US20080194353A1

US20080194353A1 - Angled golf putter head having teeth

Info

Publication number: US20080194353A1
Application number: US11/739,405
Authority: US
Inventors: Richard A. Brandt
Original assignee: Individual
Current assignee: Individual
Priority date: 2007-02-13
Filing date: 2007-04-24
Publication date: 2008-08-14
Also published as: WO2008134335A1

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.

Description

CROSS REFERENCE TO RELATED APPLICATIONS

The present application 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

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.
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 v₀(slide) but zero initial angular speed ω₀(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.
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 and the grass. After a time t, this force causes the linear speed of the ball 50 to decrease from its initial value v₀to a smaller value v(t)=v. Also, the friction force f exerts a torque τ=rf (where r is the radius of the ball 50) about the COM, which causes the angular speed to increase from its initial value ω₀=0 to a larger value ω(t)=ω.
After the impact, the linear speed v continues to decrease and the angular speed ω continues to increase until v=rω, at which point pure rolling sets in and the point of contact between the ball and the green is instantaneously at rest. When v=rω, 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.
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 v₀to the ball 50, and the torque τ=rf arising from the force F imparts an initial angular speed ω₀to the ball 50.
At all times t during the impact, the linear speed v(t) and angular speed ω(t) satisfy
mdv(t)/dt=F(t)
Idw(t)/dt=hF(t),
where I=2mr²/5 is the moment of inertia of the ball (this assuming a constant ball density). Therefore, independently of the values of F(t), the speeds v₀and ω₀are related by
or
mv ₀ =Iω ₀ /h,
v ₀=2ω₀ r ²/5h.
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 v₀=r ω₀, 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.
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.)
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.
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°),
then h will have the desired value of 2r/5.
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.
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.
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_x, which causes the ball 50 to move forward, and a vertical component F_y, which causes the ball 50 to move downward. The forward force component is opposed by the small static friction force F_f, and the downward force component is opposed by the normal ground reaction force F_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.
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 Macera putter described above.

SUMMARY

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⁻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)].
Optimally, these values are 24°≦B2≦40°, and for each value of B2, B1 is chosen based on the solution equation such that 62°≦B1≦71°, and 95°≦B1+B2≦102°, and ideally, B1 is approximately 67° and B2 is approximately 31°, and an angle between a top horizontal surface and the top forward face surface E is approximately 113°. 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°; a bottom angle D between the club face and a bottom forward face surface of the tooth that is approximately 35.42°; a back portion of the tooth adjacent to the club face has a length a of approximately 0.1364″; 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.
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

The invention is explained below with reference to preferred embodiments illustrated in the drawings and described in more detail below.

FIG. 1A is a pictorial illustration of a conventional putter contacting a golf ball;

FIG. 1B is a pictorial illustration of the forces and dynamic characteristics of the golf ball;

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;

FIGS. 2C, D are pictorial illustrations of a known angled putter head and appertaining forces acting on the golf ball;

FIG. 3 is a pictorial illustration of a putter head according to an embodiment of the invention;

FIG. 4 is a pictorial illustration of a single tooth on the putter head showing various angles and lengths;

FIG. 5 is a simplified pictorial illustration of a tooth striking the head of the golf ball and the resultant forces;

FIG. 6 is a graph illustrating the relationship between relevant tooth face angles;

FIGS. 7( a)-(h) are pictorial illustrations of various tooth configurations;

FIG. 8 is a smaller region of the graph illustrated in FIG. 6;

FIG. 9 is a pictorial illustration of the putter head illustrating various angles and lengths;

FIGS. 10A-D are sequential images of a golf ball being struck by a conventional putter head; and

FIGS. 11A-D are sequential images of a golf ball being struck by an inventive putter head.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

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.
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°, 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.
In general, the putter teeth are constructed according to the illustration in FIG. 4. In a preferred embodiment:
A is the inclination angle, which is equal to sin⁻¹(0.4)=23.58°;
B1 is the tooth angle above the horizontal axis; and
B2 is the tooth angle below the horizontal axis, so that the forward tooth angle is B=B1+B2.
The other angles inside of the triangular tooth are:
C=90°+A−B1 and
D=90°−A−B2.
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).
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 _yand a forward pointing horizontal component f1 _x, and force vector f2 will have a downward pointing vertical component f2 _yand a forward pointing horizontal component f2 _x.
The magnitude and direction of the vertical component of the net vector force f1 _y+f2 _ydepends 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.
The height h for which pure rolling is achieved will therefore no longer be independent of the exerted forcer 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.
To determine the relative magnitudes of the forces f1 and f2, a stress-strain relation σ=Yε may be utilized, where σ is the stress (force/area), ε is the strain (fractional length change δl/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⁻¹(h/r)=sin⁻¹(0.4)=23.58°:
cos(A)*sin(2B1)/sin(2(B1−A))=[cos(B2)+cos(A)/cos(B2+A)]*sin(2B2)/[4*sin(B2+A)].
For each value of B2 between 0° and 90°, there is a unique value of B1 between 0° and 90°, 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 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

Notice that, as B1 and B2 vary between 0° and 90°, the sum B1+B2 varies in the limited range between 90° and 104°.
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°. 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°, so that B1=90°. This is illustrated in FIG. 7( a).
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° and 40°. 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 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

To illustrate the construction of a putter according to a preferred embodiment, the following example is presented, wherein B1=67° and B2=31° (B=B1+B2=98°) from the middle of the above Table 2 of solutions. Also choosing d=⅛″=0.125″, the above tooth parameters become:
C=46.58°
D=35.42°
a=0.1364″
b=0.0798″
c=0.1000″.
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°−A+C=180°−B1.
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=⅞″=0.875″
so that
h=g−f*tan(A)=0.3294″.
The tooth lengths b and c and angle B are given above, and E=180°−B1=113°. The relevant parameter values are thus
f=1.25″
g=0.875″
h=0.3294″
b=0.0798″
c=0.1″
B=98°
E=113°.
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.
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.
FIGS. 10A-11D illustrate the dramatic effect of the putter head design according to the present invention. FIGS. 10A-D are a sequence of 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. 10B-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.)
Turning now to FIGS. 11A-D, a sequence of 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°; at 6 ms, the ball has rotated approximately 45° and is at this point in time in a pure rolling mode; at 14 ms, the ball has rotated 110° 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=2πr*f for pure rolling is well-satisfied.
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.
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 OF REFERENCE CHARACTERS

10 putter head
20 putter head face
22 extended element, tooth
24 contact point
26 upper tooth face
28 lower tooth face
50 golf ball

Claims

1. A golf club head, comprising:

a top-forward angled face, the face comprising a plurality of generally forward-facing teeth.

2. The golf club head according to claim 1, wherein one or more of the plurality of teeth is positioned on the face to contact the ball above the center of mass of the ball.

3. The golf club head according to claim 2, wherein the face is angled forward at an angle A of approximately the sin⁻¹(0.4) from a vertical.

4. The golf club head according to claim 3, wherein 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 from the teeth is approximately zero when the teeth strike a ball.

5. The golf club head according to claim 4, wherein the following solution equation is satisfied:

cos(A)*sin(2B1)/sin(2(B1−A))=[cos(B2)+cos(A)/cos(B2+A)]*sin(2B2)/[4*sin(B2+A)].

6. The golf club head according to claim 5, wherein 24°≦B2≦40°, and wherein for each value of B2, B1 is chosen based on the solution equation such that 62°≦B1≦71°, and 95°≦B1+B2≦102°.

7. The golf club head according to claim 6, wherein B1 is approximately 67° and B2 is approximately 31°, and an angle between a top horizontal surface and the top forward face surface E is approximately 113°.

8. The golf club head according to claim 5, wherein B2=0° and B1=90°.

9. The golf club head according to claim 1, wherein a tooth of the plurality of teeth has a triangular shape 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°;

a bottom angle D between the club face and a bottom forward face surface of the tooth that is approximately 35.42°;

a back portion of the tooth adjacent to the club face has a length a of approximately 0.1364″;

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″.

10. The golf club head according to claim 1, wherein an overall vertical height f of the non-angled surface of the club head is approximately 1.25″.

11. The golf club head according to claim 1, wherein the plurality of teeth is ten teeth.

12. The golf club head according to claim 1, 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″.

13. A golf club comprising a means for imparting a forward rotation to a golf ball during a stroke comprising:

a means for contacting the golf ball with a top forward angled face of a club head, the means comprising a plurality of protrusions on the angled face.

14. The golf club according to claim 13, wherein one or more of the plurality of protrusions contacts the golf ball above its center of gravity and, at the point of contact, imparts a horizontal force with negligible vertical force on the golf ball.

15. 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.

16. The method according to claim 15, further comprising 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.