CN116850561A

CN116850561A - Golf club body system and golf club body

Info

Publication number: CN116850561A
Application number: CN202310956799.0A
Authority: CN
Inventors: B·亚当斯; B·菲利普; J·霍尔斯特德; R·史蒂芬斯; T·纳皮尔
Original assignee: Breakthrough Golf Technology LLC
Current assignee: Breakthrough Golf Technology LLC
Priority date: 2019-12-19
Filing date: 2020-11-24
Publication date: 2023-10-10
Also published as: CN114867534A; CN114867534B; KR20220098035A; WO2021126486A1

Abstract

A golf club shaft system and golf club shaft having unique bending and torsional stiffness profiles while providing significant adjustability to fine tune the shaft for a particular golf swing.

Description

Golf club body system and golf club body

Technical Field

The present invention relates to sports equipment, and in particular to a golf club shaft.

Background

During a golf swing, the club shaft is loaded and tends to experience significant deflection and torsional rotation. It is rarely appreciated that such deflection and rotation may also occur during putting strokes, particularly as the mass of the putter head increases, but only then deflection and rotation are much smaller. As used herein, "stability" of a shaft refers to the extent to which the toe and heel portions of the face are moved in alignment with each other during a ball strike. The relative fluctuations in speed and acceleration of the toe and heel of the face before, during and after impact can be significantly improved. Controlling the face angle and face twist allows a narrower range of angles of departure for the ball from the face and significantly increases the likelihood that the ball will leave the face at an angle closer to the target line, which increases the likelihood of putting while putting.

While driver shafts, fairway metal shafts and hybrid shafts have evolved from steel pipes to a wide variety of often complex composite shafts over the past 30 years, putter shafts have not evolved rapidly. Serious golfers do not believe that their driver may perform best with inexpensive steel shafts. Serious players, when better chosen, would believe that their putters are best suited for use with inexpensive steel shafts? After all, the putter is used almost twice as much as any other club in the bag. Most conventional putter shafts are simply steel tubes (wrapped and welded constructions) and contain little engineering aspects tailored to the unique circumstances of the putter. The tips of these putter shafts are very narrow and become increasingly larger in diameter at the root end for gripping purposes, thus presenting an inherent weakness in the lower portion of the shaft. Finally, the reason for the continued mainstream of steel shafts is the cost: the push rod manufacturer mainly uses a steel shaft because the steel shaft is very inexpensive.

The present invention provides a significant advancement in tailoring the putter, but is equally applicable to all golf club shafts. Indeed, embodiments of the present invention enable a golfer or professional gym to easily adjust the characteristics of a putter or any other club to suit an individual's golf swing.

Disclosure of Invention

A golf club body having a heel portion joined to a toe portion by a coupler and possessing a unique relationship including a stiffness relationship that provides beneficial performance characteristics, including improved stability and adjustability.

Drawings

Without limiting the scope of the invention as claimed below, reference is now made to the drawings and figures:

FIG. 1 illustrates a front view of a golf club, not to scale;

FIG. 2 illustrates, not to scale, a perspective view of one embodiment of a golf club body;

FIG. 3 illustrates, not to scale, an exploded perspective view of one embodiment of a golf club body;

FIG. 4 illustrates, not to scale, a perspective cross-sectional view of one embodiment of a golf club shaft;

FIG. 5 (A) shows a side view, not to scale, of one embodiment of a tip portion;

FIG. 5 (B) shows an end view of one embodiment of the tip portion, not to scale;

FIG. 6 (A) shows a side view, not to scale, of one embodiment of a root portion;

FIG. 6 (B) shows an end view of one embodiment of the root portion, not to scale;

FIG. 7 (A) shows a side view, not to scale, of one embodiment of a root portion insert;

FIG. 7 (B) shows an end view of one embodiment of the root portion insert, not to scale;

FIG. 8 (A) shows a side view, not to scale, of one embodiment of a coupling;

FIG. 8 (B) is a side view of an embodiment of a coupling, not to scale;

FIG. 9 is a graph, not to scale, illustrating a shaft hardness profile of one embodiment of a golf club shaft;

FIG. 10 is a graph, not to scale, illustrating a shaft hardness profile of one embodiment of a golf club shaft;

FIG. 11 is a graph, not to scale, illustrating a shaft hardness profile of one embodiment of a golf club shaft;

FIG. 12 is a graph, not to scale, showing the shaft hardness distribution of a conventional step golf steel shaft;

FIG. 13 (A) is a chart, not to scale, showing heel and toe speeds of a putter head when a putter hits a ball;

FIG. 13 (B) is a chart, not to scale, showing heel and toe accelerations of the putter head when a putter hits a ball;

FIG. 14 (A) is a table not to scale showing heel and toe speeds of the putter head when a putter hits a ball;

FIG. 14 (B) is a chart, not to scale, showing heel and toe accelerations of the putter head when a putter hits a ball;

FIG. 15 illustrates, not to scale, an exploded perspective view of one embodiment of a golf club shaft system;

FIG. 16 illustrates, not to scale, a perspective view of one embodiment of a golf club shaft;

FIG. 17 illustrates a side view, not to scale, of one embodiment of a tip portion;

FIG. 18 is a diagram, not to scale, illustrating different tip portion characteristics in one embodiment;

FIG. 19 (A) is a graph not to scale showing the shaft hardness distribution of one embodiment of the tip portion, wherein the units of the vertical axis are N m ² The units of the horizontal axis are inches;

fig. 19 (B) is a graph not to scale showing a shaft hardness distribution of one embodiment of the tip portion, wherein the unit of the vertical axis is n×m ² The units of the horizontal axis are inches;

FIG. 19 (C) is a graph not to scale showing the shaft hardness distribution of the tip portion of an embodiment, wherein the units of the vertical axis are N m ² The units of the horizontal axis are inches;

fig. 19 (D) is a graph not to scale showing the shaft hardness distribution of the tip portion embodiment, wherein the unit of the vertical axis is n×m ² The units of the horizontal axis are inches;

FIG. 20 is a table showing, not to scale, the shaft hardness distribution of an embodiment of the tip portion;

FIG. 21 shows a partial cross-sectional view of an embodiment of a coupling, not to scale;

FIG. 22 illustrates, not to scale, a partial cross-sectional view of an embodiment of a coupling;

FIG. 23 (A) is a graph not to scale showing a shaft hardness distribution of one embodiment of the tip portion, wherein the units of the vertical axis are N m ² The units of the horizontal axis are inches;

FIG. 23 (B) is a graph not to scale showing a shaft hardness distribution of one embodiment of the tip portion, wherein the units of the vertical axis are N m ² The units of the horizontal axis are inches;

FIG. 23 (C) is a graph not to scale showing a shaft hardness distribution of one embodiment of the tip portion, wherein the units of the vertical axis are N m ² The units of the horizontal axis are inches;

FIG. 23 (D) is a graph not to scale showing a shaft hardness distribution of one embodiment of the tip portion, wherein the units of the vertical axis are N m ² The units of the horizontal axis are inches;

fig. 24 is a graph, not to scale, showing a shaft hardness profile of one embodiment of a tip portion, where the vertical axis is in units of N x m ² The units of the horizontal axis are inches; and

fig. 25 is a graph, not to scale, showing a shaft hardness profile of one embodiment of a tip portion, where the vertical axis is in units of N x m ² The units of the horizontal axis are inches.

These drawings are provided to assist in understanding the exemplary embodiments of the invention as described in more detail below and should not be construed as unduly limiting the invention. In particular, the relative spacing, positioning, sizes, and dimensions of various elements shown in the drawings are not to scale and may be exaggerated, reduced, or otherwise modified for clarity. Those skilled in the art will also appreciate that a range of alternative configurations have been omitted, simply to improve clarity and reduce the number of figures.

Detailed Description

The detailed description set forth below in connection with the appended drawings is intended as a description of the presently preferred embodiments of the invention and is not intended to represent the only forms in which the present invention may be practiced or utilized. The description sets forth the designs, functions, devices, and methods of implementing the invention in connection with the illustrated embodiments. It is to be understood, however, that the same or equivalent functions and features may be accomplished by different embodiments that are also intended to be encompassed within the spirit and scope of the invention.

As shown in fig. 1-8 (B), an embodiment of a shaft 100 of the present invention includes a distal shaft end 110, a proximal shaft end 120, an outer shaft diameter, and a shaft mass, with each point along the length 130 of the shaft having a shaft bending stiffness (commonly abbreviated as EI) and a shaft torsional stiffness (commonly abbreviated as GJ). The shaft 100 may include a root portion 1000 joined to the tip portion 2000 by a coupler 3000, wherein the coupler 3000 may permanently or releasably attach the root portion 1000 to the tip portion 2000. It must be understood that the shaft bending stiffness and shaft torsional stiffness may be taken at points along the shaft length 100 that take into account the area of the shaft 100 that is made up of multiple elements in a cross-section taken perpendicular to the shaft axis, whereas the bending stiffness and torsional stiffness of a particular element disclosed later is associated with only that particular element and not with the combination of elements that may make up the shaft 100.

Referring specifically to fig. 6 (a) and 6 (B), root portion 1000 has a root portion distal end 1010, a root portion proximal end 1020, a root portion length 1030, a root portion sidewall 1040 having a root portion sidewall thickness 1050, a root portion inner diameter 1060, and a root portion outer diameter 1070. Similarly, referring specifically to fig. 5 (a) and 5 (B), tip portion 2000 has a tip portion distal end 2010, a tip portion proximal end 2020, a tip portion length 2030, a tip portion sidewall 2040 having a tip portion sidewall thickness 2050, a tip portion inner diameter 2060, and a tip portion outer diameter 2070. In some embodiments, tip portion length 2030 is no longer than 65% of root portion length 1030, while in some additional embodiments, at least a portion of tip portion 200 has a tip portion outer diameter 2070 that is at least 25% smaller than root portion outer diameter 1070 of a portion of root portion 1000. Further, with particular reference to fig. 8 (a) and 8 (B), the coupler 3000 has a coupler distal end 3010, a coupler proximal end 3020, a coupler length 3030, a coupler sidewall 3040 having a coupler sidewall thickness 3050, a coupler inner diameter 3060, and a coupler outer diameter 3070. In one particular embodiment, at least a portion of root portion 1000 has a root portion sidewall thickness 1050 that is greater than a tip portion sidewall thickness 2050 of a portion of tip portion 2000, while in another embodiment root portion sidewall thickness 1050 is at least 15% thicker than tip portion sidewall thickness 2050, and in yet another embodiment root portion sidewall thickness 1050 is at least 25% thicker than tip portion sidewall thickness 2050.

Root portion sidewall thickness 1050 is not greater than 0.125 "in one embodiment, not greater than 0.100" in another embodiment, and not greater than 0.085 "in yet another embodiment. Another series of embodiments incorporate a minimum root portion sidewall thickness 1050 of at least 0.020", in another embodiment at least 0.025", and in yet another embodiment at least 0.030". In one particularly useful embodiment, the maximum tip portion sidewall thickness 2050 is greater than the maximum root portion sidewall thickness 1050, in one embodiment at least 0.005 "greater, in another embodiment at least 0.015" greater, and in yet another embodiment at least 0.020 "greater. The maximum tip portion sidewall thickness 2050 is preferably no greater than 0.125 "in one embodiment, no greater than 0.100" in another embodiment, and no greater than 0.080 "in yet another embodiment. Root portion sidewall thickness 1050 and/or tip portion sidewall thickness 2050 may vary along the length. In one embodiment, root portion sidewall thickness 1050 increases to a maximum thickness that is within a distance from root portion proximal end 1020 equal to twice coupler length 3030, and in another embodiment, within a distance of 6 "from root portion proximal end 1020. In another embodiment, root portion side thickness 1050 changes from a minimum thickness to a maximum thickness that is at least 5% thicker than the minimum thickness, in another embodiment at least 10% thicker, and in yet another embodiment at least 15% thicker. Similarly, in a similar series of embodiments, tip portion sidewall thickness 2050 varies from a minimum thickness to a maximum thickness that is at least 5% thicker than the minimum thickness, in another embodiment at least 10% thicker, and in yet another embodiment at least 15% thicker.

In another embodiment, the average coupler sidewall thickness 3050 of the entire coupler length 3030 is greater than the average root portion sidewall thickness 1050, while in yet another embodiment, the average coupler sidewall thickness 3050 is greater than the average tip portion sidewall thickness 2050. In yet another embodiment, the average coupler sidewall thickness 3050 is at least 15% thicker than the average root portion sidewall thickness 1050, and in yet another embodiment, the average coupler sidewall thickness 3050 is at least 15% thicker than the average tip portion sidewall thickness 2050.

In some embodiments, the root portion 1000 is formed from a non-metallic root portion material 1000 having a root material density, a root portion mass of 35% -75% of the shaft mass, a root portion elastic modulus, and a root portion shear modulus, and has a root portion area moment of inertia, a root portion polar moment of inertia, a root portion bending stiffness, and a root portion torsional stiffness at each point along the root portion length 1030. The density of root portion 1000 may be constant or may vary all the way along root portion length 1030. Also, in some additional embodiments, the tip portion 2000 is formed from a metallic tip portion material having a tip material density, a tip portion elastic modulus, and a tip portion shear modulus that are at least 15% greater than the root material density, and each point along the tip portion length 2030 has a tip portion area moment of inertia, a tip portion polar moment of inertia, a tip portion bending stiffness that is less than the root portion bending stiffness in some embodiments, and a tip portion torsional stiffness that is less than the root portion torsional stiffness in some embodiments.

The materials, densities, masses, stiffness, inflection point distances, shaft CG distance, and shaft length relationships disclosed herein are each and in combination critical to the feel, flexibility, and stability of the shaft 100, producing unexpected benefits when striking a golf ball with a golf club head 5000 attached to the shaft 100. These relationships result in less face distortion before, during and after impact and improve the consistency of face velocity with heel and toe accelerations, as will be explained in more detail below with reference to fig. 14 (a) and 14 (B) and fig. 13 (a) and 13 (B). Those skilled in the art will appreciate that during a swing, the golf club body is loaded and there is significant deflection and torsional rotation, however, little is appreciated that such deflection and rotation may also occur during putting, particularly as the mass of the putter head increases, but only then deflection and rotation is much less. As used herein, "stability" of a shaft refers to the extent to which the toe and heel portions of the face are moved in alignment with each other during a ball strike. These relationships can significantly improve the relative fluctuations in speed and acceleration of the toe and heel of the face before, during and after impact. For example, controlling the face angle and face twist results in a smaller angle of departure of the ball from the face and significantly increases the likelihood that the ball will leave the face at an angle closer to the target line, which increases the likelihood of putting when putting. Tests have shown that, depending on the type of putter used and the type of shot, the putting angle is reduced by 20% -33% without affecting the feel at and after the shot. Additionally, these relationships result in lower launch angles of the ball as it leaves the face, especially at low speed shots associated with putters, which means that true roll is achieved faster for putters, making deceleration of the ball more predictable, thereby providing better distance control for the golfer.

Similarly, as shown in FIG. 2, the particular relationship provided by the shaft 100 including the stiffening region 2500 located between a first point 5 "from the proximal shaft end (120) and a second point 24", 30", or 36" from the proximal shaft end (120) may further enhance the benefits. As best seen in fig. 10, in the first portion of the stiffening zone 2500, the shaft bending stiffness is at least 50% greater than the minimum tip portion bending stiffness and less than 100n x m ² The shaft torsional stiffness is at least 50% greater than the minimum tip portion torsional stiffness and less than 100n x m ² Meanwhile, in the second portion of the reinforcing region 2500, the shaft bending stiffness is at least 50% greater than the minimum root portion bending stiffness and greater than 120n x m ² The shaft torsional stiffness is at least 50% greater than the minimum root portion torsional stiffness and greater than 120n x m ² . In another embodimentThe "minimum" in the previous sentence is replaced with "average", and in yet another embodiment, the "minimum" in the previous sentence is replaced with "maximum". Those skilled in the art will appreciate that these rigidities of the tip portion and the root portion may be constant so that the minimum, maximum and average values are equal, or that these rigidities of the mentioned components may be different and thus possess different minimum, maximum and average values. These minimum, maximum and average alternative embodiments are equally applicable to all embodiments disclosed herein.

Thus, the stiffening zone 2500 has a first portion with a stiffness in bending and torsion that is much higher than the tip portion 2000, and a second portion with a stiffness that is higher than the first portion and significantly higher than the root portion 1000, wherein the root portion 1000 is stiffer than the tip portion 2000. In another related embodiment, the first portion of the reinforcing region 2500 has a bending stiffness at least 75% greater than the minimum tip portion and less than 90n x m ² Is at least 75% greater than the minimum tip portion torsional stiffness and is less than 90n x m ² . In yet another related embodiment, the second portion of the reinforcing region 2500 has a bending stiffness at least 75% greater than the minimum root portion and less than 135n x m ² Is at least 75% greater than the minimum root portion torsional stiffness and is less than 135n x m ² 。

Further, as shown in FIG. 11, a first portion of the shaft 100 extending two-thirds of the shaft length 130 from the shaft proximal end 120 has a first average bending stiffness, a second portion of the shaft 100 extending one-third of the shaft length 130 from the shaft distal end 110 has a second average bending stiffness, and the first average bending stiffness is at least 50% of the second average bending stiffness, providing a characteristic relationship that further benefits. For comparison, the hardness of the upper third of a typical steel shaft is more than twice that of the lower two-thirds. In another embodiment, the first average bending stiffness is at least 75% of the second average bending stiffness. In another related embodiment, the first average bending stiffness is at least 100% of the second average bending stiffness, and in yet another related embodiment, the first average bending stiffness is 75% -200% of the second average bending stiffness, and in yet another related embodiment, the first average bending stiffness is 100% -150% of the second average bending stiffness.

Those skilled in the art will appreciate that the bending stiffness (also commonly referred to as bending stiffness) discussed herein depends on the material stiffness or elastic modulus (E), as well as the cross-sectional geometry associated with the area moment of inertia (I), which is also the reason for the bending stiffness commonly referred to as EI. The area moment of inertia (I) of a simple tube is:

wherein r is _o Is the outer radius of the tube, r _i Is the inner radius of the tube.

In addition, the torsional stiffness (commonly referred to as torsional stiffness) discussed herein depends on the material torsional stiffness or shear modulus (G), as well as the cross-sectional geometry associated with the polar moment of inertia (J), which is also why torsional stiffness is commonly referred to as GJ. The polar moment of inertia (J) of a simple tube is:

Those skilled in the art will appreciate that these simple equations apply to a single element, however, there will be points to consider in determining the stiffness of the overall shaft bending stiffness and shaft torsional stiffness in the various layers of elements. For example, as shown in fig. 4, starting from the tip portion 2000, the calculation is simple until the tip portion 2000 enters into the coupler 3000, at which point the shaft stiffness calculation must take into account the overlap of the coupler 3000 and the tip portion 2000; further into the coupling 3000, the shaft stiffness calculation must take into account the overlap of the coupling 3000, tip portion 2000 and root portion 1000; after the coupling 3000 and within the separation distance 4080, the shaft stiffness calculation is again simplified until the region of the root portion insert 4000 is reached, at which point the shaft stiffness calculation must take into account the root portion 1000 and the root portion insert 4000. This is only one illustrative example, but emphasizes that the overall shaft bending stiffness and shaft torsional stiffness at various points along the length of the entire shaft length 130 must take into account multiple elements, while references to bending stiffness and torsional stiffness of individual components are only for the referenced individual components, which is an important distinction.

In another embodiment, the previously discussed benefits are further achieved in one embodiment wherein the minimum tip portion bending stiffness is at least 25% less than the minimum root portion bending stiffness and the minimum tip portion torsional stiffness is at least 25% less than the minimum root portion torsional stiffness. Still further, in another embodiment, the minimum tip portion bending stiffness is 25% -75% less than the maximum root portion bending stiffness and the minimum tip portion torsional stiffness is 25% -75% less than the maximum root portion torsional stiffness. In another embodiment, the previously discussed benefits are further achieved in one embodiment wherein the minimum tip portion bending stiffness is at least 25% less than the minimum root portion bending stiffness and the minimum tip portion torsional stiffness is at least 25% less than the minimum root portion torsional stiffness. Still further, in another embodiment, the minimum tip portion bending stiffness is at least 25% -75% less than the minimum root portion bending stiffness and the minimum tip portion torsional stiffness is at least 25% -75% less than the minimum root portion torsional stiffness. The minimum root portion bending stiffness is at least 40N m ² While the minimum root portion torsional stiffness is at least 20n x m ² . In another embodiment, the minimum root portion bending stiffness is at least 50n x m ² While the minimum root portion has a torsional stiffness of at least 30n x m ² . In a particularly unusual embodiment, the minimum root portion torsional stiffness is greater than the minimum root portion flexural stiffness (similar to the red tip in fig. 18).

In one embodiment, this relationship is achieved along a shaft outer diameter that is at least 50% constant along the shaft length 130, thereby ensuring that this beneficial relationship is maintained. In yet another embodiment, the shaft outer diameter is constant along at least 75% of the shaft length 130, in another embodiment, the root portion outer diameter 1070 is constant along the entire root portion length 1030, in yet another embodiment, the proximal portion outer diameter 2070 is constant along at least 50% of the tip portion length 2030, and in yet another embodiment, is constant along at least 75% of the tip portion length 2030.

This beneficial relationship can be further achieved and maintained by controlling the length of the individual components. In one such embodiment, tip portion length 2030 is no greater than 55% of root portion length 1030, in another embodiment tip portion length 2030 is at least 15% of root portion length 1030, in yet another embodiment tip portion length 2030 is at least 4", in another embodiment is at least 4-16", in yet another embodiment is at least 6-12". In another such embodiment, root portion length 1030 is at least 2 times tip portion length 2030, in another embodiment root portion length 1030 is at least 3 times tip portion length 2030, in yet another embodiment root portion length 1030 is at least 2-5 times tip portion length 2030, and in yet another embodiment root portion length 1030 is at least 2.5-4 times tip portion length 2030. Root portion length 1030 is at least 16 "in another embodiment, at least 20" in yet another embodiment, and at least 24 "in yet another embodiment. Other embodiments will limit root portion length 1030 to no more than 48", in another embodiment no more than 42", in yet another embodiment no more than 36", in yet another embodiment no more than 30", in yet another embodiment no more than 28".

In yet another embodiment, the shaft bending stiffness is constant along at least 10% of the shaft length 130 and the shaft torsional stiffness is constant along at least 10% of the shaft length 130. In yet another embodiment, the shaft bending stiffness is constant along at least 25% of the shaft length 130 and the shaft torsional stiffness is constant along at least 25% of the shaft length 130. In yet another embodiment, the shaft bending stiffness is constant along at least 40% of the shaft length 130 and the shaft torsional stiffness is constant along at least 40% of the shaft length 130. In yet another embodiment, the shaft bending stiffness is constant along at least 50% of the shaft length 130 and the shaft torsional stiffness is constant along at least 50% of the shaft length 130. Similarly, in another embodiment, the range is defined in which the shaft bending stiffness is constant along no more than 90% of the shaft length 130 and the shaft torsional stiffness is constant along no more than 90% of the shaft length 130. In yet another embodiment, the shaft bending stiffness is constant along no more than 75% of the shaft length 130 and the shaft torsional stiffness is constant along no more than 75% of the shaft length 130. In yet another embodiment, the shaft bending stiffness is constant along no more than 60% of the shaft length 130 and the shaft torsional stiffness is constant along no more than 60% of the shaft length 130.

These relationships may also be achieved by maintaining the tip portion outer diameter 2070 no more than 60% less than the maximum root portion outer diameter 1070, and in another embodiment by having a coupler 3000 with a coupler mass no more than 15% of the shaft mass. Other mass relationships also achieve some advantages by controlling the mass of specific components. For example, in one embodiment, the coupling mass is at least 5% of the shaft mass, in another embodiment, the root portion mass is 40% -70% of the shaft mass, and in yet another embodiment, the root portion mass is 45% -65% of the shaft mass. Likewise, in another embodiment, tip portion 2000 has a tip portion mass that is no more than 85% of the root portion mass, while in another embodiment, the tip portion is no more than 75% of the root portion mass, and in yet another embodiment, the tip portion is no more than 35% -75% of the root portion mass. The root portion mass preferably does not exceed 85 grams, in another embodiment does not exceed 75 grams, and in yet another embodiment does not exceed 65 grams. Yet another series of embodiments limits the lower range of root segment masses, wherein in one embodiment the root segment mass is at least 40 grams, in another embodiment the root segment mass is at least 50 grams, and in yet another embodiment the root segment mass is at least 60 grams. The coupler mass preferably does not exceed 25 grams, in another embodiment does not exceed 20 grams, and in yet another embodiment does not exceed 15 grams. Yet another series of embodiments limits the lower range of coupling masses, with one embodiment having a coupling mass of at least 5 grams, another embodiment having a coupling mass of at least 7.5 grams, and yet another embodiment having a coupling mass of at least 10 grams. In one embodiment, the kit comprises at least two root portions 1000, wherein the difference in root portion mass is at least 10 grams, in another embodiment at least 15 grams, and in yet another embodiment at least 20 grams. While another series of embodiments define a difference of no more than 50 grams, in another embodiment no more than 40 grams, and in yet another embodiment no more than 35 grams. Other kit embodiments provide high adjustability and significant hand feel variation to the user, wherein the root portion mass difference is at least 50%, in another embodiment at least 75%, and in yet another embodiment at least 95% of the heaviest tip portion mass. Lighter root selection may be beneficial to elderly and teenagers, while heavier root selection may be beneficial to users with high swing speeds.

The coupler 3000 is formed of a coupler material having a coupler material density, a coupler mass, a coupler elastic modulus, and a coupler shear modulus, while each point along the coupler length 3030 has (i) a coupler bending stiffness, and (ii) a coupler torsional stiffness. In one embodiment, at least a portion of the coupler 3000 has a coupler bending stiffness that is greater than a tip portion bending stiffness of a portion of the tip portion 2000, and at least a portion of the coupler 3000 has a coupler torsional stiffness that is greater than a tip portion torsional stiffness of a portion of the tip portion 2000. At least a portion of the coupler 3000 in another embodiment has a coupler bending stiffness that is greater than a heel portion bending stiffness of a portion of the heel portion 1000, and at least a portion of the coupler 3000 has a coupler torsional stiffness that is greater than a heel portion torsional stiffness of a portion of the heel portion 1000. At least a portion of the coupler 3000 in yet another embodiment has a coupler bending stiffness that is 75% greater than a tip portion bending stiffness of a portion of the tip portion 2000, and at least a portion of the coupler 3000 has a coupler torsional stiffness that is 75% greater than a tip portion torsional stiffness of a portion of the tip portion 2000. At least a portion of the coupler 3000 in another embodiment has a coupler bending stiffness that is 100% -500% greater than a tip portion bending stiffness of a portion of the tip portion 2000, and at least a portion of the coupler 3000 has a coupler torsional stiffness that is 100% -500% greater than a tip portion torsional stiffness of a portion of the tip portion 2000. At least a portion of the coupler 3000 in another embodiment has a coupler bending stiffness that is 200% -500% greater than a tip portion bending stiffness of a portion of the tip portion 2000, and at least a portion of the coupler 3000 has a coupler torsional stiffness that is 200% -500% greater than a tip portion torsional stiffness of a portion of the tip portion 2000. Still further, at least a portion of the coupler 3000 in another embodiment has a coupler bending stiffness that is 300-500% greater than a tip portion bending stiffness of a portion of the tip portion 2000, and at least a portion of the coupler 3000 has a coupler torsional stiffness that is 300-500% greater than a tip portion torsional stiffness of a portion of the tip portion 2000.

The disclosed stiffness relationships may be obtained in a variety of ways, one of which includes varying the root portion inner diameter 1060 along the root portion length 1030 to achieve the disclosed stiffening region 2500 stiffness relationships, and/or stiffness relationships associated with a first portion of the shaft 100 extending two-thirds of the shaft length 130 from the shaft proximal end 120, a second portion of the shaft 100 extending one-third of the shaft length 130 from the shaft distal end 110. In another embodiment, a reinforcing material may be embedded in root portion sidewall 1040 to achieve any of these relationships without changing root inner diameter 1060. In these embodiments, the reinforcement material may be composed of a tube of a relatively high stiffness material that extends 360 degrees around the root portion 1000 cross-section, or may be composed of an insert that is localized and does not extend 360 degrees around the root portion 1000 cross-section.

In another embodiment, root portion insert 4000 as shown in fig. 3, 4, and 7 (a) may be further included to achieve any of these relationships, the root portion insert 4000 being attached to the root portion 1000 and having a root portion insert distal end 4010, a root portion insert proximal end 4020, a root portion insert length 4030 of at least 25% of the tip portion length 2030, a root portion insert sidewall 4040 having a root portion insert sidewall thickness 4050, a root portion insert inner diameter 4060, and a root portion insert outer diameter 4070 that is less than the root portion inner diameter 1060, wherein a substantial portion of the root portion insert length 4030 is within the reinforced region 2500. In another embodiment, root portion insert length 4030 is at least 50% of tip portion length 2030 and no more than 50% of root portion length 1030, while in yet another embodiment root portion insert length 4030 is at least 10% of root portion length 1030 and no more than 150% of tip portion length 2030, and in yet another embodiment root portion insert inner diameter 4060 is greater than tip portion inner diameter 2060. In yet another embodiment, at least 75% of the root portion insert length 4030 is within the reinforced region 2500, while in another embodiment, the entire root portion insert 4000 is within the reinforced region 2500. In another embodiment, as shown in fig. 4, root portion insert proximal end 4020 is separated from coupler distal end 3010 by a separation distance 4080 of at least 50% of root portion outer diameter 1070, thereby achieving a drop in stiffness between root portion insert 4000 and coupler 3000 as disclosed. In one such embodiment, separation distance 4080 is no more than five times root portion outer diameter 1070, while in another embodiment separation distance 4080 is no more than 50% of root portion insert length 4030.

In one embodiment, root portion insert length 4030 is at least 2", and in another embodiment it is at least 4", and in yet another embodiment it is at least 6". However, the additional embodiments limit the root portion insert length 4030 so as not to compromise the advantages associated with the root portion insert 4000. Specifically, in one embodiment, root portion insert length 4030 does not exceed 12", while in another embodiment root portion insert length 4030 does not exceed 10", and in yet another embodiment root portion insert length 4030 does not exceed 8". Additionally, placement of root portion insert 4000 is essential to provide the described advantages. In one particular embodiment, root portion insert proximal end 4020 is at least 7", in another embodiment at least 9", and in yet another embodiment at least 11 "from shaft proximal end 120. Additional embodiments reduce the likelihood of compromising the advantages associated with root portion insert 4000 by controlling this distance. For example, in one embodiment, root portion insert proximal end 4020 is no more than 18", in another embodiment no more than 16", and in yet another embodiment no more than 14 "from shaft proximal end 120.

Those skilled in the art will appreciate that root portion insert 4000 has a Center of Gravity (CG), the location of the root portion insert CG greatly affecting the advantages associated with golf club shaft 100. In one such embodiment, the root portion insert CG is located at least 9", in another embodiment at least 11", and in yet another embodiment at least 13 "from the proximal shaft end 120. In some embodiments, when the distance from the proximal shaft end 120 becomes too great, impairment of the advantages associated with the root portion insert 4000 is observed. Thus, in another embodiment, the root portion insert CG is located no more than 19", in another embodiment no more than 17", and in yet another embodiment no more than 15 "from the proximal shaft end 120. In another embodiment, the separation distance from the shaft CG to the root portion insert CG is less than the root portion insert length 4030, in another embodiment no more than 75% of the root portion insert length 4030, and in yet another embodiment no more than 50% of the root portion insert length 4030. In another variation, the second separation distance is defined as the distance from the inflection point distance (defined later) to the location of the root portion insert CG when installed on the shaft, the second separation distance being less than root portion insert length 4030, in another embodiment no more than 75% of root portion insert length 4030, and in yet another embodiment no more than 50% of root portion insert length 4030. Thus, in one embodiment, when the insert is mounted on the shaft, the location of both the shaft CG and the inflection point falls between root portion insert distal end 4010 and root portion insert proximal end 4020.

The root portion insert 4000 is formed of a root portion insert material having a root portion insert material density, a root portion insert mass, a root portion insert elastic modulus, and a root portion insert shear modulus, having (i) a root portion insert flexural stiffness, and (ii) a root portion insert torsional stiffness at each point along the root portion insert length 4030. In one embodiment, at least a portion of root portion insert 4000 has a root portion insert bending stiffness that is greater than a tip portion bending stiffness of a portion of tip portion 2000, and at least a portion of root portion insert 4000 has a root portion insert torsional stiffness that is greater than a tip portion torsional stiffness of a portion of tip portion 2000. At least a portion of the root portion insert 4000 in another embodiment has a root portion insert bending stiffness that is greater than a root portion bending stiffness of a portion of the root portion 1000, and at least a portion of the root portion insert 4000 has a root portion insert torsional stiffness that is greater than a root portion torsional stiffness of a portion of the root portion 1000. At least a portion of root portion insert 4000 in yet another embodiment has a root portion insert bending stiffness that is 75% greater than a tip portion bending stiffness of a portion of tip portion 2000, and at least a portion of root portion insert 4000 has a root portion insert torsional stiffness that is 75% greater than a tip portion torsional stiffness of a portion of tip portion 2000. In yet another embodiment, at least a portion of the root portion insert 4000 has a root portion insert bending stiffness that is 100% -300% greater than a tip portion bending stiffness of a portion of the tip portion 2000, and at least a portion of the root portion insert 4000 has a root portion insert torsional stiffness that is 100% -300% greater than a tip portion torsional stiffness of a portion of the tip portion 2000.

As shown in fig. 7 (B), root portion insert 4000 may be a hollow tubular structure that may include at least one structural support that spans the interior of root portion insert 4000 and passes through the center thereof. In another embodiment, the structural support length extending into and out of the page in FIG. 7 (B) is at least 1/16", in another embodiment at least 1/8", and in yet another embodiment at least 1/4". In the embodiment of fig. 7 (a), the structural support length is at least 50% of the root portion insert length 4030, while in another embodiment it is at least 75% of the root portion insert length 4030, and in yet another embodiment it is at least 90% of the root portion insert length 4030.

Another embodiment includes at least two structural supports that span the interior of root portion insert 4000, pass through, and intersect at the center thereof, while another embodiment includes at least three. The root portion insert sidewall thickness 4050 preferably does not exceed the root portion sidewall thickness 1050, while in another embodiment the root portion insert sidewall thickness 4050 preferably does not exceed 75% of the root portion sidewall thickness 1050, and in yet another embodiment the root portion insert sidewall thickness 4050 preferably does not exceed 50% of the root portion sidewall thickness 1050. In another series of embodiments, root portion insert sidewall thickness 4050 is at least 50% of tip portion sidewall thickness 2050, while in another embodiment root portion insert sidewall thickness 4050 is preferably at least 75% of tip portion sidewall thickness 2050, and in yet another embodiment root portion insert sidewall thickness 4050 is preferably at least 100% of tip portion sidewall thickness 2050. In one embodiment, root portion insert 4000 is formed of a metallic material, while in another embodiment, is formed of a metallic material different from the material of tip portion 2000, and in yet another embodiment, is formed of a metallic material having a density at least 35% less than the density of tip portion 2000.

These relationships result in less face distortion before, during and after impact and improve the consistency of face speed with the acceleration of the heel and toe. Fig. 13 (a) shows the speed of the toe and heel of an Anser putter head attached to a conventional steel putter shaft attached to a robot as the ball is swung under the influence of eccentricity, while fig. 14 (a) shows an embodiment of the same putter head attached to a golf club 1000. The intersection of the heel and toe lines in fig. 13 (a) illustrates the instability of the putter head, while fig. 14 (a) illustrates that the golf club body 1000 exhibits improved performance, with no intersection of the heel and toe lines.

Similarly, fig. 13 (B) shows the acceleration of the toe and heel of the same Anser putter head attached to a conventional steel putter shaft attached to a robot when swinging a ball under the influence of eccentricity, while fig. 14 (B) shows an embodiment of the same putter head attached to a golf club shaft 1000. The differences in the heel and toe lines in fig. 13 (a) illustrate the instability of the putter head, while the differences in fig. 14 (B) illustrate that the golf club body 1000 exhibits improved performance, with the differences between the heel and toe lines being greatly reduced. These improvements demonstrate improved stability, which results in improved ball rolling characteristics, lower launch angle, and less dispersion. These relationships can significantly improve the relative fluctuations in speed and acceleration of the toe and heel of the face before, during and after impact without reducing the feel during and after impact.

Any of these embodiments may further result in the creation of a third portion of the reinforced region 2500 wherein the shaft bending stiffness is greater than the shaft bending stiffness of the first portion and less than the shaft bending stiffness of the second portion, and the shaft torsional stiffness is greater than the shaft torsional stiffness of the first portion and less than the shaft torsional stiffness of the second portion. In yet another embodiment, the third portion of the reinforcing region 2500 has a shaft bending stiffness that is at least 25% greater than the shaft bending stiffness of the first portion and at least 25% less than the shaft bending stiffness of the second portion, and a shaft torsional stiffness that is at least 25% greater than the shaft torsional stiffness of the first portion and at least 25% less than the shaft torsional stiffness of the second portion. In one embodiment, root portion insert 4000 has a root portion insert mass that is at least 10% of the shaft mass, while in another embodiment, the root portion insert mass does not exceed 25% of the shaft mass.

In one embodiment, the coupler 3000 is formed of a metal coupler material having a coupler material density that is less than the tip portion material density, but at least 15% greater than the root material density. In another embodiment, the tip material density is at least 50% greater than the root material density, while in another embodiment, the tip material density is at least 2 times the coupler material density, and in yet another embodiment, the tip material density is no more than 6 times the root material density. In one embodiment, the tip portion material density is at least 7g/cc, the coupling material density is 2.5-5.0g/cc, and the root material density is no more than 2.4g/cc. In another embodiment, the root material density and/or tip material density does not exceed 2.0g/cc, in another embodiment, 1.8g/cc, and in yet another embodiment, 1.6g/cc. The elastic modulus of the tip portion material is preferably at least 110GPa, its shear modulus is preferably at least 40GPa, while in another embodiment the elastic modulus of the tip portion material is preferably at least 190GPa, its shear modulus is preferably at least 70GPa. The coupling material preferably has an elastic modulus of at least 60GPa, preferably a shear modulus of at least 20GPa, while in another embodiment the coupling material preferably has an elastic modulus of at least 110GPa, preferably a shear modulus of at least 40GPa. The elastic modulus of the root material is preferably at least 40GPa, its shear modulus is preferably at least 15GPa, while in another embodiment the elastic modulus of the root material is preferably at least 50GPa and its shear modulus is preferably at least 22.5GPa, which is equally applicable to embodiments of non-metallic tip portions. The material of the root portion 1000, tip portion 2000, and/or coupler 3000 may include a metal alloy (e.g., titanium alloy, steel alloy, aluminum alloy, and/or magnesium alloy), a composite material (e.g., a graphite composite material, a ceramic material, a fiber-reinforced composite material, a molded composite material used to form a die body that may include a plurality of randomly oriented carbon fiber bundles), a thermoset or thermoplastic matrix material, a plastic, or any combination thereof. In one embodiment, the carbon fibers may comprise 10% -70% by volume of the composite material. In another embodiment, a method of forming a composite component includes: providing a plurality of carbon fiber bundles; mixing the plurality of bundles with a matrix material such that the bundles are randomly classified to form a composite molding feedstock; setting a male and female metal tooling die; placing the composite molding raw material in a master metal tooling mold; pressing the composite molding raw material in the female metal tooling die by using the male metal tooling die to generate a composite workpiece; and allowing the composite workpiece to cure, wherein each bundle of carbon fibers is unidirectional, and wherein each bundle comprises no more than 12000 carbon fibers. In another embodiment, each bundle comprises no more than 3000 carbon fibers. The matrix material used may be a thermosetting material, more preferably a vinyl ester or an epoxy resin. Further, the carbon fibers used in such embodiments may each be between 1/4 inch and 2 inches in length.

As shown in fig. 8 (a) and 8 (B), the coupler 3000 may have a coupler-root insert portion 3100 and a coupler-tip receiving portion 3200, which in some embodiments are separated by a variation in coupler outer diameter 3070, the coupler outer diameter 3070 forming a flange having a flange height no greater than root portion sidewall thickness 1050. The connector-root insert portion 3100 has a connector-root insert distal end 3110, a connector-root insert proximal end 3120, a connector-root insert length 3130 between the connector-root insert distal end 3110 and the connector-root insert proximal end 3120, a connector-root insert sidewall 3140, a connector-root insert sidewall thickness 3150, a connector-root insert inner diameter 3160, and a connector-root insert outer diameter 3170. Similarly, the coupler-tip receiving portion 3200 has a coupler-tip receiving distal end 3210, a coupler-tip receiving proximal end 3220, a coupler-tip receiving length 3230 between the coupler-tip receiving distal end 3210 and the coupler-tip receiving proximal end 3220, a coupler-tip receiving sidewall 3240, a coupler-tip receiving sidewall thickness 3250, and a coupler-tip receiving inner diameter 3260. In one embodiment, the coupler-root insert outer diameter 3170 does not exceed the root portion inner diameter 1060, while in another embodiment, the coupler-tip receiving inner diameter 3260 is at least as large as the tip portion outer diameter 2070. The coupler-tip receiving length 3230 is preferably greater than the tip portion outer diameter 2070, and the coupler-root insert length 3130 is preferably greater than the root portion inner diameter 1060. In another embodiment, the coupler-root insert length 3130 is at least 50% greater than the coupler-tip receiving length 3230, in another embodiment at least 75% greater, and in yet another embodiment at least 100% greater. Alternatively, those skilled in the art will appreciate that the coupler 3000 may be configured in an opposite configuration, with a portion of the root portion 1000 received within a portion of the coupler 3000 and a portion of the coupler 3000 received within a portion of the tip portion 2000. Alternatively, in another embodiment, a portion of coupler 3000 is received within a portion of root portion 1000 and a portion of tip portion 2000. Alternatively, in yet another embodiment, a portion of the root portion 1000 and a portion of the tip portion 2000 are both received within a portion of the coupler 3000.

The coupler sidewall thickness 3050 preferably does not exceed the root portion sidewall thickness 1050, and in one embodiment, the coupler sidewall thickness 3050 is at least 10% less than the root portion sidewall thickness 1050. In another embodiment, a portion of the coupler sidewall 3040 has a varying coupler sidewall thickness 3050, in another embodiment, a varying coupler-tip receiving sidewall thickness 3250, in yet another embodiment, the coupler-tip receiving sidewall thickness 3250 varies between a minimum value and a maximum value, wherein the maximum value is at least 50% greater than the minimum value. In another embodiment, the maximum coupler-tip receiving sidewall thickness 3250 is at least 50% greater than the coupler-root insert sidewall thickness 3150.

In the illustrated embodiment, the tip portion 2000 extends all the way through the coupler-tip receiving portion 3200 and into the coupler-root insert portion 3100 such that a cross-section of a portion of the entire shaft 100 includes the outer root portion 1000, the middle coupler 3000, and the inner tip portion 2000, thereby achieving the relationships described herein. In another embodiment, the tip portion distal end 2010 extends to a first distance of at least 50%, in another embodiment at least 75%, in yet another embodiment at least 100% of the root portion outer diameter 1070 in the coupler-root insert portion 3100. Another series of embodiments limit the first distance to no more than 50% of the tip portion length 2030 and no more than 10 times the root portion outer diameter 1070, in another embodiment no more than 35% of the tip portion length 2030 and no more than 6 times the root portion outer diameter 1070, and in yet another embodiment no more than 25% of the tip portion length 2030 and no more than 4 times the root portion outer diameter 1070. The embodiment of fig. 8 (a) includes an opening in the coupler distal end 3010 that allows the passage of air, the open area of which in one embodiment is at least 10%, in another embodiment at least 20%, and in yet another embodiment at least 30% of the area associated with the coupler outer diameter 3070.

The shaft 100 of any of the disclosed embodiments may be further attached to a golf club head 5000 and include a grip 6000 attached to the shaft distal end 110, thereby creating a golf club suitable for use. Those skilled in the art will appreciate that the golf club may be a putter, a driver, a fairway wood, a hybrid or rescue club, an iron and/or a wedge iron. In one specific embodiment, the golf club is a putter having a head angle of less than 10 degrees, in another embodiment having a head mass of at least 310 grams, and in yet another embodiment having a shaft length 130 of no more than 36%. In another embodiment, the club head mass is at least 320 grams, in another embodiment at least 330 grams, and in yet another embodiment at least 340 grams.

The shaft 100 may be a putter shaft, a wedge iron club shaft, an iron shaft, a rescue shaft, a fairway wood shaft, and/or a driver wood shaft. In one particular putter shaft embodiment, the shaft length 130 does not exceed 38 "and the shaft mass is at least 100 grams, while in another embodiment the shaft length 130 does not exceed 36" and the shaft mass is 100-150 grams, and in yet another embodiment the shaft length 130 does not exceed 35 "and the shaft mass is 110-140 grams. In one embodiment, tip portion 2000 is straight, and in another embodiment for some pushrods, tip portion 2000 includes double bends, as will be appreciated by those skilled in the art. Those skilled in the art will appreciate that the entire shaft 100 will have a shaft center of gravity CG, the location of which may be referenced as the distance of the shaft CG from the proximal shaft end 120. In one putter embodiment having a shaft length 130 of less than 35.5", the advantages described herein are improved when the shaft CG distance is no more than 18", in another embodiment no more than 17", in yet another embodiment no more than 16". Further, the advantages described herein are enhanced when the shaft CG distance is at least 9", in another embodiment at least 11", in yet another embodiment at least 13 ". The shaft CG distance in one particular embodiment is 13"-15.5". In another embodiment, these shaft CG distances are obtained with a shaft length 130 of no more than 35", in another embodiment the shaft length 130 is no more than 34", and in yet another embodiment the shaft length 130 is no more than 33". In further embodiments, the shaft CG distance is no more than 45% of the shaft length 130, in another embodiment no more than 40% of the shaft length 130, and in yet another embodiment no more than 35% of the shaft length 130. However, in another series of embodiments, the shaft CG distance is at least 20% of the shaft length 130, in another embodiment at least 25% of the shaft length 130, and in yet another embodiment at least 30% of the shaft length 130.

A typical tapered steel putter shaft of length 35 "has a shaft CG distance of around 20" and a turning point distance of around 14 ". By securing the root or distal shaft end 110 of the shaft, an axial compressive load is applied to the tip or proximal shaft end 120 until the distance between the ends changes by 0.5", thereby determining the turning point distance of the golf club shaft. Thereafter, the maximum deflection point is identified as a position of maximum deflection from the initial shaft axis. The turning point distance is the distance along the initial shaft axis from the proximal shaft end 120 to the point of maximum deflection.

As the shaft CG distance decreases, a surprising performance advantage is found in that the turning point distance increases and the combination of the shaft CG distance and the turning point distance or the difference therebetween decreases. In one embodiment of the invention, the inflection point distance is at least 75% of the shaft CG distance, in another embodiment at least 85% of the shaft CG distance, in yet another embodiment at least 95% of the shaft CG distance, and in yet another embodiment at least 105% of the shaft CG distance. In another series of embodiments, the inflection point distance is no more than 14%, in another embodiment no more than 135%, in yet another embodiment no more than 125%, and in yet another embodiment no more than 115% of the shaft CG distance. In a particularly useful embodiment, the inflection point is at least 85% -135%, in another embodiment at least 95% -125%, and in yet another embodiment at least 100% -115% of the shaft CG distance. In another embodiment of the invention, the shaft CG distance is no more than 50%, in another embodiment no more than 47.5%, in another embodiment no more than 45%, in yet another embodiment no more than 42.5% of the shaft length 130. In another series of embodiments, the shaft CG distance is at least 30%, in another embodiment at least 35%, in yet another embodiment at least 37.5%, in yet another embodiment at least 40% of the shaft length 130.

The difference between the shaft CG distance and the inflection point distance is preferably no more than 12.5%, in another embodiment no more than 10%, in yet another embodiment no more than 7.5%, in yet another embodiment no more than 5% of the shaft length 130. In a particularly effective embodiment, the difference between the shaft CG distance and the turning point distance is preferably no more than 4.5", in another embodiment no more than 3.5", in yet another embodiment no more than 2.5", in yet another embodiment no more than 1.5". In one embodiment, the shaft CG distance is no more than 18.0", in another embodiment no more than 16.0", in yet another embodiment no more than 15.5", in yet another embodiment no more than 15.0", wherein the shaft lengths are each 35.0".

In one embodiment, root portion outer diameter 1070 is 0.500-0.700", while in another embodiment root portion outer diameter 1070 is 0.550-0.650", and in yet another embodiment root portion outer diameter 1070 is 0.580-0.620". In another embodiment, tip portion outer diameter 2070 is 0.300-0.450", while in another embodiment, tip portion outer diameter 2070 is 0.330-0.420", and in yet another embodiment, tip portion outer diameter 2070 is 0.350-0.390".

Any embodiment disclosed herein as "a portion" of a first component having a first stiffness, relative to "a portion" of a second component having a different second stiffness, includes another embodiment wherein the relationship is correct over at least 25% of the length of the first component and/or at least 25% of the length of the second component, or in another embodiment the relationship is correct over at least 50% of the length of the first component and/or at least 50% of the length of the second component, and in yet another embodiment the relationship is correct over at least 75% of the length of the first component and/or at least 75% of the length of the second component.

Turning now to fig. 9 to 12, the shaft bending stiffness abbreviated EI and the shaft torsional stiffness abbreviated GJ. As described above, the shaft bending rigidity and the shaft torsional rigidity are the shaft bending rigidity and the shaft torsional rigidity of the cross section perpendicular to the shaft axis at each point along the shaft length 100, and a region of the shaft 100 made up of a plurality of elements within a specific cross section is considered, whereas in other regions where the shaft 100 has no independent parts overlapping, the shaft rigidity is equal to the rigidity of only the parts present at that specific position of the cross section. Referring now specifically to fig. 9, starting from the left boundary of the figure, the shaft 100 contains only a portion of the shaft bending stiffness (EI) and shaft torsional stiffness (GJ) that have a constant cross-sectional profile in the present embodiment, which are constant, i.e., horizontal along the first bending stiffness stabilization period and the first torsional stiffness stabilization period. Thereafter, the shaft bending stiffness increases along the first bending stiffness to a second bending stiffness plateau and the shaft torsional stiffness increases along the first torsional stiffness to a second torsional stiffness plateau. In this embodiment, the rise begins at the point where the tip portion 2000 enters the coupler-tip receiving portion 3200 of the coupler 3000, see fig. 8 (a), taking into account overlapping and enlarged coupler-tip receiving sidewall thickness 3250. In this embodiment, the second bending stiffness plateau and the second torsional stiffness plateau represent constant stiffness zones because they are zones along the shaft length 130 that include root portions 1000 that overlap the coupler-root insert portion 3100 of the coupler 3000, which in this embodiment have constant cross-sectional profiles. In the present embodiment, the shaft 100 only includes in the region of the root portion 1000 within the separation distance 4080, which region has a constant cross-sectional profile in the present embodiment, the stiffness then drops to the third bending stiffness stabilization period and the third torsional stiffness stabilization period, as shown in fig. 4. In the present embodiment, as shown in fig. 4, in the region where the shaft 100 includes the root portion 1000 and the root portion insert 4000, the rigidity is then raised to the fourth bending rigidity stabilization period and the fourth torsional rigidity stabilization period, which in the present embodiment have a constant cross-sectional distribution. In the present embodiment, the shaft 100 only includes in the region of the root portion 1000, which has a constant cross-sectional profile in the present embodiment, the stiffness then drops to the fifth bending stiffness stabilization period and the fifth torsional stiffness stabilization period. In one embodiment, the stationary phase described herein is not constant, but rather has a positive or negative slope that is no more than 10 degrees, much less than the variation found on a conventional tapered or stepped shaft, such as that shown in fig. 12. In another embodiment, the positive or negative slope is no more than 7.5 degrees, in yet another embodiment, the positive or negative slope is no more than 5 degrees, and in yet another embodiment, the positive or negative slope is no more than 2.5 degrees.

As graphically illustrated in fig. 9, the average second stability period bending stiffness of the second stability period is at least 2 times the average first stability period bending stiffness of the first stability period. In another embodiment, the second stationary phase average second stationary phase bending stiffness is at least 50% greater than the third stationary phase average third stationary phase bending stiffness. In yet another embodiment, the average second-stationary-phase bending stiffness of the second stationary phase is at least 25% greater than the average fourth-stationary-phase bending stiffness of the fourth stationary phase. In yet another embodiment, the average second stability period bending stiffness of the second stability period is at least 50% greater than the average fifth stability period bending stiffness of the third stability period. Similarly, the average second stationary phase torsional stiffness of the second stationary phase is at least 2 times the average first stationary phase torsional stiffness of the first stationary phase. In another embodiment, the average second stationary phase torsional stiffness of the second stationary phase is at least 50% greater than the average third stationary phase torsional stiffness of the third stationary phase. In yet another embodiment, the average second stationary phase torsional stiffness of the second stationary phase is at least 25% greater than the average fourth stationary phase torsional stiffness of the fourth stationary phase. In yet another embodiment, the average second stationary phase torsional stiffness of the second stationary phase is at least 50% greater than the average fifth stationary phase torsional stiffness of the third stationary phase.

In another embodiment, the fourth stationary phase has an average fourth stationary phase bending stiffness that is at least 10% greater than the average stationary phase bending stiffness of the adjacent stationary phase, and in one embodiment, the adjacent stationary phase is oriented toward the distal end 120 of the shaft, and in another embodiment, the adjacent stationary phase is oriented toward the proximal end 110 of the shaft. Similarly, in another embodiment, the fourth stationary phase has an average fourth stationary phase torsional stiffness that is at least 10% greater than the average stationary phase torsional stiffness of the adjacent stationary phase, and in one embodiment, the adjacent stationary phase is oriented toward the distal shaft end 120, and in another embodiment, the adjacent stationary phase is oriented toward the proximal shaft end 110.

In another embodiment, the average third stability period bending stiffness of the third stability period is at least 10% less than the average stability period bending stiffness of the adjacent stability period, while in one embodiment, the adjacent stability period is toward the distal shaft end 120, and in another embodiment, the adjacent stability period is toward the proximal shaft end 110. Similarly, in another embodiment, the average third stationary phase torsional stiffness of the third stationary phase is at least 10% less than the average stationary phase torsional stiffness of the adjacent stationary phase, and in one embodiment, the adjacent stationary phase is toward the distal shaft end 120, and in another embodiment, the adjacent stationary phase is toward the proximal shaft end 110.

In another embodiment, the second stationary phase has an average second stationary phase bending stiffness that is at least 50% greater than the average stationary phase bending stiffness of the adjacent stationary phase, and in one embodiment, the adjacent stationary phase is oriented toward the distal shaft end 120, and in another embodiment, the adjacent stationary phase is oriented toward the proximal shaft end 110. Similarly, in another embodiment, the average second stationary phase torsional stiffness of the second stationary phase is at least 50% greater than the average stationary phase torsional stiffness of the adjacent stationary phase, and in one embodiment, the adjacent stationary phase is toward the distal shaft end 120, and in another embodiment, the adjacent stationary phase is toward the proximal shaft end 110.

In one embodiment, the third stability period has a shaft bending stiffness that is (a) at least 50% greater than the tip portion bending stiffness, i.e., the first stability period bending stiffness, and (b) less than 100n x m ² . Similarly, the third stationary phase has a shaft torsional stiffness that is (a) at least 50% greater than the tip portion torsional stiffness, i.e., the first stationary phase torsional stiffness, and (b) less than 100n x m ² . In another embodiment, the second stability period has a shaft bending stiffness that is (a) at least 50% greater than the root portion bending stiffness, i.e., the third or fifth stability period bending stiffness, and (b) greater than 120n x m ² . Similarly, the second stationary phase has a shaft torsional stiffness that is (a) at least 50% greater than the root portion torsional stiffness, i.e., the third or fifth stationary phase torsional stiffness, and (b) greater than 120n x m ² 。

In another embodiment, a portion of the fourth stationary phase is within the stiffening region 2500 and has a shaft bending stiffness that is (a) greater than the shaft bending stiffness of the third stationary phase and (b) less than the shaft bending stiffness of the second stationary phase. Likewise, in another embodiment, a portion of the fourth stationary phase is within the reinforced region 2500 and has a shaft torsional stiffness that is (a) greater than the shaft torsional stiffness of the third stationary phase and (b) less than the shaft torsional stiffness of the second stationary phase.

In another embodiment, the shaft bending stiffness distribution and the shaft torsional stiffness distribution each comprise at least four distinct stability periods, each stability period being at least 2 "in length and at least one stability period being at least 6" in length. In another embodiment, the shaft bending stiffness distribution and the shaft torsional stiffness distribution each comprise at least five distinct stability periods, each stability period being at least 2 "in length, at least 6" in length, and at least 10 "in length.

In graph (a) of fig. 10, the shaft 100 is divided into a tip region and a root region, which are separated at a midpoint of the shaft length 130. Thus, the area from the midpoint to the proximal shaft end 120 is the tip area, while the area from the midpoint to the distal shaft end 110 is the root area. In one embodiment, the average tip region bending stiffness is within 25% of the average root region bending stiffness, while the average tip region bending stiffness of a conventional tapered or stepped shaft is less than 40% of the average root region bending stiffness, as shown in FIG. 12. In another embodiment, the average tip portion bending stiffness is within 15%, in yet another embodiment within 10%, and in yet another embodiment within 5% of the average root region bending stiffness. In a specific embodiment, the average tip portion bending stiffness is at least as great as the average root region bending stiffness. Similarly, in one embodiment, the average tip section torsional stiffness is within 25% of the average root zone torsional stiffness, while the average tip zone torsional stiffness of a conventional tapered or stepped shaft, as shown in FIG. 12, is less than 40% of the average root zone torsional stiffness. In another embodiment, the average tip portion torsional stiffness is within 15%, in yet another embodiment within 10%, and in yet another embodiment within 5% of the average root region torsional stiffness.

In the graph (B) of fig. 10, the shaft 100 is divided into a tip non-reinforced region, a reinforced region, and a root non-reinforced region. All of the above disclosures and embodiments of the reinforcing region 2500 apply to the reinforcing region of fig. 10. In another embodiment, the reinforced region 2500 has an average reinforced region bending stiffness and an average reinforced region torsional stiffness, the tip non-reinforced region has an average tip non-reinforced region bending stiffness and an average tip non-reinforced region torsional stiffness, and the root non-reinforced region has an average root non-reinforced region bending stiffness and an average root non-reinforced region torsional stiffness. The average tip non-reinforced region bending stiffness and the average root non-reinforced region bending stiffness are the average non-reinforced region bending stiffness, and as such the average tip non-reinforced region torsional stiffness and the average root non-reinforced region torsional stiffness are the average non-reinforced region torsional stiffness. In one embodiment, the average reinforced region bending stiffness is at least 50% greater, in another embodiment at least 60% greater, and in another embodiment at least 70% greater than the average non-reinforced region bending stiffness. Similarly, in another embodiment, the average reinforced region torsional stiffness is at least 40% greater, in another embodiment at least 50% greater, and in another embodiment at least 60% greater than the average non-reinforced region torsional stiffness. In yet another embodiment, the average reinforced region bending stiffness is 50% -150%, in another embodiment 60-125%, and in another embodiment 65-100% greater than the average non-reinforced region bending stiffness. Likewise, in another embodiment, the average reinforced region torsional stiffness is 40% -120% greater than the average non-reinforced region torsional stiffness, in another embodiment 50% -110% greater, and in another embodiment 55% -100% greater.

In graph (D) of fig. 11, the shaft 100 is divided into a tip two-thirds area and a root one-third area based on the shaft length 130. A first portion of the shaft 100 extending two-thirds of the shaft length 130 from the shaft proximal end 120 (i.e., the tip two-thirds area) has a first average bending stiffness, a second portion of the shaft 100 extending one-third of the shaft length 130 from the shaft distal end 110 (i.e., the root one-third area) has a second average bending stiffness, and the first average bending stiffness is at least 50% of the second average bending stiffness. These relationships are in contrast to what is found in conventional tapered or stepped shafts, where the two-third tip region has an average bending stiffness of less than 42% of the average bending stiffness of the root third region, as shown in FIG. 12. Similarly, two-thirds of the tip region each have a first average torsional stiffness and the root third region has a second average torsional stiffness, and the first average torsional stiffness is at least 50% of the second average torsional stiffness. These relationships differ significantly from those found in conventional tapered or stepped shafts in which the tip two-thirds region has an average torsional stiffness of at least 42% less than the average torsional stiffness of the root one-third region, as shown in fig. 12. In another embodiment, the first average bending stiffness is at least 75% of the second average bending stiffness. In another related embodiment, the first average bending stiffness is at least 100% of the second average bending stiffness, and in yet another related embodiment, the first average bending stiffness is 75% -200% of the second average bending stiffness, and in yet another related embodiment, the first average bending stiffness is 100% -150% of the second average bending stiffness. In another embodiment, the first average torsional stiffness is at least 75% of the second average torsional stiffness. In another related embodiment, the first average torsional stiffness is at least 100% of the second average torsional stiffness, and in yet another related embodiment, the first average torsional stiffness is 75% -200% of the second average torsional stiffness, and in yet another related embodiment, the first average torsional stiffness is 100% -150% of the second average torsional stiffness.

In graph (C) of fig. 11, the shaft 100 is divided into a tip third region and a root two-thirds region based on the shaft length 130. The first portion of the shaft 100 extending one third of the shaft length 130 from the proximal shaft end 120 (i.e., the tip third region) has a tip third average bending stiffness, the second portion of the shaft 100 extending two thirds of the shaft length 130 from the distal shaft end 110 (i.e., the root two-thirds region) has a root two-thirds average bending stiffness, and the tip third average bending stiffness is at least 50% of the root two-thirds average bending stiffness. These relationships are in contrast to what is found in conventional tapered or stepped shafts, where the tip third region has an average bending stiffness that is at least 36% less than the average bending stiffness of the root two-thirds region, as shown in FIG. 12. Similarly, the tip third regions each have a tip third average torsional stiffness, the root two-thirds regions have a root two-thirds average torsional stiffness, and the tip third average torsional stiffness is at least 50% of the root two-thirds average torsional stiffness. These relationships are in contrast to what is found in conventional tapered or stepped shafts, where the tip third region has an average torsional stiffness that is at least 36% less than the average torsional stiffness of the root two-thirds region, as shown in fig. 12. In another embodiment, the tip third average bending stiffness is at least 60% of the root two-thirds average bending stiffness. In another related embodiment, the tip third average bending stiffness is at least 70% of the root two-thirds average bending stiffness, while in yet another related embodiment, the tip third average bending stiffness is 60% -120% of the root two-thirds average bending stiffness, and in yet another related embodiment, the tip third average bending stiffness is 70% -110% of the root two-thirds average bending stiffness. In another embodiment, the tip third average torsional stiffness is at least 60% of the root two-thirds average torsional stiffness. In another related embodiment, the tip third average torsional stiffness is at least 70% of the root two-thirds average torsional stiffness, while in yet another related embodiment, the tip third average torsional stiffness is 60% -120% of the root two-thirds average torsional stiffness, and in yet another related embodiment, the tip third average torsional stiffness is 70% -110% of the root two-thirds average torsional stiffness.

As shown in fig. 15, the coupler 3000 may be configured to releasably engage the root portion 1000 and the tip portion 2000. The releasability of the coupler 3000 allows (a) a single tip portion 2001 to be joined to multiple root portions (1001, 1002, 1003, 1004) having different characteristics, thereby identifying the best combination for a particular golfer; (b) A single root portion 1001 is joined to a plurality of tip portions (2001, 2002, 2003, 2004) having different characteristics, thereby identifying the best combination for a particular golfer; and/or (c) any other such combination. Generally, for ease of explanation, the present invention will focus on a kit or system that includes a single root portion 1001 paired with at least two different tip portions (2001, 2002). However, those skilled in the art will appreciate that the kit may include any number of root portions (1001, 1002, 1003, 1004) and tip portions (2001, 2002, 2003, 2004) engaged by common universal couplings 3001, however, multiple couplings (3001, 3002, 3003, 3004) may also be included to provide further options and stiffness features as described herein. Further, the unique hardness characteristics and relationships disclosed herein are not limited to kits or releasable couplings, but may be incorporated into a unitary shaft, or a shaft made up of multiple parts, whether joined together directly or through incorporation of a coupling, and whether in a permanent or releasable coupling configuration. Thus, no matter how many components the shaft 100 is formed from, the shaft 100 has a shaft distal end 110, a shaft proximal end 120, a shaft outer diameter, a shaft length 130, and a shaft mass, as previously disclosed in detail and shown in fig. 16. Each point along the shaft length 130 has a shaft bending stiffness and a shaft torsional stiffness. When referring to root portion or root segment 1000 and tip portion or tip segment 2000, the terms "portion" and "segment" are used interchangeably throughout this disclosure.

In some embodiments, the shaft 100 has a root portion (1000, 1001, 1002, 1003, 1004) of the tip portion 2000 releasably engaged to at least one of the first tip portion 2001 and the second tip portion 2002 by a coupler (3000, 3001, 3002, 3003), but may also include a third tip portion 2003 or even a fourth tip portion 2004. As described in detail previously, root portion 1000 has a root portion distal end 1010, a root portion proximal end 1020, a root portion length 1030, a root portion sidewall 1040 having a root portion sidewall thickness 1050, a root portion inner diameter 1060, and a root portion outer diameter 1070. Similarly, each tip portion has the following properties, which are not repeated for each portion for brevity, but will be understood by those skilled in the art. Attributes include tip portion distal end 2021, tip portion proximal end 2020, tip portion length 2030, tip portion sidewall 2040 having tip portion sidewall thickness 2050, tip portion inner diameter 2060 (in the case of tip portion 2000 being hollow (but in some embodiments tip portion 2000 may be partially or fully solid)), tip portion outer diameter 2060, and tip portion mass.

When multiple tip portions 2000 and/or multiple root portions 1000 are provided as part of a kit, the properties just described need not be the same for each tip portion or root portion. Indeed, one or more varying attributes may be desirable, although some relationships may be particularly advantageous to provide the user with a variety of choices to achieve the best stiffness distribution, mass distribution, turning point location, and balance of a particular swing motion, as will be described later.

While many of the embodiments previously disclosed focus on a metallic tip portion 2000 and a non-metallic root portion 1000, those skilled in the art will recognize that the previous disclosure and material properties of the non-metallic root portion 1000 embodiments may be equally applicable to embodiments of the non-metallic tip portion 2000, and that the previous disclosure and material properties of the metallic tip portion 2000 embodiments may be equally applicable to embodiments of the metallic root portion 1000. In fact, non-metallic tip portion 2000 is preferred in some swings (shafts for clubs rather than putters). However, some kit embodiments may also include one or more metallic tip portions 2000 and/or one or more metallic root portions 1000.

In some embodiments, root portion 1000 is formed from a non-metallic root portion material having a root material density, a root portion mass of 35% -75% of the shaft mass, a root portion elastic modulus, and a root portion shear modulus, and has (i) a root portion area moment of inertia, (ii) a root portion polar moment of inertia, (iii) a root portion flexural stiffness, and (iv) a root portion torsional stiffness at every point along root portion length 1030. The simplified kit embodiment includes at least a first tip portion 2001 and a second tip portion 2002, which may be coupled to one or more root portions 1000 by a coupler 3000. In one embodiment, the first tip portion 2001 is formed of a non-metallic tip portion material having a first tip material density within 15% of the root material density, a first tip portion elastic modulus, and a first tip portion shear modulus, and each point along the length of the first tip portion has (i) a first tip portion area moment of inertia, (ii) a first tip portion polar moment of inertia, (iii) a first tip portion flexural stiffness, and (iv) a first tip portion torsional stiffness. Similarly, the second tip portion 2002 is formed from a non-metallic tip portion material having a second tip material density within 15% of the root material density, a second tip portion elastic modulus, and a second tip portion shear modulus, and has (i) a second tip portion area moment of inertia, (ii) a second tip portion polar moment of inertia, (iii) a second tip portion flexural stiffness, and (iv) a second tip portion torsional stiffness at each point along the length of the second tip portion. Those skilled in the art will appreciate that these basic properties are equally applicable to embodiments further comprising a third tip portion 2003 or even a fourth tip portion 2004. While these embodiments disclose nonmetallic tip portions having a density similar to that of a root portion to be disclosed later, other embodiments incorporate tip portions 2000 having a density much greater than that of the root portion, while some embodiments include metallic tip portions.

One embodiment includes at least two tip portions that meet one or more of the following criteria: (a) The maximum second tip portion bending stiffness is at least 25% greater than the maximum first tip portion bending stiffness and (b) the maximum second tip portion torsional stiffness is at least 35% greater than the maximum first tip portion torsional stiffness. For example, in fig. 18, both the blue tip portion and the white tip portion have a bending stiffness at least 25% greater than the bending stiffness of the green tip portion and the red tip portion. Similarly, the red tip portion and the white tip portion each have a torsional stiffness that is at least 50% greater than the torsional stiffness of the green tip portion and the blue tip portion. In another embodiment, at least two tip portions meet both criteria (a) and (b). The slow swing player is most likely to experience improved performance when using a tip portion having the characteristics exhibited by the green and red tips of fig. 18 (i.e., a tip portion having relatively less bending stiffness). Tip portions with torsional stiffness greater than bending stiffness (e.g., the red tip of fig. 18) are advantageous for players with average swing speeds or higher, but due to the manner of swing, it is difficult to hit the ball high, e.g., because the ball cannot be hit during an upper swing, and often is severely left-biased in the ball's flight, in part because the tip portion lacks torsional stiffness. Conversely, a golfer who has difficulty turning over the club and thus tends to be located on the right side of the golf course will benefit from a tip portion having low torsional stiffness. Further, a golfer who hits the ball at the upper swing portion during the swing most benefits from a tip portion having characteristics similar to those found in the blue and white tip portions, i.e., a tip portion having relatively high bending stiffness. Fig. 18 shows an embodiment with a torsional stiffness higher than the bending stiffness based on a low bending stiffness embodiment, i.e. the red tip of fig. 18, whereas another embodiment may be implemented as a medium or high bending stiffness embodiment, e.g. a tip portion of ei=22.5 and gj=25, or even a tip portion of ei=30 and gj=35.

The specific bending stiffness values and torsional stiffness values illustrated in fig. 18 and 20 are associated with the exemplary embodiments and help to discuss the relationship between the overall stiffness distribution of the plurality of tip portions and the associated shaft. The stiffness shown in fig. 18 and 20 is n×m ² In units of. In one embodiment, the kit includes at least two tip portions of fig. 18 or 20 with a stiffness of plus or minus 50% of the indicated value, while in another embodiment with a stiffness of plus or minus 35% of the indicated value, and in yet another embodiment with a stiffness of plus or minus 20% of the indicated value. Other embodiments of kits have at least three tip portions of fig. 18 or 20 and the same positive and negative variation, and even other kits have at least four tip portions of fig. 18 or 20 and the same positive and negative variation. In one embodiment, the bending stiffness and torsional stiffness illustrated in FIG. 18 are the maximum stiffness associated with a particular tip portion, while in an alternative embodiment they are the average stiffness associated with a particular tip portionIn yet another alternative embodiment, they are the minimum stiffness associated with a particular tip portion.

The leftmost columns EI and GJ of fig. 20 show the average bending stiffness and the average torsional stiffness of the entire shaft, which is made up of the same root portion 1000 attached to four different tip portions 2000. The following two EI and GJ columns are labeled 0-33% indicating the average bending stiffness and average torsional stiffness associated with one third of the shaft length from the proximal shaft end 120. The two EI and GJ columns, again, are labeled 33-66%, indicating the average bending stiffness and the average torsional stiffness associated with the middle third of the shaft length. The two EI and GJ columns, again, are labeled 66-100%, indicating the average bending stiffness and the average torsional stiffness associated with one third of the shaft length ending at the shaft distal end 110. The two EI and GJ columns, again, are labeled 0-66%, indicating the average bending stiffness and the average torsional stiffness associated with two-thirds of the shaft length from the proximal shaft end 120. The two EI and GJ columns are labeled 33-100% and indicate the average bending stiffness and average torsional stiffness associated with two-thirds of the shaft length terminating from the shaft distal end 110. Finally, the last four columns include two EI columns and two GJ columns labeled 0-66%, indicating the average bending stiffness and average torsional stiffness associated with one-half the shaft length from the proximal shaft end 120. The two EI and GJ columns are labeled 50-100% and indicate the average bending stiffness and average torsional stiffness associated with one-half the length of the shaft terminating at the distal end 110 of the shaft.

Still referring to fig. 20, in one embodiment, the middle third and the third terminating at the distal end 110 of the shaft each have an average bending stiffness and an average torsional stiffness that are greater than or equal to the average overall shaft bending stiffness and the average overall shaft torsional stiffness, respectively, and the third starting at the proximal end 120 of the shaft has an average bending stiffness and an average torsional stiffness that are less than 65% of the average overall shaft bending stiffness and the average overall shaft bending stiffness, respectively, and in another embodiment less than 50%, and in yet another embodiment less than 35%. Indeed, in other embodiments, not only the average bending stiffness and the average torsional stiffness are greater than or equal to the average overall shaft bending stiffness and the average overall shaft torsional stiffness, respectively, for 33-66% and 66-100% of the length columns, they are also at least 15% greater than the average overall shaft bending stiffness and the average overall shaft torsional stiffness, in another embodiment at least 20% greater, and in yet another embodiment 25% greater. However, another series of embodiments recognize that the negative performance returns are associated with a large variance, thus introducing a limitation, in one embodiment, the average overall shaft bending stiffness and the average overall shaft torsional stiffness of 33-66% and 66-100% length columns are no more than 50%, in another embodiment no more than 42.5%, and in yet another embodiment no more than 35% greater than the average overall shaft bending stiffness and the average overall shaft torsional stiffness.

The properties of a bifurcated shaft persist, in one embodiment, one third of the shaft ending at the distal end 110 of the shaft does not have the highest average bending stiffness, and in another embodiment, one third of the shaft ending at the distal end 110 of the shaft does not have the highest average torsional stiffness. Thus, one kit embodiment includes two tip portions having different bending and torsional stiffness such that (a) a first tip portion mounted at one third that terminates at the distal shaft end 110 does not have the highest average bending stiffness and (b) a second tip portion mounted at one third that terminates at the distal shaft end 110 does not have the highest average bending stiffness.

Still referring to FIG. 20 but focusing now on the columns associated with the tip and root two-thirds lengths, in one embodiment, the average bending stiffness of the 0-66% portion of the shaft is at least 55%, in another embodiment at least 60%, and in yet another embodiment at least 65-80% of the average bending stiffness of the 33-100% portion of the shaft. Attention is now drawn to the average torsional stiffness, in one embodiment, the average torsional stiffness of the 0-66% portion of the shaft being at least 80%, in another embodiment at least 85%, and in yet another embodiment at least 85-110% of the average torsional stiffness of the 33-100% portion of the shaft.

Still referring to FIG. 20 but focusing now on the rightmost column associated with tip and root half lengths, in one embodiment, the average bending stiffness of the 0-50% portion of the shaft is at least 50%, in another embodiment at least 60%, and in yet another embodiment at least 60-70% of the average bending stiffness of the 50-100% portion of the shaft. Attention is now drawn to the average torsional stiffness, in one embodiment, the average torsional stiffness of the 0-50% portion of the shaft being at least 90%, in another embodiment at least 95%, and in yet another embodiment at least 95-115% of the average torsional stiffness of the 50-100% portion of the shaft.

Referring back to fig. 18 in general, in one embodiment, the average first tip portion bending stiffness is 10-50n x m ² While the average second tip portion bending stiffness is 10-50N m ² . In another embodiment, the average first tip portion torsional stiffness is 5 to 40N x m ² While the average second tip portion torsional stiffness is 5-40n x m ² . In other embodiments, the tip portion bending stiffness is reduced to include 10-40N x m ² Within the range of (1), in another embodiment, 12.5-37.5N x m ² Within a range of (2). In other embodiments, the tip portion torsional stiffness is reduced to include 5-35N m ² Within the range of 7.5-30N x m in another embodiment ² 。

In a specific embodiment, the kit comprises at least two tip sections, wherein the tip sections differ in bending stiffness by at least 5n x m ² In another embodiment differing by at least 10n x m ² In yet another embodiment at least 15n x m apart ² . In other embodiments the bending stiffness difference is no more than 30N m ² In another embodiment no more than 25n x m ² In yet another embodiment no more than 20n x m ² . In another embodiment, the kit comprises at least two tip sections, wherein the tip sections differ in torsional stiffness by at least 5n x m ² In another embodiment at least 10n x m ² In yet another embodiment at least 15n x m2. In an additional embodiment, the torsional stiffness difference does not exceed 35N m ² In another embodiment no more than 30n x m ² In yet another embodiment no more than 25n x m ² 。

The kit may further comprise at least three tip sections or even at least four tip sections, and the stiffness relationship just disclosed may be applied to any pair of tip sections or even all tip sections. In these embodiments, at least half of the tip sections have different average bending stiffness and different average torsional stiffness, as is the case with the embodiment of fig. 18, while in another embodiment, each tip section may have a bending and/or torsional stiffness that is unique and different from the other tip sections. In another such embodiment, none of the tip sections has an average bending stiffness that exceeds three times the average bending stiffness of the other tip sections, and none of the tip sections has an average torsional stiffness that exceeds five times the average torsional stiffness of the other tip sections.

Further, the relationship of tip portion stiffness to root portion stiffness is critical to produce a product that does not feel a user waving a stiff or tip-sided strip-like plate. Thus, in one embodiment, the average root portion bending stiffness is at least 40n x m ² And an average root portion torsional stiffness of at least 20N m ² . In another embodiment, the average root portion bending stiffness is at least 50N m ² While the average root portion torsional stiffness is at least 25n x m ² . In another embodiment, the average root portion bending stiffness is 50-110N m ² While the average root portion torsional stiffness is 20-70n x m ² . In another embodiment, the average root portion bending stiffness is 60-100N m ² While the average root portion torsional stiffness is 25-60N m ² . When the average root portion bending stiffness is at least three times the tip portion bending stiffness of one of the tip portion selections and at least twice the tip portion bending stiffness of the second of the tip portion selections, a significant difference in the preferred flexibility of fit and in hand and performance is found. In another embodiment, the average root portion bending stiffness is 3-6 times the tip portion bending stiffness of one of the tip portions and 2-4 times the tip portion bending stiffness of the second of the tip portions. In these embodiments, the stiffness of the root portion provides less shot dispersion and consistency for the low swing golfer, while the tip portion The stiffness helps the low swing golfer achieve a preferred launch angle.

Continuing with the disclosure of root portion 1000, in one embodiment, the average root portion flexural stiffness is at least 2 times the average root portion torsional stiffness. In another embodiment, the average root portion bending stiffness is no more than 4 times the average root portion torsional stiffness. In another embodiment, the average root portion bending stiffness is greater than the tip portion bending stiffness of at least 50% of the tip portions in the kit, and in another embodiment, the average root portion bending stiffness is greater than the tip portion bending stiffness of all the tip portions in the kit.

In another embodiment, at least one tip portion of the kit of at least two tip portions has an average tip portion bending stiffness that is within 70% of the average root portion bending stiffness, and at least one tip portion has an average tip portion bending stiffness that is at least 70% less than the average root portion bending stiffness. Another embodiment includes at least three tip portions in the kit, at least two of which have an average tip portion bending stiffness that is within 70% of the average root portion bending stiffness, and yet another embodiment includes at least four tip portions in the kit, at least two of which have an average tip portion bending stiffness that is within 70% of the average root portion bending stiffness, and at least two of which have an average tip portion bending stiffness that is at least 70% less than the average root portion bending stiffness.

Likewise, in another embodiment, at least one tip portion of the kit of at least two tip portions has an average tip portion torsional stiffness that is within 30% of the average root portion torsional stiffness, and at least one tip portion has an average tip portion torsional stiffness that is at least 60% less than the average root portion torsional stiffness. Another embodiment includes at least three tip sections in the kit, at least two of which have an average tip section torsional stiffness that is within 30% of the average root section torsional stiffness, and yet another embodiment includes at least four tip sections in the kit, at least two of which have an average tip section torsional stiffness that is within 30% of the average root section torsional stiffness, and at least two of which have an average tip section torsional stiffness that is at least 60% less than the average root section torsional stiffness.

In another embodiment, at least one tip portion of the kit of at least two tip portions has an average tip portion bending stiffness of 50% -60% of the average root portion bending stiffness, and at least one tip portion of the kit has an average tip portion torsional stiffness of 75% -90% of the average root portion torsional stiffness. Another embodiment comprises at least three tip sections in the kit, wherein at least two of the at least two tip sections have an average tip section bending stiffness of 50% -60% of the average root section bending stiffness, and yet another embodiment comprises at least four tip sections in the kit, wherein at least two of the at least two tip sections have an average tip section bending stiffness of 50% -60% of the average root section bending stiffness, and at least two of the at least two tip sections have an average tip section torsional stiffness of 75% -90% of the average root section torsional stiffness.

Likewise, in another embodiment, at least one tip portion of the kit of at least two tip portions has an average tip portion torsional stiffness that is 75% -90% of the average root portion torsional stiffness, and at least one tip portion of the kit has an average tip portion torsional stiffness that is 20% -35% of the average root portion torsional stiffness. Another embodiment comprises at least three tip sections in the kit, wherein at least two of the at least two tip sections have an average tip section torsional stiffness of 75% -90% of the average root section torsional stiffness, and yet another embodiment comprises at least four tip sections in the kit, wherein at least two of the at least two tip sections have an average tip section torsional stiffness of 75% -90% of the average root section torsional stiffness, and at least two of the at least two tip sections have an average tip section torsional stiffness of 20% -35% of the average root section torsional stiffness. The present invention is often directed to the feature of "at least one of the tip portions of the kit", but the present disclosure is not limited to "kit" embodiments, but also includes shafts that are used alone, whether the shafts are integral or separate (permanently joined together or releasably joined together) to possess the disclosed attributes and relationships.

In a preferred embodiment, the second tip portion is no more than 50%, in another embodiment no more than 30%, in yet another embodiment no more than 20%, in yet another embodiment no more than 10%, in yet another embodiment no more than 5% heavier than the first tip portion. Further, the first tip portion mass is 25% -99% of the root portion mass, the second tip portion mass is 25% -99% of the root portion mass, and in another embodiment the tip portion mass is 30% -70% of the root portion mass, and in yet another embodiment the tip portion mass is 35% -60% of the root portion mass. In one embodiment, the tip portion mass is no more than 40 grams, and in other embodiments no more than 35 grams or 30 grams or 25 grams or 20 grams. In another embodiment, the root portion mass is no more than 70 grams, in another embodiment no more than 60 grams, and in yet another embodiment no more than 45 grams. In embodiments for mixed iron and iron, the mass of the individual components may be slightly heavier. For example, in one embodiment, the tip portion mass does not exceed 50 grams, and in other embodiments does not exceed 40 grams or 35 grams or 30 grams or 25 grams, and in another embodiment, the root portion mass does not exceed 90 grams, and in other embodiments does not exceed 80 grams, 70 grams, and 60 grams. In other embodiments, the relation of the second tip portion mass to the first tip portion mass disclosed in this paragraph may also be applied to the third tip portion mass and the fourth tip portion mass relative to the first tip portion mass, and likewise relative to the tip portion mass and the root portion mass, as well as the overall mass.

In some kit embodiments, there are at least two tip portions, wherein the mass varies by at least 15%, in another embodiment by at least 25%, and in yet another embodiment by at least 40%, thereby exhibiting a greater variety of choices to ensure that the user can actually feel the difference in the various choices. Likewise, in some kit embodiments, there are at least two root portions, wherein the mass varies by at least 15%, in another embodiment by at least 25%, and in yet another embodiment by at least 40%, thereby demonstrating a greater variety of options. Similarly, in some kit embodiments, there is at least a coupler portion wherein the mass varies by at least 15%, in another embodiment by at least 25%, and in yet another embodiment by at least 40%, thereby demonstrating a greater variety of options.

One particular kit embodiment includes at least three tip portions (referred to as a family of tips) and/or at least three root portions (referred to as a family of roots), at least two of these components in the same family having a mass that is within 5% of the mass of the other components (measured relative to the lightest family component), while the mass of the other components in the family is at least 15% heavier than the lightest family component. In another kit embodiment, the mass of at least two of these components in the same family is within 2.5% of the mass of the other components (measured relative to the lightest family component), while the mass of the other components in the family is at least 25% greater than the lightest family component. Another kit embodiment includes at least two tip portions and/or at least two root portions, at least one member within the same family being at least 15% heavier than the lightest family member, while in another embodiment at least 15% -45% heavier than the lightest family member, and in an even more specific embodiment at least 15% -30% heavier.

The bending stiffness and torsional stiffness of the tip and root portions can vary greatly while maintaining nearly the same mass (if desired) by incorporating fibers of different tensile strengths and/or modifying the ply orientation or density of the fibers. In one embodiment, the number of unidirectional prepreg layers in the root portion is different than in the tip portion. In another embodiment, the fiber orientation angle between adjacent unidirectional layers at the root portion is different from the fiber orientation angle between adjacent unidirectional layers at the tip portion. In yet another embodiment, the resin content of the root portion is different from the resin content of the tip portion, and in yet another embodiment, the resin content of the root portion is greater than the resin content of the tip portion. The above-mentioned "resin content" refers to the weight ratio of the resin relative to the total weight of the fiber-reinforced resin. The weight of the resin is obtained by chemically decomposing or removing only the resin in the fiber-reinforced resin to be measured to obtain only the fibers, and subtracting the total weight of the fibers from the weight of the fiber-reinforced resin measured previously. To chemically remove the resin from the fiber reinforced resin, a heated nitric acid solution, for example, is used. Further, in order to chemically remove the resin from, for example, a prepreg, methyl ethyl ketone, for example, is used.

In one embodiment, a preferred balance and performance is found when the tip portion mass is 20-30 grams, the root portion mass is 40-50 grams and the coupling mass is 5-17.5 grams. In fact, the coupling mass preferably does not exceed the tip portion mass and does not exceed 50% of the root portion mass, while in another embodiment the coupling mass does not exceed 75% of the tip portion mass and does not exceed 35% of the root portion mass, and in yet another embodiment the coupling mass is 35% -60% of the tip portion mass and 20% -35% of the root portion mass. Another embodiment further recognizes that it is not an objective to simply minimize the weight of the coupling mass, which in this embodiment is at least 25% of (a) the mass of the first tip portion and (b) the second tip portion. Likewise, in another embodiment, the first tip portion mass is 35% -85% of the root portion mass, and the second tip portion mass is 35% -85% of the root portion mass, and in another embodiment these ranges are narrowed to 40% -80%, 45% -75%, and 50% -70%.

Referring now to the back stiffness relationship and fig. 18, in another embodiment, the maximum second tip portion bending stiffness is at least 50% greater than the maximum first tip portion bending stiffness and the maximum second tip portion torsional stiffness is at least 75% greater than the maximum first tip portion torsional stiffness. In another embodiment, the maximum second tip portion bending stiffness is 35% -150% greater than the maximum first tip portion bending stiffness and the maximum second tip portion torsional stiffness is 75% -350% greater than the maximum first tip portion torsional stiffness. The kit of another embodiment includes a first tip portion having a maximum first tip portion torsional stiffness that is greater than the maximum first tip portion bending stiffness, such as the red tip of fig. 18, and a second tip portion having a maximum second tip portion torsional stiffness that is less than the maximum second tip portion bending stiffness, such as the green tip, blue tip, or white tip of fig. 18. In another such embodiment, the maximum first tip portion torsional stiffness is at least 30% greater than the maximum first tip portion bending stiffness and the maximum second tip portion torsional stiffness is at least 50% less than the maximum first tip portion bending stiffness.

Similar to the embodiment just discussed with respect to tip portion 2000 and fig. 18, in embodiments having multiple root portions 1000, the bending stiffness and torsional stiffness may also be varied to provide the advantages and attributes described in connection with the variation of tip portion 2000. For example, in one embodiment, the maximum second root portion bending stiffness is at least 25% greater than the maximum first root portion bending stiffness and the maximum second root portion torsional stiffness is at least 50% greater than the maximum first root portion torsional stiffness. In yet another embodiment, the maximum second root portion bending stiffness is 25% -150% greater than the maximum first root portion bending stiffness and the maximum second root portion torsional stiffness is 50% -350% greater than the maximum first root portion torsional stiffness. The kit of another embodiment includes a first root portion having a maximum first root portion torsional stiffness greater than a maximum first root portion flexural stiffness and a second tip portion having a maximum second root portion torsional stiffness less than a maximum second root portion flexural stiffness. In another such embodiment, the maximum first root portion torsional stiffness is at least 30% greater than the maximum first root portion flexural stiffness and the maximum second root portion torsional stiffness is at least 50% less than the maximum first root portion flexural stiffness.

The length and center of gravity relationship also plays an important role in providing an adjustable shaft that provides a unique relationship that improves fit, performance and feel while also distributing stresses within the shaft and avoiding stress risers that negatively impact durability. Each tip portion (2001, 2002, 2003, 2004) has a tip portion length 2030, each root portion (1000, 1001, 1002, 1003, 1004) has a root portion length 1030, and each coupler (3000, 3001, 3002, 3003, 3004) has a coupler length 3030 measured end-to-end in fig. 21. In embodiments having a single root portion 1000, at least one coupler 3000, and at least two tip portions 1000, the first tip portion length is at least 25% less than the root portion length 1030, and the second tip portion length is at least 25% less than the root portion length 1030, and the coupler length 3030 is no more than 50% of either tip portion length. In another embodiment, the tip portion lengths are each at least 25% of the root portion length 1030, and the coupler length 3030 is at least 10% of either tip portion length. In another embodiment, the first tip portion length is 25% -80% shorter than the root portion length 1030 and the second tip portion length is 25% -80% shorter than the root portion length 1030, in yet another embodiment, at least two tip portions 2000 have the same length and at least one tip portion 2000 has a different length. For swinging the club, the tip portion length is preferably 8-26", the heel portion length is preferably 22-40", the coupler length is preferably 0.5-8.0", and in another embodiment, the tip portion length is 10-22", the heel portion length is 26-36", and the coupler length is 1.0-4.0". In one embodiment, each tip portion length is at least 20% of the shaft length 130, while in another embodiment, each tip portion length is no more than 40% of the shaft length 130, and in yet another embodiment, no more than 25% -37.5%.

In another embodiment, the shaft center of gravity of the shaft 100 is no more than 65%, in yet another embodiment no more than 60%, and in yet another embodiment no more than 55% of the shaft length 130 from the shaft CG of the shaft proximal end 120, whichever tip portion is mounted. In yet another embodiment, the shaft CG distance is greater than the distance from the proximal shaft end 120 to any portion of the coupler 3000, and thus the shaft center of gravity is located between the coupler 3000 and the distal shaft end 110. A family of embodiments implements any of the relationships disclosed herein while controlling the shaft CG distance so that the shaft CG distance varies by 5mm or less while implementing the associated relationship, whether or not the relationship is related and associated with different tip portions, root portions, and/or stiffness of the union or other aspects. Further, this may only apply to two parts in a particular kit, up to each part in the kit. Another embodiment of the family achieves a 3mm or less shaft CG distance change and in another embodiment achieves a 2mm or less change. The change in the control shaft CG distance requires a unique configuration of the weight distribution of one or more components that are interchangeable to achieve a target relationship while also achieving a change in the shaft CG distance.

The variation in stiffness over the shaft length 130 significantly affects the beatability and feel of the particular combination of the root portion 1000, tip portion 2000, and coupler 3000. Further, selectively designing stiffness mutations over relatively short lengths in specific areas may lead to desirable turning points. This is in contrast to conventional shaft designs, which strive to achieve a smooth stiffness transition over the entire length, and describe abrupt changes in stiffness as undesirable. Further, for some swing types, abrupt changes in stiffness over a relatively short length in a particular region result in more efficient energy transfer.

In one such embodiment, as shown in fig. 19 (a) to (D) and 23 (a) to (D), the shaft bending stiffness exceeds 125n x m over a distance of no more than 15% of the shaft length 130 ² The shaft torsional stiffness exceeds 100n x m over a distance of no more than 15% of the shaft length 130 ² . In another embodiment, the shaft bending stiffness exceeds 150N m over a distance of no more than 15% of the shaft length 130 ² The shaft torsional stiffness exceeds 115n x m over a distance of no more than 15% of the shaft length 130 ² 。

Other embodiments recognize the minimum distance at which the stiffness abrupt change described above occurs. For example, in these embodiments, the disclosed stiffness levels are not limited to only occurring at distances no more than 15% of the shaft length 130, but must also occur at distances of at least 3.5% of the shaft length 130 in these embodiments, and at least 5% in other embodiments. The shaft 100 may also include a stiffening region located between a first point 5 "from the proximal shaft end (120) and a second point 36" from the proximal shaft end (120), the shaft bending stiffness at a location within the stiffening region being (a) at least 100% greater than the minimum first tip section bending stiffness and the minimum second tip section bending stiffness, and (B) at least 50% greater than the minimum root section bending stiffness. In another embodiment, the shaft bending stiffness at a location within the stiffening region is (A) at least 125N m ² (B) at least 200% greater than both the minimum first tip portion bending stiffness and the minimum second tip portion bending stiffness, and (C) at least 75% greater than the minimum root portion bending stiffness.

Yet another embodiment recognizes diminishing returns and negative attributes associated with excessive stiffness increases, thus limiting the increase so that the shaft bending stiffness does not exceed 600n x m ² The torsional rigidity of the rod body is not more than 450N m ² Such as the embodiment illustrated in fig. 25, wherein the joint comprises a steel alloy component. In yet another embodiment, the shaft bending stiffness is no more than 300n x m ² The torsional rigidity of the rod body is not more than 250N m ² Such as the embodiment illustrated in fig. 24, wherein the joint comprises a titanium alloy component. Further, in yet another embodiment, the shaft bending stiffness is no more than 250n x m ² The torsional rigidity of the rod body is not more than 200N m ² Such as the embodiment illustrated in fig. 23 (a), wherein the joint comprises an aluminum alloy component. Those skilled in the art will appreciate that these rigidities are due not only to material properties, but also to unique ranges that have been addressed and joints 3000 specifically designed to achieve these ranges, while balancing the trade-offs associated with weight and durability issues that are common to abrupt stress changes over shorter lengths.

The interchangeable coupler embodiment of fig. 21 and 22 incorporates a tip coupler portion 3300, a root coupler portion 3400, and fasteners 3500. Tip coupler portion 3300 is coupled to tip portion 2000 along tip coupling length 3310. In the illustrated embodiment, the tip portion 2000 extends into the tip coupler portion 3300, although possibly vice versa. The tip bond length 3310 need not be a continuous contact between the tip portion 2000 and the tip coupler portion 3300, but is merely a mating length, as most embodiments will incorporate grooves or channels on one or more surfaces to increase the adhesive strength when the tip coupler portion 3300 is adhered to the tip portion 2000. Further, the "mating length" does not require direct contact of the tip portion 2000 and the tip coupler portion 3300, as they may be separated from one another by a layer of adhesive.

Similarly, root coupler portion 3400 is joined to root portion 1000 along root joining length 3410. In the illustrated embodiment, the root portion 3400 extends into the root coupler portion 1000, although possibly vice versa. Tip bond length 3310 and root bond length 3410 significantly affect the abrupt stiffness change over a relatively short length in a specific region, and associated desirable properties, previously disclosed. The tip engagement length 3310 is at least as long as the tip portion outer diameter 2070, and in another embodiment is 2 times the tip portion outer diameter 2070. Likewise, root bond length 3410 is at least as long as tip portion outer diameter 2070, and in another embodiment is 2 times tip portion outer diameter 2070. Increasing the tip bond length 3310 and/or root bond length 3410 provides advantages associated with greater bond area, load distribution, and less stress, which increases in length may be detrimental to the performance of the shaft 100 because the abrupt stiffness changes extend over an excessive portion of the shaft length 130. Thus, in one embodiment, tip bond length 3310 and root bond length 3410 do not exceed 10 times tip portion outer diameter 2070, and in another embodiment do not exceed 7 times tip portion outer diameter 2070, and in yet another embodiment do not exceed 5 times tip portion outer diameter 2070. In another embodiment, tip bond length 3310 and root bond length 3410 are at least 0.500", in another embodiment at least 0.625", and in yet another embodiment at least 0.750".

In the embodiment of fig. 21 and 22, the fastener 2500 is configured to be coupled with the tip coupler portion 3300 and the root coupler portion 3400. In this embodiment, fastener 3500 is a sleeve internally threaded to mate with external threads on root coupler portion 3400, securing tip coupler portion 3300 within root coupler portion 3400, however in another embodiment the configuration may be reversed. Fastener 3500 is coupled to one of tip coupler portion 3300 and root coupler portion 3400 without the need for threaded coupling, other mechanical engagement methods may be employed. Further, in some embodiments, fasteners 3500 need not be simultaneously coupled with tip coupler portion 3300 and root coupler portion 3400. For example, in embodiments having a metallic tip portion 2000, fastener 3500 may be directly coupled to tip portion 2000. The root coupler portion 3400 may be external to the root portion 1000 and receive a portion of the root portion 1000 within the root coupler portion 3400. Fastener 3500 provides another adjustable point in the system, and in one embodiment, the kit includes at least two fasteners 3500, one of which is at least 2 times denser than the other.

In one embodiment, at least a portion of the coupler 3000 is comprised of a metallic material, while in another embodiment, the tip coupler portion 3300 and the root coupler portion 3400 are formed of a metallic material, and in yet another embodiment, the tip coupler portion 3300, the root coupler portion 3400, and the fastener 3500 are formed of a metallic material. In another embodiment, the coupler density of any of the just disclosed hardware is no more than 3 times the root portion density. The coupler 3000 may also include a compressible adapter 3600 that is located in a position susceptible to durability issues, such as the interface between the exposed end of the root portion 1000 and the fastener 3500, as illustrated in fig. 22. This region experiences significant deflection of the shaft 100 during a golf swing, and contact with the metal fastener 3500 on the exposed section of the heel portion 1000 may result in damage to the heel portion 1000, particularly when the heel portion is made of a non-metallic material. Thus, in one embodiment, tip coupler portion 3300 and root coupler portion 3400 are designed to ensure that there is a gap of at least 0.5mm between fully-joined fastener 3500 and one end of root portion 1000, while in another embodiment the gap is at least 1.0mm, and in yet another embodiment the gap is no more than 5.0mm.

As shown in FIG. 22, the fastener 3500 length measured along the shaft axis from end to end is less than the tip bond length 3310, in another embodiment less than the root bond length 3410, and in yet another embodiment less than one-half the length of at least one of the tip bond length 3310 and the root bond length 3410. The fasteners 3500 may be designed to be engaged by a fastening tool to adequately secure the components, in a further embodiment the tool may be a torque limiting tool to prevent a user from over tightening and damaging either component, in another embodiment the fasteners 3500 are designed to not be fully engaged with at least one of the other portions of the coupler 3000 without the use of a tool, in other words, to not do so by bare hands. One or more tool-engaging features 3520, which may include protrusions or depressions, may be formed on the outer surface of the fastener 3500 to engage with complementary structures on the fastening tool, as shown in fig. 22.

Further, fastener 3500 can incorporate a fastener taper 3510, which can be integral with fastener 3500, or can be as a separate component as illustrated in fig. 22. The tapered portion 3510 of the fastener has a taper angle measured from the outer surface to the inner surface of 10-60 degrees, in another embodiment 15-50 degrees, and in yet another embodiment 20-45 degrees. The fastener taper portion 3510 provides a more gradual transition from the root portion to the tip portion and can serve to mask variations in outer diameter and further distribute stresses. The volume of fastener tapered portion 3510 is at least 50% of the volume of fastener 3500, but no more than 25% of the mass of fastener 3500. Additionally, fastener 3500 can include undercuts 3530 to further distribute stress and prevent stress risers associated with sharp metal edges. The undercut 3530 is at an angle of at least 15 degrees from horizontal that extends at least 25% of the thickness of the fastener 3500. Another advantage of the fastener tapered portion 3510 embodiment is that the undercut 3530 is hidden, and in some embodiments extends into the undercut 3530. This region experiences significant bending of the tip portion and slight bending of fastener 3500, so it is preferable to avoid abrupt interface changes. Fastener tapered portion 3510 can be formed from a non-metallic material and also serves to dampen vibrations transmitted across fastener 3500. In one embodiment, fastener tapered portion 3510 is formed of a highly elastic material having a mass of less than 10 grams.

The mass distribution and stiffness relationship disclosed may be achieved by a variety of methods, one of which is that the tip portion 2000 may be hollow, or at least partially hollow, with a tip portion sidewall thickness 2050 that varies between a minimum tip portion sidewall thickness and a maximum tip portion sidewall thickness. In one such embodiment, the maximum tip portion sidewall thickness is at least 25% greater than the minimum tip portion sidewall thickness. In another embodiment, the maximum tip portion sidewall thickness is 25% -75% greater than the minimum tip portion sidewall thickness. Still further, in one embodiment, the sidewall thickness of tip coupler portion 3300 that is joined to tip portion 2000 is less than the maximum tip portion sidewall thickness, and in another embodiment, the sidewall thickness of root coupler portion 3400 that is joined to root portion 1000 is less than the maximum root portion sidewall thickness. Further, in yet another embodiment, the maximum tip portion sidewall thickness is greater than the root portion sidewall thickness 4050 of a portion of the root portion 4000.

Root portion 1000 may have a constant outer diameter 1070, or the outer diameter may taper, with or without steps; similarly, tip portion 2000 may have a constant outer diameter 2070, or the inner diameter may taper with or without steps. In one embodiment, at least one of the root portion 1000 and the tip portion 2000 includes a portion having a constant outer diameter, while in another embodiment, both the root portion 1000 and the tip portion 2000 include a portion having a constant outer diameter. In one embodiment, the entire root portion 1000 has a constant outer diameter, and in another embodiment, the tip portion 2000 has both a tip portion tapered section 2080 and a tip portion constant diameter section 2090, as shown in fig. 17, where there are two tip portion constant diameter sections 2090 separated by the tip portion tapered section 2080. In one embodiment, the length of the tip portion tapered section 2080 is preferably greater than the length of the tip portion constant diameter section 2090 or sections, while in another embodiment, the length of the tip portion tapered section 2080 is 50% -80% of the length of the tip portion 2030. Whether the taper is in root portion 1000, tip portion 2000, or both, in further embodiments, the taper causes the outer diameter to vary by at least 5% as measured from the minimum outer diameter.

Locating the significant change in the outer diameter at the location of the stiffening can significantly affect the location of the turning point of the shaft 100. In one such embodiment, from root portion 1000 to tip portion 2000, the shaft outer diameter is reduced by at least 15%, in another embodiment by at least 20%, and in yet another embodiment by at least 25% through coupling 3000. However, too significant a change in the shaft outer diameter at the coupling 3000 may negatively impact the performance, durability, and aesthetics of the shaft 100. Thus, in one embodiment, from root portion 1000 to tip portion 2000, the shaft outer diameter decreases by no more than 45%, in another embodiment no more than 40%, and in yet another embodiment no more than 35% through coupling 3000. The outer diameter of fastener 3500 may taper to help visually mask significant changes in the outer diameter of shaft 100.

As previously described, selectively designing stiffness mutations over relatively short lengths in specific areas can lead to desirable turning points. Thus, adjusting the location of the abrupt stiffness change along the length of the root portion 1000 and the tip portion 2000 allows for a high flexibility in locating the turning point. One such embodiment maintains a high degree of consistency in the location of the turning point while providing the golfer with two different tip portions 2000 having widely differing bending and torsional stiffness. In this embodiment, the shaft has a first inflection point distance when the first tip portion is included and a second inflection point distance when the second tip portion is included, the second inflection point distance being within 5% of the first inflection point distance, in another embodiment within 3%, and in yet another embodiment within 1% of the characteristic disclosed herein, regardless of the change in the characteristic between the first tip portion and the second tip portion. The turning point distance is the distance along the initial shaft axis from the proximal shaft end 120 to the point of maximum deflection. In the foregoing embodiments, the inflection point distance does not vary significantly, while in one embodiment, the maximum inflection point deflection associated with the inflection point distance relative to the initial shaft axis is very different for the first tip portion compared to the second tip portion. Indeed, in one embodiment, the maximum turning point deflection associated with a shaft having one tip portion is at least 10%, in another embodiment at least 15%, in yet another embodiment at least 20%, however, in another series of embodiments no more than 100%, in other additional embodiments no more than 90% and 80% greater than the other maximum turning point deflection associated with a shaft having a different tip portion.

The previous embodiments incorporate tip portions of the same length, with abrupt changes in stiffness helping to control the inflection point location while accommodating variations in tip portion length of up to 20%, however in these embodiments the first inflection point distance and the second inflection point distance are measured from the distal shaft end 110 rather than from the proximal shaft end 120. In a further embodiment, the turning point is located within 6 "of the edge of the coupling. By providing at least two tip portions with different tip portion lengths, each kit embodiment allows a user to analyze the effect of the location of the turning point, both tip portions comprising one long tip portion having a length that is at least 15%, in another embodiment at least 25%, in yet another embodiment at least 35% longer than the short tip portion. The two tip portions of different lengths may have the same bending stiffness distribution and/or torsional stiffness distribution. In another embodiment, the long tip portion is no more than 75%, in yet another embodiment no more than 65%, and in yet another embodiment no more than 50% longer than the short tip portion length.

Referring to fig. 19 (a) to 19 (D), one embodiment has at least one of: (a) A minimum first tip portion bending stiffness, and (b) a minimum second tip portion bending stiffness that is at least 30% less than a root portion bending stiffness of a portion of the root portion, the maximum root portion bending stiffness not exceeding 70% of the maximum shaft bending stiffness. In yet a further embodiment, at least one of: (a) The minimum first tip portion bending stiffness and (b) the minimum second tip portion bending stiffness being at least 50% less than the root portion bending stiffness of a portion of the root portion, the maximum root portion bending stiffness not exceeding 55% of the maximum shaft bending stiffness, and at least one of: (a) The maximum first tip portion bending stiffness and (b) the maximum second tip portion bending stiffness are at least 30% of the maximum root portion bending stiffness.

Similarly, another embodiment has at least one of the following: (a) A minimum first tip portion torsional stiffness, and (b) a minimum second tip portion torsional stiffness that is at least 30% less than a root portion torsional stiffness of a portion of the root portion, the maximum root portion torsional stiffness not exceeding 70% of the maximum shaft torsional stiffness. In yet a further embodiment, at least one of: (a) The minimum first tip portion torsional stiffness and (b) the minimum second tip portion torsional stiffness being at least 50% less than a root portion torsional stiffness of a portion of the root portion, the maximum root portion torsional stiffness not exceeding 55% of the maximum shaft torsional stiffness, and at least one of: (a) The maximum first tip portion torsional stiffness and (b) the maximum second tip portion torsional stiffness are at least 60% of the maximum root portion torsional stiffness. Additionally, in one specific embodiment, the shaft bending stiffness is constant along at least 10% of the length of the shaft and the shaft torsional stiffness is constant along at least 10% of the length of the shaft.

As shown in the embodiments of fig. 23 (a) through 23 (D), the bending stiffness and torsional stiffness vary over a substantial portion of the shaft between the proximal shaft end 120 and the most stiff portion, while the bending stiffness and torsional stiffness are constant over a substantial portion of the shaft between the most stiff portion and the distal shaft end 110. In a further embodiment, the bending stiffness and torsional stiffness vary by less than 70%, in another embodiment less than 60%, and in yet another embodiment less than 50% over a portion of the shaft between the proximal end 120 of the shaft and where the stiffness is greatest. However, the bending stiffness varies by at least 5% over a portion of the shaft between the proximal end 120 of the shaft and where the stiffness is greatest.

Any of the above disclosures may be incorporated into embodiments directed to methods of adapting a golfer to a golf club shaft, as well as methods of marketing a golf club shaft and methods of constructing or assembling a golf club shaft. In one embodiment, references to "kits" as used throughout this disclosure include systems of components sold together as a single sales unit, such as packaged together in a single box, however, a "kit" also includes cases where such components may be tried and/or purchased together, even though such components may ultimately be purchased separately, even from different sites or sources.

For example, it may be the case of a retail display containing multiple tip portions and/or multiple root portions from which a user or professional exerciser may mix and match components to perform experiments and/or purchase components individually to construct a single shaft, even if remotely ordered and assembled. For example, a golf retailer may have a wide variety of components, including at least a plurality of different tip portions, which a potential user or professional exerciser may combine and assemble into a golf club shaft, preferably with some adaptation assistance (whether from a professional, instruction, application, or other software system). The potential user may then attach the assembled golf club shaft to the club head to create a golf club, and then bring the golf club into the hitting zone to evaluate the combination by hitting multiple golf balls. The potential user may repeat the process multiple times for different combinations of components until they achieve the combination of swing and ideal ball flight characteristics that best suits them. The software system may utilize component combination recommendations to guide potential users based on data received by the system from a flight monitor or other ball flight recording or simulation device, for example, based on different flexural and/or torsional stiffness characteristics, the system may analyze the collected data and identify and optionally recommend different tip portions that help users more likely to generate test data more similar to the user selected target ball flight characteristics. The potential user then purchases only those components necessary to assemble their desired combination and orders a shaft of preferred components that can be remotely assembled and mailed to the user. Thus, in this embodiment, the kit purchased by the user does not contain multiple versions of at least one component required to construct a golf club, however, at least one of the necessary components has multiple versions for potential user selection and/or experimentation and/or purchase or order. Thus, in one embodiment, the kit may be a retail display or even self-service. Further, the online ordering system still functions as the disclosed kit, allowing a user to select from multiple versions of at least one required component and purchase other components necessary to create a final shaft, whether purchased together at once or separately in separate portions.

One embodiment comprises the steps of: (a) Selecting a first tip portion from a plurality of different tip portions; (b) Assembling a first shaft including a selected first tip portion; (c) Engaging the club head to the first shaft to create a first golf club; (d) Striking a plurality of golf balls with a first golf club, collecting a plurality of ball flight data associated with the first golf club; (e) Selecting a second tip portion from a plurality of different tip portions based on at least one of the plurality of ball flight data; (f) Removing the club head and the first tip portion from the first shaft, installing the second tip portion, creating a second shaft; (g) Joining the club head to a second shaft creating a second golf club; and (h) striking a plurality of golf balls with a second golf club, collecting a plurality of ball flight data associated with the second golf club. The software system may analyze the first ball flight data and the second ball flight data and prepare a visual comparison between the results of the two golf clubs. Further, the system may recommend a suggested tip portion between the two, or suggest to try a third tip portion and repeat the process. The method may further include the step of selecting a preferred combination of components based on a comparison of ball flight data associated with the first golf club and ball flight data associated with the second golf club, and may further include the step of deciding to purchase.

Any or all of these steps may occur in a virtual or simulated environment. For example, the potential user may upload his or her own swing video, or data representing his or her own swing, to the computer system. The software system may evaluate the swing, as well as attributes including swing speed and acceleration profile, and attack angle, and suggest the best combination of components to produce a custom-made preferred golf club shaft, achieving the best performance based on the evaluated golf swing. In a further embodiment, the system may simulate a plurality of shafts, determine simulated performance characteristics for each shaft, and display the simulated performance characteristics for potential users so that potential users can see how the combination affects simulated ball flight. The software system may also include the step of evaluating ball flight data, including any or all of the data collected by commercially available systems such as SkyGolf SkyTrak, rapsodo, flightScape Mevo, voice Caddie SC300, and equivalents.

Additionally, the disclosed interchangeable tip portion embodiments and methods may be used in creating a one-piece composite golf club shaft that possesses a bending stiffness profile and a torsional stiffness profile that best matches a particular user's golf swing. In other words, in one embodiment, the interchangeable tip section shaft system is used in a fitting process to identify a preferred bending stiffness profile and torsional stiffness profile experimentally, which is then provided to a manufacturing facility to construct an integral composite golf club shaft having the preferred bending stiffness profile and torsional stiffness profile, which shaft may be achieved by prepreg layups, orientation of the individual layers and/or sheets, material properties of the fibers, and/or a combination of resin content and material properties of the resin, to name a few. Accordingly, the present invention includes an integrated golf club shaft incorporating either the disclosed bending or torsional stiffness profiles that in one embodiment tapers uniformly over at least 70% of the shaft length, in a further embodiment without any conventional shaft "steps" at all, wherein the outer diameter varies by more than 1mm.

Further, some disclosed embodiments focus on a coupler 3000 configured to releasably engage a root portion 1000 and a tip portion 2000, another series of embodiments may incorporate a midsection portion and a second coupler. In these embodiments, the coupler 3000 releasably engages the tip portion 2000 and the midsection portion, while the second coupler releasably engages the midsection portion and the root portion 1000. In one embodiment, the bending stiffness and torsional stiffness of the midsection portion varies by less than 70%, in another embodiment less than 60%, and in yet another embodiment less than 50% over a portion of the shaft located between the couplers. However, in another embodiment, the bending stiffness varies by at least 5%, in another embodiment by at least 10%, and in yet another embodiment by at least 15% over a portion of the shaft positioned between the couplers. These embodiments selectively design the stiffness abrupt change over a relatively short length in a specific region to further bring about the desired turning point location. This is in contrast to conventional shaft designs, which strive to achieve a smooth stiffness transition over the entire length, and describe abrupt changes in stiffness as undesirable. Further, for some swing types, abrupt changes in stiffness over a relatively short length in a particular region result in more efficient energy transfer.

In one such embodiment, the shaft bending stiffness at the second coupling exceeds 125n x m over a distance no longer than 15% of the shaft length 130 ² The shaft torsional stiffness exceeds 100n x m over a distance of no more than 15% of the shaft length 130 ² . In a further embodiment, the shaft bending stiffness at the second coupling exceeds 150n x m over a distance of no more than 15% of the shaft length 130 ² The shaft torsional stiffness exceeds 115n x m over a distance of no more than 15% of the shaft length 130 ² . Other embodiments recognize the minimum distance at which the stiffness abrupt change described above occurs. For example, in these embodiments, the disclosed stiffness levels are not limited to only occurring at distances no more than 15% of the shaft length 130, but must also occur at distances of at least 3.5% of the shaft length 130 in these embodiments, and at least 5% in other embodiments. The shaft 100 may further include a second stiffening region located between a first point 5 "from the distal shaft end (110) and a second point 36" from the distal shaft end (110), the shaft bending stiffness at a location within the second stiffening region being (a) at least 100% greater than the minimum first tip section bending stiffness and the minimum second tip section bending stiffness, and (B) at least 50% greater than the minimum root section bending stiffness. In another embodiment, the shaft bending stiffness at a location within the second stiffening zone is (a) at least 125n x m ² (B) at least 200% greater than both the minimum first tip portion bending stiffness and the minimum second tip portion bending stiffness, and (C) at least 75% greater than the minimum root portion bending stiffness.

In further embodiments, at least one of the tip portion or the root portion includes a portion having filler material such that a cross-section perpendicular to the shaft axis is fully occupied by filler material, which is not to say that the filler material may not include voids or air pockets, as the filler material does in some embodiments. The tip portion, the root portion, or the hollow portion of the entire shaft may be partially or entirely filled with an elastic polymer or highly elastic material (e.g., a viscoelastic urethane polymer material), a thermoplastic highly elastic material (TPE), a thermoplastic polyurethane material (TPU), and/or other suitable types of materials to dampen vibration, isolate vibration, and/or reduce noise. Another embodiment incorporates a polymeric material, such as an ethylene copolymer material, to dampen, isolate, and/or reduce noise when the golf club head hits a golf ball. Examples include high density ethylene copolymer ionomers, modified fatty acid ethylene copolymer ionomers, highly amorphous ethylene copolymer ionomers, ionomers of ethylene acrylic acid ester terpolymers, ethylene copolymers including magnesium ionomers, injection moldable ethylene copolymers that can be used in conventional injection molding equipment to create various shapes, ethylene copolymers that can be used in conventional extrusion equipment to create various shapes, and/or ethylene copolymers having high compressibility and low elasticity similar to thermoset polybutadiene rubber. Further embodiments may incorporate a polymeric material and a plurality of microbubbles made of glass, ceramic and/or plastic, also referred to herein as micro hollow beads. When combined with polymeric materials, microbubbles serve two purposes: (1) Air is used for replacing the elastomer to lighten the overall filling weight, thereby reducing the specific gravity of the material; and (2) increasing the porosity of the filler material, allowing the formation of micropores in the polymeric material. Micropores are small air pockets that allow the polymer to bend while maintaining the sound optimization provided by the polymer itself, such as reducing decibel levels and sound durations. The polymeric material is preferably an elastomer, such as polyurethane or silicone having a poisson's ratio of 0.00 to 0.50, or more preferably 0.40 to 0.50, and the microbubbles are preferably measured in D50 microns, which is the median particle size of the measured sample, each microbubble having a diameter of about 18 to 50 microns. In one embodiment, the shore hardness of the filler material is in the range of about a20 to D90. For example, the filler material may be an acrylic epoxy. Other filler material embodiments include polyurethane rubber, polyurethane, ionomers, elastomers, silicones, rubbers, and other similar materials. Still further embodiments incorporate a filler material having a hardness less than the tip portion or root portion, and optionally include an elastic material, such as a polymeric material, natural or synthetic rubber, polyurethane, thermoplastic polyurethane material (TPU), open or closed cell foam, silicone, metal foam, viscoelastic material, or resin. In one embodiment, the density of the filler material is less than 0.9g/cc, in other embodiments less than 0.75g/cc, 0.60g/cc, and 0.45g/cc.

Many alterations, modifications and variations of the preferred embodiments disclosed herein will be apparent to those skilled in the art, and they are all intended and contemplated to be within the spirit and scope of the invention. For example, while specific embodiments have been described in detail, those skilled in the art will appreciate that the foregoing embodiments and variations may be modified to incorporate various alternatives and/or additional or alternative materials, relative arrangement of elements, and dimensional configurations. Accordingly, although only a few variations of the present invention are described herein, it is to be understood that the practice of these additional modifications and variations and the equivalents thereof are within the spirit and scope of the invention as defined in the following claims. The corresponding structures, materials, acts, and equivalents of all means or step plus function elements in the claims below are intended to include any structure, material, or act for performing the function in combination with other claimed elements as specifically claimed.

Claims

1. A golf club shaft comprising:

a shaft having a distal shaft end, a proximal shaft end, an outer shaft diameter, a shaft length, a shaft mass, a shaft center of gravity located a distance from the proximal shaft center of gravity of the shaft, a turning point located a distance from the proximal turning point of the shaft, wherein each point along the shaft length has (i) a shaft bending stiffness comprising a maximum shaft bending stiffness, and (ii) a shaft torsional stiffness comprising a maximum shaft torsional stiffness;

The shaft having a root portion joined to a tip portion by a coupler, wherein the coupler has a coupler mass that is no more than 15% of the shaft mass;

the root portion having a root portion distal end, a root portion proximal end, a root portion length of 20-40 inches, and a root portion mass of no more than 60 grams;

the tip portion having a tip portion distal end, a tip portion proximal end, a tip portion length, and a tip portion mass, the tip portion length being (a) 8-26 inches, (b) at least 25% of the root portion length, and (c) at least 20% of the shaft length, the tip portion mass not exceeding 35 grams and less than 75% of the root portion mass;

the root portion is formed from a root portion material having a root material density, a root portion mass, a root portion elastic modulus, and a root portion shear modulus, and each point along the length of the root portion has (i) a root portion area moment of inertia, (ii) a root portion polar moment of inertia, (iii) a root portion bending stiffness, and (iv) a root portion torsional stiffness, the root portion bending stiffness including an average root portion bending stiffness, a maximum root portion bending stiffness, and a minimum root portion bending stiffness, the root portion torsional stiffness including an average root portion torsional stiffness, a maximum root portion torsional stiffness, and a minimum root portion torsional stiffness;

The tip portion is formed of a tip portion material having a tip material density, a tip portion elastic modulus, and a tip portion shear modulus, and each point along the length of the tip portion has (i) a tip portion area moment of inertia, (ii) a tip portion polar moment of inertia, (iii) a tip portion bending stiffness, and (iv) a tip portion torsional stiffness, the tip portion bending stiffness including an average tip portion bending stiffness, a maximum tip portion bending stiffness, and a minimum tip portion bending stiffness, the tip portion torsional stiffness including an average tip portion torsional stiffness, a maximum tip portion torsional stiffness, and a minimum tip portion torsional stiffness;

wherein:

the average tip portion bending stiffness is 10-50N m ² The average tip portion torsional stiffness is 5-40N m ² The method comprises the steps of carrying out a first treatment on the surface of the And

the bending stiffness of the portion of the shaft located 5-36 inches from the proximal end of the shaft is at least 100% greater than the minimum tip portion bending stiffness.

2. A golf club shaft according to claim 1, wherein the tip portion mass is no more than 30 grams, the tip portion mass is less than 70% of the root portion mass, and the coupler mass is no more than 60% of the tip portion mass.

3. A golf club shaft according to claim 2, wherein the tip portion mass is no greater than 25 grams, the tip portion mass being less than 60% of the root portion mass.

4. A golf club shaft according to claim 2, wherein the maximum shaft bending stiffness is no more than 300n x m ² The maximum shaft torsional stiffness is no more than 250n x m ² 。

5. A golf club shaft according to claim 4, wherein the maximum shaft bending stiffness is no more than 250n x m ² The maximum shaft torsional stiffness is no more than 200n x m ² 。

6. A golf club shaft according to claim 4, wherein the tip portion mass is 20-30 grams, the tip portion mass not exceeding 70% of the root portion mass.

7. A golf club shaft according to claim 4, wherein the tip portion mass is no more than 20 grams.

8. A golf club shaft according to claim 4, wherein the tip portion mass is no more than 60% of the root portion mass.

9. A golf club shaft according to claim 8, wherein the tip portion mass is at least 35% of the root portion mass.

10. A golf club shaft according to claim 4, wherein the shaft center of gravity distance is no more than 65% of the shaft length.

11. A golf club shaft according to claim 10, wherein the shaft center of gravity distance is no more than 55% of the shaft length.

12. A golf club shaft according to claim 4, wherein the bending stiffness of the portion of the shaft located 5-36 inches from the shaft proximal end is at least 200% greater than the minimum tip portion bending stiffness.

13. A golf club shaft according to claim 12, wherein the bending stiffness of the portion of the shaft located 5-36 inches from the shaft proximal end is at least 50% greater than the minimum root portion bending stiffness.

14. A golf club shaft according to claim 12, wherein the bending stiffness of the portion of the shaft located 5-36 inches from the shaft proximal end is at least 125n x m ² 。

15. A golf club shaft according to claim 14, wherein the bending stiffness of the shaft for no more than 15% of the shaft length exceeds 125n x m ² 。

16. The golf club shaft of claim 4, wherein the turning point is within 6 inches of the portion of the coupler.

17. A golf club shaft according to claim 4, wherein the average root portion bending stiffness is 50-110n x m ² The average root portion torsional stiffness is 20-70N m ² The average tip portion bending stiffness is not more than 40N m ² 。

18. The golf club shaft of claim 4, wherein the tip portion length is no more than 75% of the root portion length, the average tip portion bending stiffness is no more than 35n x m ² The average rootThe flexural rigidity is 60-100N m ² The average root portion torsional stiffness is 25-60N m ² 。

19. A golf club shaft according to claim 4, wherein the bending stiffness of the portion of the shaft located 5-36 inches from the proximal end of the shaft is at least 50% greater than the minimum root portion bending stiffness.

20. The golf club shaft of claim 4, wherein the root portion mass is at least 40 grams.

21. The golf club shaft of claim 20, wherein the root portion mass is no more than 50 grams.

22. A golf club shaft according to claim 21, wherein the root portion length is 26-36 inches and the tip portion length is 10-22 inches.

23. A golf club shaft according to claim 4, wherein the coupler comprises a thermoplastic material.

24. A golf club shaft according to claim 4, wherein the coupler comprises a fiber-reinforced composite material.

25. A golf club shaft according to claim 4, wherein the shaft bending stiffness is constant over at least 10% of the shaft length.

26. A golf club shaft according to claim 4, wherein the shaft is uniformly tapered over at least 70% of the shaft length, the portion of the coupler being tapered.

27. A golf club shaft comprising:

the shaft having a root portion joined to a tip portion by a coupler;

the tip portion having a tip portion distal end, a tip portion proximal end, a tip portion length, and a tip portion mass, the tip portion length being (a) 8-26 inches, (b) 25% -75% of the root portion length, and (c) at least 20% of the shaft length, the tip portion mass not exceeding 35 grams and less than 75% of the root portion mass;

Wherein:

the average tip portion bending stiffness is 10-50N m ² The average tip portion torsional stiffness is 5-40N m ² ；

The bending stiffness of the portion of the shaft located 5-36 inches from the proximal end of the shaft is at least 100% greater than the minimum tip portion bending stiffness and at least 50% greater than the minimum root portion bending stiffness;

the maximum shaft bending stiffness is not more than 600N m ² The maximum shaft torsional rigidity is not more than 450N m ² 。

28. A golf club shaft according to claim 27, wherein the root portion mass is no more than 50 grams, the tip portion mass is no more than 30 grams, the coupler mass is no more than 60% of the tip portion mass, the tip portion length is 10-22 inches, and the root portion length is 26-36 inches.

29. A golf club shaft according to claim 28, wherein the root portion mass is no more than 45 grams, the tip portion mass is no more than 25 grams, and the coupler mass is 25% -75% of the tip portion mass.

30. A golf club shaft according to claim 28, wherein the heel portion mass is 40-50 grams, the toe portion mass is 20-30 grams, the toe portion length is 10-22 inches, and the heel portion length is 26-36 inches.

31. A golf club shaft according to claim 28, wherein the tip portion mass is no more than 70% of the root portion mass.

32. A golf club shaft according to claim 31, wherein the tip portion mass is 35% -60% of the root portion mass, the coupler having a coupler mass of 5-17.5 grams.

33. A golf club shaft according to claim 28, wherein the shaft center of gravity distance is no more than 65% of the shaft length.

34. A golf club shaft according to claim 33, wherein the shaft center of gravity distance is no more than 55% of the shaft length.

35. A golf club shaft according to claim 33, wherein the shaft center of gravity distance is greater than the distance of any portion of the coupler from the proximal end of the shaft.

36. A golf club shaft according to claim 33, wherein the maximum shaft bending stiffness is no more than 300n x m ² The maximum shaft torsional stiffness is no more than 250n x m ² 。

37. A golf club shaft according to claim 36, wherein the maximum shaft bending stiffness is no more than 250n x m ² The maximum shaft torsional stiffness is no more than 200n x m ² 。

38. A golf club shaft according to claim 33, wherein the bending stiffness of the portion of the shaft located 5-36 inches from the shaft proximal end is at least 125n x m ² At least 200% greater than the minimum tip portion bending stiffness and at least 75% greater than the minimum root portion bending stiffness.

39. A golf club shaft according to claim 38, wherein the bending stiffness of the shaft for no more than 15% of the shaft length exceeds 125n x m ² 。

40. A golf club shaft according to claim 39, wherein the bending stiffness of the shaft for at least 3.5% of the shaft length exceeds 125n x m ² 。

41. A golf club shaft according to claim 39, wherein the torsional stiffness of the portion of the shaft located 5-36 inches from the shaft proximal end is at least 100n x m ² The torsional stiffness of the portion of the shaft not exceeding 15% of the shaft length exceeds 100n x m ² 。

42. A golf club shaft according to claim 41, wherein the bending stiffness of a portion of the shaft exceeds 150n x m ² The torsional stiffness of the portion of the shaft exceeds 115n x m ² The tip material density is within 15% of the root material density.

43. A golf club shaft according to claim 28, wherein the turning point is within 6 inches of the portion of the coupler.

44. A golf club shaft according to claim 28, wherein the average root portion bending stiffness is 50-110n x m ² The average root portion torsional stiffness is 20-70N m ² 。

45. A golf club shaft system comprising:

a shaft having a shaft distal end, a shaft proximal end, a shaft outer diameter, a shaft length, and a shaft mass, wherein each point along the shaft length has (i) a shaft bending stiffness, and (ii) a shaft torsional stiffness;

the shaft having a root portion releasably engaged to a tip portion selected from one of at least a first tip portion and at least a second tip portion by a coupler, wherein the coupler has a coupler mass;

the root portion having a root portion distal end, a root portion proximal end, and a root portion length;

the first tip portion having a first tip portion distal end, a first tip portion proximal end, a first tip portion length less than the root portion length, and a first tip portion mass;

the second tip portion having a second tip portion distal end, a second tip portion proximal end, a second tip portion length less than the root portion length, and a second tip portion mass;

The root portion is formed of a root portion material having a root material density, a root portion mass, a root portion elastic modulus, and a root portion shear modulus, and has (i) a root portion area moment of inertia, (ii) a root portion polar moment of inertia, (iii) a root portion flexural stiffness, and (iv) a root portion torsional stiffness at each point along the length of the root portion;

the first tip portion is formed of a first tip portion material having a first tip material density, a first tip portion elastic modulus, and a first tip portion shear modulus, and each point along the length of the first tip portion has (i) a first tip portion area moment of inertia, (ii) a first tip portion polar moment of inertia, (iii) a first tip portion flexural stiffness, and (iv) a first tip portion torsional stiffness;

the second tip portion is formed of a second tip portion material having a second tip material density, a second tip portion elastic modulus, and a second tip portion shear modulus, and each point along the length of the second tip portion has (i) a second tip portion area moment of inertia, (ii) a second tip portion polar moment of inertia, (iii) a second tip portion flexural stiffness, and (iv) a second tip portion torsional stiffness;

Wherein at least one of the following is true: (a) The maximum second tip portion bending stiffness being at least 25% greater than the maximum first tip portion bending stiffness, (b) the maximum second tip portion torsional stiffness being at least 35% greater than the maximum first tip portion torsional stiffness;

wherein the second tip portion mass is no more than 50% greater than the first tip portion mass;

wherein the average first tip portion bending stiffness is 10-50N m ² The average bending rigidity of the second tip part is 10-50N m ² The method comprises the steps of carrying out a first treatment on the surface of the And

wherein the average first tip portion torsional stiffness is from 5 to 40N m ² The average torsional rigidity of the second tip portion is 5-40N m ² 。

46. A golf club shaft system according to claim 45, wherein the maximum second tip portion bending stiffness is at least 50% greater than the maximum first tip portion bending stiffness and the maximum second tip portion torsional stiffness is at least 75% greater than the maximum first tip portion torsional stiffness.

47. A golf club shaft system according to claim 46, wherein the maximum second tip portion bending stiffness is 50% -150% greater than the maximum first tip portion bending stiffness and the maximum second tip portion torsional stiffness is 75% -350% greater than the maximum first tip portion torsional stiffness.

48. A golf club shaft system according to claim 45, wherein the coupler mass does not exceed either (a) the first tip portion mass or (b) the second tip portion mass.

49. A golf club shaft system according to claim 48, wherein the coupler mass is at least 25% of (a) the first tip portion mass and (b) the second tip portion mass.

50. A golf club shaft system according to claim 45, wherein the first tip portion length is at least 25% shorter than the root portion length and the second tip portion length is at least 25% shorter than the root portion length.

51. A golf club shaft system as defined in claim 45 wherein the shaft has a first shaft center of gravity located a distance from the shaft proximal first shaft center of gravity when the first tip portion is installed, the first shaft center of gravity distance no more than 65% of the shaft length, and the shaft has a second shaft center of gravity located a distance from the shaft proximal second shaft center of gravity when the second tip portion is installed, the second center of gravity distance no more than 65% of the shaft length.

52. A golf club shaft system according to claim 51, wherein the first tip portion length is 25% -80% shorter than the root portion length and the second tip portion length is 25% -80% shorter than the root portion length.

53. The golf club shaft system of claim 51, wherein the first shaft center of gravity distance differs from the second shaft center of gravity distance by no more than 5mm.

54. A golf club shaft system according to claim 45, wherein (a) the maximum first tip portion torsional stiffness is greater than the maximum first tip portion flexural stiffness and (b) the maximum second tip portion torsional stiffness is less than the maximum second tip portion flexural stiffness.

55. A golf club shaft system according to claim 54, wherein (a) the maximum first tip portion torsional stiffness is at least 30% greater than the maximum first tip portion flexural stiffness and (b) the maximum second tip portion torsional stiffness is at least 50% less than the maximum second tip portion flexural stiffness.

56. A golf club shaft system according to claim 55, wherein the second tip portion mass is no more than 20% heavier than the first tip portion mass, the first tip portion mass being 35% -85% of the root portion mass, the second tip portion mass being 35% -85% of the root portion mass.

57. A golf club shaft system according to claim 45, wherein the shaft bending stiffness exceeds 125n x m over a distance of no more than 15% of the shaft length ² The shaft torsional stiffness exceeds 100n x m over a distance of no more than 15% of the shaft length ² 。

58. A golf club shaft system according to claim 45, wherein the heel portion material is non-metallic and at least one of the first tip portion material and the second tip portion material is non-metallic.

59. A golf club shaft system according to claim 45, wherein the root portion mass is 35% -75% of the shaft mass, the first tip material density is within 15% of the root material density, and the second tip material density is within 15% of the root material density.