HK1158129A - Putter head with maximal moment of inertia - Google Patents

Abstract

A putter head has a front that strikes a golf ball during putting, a length a, a width b, a weight W, and a moment of inertia I. The width extends along a horizontal width axis perpendicularly intersecting the front of the putter head. The length extends along a horizontal length axis perpendicularly intersecting the horizontal axis. The dimensions are, for example, a. 7 inches, b. a, and I/Wa2 > 0.30.

Description

Putter head with maximum moment of inertia

RELATED APPLICATIONS

This application claims priority to provisional patent application No. 61/061,440 filed on 13.6.2008, which is incorporated by reference herein in its entirety.

Technical Field

The present invention relates to a putter head design for use in golf.

Background

When the putter head strikes a golf ball, the putter exerts a force on the golf ball while the golf ball exerts an equal force on the putter in the opposite direction. In general, a golf ball has two effects on the force exerted by a putter: slowing down the forward linear motion of the push rod; and rotating the putter head about a longitudinal axis passing through its center of mass (COM).

This rotation is undesirable because it can cause errors in the direction and speed of the golf ball. If the putter head hits a ball with its face perpendicular to the intended initial direction of movement of the golf ball, as it should be, the putter head is pointed away from this intended direction due to the rotation of the putter head, resulting in errors. During the brief period that the golf ball is in contact with the putter head surface, the putter head is rotated through a small angle, so that when the golf ball leaves the putter head surface, the golf ball will move in a direction perpendicular to the rotated surface rather than perpendicular to the original surface. Also, the velocity of the struck golf ball will be less than expected due to the conversion of a portion of the kinetic energy striking the putter head into rotational energy imparted by the putter head.

However, if the golf ball is hit directly in front of the center of mass of the putter head, no rotation about the center of mass axis will be induced and the above errors in direction and speed are avoided. Of course, a golf ball cannot often be hit directly in front of the center of mass of the putter head. Thus, the moment of inertia (MOI) of the putter head through the longitudinal axis of the putter head's center of mass is notIs often important. (moment of inertia can be defined asWherein each mass unit m_iMultiplied by the perpendicular distance r between the location of the unit and a selected longitudinal axis intersecting the center of mass of the putter head_iSquare of). For a front of the center of mass that does not directly impact the putter head, the larger the moment of inertia, the smaller the angular error. In other words, the greater the moment of inertia, the greater the area of the putter head striking face that produces an acceptable stroke. This relationship also accounts for why the moment of inertia is so important.

The United States Golf Association (USGA) rules define the size of putter heads, but do not define the weight or moment of inertia of putter heads. Professional golfers consistently hit portions of the golf ball that are in close proximity to a point on the putter face that is forward of the putter head's center of mass, referred to as the center of mass point or sweet spot on the putter head's face.

Many articles, books and patents mistakenly believe that the sweet spot is the point forward of the center of percussion (COP) of the putter head. This confusion arises because at the center point of impact of the putter head, the impact does not cause a reaction force at the point where the club is inserted into the putter head. Thus, a putter head impact on the center of impact does not eliminate the putter head rotation, but rather produces a rotation about the putter head center of mass that necessarily counteracts the linear motion of the club produced by the impact. This rotation causes the golf ball to move away from the putter head striking face in the wrong direction. Thus, the optimal ball striking point for a putter head is the center of mass of the putter head rather than the center of impact.

Amateur golfers, on the other hand, typically play the golf ball using a click on the striking face of the putter head that is very far (typically 0.5 ", sometimes more than 1") from the center of mass point of the putter head. Therefore, for the benefit of most golfers, a club with as much moment of inertia as possible should be used.

Drawings

FIG. 1 shows three putter head configurations useful in explaining the present invention;

FIG. 2 shows a putter head structure useful in explaining the present invention;

FIG. 3 illustrates putter head designs in various prior art ways;

FIG. 4 illustrates the load and the shape of the connector for connecting the putter head;

FIG. 5 illustrates a four-load putter head, a three-load putter head, and a dual-load putter head having large values of moment of inertia;

FIG. 6 shows a smooth variant of the four and three load putter heads of FIG. 5;

FIG. 7 shows another four-load and three-load putter head;

FIG. 8 shows a dual load putter head;

FIG. 9 is a perspective view of a four load putter head;

FIG. 10 is a perspective view of a four-load putter head having a club;

FIG. 11 is a comparison of I/W versus length for various putter head types;

fig. 12 is a similar view to fig. 11.

Detailed Description

In accordance with embodiments of the putter head, the putter head is characterized by an extreme moment of inertia. The moment of inertia value is much greater than that of putter heads disclosed in the market or in the prior art. The large moment of inertia value can be obtained by one or more of the following four novel methods.

First, the putter head includes two to four relatively heavy load members; these load members are located as far from the center of mass of the putter head as possible and are interconnected by a minimum number of relatively light connecting members. The connecting piece comprises a panel (face plate) and a club support (back holder).

Second, the shape of the elements is selected to increase the moment of inertia of the putter head. The shape of these elements and their distribution in the putter head create a new look for the putter head.

Third, the size of the load member (larger vertically and smaller horizontally) is selected to increase the putter head moment of inertia. These dimensions also create a new look for the putter head.

Fourth, the weight of the load member is determined by mathematical optimization calculations to maximize the moment of inertia of the putter head, based on the construction, overall weight, and overall dimensions of the putter head (dimensions consistent with the rules of the United states Golf Association).

One way to obtain a putter head having a greater moment of inertia is to give it a greater weight. However, golfers prefer putter heads having weights within a limited range, such as between 11 and 16 ounces (a putter head that is too light requires a relatively large and difficult to control swing speed, whereas a putter head that is too heavy requires a relatively small and difficult to adjust swing speed). Thus, the required weight is distributed over the putter head to achieve a greater moment of inertia, moving it as far away as possible from the center of mass of the putter head. The relevant quantities to be considered are therefore the ratio I/W, where I represents the moment of inertia; w represents weight. The pushrods disclosed herein have a large I/W ratio that is much greater than previously obtained.

One way to achieve a large I/W ratio is to give the putter head a considerable size and place most of its weight far from the center of mass. Practical and official requirements, however, limit the acceptable size of putter heads. The american golf association defines the maximum size of the putter head (see below); also, a putter head that is too large may appear inflexible and difficult to control, both in appearance and feel.

The maximum linear dimension of a given putter head is denoted by a. Thus, the most relevant parameter to consider is: dimensionless ratio I/Wa². The putter head described herein has the largest possible value for this ratio.

Putter dimensions disclosed herein conform to the United states Golf Association rules. The United states Golf Association defines putter head dimensions including Overall Length (OL), Face Length (FL), Overall Width (OW), and Overall Height (OH). The limiting conditions are as follows: the overall length is greater than the overall width, but is 7 inches maximum; the surface length is at least 2/3 of the total width and at least half of the total length; the overall height is at most 2.5 inches. Therefore, the maximum linear dimension a is the total length. The total width is herein designated b; the total height is herein designated h; the surface length is herein denoted as f. Therefore, the definition of the putter head is b.ltoreq.a.ltoreq.7 ', f.gtoreq.2b/3, f.gtoreq.a/2, and h.ltoreq.2.5'. Thus, a eligible putter head must be within a rectangular frame having a length a ≦ 7 ', a width b ≦ a, and a height h ≦ 2.5'.

The international unit of moment of inertia is kg-m². However, since the specifications set forth by the United states Golf Association rules and most club manufacturers are in English units (ounces and inches), the units for moment of inertia are designated as oz-in herein². Thus, as used herein, moment of inertia, the weight, not the mass, of a piece of material in the definition of moment of inertia is used. In other words, the present moment of inertia is the moment of inertia and acceleration of gravity (32 ft/s) in International units²) The product of (a).

Below is shown a putter head I/Wa²The theoretical maximum absolute value is 0.50. In order for the putter head to conform to the American Golf Association rules (a ≦ 7 ″), I/Wa²Means that the maximum value of I/W is 24.5in²。

Theoretically, these putter heads consist of point weights only, and do not include a face plate, a connecting member, or a club support. The actual putter head includes the above elements and has a non-point weight, which of course cannot be reached. However, the I/Wa of an actual putter head²Is 0.42, therefore, I/W is 21in²Is possible.

In contrast, the market placeThe I/W value of one of the upper larger putter heads is approximately 6in². Although many patents disclose putter heads having larger I/W values, none of the actual calculated I/W values for a putter can be as large as the I/W values for a putter head according to embodiments of the present invention.

When putting using a conventional putter, the golfer must hit the golf ball at the correct swing speed, in the correct swing direction, and at the optimum stroke of the putter head face. For putter heads having a moment of inertia ratio (MOI ratio) as large as that described in the embodiments of the present invention, it is not necessary to hit the golf ball with the sweet spot on the face of the putter head. In fact, the entire putter head surface is the optimal point of impact and the hit ball will travel in the intended direction from any point of impact. Thus, the golfer may focus on only the first two requirements.

To determine I/Wa for putter heads²The theoretical upper limit of possible values should be considered for a theoretical putter head. These putter heads are mathematically structured to include only particles that are as far apart from each other as possible and from the center of mass of the system. The connectors, faceplates, and club accessories required for an actual putter do not appear in a theoretical putter. The presence of any of the above elements will lower the I/W value as they may increase the weight closer to the center of mass.

To meet the American Golf Association regulations, the particles must be within a rectangular box having a length a ≦ 7 ', a width b ≦ a, and a height h ≦ 2.5'. The best choice is b-a, only considering the case where the particles are located on the periphery of a square with side length a. The particles must be located at the corners of the square to maximize the separation distance. Fig. 1a and 2 show this structure. The weights at four corners are w1, w2, w3 and w 4; the total weight W is fixed as W1+ W2+ W3+ W4.

In fig. 2, the coordinate system is centered at w 3; the coordinates of the centroid (x0, y0) are given by the following equation:

x0＝a(w2+w3)/W，

y0＝a(w1+w2)/W。

the moment of inertia of the transverse axis through the center of mass in the system is given by the following equation:

I(w1，w2，w3)＝∑wi*ri²，

where the total is the sum of the quantities obtained when i is 1, 2, 3, 4, and ri is the distance between wi and the centroid. The maximum value of I is the solution of three simultaneous equations:

when i is 1, 2, 3.

The solution is given by the following equation:

w1＝w2，w3＝w4＝W/2-w1，

the corresponding maximum is given by the following equation:

I_max＝Wa²/2。

this is the largest possible value for the moment of inertia for a putter head having a weight w and a length a. The centroid is at the center of the square (x0 y0 a/2).

Therefore, the maximum value of I/W is a²/2；I/Wa²The maximum value of (c) is 1/2 ═ 0.50. These values serve as the upper limit for the moment of inertia of the actual putter head. For putter heads meeting the rules of the United states Golf Association, a is 7 "at the maximum, so the following values are obtained:

(I/W)_max＝a²/2＝49/2＝24.5in²，

(I/Wa²)_max＝1/2＝0.50。

the objective is to have the actual putter head, including the face plate, the connecting member and the club support, have a moment of inertia value as close as possible to the upper limit value.

A particularly advantageous case is weight equality, i.e. W1, W2, W3, W4, W/4. The theoretical putter head is left-right symmetric, as is true for most practical putter heads on the market. Another particularly advantageous case is the new option: w1 ═ W3 ═ 0, W2 ═ W4 ═ W/2. This option involves only two loads, which results in a theoretical putter head that is completely asymmetric from side to side, as shown in fig. 1 b. While such putter heads do not appear to be unusual, there are advantages in that fewer connecting pieces are required when made into a practical putter head.

There is theoretically no optimal three-load putter head, since the selection of the optimal weight does not include the case where one of wi is 0. However, it is advantageous that a three-load putter head has a very large, but not optimal, moment of inertia. Figure 1c shows the system with two equal weights w2 located at the upper two corners and a single weight w1 located at the centre of the lower side of the square.

In the latter case, the total weight W ═ W1+2W2, length a fixed; make I/Wa²The maximum weight ratio s-W1/W can be determined. The following equation gives the centroid coordinates:

x0＝a/2，

y0＝a(1-s)，

the ratio of the moments of inertia is:

I/Wa²＝1/4+3s/4-s²≡f(s)。

the best choice for s is given by f'(s) ═ 0. Solution s is 3/8, so

w1＝3W/8，

w2＝5W/16，

y0＝5a/8，

And is

(I/Wa²)_max＝f(3/8)＝25/64＝0.391。

Thus, the moment of inertia ratio is 22% less than the optimal 0.50 for the optimal four or two load putter heads, as will be shown below: this difference is quite small for a platform based actual putter head.

When panels are added to the bottom surface of four or two load platforms in fig. 1a and 1b, the I/W decreases due to the increased weight near the centroid position. However, when adding panels to the bottom of the three load platform in FIG. 1c, there is less I/W reduction because there is already weight at this location. However, this advantage is not present if a panel is added to the top surface of the three load platform.

The earliest attempts to increase the putter head moment of inertia were to place the load on the heel and toe ends of a knife edge design. Accordingly, a theoretical putter head is shown in FIG. 3 a. The best choice for this configuration is to place two equal weights 10, 12 (w/2 weight at each end) at opposite ends of the length a element 14. Thus, I/Wa²1/4-0.250. This value is much less than the value 0.500 in the case of four or two loads, or 0.391 in the case of three loads, as described above.

The benefits of a putter with a large moment of inertia are well known. The earliest attempts were to add weight to the heel and toe position of the face to change the blade putter head, the arrangement being shown in fig. 3 a. Typical patents for this type of putter include us 3,516,674 to scambeger (Scarborough), us 3,966,210 to Rozmas and us 4,898,387 to finny (Finney). As described above, the putter head is expected to have a maximum moment of inertia ratio I/Wa²Is less than 0.25. Finney proposes that values of I/Wa can be achieved when the length a is 5 "and the head weight W is 10.6oz²0.17. The push rod design has been quite close to the theoretical maximum.

It is subsequently recognized that weight may be added near the center of the putter face to further increase the moment of inertia. Thus, the putter surface has weights 16, 18 at opposite ends of the element 20 of length a and a third weight 22 added near the back of the centre of the element 20, the arrangement being shown in figure 3 b. An example of a study of this putter head is disclosed in us patent 5,080,365 to Winchell. He suggests that I/W can be achieved with a length a of 5 "and a weight W of 1 lbA value of 1.94in²。

As shown above, the theoretical maximum possible I/W value for a three-load putter head is 0.391a²When a is 5', I/W is 9.78in². The following discussion will discuss why an actual three-load putter head a of 5 "can obtain an I/W of 8-9in². The three load putter head according to this embodiment can achieve significantly higher values than those proposed by Winchell for four reasons: (1) the shape of the load and the connecting piece is better selected; (2) the size of the load is better selected; (3) the weight ratio of the load is selected in an optimal way; and (4) optimally placing two weight lines at the rear of the putter head and a third weight at the center of the face plate.

A four load putter head is disclosed in Long, us patent 4,010,958. A preferred embodiment of the putter head is shown in fig. 3 c. The square loads 24, 26, 28 and 30 are placed at the four corners of a square (typically 5 "x 5") and are interconnected by three low density tubular braces (struts) 32, 34 and 36 and a panel 38. The putter club 40 is inserted into the center of the square and connected to the rear loads 24 and 26 and the face plate 38 by three brackets 32, 34 and 36.

The weight of the loads 24, 26, 28 and 30 is not indicated, but it is required that the weight of the front loads 28 and 30 should be less than the weight of the rear loads 24 and 26 so that the centre of mass is located at the centre 40 of the square. Long does not quantitatively calculate the moment of inertia value, but can calculate the I/Wa of the structure in FIG. 3c²The value is at most 0.30.

This value of 0.30, while a great deal of progress, is not surprising enough. While the four-load putter head disclosed in embodiments of the present invention has an I/Wa of over 0.42²This is a 40% increase over the Long design putter head. As described above, I/Wa for a four-load putter head shown in section 2²The theoretical upper limit is 0.50.

The new characteristics of the putter head disclosed in the embodiments of the present invention, and the reasons why its value is much larger than the Long design and very close to the theoretical maximum, are as follows: (1) by means of mathematical methodsSelecting the load weight of a putter head as disclosed in an embodiment of the invention to enable I/Wa²Maximization; (2) the number, shape and position of the connecting pieces (brackets) of the putter head disclosed in the embodiments of the present invention are selected so that the I/Wa²Maximization; and (3) by selecting the load shape and size of the putter head disclosed in an embodiment of this invention to enable I/Wa²And (4) maximizing.

A different type of putter head is disclosed in U.S. patent 7,077,758 to basil (rohr). Rohrer states that his design yields a moment of inertia higher than that of Long, even up to I/Wa²Is measured. His declaration is inconsistent with the fact.

Rohrer describes a putter head whose majority (at least 70%) of its weight is concentrated in a circle concentric with the center of mass. Rohrer teaches that for a given size and weight, his putter head has a moment of inertia that is 34% greater than that of the Long design. This view is based on the comparison shown in fig. 3 d. In contrast to the putter head of Long design, which has a length of a and the weight of the loads 24, 26, 28 and 30 are all concentrated at the four corners, fig. 3d shows the putter head of Rohre: has a surface length a and the weight is concentrated on the two protruding circular segments 42, 44.

For each of the putter heads described above, its I/Wa²The theoretical limits of the values (zero weight volume, no panel connection) are the same and are all 0.50. However, because the Rohre putter head is significantly larger in size than the Long putter head, the contrast between the two putter heads is not fair.

The United states Golf Association defines the overall length a and the overall width b (b ≦ a ≦ 7 ") of the putter head, rather than just the surface length. Thus, if a ═ 7 ", then the Long putter meets the requirements of the american golf association, while the rohr putter does not. A fair comparison between putters must be made with the overall size (and weight) of the putter heads being equal. In contrast, as shown in FIG. 3e, the Long push rod 46 is theoretically I/Wa²The value is again 0.50, however, the I/Wa of the Rohrer push rod 48²The value is only 0.25, which is comparable to the simple knife shape of FIG. 3aThe values of the pushrods are the same.

Rohr also states that the moment of inertia of its putter head is further increased compared to Long because the club insertion point is relatively far from the center of mass. This statement is not fair because the contact time between the struck golf ball and the putter head is too short to be felt by most clubs.

Thus, the conclusion for the above analysis is: for a given weight and size, the Long putter head has a 100% greater moment of inertia than the rohr putter head, and less than a 40% moment of inertia for a four-load putter head as described in embodiments of the present invention.

U.S. patent 6,409,613 to Sato (Sato) discloses a dual load putter head as shown in fig. 3 f. The putter head is L-shaped with cylindrical loads 50, 52 of unknown weight placed at opposite corners and connected by low density arms 54 and 56 and a face plate 58. Sato does not discuss the moment of inertia concept, but states that putter head rotation due to impacts that deviate from the sweet spot is reduced as compared to a bladed putter head. He suggests that this rotation is reduced because the torque applied to the putter head is reduced due to the center of mass being further away from the surface (face). This argument is not true.

The torque is equal to the force applied times the perpendicular distance between the direction of the force and the longitudinal axis of the center of mass, and thus the torque is dependent on the distance between the impact point and the sweet spot on the surface, but independent of the distance from the sweet spot to the center of mass on the surface.

Although the reasoning of Sato is not correct, the conclusion that its rotation is reduced is correct because the moment of inertia of its putter head is relatively large. He does not quantitatively calculate the value of the moment of inertia, but can calculate the I/Wa of the structure he designed for²The value is at most 0.27. This I/Wa²The values are large, but the dual load putter head according to embodiments of the present invention has an I/Wa of up to 0.41²The value, increased by 52%. For the dual load putter head described above, I/Wa²The theoretical upper limit of (b) is 0.50.

The novel characteristics of the double-load push rod head disclosed by the embodiment of the invention and the I/Wa thereof²The reason for the much larger value than the design of Sato and closer to the theoretical maximum is as follows: (1) the load weight of the dual load putter head disclosed in an embodiment of the present invention is selected mathematically to give I/Wa²Maximization; (2) the shape and position of the connecting piece of the dual-load push rod head disclosed by the embodiment of the invention are selected to enable the I/Wa²Maximization; and (3) selecting the load shape and size of the dual load putter head disclosed in the embodiments of this invention to make I/Wa²And (4) maximizing.

In one embodiment, embodiments of the present invention contemplate a putter head that includes four components: load, face plate, connector and club support. The first three will be fully discussed in embodiments of the present invention. The cue stick holder is a simple low weight addition, described after the first three. These modules are located within a rectangular frame having a length a0 ≦ 7 ≦ a0 ≦ 0, and a height c0 ≦ 2.5 ″. For simplicity, each component is assumed to have a constant density, but such an assumption is not necessary.

First, for the load assembly, it must be placed as far as possible from the longitudinal axis passing through the center of mass of the putter head to obtain the maximum possible moment of inertia. Thus, the load will be at the four corners of the rectangle with base a0 × b0, and extend upward in the vertical direction. Similarly, the center of mass of each load can be as far from the center of mass of the putter head as possible. In the actual load shape, the present embodiment employs a triangle shape. Any other simple shape will bring the center of mass of the load and the center of mass of the putter head close to each other, as will be shown below.

Figure 4a shows a typical triangular load. The size of the substrate is a multiplied by b; the height of the load is denoted c (not shown). While a triangular load base is a preferred design, the putter heads disclosed in this embodiment will achieve a substantial ratio of moment of inertia for various other shapes.

Another novel feature of the putter head disclosed in this embodiment is that: the putter head height adopts the american golf association maximum 2.5 ". Regardless of the shape of the load bed, the use of a load height near this upper limit helps to achieve very large ratios of moments of inertia. The load of the prior art putter heads does not take advantage of this freedom. If the load in the vertical direction is greater, the base of the load may be smaller; thus, more load can be moved further away from the center of mass, resulting in a larger ratio of moments of inertia.

The simplest shape of the connector is a stable rectangular frame. The rectangular base of the element is shown in figure 4 b. Because they are closer to the center of mass of the putter head, these connections must be as light as possible in order to minimize the reduction in the overall moment of inertia ratio I/W caused by them. However, the connector must be strong enough to securely connect the other components.

There are two possibilities for the orientation of the connecting elements, as shown in fig. 4c and 4 d. In fig. 4c, the short side of the length a on the joint is in the horizontal direction, while the long side of the length b is in the vertical direction. The opposite is true in fig. 4 d. Both connectors may have a width c rearward. The connector in fig. 4c will be further from the center of mass of the putter head, but with a smaller moment of inertia about a longitudinal axis passing through the center of mass; while the link in fig. 4d would be closer to the center of mass of the putter head, it would have a greater moment of inertia about a longitudinal axis through the center of mass. The connection in fig. 4c achieves the maximum putter head moment of inertia ratio as follows.

To define the distance, the x-axis (axis 1) is chosen along the length of the pusher surface (heel-toe direction); selecting the width direction (front-rear direction) along the surface of the push rod as the y-axis (axis 2); the vertical direction is chosen to be the z-axis (axis 3). The triangular solid load with the base as shown in fig. 4a has a centroid of x ═ a/3, y ═ b/3, and z ═ c/2. The ratio of the moments of inertia of the triangle to the longitudinal axis through the center of mass is given by the following equation:

I_T0/W_T＝(a²+b²)/18。

the centroid of the rectangular parallelepiped connector with the base as shown in fig. 4b is x ═ a/2, y ═ b/2, and z ═ c/2. The ratio of the moment of inertia of the cuboid to the longitudinal axis through the centroid can be given by the following equation:

I_R0/_WR＝(a²+b²)/12。

the ratio of the moment of inertia of each assembly (C ═ T or R) to the longitudinal axis through the center of mass of the putter head is given by the parallel axis theorem and by the following equation:

I_C/W_C＝I_C0/W_C+l²。

where 1 is the distance between a longitudinal axis through the center of mass of the load or attachment and a longitudinal axis through the center of mass of the putter head.

It can now be determined that the ratio of the moment of inertia of the triangular shaped load to the putter head center of mass is greater than the ratio of the moment of inertia of a rectangular shaped load of the same size and weight W to the putter head center of mass. Fig. 4e shows a triangular load (bottom right triangle "T" at base a and height b) and a rectangular load (full rectangle "R" at base a and height b) at the same position on one corner of the putter head. The centroid of the triangle is x, which is a/3, and y, which is b/3; the centroid of the rectangle is x ═ a/2, and y ═ b/2. The ratio of moments of inertia to these centroids is given by the following equation:

I_T0/W＝(a²+b²)/18，

I_R0/W＝(a²+b²)/12。

the larger the ratio of moments of inertia of the rectangle, it will be shown that this difference is greater than the portion of the triangle that can be offset away from the putter head.

FIG. 4e shows the correlation distance, whereRepresenting the distance between the origin and the triangle centroid; d represents the distance between the outside corners of the rectangle and the center of mass of the putter head. Thus, the ratio of the moment of inertia of the rectangular head to the center of mass of the putter head is given by the following equationTo obtain:

I_R/W＝I_R0/W+(D+3d/2)²＝3d²/4+(D+3d/2)²

the ratio of the moment of inertia of the triangle to the center of mass of the putter head is given by the following equation:

I_T/W＝I_T0/W+(D+2d)²＝d²/2+(D+2d)²

the difference is represented by the following formula:

I_T/W-I_R/W＝Dd+3d²/2，

the difference is always a positive number. It is confirmed above that the ratio of the moments of inertia of the triangular load is always larger than that of the rectangular load.

In confirming this conclusion, fig. 4e shows a specific geometric relationship between the load and the putter head center of mass, but this conclusion is entirely general. For any practical geometry, the difference in moments of inertia is always a positive number and approaches the values given above.

It can also be determined that the "vertical" rectangular connector in FIG. 4c achieves a greater ratio of moment of inertia to the putter head's center of mass than the "horizontal" rectangular connector of FIG. 4d, which has the same dimensions a x b x c and weight W. Referring to fig. 4, the formula for the vertical connection is as follows:

I_c/W＝a²/3+c²/12+l²-a1，

the formula for the horizontal connector is as follows:

I_d/W＝b²/3+c²/12+l²-b1。

the difference is represented by the following formula:

(I_c-I_d)/W＝(b-a)(1-a/3-b/3)。

the difference is positive for all relevant parameter values (0.125 "≦ a ≦ 0.25", 0.5 "≦ b ≦ 1", 1 ≧ 2 "), so the" vertical "rectangular connector in FIG. 4c provides a larger ratio of moments of inertia.

In a preferred embodiment, the load is selected as a triangle with base dimensions a and b selected between 0.25 "and 1", depending on the selected density and the desired weight. The height dimension is selected between 1 "and 2.5" (the maximum specified by the rules of the golf association of america) depending on the load density, the desired weight and the optimum specifications. As a new contribution, in order to achieve the maximum possible ratio of the moments of inertia, a load height close to the limit value of 2.5 "is selected. In order to ensure overall stability of the putter head, it is preferred that the length a of the short side of the connecting element is at least selected to be 0.125 "and the height b of the long side is preferably about 1".

For simplicity and economy, the panel selection should be compatible with the connection between the front loads. This choice can also minimize the resulting reduction in the total I/W value. The height of the panel member should be a minimum of 1 "to avoid a vertical miss on the golf ball. The length of the face plate must be long enough to connect the front load and, in order to comply with the american golf association rules, it is at least two-thirds of the total length. The thickness (width) of the panel should be at least 0.125 "to allow for stable impact (momentum transfer) between the club and the golf ball.

It will now be shown how three putter head elements may be combined into a complete entity having a moment of inertia ratio I/Wa as large as possible². Placing as much weight as possible as far away from the center of mass of the putter head as possible. This structure is limited by the United states Golf Association size regulations and is also a desirable and manageable appearance requirement. The specific structures to be described in this invention, including these specifications, are preferred embodiments; the particular configuration will achieve the best maximum moment of inertia ratio when using the best weight ratio as derived below. Those skilled in the art can use similar components and optimization calculations to arrive at other structures with very large ratios of moments of inertia.

The four load putter head will first be described. For a given total weight W and total length a, the structure has the largest absolute value of the moment of inertia, which is as close as possible to the theoretical limit value I ═ Wa²/2. Fig. 5a shows the general structure of the putter head 60. The total length is designated a 0; the total width is designated b 0. The American Golf club rules require b0 ≦ a0, so the best choice is b0 ≦ a 0.

Four triangular loads 62, 64, 66 and 68 are located at the four corners of the base rectangle. The length of the triangle is c1 (front loads 66, 68) and d1 (rear loads 62, 64); widths c2 and d 2. The height of the front loads 66, 68 (not shown in fig. 5 a) is c 3; the rear loads 62, 64 have a height d 3. The panel 70, as a front connector, is rectangular with a length a 1-a 0-2c1, a width (thickness) a2, and a height (not shown in fig. 5 a) a 3. The left and right connectors 72, 74 are rectangular with a length b1, a width b 2-b 0-c2-d2, and a height b3 (not shown in fig. 5 a). This is the minimum configuration required, except for a club support (not shown in figure 5 c) which can be stowed in any desired position.

This arrangement keeps the relatively heavy loads 62, 64, 66 and 68 as far as possible from the center of mass of the putter head 60 and the relatively light links 70, 72 and 74 as far as possible from the center of mass, given that the loads 62, 64, 66 and 68 and the face plate 70 must be fixed in place.

The last step in the structural specification will be performed below: values are selected for the free parameters (a0, b1, c1, etc.). These choices are determined by the following four conditions: (1) as in fig. 4c, the connections 70, 72 and 74 are oriented vertically to maximize their contribution to the total moment of inertia; (2) various component sizes are selected based on the desired overall size of the putter head 60; (3) in practical terms, the footprint of the loads 62, 64, 66 and 68 is made as small as possible and their height as large as possible to maximize their contribution to the total moment of inertia; and (4) selecting the respective weights of the front loads 66, 68 and the rear loads 62, 64 according to an optimization calculation to maximize the final total moment of inertia.

Fig. 5b shows a three load pusher head 80 with one central front load 82 and two rear loads 84, 86. The corners of the triangle may be cut away, or may be made of a low density material, or may be replaced by a bent profile to make a U-shaped connection. However, this design necessarily results in a putter head having a moment of inertia ratio that is less than the moment of inertia ratio of a four-load putter head. The three load push rod head 80 is a T-shaped design. The panel is integrated with a central front load 82 and rear triangular loads 84, 86 are located at the two rear corners of the base, this design being very novel. The surface of the aforementioned three-load pusher head is located at the other end of the base (the apex of the T). When a moment of inertia ratio is achieved that is not as great as that of the four-load head 60, the three-load putter head 80 has the advantage of a more compact front structure, yet the front load is integrated with the face plate, thereby providing a more powerful impact.

The various components of the three load push rod head 80 are sized for an overall length a0 and an overall width b 0. Optimally, as previously described: b0 ═ a 0. Each rear load 84, 86 has a length d1, a width d2, and a height (not shown in fig. 5 b) d 3. The panel, also serving as the front load 82, is a triangle with a length a1 ≧ 2b2/3, a width a2, and a height (not shown in FIG. 5 b) a 3. The rear link 88 is rectangular with a length c1 of a0-2d1, a width c2 and a height (not shown in fig. 5 b) c 3. The central link 90 is rectangular with a length of b1, a width of b 2-b 0-c2-a2, and a height (not shown in fig. 5 b) of b 3. This is the minimum configuration required, except for the club support which can be stowed in any desired position.

In view of the constraints of ideal geometry, this structure has achieved the object of: relatively heavy loads are placed as far away from the center of mass as possible and relatively light links are placed as far away from the center of mass as possible. The last step in the structural specification will be performed below: values are selected for the free parameters (a0, b1, c1, etc.). These choices are determined by the following four conditions: (1) as shown in fig. 4c, the rear connector 88 is oriented vertically; as in fig. 4d, the central links 90 are oriented horizontally to maximize their contribution to the total moment of inertia; (2) various component sizes are selected based on the desired overall size of the putter head 80; (3) in practical use, the base area of the loads 82, 84, 86 is made as small as possible and the height thereof is made as large as possible; and (4) selecting respective weights for the front and rear loads 82, 84, 86 based on optimization calculations.

Fig. 5c shows a dual load putter head 100. Basically, the load head 100 is 2/3 for the four-load pusher head shown in fig. 5a, and the same length labels can be used. The dual load putter head 100 has solid triangular loads 102, 104 at the top right and bottom left corners, respectively; and lighter connectors 106, 108, which are also stable rectangular frames, as previously described. The lower link 108 comprises the face plate of the dual load putter head 100; the lower right lightweight triangular piece 110 provides structural support. The lightweight triangular piece 110 facilitates insertion of the cue stick as indicated by the circular hole. Other possible dual load configurations are discussed below.

With respect to theoretical limitations (point-load and weightless connection), the dual-load putter head 100 has the same moment of inertia (Wa) as the four-load putter head 60²/2). However, the resulting effects of using the actual load size and the weight of the coupling are mixed: on the one hand, the dual load putter head 100 is more advantageous because there are fewer links (two, rather than three); on the other hand, however, for a given total weight, a four-load putter head 60 is more advantageous because the loads 62, 64, 66, 68 may be smaller than the loads 102, 104, and thus farther from the center of mass. The first effect increases the I/W of the dual load putter head 100 and the second effect increases the I/W of the four load putter head 60. The results prove that: the second effect dominates, so the actual four-load head 60 has a (slightly) larger ratio of moments of inertia.

The last step in the dual load head structure will be performed below: values are selected for the free parameters (a0, b1, c1, etc.). This choice is determined by the following four conditions: (1) as in fig. 4c, the connections 106, 108 are oriented vertically to maximize their contribution to the total moment of inertia; (2) selecting various component sizes according to the required total size of the push rod head; (3) in practical cases, the base area of the loads 102, 104 is made as small as possible and the height thereof is made as large as possible; and (4) selecting respective weights of the front load 104 and the rear load 102 according to an optimization calculation to maximize the final total moment of inertia.

The putter head structure shown in fig. 5 includes a simple combination of the most basic triangular shaped loads and a rectangular shaped connector. To achieve a more aesthetic and marketable appearance, these structures may be smoothed without significantly reducing their ratio of moments of inertia. Fig. 6 shows some of the many possibilities. FIG. 6a shows a smooth version of a four-load putter head 60; fig. 6b shows a smooth plate of a three-load pusher head 80. Fig. 6c shows another version of a dual load putter head 120. The dual load push rod head 120 has loads 122, 124, the loads 122, 124 being interconnected by links 126, 128 and 130. Because the links 126, 128, and 130 are farther from the center of mass, the ratio of moments of inertia for the dual-load putter head 120 is greater than that of the three-load putter head 80, but is less compact, and the ratio of moments of inertia for the dual-load putter head 120 is less than that of the four-load putter head 60. The smooth version of the dual load head 100 is similar to the smooth version of the four load pusher head 60 without the lower arm.

Fig. 7a, 7b and 7c show some other possibilities for a four-load putter head. FIGS. 7d, 7e, and 7f illustrate some other possibilities for a three load putter head; figures 8a-8f show some other possibilities for a dual load putter head. Fig. 9a is a perspective view of a four-load putter head 60; FIG. 9b provides a smooth plate of the putter head of FIG. 9 a.

For a given structure, the moment of inertia I depends on the size and density of the components involved. For simplicity, it is assumed here that only two different densities are used for each putter head: the density dh of the heavy load elements and the density dl of the light connecting elements. The ratio of moments of inertia I/W is a function of the ratio of density r dh/dl. A lightweight joint may be constructed from aluminum with a weight density of about 1.6oz/in³. Possible materials for the heavy load member include copper (dh ═ 5.3 oz/in)³) Lead (dh ═ 6.7 oz/in)³) And tungsten (dh)＝11.4oz/in³). The density ratios obtained were r-3.3, r-4.2 and r-7.1. The choice of r depends on the desired weight, size and moment of inertia of the putter head.

The first step in optimizing the putter head is to select the best parameters. Possible choices for these parameters include: a load weight ratio, a size ratio, or a density ratio. For purposes of illustration, a single parameter, s, is used, i.e., the ratio of the dimensions of the front and rear load members.

The second step is to select the component size that is not determined by the optimum variable s. These dimensions are defined by the desired size, weight, and moment of inertia of the putter head. Each choice affects the optimal value s1 for s; the part size values must be adjusted to achieve the desired weight and moment of inertia.

The third step is to represent the centroid (x(s), y (s)), the total weight w(s), the moment of inertia i(s), and the ratio f(s) ═ i (s)/w(s) as a function of s. Determining an optimal value s1 for s by solving an optimal solution of the following differential equation:

df(s)/ds＝f’(s)＝0。

for the selected density and size, this step determines the optimal values of the center of mass (x1, y1), weight W1, moment of inertia I1, and ratio f 1-f (s 1).

If the resulting weight is undesirable, the part size and/or density may be adjusted; and again optimization calculations are performed to find the required weight. Alternatively, the weight condition w(s) is adjusted to be constant, and the weight condition w(s) is solved simultaneously with f'(s) being 0.

As a first example of the optimization step described above and the resulting moment of inertia value, consider a four-load putter head 60. The overall dimension of the base rectangle is ab0 ═ a0 ═ b 0. Heel-toe sizes a1, b1, etc.; anterior-posterior dimensions a2, b2, etc.; the vertical dimensions are a3, b3, etc. The thickness of connectors 70, 72, and 74 is selected to be a2 ═ b1 ═ b 1/8 ═ 0.125 ″, and the height a3 ═ b3 ═ 1 ″. The parameter ab0 may vary between 4 "and 7" (the maximum permitted by the golf Association); the load/connector density ratio r varies between 3 (e.g., copper/aluminum) and 7 (e.g., tungsten/aluminum). The optimum variable s is selected as c3/d3, which is the ratio of the front load to the rear load height. The rear load height d3 is selected from between 1 "and 2.5" (the maximum allowed by the golf association of america). The load base size (cd12 ═ c1 ═ c2 ═ d1 ═ d2) was chosen between 0.5 "and 1" to maintain a total weight between 11oz and 17 oz.

Table 1 gives the results of the optimization calculations for the above partial selection of a four load putter head:

TABLE 1

In the first row of data, the overall size of the putter head substrate is 7 "by 7"; the density ratio is r-3. The load triangle has a base of 1 "× 1"; the height of the rear load is also 1 ". The optimization calculation gives s1 ═ 0.986, and therefore the height of the front load is also 1 ″ (c3 ═ s1 ═ d3 ═ 0.99 "). Because the four-load putter head is left-right symmetric, the center of mass position is 3.5 "at x 1in the heel-toe direction. In the anterior-posterior direction, the centroid position is y1 ═ 3.24 ″. Value of I/W18.6 in²Has been much larger than any of the putter heads previously disclosed and is quite close to the theoretical limit of 24.5in for a 7 "putter head². In the same way, I/Wa²The value of (a) 0.38 is very large and is close to its theoretical limit value of 0.50. The putter head weight W is 12.5oz, but the weight can be adjusted to any desired value without changing I/W.

By choosing a smaller load floor, the I/W value can be further reduced. This moves the center of mass of the load away from the putter head center of mass, thereby increasing the moment of inertia. This can be done in two ways: can increase the load heightDegree d3, c3, and/or load density r. The next two rows in table 1 show the effect of increasing d 3. Without changing the weight of the putter head, d3 was increased to 1.5 ", cd12 was decreased to 13/16", and I/W was increased to 19.1in². Adding d3 to the american golf association defined 2.5 "is undesirable because the corresponding best choice for c3 would be greater than the limit of 2.5", but setting d3 to 2.4 ", cd12 to 5/8" to 0.625 "would give a regulatory compliance value of c3 to 2.43" and increase I/W to 19.6in²。

The next few rows in table 1 show the effect of increasing r. R is increased to 5 and then to 7 while decreasing cd12 to maintain reasonable weight W, increasing the ratio of moments of inertia for each choice of d 3. When r and d3 are both increased, the ratio of moments of inertia is further increased. When the maximum density ratio r is 7 and the maximum load height d3 is 2.4 ″, the maximum value of I/W is 20.6in²。

Already considerable I/W values can be further increased by fine-tuning the individual loads and the dimensions of the connections. This can easily make the I/W value exceed 21in²Corresponding I/Wa²The value may exceed 0.43. Even moments of inertia near these values have never been obtained before. Of course, when the putter head size is 7 "x 2.5", the size, while meeting the American Golf Association rules, is larger than the ideal range for most golfers. However, the method described in this embodiment gives the maximum possible moment of inertia ratio for a putter head of any desired size. The remaining rows in table 1 show this.

It can be seen from the table that as ab0 decreases to 6 ", 5" or 4 ", the maximum value of I/W decreases to 15.1in (when r is 7, d3 is 2.4" -2.5 "), respectively²、10.4in²、6.5in²And I/Wa²Respectively from 4.2 to 4.1. These values are more than three times greater than previously disclosed putter heads of the same size.

The optimal calculation and moment of inertia estimation for a dual load putter head will be considered below. The double load configuration has fewer connections, which increases the I/W. However, for a given total weight, the loads must be greater because their number is smaller which reduces the I/W. The result is that the latter effect will prevail. Thus, for a given size and weight, the I/W will be less than that of a four-load configuration.

Fig. 5c shows a double load configuration, which is of the same sign as the four load configuration. As described above, the fixed sizes are selected from a2 ═ b1 ═ 1/8 ″, a3 ═ b3 ═ 1 ″, and c1 ═ c2 ═ 5/8 ″. As described above, I is the same as the above, and the optimal parameter is s-c 3/d 3. The results of the optimization calculations for the respective values of ab0, r, d12, and d3 are shown in table 2 below. Because the putter head is no longer left-right symmetric, the coordinates of the center of mass (x1, y1) are now given. It can be seen that the I/W value is 3% to 4.5% less than that of the four-load putter head. According to c3 being less than 2.5 "of the United states Golf Association definition requirement, the maximum selection value of d3 is defined.

TABLE 2

Consider the construction of a three load putter head. The above are of two different types: the U-shape is shown in fig. 5 d; the T-shape is shown in fig. 5 b. Consider first a U-shaped putter head. As mentioned above, the fixed dimension is a2 ═ b1 ═ 1/8 ═ a3 ═ b3 ═ 1 ″, and the thickness of the front load is fixed at e2 ═ 1/8 ″. The optimum parameter is chosen as the front load to rear load width ratio s-e 2/d 2. The results of the optimization calculations when ab0, r 3 and 7, e3, 1 and 0.5, and d3, 1 and 2.5 are given in table 3. The rear load base size d 1-d 2-d 12 was adjusted to give reasonable weight. It can be seen that the I/W value is 13% to 15% less than that of the four load putter head, but still much greater than that of the prior art.

TABLE 3

A final example is a T-type triple load structure. As mentioned above, the fixed dimensions are selected as: a3 ═ b1 ═ c3 ═ 1 ═ b3 ═ c2 ═ 1/8 ″. Putter head size ab0 varies between 4 "and 7"; the density ratio r is 3 or 7; the rear load height is 1 "or 2.5". The length of the front surface a1 of the front load is selected to be 2a 0/3; the minimum surface length conforms to the american golf association rules. I this length is chosen to be as small as possible, since this configuration has the advantage over the above-described configurations of being more compact in size. Again the optimum parameter is chosen as the front load to rear load width ratio s-a 2/d 2. The rear load base dimension d12 is adjusted again to give reasonable weight. Table 4 gives the results of the optimization calculations:

TABLE 4

The maximum value of I/W again corresponds to the larger dimension ab0 and the larger density ratio r. For a given size and density, the maximum value corresponds to the maximum rear load height d 3. It can be seen that the I/W value is 20% to 21% less than that of the four-load putter head, but still much greater than that of the prior art.

Table 5 summarizes the results above and provides the I/W values for the four lengths (7 ", 6", 5 "and 4") for the four putter head types.

Type/length	7	6	5	4
					4S	20.6	15.1	10.4	6.5

2L	20.0	14.6	10.0	6.2
					3U	18.0	13.0	8.8	5.6
3T	16.2	11.9	8.2	5.2

TABLE 5

For various putter head lengths (4 ', 5', 6 ', and 7') and four putter head types (four load square 4S, double load L type 2L, triple load U type 3U, and triple load T type 3T), the moment of inertia ratio I/W (in units of in) is shown²) The maximum resulting value of (c). For each putter head type, the I/W value decreases as the putter head size a decreases; the I/W value for the quad-load square configuration is greatest for each putter head type; the I/W value of the triple load T-shaped structure is the minimum. The magnitude of the reduction in I/W with size is much greater than the magnitude of the reduction in I/W with putter head type. The resulting I/W value is much greater for all sizes and types than for all known art or commercially available push rods.

For each putter head type, the I/W value is associated with a²Is approximately proportional, therefore, when the I/W value is divided by a²Its solution is approximately constant. For these same putter head types and sizes, I/Wa is given in Table 6²The value is obtained. For each putter head type, it can be seen that I/Wa²The percentage of change in the value was small.

TABLE 6

Fig. 11 graphically illustrates the data in table 5. The highest curve in the figure gives the theoretical maximum possible value of I/W a2/2 for a four-load putter head. The next two curves correspond to a four load putter head and a dual load putter head. The fourth curve gives the theoretical maximum possible I/W values 25a2/64 for a three-load putter head; the two lowest curves correspond to the three-load U-shaped push rod head and the three-load T-shaped push rod head respectively. The resulting value for each putter head type is as close as possible to the theoretical upper limit. The prior art putter heads have a ratio of moments of inertia that is even far from these resulting values.

The data shown in tables 1 to 6 and the curves in fig. 11 enable each golfer to select a desired putter head size and type from the construction described in the embodiments of the present invention. The choice made can be determined by the ratio of I/W to size in fig. 11. Each golfer may select an appropriate standard in one of two ways, the golfer may specify the maximum putter head size that he or she is most comfortable with, or the golfer may specify the minimum I/W value that he or she deems necessary. The size criteria are based on the appearance and feel desired by the golfer, while the moment of inertia criteria are based on the magnitude of the eccentricity errors typically made by the golfer. The greater the miss, the greater the moment of inertia required to control the ball strike (putt). The desired putter head weight W for a golfer determines the ratio of moment of inertia I/W for that golfer.

Fig. 12 is similar to fig. 11, but with the theoretical four load putter head and four load putter head curves removed.

To illustrate this step, assume that a golfer needs 11 in²The ratio of the moments of inertia of the ball to control off-center ball hitting errors. Through 11 in FIG. 12²The intersection of the horizontal line at which the putter head intersects the appropriate curve gives the minimum length of the putter head. Thus, a golfer may use a four-load putter head having a size a of 5.1 ", a two-load putter head having a size a of 5.2", a three-load U-type putter head having a size a of 5.5 ", and a three-load T-type putter head having a size a of 5.8". Which selection is made depends on the size and shape of the putter head that the golfer feels most comfortable.

Alternatively, assume that the golfer does not want to use a putter head having a dimension a greater than 5.5 ". The feasible range of maximum moment of inertia ratios for this golfer is determined by the intersection of the 5.5 "vertical line with the appropriate curve in fig. 12. Therefore, the golfer can use I/W12.5 in²Four loads ofPush rod head with I/W of 12.25 in²I/W of the double-load push rod head is 10.75 in²Three-load U-shaped push rod head or I/W (9.75 in)²The three-load T-shaped push rod head. Which selection is made depends on the ratio of moments of inertia required by the golfer to control the off-center hitting fault.

The putter head described in this embodiment provides the maximum possible moment of inertia for the golfer, whatever the golfer desires. If the golfer has the highest size requirements, the vertical line in FIG. 12 can be used or the data in Table 5 can be used to select the appropriate moment of inertia value. If the golfer's requirements for moment of inertia are highest, the appropriate length value can be selected using the horizontal lines in FIG. 12 or using the data in Table 7 below.

type/IW	7	11	15	19
					4S	4.07	5.11	5.97	6.72
2L	4.13	5.19	6.07	6.83
					3U	4.38	5.49	6.41	＞7
3T	4.59	5.75	6.73	＞7

TABLE 7

For example, if the golfer requires I/W7 in²A 4S putter head with a 4.1 "or a 3T putter head with a 4.6" etc. may be used. Conversely, if the player uses a conventional putter head, the size would be 6 "or 7". If the golfer requires I/W11 in²A 4S putter head with an a-5.1 "or a 3T putter head with an a-5.75" may be used. Conversely, if a player wants to use a conventional putter head, then nothing will be found to be usable. (none of the conventional putter heads provide 11 in all of the dimensions specified by the United states Golf Association²Large ratio of moments of inertia. These considerations demonstrate the important advantages of the putter head disclosed in this embodiment. They provide the maximum moment of inertia for a given weight and size; or, equivalently, a putter head of minimum size is provided for a given weight and moment of inertia.

The same applies to larger values of I/W. As an extreme case, if I/W19 in is required²(the golfer hits the ball several inches off center), then the putter head selection range is limited to 6.A 7 "4S putter head or a 6.8" 2L putter head. The three-load putter head requires a size exceeding 7 "as defined by the american golf association, whereas the conventional putter head would require a size exceeding 10".

The putter head data with the largest ratio of moments of inertia is shown in the tables and graphs for each putter head type. The maximum I/W value is obtained using a load height of 2.5 "or a height close to the maximum specified by the American Golf Association rules, and using a load density as large as possible under the circumstances of use. If a smaller load height is selected, the method disclosed in this embodiment can be used to design a putter head having the greatest ratio of moment of inertia for a given putter head length and load height.

The large inertia moment ratio disclosed by the embodiment of the invention is obtained by adopting the following principle: 1) because of the putter head load and connector arrangement and shape, the putter head load and connector are as far from the putter head center of mass as possible; 2) because of the putter head load and the size and shape of the connector, the putter head load should be as heavy as possible and the connector as light as possible; and 3) the load-to-weight ratio is preferably determined by a mathematical maximization calculation.

The embodiments of the principles disclosed above illustrate these principles. Those skilled in the art can readily utilize these principles to design larger moment of inertia putter heads having a variety of different sizes, shapes, densities, and appearances. Similarly, it is also easy to integrate conventional elements such as a rake surface to assist in lifting the golf ball, a corrugated surface to provide more friction and spin, an embedded elastomer to provide better feel, an (adjustable) club support, and a visible line to indicate the position of the center of mass (the last element is not actually necessary due to the large moment of inertia). Figure 10 shows a prototype of a four-load push rod.

Structural ratio of push rod with large inertia moment

1. The connectors have a relatively low density, e.g., 1.6oz/in³(aluminum); the load elements having a relatively high density, e.g. 5.3oz/in³(copper) and11.6oz/in³(tungsten). Thus, the density ratio varied from 3.3 to 7.3.

2. The height of the load is much greater than the width, preferably a height of approximately 2.5 "as defined by the United states Golf Association and a width of 0.5" to 0.75 ". The ratio of the height h to the width d of the load is at least 3, preferably about 5.

3. Preferably, the base of the putter head is square (side a), with the four loads of the putter head placed at the four corners; the loads for the dual load putter head are placed at two opposite corners or the loads for the triple load putter head are placed at two rear corners and the center of the front. Preferably, the angular load is substantially a regular triangle with regular sides of equal length d. Preferably, the width d is about 0.5 ", so that the ratio of the base width a to the load width d is about 8 when a is 4" and about 14 when a is 7 ".

4. With as few connectors as possible (three for a four-load putter head and a three-load putter head; two for a dual-load putter head), the connectors are placed on the perimeter of the putter head base. The height of the connector is much greater than the width, and for stability, the height is about 1 "and the width is about 1/8". Thus, the aspect ratio of the connector is at least about 8.

5. The total weight wc of the (aluminum) connector is about a x (0.6oz/in), and the total weight of the putter head is typically about W-12 oz. Thus, the ratio of wc to W is about a/20 ", when a is 4", wc/W is 0.20; when a is 7 ", wc/W is 0.35.

6. The ratio of the front load weight w1 to the rear load weight w2 is s-w 1/w2, so that the moment of inertia ratio f(s) -I/Wa²Is the largest. That is, s is a solution where df/ds is 0. This ratio varies between 1.0 and 1.5 depending on the size and configuration of the putter head.

Certain modifications of the invention have been discussed above. Other modifications to the present invention are possible to those skilled in the art. Accordingly, the description of the present invention is for illustrative purposes only to enable those skilled in the art to best practice the present invention. Various modifications may be made in the details of the invention without departing from the spirit thereof, and it is intended to cover all such modifications as fall within the scope of the appended claims.

Claims (35)

1. A putter head for a putter, comprising:

a toe portion;

a heel portion;

a front portion for striking a golf ball;

a rear portion opposite the front portion;

a length a between the heel and toe;

a width b between the front and rear portions;

a weight W;

moment of inertia, I, for the putter head mass center longitudinal axis;

wherein, I/Wa²Greater than 0.30.

2. The putter head of claim 1 wherein a is less than or equal to the maximum allowable american association for professional golf club tournaments and b is less than or equal to a.

3. The putter head of claim 1 wherein said I/Wa²Greater than 0.40.

4. The putter head of claim 1 further comprising: a plurality of loads interconnected by at least one connecting member; wherein the load has a load density and the connection has a connection density, the ratio of the load density to the connection density being between 3 and 8.

5. The putter head of claim 1 further comprising: a plurality of loads interconnected by at least one connecting member; wherein each load has a load width and a load height, the ratio of the load height to the load width being at least 3.

6. The putter head of claim 1 further comprising: a plurality of loads interconnected by at least one connecting member; wherein each of said loads has a load width, and the ratio of said width b to said load width is at least 8.

7. The putter head of claim 1 further comprising: a plurality of loads interconnected by a plurality of connectors; wherein all of the connectors are disposed on a periphery of the putter head.

8. The putter head of claim 1 having a rectangular shape with loads disposed on two or more corners of the rectangular shape.

9. The putter head of claim 8 further comprising: a vertically oriented link connected to the load.

10. The putter head of claim 1 having a triangular shape with loads disposed on two or more corners of the rectangular shape.

11. The putter head of claim 10 further comprising: a vertically oriented link connecting the loads.

12. The putter head of claim 1 having a T-shape with a load disposed at two or more arm ends of the T-shape.

13. The putter head of claim 12 wherein the loads include at least two rear loads and a front load; the putter head further includes:

at least one vertically oriented link connecting the rear load; and

at least one horizontally oriented link connecting the vertically oriented link to the front load.

14. The putter head of claim 1 having a U-shape with a load disposed at two or more arm ends of the U-shape.

15. The putter head of claim 14 further comprising: a vertically oriented link connecting the loads.

16. The putter head of claim 1 further comprising:

a first load disposed on the front portion of the putter head; and

a second load disposed on the rear portion of the putter head;

wherein the first load has a first weight and the second load has a second weight, and the ratio of the first weight to the second weight is between 1.0 and 1.5 inclusive.

17. The putter head of claim 1 further including:

a total of four loads; wherein each of said loads is disposed at a respective corner of a generally square shape, each of said loads having a generally triangular base and a height, said height being less than or equal to 2.5 inches; and

a connector connecting the four loads to each other; wherein each link is vertically oriented, has a length l, a height h, a width w, l > h > w, and the length l of each link extends between a corresponding pair of the loads.

18. The putter head of claim 8 wherein w is equal to 0.125 inches and h is equal to 1 inch.

19. The putter head of claim 1 further including:

a total of three loads; wherein two of the three loads are located on respective corners of the rear portion, a third of the three loads is located on the front portion of the putter head, each of the rear loads having a generally triangular base and a height, the height being less than or equal to 2.5 inches; and

a connecting member connecting the three loads to each other; wherein each link is vertically oriented, having a length l, a height h, a width w, l > h > w, the length l of one of the links extending in the two rear loads.

20. The putter head of claim 19 wherein w is equal to 0.125 inches and h is equal to 1 inch.

21. The putter head of claim 1 further including:

two loads in total; wherein one of the two loads is located at a corner of a rear of one of the heel and the toe and the other of the two loads is located at a corner of a front of the other of the heel and the toe, each of the loads having a generally triangular base and a height, the height being less than or equal to 2.5 inches; and

a connecting member connecting the two loads to each other; each connecting piece is in a vertical orientation and has a length l, a height h and a width w, wherein l is larger than h and larger than w, and one end of the length l is connected with a corresponding load.

22. The putter head of claim 21 wherein w is equal to 0.125 inches and h is equal to 1 inch.

23. The putter head of claim 1 wherein a is less than or equal to 7 inches and b is less than or equal to a.

24. A putter, comprising:

a shaft; and

a putter head engaged with the club; wherein the putter head includes: striking the front of the golf ball during putting; length a, width b, weight W, moment of inertia I; the width b is along the length of the putter headThe front portions extend along vertically intersecting horizontal width axes; the length a extends along a horizontal length axis that perpendicularly intersects the horizontal axis; a is less than or equal to 7 inches, b is less than or equal to a, and I/Wa²Greater than 0.30.

25. The putter head of claim 24 wherein said I/Wa²Greater than 0.40.

26. The putter head of claim 24 further comprising: a plurality of loads interconnected by at least one connecting member; wherein:

the load has a load density and the connection has a connection density, the ratio of the load density to the connection density being between 3 and 8;

each of said loads having a load width and a load height, the ratio of said load height to said load width being at least 3;

the ratio of the width b to the load width is at least 8; and

a first load is disposed at the front portion having a first weight and a second load is disposed at the rear portion having a second weight, the ratio of the first weight to the second weight being between 1.0 and 1.5, inclusive.

27. The putter head of claim 24 further comprising:

a total of four loads; wherein each of the loads is disposed at a respective corner of the generally square shape, each of the loads having a generally triangular base and a height, the height being less than or equal to 2.5 inches; and

a connector connecting the four loads to each other; wherein each link is vertically oriented, has a length l, a height h, a width w, l > h > w, the length l of each link extends between a corresponding pair of the loads, w equals 0.125 inches, and h equals 1 inch.

28. The putter head of claim 24 further comprising:

a total of three loads; wherein two of the three loads are located on respective corners of the rear portion, a third of the three loads is located on the front portion of the putter head, each of the rear loads having a generally triangular base and a height, the height being less than or equal to 2.5 inches; and

a connecting member connecting the three loads to each other; wherein each link is vertically oriented, has a length l, a height h, a width w, l > h > w, the length l of each link extends between a corresponding pair of the loads, w equals 0.125 inches, and h equals 1 inch.

29. The putter head of claim 24 further comprising:

two loads in total; wherein one of the two loads is located at a corner of a rear of one of the heel and the toe and the other of the two loads is located at a corner of a front of the other of the heel and the toe, each of the loads having a generally triangular base and a height, the height being less than or equal to 2.5 inches; and

a connecting member connecting the two loads to each other; wherein each connector is vertically oriented, has a length l, a height h, a width w, l > h > w, one end of the length l connects to a corresponding load, w equals 0.125 inches, and h equals 1 inch.

30. A method of designing a putter head for a putter, comprising:

a) selecting an optimal parameter op for the putter head;

b) selecting a size and/or density for the putter head that is not determined by the optimal parameters op;

c) expressing the center of mass com (op), the total weight w (op), the moment of inertia i (op), and the ratio f (op) i (op)/w (op) as a function of op;

d) the optimal value of op is determined from the solution of the following differential equation:

df (op)/dop ═ f' (op) ═ 0; and

e) and determining the optimal values of the center of mass COM, the weight W and the inertia moment I according to the optimal value op.

31. The method of claim 30, further comprising: modifying at least one of said size and/or said density when said weight W is undesirable, thereby repeating said steps a) -e).

32. The method of claim 30, further comprising: when the weight W is not satisfactory, the weight conditions can be solved: w (op) ═ constant, and f' (op) ═ 0.

33. The method of claim 30, wherein the putter head includes a front load and a rear load; the optimal parameter op comprises a weight ratio of the front load to the rear load.

34. The method of claim 30, wherein the putter head includes a front load and a rear load; the optimal parameter op comprises a size ratio of the front load to the rear load.

35. The method of claim 30, wherein the putter head includes a load and a connector to connect the load; the optimal parameter op comprises the ratio of the load to the density of the connection.