providing a frequency of vibration f in
cycles per second when tested in accordance with test 13 of FIG. 40
herein before defined, and said racket having a length L in inches
from the end of the grip portion to the end of the head portion;
said racket further characterized in that the product of the said
length squared and the said frequency of vibration f given by the
expression L.sup.2 f is greater than 65,000.
67. A tennis racket having great rigidity and strength with a
minimum of weight comprising a head member and a handle member;
said head member being an elongated hollow tubular metal strip
having a center portion and two adjacent end portions shaped to
partially inclose a space, said head member adapted to support a
string netting in a plane; said handle member being a thin wall
aluminum alloy tube having a yield strength greater than 55,000
pounds per square inch, said wall having a thickness less than
0.025 inches and said tube having a grip portion, and a shaft
portion, said grip portion suitably formed for the hand to grip and
said shaft portion gradually formed along the length toward the
head member into a crossectional shape having an upper wall and a
lower wall and two side walls, said walls being substantially
planar and said side walls being substantially perpendicular to
said upper and lower walls; said end portions of the head member
having a crossectional shape to provide an upper surface and a
lower surface located at a distance from a plane bisecting the head
member lengthwise and said plane being parallel to the plane of
said string netting; and said upper and lower walls of said shaft
portion being located at substantially the same distance from said
plane, and said upper and lower walls of the shaft portion being
fastened to the said upper and lower surfaces of the end portions
of said head member; and wherein the portion of said handle member
having an axial length of 14 inches from the handle end of the
racket, has a weight less than 3.0 ounces, and the weight of the
racket extending beyond the said length of 14 inches is greater
than 6.0 ounces.
68. A tennis racket as in claim 67 wherein said side walls are
selectively perforated to provide apertures in portions there of to
reduce the weight with a minimum reduction in strength and
rigidity.
69. A tennis racket as in claim 67; and a string netting supported
by said head member; a planar strip of material having a first
surface lying in a plane, placed at a location on a surface of said
string netting, said strip having sufficient length and breadth to
extend over the spaces between multiple strings and said surface of
said strip having adhesive means to fasten to said strings, and
said location on said string netting positioned to reduce the
probability of impact of said strip with a ball during play; and
said strip comprised of material capable of damping the vibratory
motion of said strings subsequent to the impact of a ball upon said
strings; said strip having a second surface parallel to said first
surface and said second surface being substantially durable, non
abrasive, and non-adhesive.
70. A tennis racket as in claim 67; and a removable thin sleeve
tightly secured without pleats over said grip portion of said
handle member, said sleeve being made of thin cloth, said cloth
having all fibers woven and lying substantially in a surface, said
cloth having an upper side and a lower side, and said cloth having
at least one side free of adhesive material, and said cloth being
durable, washable, and light in weight; and said sleeve being
capable of allowing water to pass through said sleeve quickly.
71. A tennis racket comprising a head member and a handle member;
said head member being an elongated metal strip having a center
portion and two adjacent end portions shaped to partially inclose a
space, said head member adapted to support a string netting in a
plane; said handle member being a thin wall tube having located at
a first end a grip portion, said grip portion suitably formed for
the hand to grip and said tube generally formed along the length
toward the second end portion into a crossectional shape having an
upper wall and a lower wall located at a substantial distance from
a plane bisecting said handle member lengthwise and said plane
being parallel to the plane of said string netting, said second end
portion being fastened to the said end portions of the said head
member; said head member having the center portion substantially
straight and lying perpendicular to a first axis, said axis running
longitudinally from the center of the head end of the racket to the
center of the handle end, and the said two adjacent end portions
each substantially straight and forming corners with the center
portion, and having the said end portions directed to converge
toward a location in the second end portion of said handle member;
a second axis perpendicular to the said first axis, said second
axis being at a distance of 3.0 inches from the head end of the
racket, said second axis intersecting said head member at
locations, said locations being at the surface of said head member
laterally outermost from said first axis, and the distance between
said locations being greater than 9.0 inches; a third axis starting
at one of the said locations on said head member, and running
toward a point on the said first axis, said point being at a
distance of 19 inches from the head end of the racket; a first
plane being perpendicular to the said first axis and containing the
said second axis, and a second plane being perpendicular to the
said first axis and being located at a distance of 16.5 inches from
the head end of the racket, and the portion of the racket lying
between said first and second planes having a surface laterally
outermost from said third axis, said surface being laterally on the
same side of the first axis as the third axis, and said surface
being at a maximum distance from said third axis less than 0.75
inches.
72. A tennis racket as in claim 71 wherein said head member has a
greater weight per inch of length at the locations of said corners
than at other locations on said head member.
73. A tennis racket having great rigidity and light weight
comprising a head member, a throat member, and a handle member;
said head member being an elongated hollow tubular metal strip
having a center portion and two adjacent end portions shaped to
partially inclose a space, said head member adapted to support a
string netting in a plane; said handle member being a thin wall
aluminum alloy tube having a yield strength greater than 55,000
pounds per square inch and said wall having a thickness less than
0.025 inches and said tube having a grip portion and a shaft
portion, said grip portion suitably formed for the hand to grip and
said shaft portion gradually formed along the length toward the
head member into a crossectional shape having an upper wall and a
lower wall and two side walls, said upper and lower walls lying
parallel to the plane of said string netting and said sidewalls
lying perpendicular to said plane and said walls being
substantially planar; said end portions of said head member having
a crossectional shape having an upper surface and a lower surface
located at a distance from a plane bisecting said head member
lengthwise and said plane being parallel to the plane of said
string netting; and said upper and lower walls of said shaft
portion being located at substantially the same distance from said
plane bisecting said head member lengthwise; and said throat member
comprising a separate first planar sheet of thin wall metal having
a portion fastened to the exterior of said upper wall of the shaft
portion of said handle member and another portion of said first
sheet fastened to the said upper surface of said head member, and a
second separate planar sheet of thin wall metal having a portion
fastened to the exterior of the said lower wall of the shaft
portion of the handle member, and another portion of said second
sheet fastened to the lower surface of said head member; and
wherein the portion of said handle member having an axial length of
.Badd..[.14.]..Baddend. .Iadd.8 .Iaddend.inches from the handle end
of the racket has a weight less than 3.0 ounces, and the weight of
the racket extending beyond the said length of
.Badd..[.14.]..Baddend. .Iadd.8 .Iaddend. inches is greater than
6.0 ounces.
74. A tennis racket as in claim 73, and a string netting supported
by said head member, and wherein the said first and second sheets
of thin wall metal of the throat member having portions of said
sheets adjacent to said string netting suitably adapted to support
said string netting; and said string netting supported by said
throat member.
75. A tennis racket having rigidity and light weight comprising a
head member, a throat member, and a handle member; said head member
being an elongated hollow tubular metal strip having a center
portion and two adjacent end portions shaped to partially inclose a
space, said head member adapted to support a string netting in a
plane; said handle member being a thin wall aluminum alloy tube
having a yield strength greater than 55,000 pounds per square inch
and said wall having a thickness less than 0.025 inches and said
tube having a grip portion suitably formed for the hand to grip and
a shaft portion gradually formed along the length toward the head
member into a crossectional shape having a planar upper wall and a
planar lower wall and two planar side walls, said upper and lower
walls lying parallel to the plane of said string netting and said
side walls lying perpendicular to said upper and lower walls; said
end portions of said head member having a crossectional shape
having an upper surface and a lower surface located at a distance
from a plane bisecting said head member lengthwise and said plane
being parallel to the plane of said string netting; and said upper
and lower walls of said shaft portion being located at
substantially the same distance from said plane bisecting said head
member lengthwise; and said throat member comprising a sheet of
thin wall material formed into a substantially u-shaped crossection
having a first planar side opposing a second planar side and a
third substantially planar side therebetween, said third side being
straight in a direction perpendicular to a plane passing through
the longitudinal axis of said racket, said plane being
perpendicular to the plane of said string netting; said first and
second sides being fastened to the said upper and lower surfaces of
the said end portions of said head member and said first and second
sides lying exterior to and being fastened to the said upper wall
and lower wall of said shaft portion of said handle member, and the
third side of said throat member adapted to support said string
netting.
76. A tennis racket frame having strength and rigidity with a
minimum weight; said frame having a head portion, supporting a
string netting in a plane, a throat portion, and a handle portion;
a throat member comprising a sheet of thin wall material formed
into a substantially u-shaped crossection having a first planar
side opposing a second planar side and a third substantially planar
side between said first and second sides, and said first and second
sides each lying in single planes, and said third side being
straight in a direction perpendicular to a plane passing through
the longitudinal axis of said racket frame, said plane being
perpendicular to the plane of said string netting; said first and
second sides being fastened to the outer surfaces of the throat
portion of said frame.
77. A tennis racket as in claim 76 wherein the said first and
second sides are selectively perforated to provide multiple
apertures, in portions thereof to reduce the weight, the number of
said apertures occurring in an inch of length of said sides being
greater than 3.
78. A tennis racket having ridigity and strength with a minimum of
weight, said tennis racket comprising at least a head member
supporting a string netting in a plane, a throat member, and a
handle member; said handle member comprising a thin wall material
formed into a tube having a first end grip portion suitably formed
for the hand to grip, and said tube gradually formed along the
length toward the second end portion into a crossectional shape
having a substantially planar upper wall and a substantially planar
lower wall and two substantially planar side walls, said upper and
lower walls being located at a substantial distance from a plane
bisecting said handle lengthwise, and said plane being parallel to
the plane of said string netting, and said side walls being
substantially perpendicular to said upper and lower walls; and said
second end portion being fastened to the other members of said
racket; and wherein a portion of said racket having an axial length
of .Badd..[.14.]..Baddend. .Iadd.8 .Iaddend.inches from the handle
end has a weight less than 3.0 ounces, and the said grip portion of
the handle has a circumference greater than 4.25 inches and less
than 5.25 inches, and the weight of the portion of the racket
extending beyond the said distance of .Badd..[.14.]..Baddend.
.Iadd.8 .Iaddend.inches from the handle end is greater than 6.0
ounces.
79. A racket as in claim 78 wherein said side walls being
selectively perforated to provide apertures in portions thereof to
reduce the weight with a minimum reduction in strength and
rigidity.
80. A racket as in claim 78 wherein the material of said handle
member is an aluminum alloy having a yield strength greater than
55,000 pounds per square inch and having a wall thickness less than
0.025 inches.
81. A tennis racket comprising at least a head portion, a throat
portion, and a grip portion; said head portion being an elongated
strip of material shaped to partially inclose a space for a string
netting, said head portion adapted to support said string netting;
said head portion comprising a center portion and two adjacent side
portions, said center portion being substantially straight and
placed perpendicular to a first axis running longitudinally from
the center of the head portion to the center of the grip portion
end, and the two adjacent side portions being substantially
straight and forming corners with the center portion and said side
portions directed to converge toward the throat portion of said
racket; a second axis perpendicular to the said first axis, said
second axis being at a distance of 3.0 inches from the head end of
the racket, said second axis intersecting said head portion at
locations, said locations being at the surface of said head portion
laterally outermost from said first axis and the distance between
said locations being greater than 9.0 inches, a third axis starting
at one of the said locations on said head portion, and running
toward a point on the said first axis said point being at a
distance of 19 inches from the head end of the racket; a first
plane being perpendicular to said first axis and containing said
second axis, and a second plane being perpendicular to the said
first axis and being located at a distance of 16.5 inches from the
head end of the racket, and the portion of the racket lying between
said first and second planes having a surface laterally outermost
from said third axis, said surface being laterally on the same side
of the first axis as the third axis and said surface being at a
minimum distance from said third axis less than 0.75 inches; and
said material of said head portion having a modulus of elasticity
in tension greater than 2.5.times.10.sup.6 pounds per square inch
and said material having a yield strength in tension greater than
15.times.10.sup.3 pounds per square inch.
82. A tennis racket as in claim 81, wherein said head portion has a
greater weight per inch of length at the positions of said corners
than at other positions on said head portion. .Iadd. 83. A complete
racket comprising at least a frame having a head portion supporting
a string netting in a plane and a handle portion having a grip
portion suitably adapted for the hand to grip; said racket having a
weight and stiffness distribution providing a frequency of
vibration f in cycles per second when tested in accordance with
test 13 of FIG. 40 herein before defined; said racket having a
weight and stiffness distribution providing for the nodal pivot
closest to the grip portion end to be located at a distance N in
inches from the end of said grip portion when tested in accordance
with test 15 of FIG. 40 herein before defined; said racket
characterized in that the magnitude of said frequency f is greater
than 135 cycles per second; and the magnitude of said distance N is
greater than 6.75 inches. .Iaddend..Iadd. 84. A complete racket
comprising at least a frame having a head portion supporting a
string netting in a plane and a handle portion having a grip
portion suitably adapted for the hand to grip; said racket having a
stiffness and weight distribution providing for the nodal pivot
closest to the grip portion end to be located at a distance N in
inches from the end of said grip portion when tested in accordance
with test 15 of FIG. 40 herein before defined; said racket having a
center of percussion located at a distance Cp in inches from the
end of the grip portion when tested in accordance with test 4 in
FIG. 40 herein defined, said center of percussion being taken about
a pivot located at the end of the grip portion, said pivot having
an axis perpendicular to the longitudinal axis of said frame and
parallel to the plane of said string netting; said racket
characterized in that the magnitude of said distance N is greater
than 7.0 inches; and the magnitude of said distance Cp is greater
than 18.75 inches. .Iaddend..Iadd. 85. A complete racket comprising
at least a frame having a head portion supporting a string netting
in a plane and a handle portion having a grip portion suitably
adapted for the hand to grip; said racket having a stiffness and
weight distribution providing for the nodal pivot closest to the
grip portion end to be located at a distance N inches from the end
of the grip portion when tested in accordance with test 15 of FIG.
40 herein before defined; said racket having a weight W in ounces;
a center of percussion located at a distance Cp in inches from the
end of the grip portion, when tested in accordance with test 4 of
FIG. 40 herein before defined, said center of percussion taken
about a pivot located at the end of the grip portion, said pivot
having an axis perpendicular to the longitudinal axis of said frame
and parallel to the plane of said string netting; said racket
having a center of gravity located at a distance Cg in inches from
the end of the grip portion; said racket having a first moment of
inertia I.sub.s in ounce inches squared about said pivot and
I.sub.s is directly proportional to the product of Cp, Cg, W, given
by the formula I.sub.s =(C.sub.p)(Cg)(W); a second moment of
inertia I.sub.a in ounce inches squared about a longitudinal axis
running from the center of the head portion end to the center of
the grip portion end; said racket characterized in that the
magnitude of the moment of inertia I.sub.a divided by the magnitude
of the moment of inertia I.sub.s given by the formula I.sub.a
/I.sub.s is greater than 0.021 and the magnitude of the said
distance N is greater than 6.75 inches. .Iaddend..Iadd. 86. A
complete racket comprising at least a frame having a head portion
supporting a string netting in a plane and a handle portion having
a grip portion suitably adapted for the hand to grip; said racket
having a stiffness and weight distribution providing for the nodal
pivot closest to the grip portion end to be located at a distance N
in inches from the end of said grip portion, when tested in
accordance with test 15 of FIG. 40 herein before defined; said
racket having a displacement D.sub.1 in inches when tested in
accordance with test 14 of FIG. 40 herein before defined, said
racket having a length L in inches from end of the grip portion to
the end of the head portion; said racket characterized in that the
magnitude of said distance N is greater than 6.75 inches; the
magnitude of said displacement D.sub.1 is less than 0.008 inches;
and the magnitude of said length L is greater than 25.5 inches.
.Iaddend..Iadd. 87. A complete racket comprising at least of frame
having a head portion supporting a string netting in a plane, and a
grip portion suitably adapted for the hand to grip; said racket
having a weight and stiffness distribution providing for the nodal
pivot closest to the grip portion end being located at a distance N
in inches from the end of the grip portion, when tested in
accordance with test 15 of FIG. 40 herein before defined; said
racket having a center of gravity located at a distance Cg in
inches from the end of said grip portion; said racket characterized
in that the magnitude of said distance N is greater than 7.0
inches; and the magnitude of said distance Cg is greater than 14.5
inches. .Iaddend. .Iadd. 88. A complete racket comprising at least
a frame having a head portion supporting a string netting in a
plane and a handle portion having a grip portion suitably adapted
for the hand to grip; said racket having a stiffness and weight
distribution providing for the nodal pivot closest to the grip
portion end to be located at a distance N in inches from the end of
the grip portion when tested in accordance with test 15 of FIG. 40
herein before defined; said racket having a length L in inches from
the end of the grip portion to the end of the head portion; said
racket having a center of gravity located at a distance Cg in
inches from the end of the grip portion; said racket having a
center of percussion located at a distance Cp in inches from the
end of the grip portion when tested in accordance with test 4 of
FIG. 40 herein before defined, said center of percussion taken
about a pivot located at the end of the grip portion, said pivot
having an axis perpendicular to the longitudinal axis of said frame
and parallel to the plane of said string netting; said racket
characterized in that the magnitude of said distance N divided by
the magnitude of said distance L given by the formula N/L is
greater than 0.26; and the magnitude of said distance Cg divided by
the magnitude of said distance Cp given by the formula Cg/Cp is
greater than 0.76. .Iaddend..Iadd. 89. A complete racket comprising
of least a head portion, a throat portion, and a grip portion; said
head portion being an elongated strip of material shaped to
partially inclose a space for a string netting; a string netting
supported by said head portion; said head portion comprising a
center portion and two adjacent side portions, said center portion
placed perpendicular to a first axis running longitudinally from
the center of the head portion end to the center of the grip
portion end, and the two adjacent side portions forming curved
corners with the center portion, and said side portions directed to
converge toward the throat portion of said racket; a second axis
perpendicular to said first axis, said second axis being at a
distance of 1.5 inches from the head end of the racket, said second
axis intersecting said head portion at locations, said locations
being at the surface of said head portion laterally outermost from
said first axis and the distance between said locations being
greater than 6.75 inches; said racket having a weight and stiffness
distribution providing for the nodal pivot closest to the grip
portion end to be located at a distance N in inches from the end of
said grip portion when tested in accordance with test 15 in FIG. 40
herein before defined; said racket having a length L in inches from
the end of the grip portion to the end of the head portion; said
racket further characterized in that the magnitude of said distance
N divided by the magnitude of said distance L given by the formula
N/L, is greater than 0.25. .Iaddend. .Iadd. 90. A complete racket
comprising at least a head portion, a throat portion, and a grip
portion; said head portion being an elongated strip of material
shaped to partially inclose a space for a string netting, a string
netting supported by said head portion; said head portion
comprising a center portion and two adjacent side portions, said
center portion placed perpendicular to a first axis running
longitudinally from the center of the head portion end to the
center of the grip portion end, and the two adjacent side portions
forming curved corners with the center portion, and said side
portions directed to converge toward the throat portion of said
racket; a second axis perpendicular to the said first axis, said
second axis being at a distance of 1.5 inches from the head end of
the racket, said second axis intersecting said head portion at
locations, said locations being at the surface of said head portion
laterally outermost from said first axis and the distance between
said locations being greater than 7.5 inches; said racket having a
weight and stiffness distribution providing for a frequence of
vibration f in cycles per second when tested in accordance with
test 14 of FIG. 40 herein before defined; said racket further
characterized in that the said frequency f is greater than 135
cycles per second. .Iaddend..Iadd. 91. A complete racket comprising
at least a frame including a head portion supporting a string
netting, and a grip portion suitably adapted for the hand to grip;
said racket having a weight and stiffness distribution providing a
frequency of vibration f in cycles per second when tested in
accordance with test 13 of FIG. 40 herein before defined; said
racket having a length L in inches from the end of the grip portion
to the end of the head portion; said racket having a displacement
D.sub.1 in inches when tested in accordance with test 14 of FIG. 40
herein before defined; said racket characterized in that the
magnitude of said frequency f is greater than 140 cycles per
second; the magnitude of said displacement D.sub.1 is less than
0.008 inches; and the said length L is greater than 25.5 inches.
.Iaddend..Iadd. 92. A complete racket comprising at least a frame
having a head portion supporting a string netting in a plane and a
handle portion having a grip portion suitably adapted for the hand
to grip; said racket having a weight and stiffness distribution
providing for a frequency of vibration f in cycles per second when
tested in accordance with test 13 of FIG. 40 herein before defined;
said racket having a center of gravity located at a distance Cg in
inches from the end of the grip portion, said racket having a
center of percussion Cp in inches from the end of the grip portion
when tested in accordance with test 4 of FIG. 40 herein before
defined, said center of percussion taken about a pivot located at
the end of the grip portion, said pivot having an axis
perpendicular to the longitudinal axis of said frame and parallel
to the plane of said string netting; said racket characterized in
that the magnitude of said frequency f is greater than 140 cycles
per second; the ratio of said distance Cg to the said distance Cp
given by the formula Cg/Cp is greater than 0.75; and the said
distance L is greater than 25.5 inches. .Iaddend..Iadd. 93. A
complete racket comprising at least a frame having a head portion
supporting a string netting in a plane and a handle portion having
a grip portion suitably adapted for the hand to grip; said racket
having a weight and stiffness distribution providing a frequency of
vibration f in cycles per second when tested in accordance with
test 13 of FIG. 40 hereinbefore defined; said racket having a
center of percussion located at a distance Cp in inches from the
end of the grip portion when tested in accordance with test 4 of
FIG. 40 herein before defined, said center of percussion taken
about a pivot located at the end of the grip portion, said pivot
having an axis perpendicular to the longitudinal axis of said frame
and parallel to the plane of said string netting; said racket
characterized in that the magnitude of said frequency f is greater
than 140 cycles per second; and the magnitude of said distance Cp
is greater than 18.75 inches. .Iaddend. .Iadd. 94. A complete
racket comprising at least a frame having a head portion supporting
a string netting in a plane and a handle portion having a grip
portion suitably adapted for the hand to grip; said racket having a
weight and stiffness distribution providing a frequency of
vibration f in cycles per second when tested in accordance with
test 13 of FIG. 40 herein before defined; said racket having a
center of gravity located at a distance Cg in inches from the end
of the grip portion; said racket characterized in that the
magnitude of said frequency f is greater than 140 cycles per
second; and said distance Cg is greater than 14.5 inches.
.Iaddend..Iadd. 95. A complete racket comprising at least a frame
having a head portion supporting a string netting in a plane and a
handle portion having a grip portion suitably adapted for the hand
to grip; said racket having a stiffness and weight distribution
providing for a frequency of vibration f in cycles per second when
tested in accordance with test 13 of FIG. 40 herein before defined;
said racket having a weight W in ounces; a center of percussion
located at a distance Cp in inches from the end of the grip portion
when tested in accordance with test 4 of FIG. 40 herein before
defined, said center of percussion taken about a pivot located at
the end of the grip portion, said pivot having an axis
perpendicular to the longitudinal axis of said frame and parallel
to the plane of said string netting; said racket having a center of
gravity located at a distance Cg in inches from the end of the grip
portion; said racket having a first moment of inertia I.sub.s in
ounce inches squared about said pivot; and I.sub.s is directly
porportional to the product of Cp, Cg, W, given by the formula
I.sub.s =(Cp)(Cg)(W); a second moment of inertia I.sub.a in ounce
inches squared about a longitudinal axis running from the center of
the head portion end to the center of the grip portion end; said
racket having a length L in inches from the end of the grip portion
to the end of the head portion; said racket characterized in that
the magnitude of said frequency f is greater than 140 cycles per
second; the magnitude of the said moment of inertia I.sub.a divided
by the said moment of inertia I.sub.s given by the formula I.sub.a
/I.sub.s is greater than 0.021; and the magnitude of said length L
is greater than 25.5 inches. .Iaddend..Iadd. 96. A complete racket
comprising at least a head portion, a throat portion and a grip
portion; said head portion being an elongated strip of material
shaped to partially inclose a space for a string netting; a string
netting supported by said head portion; said head portion
comprising a center portion and two adjacent side portions, said
center portion positioned perpendicular to a first axis running
longitudinally from the center of the head portion end to the
center of the grip portion end, and the two adjacent side portions
forming curved corners with the center portion, and said side
portions directed to converge toward the throat portion of said
racket; a second axis perpendicular to the said first axis; said
second axis being at a distance of 1.5 inches from the head end of
the racket, said second axis intersecting said head portion at
locations, said locations being at the surface of said head portion
laterally outermost from said first axis, and the distance between
said locations being greater than 7.5 inches, said racket having a
weight W in ounces, said racket having a center of percussion Cp in
inches from the end of the grip portion when tested in accordance
with test 4 of FIG. 40 herein before defined, said center of
percussion taken about a pivot located at the end of the grip
portion, said pivot having an axis perpendicular to the
longitudinal axis of said frame and parallel to the plane of said
string netting; said racket having a center of gravity located at a
distance Cg in inches from the end of the grip portion; said racket
having a first moment of inertia I.sub.s in ounce inches squared
about said pivot, and I.sub.s is directly proportional to the
product of Cp, Cg, W, given by the formula I.sub.s =(Cp)(Cg)(W) a
second moment of inertia I.sub.a in ounce inches squared about a
longitudinal axis running from the center of the head portion end
to the center of the grip portion end; said racket characterized in
that the magnitude of the said moment of inertia I.sub.a divided by
the magnitude of said moment of inertia I.sub.s given by the
formula I.sub.a /I.sub.s is greater than 0.021. .Iaddend..Iadd. 97.
A racket as in claim 84, and said racket having a weight and
stiffness distribution providing for a frequency of vibration
greater than 135 cycles per second when tested in accordance with
test 13 of FIG. 40 herein before defined. .Iaddend..Iadd. 98. A
racket as in claim 88; and said racket having a weight and
stiffness distribution providing for a frequency of vibration
greater than 135 cycles per second when tested in accordance with
test 13 of FIG. 40 herein before defined. .Iaddend. .Iadd. 99. A
racket as in claim 89; and said racket having a weight and
stiffness distribution providing for a frequency of vibration
greater than 135 cycles per second when tested in accordance with
test 13 of FIG. 40 herein before defined. .Iaddend..Iadd. 100. A
racket as in claim 85; and said racket having a weight and
stiffness distribution providing a frequency of vibration greater
than 135 cycles per second when tested in accordance with test
13
of FIG. 40 herein before defined. .Iaddend..Iadd. 101. A racket as
in claim 83; and said racket having a center of gravity located at
a distance Cg from the end of the grip portion, said distance Cg
being greater than 14.5 inches. .Iaddend..Iadd. 102. A racket as in
claim 93; and said racket having a weight less 12 ounces.
.Iaddend..Iadd. 103. A racket as in claim 95; and said racket
having a center of percussion located at a distance Cp in inches
from the end of the said grip portion, when tested in accordance
with test 4 of FIG. 40 herein before defined, said center of
percussion taken about a pivot located at the end of the grip
portion, said pivot having an axis perpendicular to the
longitudinal axis of said frame and parallel to the plane of said
string netting; said racket further characterized in that the
magnitude of said distance Cp is greater than 18.75 inches.
.Iaddend. .Iadd. 104. A racket as in claim 90; and said racket
having a center of percussion located at a distance Cp in inches
from the end of the said grip portion, when tested in accordance
with test 4 of FIG. 40 herein before defined, said center of
percussion taken about a pivot located at the end of the grip
portion, said pivot having an axis perpendicular to the
longitudinal axis of said frame and parallel to the plane of said
string netting; said racket further characterized in that the
magnitude of said distance Cp is greater than 18.75 inches.
.Iaddend..Iadd. 105. A racket as in claim 95; and said racket
having a center of percussion located at a distance Cp in inches
from the end of said grip portion, when tested in accordance with
test 4 of FIG. 40 herein before defined, said center of percussion
taken about a pivot located at the end of the grip portion, said
pivot having an axis perpendicular to the longitudinal axis of said
frame and parallel to the plane of said string netting; said racket
having a center of gravity located at a distance Cg in inches from
the end of the grip portion; said racket further characterized in
that the magnitude of Cg divided by the magnitude of the said
distance Cp given by the formula Cg/Cp is greater than 0.75.
.Iaddend..Iadd. 106. A racket as in claim 96; and said racket
having a weight and stiffness distribution providing a frequency of
vibration greater than 135 cycles per second, when tested in
accordance with test 13 of FIG. 40 herein before defined. .Iaddend.
.Iadd. 107. A racket as in claim 89; and said racket having a
center of percussion located at a distance Cp in inches from the
end of said grip portion, when tested in accordance with test 4 of
FIG. 40 herein before defined, said center of percussion taken
about a pivot at the end of the grip portion, said pivot having an
axis perpendicular to the longitudinal axis of said frame and
parallel to the plane of said string netting; said racket further
characterized in that the magnitude of said distance Cp is greater
than 18.75 inches. .Iaddend..Iadd. 108. A racket as in claim 85;
and said racket having a center of percussion located at a distance
Cp in inches from the end of the grip portion, when tested in
accordance with test 4 of FIG. 40 herein before defined, said
center of percussion taken about a pivot at the end of the grip
portion, said pivot having an axis perpendicular to the
longitudinal axis of said frame and parallel to the plane of the
string netting; said racket further characterized in that the
magnitude of said distance Cp is greater than 18.75 inches.
.Iaddend..Iadd. 109. A racket as in claim 84 and said racket having
a weight less than 12 ounces. .Iaddend..Iadd. 110. A racket as in
claim 86 and said racket having a center of percussion located at a
distance Cp in inches from the end of the grip portion, when tested
in accordance with test 4 of FIG. 40 herein before defined, said
center of percussion taken about a pivot at the end of the grip
portion, said pivot having an axis perpendicular to the
longitudinal axis of said frame and parallel to the plane of the
string netting; said racket further characterized in the magnitude
of said distance Cp is greater than 18.75 inches. .Iaddend. .Iadd.
111. A racket as in claim 86; and said racket having a center of
percussion located at a distance Cp in inches from the end of the
grip portion, when tested in accordance with test 4 of FIG. 40
herein before defined, said center of percussion taken about a
pivot at the end of the grip portion, said pivot having an axis
perpendicular to the longitudinal axis of said frame and parallel
to the plane of the string netting; said racket having a center of
gravity located at a distance Cg in inches from the end of the grip
portion; said racket further characterized in that the magnitude of
said distance Cg divided by the said distance Cp given by the
formula Cg/Cp is greater than 0.75. .Iaddend..Iadd. 112. A racket
as in claim 89 and said racket having a displacement D.sub.1 when
tested in accordance with test 14 of FIG. 40 herein before defined,
said displacement D.sub.1 having a magnitude less than 0.008
inches. .Iaddend..Iadd. 113. A racket as in claim 85 and said
racket having a displacement D.sub.1 when tested in accordance with
test 14 of FIG. 40 herein before defined, said displacement D.sub.1
having a magnitude less than 0.008 inches. .Iaddend..Iadd. 114. A
racket as in claim 86 said racket having a center of gravity
located at a distance greater than 14.5 inches from the end of said
grip portion. .Iaddend..Iadd. 115. A racket as in claim 85 and said
racket having a center of gravity located at a distance greater
than 14.5 inches from the end of said grip portion. .Iaddend.
.Iadd. 116. A complete racket comprising at least a frame having a
head portion supporting a string netting and a handle portion
having a grip portion suitably adapted for the hand to grip; said
racket having a stiffness and weight distribution providing for a
nodal pivot closest to the grip portion end to be located at a
distance N inches from the end of the grip portion when tested in
accordance with test 15 of FIG. 40 herein before defined; said
racket having a length L in inches from the end of the grip portion
to the end of the head portion; said racket having a center of
gravity located at a distance Cg in inches from the end of the grip
portion; said racket characterized in that the magnitude of said
distance N divided by the magnitude of said distance L given by the
formula N/L, is greater than 0.26; and the magnitude of said
distance Cg divided by the magnitude of said distance L given by
the formula Cg/L is greater than 0.54. .Iaddend.
Description
BACKGROUND
Tennis rackets in the prior art weigh from 12 ounces for a light
racket to over 14 ounces for a heavy racket. The center of
percussion or sweet spot ranges from 17 inches to 18.50 inches,
from the end of the racket handle. This center does not coincide
with the center of the strings, but is closer to the handle end.
Thus, when a ball is struck at the center of the racket face, a
shock is felt at the handle grip. Because the prior art rackets are
more flexible than is desired, vibrations are set up in the frame
which robs energy from the rebound of the ball and causes
vibrations to be transmitted to the arm of the player, as well as
cause inaccuracy in the rebound of the ball. The weight of the
prior art rackets contributes heavily to the development of tennis
elbow, as well as the fatigue of the player's arm and body.
Further, rackets of the past have utilized wood, aluminum,
steel,fiberglass, boron and graphite composites.
The prior art, while utilizing these materials, have not utilized
the structural configurations to take advantage of the stiffness to
unit weight ratio, as well as the strength to unit weight ratio of
these materials to obtain a reduction in weight, increase the
center of percussion, reduce the deflection, reduce the vibration,
and yet maintain the same swing weight.
It is noted that in U.S. Pat. No. 1,539,019, by Nikonow, an attempt
was made to reduce the weight of the racket, increase the distance
of the center of percussion from the handle end, by increasing the
distance of center of gravity or balance point further from the
handle end. He states he attained a weight of 12 ounces, a center
of balance of between 15 to 17 inches. The overall length of the
racket was 26 inches and the striking power was equivalent to a
141/2 ounce racket. This racket was made of wood and the
crossectional areas shown were not the best to achieve the results
desired.
Another difficulty with the prior art is that when balls are hit
which are to the left or right of a line running from the tip of
the racket to the handle down the center, henceforth called the
longitudinal axis of the racket, the racket tends to turn in hand
of the player causing a poorly hit ball with little power or
accuracy.
Another difficulty with the prior art rackets is that they are
rated as light, medium and heavy, but very little is said about the
swing weight of a racket. This swing weight is the important
parameter in determining the striking power of a racket. For
example, in a set of golf clubs, the swing weight of all the clubs
are substantially the same, and sets may be obtained in combination
of categories A,B,C,D and 1,2,3,4, providing for 16 graduations of
swing weight for a user to choose from. This swing weight is the
moment of inertia about a point 2.25 inches above the end of the
club handle (see U.S. Pat. No. 3,473,370 by E. J. Marciniak.).
Further, the prior art does not provide for easily available means
for measuring the moment of inertia of a racket.
Further, the prior art does not provide for an analysis to
determine the proper moment of inertia to be used, considering the
weight of a tennis ball, the velocity of the on-coming ball with
respect to the player.
Another difficulty with the prior art rackets is that the force
necessary to deflect the strings a given amount perpendicular to
the face of the racket varies considerably from the center .[.of.].
.Iadd.to .Iaddend.the edges, in part because of the smaller length
of the strings at the edges from those used at the center. This
variation contributes further to inaccurate hits.
SUMMARY
It is an object of this invention to provide a tennis racket having
the same swing weight as rackets of the prior art, but having a
significant reduction in weight, and a significant increase in the
distance of the center of percussion and in the distance of the
center of gravity from the end of the handle.
It is an object of this invention to provide a tennis racket having
a significant reduction in the deflection and vibration of a racket
frame caused by the impact of the ball.
It is another object of this invention to provide a tennis racket
having a reduction in the tendency of the racket to turn in the
players hand when a ball hits the racket off of the longitudinal
axis.
It is an object of this invention to provide a method to rate
rackets by their swing weight, vibratory characteristics, and other
physically measurable parameters.
It is an object of this invention to provide an easy method for
measuring the swing weight and other physically measurable
parameters of a racket such as the frequency of vibration after
impact, nodal points associated with the vibration, and the center
of percussion.
It is an object of this invention to accomplish these improvements
by controlling the distribution of material and the crossectional
shape along the length width and depth of the racket, and by the
utilization of material having a high stiffness and strength per
unit of weight.
It is an object of this invention to determine the proper swing
weight of a racket considering the velocity of the of the oncoming
ball with respect to the racket, and provide a means to change the
swing weight of the racket.
It is an object of this invention to minimize the variation of the
force necessary to deflect the strings a given amount perpendicular
to the face of the racket over the face of the racket.
In the drawings,
FIG. 1 is a front view of the racket, showing points of application
of impulsive forces, axis of rotation, center of gravity and center
of percussion.
FIG. 2 is a side view of FIG. 1 and a ball traveling with a
velocity v toward the racket.
FIG. 3 is a view of a pendulum with two weights.
FIG. 4 is a front view of an embodiment of the invention.
FIG. 5 is a side view of FIG. 4.
FIG. 6 is a bottom view of FIG. 4.
FIG. 7 is a front view of a sweat absorbent sleeve handle
insert.
FIG. 8 is an expanded assembly of the component members of FIG.
4.
FIG. 9 is a side view of a portion of a component member 9 of FIG.
4 and FIG. 8.
FIG. 10 is a crossection view of the section 10--10 of component 9
of FIG. 4 and FIG. 8.
FIG. 11 is a crossection view of section 11--11 of member 8 of FIG.
8.
FIG. 12 is a crossection view of section 12--12 of member S5 of
FIG. 8.
FIG. 13 is another crossection view of section 13--13 of member S5
of FIG. 8.
FIG. 14 is a side view of the handle member of FIG. 8.
FIG. 15 is a front view of an alternate component member 9 of FIG.
4 and FIG. 8.
FIG. 16 is a front view of another alternate component member 9 of
FIG. 4 and FIG. 8.
FIG. 17 is a front view of another embodiment of the invention.
FIG. 18 is a side view of FIG. 17.
FIG. 19 is a crossection view of section 19--19 of head portion of
FIG. 17.
FIG. 20 is a crossection view of section 20--20 of the throat
portion of the racket shown in FIG. 17.
FIG. 21 is a crossection view of section 21--21 of the handle
portion of the racket shown in FIG. 17.
FIG. 22 is a front view of a racket which is another embodiment of
the invention.
FIG. 23, FIG. 24, FIG. 25 and FIG. 26 are crossectional views of
the sections 23--23, 24--24, 25--25 and 26--26 shown in FIG.
22.
FIG. 27 is a front view of a racket which is another embodiment of
the invention.
FIG. 28 is a crossectional view of the section 28--28 shown in FIG.
27.
FIG. 29 is a side view of the embodiment shown in FIG. 27.
FIG. 30 is a crossectional view of the section 30--30 of the handle
shown in FIG. 29.
FIG. 31 is a front view of a racket which is another embodiment of
the invention.
FIG. 32 is a side view of the racket shown in FIG. 31.
FIGS. 33, 34, 35, and 36 are crossectional views of the sections
33--33, 33a--33a, 34--34, 35--35, shown in FIGS. 31 and section
36--36 shown in FIG. 32.
FIG. 37 is a front view of a racket which is another embodiment of
the invention, which allows the moment of inertia to be changed by
the player.
FIG. 38 is a crossectional view of the section 38--38 shown in FIG.
37.
FIG. 39 is a crossectional view of the section 39--39 shown in FIG.
37.
FIG. 40 is a chart of results of tests made on prior art rackets
fabricated in accordance with the objectives of this invention.
DESCRIPTION OF INVENTION
If one imagines a racket to be suspended in space without any
encumberances and it is struck by a ball, the racket, after the
impact, will move and ball will also rebound. In FIGS. 1 and 2, if
the ball strikes the racket at .[.C.]. .Iadd.C.sub.p .Iaddend. such
that point a does not move in space, the rest of the racket will
rotate about the axis o--o. The point .[.C.]. .Iadd.C.sub.p
.Iaddend. is known as the center of percussion. The axis o--o at
the end of the handle is against the heel of the hand, which is at
the pivot point of the wrist joint. It can be seen that if the
racket is struck at point other than C.sub.p such as C.sub.1, above
C.sub.p, the axis o--o would move and if it is to be restrained a
reaction force R is required. Likewise, if the point C.sub.3 is
below C.sub.p the reactive force R would be reversed. This reactive
force R increases proportionately in magnitude when the point of
impact departs from the point C.sub.p. Thus, if the impulsive force
is P between the racket and the ball, and the point of contact is
C.sub.p, there is no reactive force R at the handle. If the point
of contact is not at C.sub.p, but departs from C.sub.p by 10%, then
the reactive force R at the handle is 10% of P.
It is very desirable to have the point C.sub.p placed out toward
the center of the racket face.
Again returning to the racket suspended in space, when the racket
is struck by the ball, the racket strings will deform and the ball
will deform. The deformation of these bodies result in energy being
stored in each and then being dissipated by vibration, heat and
some of the energy being given back to the ball in its rebound
motion. The energy stored in the strings is mostly given back to
the rebound motion of the ball. The energy which remains in the
vibration of the strings is a small portion of the energy stored
since the weight of the strings is small compared to that of the
ball.
About 55% of the energy stored in the ball is given back as rebound
motion between the ball and the racket.
The energy stored in the racket frame due to its bending and
torsion under the impact is mostly dissipated in the racket by
vibrations. Furthermore, in order for the racket frame to give back
some energy to the rebound motion of the ball, it must be moving in
the direction of the ball's motion when it departs from the racket
strings and this would occur infrequently. This action would be
similar to a diver using a springboard which requires split second
timing. Further, after the diver has left the board, the board
vibrates violently, dissipating the energy. This is the job the
strings should do, not the frame.
Thus, it can be concluded that deformation of the racket frame
reduces the velocity of the ball's rebound and results in vibration
of the racket frame after the ball has departed the strings. It is
a feature of this invention to reduce this frame deformations in
bending and torsion.
The velocity of the ball's rebound after striking the racket
depends on the moment of inertia of the racket about the pivot
axis, the weight of the ball, the velocity of the ball, and the
velocity of the racket. It we again return to the racket as shown
in FIGS. 1 and 2, and a ball b traveling with a velocity, v, with
respect to the ground strikes the racket at the center of
percussion, C.sub.p, the racket will rebound from the impact by
rotating about the pivot axis o--o and the velocity of the point
C.sub.p will be v'. Theoretically, if the collision resulted in no
loss of energy or momentum, and the moment of inertia of the racket
about the axis o--o was 1012 ounce-inches.sup.2, the ball would
come to a complete stop with respect to the ground, and the
velocity, v' of C.sub.p, would be equal to v, the original velocity
of the ball.
The value of 1012 ounce-inches.sup.2 for the moment of inertia is
obtained by multiplying the weight of the ball, 2 ounces, by the
distance C.sub.p in inches squared, (22.5).sup.2. Thus, all the
energy in the ball would have been given to the rotation of the
racket. These conditions are based on the racket being stationary
with respect to the ground prior to the impact of the ball. This
action is similar to the result when a stationary pool ball is
struck by the cue ball, in the game of pool. The pool ball which is
struck is given the velocity of the cue ball, and the cue ball
becomes stationary after the impact, regardless of how fast the cue
ball was going originally.
However, if the .[.output.]. .Iadd.point .Iaddend.C.sub.p of the
racket had been moving with a velocity v, with respect to the
ground, having the same magnitude as the velocity of the ball with
respect to ground, then the amount of inertia would have to be 3
times, 1012 ounces in..sup.2, or 3036 oz. in..sup.2 for the racket
to come to a complete stop and the ball would rebound with a
velocity, 2v. Since the racket came to a complete stop, all the
energy in the motion of the racket would be transferred to the
ball, and hence under the conditions stipulated, could provide for
the most efficient transfer of energy. It is noted that most of the
rackets used possess moments of inertia about the handle end which
are between 3000 and 4000 oz. in..sup.2. It is noted that when a
player tosses a ball up for a serve, the ball has very little
velocity in direction parallel to ground, thus the point C.sub.p of
a racket possessing a moment of inertia of 1012 oz. in..sup.2,
under the theoretical conditions, would momentarily come to a
complete stop when it struck the ball and provide for the most
efficient transfer of energy from the racket to the ball.
This analysis provides some insight about the transfer of the
racket energy to the ball. The energy in the racket must come from
the player's body. The optimum moment of inertia of a racket for a
player to get the energy from his body to the racket depends on the
player and his stroke. Considerable energy is available and this
transfer of energy is not as critical as the transfer of the energy
from the racket to the ball.
Thus, it can be concluded that a racket with much smaller amount of
inertia about the handle end is required for the serve than for a
ground stroke. It is noted that in baseball a batter hitting
practice fly balls to the outfield by tossing the ball up similar
to a serve, then hitting the ball, uses a very light swing weight
bat, called a fungo bat. However, when facing a pitcher he uses a
much heavier bat.
Thus, the moment of inertia of a racket about the handle end is a
criteria for determining the striking power of a racket. The amount
of inertia is sometimes called the swing weight of a racket.
It is an object of this invention to provide a racket which can
have its swing weight changed by the shifting of weights for the
serve and ground strokes.
If a weight, W, is added to the end of the handle, there is no
change in the swing weight of the racket. If this weight is shifted
to the center of percussion, the swing weight is increased by W
C.sub.p.sup.2, and the center of percussion is not changed. Thus,
if the shift in weight is from the handle end to C.sub.p and vice
versa it does not affect the distance, C.sub.p. If the weight is
shifted to other than C.sub.p, the center of percussion will be
modified. This shift in weight can be accomplished by holding the
head of the racket up and restraining round lead pellets in the
handle end when serving and releasing them when hitting a ground
stroke. The pellets can be retained in a tube within the racket
handle and frame.
It has been observed that if the pellets are restrained in the
handle end by a valve until the last part of the swing in a serve
or a ground stroke and then released, considerable more impact is
given to the ball. The pellets are placed back in the handle end by
raising the racket head up and allowing the pellets to drop back
into the handle end and opening the valve and then closing the
valve. Mercury and a plastic tube may be used in place of the lead
pellets.
Another object of this invention relates to a tennis racket which
possesses the same striking power of swing weight as rackets of the
prior art, but has a significant reduction in the weight, a
significant increase in the center of percussion, a significant
decrease in vibration and a significant decrease in flexibility,
thereby resulting in a more efficient and accurate racket. This
racket will minimize the development and aggravation of tennis
elbow. This racket is fabricated of material which has a high
stiffness per unit weight. Materials that can be used in descending
order of stiffness are beryllium, graphite composite, boron
composite, steel, aluminum, wood and fiberglass. At the present
time aluminum is the most cost effective. The crossections of the
racket at various points along its length is designed to provide
sufficient stiffness with the minimum amount of material.
A formula which can be used to determine the amount of inertia or
swing weight follows
where
C.sub.p =center of percussion in inches, the distance from the
pivot point.
C.sub.g =center of balance or gravity, in inches the distance from
the pivot point.
W=the weight of the racket in ounces.
The center of percussion is that point on the racket which, when
struck by a force of short time duration, will cause no lateral
shock or movement at the pivot point.
It can be shown that for a rigid body the distance the center of
percussion is from the pivot point is identical to the distance of
pendulum weight to the pivot point, when this distance is adjusted
so as to take the same amount of time to complete one swing as the
racket does when it is allowed to swing as a pendulum, with a small
excursion. Thus, to find the center of percussion of a racket we
support it at a pivot at the handle end, and measure the time for
one complete swing. This is most accurately done with a stop watch
and measuring the time for ten swings. The length of the pendulum
and hence the center of percussion is given by
where T is in seconds.
The pivot point selected was the end of the handle because the butt
of the racket is usually resting against the heel of the hand which
is very close to the wrist pivot joint. All measurements were taken
on different rackets at the handle end for reference purposes. If
the pivot point is selected at some other point such as four inches
from the end, the center of percussion moves toward the center of
the racket face somewhat, but is still below the center of the
racket face. As long as comparisons between rackets are done from
the same pivot point, the results of the analysis are the same.
We can analyze the affect of the removal or the addition of weight
along the length of a racket by the following example.
If we take a very thin light rod R.sub.1 as shown in FIG. 3 and
place a weight W.sub.3 at its end and allow it to swing as a
pendulum about the pivot Po, we can observe the affect of placing
an additional weight W.sub.4 equal to W.sub.3 at various points
along its length.
If W.sub.4 is placed at the end of the rod R.sub.1, the same point
as W.sub.3, the period of the swing will not change from what it
was. If we place W.sub.4 right over the pivot point Po so that the
weight W.sub.4 doesn't swing, the period again will remain the
same. However, if we place the weight W.sub.4 near the center of
the rod the period will be shortened, indicating that the effective
length of the pendulum has been decreased. Thus, the addition of
weight to the throat portion of a racket is very detrimental in
that it moves the center of percussion toward the handle more
significantly than the addition of weight at the handle end. It is
noted that when the weight W.sub.4 was moved right over the pivot
point the center of gravity was reduced in half. Thus, it is not
enough to say that an increase in the distance of the center of
gravity from the handle end will increase the center of percussion
significantly.
The formula
can be written
If we keep the swing weight the same, i.e. constant, we see that we
must make the denominator C.sub.g W smaller to make C.sub.p
larger.
The denominator is made smaller by making W smaller and keeping the
magnitude of the increase in C.sub.g smaller than the magnitude of
the decrease in W, thus the product of C.sub.g W will be made
smaller. Refer to FIG. 1. If a particle of material of weight,
W.sub.1 in the handle at a distance of l.sub.1 from the handle end
is removed, the moment of inertia is reduced by W.sub.1
l.sub.1.sup.2. If a particle of material of weight W.sub.2 is added
at a distance l.sub.2, the moment of inertia is increased by
W.sub.2 l.sub.2.sup.2. If we select W.sub.2 =W.sub.1 l.sub.1.sup.2
/l.sub.2.sup.2, then W.sub.1 l.sub.1.sup.2 =W.sub.2 l.sub.2.sup.2,
and there would be no overall net increase in the moment of inertia
by the subtraction of W.sub.1 and the addition of W.sub.2. We note
that W.sub.2 is smaller than W.sub.1 since W.sub.2 =W.sub.1
l.sub.1.sup.2 /l.sub.2.sup.2 and l.sub.1 < l.sub.2 Thus the
total weight will be decreased. To attain the smallest weight,
l.sub.2 should be made as large as possible, which means that we
should be adding the weight to the head end of the racket at
approximately 27 inches, which is the length of most rackets.
To determine how much we affected the center of percussion by this
subtraction of W.sub.1 and addition of W.sub.2 we examine the
product of W C.sub.g and see how it changed. ##EQU1## Since l.sub.1
/l.sub.2 <l, WC.sub.g-- .[.C.sub.g W.sub.1 .]. .Iadd.C.sub.g 'W'
.Iaddend.is always positive, hence WC.sub.g .[.<.].
.Iadd.>.Iaddend.C.sub.g 'W' and the C.sub.p is increased.
As noted before, if we wish to have the lightest racket for a given
moment of inertia, l.sub.2 is chosen to be as large as possible and
is fixed at the racket head end.
We can now see the affect of removing W.sub.1 at different lengths,
l.sub.1.
The formula for the center of percussion is
When the expression in the denominator is a minimum we have the
greatest increase in C.sub.p '. We examine this expression
We differentiate
d(C.sub.g 'W')/dl.sub.1 =--W.sub.1 (1--2l.sub.1 /l.sub.2)
and equate to zero.
solve for l.sub.1.
l.sub.1 =.[.2l.sub.2 .]. .Iadd.l/2l.sub.2 .Iaddend. for the minimum
value of C.sub.g 'W'.
Thus, it is most effective to remove material from the middle of
the racket and add it to the end to effect the greatest change in
the center of percussion.
If material is removed from the end of the handle, l.sub.1 is very
small and hence W'C.sub.g ' is not changed much nor is C.sub.p
changed much.
The procedure followed in designing the racket is to make the
weight of the racket as small as possible, by using only sufficient
material at each point of maintain adequate strength and adequate
stiffness at that point.
Next we add weight to the racket head to increase the center of
percussion and to attain the desired swing weight or moment of
inertia. Shown in FIG. 1 and FIG. 4 is a racket showing various
portions such as A, B, C, D, E. Material is removed from the grip
portion A to reduce the overall weight. Sufficient material must be
provided to withstand the grip pressure of the hand. Also, a large
bending moment occurs at the junction of portions A and B at the
instant of impact of the ball. Very little torsion stress is
experienced by the material here because the hand cannot exert
strong torsion in the short space of time of the ball impact.
Reduction in the material from portion A will increase the center
of percussion only slightly while the center of gravity will be
increased greatly.
Material removed from the handle portion B and the addition of less
material at the end of the racket will decrease the total weight of
the racket, and will be effective in increasing the center of
percussion. It will increase the center of gravity slightly. The
stresses here are purely bending; that is, the material in the
upper face is stressed in tension and lower face in compression.
There is very little torsion. Material removed from the throat
portion C will be most effective in increasing the center of
percussion, and it will not effect the center of gravity very much.
Considerable bending stress occurs in this portion and a large
bending stress occurs at the center of gravity at the impact of the
ball. In addition, torsion stresses occur in the throat arm
portions. The throat arm portions must be reinforced to attain
sufficient rigidity to prevent excessive vibration. This
reinforcement must utilize the minimum amount of material. The
upper part of the throat must also withstand the static tension of
the strings and provide an anchor which is rigid.
Material removed from the head portion D and the addition of less
material to the head end portion E is also effective in increasing
the center of percussion, decreasing the center of gravity, and the
overall weight slightly. The stresses in these members consist of a
small bending moment when the ball impacts the racket and also the
static tension imposed by the racket strings. These members must be
sufficiently rigid to prevent movement when the ball impacts the
racket and vibration thereafter.
Material in portion E should not be removed except to reduce the
swing weight to the required value. There is no bending stress
except the member must withstand the stress of the string tension.
Sufficient material must be provided in the portion E near the axis
a--a to withstand the bending stress of the string tension and also
the additional tension at the impact of the ball. The material
which is removed from the other portions and added to portion E
should be added at the outer corners of the racket, at locations N
and Q in FIG. 4.
The addition of material to the corner locations not only increases
the center percussion of the racket, and determines moment of
inertia to the value desired, it also increases the moment of
inertia of the racket about the longitudinal axis, a--a.
The inertia about this axis is important since it determines how
far off the longitudinal axis a ball can be hit before rotation of
the racket in the hand of the player results in a weakly hit
inaccurate return of the ball.
Refer to FIG. 1 and FIG. 2. If the ball strikes the racket face at
the point C.sub.2 at a distance X from the longitudinal axis a--a,
a torque exists for a short interval of time.
This impulsive moment results in an angular momentum about a--a and
is found by P.sub.2 X=I.sub.a w.sub.a.
Where
w.sub.a =the angular velocity about the axis a--a
I.sub.a =the moment of inertia about the axis a--a
P.sub.2 =the impulsive force caused by the impact of the ball.
The angular momentum about the axis o--o is given by
where
w.sub.o =the angular velocity about the axis o--o
I.sub.s =moment of inertia about the axis o--o
The ratio of the angular momentums is,
For a given ratio of w.sub.a /w.sub.o =K, which corresponds to a
given degree of a poorly hit ball.
Thus the higher the ratio I.sub.a /I.sub.s, the greater one can hit
the ball off the center longitudinal axis, at a given distance
Y.
This analysis is based on the observation that the hand cannot
prevent the racket from turning at the instant that the ball is hit
off the center longitudinal axis. Slow motion pictures taken at 64
frames a second and 1/500 second exposure show the racket to turn
at times as much as 60 degrees and then return in 1/64 of a
second.
Thus, the moment of inertia about the axis a--a is the primary
factor in determining how far off the longitudinal axis a miss hit
ball can be tolerated.
A weight which is added to the racket at a maximum distance from
the axis a--a is most effective in increasing this moment of
inertia.
The moment of inertia about the axis a--a can be determined by
suspending the racket from the handle end by a carrier and a length
of wire. The other end of the wire is fixed in a heavy body which
is held in the observer's hand. The racket is caused to oscillate
in torsion and the time of one oscillation is measured. The carrier
itself is allowed to oscillate and its period is measured.
Then I.sub.2 =I.sub.1 (T.sub.2.sup.2
--T.sub.o.sup.2)/(T.sub.1.sup.2 --T.sub.o.sup.2)
where
I.sub.2 =unknown moment of inertia
I.sub.1 =known moment of inertia
T.sub.2 =period of racket
T.sub.1 =period of bar with known moment of inertia
T.sub.o =period of torsional carrier
This method of measurement is described in the U.S. Pat. No.
3,473,370 by Emil Marcinak, and is used on a golf club.
With regard to the stiffness of the racket, it is noted, that if
the racket is designed to obtain the most desired rigidity, it will
be strong enough to withstand the stresses required to prevent
bending or breaking.
Refer to FIG. 1 and FIG. 2 when a ball strikes the racket with a
force P.sub.1 at point C.sub.1, the force F.sub.1 at the center of
gravity is in the opposite direction. This gives rise to a large
bending moment occurring at the center of gravity. If the center of
gravity has been moved up to the throat portion C from portion B, a
much stronger and rigid crossection exists than the crossection at
the top of the handle in the portion B. Hence the racket will be
stiffer.
When a racket is struck it vibrates in discrete modes at discrete
frequencies.
The mode of vibration and the frequency is determined by the
stiffness, weight, the weight distribution of the racket, and the
manner in which the racket is held.
The more flexible a racket is, the lower the frequency of vibration
will be and also the greater the amplitude of the vibration will
be.
The amplitude of a particular mode of vibration also depends upon
where the racket is struck.
Some modes of vibrations have points which do not move with respect
to the ground during the vibration. These points are known as nodal
points. When a racket is held at a nodal point and the racket is
caused to vibrate in the mode associated with this nodal point, the
vibration is not affected very much by the means by which the
racket is held, and the vibration lasts longer. The frequency of
this free vibration is determined by the stiffness, the weight and
the weight distribution alone.
It has been observed that the vibration in metal rackets persist
for a longer period of time after they are initiated, than the
vibrations in wood or composite rackets, or rackets which employ
vibration damping material. The wood and and plastic material
dampens the vibrations. However, the vibrations are present and can
be observed for a short interval of time.
There are many ways to hold a racket when testing for vibration.
Two significant ways of holding the racket when testing for
vibration are:
Holding the racket only at a nodal point near the handle end and
holding the racket in a heavy vise six inches from the handle, as a
cantilever.
The frequency of vibration when the racket is held in a player's
hand is close to the frequency observed when it is held at the
nodal point near the handle end.
One of the modes of vibration of a racket occurs when the center of
gravity moves with respect to the racket head end, and the handle
end, and both ends are free to vibrate.
This mode of vibration can easily be observed by holding the racket
handle between the forefinger and thumb at a point so that the
pivot axis is parallel to the racket face and then striking the
head end perpendicular to the face and noting the strength of the
vibration. The point at which the racket handle is held is moved up
or down, and the process repeated until the vibration is observed
to last the longest length of time. On prior art rackets this nodal
point is about six inches from the handle end. There are other
nodal points at which the racket may be held, and these other
points occur on each side of the racket frame head approximately
opposite the center of the racket face. If the racket is held by
forefinger and thumb at either of these two points and the handle
end is struck, strong vibrations occur, and there is little
interference with the free vibrations of the racket. Also, if the
racket is held by the strings in the center of its face, strong
vibrations will be observed when the racket handle is struck.
These nodal points vary from racket to racket depending on the
design.
The strings vibrate also when the center of the racket face is
struck by a ball. The strings move perpendicular to the face of the
racket frame. The center of the racket face strings is known as a
pole or anti-node, since when it is struck it moves the most and
vibrates the most. Also, if designed properly, the face frame
becomes a nodal line for the vibration of the strings, so that very
little of the string vibration is transmitted to the frame head
when the racket face strings are struck in the center.
The racket can be caused to vibrate in a direction parallel to the
face of the racket by holding the handle so that the pivot axis is
perpendicular to the face of the racket, and the racket head is
struck parallel to the racket face.
As mentioned when the racket is held at the nodal point near the
handle end, and the head end is struck strong vibrations are
observed. However, if the racket is held at the nodal point near
the handle end and the racket is struck at the nodal point in the
center of the racket face or on the nodal points in the head frame
opposite the center, the amplitude of the vibration associated with
these nodes will not be present in the vibration. Likewise, if the
racket is held at one of the nodal points in the head end and the
racket is struck at the node at the handle end, the vibration
associated with these nodes will not be present.
Hence, if a ball strikes the racket in the center of its face
opposite to the nodes in the frame, vibration of the center gravity
with respect to the head end and handle end will not be initiated.
Further vibration of the strings will not be transmitted to the
head face frame, since the head face frame is a nodal line for the
string vibration.
It is very desirable to design the racket to have nodes located in
the frame head at points opposite the center of the racket face,
and have the head frame a nodal line for the vibration of the
strings.
As mentioned, another method for holding the racket when testing it
is to hold the handle end in a heavy vise six inches from the end.
The racket is caused to vibrate by striking it at particular points
to observe a particular mode of vibration.
Vibrations perpendicular to the face can be caused by striking the
head end in a direction perpendicular to the face and vibrations
parallel to the face can be caused by striking the racket in a
direction parallel to the face. The torsional vibration can be
caused by striking one side of the head frame opposite the center
of the face and holding the head end of the racket with the tip of
the forefinger to dampen out other modes of vibration.
Other modes of vibration occur in prior art rackets. The frame can
vibrate in a direction perpendicular to the face of the racket, in
a direction parallel to the face of the racket, and the head end of
the frame can vibrate in torsion with respect to the racket handle.
There are other modes which are peculiar to a particular design. In
addition, each frequency of vibration can have related overtone
frequencies of vibrations and modes.
These modes of vibration can be observed by placing a
piezo-electric crystal pickup, which generates a voltage when
stressed, at various points on the racket frame, and feeding the
voltage generated by the vibration at that particular point to the
vertical plates of a cathode ray oscilloscope. A calibrated
variable audio voltage oscillator is fed to the horizontal plates
of the oscilloscope. When the frequency of the crystal voltage and
the audio voltage oscillator are the same, a visual elliptical
pattern is observed on the oscilloscope cathode ray tube.
To observe the voltages caused by the vibration of the center of
gravity with respect to the handle end and the head end, the
crystal is placed near the handle end and the racket is struck at
the head end. The racket is held between the forefinger and the
thumb at the node near the handle end.
To observe the voltages caused by the vibration of the strings the
crystal pickup is placed at one of the nodes in the frame head, and
the center of the strings is struck. The racket handle is held in
one hand. Vibration of the center of gravity will be minimized and
the voltages caused by the string vibration will be emphasized.
To observe the voltages by the vibrations perpendicular to the
face, the frame is struck in a direction perpendicular to the
face.
To observe the voltages caused by the vibrations parallel to the
face of the racket the frame is struck in a direction parallel to
the face.
To observe the voltages caused by the torsional vibrations of the
racket head, the handle end is held in a heavy vise. The racket is
struck at the other node in the head frame opposite the face
center, in a direction perpendicular to the racket face. The center
of the head end is held with the tip of the forefinger to dampen
out vibrations other than the torsion vibration.
To observe the voltages caused by other modes of vibration of the
head frame, the crystal pickup is placed at one of the nodes in the
head frame opposite the center of the racket face, and the racket
is struck at the other node in the head frame. The racket is held
by the handle in the other hand.
The frequency of vibration of a racket supported near the handle
end and the head end as a beam can be approximated by the formula
f=.sqroot.K.sub.1 /D.sub.g
where
D.sub.8 =the deflection of the center of gravity under its own
weight, and
K.sub.1 =a factor which is dependent on the racket weight and also
the weight distribution along its length.
Thus, the smaller the deflection, the higher the frequency of
vibration will be.
However, in comparing rackets of different designs, the factor
K.sub.1 is somewhat different for each racket; hence, the frequency
will not be exactly inversely proportional to the square root of
the deflection from racket to racket.
The deflection of the racket as a beam under its own static weight,
when it is supported at the node near the handle end and the nodes
at the head end is very small, and it is difficult to measure. When
a ball strikes the racket, the weight of the racket is effectively
increased by the acceleration of the racket and, hence, the
deflection of the center of gravity is momentarily increased, which
then results in the vibration of the racket.
The deflection of the racket as a beam under its own weight can be
related to the deflection of the racket as a beam, when additional
static weight is placed over the center of gravity, and the racket
is supported at the node near the handle end and the nodes near the
head end, by appropriate beam deflection formula.
Measurement of this deflection at the center of gravity when a
weight is placed over the center of gravity is related to the
performance of the racket at the instant of impact, and the
subsequent vibrations of the racket which occur.
When the racket is held in a player's hand and it strikes a ball,
the racket is also stressed as a cantilever. The head end of the
racket deflects with respect to the handle end held by the player,
and the racket end vibrates subsequently as a cantilever.
The deflection of the racket head end when the handle end is held
in a heavy vise six inches from the handle end, and a weight is
placed at the center of the racket face is related to the
performance of the racket at the instant of the ball impact and
subsequent vibration of the racket.
The frequency of vibration of the racket head end with respect to
the handle end can be approximated by the formula ##EQU2## where
f.sub.3 =the frequency of vibration, in cycles per second
g=the acceleration of gravity in inches per squared second
D.sub.3 =the deflection of the racket head end in inches
l.sub.4 =the distance of the racket head end from the cantilever
base, in inches
w.sub.3 =the weight added to the racket face center in ounces
l.sub.3 =the distance of the racket face center to the cantilever
base, in inches
I.sub.c =the moment of inertia of the racket about the cantilever
base, in ounce-inches squared
The amplitude of vibration and deflection as measured when the
racket is held in a vise as a cantilever is much greater than that
which is experienced when a racket is held by a player's hand,
since the player's hand is not capable of gripping the racket as
rigidly as a vise, and it does not have the weight the vise has.
The hand acts more as a pivot point and a weight at the pivot
point.
As mentioned previously, the vibrations measured when the racket is
caused to vibrate freely and holding the racket at the node near
the handle end is closely related to the frequency measured when
the racket is held in a player's hand, and the racket is
.[.strung.]. .Iadd.struck .Iaddend.at the .[.hand.]. .Iadd.head
.Iaddend.end by a ball.
As previously mentioned, the nodal point of a racket does not move
with respect to the ground when a racket vibrates in a mode that is
associated with that node. To determine the location of the nodes,
the racket is held between the forefinger and thumb, and the racket
is struck at the head end. The point at which the racket is held is
shifted up and down until the vibrations caused by the impact of a
small rubber hammer at the head end persist the longest. The
position at which the racket is held is the node in the handle end.
By placing the piezo crystal pickup near the handle end and feeding
the voltage to the oscilloscope, the amplitude of the vibration can
be measured by the amplitude of the visual pattern on the cathode
ray tube. By striking the racket head with the rubber hammer in the
vicinity of the nodes in the center of the racket face until the
minimum amplitude is observed, a more precise location of the node
in head can be determined. The nodes in the sides of the head frame
can also be determined this way. Further, if the racket is held at
one of the nodes in the head, and the racket handle is tapped with
the rubber hammer in the vicinity of the node in the handle, a more
precise location of this node can be determined, when the minimum
amplitude of vibration is observed on the oscilloscope.
When the weight is added directly at a nodal point, there is no
shift in the nodal position, since that point doesn't move during
the vibration anyway, and no energy is imparted to the additional
weight.
It has been observed that when the center of percussion is moved
toward the head end of the racket, and the racket is made to be
stiff and have little vibration, the node near the handle end moves
away from the handle end toward the head of the racket.
This nodal point in prior art rackets occurs approximately six
inches from the handle end.
Rackets made in accordance with the objectives of this invention
have nodal points much farther away from the handle end.
In order to illlustrate the marked differences between rackets made
in accordance with the objectives of this invention and prior art
rackets, a series of tests and measurements as described in this
invention were made and the results are tabulated in FIG. 40. All
distances are in inches measured from the handle end.
The various tests have been described previously; however, some
tests are further described and discussed.
The code used in FIG. 40 to designate the racket under test is as
follows:
Y, represents a Yonex aluminum racket of prior art.
H, represents a Headmaster aluminum racket of prior art.
D, represents a Dunlop steel racket of prior art.
TA, represents a TAD wood racket of prior art.
TE, represents a Tensor aluminum racket of prior art.
W, represents a Wilson steel racket of prior art.
1, represent a racket similar to the embodiment of FIG. 31 without
the openings 36.
2, represents a racket similar to the embodiment in FIG. 17, but
provided with an attached tubular aluminum handle with a fiberglass
grip.
3, represents a racket similar to the embodiment in FIG. 27.
4, represents a racket similar to the embodiment in FIG. 4 without
the openings 4 and without the weights 13a and 14a of the
embodiment in FIG. 15.
5, represents a racket similar to the embodiment in FIG. 4 but was
repaired due to breakage in fabrication.
6, represents a racket similar to the embodiment in FIG. 17, but
repaired due to the breakage in fabrication.
7, represents a racket similar to the embodiment in FIG. 4, without
the openings 4.
Rackets designated above 1 through 7 were hand made. With the use
of proper tools and facilities for heat treatment, forming,
punching, and molding of composite materials, substantial
improvement in the performance of these models can be obtained. The
columns in FIG. 40 indicate:
Col. 1, the racket under test.
Col. 2, Test 2, for the length of the racket .[.p1.].
Col. 3, Test 3, for the face center.
Col. 4, Test 4, for the center of percussion. The racket is
supported at a piviot at the handle end. The racket is caused to
swing as a pendulum having a small amplitude for more than 10
consecutive swings. The time T in seconds, is measured for the
pendulum to complete 10 swings. The center of percussion C.sub.p in
inches, is given by the formula C.sub.p =9.79 T.sup.2.
Col. 5, Test 5, for the difference of Col. 3 and Col. 4 divided by
Col. 4.
Col. 6, Test 6, for the cener of gravity.
Col. 7, Test 7, for the weight in ounces.
Col. 8, Test 8, for the ratio of Col. 6 to Col. 4.
Col. 9, Test 9, for the product of Col. 6 and Col. 7.
Col. 10, Test 10, for the moment of inertia about the the axis
o--o, in ounce-in.sup.2, shown in FIG. 1.
Col. 11, Test 11, for the moment of inertia about the axis a--a, in
ounce-in.sup.2.
Col. 12, Test 12, for the ratio of Col. 11 to Col. 10.
Col. 13, Test 13, for the frequency, f.sub.1, in cycles per second,
of vibration perpendicular to the racket face with the ends free,
and the racket is held at the nodal pivot at the handle end. This
mode of vibration has a node near the handle end and a node in each
side of the head portion of the frame near the head end of the
racket.
Col. 14, Test 14, for the deflection perpendicular to the racket
face, D.sub.1, in inches of the middle of the racket between the
ends when a weight of 80 ounces is applied to the middle of the
racket, and the racket is supported six inches from the handle end,
and the head frame sides are supported at points opposite the
center of the face.
Col. 15, Test 15, for the distance of the node closest to the
handle end, from the handle end, associated with the frequency
f.sub.1. The racket is held between the forefinger and thumb in the
vicinity of the node located in one side of the head portion of the
frame. The racket is tapped repeatedly with a rubber tipped hammer
along the longitudinal axis of the racket in a direction
perpendicular to the face of the racket, in the vicinity of the
node located near the handle end. The location at which the minimum
amplitude of vibration occurs when tapped, having the frequency
f.sub.1 is the precise location of the node.
Col. 16, Test 16, for the frequency, f.sub.2, in cycles per second,
of the vibration parallel to the racket face when the ends are free
and the racket is held at node near the handle end. This mode of
vibration has a node near the handle end and a node in each side of
the head portion of the frame near the head end of the racket.
Col. 17, Test 17, for the deflection parallel to the racket face,
D.sub.2, in thousandths of an inch at the middle of the racket
frame between the ends when a weight of 80 ounces is applied at the
middle of the racket frame, and the racket is supported as a beam
six inches from the handle end, and also at head frame side at a
point opposite the center of the face.
Col. 18, Test 18, for the frequency, f.sub.3, in cycles per second,
of the vibration perpendicular to the racket face, when the racket
handle is held in a heavy vise as a cantilever six inches from the
handle end. This mode of vibration has no nodes. The base of the
cantilever is not considered a node.
Col. 19, Test 19, for the deflection D.sub.3 in thousandths of an
inch of the head end of the racket perpendicular to the face, when
the racket is held as a cantilever by a downward force on the
handle end, and an upward force applied six inches from the handle
end when a weight of 15.62 ounces is applied at the center of the
racket face.
Col. 20, Test 20, for the frequency, f.sub.4, in cycles per second,
of the vibration of the racket parallel to the racket face when the
racket is held in a heavy vise six inches from the handle end. This
mode of vibration has no nodes. The base of the cantilever is not
considered a node.
Col. 21, Test 21, for the deflection, D.sub.4, in inches of the
head end of the racket parallel to the face of the racket, when a
weight of 15.62 ounces is applied to the center of the racket face,
and the handle is supported as in test 19.
Col. 22, Test 22, for the frequency, f.sub.5, in cycles per second,
of the racket in torsion, when the racket is held in a heavy vise
as a cantilever six inches from the handle end. The torsional mode
of vibration is initiated by striking the racket on one side of the
head frame opposite the center of the face. The frame is held at
the center of the head end with the tip of the forefinger to dampen
out vibrations other than the torsional vibration. This mode of
vibration has no nodes. The base of the racket held by the vise is
not considered a node.
Test Number 5 indicates the distance between the center of
percussion and the center of the face divided by the distance of
the center of percussion. The center of the face has the softest
deflection to the impact of the ball compared to other impact
points on the face of the strings. This results in the most
efficient rebound of the ball from the strings, since the strings
are doing more work at this point, and they are more efficient than
the deformation of the ball. The impact of the ball at the center
of percussion of the racket frame results in the most efficient
rebound from the frame, since no energy is lost in movement of the
reaction force at the handle end. The closer these points are, the
more efficient the overall rebound of the ball is.
Test Number 8 indicates the ratio of the center of gravity to the
center of percussion. The more ideal the racket design, the closer
this ratio approaches the value 1. This is explained as
follows:
For a given moment of inertia, the ideal racket would have all its
weight concentrated at the point which contacts the ball. The
handle and frame would weight nothing and be perfectly rigid. The
strings would weigh nothing.
The formula previously given I.sub.s =C.sub.p C.sub.g W, would
pertain.
If the ratio of
then
For a given moment of inertia, and a given distance for the center
of percussion, the minimum weight W would occur when K.sub.2 is as
large as possible.
In the case where the weight is concentrated at one point
and
This is the largest value K.sub.2 can have. The ratio of C.sub.g
/C.sub.p is a measure of how ideal the weight distribution of the
racket is.
As an indication of how K.sub.2 varies with the weight
distribution, the value for K.sub.2 for a uniform crossection bar
is
whereas for the weight concentrated at a point
Test Number 9 indicates the product of the weight W in ounces,
times the distance of the center of gravity, in inches. If a player
holds the racket in his hand with the handle parallel to the
ground, this product indicates the static bending moment the player
feels at his wrist. The smaller this moment is the less strain on
the player's wrist and arm. Further for a given moment of inertia
about the axis, o--o, the smaller this product is the larger the
distance the center of percussion will be from the handle end.
An embodiment of the invention is shown in FIG. 4. The handle 1 of
the racket is formed of type 7075 T6 aluminum, 0.020 inches thick
sheet with two edges fastened together with pop rivets. The handle
end grip portion A is formed to be six sided polygon, with the
upper and lower faces of S.sub.1 and S.sub.2 in FIG. 5 to be
larger. The surface of the portion A is perforated with holes 2 to
provide for air circulation, cushioning for shocks to reduce the
weight, and to provide for drainage holes for sweat from the
player's hands. The surface may be covered with a thin epoxy
coating to present a warm feeling for the hand, or with a light
porous nylon sleeve, or a perforated leather or rubber sleeve.
Further, a sweat absorbing sleeve 3 in FIG. 6 may be inserted
inside the handle contacting the inside surface, and the sweat
drainage holes.
The handle extends into portion B which must withstand bending when
the racket is swung and also when the ball is struck.
Portion B has the sides perforated with openings 4 as shown in FIG.
5, to remove material and reduce the weight. The edges of the
openings 4 are bent inward to provide for more rigidity to keep the
upper and lower surfaces S.sub.3 and S.sub.4 in FIG. 5 in place
when the racket is stressed. In FIG. 4 and FIG. 5, throat portion C
has the plates S.sub.5 and S.sub.6 riveted to the handle by the use
of steel "pop" rivets, 7. In addition, the surfaces of the plates
and handle which are in contact are cleaned thoroughly and then
coated with an epoxy glue. These plates are fabricated of type
7075-T6 aluminum, 0.020 thick. They may be perforated with holes,
2, again to reduce the weight. The reduction in weight in this area
is very important in causing the center of percussion to be moved
further out from the handle end. Sufficient material must be
provided to obtain the required rigidity. It is known that when a
.[.number.]. .Iadd.member .Iaddend.is stressed in bending, the
outer most material from the neutral axis does most of the work and
receives the most stress. By using two plates situated as the outer
most surfaces provides for the greatest stiffness per unit of
weight. The plate S.sub.5 is also shown in FIG. 8. FIG. 12 and FIG.
13 are views of the crosssection 12--12 and 13--13 shown in FIG. 8
of the member S.sub.5.
FIG. 8 is an expanded assembly of FIG. 4. Shown in FIG. 8 is a
curved member 8 which is also shown in FIG. 4 and FIG. 5. The
crossection 11--11 of this member in FIG. 8 is shown in FIG. 11.
This curved member 8 provides a rigid anchor for the strings to
feed through. Steel "pop" rivets 7 are used to attach this member
to the head frame 9 and the members S.sub.5, S.sub.6 and the handle
1 shown in FIG. 4. In FIG. 4, locations G and H shown in portion C
are stressed in torsion as well as bending.
Further, this torsional stress in location G and H is increased on
the inside edge of the frame 9 and member 8 facing the racket face
center by the shear stress caused by the impact of the ball. The
addition of member 8 gives the required additional strength and
rigidity for these stresses.
In FIG. 4, the locations J and M of the frame 9 shown in the
portion D must withstand the tension of the strings, and has less
and less bending stress as the stress proceeds toward the end of
the racket. In FIG. 5, the sides of the frame 9 are perforated with
holes 10 for the strings to pass through the additional openings 11
are provided to reduce the weight as shown. The crossection 10--10
of FIG. 8, of the extruded aluminum frame 9 is shown in FIG. 10.
Since the main stress is compression and tension in the upper and
lower surfaces, as much of the material as possible should be
placed there. To increase the resistance to warping the upper and
lower areas are made in hollow tubes which give the crossection
more strength in torsion. The crossection used in this embodiment
is shown in FIG. 10. Many other crossections may be used. The
weight of the extruded tubing prior to reducing te weight by
putting openings in the central web area was 0.16 oz/inch.
In FIG. 4, in the head end portion E material from the frame 9 is
not removed from the corner locations N and Q. Since the material
in these corners provide for the least amount of weight to achieve
the required moment of inertia about the longitudinal axis a--a,
and also the required moment of inertia about the axis o--o through
the end of the handle parallel to the face of the racket and
perpendicular to the handle length. Material may be removed from
the central location T since it does not contribute to the moment
of inertia about the longitudinal axis a--a. However, sufficient
material must be used to withstand the bending caused by the static
string tension, and also the increased string tension when the ball
is struck by the racket.
FIG. 14 shows a side view of the handle 1.
In FIG. 4 is shown a strip 12 of sticky mastic material with a
vinyl plastic outer coating on one side placed upon the strings. It
has been found that when a ball is struck the strings vibrate and
give rise to a loud audio sound, such as a "bong". Placing the
mastic tape at various locations dampens this sound. The more the
strip is lengthened, and with the use of additional strips at the
head end, sides and center, the sound can be caused to be quite
dead. The ball bounces from the racket with a dull sound. The use
of the strip is at the desire of the player. It is easily applied
and removed by the player, by placing two strips face to face from
opposite sides of the racket strings. A strip 12 at the location
shown approximately 5 inches long and 1/4 inch wide resulted in a
very pleasing sound. The use of the strip prevents excessive
vibration and wear of the strings as well.
Shown in FIG. 15 is an embodiment wherein the frame 9 in FIG. 4 has
been modified and is shown as 9a. Weight is removed from the
locations N and Q and by additional openings 11, as shown in FIG.
5. Additional weights 13a and 14a are placed opposite the center of
the racket face at the locations J and M. The additional weights
that are placed at locations J and M increase the moment of inertia
of the racket about a longitudinal axis a--a shown in FIG. 4. This
additional weight also increases the overall weight of the racket
from the minimum weight which is required to attain the required
moment of inertia about the axis o--o.
For example, a racket having a minimum weight for a given moment of
inertia about the axis o--o, and also a large moment of inertia
about the longitudinal axis a--a would have as much weight located
in the corners N and .[.M.]. .Iadd.Q .Iaddend.as permissible.
Having chosen a moment of inertia about the axis o--o, the moment
of inertia of the racket about the longitudinal axis a--a may be
increased by removing material from the corner locations N and
.[.M.]. .Iadd.Q .Iaddend.of the frame which are 27 inches from the
handle end and adding weights 13a and 14a to the frame sides at the
locations J and M, which are 21.5 inches from the handle end,
opposite the center of the racket face. In order to keep the moment
of inertia about the axis o--o the same, the weight of the material
added at the locations J and M must be (27/21.5).sup.2 times
greater than the weight of the material removed, from the locations
N and Q. Thus, the total weight of the racket would be increased.
The moment of inertia about the longitudinal axis a--a would be
increased by this increased weight, 13a and 14a. This will allow
the ball to be struck further off the longitudinal axis.
FIG. 16 shows another shape for the racket frame as 9b. The shape
of the frame 9b removes more weight from the locations N and Q than
does the frame 9a, and allows the weights 13b and 14b to be
greater.
Shown in FIGS. 17 and 18 is a racket fabricated by the assembly of
two metal formings of aluminum 15 and 16. In FIG. 19, the
crossection 19--19 of FIG. 17 is shown. The racket is made of
7075-T6 aluminum, 0.020 inches thick. The formings are assembled by
the application of epoxy glue to the mating surfaces. Holes
utilizing pop rivets 7 are used as feed through holes for the
strings and also to assist in fastening the two halves 15 and 16
together. The shape of the racket, weight, weight distribution and
stiffness conform to the objectives given for the previous
embodiments. In FIG. 17, material is formed at the locations U, V,
and W, to improve the stiffness. It is known that crossections
which have thin walled material have greter strength and rigidity
per unit weight, than solid or thicker crossection. The material
may have the wall thickness reduced to gain this advantage, until a
point is reached wherein the material is too easily dented.
Further, as the wall becomes thinner, the ability of the
crossection to maintain its shape under stress is diminished. Thus,
the material which is being stressed is not held in place, and the
rigidity which might be expected from a calculation of the
applicable formula is not realized. The crossection acts under
stress as though a material with a reduced modulus of elasticity
was being employed. In order to keep the material in place
additional material and formed ribs and braces are used in
locations such as U, V, and W, shown in FIG. 17.
FIG. 20 is a view of section 20--20 of FIG. 17.
FIG. 21 is a view of section 21--21 of FIG. 17.
In FIG. 18, openings 18 and 19 are provided to reduce the weight of
the handle and the grip.
Another embodiment is shown in FIG. 22. A racket is fabricated of a
composite material such as epoxy with fiberglass, epoxy with
graphite fibers, or epoxy with boron fibers. The racket frame 20
molded over a core made of Woods metal which has previously molded
to shape. The core is removed by heating to a relatively low
temperature at which the Woods metal melts. The racket frame 20 is
molded so as to provide ribs and thicker crossections as required
by the stresses. Such crossections are shown in FIGS. 23, 24 and 25
for the crossections 23--23, 24--24 and 25--25 shown in FIG. 22.
These ribs and thicker surfaces provided for additional stiffening
with a minimum of weight. FIG. 26 shows the crossection 26--26 of
FIG. 22. The weight distribution and the use of reinforcement
material, the frame 20, is in accordance with the objectives given
for the previous embodiments.
The use of epoxy with graphite fibers or epoxy with boron fibers as
the fabrication material for the frame 20 should provide for
approximately a twenty percent reduction in weight for the same
stiffness and swing weight over a racket fabricated of aluminum.
The use of epoxy with fiberglass material should weigh more than
aluminum. The use of these composite materials provide that
vibrations are damped out quickly.
Shown in FIG. 27 is another embodiment of the invention. The
crossection 28--28 of FIG. 27 is shown in FIG. 28. The frame 21 is
fastened to the plates 22a and 22b by the use of steel pop rivets
7. The mating surfaces are cleaned and glued with epoxy. These
plates 22a and 22b are made of 7075-T6 aluminum, 0.020 inches thick
and holes 28 are provided to reduce the weight with a minimum
reduction in rigidity. Yoke 23 is also fastened to the frame 21 and
the plates 22a and 22b by pop rivets 7 and epoxy glue. Holes 24a
are provided for the racket strings. The frame 21 in FIG. 29 shows
openings 24 to feed the racket strings through and openings 25 and
26 to reduce the weight. The section of the handle 30--30 of FIG.
29 is shown in FIG. 30. The handle 27 is mode of 7075-T6 aluminum,
0.020 inches thick and is perforated with holes 28. The handle 27
is fastened to the spread frame 21 by the use of steel pop rivets 7
and the use of epoxy glue on the mating surfaces. The weight
distribution and the rigidity is in accordance with the objectives
given for the previous embodiments.
Shown in FIG. 31 is another embodiment of the invention. The frame
members 29, 30a, 30b, 31a, 31b, 32a, 32b, 33a, 33b and 34 are made
of 7075 T-6 aluminum, 0.020 thick. Crossections 33a--33a and
33b--33b of FIG. 31 are the same and are shown in FIG. 33. The
metal is formed as shown and fastened together by the use of the
pop rivet 7. A plastic tube 38 is used in the holes as a guide for
the racket strings and prevents the metal edges from cutting the
strings. Shown in FIG. 34 is the crossection 34--34 shown in FIG.
31. FIG. 35 shows the crossection 35--35 shown in FIG. 32. FIG. 36
shows the crossection of the handle grip 36--36 in FIG. 31. In FIG.
32 openings 35 are provided for the plastic tube 38, openings 36
are provided in the handle to reduce the weight yet maintain
bending and torsional rigidity. Openings 37 are provided in the
handle end to reduce the weight. The weight, weight distribution,
and rigidity is in accordance with the objectives given for the
previous embodiments.
Shown in FIG. 37 is an embodiment which allows the moment of
inertia of the racket to be changed. In FIG. 37, 38 is the extruded
frame. Cross member 39 in FIG. 37 is fastened to member 38 by
rivets. Member 49 is a handle suitably fastened to member 38.
FIG. 38 is a view of the section 38--38 of FIG. 37. Shown in FIG.
38 the member 38 has tubular openings 40a and 40b and a central
portion 41.
FIG. 39 is a view of the section 39--39 of a portion of member 38
as shown in FIG. 37.
Shown in FIG. 39 are lead pellets 42 located in the tubular
openings 40a and 40b. These lead pellets may move in these tubular
openings but are stopped by the pins 50 shown in FIG. 37. These
lead pellets can be restrained in their movement by the spring 44
shown in FIG. 39. When the spring 44 is in the normal position
shown, the lead pellets cannot move in the direction shown past the
spring end. However, they can move in the opposite direction past
the spring end, since the movement of the weight forces the spring
to swing out of the way. To allow the pellets to move in the
direction opposite to that indicated, the flexible nylon string 45
is pulled through the hole 46 so as to pull the ends of the spring
44 out of the way of the pellets. The spring 44 is shaped as shown
in FIG. 39, and is fastened to the central portion 41 of frame
member 38 by a rivet 47. The members 38, 45, 44 and the hole 46
constitutes a valve which allows the player to lock a group of lead
pellets between the stops 50 and the ends of the spring 44. Valves
are positioned at locations K, L, H and J shown in FIG. 37. Thus,
the player can hold the racket vertical and allow the pellets to be
locked between the locations H and J and the stops 50. As the
player executes the swing, the string 45 may be pulled releasing
the lead pellets under centrifugal force to lodge between locations
K and L and the stops 50 and be locked there until released. The
player may also shift the pellets without swinging the racket by
raising or lowering the racket head vertically and operating the
valves. The weight, weight distribution, and rigidity of the rest
of the embodiment conforms to the objectives of this invention
shown in the previous embodiments.
It is understood that minor changes may be made in the devices of
the invention without departing from the spirit of the invention
and the scope of the appended claims.
* * * * *