Golf club head with a high coefficient of restitution

Abstract
The present invention relates to a golf club head provided with a face and a body. The face has a central zone and a intermediate zone adjacent and surrounding the central zone. The central zone has a first flexural stiffness and the intermediate zone has a second flexural stiffness. The club head face is configured and dimensioned such that the first flexural stiffness is significantly greater than the second flexural stiffness such that upon ball impact with the face, the intermediate zone exhibits substantial deformation so that the central zone moves into the club head. At the same time, the central zone exhibits minimal deformation so that it moves into and out of the club head as a unit. Furthermore, the face exhibits a high coefficient of restitution.
Description




FIELD OF THE INVENTION




The invention is an improved golf club head. More particularly, the invention is a golf club head with an improved striking face having discrete zones with varying flexural stiffness, improved accuracy, and a high coefficient of restitution.




BACKGROUND OF THE INVENTION




The complexities of golf club design are well-known. The choice of specifications for each component of the club (i.e., the club head, shaft, hosel, grip, and subcomponents thereof) directly impacts the performance of the club. Thus, by varying the design specifications, a golf club can be tailored to have desirable performance characteristics.




The design of club heads has long been studied. Among the more prominent considerations in club head design are loft, lie, face angle, horizontal face bulge, vertical face roll, face progression, face size, sole curvature, center of gravity, material selection, and overall head weight. While this basic set of criteria is generally the focus of golf club engineering, several other design aspects must also be addressed. The interior design of the club head may be tailored to achieve particular characteristics, such as by including hosel or shaft attachment means, perimeter weighting on the face or body of the club head, and fillers within hollow club heads.




The designs for golf club heads must also be strong enough to withstand the impact forces that occur during collision between the head and the ball. The loading that occurs during this transient event can cause an acceleration to the golf ball that is four orders of magnitude greater than that of gravity. Thus, the club face and body should be designed to resist permanent deformation or catastrophic failure, by material yield or fracture.




It is not unusual for club heads of prior art hollow metal woods, produced from titanium, to have a uniform face thickness exceeding 0.15 inch. This thickness has been required to ensure structural integrity of the club head during impact.




Players generally seek a wood and golf ball combination that delivers maximum distance and landing accuracy. The distance a ball travels after impact is dictated by the magnitude and direction of the ball's translational velocity and the magnitude and direction of the ball's rotational velocity or spin. Environmental conditions, including atmospheric pressure, humidity, temperature, and wind speed further influence ball flight. However, these environmental effects are beyond the control of the golf equipment manufacturer. Golf ball landing accuracy is driven by a number of factors as well. Some of these can be attributed to club head design. Primarily, of concern here are center of gravity and club face flexibility.




Golf ball distance is a function of the total kinetic energy imparted to the ball during impact with the club head, neglecting environmental effects. During impact, kinetic energy is transferred from the club and stored as elastic strain energy in the club head and the ball. After impact, the stored elastic energy is transformed back into kinetic energy in the form of translational and rotational velocity of the ball as well as the club. Since the collision is not perfectly elastic, a portion of energy is dissipated in club head vibration and viscoelastic relaxation of the ball. Viscoelastic relaxation is a material property of the polymeric materials used in all manufactured golf balls.




The United States Golf Association (USGA), the governing body for the rules of golf in the United States, has specifications for the performance of golf balls. These performance specifications dictate the size and weight of a golf ball that conforms to the USGA. Furthermore, there are USGA rules which limit the golf ball velocity after a prescribed impact to 250 feet per second ±5%. To achieve greater golf ball distance, ball velocity after impact must be maximized while remaining within these guidelines. Viscoelastic relaxation of the ball is a parasitic energy source, which is dependent upon the rate of deformation. To minimize this effect, the rate of deformation must reduced. This may be accomplished by allowing more club face deformation during impact. Since metallic deformation maybe purely elastic, the strain energy stored in the club face is returned to the ball after impact thereby increasing the ball's outbound velocity after impact.




A variety of techniques may be utilized to vary the allowable deformation of the club face. For example, uniform face thinning, thinned faces with ribbed stiffeners and a varied thickness on the face profile are three possibilities. Any design must have sufficient structural integrity to withstand impact without permanent deformation of the club face.




In general, prior art club heads exhibit large variations in the coefficient of restitution (COR) magnitude with impact location on the face of the club. Furthermore, accuracy of those prior art clubs are highly dependent on this impact location.




Thus, there is a need for a golf club with a face that maximizes golf ball distance while maintaining accuracy due to a reduced sensitivity to face impact location. Furthermore, it would be desirable for the improved club design to minimize the dissipation of spurious energy modes of structural vibration of the club to further maximize efficient energy transfer after impact.




SUMMARY OF THE INVENTION




The present invention relates to a golf club head adapted for attachment to a shaft. The head includes a face and a body. The face is configured and dimensioned so that it includes a central portion and an adjacent surrounding intermediate portion. The central portion is rigid and the intermediate portion is relatively flexible so that upon ball impact, the intermediate portion of the face deforms to provide high ball velocity, while the central portion is substantially undeformed so that the ball flies on-target. Thus, upon ball impact the deformation of the intermediate portion allows the central region to move into and out of the club head as a unit. As a result, the head exhibits a coefficient of restitution greater than 0.81.




The above is accomplished by providing the central portion with a first flexural stiffness and the intermediate portion with a second flexural stiffness. Flexural stiffness is defined as the portion's Elastic modulus (E) times the portion's thickness (t) cubed or Et


3


. The first flexural stiffness is substantially different from the second flexural stiffness. As a result, upon ball impact, the intermediate portion exhibits substantial deformation so that the central portion moves into the club head, and the central portion exhibits minimal deformation.




In one embodiment, the first flexural stiffness is at least three times the second flexural stiffness. In other embodiments, the first flexural stiffness is six to twelve times the second flexural stiffness.




More preferably, the first flexural stiffness is greater than 25,000 lb-in. Most preferably, the first flexural stiffness is greater than 55,000 lb-in. Preferably, the second flexural stiffness is less than 16,000 lb-in. More preferably, the second flexural stiffness is less than 10,000 lb-in.




Since the flexural stiffness is a function of material and thickness, the following techniques can be used to achieve the substantial difference between the first and second flexural stiffnesses: 1) different materials can be used for each portion, 2) different thicnkesses can be used for each portion, or 3) different materials and thicknesses can be used for each portion. For example, in one embodiment, the thickness of the central portion is greater than the thickness of the intermediate portion and the material for both portions is titanium.




The golf club head further includes a perimeter portion disposed between the intermediate portion and the body. In one embodiment, the perimeter portion has a third flexural stiffness that is at least two times greater than the second flexural stiffness. The area of the perimeter portion preferably comprises less than 30% of the total area of the club head face.




In an alternative embodiment, a golf club head includes a shell that defines an inner cavity and a face. The face defines a face area and includes a first portion in the center and a second portion adjacent thereto. The first portion has a first thickness and defines a first area. The second portion has a second thickness. The first area is between about 15% and about 60% of the total face area, and the first thickness is greater than the second thickness. More preferably, the first area is between about 20% and 50% of the face area.




In the club heads discussed above, the first, second, and third portions can have various shapes, such as the shape of the face or an elliptical shape. Furthermore, the club head inner cavities can have a volume greater than about 250 cubic centimeters, and more preferably a volume greater than about 275 cubic centimeters. It is recommended that the face of the club head have a loft of greater than about 13°.




In addition, the central, intermediate, and perimeter portions can each have variable thicknesses. One feature of the present invention is specifically locating the center of gravity of the club head with respect to a first, second and third axes. The shell further includes a top portion and a spaced sole plate, a heel portion and a spaced toe portion, and a rear spaced from the face. The first axis extends between the top portion and the sole plate. The second axis extends between the heel portion and the toe portion. The third axis extends between the face and the rear portion. The axes meet at the geometric center of the face and the center of gravity is defined with respect to the geometric center of the face. The center of gravity is preferably toward the middle of the second axis and on the third axis at or below the first axis such that the center of gravity is behind the center of the face or lower. Preferably, the center of gravity is on a point of the third axis within the central portion. In one embodiment, the center of gravity is spaced from the geometric center along the first axis by a first distance of at least about 0.1″. More preferably, the center of gravity is spaced from the geometric center along the first axis toward the sole plate, wherein the first distance is at least about 0.15″. In another embodiment, the center of gravity is spaced a second distance from the geometric center along the second axis, wherein the second distance is less than about 0.02″. In addition, the center of gravity is spaced a third distance from the geometric center along the third axis toward the rear portion, wherein the third distance is less than about 1.25″.




The present invention is also directed to a golf club head adapted for attachment to a shaft that comprises a face. The face includes a total face area and first primary resonant frequency, which is less than about 2900 Hz. The face further includes a central zone that includes a geometric center of the face, and an intermediate zone disposed adjacent the central zone. The central zone has a first flexural stiffness and a central zone area that is at least 15% of the total face area. The intermediate zone has a second flexural stiffness. The first flexural stiffness is at least 25,000 lb-in and greater than the second flexural stiffness.











BRIEF DESCRIPTION OF THE DRAWINGS




Preferred features of the present invention are disclosed in the accompanying drawings, wherein similar reference characters denote similar elements throughout the several views, and wherein:





FIG. 1

is a toe side, front, perspective view of a first embodiment of a golf club head of the present invention;





FIG. 2

is a heel side, rear, perspective view of the golf club head of

FIG. 1

;





FIG. 3

is a front, elevational view of the golf club head of

FIG. 1

;





FIG. 3A

is a cross-sectional view of the face of the golf club head of

FIG. 3

along line


3


A—


3


A;





FIG. 3B

shows a cross-sectional view the face of the golf club head of

FIG. 3

along line


3


B—


3


B;





FIG. 4

is a top view of the golf club head of

FIG. 1

;





FIG. 5

is a bottom, perspective view of the golf club head of

FIG. 1

;





FIG. 6

is a toe side, front, perspective view of a second embodiment of a golf club head of the present invention;





FIG. 7

is a front, elevational view of the golf club head of

FIG. 6

;





FIG. 7A

is a cross-sectional view of the face of the golf club head of

FIG. 7

along line


7


A—


7


A;





FIG. 7B

shows a cross-sectional view the face of the golf club head of

FIG. 7

along line


7


B—


7


B;





FIG. 8

is a toe side, front, perspective view of a third embodiment of a golf club head of the present invention;





FIG. 9

is a front, elevational view of the golf club head of

FIG. 8

;





FIG. 9A

is a cross-sectional view of the face of the golf club head of

FIG. 9

along line


9


A—


9


A;





FIG. 10

is a toe side, front, perspective view of a fourth embodiment of a golf club head of the present invention;





FIG. 11

is a front, elevational view of the golf club head of

FIG. 10

;





FIG. 11A

is a cross-sectional view of the face of the golf club head of

FIG. 1

along line


11


A—


11


A;





FIG. 12

is an enlarged, front view of a golf club head with ultrasonic thickness measurement locations indicated;





FIG. 13

is a schematic representation of the apparatus for taking an ultrasonic thickness measurement on the face of a club head.;





FIG. 14

is an enlarged, elevational view of a portion of the face of a laminated golf club head of the present invention;





FIG. 15

is a schematic representation of a testing apparatus for obtaining frequency response data from a club head;





FIG. 15A

is a perspective view of an attached mass for use with the testing apparatus of

FIG. 15

;





FIG. 16

is a graph of inertance versus frequency for a conventional club head;





FIG. 17

is a graph of inertance versus frequency for the inventive club head;





FIG. 18

is a graph of COR versus face thickness for two alternative titanium alloys; and





FIG. 19

, is a graph of COR versus first resonant frequency for two alternative titanium alloys.











DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT




Referring to

FIGS. 1-5

, a first embodiment of a golf club head


10


of the present invention is shown. Club head


10


includes shell


12


with body


14


, face


16


, toe portion


18


, heel portion


20


, sole plate


22


, hosel


24


, bottom portion


26


, crown portion


28


, and rear portion


29


. The sole plate


22


fits in a recess


30


(as shown in

FIG. 5

) in the bottom portion


26


of body


14


. The shell


12


and sole plate


22


create an inner cavity


31


(as shown in FIG.


5


). The face


16


has an exterior surface


32


and an interior surface


34


. The exterior surface


32


may optionally have grooves


35


.




A golf club shaft (not shown) is attached at hosel


24


and is disposed along a shaft axis SHA. The hosel may extend to the bottom of the club head, may terminate at a location between the top and bottom portions of the head, or the hosel can terminate flush with the top portion and extend into the cavity in the head.




Inner cavity


31


of club head


10


may be empty, or alternatively may be filled with a foam or other low specific gravity material. It is recommended that the inner cavity


31


has a volume greater than 250 cubic centimeters, and more preferably greater than 275 cubic centimeters. Preferably, the mass of the inventive club head is greater than 150 grams but less than 220 grams.




Referring to

FIGS. 3-3B

, the face


16


includes a central zone or portion


36


, an intermediate zone or surrounding portion


38


adjacent the central zone


36


, and a perimeter zone or outer portion


40


. The central zone


36


is surrounded by the intermediate zone


38


and the perimeter zone


40


surrounds the intermediate zone


38


. The perimeter zone


40


is the zone between the intermediate zone


38


and crown portion


28


. In the following specification and claims, the central zone


36


is a contiguous zone centrally located on the face


16


and containing a geometric center GC of the face.




The zone


36


,


38


and


40


have a shape that is the similar to the shape of the face


16


only with a smaller area, as discussed in detail below. The central zone


36


has a first thickness t


1


. The intermediate zone


38


has a second thickness t


2


. The first thickness t


1


is greater than the second thickness t


2


. Typically, when the club head is cast, the perimeter zone


40


will be thicker than the intermediate zone


38


. However, the present invention is not limited to this configuration. Preferably, the first thickness t


1


is equal to about one and a half (1.5) times the thickness t


2


to about four (4) times the thickness t


2


of the intermediate zone


38


or surrounding portion.




The thickness relationships between the zones


36


,


38


, and


40


are provided so that a predetermined relationship exists between flexural stiffness exhibited by each of the zones. Flexural stiffness (FS) is defined by the following formula:








FS=E*t




3








where,




E=the Elastic Modulus of the material; and




t=the thickness of the material.




The central zone


36


has a first flexural stiffness FS


1


. The intermediate zone


38


has a second flexural stiffness FS


2


. The perimeter zone


40


has a third flexural stiffness FS


3


. The predetermined relationship between the portions is that the first flexural stiffness FS


1


is substantially greater than the second flexural stiffness FS


2


, and optionally the third flexural stiffness FS


3


is substantially greater than the second flexural stiffness FS


2


. Preferably, the first flexural stiffness FS


1


is at least three times greater than the second flexural stiffness FS


2


. As a ratio the following relationship must be satisfied








FS
1


FS
2



3.










This expression means the ratio of the central zone flexural stiffness FS


1


over the intermediate zone flexural stiffness FS


2


is equal to or greater than 3.0. When the above ratio of flexural stiffnesses is less than three the central zone sustains excessive deformation during impact and accuracy of the club is diminished. More preferably, the first flexural stiffness FS


1


is at least six to twelve times greater than the second flexural stiffness FS


2


. Most preferably, the first flexural stiffness FS


1


is about eight times greater than the second flexural stiffness FS


2


.




Preferably, the third flexural stiffness FS


3


is at least two times greater than the second flexural stiffness FS


2


. Thus, the following relationship must be satisfied:








FS
3


FS
2



2.










In club head


10


(as shown in FIG.


3


), the above flexural stiffness relationships are achieved by selecting a certain material with a particular Elastic modulus and varying the thickness of the zones. In another embodiment, the flexural stiffness relationships can be achieved by varying the materials of the zones with respect to one another so that the zones have different Elastic moduli and the thickness is changed accordingly. Thus, the thickness of the portions can be the same or different depending on the Elastic modulus of the material of each portion. It is also possible to obtain the required flexural stiffness ratio through the use of structural ribs, reinforcing plates, and thickness parameters.




Quantitatively, it is preferred that the first flexural stiffness FS


1


is greater than 20,000 lb-in. When the first flexural stiffness is less than 20,000 lb-in excessive deformation of the central region can occur during impact and accuracy is dimished. More preferably, the first flexural stiffness FS


1


is greater than 55,000 lb-in. Preferably, the second flexural stiffness FS


2


is less than 16,000 lb-in. When the second flexural stiffness is greater than 18,000 lb-in the COR the resultant ball velocity is reduced. More preferably, the second flexural stiffness FS


2


is less than 10,000 lb-in and, most preferably, less than 7,000 lb-in.




Referring to

FIG. 3

, it is recommended that central portion


36


has a first area that is between about 15% and about 60% of the exterior surface area


32


or face area. The percentage of face area is computed by dividing the area of each zone


36


,


38


, or


40


by the total face area of exterior surface


32


. It should be noted that the total face area of the exterior surface


32


is equivalent to the sum of areas of the zones


36


,


38


, and


40


. In a preferred embodiment, the central zone first area is greater than about 15% and less than about 60% of the total face area. When the central zone


36


is less than 15% of the total face area, then accuracy can be diminished. When central portion


36


is greater than 60% of the face area


32


, then COR can be diminished.




Referring again to

FIG. 1

, the club head


10


is further formed so that a center of gravity of the club head has a predetermined relationship with respect to a Cartesian Coordinate System with a center located on the exterior surface and coincident with the geometric center GC of the face


16


. The face includes a vertical centerline VCL and a horizontal centerline HCL perpendicular thereto. The geometric face center GC is at the intersection of these centerlines VCL and HCL. Preferably, the geometric center of the central zone


36


is coincident with the club face geometric center GC.




The Cartesian Coordinate System is defined when the club head is resting on a flat surface (i.e., at its natural loft) and includes three axes. A vertical or Z-axis is coincident with a gravity vector, g, that acts on the club head. A first direction of the club head extends along the verticle or Z-axis between the crown portion


28


and the sole plate


22


. The positive Z-direction is toward the crown portion


28


. A horizontal or X-axis is perpendicular to the z-axis. A second direction of the club head extends along the X-axis between heel portion


20


(as shown in

FIG. 2

) and toe portion


18


. The positive X-direction is toward the toe portion


20


. A Y-axis is perpendicular to both the Z-axis and the X-axis. A third direction of the club head extends along the Y-axis between the face


16


and the rear portion


29


. The positive Y-direction is toward the rear portion


29


.




Referring to

FIG. 1

, the location of the center of gravity is defined by coordinates for the center of gravity CG


z


, CG


y


, and CG


x


with respect to the Z, X, and Y axes, respectively. In the vertical direction along the Z-axis, the center of gravity coordinate is designated CG


z,


and is spaced a first distance D


1


from the geometric face center G along the Z-axis. The first distance D


1


is at least about −0.1 inch, and more preferably the first distance D


1


is at least about −0.15 inch so that the center of gravity in the vertical direction is below the geometric center GC.




In the horizontal direction along the X-axis, the center of gravity coordinate is designated CG


x


, and is spaced a second distance D


2


from the geometric face center GC. The second distance D


2


is less than about 0.02 inch and greater than −0.02 inch so that the center of gravity in the horizontal direction is spaced from the center GG by no further than the magnitude of distance D


2


.




Referring to

FIG. 1

, along the Y-axis, the center of gravity coordinate is designated CG


y


, and is spaced a third distance D


3


from the geometric face center GC preferably toward the rear portion


29


. The center of gravity CG


y


in the third direction is spaced from the center GC toward the heel portion


29


by no further than the magnitude of the third distance D


3


. The third distance D


3


is preferably equal to or less than about 1.25 inches and, more preferably, less than about 1 inch.




EXAMPLES




These and other aspects of the present invention may be more fully understood with reference to the following non-limiting examples, which are merely illustrative of embodiments of the present invention golf club head, and are not to be construed as limiting the invention, the scope of which is defined by the appended claims.












TABLE 1











FLEXURAL STIFFNESS INFORMATION
















Comparative




Comparative




Comparative




Inventive






Parameter




Example 1




Example 2




Example 3




Example









Thickness of Center Zone




0.115




0.130




0.095




0.150






(inches)






Thickness of First




0.115




0.100




0.098




0.075






Intermediate Zone (inches)






Thickness of Second




0.115




0.080




0.100




0.075






Intermediate Zone (inches)






Thickness of Perimeter




0.115




0.150




0.120




0.120






Portion (inches)






E of All Portions (psi)




1.65 E+07




1.65 E+07




1.65 E+07




1.65 E+07






FS of Central Portion (lb-in)




25094




36251




14147




55688






FS of First Intermediate




25094




16500




15530




6961






Zone (lb-in)






FS of Second Intermediate




25094




8448




16500




6961






Zone (lb-in)






FS of Perimeter Zone (lb-in)




25094




55688




28512




28512






FS


1


/FS


2






1.0




2.2




0.9




8.0






FS


3


/FS


2






1.0




3.4




1.8




4.1














Comparative Examples 1-3 are club heads configured and dimensioned as indicated above with materials so that the zones have certain values. As a result, the ratio of the central zone flexural stiffness and adjacent intermediate zone flexural stiffness for the Comparative Examples are 1.0, 2.2, and 0.9. These ratios do not satisfy the relationship that the central zone flexural stiffness is at least three times the adjacent intermediate zone flexural stiffness. On the other hand, the Inventive Example is configured and dimensioned of a material so that the ratio of central zone flexural stiffness to the adjacent intermediate portion flexural stiffness is about 8. In the examples above, the intermediate zone is defined by a first intermediate zone adjacent the central zone and a second intermediate zone adjacent the first intermediate zone. The perimeter zone is adjacent the intermediate zone(s).




Comparative Examples 1 and 3 have a ratio of perimeter zone flexural stiffness FS


3


to adjacent intermediate zone flexural stiffness FS


2


of 1.0 and 1.8. These ratios do not satisfy the relationship that perimeter zone flexural stiffness is at least twice the intermediate zone flexural stiffness. Comparative Example 2 and the Inventive Example satisfy such a ratio with values of about 3.4 and 4.1, respectively.












TABLE 2











CENTER OF GRAVITY INFORMATION
















Compara-




Compara-




Compara-








tive




tive




tive




Inventive






Parameter




Example 1




Example 2




Example 3




Example


















CG


z


Location (inches)


1






0.074




0.074




0.074




−0.120






CG


x


Location (inches)


2






0.133




0.137




0.137




−0.001






CG


y


Location (inches)


3






1.159




1.159




1.182




0.991













1


Positive z is above the GC












2


Positive x is toward the toe from GC












3


Positive y is toward the back from the GC













The center of gravity for the Inventive Example club head was achieved by the configuration and dimensions of the club head in additional to adding a weight of 31.5 grams to the sole plate. Other known methods of weight manipulation can be used to achieve the inventive center of gravity location as set forth above.




Thus, referring to

FIG. 1

, in the club head example of the present invention the center of gravity is preferably located along the Z-axis at least 0.10 inch below the geometric face center GC, along the X-axis within 0.01 inch from the geometric face center GC, and along the y-axis within 1.25 inches from the geometric face center GC. The Parameter column of Table 2 describes for each center of gravity location or coordinate the distance that the center of gravity is spaced from the face geometric center GC with respect to a Cartesian Coordinate System along particular axes. The centers of gravity for Comparative Examples 1-3 are not located properly with respect to the inventive requirements along the Z- and X-axes. The center of gravity for the Inventive Example is located properly with respect to the inventive requirements in the Z, X, and Y axes.












TABLE 3











TEST RESULTS
















Compara-





Compara-








tive




Comparative




tive




Inventive






Parameter




Example 1




Example 2




Example 3




Example


















Maximum COR




0.807




0.808




0.829




0.830






Average COR




0.765




0.766




0.783




0.789






Maximum Total




290




286




291




298






Distance (yards)






Landing Area (yards


2


)




950




255




1000




341














The test results enumerated in Table 3 were generated using computational techniques, which included finite element analysis models. When computer modeling the exemplary club heads, the following assumptions were made: club head loft of 8.5; club head mass of 201 grams; and club head material is 6AL-4V titanium alloy. The golf ball used was a two-piece solid ball. Finite element models were used to predict ball launch conditions and a trajectory model was used to predict distance and landing area. The impact condition for the swing used in the total distance and landing area predictions or tests had a club head velocity of 109.1 mph and an attack angle of +2 degrees, the club was oriented such that the vertical plane of the face was at an angle of 8.5 degrees relative to the velocity vector. The impact condition used for club coefficient of restitution (COR) tests was consistent with the USGA Rules for Golf, specifically, Rule 4-1e Appendix II Revision 2 dated Feb. 8, 1999. The impact conditions prescribed by Rule 4-1e include firing a ball at a stationary club head with a ball velocity of 160 feet per second. Rule 4-1e also prescribes that the velocity vector of the ball is nearly perpendicular to the plane of the club face.




COR or coefficient of restitution is one way of measuring ball resiliency. The coefficient of restitution (COR) is the ratio of the velocity of separation to the velocity of approach. In this model, therefore, COR was determined using the following formula:






(


V




club-post




−V




ball-post


)/(


V




ball-pre




−V




club-pre


)






where,




V


club-post


represents the velocity of the club after impact;




V


ball-post


represents the velocity of the ball after impact;




V


club-pre


represents the velocity of the club before impact (a value of zero for USGA COR conditions); and




V


ball-post


represents the velocity of the ball before impact.




The COR, in general, depends on the shape and material properties of the colliding bodies. A perfectly elastic impact has a COR of one (1), indicating that no energy is lost, while a perfectly inelastic or plastic impact has a COR of zero, indicating that the colliding bodies did not separate after impact resulting in a maximum loss of energy. Consequently, high COR values are indicative of greater ball velocity and travel and total distance. Club heads with thinner faces also have higher COR values, as exhibited by Comparative Example 3 as compared to the Comparative Club 1. However, unexpectedly the Inventive Example has the highest COR. For the inventive club head, preferably the COR is greater than about 0.81, and more preferably greater than about 0.83.




It is expected that as the COR increases the ball flight distance will increase and the maximum total distance will increase. The Inventive Example with the highest COR also has the highest maximum total distance.




It as also expected that as the COR increases the shot accuracy will decrease. However, the Inventive Example with the highest COR has the greatest accuracy as illustrated by the data for Landing Area. The Landing Area is an area encompassing the position of nine balls, which impact the club face at various locations. The nine impact locations were equally spaced within a rectangular region 1 inch wide and 0.5 inches high, centered on the club face. The club head of the Inventive Example has a very small Landing Area of 341 square yards. The Comparative Example 3, which is the only Comparative Example with a sufficient COR of at least 0.81, has a Landing Area of 1000 square yards which is significantly greater than the Landing Area for the Inventive Club. The smaller the landing area, the greater the accuracy of the club.




Several alternative embodiments of the invention are possible. The features of the invention include flexural stiffness for distinct zones or portions of the club face as well as the ratio of flexural stiffness between portions. A wide variety of rib configurations and material alternatives may be used to attain the requisite flexural stiffness and flexural stiffness ratio of the face portions.




In

FIGS. 3-3B

, a preferred embodiment of the club


10


is shown. The club


10


has a face


16


with the following construction. The central zone


36


has a thickness, t


1


, of about 0.150 inch, the intermediate zone


38


has thickness, t


2


, of about 0.075 inch, and the perimeter zone


40


has thickness, t


3


, of about 0.120 inches. Furthermore, the central zone


36


comprises about 20% of the total face surface area and the perimeter zone


40


is less than about 20% of the total face surface area. Each of the three zones


36


,


38


, and


40


have uniform thickness and are constructed from a single homogeneous material, preferably a titanium alloy, with a Young's Modulus (Et) of approximately 16.5×10


6


lbs/in


2


.




Referring to

FIGS. 3-3B

, the flexural stiffness, FSz, can also be defined by the following relationship:






FSz
=




i
=
1

n









A
i





j
=
1

n







A
j









E
i



t
i
3













where;




A


i


is defined as the area of a constituent within a zone.




E


i


is the Young's Modulus in pounds per square inch of a constituent within a zone




t


i


is the thickness or average thickness in inches of a constituent within a zone




n is the number of constituents within a zone.




Using this expression, the flexural stiffness can be calculated for the central and abutting zones and a ratio, defined as the flexural stiffness ratio, can be computed. The flexural stiffness ratio for the preferred embodiment golf club head


10


is calculated as,










FS
C

=



E
C



t
C
3


=


(

16.5
×

10
6







16

in
2



)




(

0.15





in

)

3









=

55
,
688






in
·
lb













FS
I

=



E
I



t
I
3


=


(

16.5
×

10
6







16

in
2



)




(

0.075





in

)

3









=

6981






in
·
lb











FS
C


FS
I


=
8










In

FIG. 6

, an alternate embodiment of the club head


110


is shown to illustrate an alternate construction of face


116


that results in a similar flexural stiffness ratio of the central to the abutting intermediate zone as the embodiment of FIG.


3


. In the club head


10


, the face


116


has an elliptically shaped central zone


136


there about and adjacent thereto is an intermediate zone


138


. The central zone


136


is about


30


percent of the total face surface area.




Referring to

FIGS. 7-7B

, the central zone


136


includes a ribbed support structure


137




a


(shown in phantom) that extends from the interior surface of the face. The ribbed structure asterisk-shaped, which is formed of a plurality of ribs or legs stiffens the central zone. The thickness of the ribbed portion


137




a


of the central zone t


1A


is about 0.225 inch. The width of the rib, w, is about 0.085 inch. The thickness of the remaining portion


137




b


between the ribs of the central zone t


1B


is about 0.09 inch. The ribbed structure


137




a


is defined such that it comprises about 25 percent of the surface area of the central zone. The intermediate zone


138


has a uniform thickness, t


2


, of about 0.075 inch and extends to the boundary of the face


116


with no defined perimeter zone. The face


116


is preferably made of a homogeneous titanium alloy with a Young's Modulus (Et) of 16.5×10


6


lbs/in


2


.




Referring to

FIGS. 6-7B

, the flexural stiffness ratio between the central and the abutting intermediate zone is computed.




Ellipse




Major axis


2




b


=2″




Minor axis


2




a


=1″






&AutoLeftMatch;





Ellipse





Area






A
C


=

π





b





a







=


π






(
1
)



(
0.5
)


=

1.57






in
2

















Rib Area WI=0.085 in




LI=4.60 in




A


r


=WILI=0.39 in


2






Non Rib Area A


IVR


=A


c−A




r


=(1.57−0.39)=1.18 in


2













FS
C

=




A
r


A
C










E
A



(

t

1

A


)


3


+



A
NR


A
C










E
NR



(

t

1

B


)


3









=



(
.25
)



(

16.5
×

10
6







16

in
2



)




(
.225
)

3


+


(
.75
)



(

16.5
×

10
6







16

in
2



)



(
.090
)









=

56008






in
·
lb













FS
I

=



E
I



t
2
3


=


(

16.5
×

10
6







16

in
2



)




(

0.075





in

)

3









=
6961









FS
C


FS
I


=
8.05










It should be noted that ribs, welts, pimples, or other discrete thickness variations within a zone are handled as discrete elements within a particular zone and are computed in accordance with the governing definition for flexural stiffness previously detailed.




In

FIG. 8

, an alternate embodiment of the club head


210


is shown to illustrate an alternate construction of face


216


that results in a similar flexural stiffness ratio of the central to the abutting intermediate zone as the embodiment of FIG.


3


. In the club head


210


, the face


216


has a central zone


236


and there about and adjacent thereto is an intermediate zone


238


. The central zone


236


is about


30


percent of the total face surface area. The club head


210


does not have a defined perimeter zone.




Referring to

FIGS. 9-9A

, the central zone


236


has a uniform thickness of t


1


of about 0.140 inch. The intermediate zone


238


has a continuously tapering thickness from the face perimeter inward to the central zone


236


. The thickness of the intermediate zone


238


is defined to change linearly.




The intermediate zone


238


has an inner thickness, t


2A


, of about 0.074 inch at the boundary of the central zone


236


and the intermediate zone


238


. The intermediate zone


238


has an outer thickness, t


2B


, of about 0.10 inch. The outer thickness is at the face perimeter. In instances of nonuniform thickness, within the zone, and primarily in relation to a continuous taper, an average thickness may be used to compute the flexural stiffness for the zone. This approximation simplifies the calculation and is physically based on elastic shell theory.




In this embodiment, two different homogenous materials are used. The central zone


236


is preferably made from a stainless steel having a Young's Modulus (Es) of 30.0×10


6


lbs/in


2


and the adjacent intermediate zone


238


is made from a titanium alloy with a Young's Modulus (Et) of 16.5×10


6


lbs/in


2


.




Referring to

FIGS. 8-9A

, the flexural stiffness ratio between the central and adjacent zone is computed.










FS
C

=



E
C



t
1
3


=

30
×

10
6







16

in
2





(

0.140





in

)

3









=

82320






in
·
lb













FS
I

=




E
I



(


(


t

2

A


+

t

2

B



)

/
2

)


3

=

16.5
×

10
6







16

in
2





(


[

0.1
+
0.07

]

/
2

)

3









=

10133






in
·
lb











FS
C


FS
I


=
8.12










In

FIG. 10

, an alternate embodiment of the club head


310


is shown to illustrate an alternate construction of face


316


that results in a similar flexural stiffness ratio of the central to the abutting intermediate zone as the embodiment of FIG.


3


. In the club head


310


, the face


316


has an elliptically shaped central zone


336


there about and adjacent thereto is an intermediate zone


338


. The central zone


336


is formed using two materials


337




a


(shown in phantom) and


337




b


(shown in phantom).




The central zone


336


has a uniform thickness, t


1


, of about 0.140 inches. The first material


337




a


is a titanium alloy with a Young's Moduli, Et, of 16.5×10


6


lbs/in


2


. The second material


337




b


is stainless steel and has a Young's Moduli, Es, of 30×10


6


lbs/in


2


. The central zone


336


is comprised of about 60 percent stainless steel


337




b.






Furthermore, the central zone


338


is elliptically shaped and comprises about 25 percent of the total face surface area. The intermediate zone


338


with the perimeter zone,


340


comprises of no more than 20 percent of the total face surface area. The intermediate zone has a uniform thickness, t


2


, of about 0.08 inch and is constructed from the same titanium alloy as the central zone


336


.




Referring to

FIGS. 10-14



11


A, the flexural stiffness ratio between the central and intermediate zone


336


and


338


is computed.




Ellipse Area, A


c




2




b


=1.8″






2




a


=0.9″




Ac=πba




A


c


=1.272 in


2






Area Steel, A


s


=0.763 in


2






Area Non Steel, A


NS


=A


C


−A


S













FS
C

=




A
r


A
C








E
S



t
1
3


+



A
NS


A
C








E
t



t
1
3









=



(
.6
)



(

30
×

10
6







16

in
2



)




(
.14
)

3


+


(
0.4
)



(

16.5
×

10
6







16

in
2



)




(
.14
)

3









=

67502






in
·
lb













FS
I

=



E
t



t
2
3


=


(

16.5
×

10
6







16

in
2



)




(

0.08





in

)

3









=

8448






in
·
lb











FS
C


FS
I


=
8.0










The golf club head embodiments


10


,


110


,


210


, and


310


discussed in

FIGS. 1-11A

demonstrate four unique face constructions which result in a similar flexural stiffness ratio, where the central zone to the adjacent zone ratio is greater than or equal to three and, more particularly, about eight. In cases where the face construction is uncertain due to manufacturing tolerances or methods or for other possible reasons, a nondestructive test method of determining the flexural stiffness ratio for a given face construction may be used.




Referring to

FIG. 12

, a typical club


410


is shown with an unknown face thickness profile. Preferably, something is known regarding the construction materials of the face or has been determined experimentally through test methods known to those of ordinary skill in the art. In

FIG. 7

, a random distribution of points is shown on face


416


. This distribution is referred to herein as a “point cloud” or predetermined point distribution. Points labeled C indicate a position in the central zone


436


. Points labeled


1


indicate a position in the intermediate zone


438


. Points labeled P indicate a position in the perimeter zone


440


. The numbers following the position letters “C”, “I” or “P” indicate relative face position.




Using the defined point cloud, an ultrasonic measurement device


450


(as shown in

FIG. 13

) can be used to map the face


416


thickness profile. The point cloud technique has the advantage of capturing discrete variations in face thickness such as the presence of ribs or abrupt thickness changes. One recommended ultrasonic measurement device includes a Panametrics Model 25DL ultrasonic thickness device


455


and a Panametrics model M208 probe


460


. The sensor or device


455


and the probe or transducer


460


are commercially available from Panametrics, Inc. of Waltham, Mass.




Referring to

FIG. 12

, the face thickness data obtained from the ultrasonic measurement, along with material modulus information, is then used to define the central, intermediate and possibly perimeter zones. The central zone


436


is defined by constructing an area comprising of a specific percentage of the total face surface area and including the geometric center GC. The point cloud thickness data within the defined zone is then averaged or broken into distinct elements within the zone. If the latter is required, the area percentages for the elements within the zone are calculated. The calculation for FSz previously outlined is then carried out to determine the flexural stiffness ratio between the central and adjacent zone


436


and


438


, respectively.




The following example illustrates the technique. In Table 4, random face thickness measurements are shown for titanium alloy club


410


(as shown in

FIG. 12

) with an unknown face thickness profile. The technique described above is used.












TABLE 4











ULTRASONIC FACE THICKNESS DATA
















Position




Thickness




Position




Thickness




Position




Thickness



















C1




0.132




I1




0.102




P1




0.110






C2




0.127




I2




0.103




P2




0.115






C3




0.131




I3




0.098




P3




0.117






C4




0.125




I4




0.096




P4




0.119






C5




0.136




I5




0.088




P5




0.120






C6




0.130




I6




0.089




P6




0.114






C7




0.127




I7




0.089




P7




0.117






C8




0.129




I8




0.094




P8




0.109






C9




0.133




I9




0.097




P9




0.108






C10




0.138




I10




0.099




P10




0.111






C11




0.134




I11




0.100




P11




0.115






C12




0.131




I12




0.103




P12




0.118








I13




0.106




P13




0.109








I14




0.102




P14




0.108








I15




0.105




P15




0.112








I16




0.101




P16




0.112








I17




0.100




P17




0.115








I18




0.103




P18




0.109








I19




0.107




P19




0.117








I20




0.106




P20




0.120















FIG. 12

shows the measured data points and the projected central, intermediate and perimeter zones


436


,


438


and


440


. Based on these projected areas, the percentage of each zone can be estimated or computed more accurately by other techniques, such as face scanning. The data defines three zones, the actual central zone with an average thickness of 0.131 inches; the actual intermediate zone with an average thickness of 0.099 inches, and the perimeter zone with an average thickness of 0.114 inches. Furthermore, the area of the central zone has been estimated to be about 23 percent of the total face surface area, and the perimeter zone is estimated to comprise of about 35 percent of the total face area. Based on this information a flexural stiffness ratio can be computed as set forth below.




With regard to the calculation of face flexural stiffness and the flexural stiffness ratio. The aforementioned embodiments and point cloud example all consider faces, which possess the property of material isotropy and symmetry with regard to a mid-surface of the face structure. Material isotropy is not a necessary condition of the invention. And the invention can include club heads with anisiotropic constructions. The flexural stiffness or the flexural stiffness ratio can be used with ansiotropic constructions. These calculations would still be applicable but of a more general form, as discussed below.




The notion of symmetry with regard to a mid-surface of the face simplifies the calculations of flexural stiffness. The calculation of flexural stiffness for asymmetric shell structures with respect to the mid-surface are common in composite structures where laminate shell theory is applicable. Here the Kirkhoff shell assumptions are applicable. Referring to

FIG. 14

, an unsymmetric isotropic laminate


500


is shown with N lamina or layers


502


. Furthermore, the laminate is described to be of thickness, t, with x


i


being directed distances or coordinates in accordance with FIG.


14


. The positive direction is defined to be downward and the laminate points x


i


defining the directed distance to the bottom of the k


th


laminate layer. For example, x


0


=−t/2 and X


N


=+t/2 for a laminate of thickness t made comprised of N layers.




Further complexity is added if the lamina can be constructed of multiple materials, M. In this case, the area percentage, Ai is included in the flexural stiffness calculation, as before in a separate summation over the lamina. The most general form of computing the flexural stiffness is:






FSz
=


1
3










j
=
1

N








Ar
j










i
=
1

M








[

E


(


x
k
3

-

x

k
-
1

3


)


]

i















Due to the geometric construction of the lamina about the mid-surface, asymmetry results, i.e., the laminate lacks material symmetry about the mid-surface of the laminate. However, this asymmetry does not change the calculated values for the flexural stiffness only the resulting forces and moments in the laminate structure under applied loads.




A conceivable example of this type of construction would be a titanium alloy face of uniform thickness and modulus E


t


, where the central zone is backed by a steel member of with half the thickness of the titanium portion, and having modulus E


s


. In this case, the flexural stiffness would be approximated in the following manner:









FSz
=


1
3






i
=
1









[

E


(


x
k
3

-

x

k
-
1

3


)


]

i









=


1
3



{


[


E
S



(


x
0
3

-

x
1
3


)


]

+

[


E
t



(


x
1
3

-

x
2
3


)


]


}








here
,






x
0

=


-
t

2


,






x
1

=


t
2

-
WI


,






x
2

=

t
2


,





substitution





yielding







=


1
3



{


[


E
S



(



(


-
t

2

)

3

-


(


t
2

-
WI

)

3


)


]

+

[


E
t



(



(


t
2

-
WI

)

3

-


(

t
2

)

3


)


]


}















Referring to

FIG. 15

, a testing apparatus


650


for measuring inertance is schematically illustrated. Generally, inertance is a frequency response. More specifically, inertance is a measure of the stiffness of a structure, in this instance the club face, at various frequencies of vibration. The units of inertance are acceleration units over force units. A preferred first resonant frequency for the inventive face is located where the inertance is maximized.




The test apparatus


650


includes club head


652


, a rigid mass


654


, an accelerometer


656


, and an impact hammer


658


. The mass


654


is preferably a cylindrical steel rod with a diameter of 1 inch. Referring to

FIGS. 15 and 15A

, the mass


654


preferably has a cylindrical cavity


659


at one end for receiving the accelerometer


656


and a slot


660


to accommodate the cable


662


. The accelerometer


656


is connected to the geometric center of the face of the club head


652


with a high modulus adhesive


657


, such as a cyanoacrylate based adhesive, Loctite 409, available from Loctite Corp., Newington, Conn. The mass


654


is then placed over the accelerometer


656


and also secured to the club face with cyanoacrylate adhesive. The combined mass of the mass


654


and the accelerometer


656


should equal the mass of a golf ball or 1.62 oz. The impact hammer


658


has an integral force transducer


658




a


and is movable toward and away from the free end


654




a


of the rigid mass, as indicated by the arrow I, to impact the mass


654


, which is attached to the club head face at the geometric center. The impact force or excitation force is normal to the club face, and upon impact is transmitted to the face through the mass


654


.




The testing apparatus


650


further includes a junction box and ICP power supply


660


and cables


662


electrically connected to the accelerometer


656


and the impact hammer transducer


658




a


. The junction box and ICP power supply


660


is in turn connected to a digital signal processing board


664


, located within a computer


665


with signal processing software


667


. The digital signal processing board


664


, computer


665


and software


667


are used to condition frequency signals and calculate the frequency response functions. The accelerometer


656


, transducer


658




a


, junction box and ICP power supply


660


, cables


662


, digital signal processing board


664


, computer


665


, and software


667


are commercially available and one of ordinary skill in the art can readily identify and obtain inertance values for golf clubs using these components. Typically, the data from


20


impacts are averaged to reduce noise and improve measurement accuracy. The following TABLE 5 lists specific model numbers for the vibration equipment shown in FIG.


13


.












TABLE 5











VIBRATION EQUIPMENT














Reference









Number




Part




Model #




Supplier









656




Accelerometer




352A10




Modal Shop of Cincinnati,









OH






658




Impact




086C01




Modal Shop







Hammer






662




Cables




002T01




Modal Shop






660




Junction Box &




BNC 2140




National Instruments of







ICP power





Dallas, TX






664




DSP Board




NI 4551




National Instruments






665




Computer




Dell Optiplex




Dell Computers of Round








Gxi




Rock, TX






667




Software




Virtual Bench




National Instruments








DSA 2.5.1














Referring to

FIG. 16

, a graph of inertance versus frequency for a conventional club head is shown. The conventional club head is a Callaway Great Big Bertha War Bird with an eight degree loft. The inertance I shown is the result of testing using apparatus


650


of FIG.


15


. The point II at a frequency of 3330 Hertz represents the first primary resonant frequency which occurs at the first primary maxima inertance for the inertance function I. A maxima which does not represent a primary resonant natural frequency of the face is also present in

FIG. 16

at a frequency of 2572 Hertz, which is the point I


2


. These secondary maxima I


2


are characterized by inertance transitions of a magnitude of less than 10 decibels. These secondary maxima may be due to crown, sole or skirt vibrations that are not acting perpendicular to the plane of the club face. Secondary maxima do not correlate with COR and ball velocity, since the vibration response is either small in magnitude or alternately not coincident with ball response. The COR for the conventional club head tested was measured in accordance with USGA, Rule 4-1e Appendix II Revision 2 dated Feb. 8, 1999 and was found to be 0.785. The preferred first primary resonant frequency of vibration is defined by the following relationship:






1/(2*contact duration)<I


1


<3/(2*contact duration)






The contact duration is the time interval during which the ball is in contact with the club face. The contact duration for a typical driver impact is about 500 microseconds. Thus, the preferred primary resonant frequency of vibration for the club head is between about 1000 and 3000 Hz. The closer the COR is to the lower limit, the higher the COR and thus the higher the rebound ball velocity. More preferably, the first primary resonant frequency is less than 2900.





FIG. 17

illustrates the inertance function of the invention club head. The first primary resonant frequency is at 2632 Hz, and the COR of this invention club was measured to be 0.824. The COR of the invention club is greater than the conventional club of

FIG. 16

, and therefore will provide greater ball rebound velocity.




Several example club heads were produced with two commercially available titanium alloys 6AL-4V and SP700. The clubs were produced with a variety of uniform face thickness'.

FIG. 18

illustrates that as face thickness is reduced for a given titanium alloy the COR increases in a linear fashion. However, different titanium alloys with slightly different moduli have distinct trend lines and thickness alone is insufficient to predict COR.

FIG. 19

illustrates a plot of COR versus first primary resonant frequency for the same set of club heads as those of FIG.


18


.

FIG. 18

illustrates that first primary resonant frequency is predictive of COR regardless of titanium alloy. The first primary resonant frequency of a club head may be used as a quality control factor to ensure compliance with USGA COR rules.




While various descriptions of the present invention are described above, it should be understood that the various features of each embodiment can be used alone or in any combination thereof. Therefore, this invention is not to be limited to only the specifically preferred embodiments depicted herein. Further, it should be understood that variations and modifications within the spirit and scope of the invention may occur to those skilled in the art to which the invention pertains. For example, the face and/or individual portions can have thickness variations in a step-wise or continuous fashion. Other modifications include a perimeter portion that has a thickness that is greater than or less than the adjacent, intermediate portion. In addition, the shapes of the central, intermediate, and perimeter portions are not limited to those disclosed herein. Accordingly, all expedient modifications readily attainable by one versed in the art from the disclosure set forth herein that are within the scope and spirit of the present invention are to be included as further embodiments of the present invention. The scope of the present invention is accordingly defined as set forth in the appended claims.



Claims
  • 1. A golf club head adapted for attachment to a shaft comprising:a shell defining an inner cavity; and a face having a total face area, and the face including a perimeter zone around an outer perimeter of the face and having a perimeter zone area being from 0 to 20% of the total face area; a central zone having a first flexural stiffness and including a geometric center of the face, the central zone further having a central zone area being between 15% and 60% of the total face area; and an intermediate zone surrounding the central zone, the intermediate zone having a second flexural stiffness; wherein the first flexural stiffness is at least three times greater than the second flexural stiffness and the face exhibits a coefficient of restitution of greater than or equal to 0.81, and wherein the central zone is formed of a first material and the intermediate zone is formed of a second material different from the first material.
  • 2. The golf club head of claim 1, wherein the first flexural stiffness is at least six times greater than the second flexural stiffness.
  • 3. The golf club head of claim 1, wherein the first flexural stiffness is between six and 12 times greater than the second flexural stiffness.
  • 4. The golf club head of claim 1, wherein the perimeter zone has a third flexural stiffness, and the third flexural stiffness is at least two times greater than the second flexural stiffness.
  • 5. The golf club head of claim 1, wherein the intermediate zone has an intermediatezone area being at least 30% of the total face are.
  • 6. The golf club head of claim 1, wherein the intermediate zone has an intermediate zone area being from about 30 to about 70% of the total face area.
  • 7. The golf club head of claim 1, further including a shell defining an inner cavity with a volume greater than about 250 cubic centimeters.
  • 8. The golf club head of claim 1, wherein the face has a loft of greater than about 13°.
  • 9. The golf club head of claim 1, wherein the central zone has a plurality of ribs on an inner surface thereof.
  • 10. The golf club head of claim 1, wherein the shell further includes a top portion, a sole plate spaced from the top portion, a heel, a toe spaced from the heel, a rear portion spaced from the face, and a center of gravity therebetween and being spaced from the geometric center a first distance along a horizontal direction between the heel and toe of less than 0.01 inch.
  • 11. The golf club head of claim 10, wherein the center of gravity is spaced from the geometric center a second distance along a vertical direction toward the sole plate, wherein the second distance is at least about 0.10 inch.
  • 12. The golf club head of claim 11, wherein the center of gravity is spaced a third distance from the geometric center in a horizontal direction toward the rear portion, wherein the third distance is less than about 1.25 inches.
  • 13. The golf club head of claim 1, wherein the second flexural stiffness is less than about 16,000 lb-in.
  • 14. The golf club head of claim 1, wherein the first flexural stiffness is greater tan about 55,000 lb-m.
  • 15. The golf club head of claim 1, wherein the central zone has a first average thickness and the intermediate zone has a second average thickness and the first average thickness is greater than 1.5 times the second average thickness.
  • 16. The golf club head of claim 1, wherein the face has a primary resonant frequency less than about 2900 Hz.
US Referenced Citations (180)
Number Name Date Kind
1318325 Klin Oct 1919 A
1319233 Mattern Oct 1919 A
1467435 Kinnear Sep 1923 A
1525352 Aitken Feb 1925 A
1543691 Beat Jun 1925 A
1582836 Link Apr 1926 A
1589363 Butchart Jun 1926 A
1595589 Tyler Aug 1926 A
1605551 Mattern Nov 1926 A
1699874 Buhrke Jan 1929 A
1704119 Buhrke Mar 1929 A
1704165 Buhrke Mar 1929 A
1720867 Webster et al. Jul 1929 A
2034936 Barnhart Mar 1936 A
2087685 Hackney Jul 1937 A
3567228 Lynn Mar 1971 A
3571900 Hardesty Mar 1971 A
3625518 Solheim Dec 1971 A
3659855 Hardesty May 1972 A
3863932 Lezatte Feb 1975 A
3985363 Jepson et al. Oct 1976 A
4023802 Jepson et al. May 1977 A
4193601 Reid, Jr. et al. Mar 1980 A
4213613 Nygren Jul 1980 A
4214754 Zebelean Jul 1980 A
D267965 Kobayashi Feb 1983 S
4429879 Schmidt Feb 1984 A
4432549 Zebelean Feb 1984 A
4449707 Hayashi et al. May 1984 A
4451041 Hayashi et al. May 1984 A
4451042 Hayashi et al. May 1984 A
4465221 Schmidt Aug 1984 A
4471961 Masghati et al. Sep 1984 A
4489945 Kobayashi Dec 1984 A
4511145 Schmidt Apr 1985 A
4762324 Anderson Aug 1988 A
4792140 Yamaguchi et al. Dec 1988 A
4826172 Antonious May 1989 A
4842243 Butler Jun 1989 A
4913438 Anderson Apr 1990 A
4915385 Anderson Apr 1990 A
4915386 Antonious Apr 1990 A
4919430 Antonious Apr 1990 A
4919431 Antonious Apr 1990 A
4921252 Antonious May 1990 A
4928965 Yamaguchi et al. May 1990 A
4930781 Allen Jun 1990 A
4932658 Antonious Jun 1990 A
4955610 Creighton et al. Sep 1990 A
D312858 Anderson et al. Dec 1990 S
5000454 Soda Mar 1991 A
5024437 Anderson Jun 1991 A
5028049 McKeighen Jul 1991 A
5046733 Antonious Sep 1991 A
5056705 Wakita et al. Oct 1991 A
5060951 Allen Oct 1991 A
5067715 Schmidt et al. Nov 1991 A
5090702 Viste Feb 1992 A
5094383 Anderson et al. Mar 1992 A
5106094 Desbiolles et al. Apr 1992 A
5141230 Antonious Aug 1992 A
5163682 Schmidt et al. Nov 1992 A
5180166 Schmidt et al. Jan 1993 A
5183255 Antonious Feb 1993 A
5213328 Long et al. May 1993 A
5221087 Fenton et al. Jun 1993 A
5240252 Schmidt et al. Aug 1993 A
5242167 Antonious Sep 1993 A
5255918 Anderson et al. Oct 1993 A
5261663 Anderson Nov 1993 A
5261664 Anderson Nov 1993 A
5271621 Lo Dec 1993 A
5292129 Long et al. Mar 1994 A
5295689 Lundberg Mar 1994 A
5301945 Schmidt et al. Apr 1994 A
5318300 Schmidt et al. Jun 1994 A
5328184 Antonious Jul 1994 A
5344140 Anderson Sep 1994 A
5346218 Wyte Sep 1994 A
5351958 Helmstetter Oct 1994 A
5358249 Mendralla Oct 1994 A
5362047 Shaw et al. Nov 1994 A
5362055 Rennie Nov 1994 A
5390924 Antonious Feb 1995 A
5395113 Antonious Mar 1995 A
5397126 Allen Mar 1995 A
5401021 Allen Mar 1995 A
5405136 Hardman Apr 1995 A
5405137 Vincent et al. Apr 1995 A
5407202 Igarashi Apr 1995 A
RE34925 McKeighen May 1995 E
5417419 Anderson et al. May 1995 A
5417559 Schmidt May 1995 A
5423535 Shaw et al. Jun 1995 A
5429357 Kobayashi Jul 1995 A
5431396 Shieh Jul 1995 A
5433440 Lin Jul 1995 A
5447307 Antonious Sep 1995 A
5447309 Vincent Sep 1995 A
5451056 Manning Sep 1995 A
5460376 Schmidt et al. Oct 1995 A
5467983 Chen Nov 1995 A
5470069 Schmidt et al. Nov 1995 A
5474296 Schmidt et al. Dec 1995 A
5482279 Antonious Jan 1996 A
5497993 Shan Mar 1996 A
5505453 Mack Apr 1996 A
5522593 Kobayashi et al. Jun 1996 A
5524331 Pond Jun 1996 A
5533729 Leu Jul 1996 A
5536006 Shieh Jul 1996 A
5547630 Schmidt Aug 1996 A
5549297 Mahaffey Aug 1996 A
5564994 Chang Oct 1996 A
5584770 Jensen Dec 1996 A
5595552 Wright et al. Jan 1997 A
5611741 Schmidt et al. Mar 1997 A
5611742 Kobayashi Mar 1997 A
D379393 Kubica et al. May 1997 S
5626530 Schmidt et al. May 1997 A
5643104 Antonious Jul 1997 A
5643108 Cheng Jul 1997 A
5643110 Igarashi Jul 1997 A
5649872 Antonious Jul 1997 A
5651409 Sheehan Jul 1997 A
5655976 Rife Aug 1997 A
5669827 Nagamoto Sep 1997 A
5669829 Lin Sep 1997 A
5674132 Fisher Oct 1997 A
D387113 Burrows Dec 1997 S
5695411 Wright et al. Dec 1997 A
5709614 Horiba Jan 1998 A
5709615 Liang Jan 1998 A
5711722 Miyajima et al. Jan 1998 A
5716292 Huang Feb 1998 A
5718641 Lin Feb 1998 A
5720673 Anderson Feb 1998 A
5743813 Chen et al. Apr 1998 A
5753170 Muang May 1998 A
5755624 Helmstetter May 1998 A
6755627 Yamazaki et al. May 1998
5762567 Antonious Jun 1998 A
5766092 Mimeur et al. Jun 1998 A
5766094 Mahaffey et al. Jun 1998 A
5766095 Antonious Jun 1998 A
5776011 Su et al. Jul 1998 A
5807190 Krumme et al. Sep 1998 A
5827132 Bamber Oct 1998 A
RE35955 Lu Nov 1998 E
D401652 Burrows Nov 1998 S
5830084 Kosmatka Nov 1998 A
5839975 Lundberg Nov 1998 A
5842934 Ezaki et al. Dec 1998 A
5851159 Burrows Dec 1998 A
5863261 Eggiman Jan 1999 A
5873791 Allen Feb 1999 A
5873795 Wozny et al. Feb 1999 A
D406294 Burrows Mar 1999 S
5888148 Allen Mar 1999 A
5890973 Gamble Apr 1999 A
D411272 Burrows Jun 1999 S
5908357 Hsieh Jun 1999 A
5921872 Kobayashi Jul 1999 A
5931746 Soong Aug 1999 A
5935019 Yamamoto Aug 1999 A
5938541 Allen et al. Aug 1999 A
5941782 Cook Aug 1999 A
5944619 Cameron Aug 1999 A
5954596 Noble et al. Sep 1999 A
5961394 Minabe Oct 1999 A
5967905 Nakahara et al. Oct 1999 A
5971868 Kosmatka Oct 1999 A
6007432 Kosmatka Dec 1999 A
6027416 Schmidt et al. Feb 2000 A
6248025 Murphy Jun 2001 B1
6338683 Kosmatka Jan 2002 B1
6354962 Galloway Mar 2002 B1
6368234 Galloway Apr 2002 B1
6381828 Boyce May 2002 B1
6390933 Galloway May 2002 B1
Foreign Referenced Citations (49)
Number Date Country
1114911 Jan 1996 CN
2268693 Jan 1994 GB
2331938 Jun 1999 GB
59207169 Nov 1984 JP
61033682 Feb 1986 JP
61162967 Jul 1986 JP
61181477 Aug 1986 JP
61185281 Aug 1986 JP
61240977 Oct 1986 JP
1244770 Sep 1989 JP
02130519 May 1990 JP
4020357 Jan 1992 JP
4327864 Nov 1992 JP
5212526 Aug 1993 JP
05237207 Sep 1993 JP
6007487 Jan 1994 JP
06031016 Feb 1994 JP
6114126 Apr 1994 JP
6126002 May 1994 JP
6154367 Jun 1994 JP
6182005 Jul 1994 JP
6269518 Sep 1994 JP
8168541 Jul 1996 JP
8243194 Sep 1996 JP
8280853 Oct 1996 JP
8280854 Oct 1996 JP
8294550 Nov 1996 JP
9028842 Feb 1997 JP
9047531 Feb 1997 JP
9154985 Jun 1997 JP
9168613 Jun 1997 JP
09192270 Jul 1997 JP
09192273 Jul 1997 JP
9239074 Sep 1997 JP
9239075 Sep 1997 JP
9248353 Sep 1997 JP
2717759 Nov 1997 JP
9294833 Nov 1997 JP
9299519 Nov 1997 JP
10024126 Jan 1998 JP
10024128 Jan 1998 JP
10085369 Apr 1998 JP
10118227 May 1998 JP
10137372 May 1998 JP
10155943 Jun 1998 JP
10258142 Sep 1998 JP
10263121 Oct 1998 JP
10323410 Dec 1998 JP
10337347 Dec 1998 JP
Non-Patent Literature Citations (3)
Entry
Golf Digest, Sep., 1982, p. 25.
Golf Digest, Dec., 1981, pp. 58-59.
“Variable Face Thickness Technology,” Calloway Golf advertisement, undated.