# Patent application title: GOLF CLUB HEAD

##
Inventors:
Hitoshi Kodama (Toyohashi-Shi, JP)
Tsutomu Ibuki (Toyohashi-Shi, JP)
Lee Kung Wen (Ping-Tung Hsien, TW)
Lin Chon Chen (Pingtung Hsien, TW)

Assignees:
O-TA PRECISION INDUSTRY CO., LTD.
MRC COMPOSITE PRODUCTS CO., LTD.,

IPC8 Class: AA63B5304FI

USPC Class:
473330

Class name: Club or club support head curved, grooved, or roughened striking face

Publication date: 2011-10-27

Patent application number: 20110263349

## Abstract:

Disclosed is a golf club head which enables to improve a direction of a
hit ball while assuring a carry and run of the ball corresponding to a
head speed and a position at which the ball is hit on a face part, and
enables to assure a stable direction of a hit ball while realizing a
stable carry and run of the ball even if the ball is hit at a position
other than the sweet spot. More specifically, in the golf club head,
center of figure Cf of the face part roughly coincides with sweet spot Ss
which is a point of intersection of the face part and a perpendicular
line dropped from the center of gravity of the head toward the face part,
and roll radius R2 of the face part at a position distance Z apart from
center of figure Cf of the face part along vertical axis Lz fulfils a
predetermined conditional equation, provided that a moment of inertia
around an axis orthogonal to a vertical plane containing sweet spot Ss
and a center of gravity of the head is Ix, a distance from the sweet spot
to the center of gravity of the head is Yg, and a loft angle is
θ_{0}.

## Claims:

**1.**A golf club head comprising: a face part having a curved surface and being a ball-hitting surface; a crown part connecting to an upper edge of said face part and composing an upper part; and a sole part connecting to a lower edge of said face part and composing a lower part, and satisfying a requirement that a center of figure of said face part roughly coincide with a sweet spot which is a point of intersection of said face part and a perpendicular line dropped from a center of gravity of the head toward said face part.

**2.**The golf club head according to claim 1, wherein bulge radius R1 of said face part fulfils the following conditional Equation 1, provided that a moment of inertia around a vertical axis is Iz and a distance from the sweet spot to the center of gravity of the head is Yg. ( Sp + 16 ) Iz 1930 Yg Rb -

**30.**4 < R 1 < ( Sp + 32 ) Iz 1930 Yg Rb -

**60.**8 [ Equation 1 ] ##EQU00020##

**3.**The golf club head according to claim 2, wherein bulge radius R1 of said face part is constant throughout said face part.

**4.**A golf club head comprising: a face part having a curved surface and being a ball-hitting surface; a crown part connecting to an upper edge of said face part and composing an upper part; and a sole part connecting to a lower edge of said face part and composing a lower part, and satisfying requirements that a center of figure of said face part roughly coincide with a sweet spot which is a point of intersection of said face part and a perpendicular line dropped from a center of gravity of the head toward said face part and roll radius R2 of said face part at a position distance Z apart from a center of figure of said face part along a vertical axis fulfill the following conditional Equation 2, provided that a moment of inertia around an axis orthogonal to a vertical plane containing a sweet spot and a center of gravity of the head is Ix, a distance from the sweet spot to the center of gravity of the head is Yg, and a loft angle is θ.sub.

**0.**170 z ( 106 Yg - 224 ) z Ix -

**2.**97 θ 0 +

**68.**1 < R 2 < 170 z ( 106 Yg - 224 ) z Ix -

**2.**97 θ 0 +

**64.**6 [ Equation 2 ] ##EQU00021##

**5.**The golf club head according to claim 4, wherein roll radius R2 of said face part is constant throughout said face part.

## Description:

**TECHNICAL FIELD**

**[0001]**The present invention relates to a golf club head having a curvature on a face.

**[0002]**The present application claims the priority of Japanese Patent Application No. 2010-081,166 filed on Mar. 31, 2010 and Japanese Patent Application No. 2010-081,167 filed on Mar. 31, 2010, the contents of which are incorporated herein by reference.

**BACKGROUND ART**

**[0003]**In general, a wood-type golf club head is equipped with a face part which is a ball-hitting surface, a crown part which connects to an upper edge of the face part and composes an upper part, and a sole part which connects to a lower edge of the face part and composes a lower part, and the face part has a curved surface. The wood-type golf club head has an entire shape such that the height and the size become smaller in the direction from the face part to the rear part.

**[0004]**In recent years, various shapes have been proposed for such a wood-type golf club head for improvement of a direction of a hit golf ball or a distance to the position where a hit golf ball finally stopped, which is hereinafter referred to as a carry and run of the ball.

**[0005]**For example, it is proposed that bulge radius (a radius of curvature of the curve that is obtained when the face part is cut by a horizontal plane) of a curved surface which composes a face part is set in different values at the center and at right and left sides of the face part (for example, Patent Documents 1 and 2), or roll radius (a radius of curvature of the curve that is obtained when the face part is cut by a vertical plane) of a curved surface which composes a face part is set in different values at the center and at upper and lower sides of the face part (for example, Patent Document 5).

**[0006]**In addition, it is proposed that bulge radius is set at 400 mm or more (for example, Patent Document 3). In addition, it is proposed that bulge radius is determined in such a way that it fulfils a predetermined conditional equation concerning a moment of inertia (for example, Patent Document 4). Further, it is described, in each document, that the golf club head can improve the direction of a hit ball.

**PRIOR ART REFERENCES**

**Patent Documents**

**[0007]**Patent Document 1: Japanese Patent Application Laid-Open No. 2005-111,281

**[0008]**Patent Document 2: Japanese Patent Application Laid-Open No. 2005-34,540

**[0009]**Patent Document 3: Japanese Patent Application Laid-Open No. Hei 11-89,976

**[0010]**Patent Document 4: Japanese Patent Application Laid-Open No. 2004-216,173

**[0011]**Patent Document 5: Japanese Patent Application Laid-Open No. 2004-501,688

**DISCLOSURE OF INVENTION**

**Problem to be Solved by the Invention**

**[0012]**However, by those golf club heads as mentioned above, it was not always possible to hit a ball correctly to the aimed direction and thus it was not possible to assure a stable direction of a hit ball even if the ball was hit at a sweet spot which enables a large carry and run of the ball.

**[0013]**In addition, there was a problem such that a carry and run of the ball was remarkably lowered when the ball was hit at a position other than the sweet spot.

**[0014]**The present invention has been made in view of the above-mentioned circumstances and an object of the present invention is to provide a golf club head which enables to improve a direction of a hit ball while assuring a carry and run of the ball corresponding to a head speed and a position at which the ball is hit on a face part, and enables to assure a stable direction of a hit ball while realizing a stable carry and run of the ball even if the ball is hit at a position other than the sweet spot.

**Means for Solving the Problem**

**[0015]**In order to solve the above-mentioned problems, the present invention proposes the following measures.

**[0016]**(1) The present invention is a golf club head having: a face part having a curved surface and being a ball-hitting surface; a crown part connecting to an upper edge of said face part and composing an upper part; and a sole part connecting to a lower edge of said face part and composing a lower part, and satisfying a requirement that a center of figure of said face part roughly coincide with a sweet spot which is a point of intersection of said face part and a perpendicular line dropped from a center of gravity of the head toward said face part.

**[0017]**(2) The golf club head according to (1), wherein bulge radius R1 of said face part fulfils the following conditional Equation 1, provided that a moment of inertia around a vertical axis is Iz and a distance from the sweet spot to the center of gravity of the head is Yg.

**( Sp + 16 ) Iz 1930 Yg Rb - 30.4 < R 1 < ( Sp + 32 ) Iz 1930 Yg Rb - 60.8 [ Equation 1 ] ##EQU00001##**

**[0018]**(3) The golf club head according to (2), wherein bulge radius R1 of said face part is constant throughout said face part.

**[0019]**(4) A golf club head having: a face part having a curved surface and being a ball-hitting surface; a crown part connecting to an upper edge of said face part and composing an upper part; and a sole part connecting to a lower edge of said face part and composing a lower part, and satisfying requirements that a center of figure of said face part roughly coincide with a sweet spot which is a point of intersection of said face part and a perpendicular line dropped from a center of gravity of the head toward said face part and roll radius R2 of said face part at a position distance Z apart from a center of figure of said face part along a vertical axis fulfill the following conditional Equation 2, provided that a moment of inertia around an axis orthogonal to a vertical plane containing a sweet spot and a center of gravity of the head is Ix, a distance from the sweet spot to the center of gravity of the head is Yg, and a loft angle is θ

_{0}.

**170 z ( 106 Yg - 224 ) z Ix - 2.97 θ 0 + 68.1 < R 2 < 170 z ( 106 Yg - 224 ) z Ix - 2.97 θ 0 + 64.6 [ Equation 2 ] ##EQU00002##**

**[0020]**(5) The golf club head according to (4), wherein roll radius R2 of said face part is constant throughout said face part.

**[0021]**According to the present invention, it is possible to hit a ball correctly to the aimed direction as well as to realize a carry and run of the ball corresponding to a head speed when the ball is hit at the sweet spot because the center of figure of the face part roughly coincides with the sweet spot.

**[0022]**Even if the ball is hit at a position off the sweet spot, it is possible to realize a carry and run of the ball corresponding to the position and the head speed and at the same time it is possible to assure a stable direction of the hit ball corresponding to bulge radius of the curved surface of the face part.

**[0023]**In addition, when bulge radius R1 of the face part fulfils the above conditional Equation 1 depending on a moment of inertia to be determined by the entire shape of the head and a distance from the sweet spot to the center of gravity of the head, it is possible to allow a hit ball to reach in the vicinity of an aimed position even if the ball is hit at a position other than the sweet spot because the balance between the direction of the hit ball and a number of revolutions around the vertical axis to be given to the ball can be made suitable.

**[0024]**Further, when roll radius R2 of the curved surface of the face part at a position, which is distance Z apart from the center of figure of the face part along the vertical axis, fulfils the above conditional Equation 2 depending on a moment of inertia to be determined by the entire shape of the head, a distance from the sweet spot to the center of gravity of the head, and a loft angle, it is possible to realize a stable carry and run of the ball even if the ball is hit at a position other than the sweet spot because the balance between the direction of the hit ball and a number of revolutions around the horizontal axis to be given to the ball can be made suitable.

**[0025]**Further, as for the above-mentioned golf club head, it is preferable that bulge radius R1 of the face part be constant throughout the face part.

**[0026]**Further, as for the above-mentioned golf club head, it is preferable that roll radius R2 of the face part be constant throughout the face part.

**[0027]**According to this constitution, the curved surface of the face part can be formed easily and precisely, and at the same time the balance between the direction of the hit ball and a number of revolutions around the vertical axis to be given to the ball can be made suitable as mentioned above and thus it is possible to allow the hit ball to reach in the vicinity of an aimed position, because bulge radius R1 of the face part is constant throughout the face part.

**[0028]**According to this constitution, the curved surface of the face part can be formed easily and precisely, and at the same time the balance between the direction of the hit ball and a number of revolutions around the horizontal axis to be given to the ball can be made suitable as mentioned above and thus it is possible to realize a stable carry and run of the ball, because roll radius R2 of the face part is constant throughout the face part.

**Effect of the Invention**

**[0029]**According to the golf club head of the present invention, it is possible to improve a direction of a hit ball while assuring a carry and run of the ball corresponding to a head speed and a position at which the ball is hit on the face part because the center of figure of the face part roughly coincides with the sweet spot.

**[0030]**In addition, it is possible to assure a stable direction of a hit ball while realizing a stable carry and run of the ball even if the ball is hit at a position other than the sweet spot because the roll radius is set to fulfill the above-mentioned conditional equation depending on the moment of inertia, the position of the center of gravity of the head, and the loft angle.

**BRIEF DESCRIPTION OF DRAWINGS**

**[0031]**FIG. 1: A schematic front view of the golf club head in the embodiments of the present invention

**[0032]**FIG. 2: A schematic side sectional view of the golf club head in the embodiments of the present invention

**[0033]**FIG. 3: A schematic top view explaining a state when a ball is hit by the golf club head in the embodiments of the present invention

**[0034]**FIG. 4: A schematic side view explaining a state when a ball is hit by the golf club head in the embodiments of the present invention

**[0035]**FIG. 5: A graph representing the relation between the elevation angle and the number of revolutions around the horizontal axis of the golf club head in the embodiments of the present invention

**BEST MODE FOR CARRYING OUT THE INVENTION**

**[0036]**FIGS. 1 to 5 show the embodiments of the present invention.

**[0037]**As shown in FIGS. 1 to 2, a golf club head 1 of the present embodiments is equipped with a face part 2 composing a front part, a crown part 3 composing an upper part, a sole part 4 composing a lower part, a heel part 5 composing a side part to which a shaft 10 is attached, and a toe part 6 composing a side part opposite to the heel part 5, and has an entire shape such that the height and the size become smaller in the direction from the face part 2 to the rear part.

**[0038]**The face part 2 composes a ball-hitting surface having a predetermined bulge radius R1 in the horizontal direction and a curved surface formed with a predetermined roll radius R2 in the vertical direction, as described below in detail. In addition, the crown part 3 connects to an upper edge of the face part 2 and has a curved surface which goes downward in the direction toward the rear part. In addition, the sole part 4 connects to a lower edge of the face part 2 and has a curved surface which goes upward in the direction toward the rear part.

**[0039]**In the figures, the mark G represents the center of gravity of the golf club head 1 of the present embodiments and the position thereof is unequivocally determined from the shapes, the materials, and the like of the face part 2, crown part 3, sole part 4, heel part 5, and toe part 6. In addition, the mark Ss is a point of intersection of the face part 2 and a perpendicular line dropped from the center of gravity G of the head toward the face part 2 and represents a sweet spot. The mark Cf represents the center of figure of the face part 2. In the present embodiments, the sweet spot Ss and the center of figure Cf of the face part 2 are allowed to roughly coincide. Note that, in the present embodiments, the perpendicular line dropped from the center of gravity G of the head toward the sole part 4 is referred to as a vertical axis Lz.

**[0040]**In addition, an axis orthogonal to a vertical plane containing the center of gravity G of the head and the sweet spot Ss and extending to the right and left direction is referred to as a first horizontal axis Lx, and an axis orthogonal to the first horizontal axis Lx and the vertical axis Lz and extending to the front-back direction is referred to as a second horizontal axis Ly.

**[0041]**As for the golf club head 1 of the present embodiments, it is possible to hit a ball correctly to the aimed direction as well as to realize a carry and run of the ball corresponding to a head speed when the ball is hit at the sweet spot Ss because the center of figure Cf of the face part 2 roughly coincides with the sweet spot Ss.

**[0042]**In addition, as for the golf club head 1 of the present embodiments, it is possible to realize a stable direction and carry and run of a hit ball because the face part 2 is formed in such a way that the bulge radius R1 and the roll radius R2 fulfill the conditions shown by Equation 3 and Equation 4, respectively.

**( Sp + 16 ) Iz 1930 Yg Rb - 30.4 < R 1 < ( Sp + 32 ) Iz 1930 Yg Rb - 60.8 [ Equation 3 ] 170 z ( 106 Yg - 224 ) z Ix - 2.97 θ 0 + 68.1 < R 2 < 170 z ( 106 Yg - 224 ) z Ix - 2.97 θ 0 + 64.6 [ Equation 4 ] ##EQU00003##**

**[0043]**The mark Yg represents a depth of the center of gravity, which is a distance from the center of gravity G of the head to the sweet spot Ss. In addition, the mark θ

_{0}represents a loft angle (degree), which is an inclination angle of the face part 2 against the vertical axis Lz at the center of figure Cf. In addition, the marks Iz and Ix represent moments of inertia of the golf club head 1 of the present embodiments around the vertical axis Lz and the first horizontal axis Lx, respectively. In addition, Z represents a position on the face part 2 in the direction of the vertical axis Lz, taking the origin at the center of figure Cf.

**[0044]**Hereinafter, Equation 3 which is a conditional equation concerning the bulge radius R1 and Equation 4 which is a conditional equation concerning the roll radius R2 will be explained in detail, in turn.

(Concerning Bulge Radius R1)

**[0045]**FIG. 3 shows a state in which a ball is hit at a position a predetermined distance X shifted from the origin along the first horizontal axis Lx on the face part 2, taking the center of figure Cf (the sweet spot Ss) as the origin.

**[0046]**In FIG. 3, a ball radius is referred to as Rb (mm), a contact time between the ball and the face part 2 when the ball is hit is referred to as t (s), and a force to be allowed to act on the face part 2 by the ball is referred to as F (N). Number of revolutions Ng1 (rpm) of gear revolution (hereinafter, referred to as number of gear revolutions) which is generated by an action of the moment caused by hitting the ball at a position shifted from the center of figure Cf, among the revolutions around the vertical axis Lz to be generated on the ball, is determined by the following equation.

**Ng**1 = F t 2 6 t Rb Yg Iz 180 π X [ Equation 5 ] ##EQU00004##

**[0047]**In addition, a spin rate which represents a friction coefficient between the ball and the face part 2 of the golf club head 1 of the present embodiments is referred to as Sp. Number of revolutions Na1 (rpm) of compression revolution (hereinafter, referred to as number of compression revolutions) which is generated by an angle change during the contact time t (s) which starts with the contact between the ball and the face part 2 and ends with the separation thereof caused by repulsion of the ball, among the revolutions around the vertical axis Lz to be generated on the ball, is determined by the following equation.

**Na**1 = - Sp 1 R 1 180 π X [ Equation 6 ] ##EQU00005##

**[0048]**Therefore, in the state shown by FIG. 3, total number of revolutions Nt1 (rpm) around the vertical axis Lz to be generated on the ball is a sum of number of gear revolutions Ng1 and number of compression revolutions Na1, which is shown by the following equation.

**Nt**1 = F t 2 6 t Rb Yg Iz 180 π X - Sp 1 R 1 180 π X [ Equation 7 ] ##EQU00006##

**[0049]**In addition, in FIG. 3, gear angle Ag1 (degree), which is a shift of a direction to be generated against the direction along the second horizontal axis Ly by hitting the ball at a position shifted from the center of figure Cf, is determined by the following equation.

**Ag**1 = K ( F t 2 ) 1 Iz 180 π X [ Equation 8 ] ##EQU00007##

**[0050]**In addition, compression angle Aa1 (degree), which is a shift of a direction to be generated against the direction along the second horizontal axis Ly by an angle change during the contact time t (s) which starts with the contact between the ball and the face part 2 and ends with the separation thereof caused by repulsion of the ball, is determined by the following equation.

**Aa**1 = K 1 R 1 180 π X [ Equation 9 ] ##EQU00008##

**[0051]**Note that, the mark K in [Equation 8] and [Equation 9] represents a substantial efficiency.

**[0052]**Therefore, in the state shown by FIG. 3, shift angle At1 (degree), which causes a shift of a direction in which the ball substantially flies against the direction along the second horizontal axis Ly, is a sum of gear angle Ag1 and compression angle Aa1 as shown by the following equation.

**At**1 = { K ( F t 2 ) 1 Iz 180 π X + K 1 R 1 180 π X } [ Equation 10 ] ##EQU00009##

**[0053]**As described above, when the ball is hit at a predetermined position of the face part 2, the ball flies depending on shift angle At1 against the second horizontal axis Ly and depending on total number of revolutions Nt1 around the vertical axis Lz while rotating. Provided that the ratio of shift angle At1 to total number of revolutions Nt1 is P (=Nt1/At1), bulge radius R1 is expressed by the following equation.

**R**1 = ( Sp + P K ) Iz F t 2 ( Yg 6 t Rb - P K ) [ Equation 11 ] ##EQU00010##

**[0054]**In the case of ordinary balls, a range of radius Rb is around 13 to 22 mm, and spin rate Sp is around 100 to 200. In addition, substantial efficiency K is generally around 0.8.

**[0055]**In addition, contact time t of the ball and the face part 2 at the time of hitting and force F to be allowed to act on the face part 2 by the ball are around 2/10,000 (s) and 7,000 (N), respectively, when calculated by use of the head speed (35 m/s) of ordinary users.

**[0056]**Therefore, by substituting these values in Equation 11, bulge radius R1 is expressed by the following equation by use of ratio P of shift angle At1 to total number of revolutions Nt1, moment of inertia Iz of the golf club head 1 around the vertical axis Lz, and depth Yg of the center of gravity.

**R**1 = ( Sp + 0.8 P ) Iz 1930 Yg Rb - 1.52 P [ Equation 12 ] ##EQU00011##

**[0057]**Now, the balls were practically hit while bulge radius R1 of the face part 2 was varied and the position of the face part 2 at which the balls were hit was shifted in various ways along the first horizontal axis Lx, and the direction where the ball finally dropped was measured.

**[0058]**Note that, in the present measurement, it is necessary to hit the ball with a constant head speed and orbit and precisely at a desired position of the face part 2. Consequently, the measurement was carried out by use of a golf swing robot, ROBO IV, manufactured by Miyamae Co., Ltd., while various golf clubs having various club heads with various bulge radii R1 were independently attached to this machine.

**[0059]**Ratio P of shift angle At1 to total number of revolutions Nt1, when the balls were hit while bulge radius R1 of the face part 2 was varied and the position of the face part 2 at which the balls were hit was shifted in various ways along the first horizontal axis Lx, was calculated based on the above-mentioned Equation 5 to Equation 10.

**[0060]**As a result, it was found that, when ratio P of shift angle At1 to total number of revolutions Nt1 fulfils the following equation, the ball can be dropped at a desired direction because, even if the ball flies out with shift angle At1, it rotates around the vertical axis Lz with total number of revolutions Nt1 and curves adequately.

**20≦P≦40 [Equation 13]**

**[0061]**By substituting Equation 12 into Equation 13, a relational expression was obtained as shown by Equation 14. Therefore, it is possible to allow a hit ball to drop at a desired direction by setting bulge radius R1 in such a way that it can fulfill Equation 14, even if the position of the face part 2 at which the ball is hit is shifted along the first horizontal axis Lx in any amount.

**[0062]**Note that, each numerical value contained in Equation 14 changes depending on a kind of a ball or a head speed, but the change thereof is small as compared with the change in the value of P. In the case when an ordinarily ball is used and a head speed is in the ordinary range of 25 to 55 m/s, the same effect as above can be obtained by allowing bulge radius R1 to fulfill Equation 14.

**[0063]**In addition, bulge radius R1 may be changed along the first horizontal axis Lx as long as it fulfils Equation 14.

**[0064]**However, it is possible to form a curved surface of the face part easily and precisely by allowing bulge radius R1 to be constant throughout the face part 2 while allowing bulge radius R1 to fulfill Equation 14.

**( Sp + 16 ) Iz 1930 Yg Rb - 30.4 < R 1 < ( Sp + 32 ) Iz 1930 Yg Rb - 60.8 [ Equation 14 ] ##EQU00012##**

(Concerning Roll Radius R2)

**[0065]**FIG. 4 shows a state in which a ball is hit at a position a predetermined distance Z shifted from the origin along the vertical axis Lz on the face part 2, taking the center of figure Cf (the sweet spot Ss) as the origin.

**[0066]**In FIG. 4, number of gear revolutions Ng2 (rpm) which is generated by an action of the moment caused by hitting the ball at a position shifted from the center of figure Cf, among the revolutions around the first horizontal axis Lx to be generated on the ball, is determined by the following equation.

**Ng**2 = F t 2 6 t Rb Yg Ix 180 π Z [ Equation 15 ] ##EQU00013##

**[0067]**In addition, number of compression revolutions Na2 (rpm) which is generated by an angle change during the contact time t (s) which starts with the contact between the ball and the face part 2 and ends with the separation thereof caused by repulsion of the ball, among the revolutions around the first horizontal axis Lx to be generated on the ball, is determined by the following equation.

**Na**2 = - Sp ( 1 R 2 Z + θ 0 ) 180 π [ Equation 16 ] ##EQU00014##

**[0068]**Therefore, in the state shown by FIG. 4, total number of revolutions Nt2 (rpm) around the first horizontal axis Lx to be generated on the ball is a sum of number of gear revolutions Ng2 and number of compression revolutions Na2, which is shown by the following equation.

**Nt**2 = F t 2 6 t Rb Yg Ix 180 π Z - Sp ( 1 R 2 Z + θ 0 ) 180 π [ Equation 17 ] ##EQU00015##

**[0069]**In addition, in FIG. 4, gear angle Ag2 (degree), which causes a changed portion to be generated by hitting the ball at a position shifted from the center of figure Cf in a hitting angle of the ball against the second horizontal axis Ly, namely an elevation angle, is determined by the following equation.

**Ag**2 = K F t 2 1 Ix 180 π Z [ Equation 18 ] ##EQU00016##

**[0070]**In addition, compression angle Aa2 (degree), which causes a changed portion to be generated by an angle change during the contact time t (s) which starts with the contact between the ball and the face part 2 and ends with the separation thereof caused by repulsion of the ball in the elevation angle, is determined by the following equation.

**Aa**2 = - K ( 1 R 2 Z + θ 0 ) 180 π [ Equation 19 ] ##EQU00017##

**[0071]**Therefore, in the state shown by FIG. 4, elevation angle At2 (degree) of the ball is a sum of gear angle Ag2 and compression angle Aa2 as shown by the following equation.

**At**2 = K ( 1 R 2 + F t 2 1 Ix ) 180 π Z + K θ 0 180 π [ Equation 20 ] ##EQU00018##

**[0072]**Now, the balls were practically hit while roll radius R2 of the face part 2 was varied and the position of the face part 2 at which the balls were hit was variously shifted along the vertical axis Lz, and the distance to the position where the ball finally stopped, namely, the carry and run of the ball, was measured.

**[0073]**Note that, in the present measurement, the measurement was carried out in the same manner as mentioned above by use of a golf swing robot, ROBO IV, manufactured by Miyamae Co., Ltd., while various golf clubs having various club heads with various roll radii R2 were independently attached to this machine.

**[0074]**Note that, in the present measurement, two conditions of the head speed, 35 m/s and 40 m/s, were used. In addition, shift angle At2 and total number of revolutions Nt2, when the ball was hit while roll radius R2 of the face part 2 was varied and the position of the face part 2 at which the ball was hit was variously shifted along the vertical axis Lz, were calculated based on the above-mentioned Equation 15 to Equation 20.

**[0075]**Note that, in the same manner as in the calculation of bulge radius R1, radius Rb of the ball of 22 mm, spin rate Sp of 90, substantial efficiency K of 0.8, contact time t of 2/10,000 (s), and force F of 7,000 (N) were used in the above-mentioned Equation 15 to Equation 20.

**[0076]**Each carry and run of the ball (including runs) in each case of head speed 35 m/s and 40 m/s, and the corresponding calculated values of elevation angle At2 and total number of revolutions Nt2 are shown in Table 1. In addition, the relation between elevation angle At2 and total number of revolutions Nt2 shown in Table 1 is shown in FIG. 5.

**[0077]**As shown in Table 1 and FIG. 5, in the case when the predetermined carry and run of the ball corresponding to the head speed is assured (specifically, a carry and run of 183 m or more in the case of the head speed of 35 m/s and a carry and run of 242 m or more in the case of the head speed of 40 m/s), it is found that the plots of elevation angle At2 versus total number of revolutions Nt2 distribute within a linear belt-like range, regardless of the head speed.

**[0078]**In other words, in order to assure a carry and run of the ball not less than a certain distance, it is only necessary to allow elevation angle At2 of the ball hit out and total number of revolutions Nt2 around the first horizontal axis Lx given to the ball to fulfill a predetermined relation, and this relation can be shown by the following approximation derived from FIG. 5.

**TABLE**-US-00001 TABLE 1 Head speed Carry Elevation angle Gear angle Compression angle Total number of Number of gear Number of compression (m/sec) (m) At2 (degree) Ag2 (degree) Aa2 (degree) revolutions Nt2 (rpm) revolutions Ng2 (rpm) revolutions Na2 (rpm) 40 237 16.9 0.368 16.6 -2312 528 -2840 40 247 15.9 0.368 15.6 -2142 528 -2670 40 239 15.4 0.368 15.1 -2057 528 -2585 40 239 10.3 -0.368 10.7 -2357 -528 -1829 40 244 11.3 -0.368 11.6 -2524 -528 -1996 40 241 11.8 -0.368 12.1 -2607 -528 -2080 35 175 18.5 0.306 18.2 -2312 417 -2729 35 184 17.5 0.306 17.2 -2162 417 -2578 35 181 17.0 0.306 16.7 -2087 417 -2503 35 180 11.9 -0.306 12.3 -2254 -417 -1838 35 186 12.9 -0.306 13.2 -2401 -417 -1984 35 182 13.4 -0.306 13.7 -2475 -417 -2058

**100At2-3900≦Nt2≦100At2-3700 [Equation 21]**

**[0079]**By substituting Equation 17 and Equation 20 in which radius Rb, spin rate Sp, substantial efficiency K, contact time t, and force F having the above-mentioned values are used into Equation 21, a relational expression can be obtained as shown by Equation 22. Therefore, it is possible to allow the ball to realize a carry and run not less than a certain distance corresponding to the head speed by setting roll radius R2 in such a way that it can fulfill Equation 22, even if the position of the face part 2 at which the ball is hit is shifted along the vertical axis Lz in any amount.

**[0080]**Note that, each numerical value contained in Equation 22 changes depending on a kind of ball or a head speed, but, similarly as in Equation 14, the change thereof is small as compared with the change in the value of P. In the case when an ordinarily ball is used and a head speed is in the ordinary range of 25 to 55 m/s, the same effect as above can be obtained by allowing roll radius R2 to fulfill Equation 22.

**[0081]**In addition, in Equation 22, when the position of the face part 2 at which the ball is hit is shifted along the vertical axis Lz, the value of Z changes and thereby the conditional equation differs. However, it is possible to form a curved surface of the face part easily and precisely by allowing a constant roll radius R2 to fulfill the condition throughout the face part 2.

**170 z ( 106 Yg - 224 ) z Ix - 297 θ 0 + 68.1 < R 2 < 170 z ( 106 Yg - 224 ) z Ix - 297 θ 0 + 64.6 [ Equation 22 ] ##EQU00019##**

**[0082]**As mentioned above, according to the golf club head 1 of the present embodiments, it is possible to improve a direction of a hit ball while assuring a carry and run of the ball corresponding to a head speed and a position at which the ball is hit on the face part 2 because the center of figure Cf of the face part 2 roughly coincides with the sweet spot Ss.

**[0083]**In addition, the balance between the direction of a ball hit out (directional angle) and the number of revolutions around the vertical axis Lz to be given to the ball can be made suitable and thus it is possible to allow the hit ball to reach in the vicinity of an aimed position even if the ball is hit at a position other than the sweet spot Ss because bulge radius R1 fulfils Equation 14.

**[0084]**Further, the balance between the direction of a ball hit out (elevation angle) and the number of revolutions around the first horizontal axis Lx to be given to the ball can be made suitable and thus it is possible to realize a stable carry and run of the ball even if the ball is hit at a position other than the sweet spot Ss because roll radius fulfils Equation 22.

**[0085]**The embodiments of the present invention have been explained in detail with reference to Figures, but the specific constitution is not limited to these embodiments and can include variations without departing from the scope or spirit of the invention.

**INDUSTRIAL APPLICABILITY**

**[0086]**The present invention can provide a golf club head which enables to improve a direction of a hit ball while assuring a carry and run of the ball corresponding to a head speed and a position at which the ball is hit on a face part, and enables to assure a stable direction of a hit ball while realizing a stable carry and run of the ball even if the ball is hit at a position other than the sweet spot.

**EXPLANATION OF NUMERALS**

**[0087]**1: golf club head

**[0088]**2: face part

**[0089]**3: crown part

**[0090]**4: heel part

**[0091]**Cf: center of figure (of the face part)

**[0092]**G: center of gravity of the head

**[0093]**R1: bulge radius

**[0094]**R2: roll radius

**[0095]**Ss: sweet spot

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