Abstract:
Methods of forming a golf club head having improved aerodynamic characteristics are disclosed herein. A preferred method is the largest tangent circle method, which utilizes a Cartesian coordinate system. The method results in identification and measurement of certain club head features, which can be adjusted to improve aerodynamic properties of the golf club head. One method of the present invention lowers the drag of the club head by specifying dimensional relationships of the driver head based on location of apex and nadir points, while another method lowers the drag of the club head by improving overall face design.

Description:
CROSS REFERENCES TO RELATED APPLICATIONS 
       [0001]    The present application claims priority to U.S. Provisional Patent Application Ser. No. 61/365,233, filed on Jul. 16, 2010. 
     
    
     STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT 
       [0002]    Not Applicable 
       BACKGROUND OF THE INVENTION 
       [0003]    1. Field of the Invention 
         [0004]    The present invention relates to designs and methods for reducing the effects of drag force when using a driver. 
         [0005]    2. Description of the Related Art 
         [0006]    Golf club driver designs have recently trended to include characteristics intended to increase the driver&#39;s inertia values to help off-center hits go farther and straighter. Driver designs have also recently included larger faces, which may help the driver deliver better feeling shots as well as shots that have higher ball speeds if hit away from the face center. These recent trends can, however, be detrimental to the driver&#39;s performance due to the head speed reductions that these design features introduce due to the larger geometries. The prior art generally fails to provide driver designs that efficiently reduce drag forces and consequentially enable the driver to be swung faster along its path and contribute to an improved impact event with the golf ball. 
         [0007]    The United States Golf Association (USGA) has increasingly limited the performance innovations of golf clubs, particularly drivers. Recently, the USGA has limited the volume, dimensions of the head, such as length, width, and height, face compliance, inertia of driver heads and overall club length. Current methods previously used to improve the performance of a driver have been curtailed by limitations on design parameters set by the USGA. 
         [0008]    An area of driver performance improvement that exists, as of this date, is the potential to reduce the drag force that opposes the driver&#39;s travel through the air during its path to the golf ball on the tee. A reduction in drag force would allow the driver club head to travel faster along its path and contribute to an improved impact event with the golf ball, resulting in higher golf ball velocities and consequentially, in longer golf shots. The purpose of the present invention is to effectively incorporate several design features in the driver club head that will enable lower drag coefficients as the driver is swung by a golfer. The design features will reduce drag forces and consequently allow the driver to be swung faster than conventional driver designs that currently exist. Improving the drag coefficients of the face, crown and sole surfaces will reduce the overall drag forces that impede the driver club head from moving faster through the air and the head speed of the driver is increased by approximately 1 to 5 mph. 
       BRIEF SUMMARY OF THE INVENTION 
       [0009]    The designs and methods of the present invention relate to cross-sectional dimensional relationships between the face, the transitional surfaces which join the face and blend into body surfaces of the club head, and the body surfaces themselves, and the two-dimensional face area as compared with the two-dimensional area of a silhouette of the club head. The present invention provides for drivers with higher inertias, larger volumes, and robust face designs in addition to driver designs that lower the drag forces on the club head, improve drag coefficients on the face, sole, and crown surfaces, and increase the head speed during a swing, thus enabling all shots, whether at the sweet spot or off-center, to have higher ball speeds and longer driving distances. 
         [0010]    One objective of the present invention is to lower the drag of the club head by improving the overall driver body design. To improve body design of the driver club head, specific dimensions A, B, C, D, E, and H, and more particularly dimensions A, B, D, and E are set such that the driver&#39;s dimensions comply with one or more of the following formulas: 
         [0000]      (( A+B )/ C )≧30%
 
         [0000]      A≧0.36 inches and D&gt;1.0 inch
 
         [0000]      B≧0.3 inches and E&gt;1.0 inch
 
         [0000]      A≧0.25 inches and C≦2.0 inches
 
         [0000]      B≧0.25 inches and C≦2.0 inches
 
         [0000]      A≧0.25 inches and B≧0.25 inches AND C≧2.0 inches
 
         [0000]      C/H&lt;80% 
         [0011]    Another objective of the present invention is to lower the drag of the club head by improving the overall face design. To improve face design, the overall two-dimensional projected areas of the driver face and the driver club head silhouette are derived, and then are set such that the driver&#39;s area dimensions comply with the following formula: (two-dimensional projected face area /two-dimensional projected driver club head silhouette area)&lt;59% 
         [0012]    Having briefly described the present invention, the above and further objects, features and advantages thereof will be recognized by those skilled in the pertinent art from the following detailed description of the invention when taken in conjunction with the accompanying drawings. 
     
    
     
       BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS 
         [0013]      FIG. 1  is a Cartesian coordinate system for use with a method of the present invention. 
           [0014]      FIG. 2  is a perspective view of a golf club head superimposed on a Cartesian coordinate system according to a method of the present invention. 
           [0015]      FIG. 3A  is a perspective view of a golf club head showing the location of the horizontal face center of the club head. 
           [0016]      FIG. 3A  is a perspective view of a golf club head showing the location of the horizontal face center of the club head. 
           [0017]      FIG. 4  is a perspective view of a golf club head superimposed on the Y and Z axes of a Cartesian coordinate system showing a hosel axis and its angle with respect to the Y axis and the locations of the top of the face, the bottom of the face, the face center point, and the horizontal center of the face. 
           [0018]      FIG. 5  is a two-dimensional cross sectional view of the golf club head in  FIG. 5 , showing dimensions of the face, including the center of the face. 
           [0019]      FIG. 6  is a perspective view of a golf club head superimposed on the Y and Z axes of a Cartesian coordinate system showing a hosel axis and its angle with respect to the Y axis, heel and toe contact points, and the face center point. 
           [0020]      FIG. 7  is a perspective view of a golf club head superimposed on the Y and X axes of a Cartesian coordinate system showing toe and heel points and the face center point. 
           [0021]      FIG. 8  is a perspective view of a golf club head superimposed on the Y and Z axes of a Cartesian coordinate system showing crown and sole silhouette curves, a line at the tangent points, and the largest tangent circle touching the crown and sole silhouette curves. 
           [0022]      FIG. 9  is a three-dimensional perspective view of a golf club head superimposed on a Cartesian coordinate system showing a projected plane to derive two-dimensional intersection curves of the club head. 
           [0023]      FIG. 10  is a two-dimensional cross sectional view of a golf club head showing dimensions of the club face and body. 
           [0024]      FIG. 11  is a chart showing the dimensions of six sample drivers in contrast with a driver whose dimensions are optimized according to the invention. 
           [0025]      FIG. 12  is a perspective view of a golf club head superimposed on the Y and Z axes of a Cartesian coordinate system showing an origin point and the silhouette of the club head. 
           [0026]      FIG. 13  is a three-dimensional perspective view of a golf club head superimposed on a Cartesian coordinate system showing a projected area of a silhouette of the club head on a plane parallel to the YZ plane. 
           [0027]      FIG. 14  is a perspective view of a golf club head superimposed on the Y and Z axes of a Cartesian coordinate system showing a face center point and the area of the club head face calculated using an 8 inch radius gage. 
           [0028]      FIG. 15  is a three-dimensional perspective view of a golf club head superimposed on a Cartesian coordinate system showing projected areas of a silhouette of the club head and a silhouette of the club face on a plane parallel to the YZ plane. 
           [0029]      FIG. 16  is a chart showing the two-dimensional projected face areas and two dimensional projected club head areas of nine sample drivers and a driver optimized according to the invention. 
           [0030]      FIG. 17  is an image showing the airflow separation over the contours of a conventional club head design. 
           [0031]      FIG. 18  is an image showing the airflow separation over the contours of a club head optimized according to the invention. 
       
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
       [0032]    The present invention relates to design relationships and methods of measurement to improve the shape of a driver golf club head  20 . To verify the existence of conforming or non-conforming geometries of a driver club head  20 , a specific club head orientation with respect to a Cartesian Coordinate System (CCS) is used and is described herein. An exemplary CCS having an origin point  15  is shown in  FIG. 1 . 
         [0033]    As shown in  FIG. 2 , a driver club head  20  is oriented onto a CCS where three perpendicular planes exist. The point at which all three planes intersect each other is called the origin point  15 . The resulting lines of intersection of the three planes with each other are perpendicular lines representing the axis of the CCS, with each line or axis labeled appropriately X, Y, and Z and passing through the origin point of the CCS. The values on either side of the origin of the X, Y, and Z axis are labeled either positive or negative, as defined and understood in the CCS. 
         [0034]    In the preferred embodiment, the club head  20  placed within the CCS comprises a hosel  24  having a hosel axis  32 , a crown  26 , a sole  25  and a face  30 , as shown in  FIG. 2 . Preferably, the driver type golf club head  20  placed within the CCS has a volume of less than 500 cubic centimeters. Preferably, the sole  25  is composed of a metal material and the crown  26  is composed of a non-metal material. The sole of the golf club head  20  preferably is composed of a titanium alloy material. 
         [0035]    The driver golf club head  20  is oriented in the CCS in such a manner that the hosel line  32  lies in the YZ plane and passes through the origin point  15  of the CCS. The driver golf club head  20  is further oriented such that the hosel axis line  32  of the golf club head  20  lies at a 60 degree angle measured from the -Y axis, as shown in  FIGS. 2 ,  4 , and  6 . 
         [0036]    Once the club head  20  is oriented as described above, it is further adjusted by rotating the club head  20  around the hosel axis line  32  until two points, a toe point  62  and a heel point  64 , each of which are approximately one inch on either side of the face center point  35 , have the same distance D to the YZ plane, as shown in  FIGS. 6 and 7 . 
         [0037]    The horizontal face center point  37  can be located as shown in  FIGS. 3A and 3B . If the golf club face  30  has scorelines  33  with a blank space  31  in the middle, as shown in  FIG. 3A , diagonal lines are drawn from the central ends of the upper scorelines  33  to the central ends of the lower scorelines  33  across the blank space  31  to locate the horizontal center point  37 . If the golf club face  30  has scorelines  33  stretching across the face  30 , diagonal lines are drawn from the ends of the second scoreline  33  from the top to the ends of the second scoreline  33  from the bottom, as shown in  FIG. 3B . In both  FIGS. 3A and 3B , the horizontal center point  37  is located where the diagonal lines intersect. 
         [0038]    The face center point  35  is shown in  FIGS. 4 and 5 , which illustrate how to define the face center point  35  in relation to the bottom  30   a  and top  30   b  of the club face  30 . As shown in these Figures, the golf club head  20  is sectioned along lines A-A parallel to the Z axis through the horizontal face center point  37  measured along the Y axis, and the height FH of the face  30  is measured and divided in half to arrive at the location of the center of the face  35 . 
         [0039]    When the golf club head  20  is oriented as described above and in  FIGS. 1-7 , it is in the optimal position to obtain a preferred cross-sectional orientation through the club head. This can be accomplished using the Largest Tangent Circle Method (LTCM). Pursuant to the LTCM, and as shown in  FIGS. 8 and 9 , 3D silhouette curves of the sole  25  and crown  26  surfaces are projected onto a measurement plane  74 , parallel to the YZ plane, along a vector parallel to the X axis, creating 2D curves  70 ,  72  on the measurement plane. A circle  80  is then placed on the measurement plane  74  between the projected 2D sole curve  70  and crown curve  72  and enlarged until the circle  80  has the maximum diameter possible, preferably rounded to the nearest 0.001 inch, and is tangent to both the projected curves  70 ,  72 . As shown in  FIG. 8 , a line  85  is then drawn from the tangent point where the circle  80  touches the projected crown silhouette curve  72  to the tangent point where the circle touches the projected sole silhouette curve  70 . 
         [0040]    As shown in  FIG. 9 , the line  85  created between the tangent points is projected in a direction parallel to the X axis, thus creating a plane  90  to derive the two-dimensional intersection curves  95  of the golf club head  20 . These two-dimensional intersection curves  95  represent the outline or cross-section of the club head  20 , as shown in  FIG. 10 , in an optimal orientation for determining the relationships between the face  30 , crown  26 , and sole  25  surfaces. 
         [0041]    Computational Fluid Dynamics (CFD) analysis has shown that as the airflow moves from the face onto the crown and sole surfaces of the club head, it may accelerate and can promote negative drag on the transitional surfaces. According to the present invention, this desirable negative drag can be achieved by altering the dimensions A, B, C, D, E, and H, and preferably the dimensions A, B, D, and E, defined below, such that their values satisfy one or more of the following equations: 
         [0000]      (( A+B )/ C )≧30%;
 
         [0000]      A≧0.36 inches and D&gt;1.0 inch;
 
         [0000]      B≧0.3 inches and E&gt;1.0 inch;
 
         [0000]      A≧0.25 inches and C≦2.0 inches;
 
         [0000]      B≧0.25 inches and C≦2.0 inches;
 
         [0000]      A≧0.25 inches and B≧0.25 inches AND C≧2.0 inches; and
 
         [0000]      C/H&lt;80%. 
         [0042]    Referring to the cross-section  95  derived according to the LTCM described above and in  FIGS. 1-9 , which is illustrated in  FIG. 10 , H is defined as a distance along the tangent line  85  between the crown apex point  42  and the face-most sole nadir point  40 . C is defined as a distance along the tangent line  85  between the top of the club face  30  and the bottom of the club face  30 . A is defined as a distance along the tangent line  85  between the top of the club face  30  and the crown apex point  42 . B is defined as a distance along the tangent line  85  between the bottom of the club face and the face-most sole nadir point  40 . D is defined as a distance along the X axis between the top of the club face  30  and the crown apex point  42 . E is defined as a distance along the X axis between the bottom of the club face  30  and the face-most sole nadir point  40 . The cross-section  95  also includes transitional surfaces  92 ,  94  between the face  30  and the sole  25  and crown  26  surfaces, the heights along the Z axis of which are represented by values A and B. 
         [0043]    A preferred embodiment of the present invention is a driver having a shape optimized with regard to transitional heights A and B as a percentage of face height C, e.g., ((A+B)/C)≧30%. When a driver optimized according to this embodiment is compared with six sample drivers, as shown in  FIG. 11 , it becomes evident that an optimized driver has a greater percentage of transitional height than sample drivers  1  through  6 . 
         [0044]    In a second embodiment of the present invention, when the golf club head  20  is oriented as described above according to the LTCM and as shown in  FIGS. 1-9 , it is in an optimal position to obtain design relationships of the overall projected silhouette of the club head to the area of its face  30 . According to this embodiment of the present invention, the two-dimensional projected area of the face  30  surface of the golf club head is compared with the two-dimensional projected area of the club head  20 , excluding any attached ferrule or shaft, and before artwork, scorelines, dots, and graphics are added to the club face. 
         [0045]    According to this second embodiment, the two-dimensional silhouette  76  of the club head  20  is obtained by projecting a plane  74  parallel to the YZ plane, as shown in  FIGS. 12 and 13 . The face area  78  of the club head  20  is obtained by using an  8 . 0  inch radius gauge as shown in  FIG. 14 . The radius gauge is kept parallel with the XZ plane and is touched against the club head  20  so that it contacts the top and bottom edges of the face  30 . As illustrated in  FIG. 14 , each successive contact location  100  is at 0.25 inch increments towards the toe and heel from the face center point  35 , with the exception of the last interval at the ends of the face. Each location  100  touched by the radius gauge is marked. A smooth spline curve is ‘fit’ or ‘lofted’ to the marked contact points to create a boundary that sufficiently defines the area of the face  30  of the club head  20 . 
         [0046]    The newly determined face boundary  78  is then projected onto the same plane  74  as the silhouette curves  76  of the club head to obtain the two-dimensional projected area of face  30 , as shown in  FIG. 15 . The two-dimensional projected curves  78 ,  76  of the face boundary and the driver club head&#39;s silhouette curves are then obtained and measured using an optical comparator that can accurately report 1:1 projections. 
         [0047]    According to the present invention, improvements in club head drag can be obtained by designing a club head wherein the two-dimensional projected face area  78  is below 60% of the overall two-dimensional projected area  76  of the driver club head  20 . As demonstrated in  FIG. 16 , driver club head designs with poor aerodynamic features have face areas that are more than  59 % of their overall projected club head areas. In other words, an optimized driver club head according to the present invention complies with the equation (2D projected face area/2D projected driver club head silhouette area)≦59%. 
         [0048]    Computational Fluid Dynamics (CFD) analysis shows that the face  30  contributes significantly to the overall drag of the club head  20 . Reducing the face area of the club head  20  according to the embodiments of the invention reduces the overall drag on the club head  20  in a proportional manner. In addition, when the face area of the club decreases, the designs of the transitional surfaces which connect the face to the body become influential in reducing club head drag. Though a large face area can provide the golfer with a hitting surface that is forgiving with regard to mishits and offers good compliance properties (Coefficient of Restitution and Characteristic Time), the present invention reveals that a balance of face area, transitional surface shape, and overall projected area of the club head are important to reduce the overall drag on the club head while at the same time providing a club that is easy to hit and acceptable to golfers. 
         [0049]    Driver type golf club heads  20  created using the methods discussed herein enable the golfer to benefit from an improved driver  20  design more suited to hitting shots with higher ball velocities due to the increased head speed produced by lower drag forces opposing the driver head  20  as it travels through the air. A conventional golf club head design that has not been optimized using the methods of the invention, shown in  FIG. 17 , has inferior air flow separation when compared to a golf club whose transitional surfaces have been optimized for drag reduction, shown in  FIG. 18 . CFD analysis shows that optimizing transitional surfaces of the club head reduces drag by over 100% when compared with conventional golf club heads. 
         [0050]    The designs of the present invention have crown surfaces with increased curved shapes when compared to conventional golf club heads, and have apex points that are higher and farther back from the top of the face than conventional designs. Similarly, the nadir points on the soles of the driver club heads of the invention are lower and further away from the bottom of the face. These design changes lead to a reduction in the face area. While making faces too small may lead to undesirable club performances, making the faces smaller in ways that still provide adequate hitting zones can produce a high performing and forgiving face as well as allow the apex and nadir points of the club head to be located optimally for reduced drag on the club head. 
         [0051]    The golf club head  20  of the present invention may be made of one or more materials, may include variable face thickness technology, and may have one or more of the structural features described in U.S. Pat. No. 7,163,468, U.S. Pat. No. 7,163,470, U.S. Pat. No. 7,166,038, U.S. Pat. No. 7,214,143, U.S. Pat. No. 7,252,600, U.S. Pat. No. 7,258,626, U.S. Pat. No. 7,258,631, U.S. Pat. No. 7,273,419, each of which is hereby incorporated by reference in its entirety. 
         [0052]    From the foregoing it is believed that those skilled in the pertinent art will recognize the meritorious advancement of this invention and will readily understand that while the present invention has been described in association with a preferred embodiment thereof, and other embodiments illustrated in the accompanying drawings, numerous changes, modifications and substitutions of equivalents may be made therein without departing from the spirit and scope of this invention which is intended to be unlimited by the foregoing except as may appear in the following appended claims. Therefore, the embodiments of the invention in which an exclusive property or privilege is claimed are defined in the following appended claims.