WO2008134335A1

WO2008134335A1 - Angled golf putter head having teeth

Info

Publication number: WO2008134335A1
Application number: PCT/US2008/061216
Authority: WO
Inventors: Richard Brandt
Original assignee: Individual
Current assignee: Individual
Priority date: 2007-04-24
Filing date: 2008-04-23
Publication date: 2008-11-06
Anticipated expiration: 2009-10-24
Also published as: US20080194353A1

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

SPECfFiCATlON

TITLE

ANGLED GOLF PUTTER HEAD HAVING TEETH

CROSS REFERENCE TO RELATED APPLICATIONS The present application is a contiπυatioπ-iπ-part of parent application no. 11/674,249, filed February 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 bail when striking it.

Various putter designs have been put forward with the aim of improving putting accuracy. AIS of these designs are variants off of the most fundamental design that is iSiustrated in Figure 1A. Sn this design, a fiat and verticai face 20 of the putter head 10 strikes a goif bail 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 5O₁ but it exerts no torque about the COM. The bal! 50 therefore acquires an initial horizontal linear speed v₀ (slide) but zero initial angular speed ω_δ (spin). The bail 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 irreguiarities in the green,

As Figure 1 B 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 V₀ to a smaller value v(t) = v. Also, the friction force f exerts a torque T ~ 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 vaiue ω(t) = ω. After the impact, the linear speed v continues to decrease and the angular speed ω continues to increase υntii v ^™ rω, at which point pure railing sets in and the point of contact between the bail 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 roliing friction force is miniscule) and so the bal! 50 continues to roll. During the roϋing phase of the motion, the ball's 50 trajectory is smooth and regular because the green exerts almost no frictionaS force on the ball 50.

It is obviously highly desirable to eliminate the initial sliding phase of the bail's 50 motion, which can last for several feet. To see how to accomplish this, consider (referring to Figure 2B) a horizontal impact force F exerted on a ball 50 at a distance h above the center of the bail. This force imparts an initial horizontal linear speed V₀ to the ball 50, and the torque T = rf arising from the force F imparts an initial anguiar speed ω₀ to the bali 50. At all times t during the impact the linear speed v(t) and angular speed ω(t) satisfy m dv(t)/dt ~ F(t)

S dw(t)/dt = hF{t), where I = 2IDr²ZS 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 ωo are related by or mvo - I ωo/h,

V₀ = 2 ωorVδh.

This relation suggests how to impact the bail 50 so that it begins rolling immediately. If the impact is made at a height h = 2r/5 above the center of the bail 50, then vo = 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 bail. A bali 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 fiat surface, as illustrated in Figure 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 wiil result, (This assumes that the force exerted on the baii 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 SVlacera Putter") has been suggested by U.S. Patent No. 4,644,385, and is illustrated in Figure 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 bail 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 tangentiaiSy, exerts a vector force F on the ball that is directed essentially straight towards the center COM of the bail 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 ciυb, as illustrated in Figure 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 baii 50 to move forward, and a vertical component F_y, which causes the ba Ii 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 bβ&n disclosed that have a plurality of lateral grooves on the forward face; see U.S. Patent 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 baii. 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. Sn this embodiment, each of the teeth comprise a top forward face surface having an angle B1 from a horizontal pSane and a bottom forward face surface having an angle B2 from the horizontal plane, wherein 81 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(82 + 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 87° 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. Sn 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.

Figure 1 A is a pictorial illustration of a conventional putter contacting a goif ball;

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

Figures 2A₁ B are pictorial illustrations of a golf putter head having a forward extended element and the appertaining forces acting on the golf bail;

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

Figure 3 is a pictorial illustration of a putter head according to an embodiment of the invention; Figure 4 is a pictorial illustration of a single tooth on the putter head showing various angles and lengths;

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

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

Figures 7{a)-{h) are pictorial illustrations of various tooth configurations; Figure 8 is a smaller region of the graph illustrated in Figure 6;

Figure 9 is a pictoria! illustration of the putter head illustrating various angles and lengths; Figures 10A-D are sequential images of a golf ball being struck by a conventional putter head; and

Figures 11 A-D are sequential images of a goif ball being struck by an inventive putter head. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

Figure 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 Figure 2A) and the forward inclined head (illustrated in Figure 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 Figure 3, a tooth 22 of the putter head 10 strikes the bail 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 roiling immediately due to the torque component induced in the ball with the impact force F vector being above the center of mass CQfVt 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^s, 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 gen era i, the putter teeth are constructed according to the illustration in Figure 4. In a preferred embodiment:

A is the inclination angle, which is equal to sin^"1{0.4) = 23.58°; B1 is the tooth angie above the horizontal axis; and B2 is the tooth angie below the horizontal axis, so that the forward tooth angie 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(B2M)/ssn(B), and

Although there is a range of tooth geometries which give rise to an improved bail rotation upon impact, there are optima! choices which can be arrived at as follows. Consider the (exaggerated) impact (depicted in Figure 5) of a tooth 22 on a bal! 50 at height h above the COM. The upper face 26 of the tooth 22 will exert a compressiona! force f 1 on the bal! 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_y and a forward pointing horizontal component f1_x, and force vector f2 will have a downward pointing vertical component f2_y and a forward pointing horizontal component f2_x.

The magnitude and direction of the vertical component of the net vector force fly + f2_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 bal! 50 into the air and away from the surface. Also, a net vertical component wil! contribute to the torque on the ball 50 and therefore change, in an uncontrollable way, the rotation imparted to the bal! 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 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. 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 f 1 and f2 cancel can be derived from the geometry of Figure 5 . This condition is equivalent to the following relation between the angles B1 , B2, and A ~ sin^'1{h/r) - ssn^{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° aπd 90°, there is a unique vaiue of B1 between 0^s and 90°, which satisfies the equation. The values of B1 and B2 which solve the equation are given in the following Tabie 1 and the graph illustrated in Figure 6,

Table 1

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 iimit 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 wiil instead be exerted by the sides of teeth. B2 can therefore, optimally, be restricted to be iess 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 Figure 7(a).

A practical advantage to further restricting the B2 range can be found from consideration of the previously discussed solution graph given in Figure 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 iie between approximately 24° and 40°. The values of B1 and B2 in this narrower range are given in Tabie 2 and graph illustrated in Figure 8. Sn this range the relation between B1 and B2 is seen to be essentially linear.

Table 2

To iiSustrate the construction of a putter according to a preferred embodiment, the following example is presented, wherein 81 = 67° and B2 = 31° (B = B1 + B2 = 98°) from the middle of the above Table 2 of solutions. Also choosing d = 1/8" - 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 tn Figure 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 ~ 7/8" ~ 0.875" so that h = Q - 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". Oπiy 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 bail. 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 άue to rotation of the ball 50, the tooth 22 below it wtil 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.

Figures 10A - 11 D illustrate the dramatic effect of the putter head design according to the present invention. Figures 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. Figure 10A shows the ball at the point of impact, with the vertical line being in a vertical position. Figures 10B-1 GD show the golf bail 3ms, 6ms, and 14ms respectively after impact, it can be seen that the bal! is in a pure slide, with no rotation of the ball occurring (Figure 10D even suggests the possibility that the ball is slightly rotating backwards, increasing the slide. This occurs because the club has a slight up-swmg when striking the ball, resulting in an impact slightly below the COM.)

Turning now to Figures 11 A-D₁ a sequence of photographs of the struck golf ball can be seen using the inventive putter. The sequence shows approximately the same timing: impact, 3ms, 6ms, and 14 ms. It can be seen that at 3ms, the ball has rotated approximately 20°; at 8 ms, the bal! has rotated approximately 45° and is at this point in time in a pure rolling mode; at 14ms, the ball has rotated 110" and remains in a pure rolling mode, and thereby providing an advantageous motion of the bail. 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 we Il -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 extended element, tooth contact point upper tooth face lower tooth face golf ball

Claims

WHAT IS CLAIMED is-

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 bali.

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 81 and B2 are chosen such that the net vertical force on the ball from the teeth is approximately zero when the teeth strike a baii.

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{82) + cos(A) / cos{82 + 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 horizonta! surface and the top forward face surface E is approximateiy 113°.

8. The golf club head according to claim 5, wherein 82 - 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 ciub face and a top forward face surface of the tooth that is approximately 46,58°; a bottom angle D between the dub 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 approximateiy 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 goif dub comprising a means for imparting a forward rotation to a golf bat! during a stroke comprising: a means for contacting the golf baS! with a top forward angled face of a dub 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 goif bal! above its center of gravity and, at the point of contact, imparts a horizontal force with negligible vertical force on the golf bali.

15, A method for putting, comprising: striking a goif 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 bail is purely forward and horizontal.

16. The method according to claim 15, further comprising simultaneously imparting a rotationai motion on the bali 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