U.S. patent application number 13/690876 was filed with the patent office on 2014-06-05 for angled golf putter head having teeth.
The applicant listed for this patent is Richard A. Brandt. Invention is credited to Richard A. Brandt.
Application Number | 20140155191 13/690876 |
Document ID | / |
Family ID | 50825985 |
Filed Date | 2014-06-05 |
United States Patent
Application |
20140155191 |
Kind Code |
A1 |
Brandt; Richard A. |
June 5, 2014 |
ANGLED GOLF PUTTER HEAD HAVING TEETH
Abstract
An angled putting golf club head has a forward-angled face
comprising a plurality of teeth constructed so as to impart to the
ball a horizontal force with little or no vertical force at the
point of impact, and to contact the ball above its center of
gravity so that the ball has negligible sliding motion when first
struck.
Inventors: |
Brandt; Richard A.; (New
York, NY) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
Brandt; Richard A. |
New York |
NY |
US |
|
|
Family ID: |
50825985 |
Appl. No.: |
13/690876 |
Filed: |
November 30, 2012 |
Current U.S.
Class: |
473/330 |
Current CPC
Class: |
A63B 53/0445 20200801;
A63B 53/0462 20200801; A63B 53/0487 20130101 |
Class at
Publication: |
473/330 |
International
Class: |
A63B 53/04 20060101
A63B053/04 |
Claims
1-16. (canceled)
17. A golf club head comprising: a top-forward angled face; and, a
plurality of generally forward-facing teeth, wherein each of the
teeth has a tooth tip for striking a ball, wherein each of the
teeth comprises an upper tooth surface and a lower tooth surface
intersecting the top-forward angled face and meeting at the tooth
tip such that the tooth tip is in a top forward plane, wherein the
upper tooth surface and the lower tooth surface of each tooth form
an angle B at the tooth tip, and wherein
90.degree..ltoreq.B.ltoreq.104.12.degree.. and wherein each of the
teeth has a height of about 0.2 to about 0.3 inches measured from a
line defining a base of a tooth to the top of the tooth.
18. The golf club head of claim 17, wherein at least one of the
teeth is positioned on the top-forward angled face so as to contact
the ball above a center of mass of the ball.
19. The golf club head of claim 17, wherein the face is angled
forward at an angle A of approximately the sin.sup.-1(0.4) from
vertical.
20. The golf club head of claim 17, wherein the angle B comprises
an angle B1 between the upper tooth surface and a horizontal plane
and an angle B2 between the horizontal plane and the lower tooth
surface, wherein B1+B2=B, wherein
90.degree..ltoreq.B1.ltoreq.0.degree., and wherein
0.degree..ltoreq.B2.ltoreq.90.degree..
21. The golf club head of claim 20, wherein
24.degree..ltoreq.B2.ltoreq.40.degree.,
70.degree..ltoreq.B1.ltoreq.62.degree., and wherein
94.degree..ltoreq.B.ltoreq.102.degree..
22. The golf club head of claim 21, wherein the face is angled
forward at an angle A of approximately the sin.sup.-1(0.4) from
vertical.
23. The golf club head of claim 17, wherein at least one tooth of
the plurality of teeth comprises a triangular shape, wherein the
one tooth comprises a vertical height d between an upper horizontal
plane through the intersection of the upper tooth surface and the
face and a lower horizontal plane through the intersection of the
lower tooth surface, and wherein d is approximately 0.125''.
24. The golf club head of claim 23, wherein the face is angled
forward at an angle A of approximately the sin.sup.-1(0.4) from
vertical.
25. The golf club head of claim 17, wherein a bottom surface of the
head has a length h of approximately 0.3294'', and a top surface of
the head has a length g of approximately 0.875''.
26. A golf club head that imparts a pure forward rotation to a golf
ball at impact between the golf club head and the golf ball, the
golf club head comprising: a top forward angled face; a plurality
of teeth extending from the angled face, wherein an angle of the
face and the teeth are arranged to impart forward rolling motion
and substantially no sliding motion on a golf ball immediately upon
impact by the club head substantially according to the following
equation: v.sub.0=r.omega..sub.0 wherein v.sub.0 is the initial
horizontal speed of the golf ball at impact, wherein .omega..sub.0
is the initial angular speed of the golf ball at impact, wherein r
is the radius of the golf ball and wherein each of the plurality of
generally forward facing teeth a has height of about 0.2 to about
0.3 inches measured from a line defining a base of a tooth to a top
of the tooth.
27. The golf club head of claim 26 wherein each of the teeth has a
tooth tip for striking a ball, wherein each of the teeth comprises
an upper tooth surface and a lower tooth surface intersecting the
top-forward angled face and meeting at the tooth tip such that the
tooth tip is in a top forward plane, wherein the upper tooth
surface and the lower tooth surface of each tooth form an angle B
at the tooth tip, and wherein
90.degree..ltoreq.B.ltoreq.104.12.degree..
28. The golf club head of claim 27, wherein the angle B comprises
an angle B1 between the upper tooth surface and a horizontal plane
and an angle B2 between the horizontal plane and the lower tooth
surface, wherein B1+B2=B, wherein
90.degree..ltoreq.B1.ltoreq.0.degree., and wherein
0.degree..ltoreq.B2.ltoreq.90.degree..
29. The golf club head of claim 28, wherein
24.degree..ltoreq.B2.ltoreq.40.degree.,
70.degree..ltoreq.B1.ltoreq.62.degree., and wherein
94.degree..ltoreq.B.ltoreq.102.degree..
30. The golf club head of claim 26, wherein at least one of the
teeth is positioned on the top-forward angled face so as to contact
the ball above a center of mass of the ball.
31. The golf club head of claim 29, wherein the face is angled
forward at an angle A of approximately the sin.sup.-1(0.4) from
vertical.
32. The golf club head of claim 26, wherein each of the teeth has a
tooth tip for striking a ball, wherein each of the teeth comprises
an upper tooth surface and a lower tooth surface intersecting the
top-forward angled face and meeting at the tooth tip such that the
tooth tip is in a top forward plane, wherein at least one tooth of
the plurality of teeth comprises a triangular shape, wherein the
one tooth comprises a vertical height d between an upper horizontal
plane through the intersection of the upper tooth surface and the
face and a lower horizontal plane through the intersection of the
lower tooth surface, and wherein d is approximately 0.125''.
33. The golf club head of claim 26, wherein a bottom surface of the
head has a length h of approximately 0.3294'', and a top surface of
the head has a length g of approximately 0.875''.
Description
CROSS REFERENCE TO RELATED APPLICATIONS
[0001] The present application is a continuation of U.S. patent
application Ser. No. 11/739,405, filed on Apr. 14, 2007, which is a
continuation-in-part of parent application Ser. No. 11/674,249,
filed Feb. 13. 2007. The parent application is herein incorporated
by reference.
BACKGROUND
[0002] The present invention is directed to an angled golf putter
head that has teeth on its face in order to present an optimum
rotation to the golf ball when striking it.
[0003] Various putter designs have been put forward with the aim of
improving putting accuracy. All of these designs are variants off
of the most fundamental design that is illustrated in FIG. 1A. In
this design, a flat and vertical face 20 of the putter head 10
strikes a golf ball 50 at a contact point 24 and exerts a force F
directed towards the center of the ball. The impact results in an
applied force F on the center of mass (COM) of the ball 50, but it
exerts no torque about the COM. The ball 50 therefore acquires an
initial horizontal linear speed v.sub.0 (slide) but zero initial
angular speed .omega..sub.0 (spin). The ball 50 therefore starts
its motion with a pure forward slide. This sliding motion is
undesirable because it causes the ball to skip and become deflected
by irregularities in the green.
[0004] As FIG. 1B illustrates, this sliding is immediately opposed
by a sliding friction force f pointing backwards at the (bottom)
point of contact between the ball 50 arid the grass. After a time
t, this force causes the linear speed of the ball 50 to decrease
from its initial value v.sub.0 to a smaller value v(t)=v. Also, the
friction force f exerts a torque .tau.=rf (where r is the radius of
the ball 50) about the COM, which causes the angular speed to
increase from its initial value .omega..sub.0=0 to a larger value
.omega.(t)=.omega..
[0005] After the impact, the linear speed v continues to decrease
and the angular speed .omega. continues to increase until
v=r.omega., at which point pure rolling sets in and the point of
contact between the ball and the green is instantaneously at rest.
When v=r.omega., the forward linear motion of the contact point is
exactly canceled by the backward rotational motion. From this time
on, the friction force becomes almost zero (the rolling friction
force is miniscule) and so the ball 50 continues to roll. During
the rolling phase of the motion, the ball's 50 trajectory is smooth
and regular because the green exerts almost no frictional force on
the ball 50.
[0006] It is obviously highly desirable to eliminate the initial
sliding phase of the ball's 50 motion, which can last for several
feet. To see how to accomplish this, consider (referring to FIG.
2B) a horizontal impact force F exerted on a ball 50 at a distance
h above the center of the ball. This force imparts an initial
horizontal linear speed v.sub.0 to the ball 50, and the torque
.tau.=rf arising from the force F imparts an initial angular speed
.omega..sub.0 to the ball 50.
[0007] At all times t during the impact, the linear speed v(t) and
angular speed .omega.(t) satisfy
m dv(t)/dt=F(t)
ld.omega.(t)/dt=hF(t).
[0008] where I=2mr.sup.2/5 is the moment of inertia of the ball
(this assuming a constant ball density). Therefore, independently
of the values of F(t), the speeds Vo and To are related by
mv.sub.o=IT.sub.o/h,
or
V.sub.o=2T.sub.or.sub.2/h.
[0009] This relation suggests how to impact the ball 50 so that it
begins rolling immediately. If the impact is made at a height
h=2r/5 above the center of the ball 50, then
v.sub.0=r.omega..sub.0, which is the condition for rolling. This
height corresponds to a distance H=r+h=7D/10 above the bottom of
the ball 50, where D=2r is the diameter of the ball. A ball 50
struck at this point will execute pure rolling motion throughout
its entire trajectory. There will be no initial sliding phase, with
its awkward skipping and veering away from the desired direction
towards the hole.
[0010] One way to accomplish such an impact is to use a putter with
a forward extended element 22 instead of the conventional forward
flat surface, as illustrated in FIG. 2A. If the putt is executed
such that the forward element 22 strikes the ball 50 at a distance
h=2r/5 above its center COM, then the desirable rolling motion will
result. (This assumes that the force exerted on the ball is purely
horizontal.)
[0011] There are, unfortunately, two serious problems with this
putter. The first problem is that it is extremely difficult to hit
the ball 50 at the correct height. The second problem is that, once
the forward element 22 strikes the ball 50, it tends to slip
upwards, resulting in an uncontrolled motion of the struck ball
50.
[0012] An alternative putter design ("the Macera Putter") has been
suggested by U.S. Pat. No. 4,644,385, and is illustrated in FIG.
2C. This patent discloses a forward face 20 of a putter 10 that is
inclined forward at an angle A. Such a putter 10 will strike the
ball 50 at a height h=r sin(A), independently of the height of the
putter head above the green. If A is optimally chosen such
that:
sin(A)=2/5=0.4(A=23.58.degree.),
[0013] then h will have the desired value of 2r/5.
[0014] Unfortunately, the Macera putter does not work in an optimal
manner, because it fails to impart the desired rolling motion and
furthermore forces the ball 50 downward into the green. This is
because the inclined face 20 of the putter 10, which strikes the
ball 50 tangentially, exerts a vector force F on the ball that is
directed essentially straight towards the center COM of the ball
50.
[0015] The exerted force F on the ball 50 therefore does not exert
a torque about the center COM. The initial motion of the ball 50 is
thus pure sliding, just as with a conventional putter. Furthermore,
the downward component of the exerted force causes the ball 50 to
move downward, into the grass, during the impact. This results in
an extremely uncontrollable putt.
[0016] To see what is happening in more detail, consider the forces
acting on the ball 50 during the impact with the club, as
illustrated in FIG. 2D. The force F exerted by the putter 10 on the
ball 50, directed towards the center (COM), has a horizontal
component F.sub.x, which causes the ball 50 to move forward, and a
vertical component F.sub.y, which causes the ball 50 to move
downward. The forward force component is opposed by the small
static friction force F.sub.f, and the downward force component is
opposed by the normal ground reaction force F.sub.N. The result is
problematic, with the ball 50 pushed into the grass and sliding
forward through the grass. By the time pure rolling sets in and the
ball returns on top of the grass, the trajectory can significantly
deviate from the intended direction and speed.
[0017] Putters have been disclosed that have a plurality of lateral
grooves on the forward face; see U.S. Pat. No. 5,348,301. Although
such grooves can increase the friction between the club and ball,
so that some forward spin can be imparted to the ball during the
upswing, this effect is very small (because the upswing during the
impact time is very small) and does not appreciably shorten the
time needed for pure rolling to occur. Furthermore, if the grooved
face is inclined forward, as with the Ma putter, the same problems
arise as with the Madera putter described above.
SUMMARY
[0018] The present invention is a golf club head that is able to
impart a forward rolling motion to a golf ball in addition to a
forward motion of the ball to avoid sliding. According to an
embodiment, a golf club head comprises a top-forward angled face,
the face comprising a plurality of generally forward-facing teeth.
One or more of the plurality of teeth may be positioned on the face
to contact the ball above a center of mass of the ball. The face
may be angled forward at an angle A of, in an embodiment,
approximately the sin.sup.-1(0.4) from a vertical. The teeth,
although possibly comprising any polygonal or curved surface shape,
are discussed in terms of a preferred triangular shape embodiment
below. In this embodiment, each of the teeth comprise a top forward
face surface having an angle B1 from a horizontal plane and a
bottom forward face surface having an angle B2 from the horizontal
plane, wherein B1 and B2 are chosen such that the net vertical
force on the ball is approximately zero when the teeth strike a
ball. An ideal configuration which accomplishes this is when these
parameters satisfy the following equations
cos(A)*sin(2B1)/sin(2(B1-A))=[cos(B2)+cos(A)/cos(B2+A)]*sin(2B2)/[4*sin(-
B2+A)].
[0019] Optimally, these values are
24.degree..ltoreq.B2.ltoreq.40.degree., and for each value of B2,
B1 is chosen based on the solution equation such that
62.degree..ltoreq.B1.ltoreq.71.degree., and
95.degree..ltoreq.B1+B2.ltoreq.102.degree., and ideally, B1 is
approximately 67.degree. and B2 is approximately 31.degree., and an
angle between a top horizontal surface and the top forward face
surface E is approximately 113.degree.. The teeth may be
constructed according to the following specifications: a vertical
height of the tooth d is approximately 0.125'''' high; an upper
angle C between the club face and a top forward face surface of the
tooth that is approximately 46.58.degree.; a bottom angle D between
the club face and a bottom forward face surface of the tooth that
is approximately 35.42.degree.; a back portion of the tooth
adjacent to the club face has a length a of approximately
0.1364.degree.; the top forward face surface has a length b of
approximately 0.0798''''; and the bottom forward face surface has a
length c of approximately 0.1''. The overall vertical height f of
the non-angled surface of the club head may be approximately
1.25'', and a bottom surface of the head may have a length h of
approximately 0.3294'', and a top surface of the head may have a
length g of approximately 0.875''. Optimally, the face comprises
ten teeth.
[0020] Various embodiments of the invention are further directed to
a method for putting, comprising: striking a golf ball with an
angled putter face comprising a plurality of teeth; and contacting
the ball during the striking by one or more of the plurality of
teeth such that a force exerted by the teeth on the ball is purely
forward and horizontal. In such an embodiment, the method can
involve simultaneously imparting a rotational motion on the ball in
combination with a forward motion that essentially eliminates
sliding friction at a start of a putting motion beginning with the
striking of the golf ball.
DESCRIPTION OF THE DRAWINGS
[0021] The invention is explained below with reference to preferred
embodiments illustrated in the drawings and described in more
detail below.
[0022] FIG. 1A is a pictorial illustration of a conventional putter
contacting a golf ball;
[0023] FIG. 1B is a pictorial illustration of the forces and
dynamic characteristics of the golf ball;
[0024] FIGS. 2A, B are pictorial illustrations of a golf putter
head having a forward extended element and the appertaining forces
acting on the golf ball;
[0025] FIGS. 2C, D are pictorial illustrations of a known angled
putter head and appertaining forces acting on the golf ball;
[0026] FIG. 3 is a pictorial illustration of a putter head
according to an embodiment of the invention;
[0027] FIG. 4 is a pictorial illustration of a single tooth on the
putter head showing various angles and lengths;
[0028] FIG. 5 is a simplified pictorial illustration of a tooth
striking the head of the golf ball and the resultant forces;
[0029] FIG. 6 is a graph illustrating the relationship between
relevant tooth face angles;
[0030] FIGS. 7(a)-(h) are pictorial illustrations of various tooth
configurations;
[0031] FIG. 8 is a smaller region of the graph illustrated in FIG.
6;
[0032] FIG. 9 is a pictorial illustration of the putter head
illustrating various angles and lengths;
[0033] FIGS. 10A-D are sequential line drawing illustrations of a
golf ball being struck by a conventional putter head; and
[0034] FIGS. 11A-D are sequential line drawing illustrations of a
golf ball being struck by an inventive putter head.
DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS
[0035] FIG. 3 illustrates an embodiment of the putter head 10
according to the present invention that combines the advantages of
the leading edge head (illustrated in FIG. 2A) and the forward
inclined head (illustrated in FIG. 2C), without the disadvantages
of either. The inventive putter head incorporates a plurality of
teeth onto a forward face which is inclined at the angle A.
[0036] As can be seen in FIG. 3, a tooth 22 of the putter head 10
strikes the ball 50 at the desired location 24 and with no slippage
independently of the height of the head 10 during impact. The
impact force F is directed forward, causing the ball 50 to start
rolling immediately due to the torque component induced in the ball
with the impact force F vector being above the center of mass COM
and in a direction that is generally horizontal, with little or no
downward motion or component to the force vector F. The forward
face inclined forward at the optimal angle A=23.58.degree., so that
impact occurs at the optimal height h=r sin(a)=2r/5, with attached
forward facing teeth 22, so that the impact force F is directed
forward.
[0037] In general, the putter teeth are constructed according to
the illustration in FIG. 4. In a preferred embodiment:
[0038] A is the inclination angle, which is equal to
sin.sup.-1(0.4)=23.58.degree.;
[0039] B1 is the tooth angle above the horizontal axis; and
[0040] B2 is the tooth angle below the horizontal axis, so that the
forward tooth angle is B=B1+B2.
[0041] The other angles inside of the triangular tooth are:
C=90.degree.+A-B1 and
D=90.degree.-A-B2.
[0042] The overall dimension of the tooth will be specified by the
value of the vertical height d. The sides of the tooth are then
a=d/cos(A),
b=a*cos(B2+A)/sin(B), and
c=a*cos(B1-A)/sin(B).
[0043] Although there is a range of tooth geometries which give
rise to an improved ball rotation upon impact, there are optimal
choices which can be arrived at as follows. Consider the
(exaggerated) impact (depicted in FIG. 5) of a tooth 22 on a ball
50 at height h above the COM. The upper face 26 of the tooth 22
will exert a compressional force f1 on the ball 50, and the lower
face 28 of the tooth 22 will exert a compressional force f2 on the
ball. In general, force vector f1 will have an upward pointing
vertical component f1.sub.y and a forward pointing horizontal
component f1.sub.x, and force vector f2 will have a downward
pointing vertical component f2.sub.y and a forward pointing
horizontal component f2.sub.x.
[0044] The magnitude and direction of the vertical component of the
net vector force f1.sub.y+f2.sub.y depends on the values of the
angles B1 and B2. However, a net vertical component is undesirable
because, if it points downward, it will tend to push the ball 50
into the surface upon which it rests, and if it points upward, it
will tend to push the ball 50 into the air and away from the
surface. Also, a net vertical component will contribute to the
torque on the ball 50 and therefore change, in an uncontrollable
way, the rotation imparted to the ball 50. This is because, if
there is a vertical force component G(t) on the ball during impact,
the force equation in paragraph [0006] is unchanged, but the torque
equation acquires an additional term on the right-hand side.
[0045] The height h for which pure rolling is achieved will
therefore no longer be independent of the exerted force, but will
depend on the integral of G(t) over the impact time, the weight of
the ball, and the speed of the putt. The optimal choice of B1 and
B2 is therefore such that the net vertical component is zero.
[0046] To determine the relative magnitudes of the forces f1 and
f2, a stress-strain relation .sigma.=Y.epsilon. may be utilized,
where .sigma. is the stress (force/area), .epsilon. is the strain
(fractional length change .delta.l/l), and Y is the Young's modulus
for the golf ball material. The condition that the vertical
components of f1 and f2 cancel can be derived from the geometry of
FIG. 5. This condition is equivalent to the following relation
between the angles B1, B2, and
A=sin.sup.-1(h/r)=sin.sup.-1(0.4)=23.58.degree.:
cos(A)*sin(2B1)/sin(2(B1-A))=[cos(B2)+cos(A)/cos(B2+A)]*sin(2B2)/[4*sin(-
B2+A)],
[0047] For each value of B2 between 0.degree. and 90.degree., there
is a unique value of B1 between 0.degree. and 90.degree., which
satisfies the equation. The values of B1 and B2 which solve the
equation are given in the following Table 1 and the graph
illustrated in FIG. 6.
TABLE-US-00001 TABLE 1 B2 B1 B1 + B2 0 90 90 2 88.02 90.02 4 86.08
90.08 6 84.20 90.20 8 82.38 90.38 10 80.64 90.64 12 78.98 90.98 14
77.41 91.41 16 75.92 91.92 18 74.52 92.52 20 73.20 93.20 22 71.95
93.95 24 70.76 94.76 26 69.64 95.64 28 68.56 96.56 30 67.51 97.51
32 66.47 98.47 34 65.44 99.44 36 64.39 100.39 38 63.30 101.30 40
62.14 102.14 42 60.88 102.88 44 59.49 103.49 46 57.92 103.92 48
56.12 104.12 50 54.03 104.03 52 51.60 103.60 54 48.75 102.75 56
45.44 101.44 58 41.67 99.67 60 37.51 97.51 62 33.11 95.11 64 28.67
92.67 66 24.43 90.43 68 20.55 88.55 70 17.13 87.13 72 14.16 86.16
74 11.62 85.62 76 9.45 85.45 78 7.58 85.58 80 5.96 85.96 82 4.53
86.53 84 3.26 87.26 86 2.10 88.10 88 1.02 89.02 90 0 90
[0048] Notice that, as B1 and B2 vary between 0.degree. and
90.degree., the sum B1+B2 varies in the limited range between
90.degree. and 104.degree.. The height of a tooth is determined by
the geometry of each tooth. Using trigonometry, one can calculate
the range of heights to be in the range of to, or about 0.2 to
about 0.3 inches, for the teeth having the dimensions and angles
set forth herein.
[0049] Nothing in this application is intended to limit the scope
of the angle B2 in any way (positive or negative), however, from a
practical standpoint, for very large values of B2, the teeth become
so small that the desired effect is minimized. Additional downward
forces will instead be exerted by the sides of teeth. B2 can
therefore, optimally, be restricted to be less than about
50.degree.. Small values of B2 are, on the other hand, perfectly
acceptable. One advantageous configuration that is easy to
manufacture occurs when B2 is chosen to be 0.degree., so that
B1=90.degree.. This is illustrated in FIG. 7(a).
[0050] A practical advantage to further restricting the B2 range
can be found from consideration of the previously discussed
solution graph given in FIG. 6. It is desirable to choose B2 such
that the corresponding value of B1 is relatively stable so that a
small error in the construction of B2 does not lead to appreciably
alter the desired cancellation of vertical forces. The choice of B2
can therefore be restricted to the relatively flat portion of the
graph. B2 should therefore, in a preferred embodiment, be
restricted to lie between approximately 24.degree. and 40.degree..
The values of B1 and B2 in this narrower range are given in Table 2
and graph illustrated in FIG. 8. In this range the relation between
B1 and B2 is seen to be essentially linear.
TABLE-US-00002 TABLE 2 B2 B1 B1 + B2 24 70.76 94.76 25 70.19 95.19
26 69.64 95.64 27 69.09 96.09 28 68.56 96.56 29 68.03 97.03 30
67.51 97.51 31 66.99 97.99 32 66.47 98.47 33 65.96 98.96 34 65.44
99.44 35 64.92 99.92 36 64.39 100.39 37 63.85 100.85 38 63.30
101.30 39 62.73 101.73 40 62.14 102.14
[0051] To illustrate the construction of a putter according to a
preferred embodiment, the following example is presented, wherein
B1=67.degree. and B2=31.degree. (B=B1+B2=98.degree.) from the
middle of the above Table 2 of solutions. Also choosing
d=1/8''=0.125'', the above tooth parameters become:
[0052] C=40.58.degree.
[0053] D=35.42.degree.
[0054] a=0.1364''
[0055] b=0.0798''
[0056] c=0.1000''.
[0057] The inventive putter head incorporates the above teeth onto
a forward face which is inclined at the angle A. The side view of
this head is depicted in FIG. 9. The height is f, the width of the
bottom surface is h, and the width of the top surface is
g=h+f*tan(A). The lengths of the top and bottom of each tooth are b
and c, as above. The forward angle of each tooth, and the angle
between each tooth, is B=B1+B2. The angle between the top surface
of the club head and the top surface of the first tooth is
E=90.degree.-A+C=180.degree.-B1.
[0058] For the exemplified inventive putter, the value of f may be
chosen as f=1.25'' so that there are f/d=10 teeth, and g may be
chosen such that
g=7/8''=0.875''
[0059] so that
h=g-f*tan(A)=0.3294''.
[0060] The tooth lengths b and c and angle B are given above, and
E=180.degree.-B1=113.degree.. The relevant parameter values are
thus
[0061] f=1.25''
[0062] g=0.875''
[0063] h=0.3294''
[0064] b=0.0798''
[0065] c=0.1''
[0066] B=98.degree.
[0067] E=113.degree..
[0068] The complete putter head extends perpendicularly from this
forward face any desired distance. A typical example is 2''. Only
the part of the forward face of the putter that makes contact with
the ball is important to achieve the desired rolling motion of the
ball. The structure of the other parts of the putter can be chosen
as desired.
[0069] With this design, the disadvantages of the prior art putters
are thus avoided. The impact height is automatically correct, and
there is no slippage because, if the impacting tooth 22 starts to
slide upward or is moved out of contact with the ball 50 due to
rotation of the ball 50, the tooth 22 below it will come into
contact with the ball 50 and stop the sliding. The impact force F
is directed forward, creating the desired torque which imparts the
correct initial spin, with little or no vertical component to push
the ball downward.
[0070] FIGS. 10A-11D illustrate the dramatic effect of the putter
head design according to the present invention. FIGS. 10A-D are a
sequence of line drawings based on photographs of a golf ball being
struck with a conventional putter. A vertical line is visible on
the golf ball so that its rotation can be observed. FIG. 10A shows
the ball at the point of impact, with the vertical line being in a
vertical position. FIGS. 108-10D show the golf ball 3 ms, 6 ms, and
14 ms respectively after impact. It can be seen that the ball is in
a pure slide, with no rotation of the ball occurring (FIG. 10D even
suggests the possibility that the ball is slightly rotating
backwards, increasing the slide. This occurs because the club has a
slight up-swing when striking the ball, resulting in an impact
slightly below the COM.)
[0071] Turning now to FIGS. 11A-D, a sequence of line drawings
based on photographs of the struck golf ball can be seen using the
inventive putter. The sequence shows approximately the same timing:
impact, 3 ms, 6 ms, and 14 ms. It can be seen that at 3 ms, the
ball has rotated approximately 20.degree.; at 6 ms, the ball has
rotated approximately 45.degree. and is at this point in time in a
pure rolling mode; at 14 ms, the ball has rotated 110.degree. and
remains in a pure rolling mode, and thereby providing an
advantageous motion of the ball. The angular speed of the ball is
about f=23 rps, and the linear speed is about v=10 fps, so that the
condition v=2.pi.r*f for pure rolling is well-satisfied.
[0072] For the purposes of promoting an understanding of the
principles of the invention, reference has been made to the
preferred embodiments illustrated in the drawings, and specific
language has been used to describe these embodiments. However, no
limitation of the scope of the invention is intended by this
specific language, and the invention should be construed to
encompass all embodiments that would normally occur to one of
ordinary skill in the art.
[0073] The present invention may be described in terms of
functional block components and various steps. Such functional
blocks may be realized by any number of components configured to
perform the specified functions. Furthermore, the present invention
could employ any number of conventional aspects. The particular
implementations shown and described herein are illustrative
examples of the invention and are not intended to otherwise limit
the scope of the invention in any way. For the sake of brevity,
conventional aspects may not be described in detail. Furthermore,
the connecting lines, or connectors shown in the various figures
presented are intended to represent exemplary functional
relationships and/or physical or logical couplings between the
various elements. It should be noted that many alternative or
additional functional relationships, physical connections or
logical connections may be present in a practical device. Moreover,
no item or component is essential to the practice of the invention
unless the element is specifically described as "essential" or
"critical". Numerous modifications and adaptations will be readily
apparent to those skilled in this art without departing from the
spirit and scope of the present invention.
TABLE-US-00003 TABLE OF REFERENCE CHARACTERS 10 putter head 20
putter head face 22 extended element, tooth 24 contact point 26 up
per tooth face 28 lower tooth face 50 golf ball
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