Patent Application
20160317879
Aspects of this invention relate generally to golf clubs and golf club heads, and, in particular, to golf clubs and golf club heads with improved aerodynamic features.
The distance a golf ball travels when struck by a golf club is determined in large part by club head speed at the point of impact with the golf ball. Club head speed in turn can be affected by the wind resistance or drag provided by the club head during the entirety of the swing, especially given the large club head size of a driver. The club head of a driver or a fairway wood in particular produces significant aerodynamic drag during its swing path. The drag produced by the club head leads to reduced club head speed and, therefore, reduced distance of travel of the golf ball after it has been struck.
Air flows in a direction opposite to the golf club head's trajectory over those surfaces of the golf club head that are roughly parallel to the direction of airflow. An important factor affecting drag is the behavior of the air flow's boundary layer. The “boundary layer” is a thin layer of air that lies very close to the surface of the club head during its motion. As the airflow moves over the surfaces, it encounters an increasing pressure. This increase in pressure is called an “adverse pressure gradient” because it causes the airflow to slow down and lose momentum. As the pressure continues to increase, the airflow continues to slow down until it reaches a speed of zero, at which point it separates from the surface. The air stream will hug the club head's surfaces until the loss of momentum in the airflow's boundary layer causes it to separate from the surface. The separation of the air streams from the surfaces results in a low pressure separation region behind the club head (i.e., at the trailing edge as defined relative to the direction of air flowing over the club head). This low pressure separation region creates pressure drag. The larger the separation region, the greater the pressure drag.
One way to reduce or minimize the size of the low pressure separation region is by providing a streamlined form that allows laminar flow to be maintained for as long as possible, thereby delaying or eliminating the separation of the laminar air stream from the club surface.
Reducing the drag of the club head not only at the point of impact, but also during the course of the entire downswing prior to the point of impact, would result in improved club head speed and increased distance of travel of the golf ball. When analyzing the swing of golfers, it has been noted that the heel/hosel region of the club head leads the swing during a significant portion of the downswing and that the ball striking face only leads the swing at (or immediately before) the point of impact with the golf ball. The phrase “leading the swing” is meant to describe that portion of the club head that faces the direction of swing trajectory. For purposes of discussion, the golf club and golf club head are considered to be at a 0° orientation when the ball striking face is leading the swing, i.e. at the point of impact. It has been noted that during a downswing, the golf club may be rotated by about 90° or more around the longitudinal axis of its shaft during the 90° of downswing prior to the point of impact with the golf ball.
During this final 90° portion of the downswing, the club head may be accelerated to approximately 65 miles per hour (mph) to over 100 mph, and in the case of some professional golfers, to as high as 140 mph. Further, as the speed of the club head increases, typically so does the drag acting on the club head. Thus, during this final 90° portion of the downswing, as the club head travels at speeds upwards of 100 mph, the drag force acting on the club head could significantly retard any further acceleration of the club head.
Club heads that have been designed to reduce the drag of the head at the point of impact, or from the point of view of the club face leading the swing, may not function well to reduce the drag during other phases of the swing cycle, such as when the heel/hosel region of the club head is leading the downswing.
It would be desirable to provide a golf club head that reduces or overcomes some or all of the difficulties inherent in prior known devices. Particular advantages will be apparent to those skilled in the art, that is, those who are knowledgeable or experienced in this field of technology, in view of the following disclosure of the invention and detailed description of certain embodiments.
This application discloses a golf club head with improved aerodynamic performance. In accordance with certain aspects, a golf club head may include a body member having a ball striking face, a crown, a toe, a heel, a sole, a rear, and a hosel region located at the intersection of the ball striking face, the heel, the crown and the sole. A drag reducing structure on the body member may be configured to reduce drag for the club head during at least a portion of a golf downswing from an end of a backswing through a point-of-impact with the golf ball, and optionally, through at least the last 90° of the downswing up to and immediately prior to impact with the golf ball.
In accordance with certain aspects, a golf club head for a driver, having a volume of 400 cc or greater and a club breadth-to-face length ratio of 0.90 or greater, includes a body member having a crown, a sole, and a heel. A leading edge may be included on the heel, the leading edge defined as the surface of the heel having a vertical slope when the club head is in a 60 degree lie angle position. The body member may further have a first cross-section, wherein the first cross-section includes an apex point located on the leading edge, a first crown-side surface extending from the apex point, and a first sole-side surface extending from the apex point. The first cross-section may be oriented perpendicular to a centerline of the club head. The apex point may represent an origin of a first x1- and z1-coordinate system oriented in the plane of the first cross-section at a roll angle of approximately 15°. The first crown-side surface may be defined by the following spline points:
According to certain aspects, the first sole-side surface may be defined by the following spline points:
According to other aspects, the body member further may have a second cross-section, wherein the second cross-section includes the apex point located on the leading edge, a second crown-side surface extending from the apex point, and a second sole-side surface extending from the apex point. The second cross-section may be oriented at approximately 70° from the centerline of the club head. The apex point further may represent an origin of a second x2- and z2-coordinate system oriented in the plane of the second cross-section at a roll angle of approximately 15°. The second crown-side surface may be defined by the following spline points:
The second sole-side surface may be defined by the following spline points:
According to even other aspects, the body member may be configured for attachment to a shaft having a longitudinal axis, and the apex point may be located approximately 15 mm to approximately 25 mm from the longitudinal axis of the shaft. Alternatively, the apex point may be located approximately 20 mm from the longitudinal axis of the shaft.
According to certain aspects, the club head may have a volume greater than or equal to 420 cc. The club head may have a face height greater than or equal to 53 mm. Further, the club breadth-to-face length ratio of 0.92 or greater.
According to certain aspects, the body member may further include a groove extending at least partially along a length of the toe and extending at least partially along a length of the back. The groove may be a Kammback feature.
According to even other aspects, the body member may even further include a diffuser located on the sole and oriented at an angle from the centerline of the club head of from approximately 10° to approximately 80°. Alternatively, the diffuser may be oriented at an angle from the centerline of the club head of from approximately 50° to approximately 70°.
According to certain aspects, a golf club head may include a first cross-section oriented perpendicular to a centerline of the club head, and x1- and z1-coordinates of a first crown-side surface curve of the first cross-section may be defined by the following Bézier equations:
x
1U=3(17)(1−t)t2+(48)t3
z
1U=3(10)(1−t)2t+3(26)(1−t)t2+(26)t3
According to other aspects, x1- and z1-coordinates of a first sole-side surface curve of the first cross-section may be defined by the following Bézier equations:
x
1L=3(11)(1−t)t2+(48)t3
z
1L=3(−10)(1−t)2t+3(−26)(1−t)t2+(−32)t3
The golf club head may further include a second cross-section, wherein the second cross-section is oriented at approximately 70° from the centerline of the club head. The x2U- and z2U-coordinates of a second crown-side surface curve of the second cross-section may be defined by the following Bézier equations:
x
2U=3(19)(1−t)t2+(48)t3
z
2U=3(10)(1−t)2t+3(25)(1−t)t2+(25)t3
Further, the xm- and zm-coordinates of a second sole-side surface curve of the second cross-section may be defined by the following Bézier equations:
x
2L=3(13)(1−t)t2+(48)t3
z
2L=3(−10)(1−t)2t+3(−26)(1−t)t2+(−30)t3
According to even other aspects, the body member may have a first cross-section oriented at approximately 90° from a centerline of the club head and a second cross-section oriented at approximately 45° from the centerline of the club head. The first and second cross-sections may each include the apex point located on the heel and may each have a respective crown-side surface extending from the apex point and a respective sole-side surface extending from the apex point. The first cross-section may have a first airfoil-shaped surface in the heel and a first concave-shaped surface opposed to the first airfoil-shape surface. The second cross-section may have a second airfoil-shaped surface in the heel and a second concave-shaped surface opposed to the second airfoil-shape surface.
The first and the second concave-shaped surfaces may be formed by a continuous groove extending at least partially along the length of the toe and at least partially along the length of the back.
According to certain aspects, golf clubs including the disclosed golf club heads are also provided.
These and additional features and advantages disclosed here will be further understood from the following detailed disclosure of certain embodiments.
The figures referred to above are not drawn necessarily to scale, should be understood to provide a representation of particular embodiments of the invention, and are merely conceptual in nature and illustrative of the principles involved. Some features of the golf club head depicted in the drawings may have been enlarged or distorted relative to others to facilitate explanation and understanding. The same reference numbers are used in the drawings for similar or identical components and features shown in various alternative embodiments. Golf club heads as disclosed herein would have configurations and components determined, in part, by the intended application and environment in which they are used.
An illustrative embodiment of a golf club 10 is shown in
In the example structure of
Referring to
Still referring to
Referring now to
The sole 28, which is located on the lower or ground side of the club head 14 opposite to the crown 18, extends from the ball striking face 17 back to the back 22. As with the crown 18, the sole 28 extends across the width of the club head 14, from the heel 24 to the toe 20. When the club head 14 is viewed from above, i.e., along the Z0-axis in the negative direction, the sole 28 cannot be seen.
Referring to
The heel 24 extends from the ball striking face 17 to the back 22. When the club head 14 is viewed from the toe side, i.e., along the X0-axis in the positive direction, the heel 24 cannot be seen. In some golf club head configurations, the heel 24 may be provided with a skirt or with a Kammback feature 23 or with a portion of a skirt or with a portion of a Kammback feature 23.
The toe 20 is shown as extending from the ball striking face 17 to the back 22 on the side of the club head 14 opposite to the heel 24. When the club head 14 is viewed from the heel side, i.e., along the X0-axis in the negative direction, the toe 20 cannot be seen. In some golf club head configurations, the toe 20 may be provided with a skirt or with a Kammback feature 23 or with a portion of a skirt or with a portion of a Kammback feature 23.
The socket 16 for receiving the shaft is located within the hosel region 26. The hosel region 26 is shown as being located at the intersection of the ball striking face 17, the heel 24, the crown 18 and the sole 28 and may encompass those portions of the heel 24, the crown 18 and the sole 28 that lie adjacent to the hosel 16. Generally, the hosel region 26 includes surfaces that provide a transition from the socket 16 to the ball striking face 17, the heel 24, the crown 18 and/or the sole 28.
Thus it is to be understood that the terms: the ball striking face 17, the crown 18, the toe 20, the back 22, the heel 24, the hosel region 26 and the sole 28, refer to general regions or portions of the body member 15. In some instances, the regions or portions may overlap one another. Further, it is to be understood that the usage of these terms in the present disclosure may differ from the usage of these or similar terms in other documents. It is to be understood that in general, the terms toe, heel, ball striking face and back are intended to refer to the four sides of a golf club, which make up the perimeter outline of a body member when viewed directly from above when the golf club is in the address position.
In the embodiment illustrated in
Another embodiment of a club head 14 is shown as club head 54 in
In fact, referring to
The yaw, pitch, and roll angles may be used to provide the orientation of the club head 14 with respect to the direction of air flow (which is considered to be the opposite direction from the instantaneous trajectory of the club head). At the point of impact and also at the address position, the yaw, pitch and roll angles may be considered to be 0°. For example, referring to
Moreover, referring to
Similarly, still referring to
The speed of the golf club head also changes during the downswing, from 0 mph at the beginning of the downswing to 65 to 100 mph (or more, for top-ranked golfers) at the point of impact. At low speed, i.e., during the initial portion of the downswing, drag due to air resistance may not be very significant. However, during the portion of the downswing when club head 14 is even with the golfer's waist and then swinging through to the point of impact, the club head 14 is travelling at a considerable rate of speed (for example, from 60 mph up to 130 mph for professional golfers). During this portion of the downswing, drag due to air resistance causes the golf club head 14 to impact the golf ball at a slower speed than would be possible without air resistance.
Referring back to
At point B shown on
At point C of
Referring back to
A further embodiment of the club head 14 is shown as club head 64 in
A Kammback feature 23, located between the crown 18 and the sole 28, continuously extends from a forward portion (i.e., a region that is closer to the ball striking face 17 than to the back 22) of the toe 20 to the back 22, across the back 22 to the heel 24 and into a rearward portion of the heel 24. Thus, as best seen in
One or more diffusers 36 may be formed in sole 28, as shown in
Referring back to
A further embodiment of the club head 14 is shown as club head 84 in
Referring to
A diffuser 36 may be formed in sole 28, as shown in
Some of the example drag-reducing structures described in more detail below may provide various means to maintain laminar airflow over one or more of the surfaces of the club head 14 when the ball striking face 17 is generally leading the swing, i.e., when air flows over the club head 14 from the ball striking face 17 toward the back 22. Additionally, some of the example drag-reducing structures described in more detail below may provide various means to maintain laminar airflow over one or more surfaces of the club head 14 when the heel 24 is generally leading the swing, i.e., when air flows over the club head 14 from the heel 24 toward the toe 20. Moreover, some of the example drag-reducing structures described in more detail below may provide various means to maintain laminar airflow over one or more surfaces of the club head 14 when the hosel region 26 is generally leading the swing, i.e., when air flows over the club head 14 from the hosel region 26 toward the toe 20 and/or the back 22. The example drag-reducing structures disclosed herein may be incorporated singly or in combination in club head 14 and are applicable to any and all embodiments of club head 14.
According to certain aspects, and referring, for example, to
Thus, due to the yaw angle rotation during the downswing, it may be advantageous to provide a streamlined region 100 in the heel 24. For example, providing the streamlined region 100 with a smooth, aerodynamically-shaped leading surface may allow air to flow past the club head with minimal disruption. Such a streamlined region 100 may be shaped to minimize resistance to airflow as the air flows from the heel 24 toward the toe 20, toward the back 22, and/or toward the intersection of the back 22 with the toe 20. The streamlined region 100 may be advantageously located on the heel 24 adjacent to, and possibly even overlapping with, the hosel region 26. This streamlined region of the heel 24 may form a portion of the leading surface of the club head 14 over a significant portion of the downswing. The streamlined region 100 may extend along the entire heel 24. Alternatively, the streamlined region 100 may have a more limited extent.
Referring to
According to certain aspects and referring to
Referring to
An apex point 112, which lies on the leading edge 111 of the heel 24 may be defined at Y=20 mm (see
Thus, according to certain aspects, the airfoil-like surface 25 of the streamlined region 100 may be described as being “quasi-parabolic.” As used herein, the term “quasi-parabolic” refers to any convex curve having an apex point 112 and two arms that smoothly and gradually curve away from the apex point 112 and from each other on the same side of the apex point. The first arm of the airfoil-like surface 25 may be referred to as a crown-side curve or upper curve 113. The other arm of the airfoil-like surface 25 may be referred to as a sole-side curve or lower curve 114. For example, a branch of a hyperbolic curve may be considered to be quasi-parabolic. Further, as used herein, a quasi-parabolic cross-section need not be symmetric. For example, one arm of the quasi-parabolic cross-section may be most closely represented by a parabolic curve, while the other arm may be most closely represented by a hyperbolic curve. As another example, the apex point 112 need not be centered between the two arms. In which case, the term “apex point” refers to the leading point of the quasi-parabolic curve, i.e., the point from which the two curves 113, 114 curve away from each other. In other words, a “quasi-parabolic” curve oriented with the arms extending horizontally in the same direction has a maximum slope at the apex point 112 and the absolute values of the slope of the curves 113, 114 gradually and continuously decrease as the horizontal distance from the apex point 112 increases.
The x- and z-axes associated with cross-section 120 are oriented in the plane of the cross-section 120 at an angle of 15° from the X0- and Z0-axes, respectively, associated with the club head 14. Once again, this orientation of the cross-sectional axes at 15° corresponds to a roll angle of 15°, which was considered to be representative over the course of a waist-to-knee portion of the downswing (i.e., when the club head 14 approaches its greatest velocity).
The x- and z-axes associated with cross-section 130 are oriented in the plane of the cross-section 130 at an angle of 15° from the X0- and Z0-axes, respectively, associated with the club head 14. Once again, this orientation of the cross-sectional axes at 15° corresponds to a roll angle of 15°, which was considered to be representative over the course of a waist-to-knee portion of the downswing (i.e., when the club head 14 approaches its greatest velocity).
Referring to
As shown in
Referring to
For example, a quadratic function may be determined with the vertex of the quadratic function being constrained to be the apex point 112, i.e., the (0, 0) point. In other words, the curve fit may require that the quadratic function extend through the apex point 112. Further the curve fit may require that the quadratic function be perpendicular to the x-axis at the apex point 112.
Another mathematical technique that may be used to curve fit involves the use of Bézier curves, which are parametric curves that may be used to model smooth curves. Bézier curves, for example, are commonly used in computer numerical control (CNC) machines for controlling the machining of complex smooth curves.
Using Bézier curves, the following generalized parametric curves may be used to obtain, respectively, the x- and z-coordinates of the upper curve of the cross-section:
x
U=(1−t)3Pxu0+3(1−t)2t Pxu1+3(1−t)t2Pxu2+t3Pxu3 Equ. (1a)
z
U=(1−t)3Pzu0+3(1−t)2t Pzu1+3(1−t)t2Pzu2+t3Pzu3 Equ. (1b)
Pxu0, Pxu1, Pxu2 and Pxu3 are the control points for the Bézier curve for the x-coordinates associated with the upper curve, and Pzu0, Pzu1, Pzu2 and Pzu3 are the control points for the Bézier curve for the z-coordinates associated with the upper curve.
Similarly, the following generalized parametric Bézier curves may be used to obtain, respectively, the x- and z-coordinates of the lower curve of the cross-section:
L=(1−t)3P
L=(1−t)3P
P
Since curve fits are used to generally fit the data, one way to capture the data may be to provide curves that bound the data. Thus, for example, referring to
Further, it is noted that the cross-sections 110, 120 and 130 presented in
Referring back to
According to certain aspects and as best shown in
Further, the sole 28 may extend across the length of the club head 14, from the ball striking face 17 to the back 22, with a generally convex smooth curvature. This generally convex curvature may extend from adjacent the ball striking surface 17 to the back 22 without transitioning from a positive to a negative curvature. In other words, the sole 28 may be provided with a convex curvature along its entire length from the ball striking face 17 to the back 22.
Alternatively, according to certain aspects, as illustrated, for example, in
Still referring to
Thus, according to certain aspects and as best shown in
The one or more diffusers 36 may be oriented to mitigate drag during at least some portion of the downswing stroke, particularly as the club head 14 rotates around the yaw axis. The sides of the diffuser 36 may be straight or curved. In certain configurations, the diffuser 36 may be oriented at an angle from the Y0-axis in order to diffuse the air flow (i.e., reduce the adverse pressure gradient) when the hosel region 26 and/or the heel 24 lead the swing. The diffuser 36 may be oriented at angles that range from approximately 10° to approximately 80° from the Y0-axis. Optionally, the diffuser 36 may be oriented at angles that range from approximately 20° to approximately 70°, or from approximately 30° to approximately 70°, or from approximately 40° to approximately 70°, or even from approximately 45° to approximately 65° from the T0 direction. Thus, in certain configurations, the diffuser 36 may extend from the hosel region 26 toward the toe 20 and/or toward the back 22. In other configurations, the diffuser 36 may extend from the heel 24 toward the toe 20 and/or the back 22.
Optionally, as shown in
As shown, according to one embodiment, in
Generally, Kammback features are designed to take into account that a laminar flow, which could be maintained with a very long, gradually tapering, downstream (or trailing) end of an aerodynamically-shaped body, cannot be maintained with a shorter, tapered, downstream end. When a downstream tapered end would be too short to maintain a laminar flow, drag due to turbulence may start to become significant after the downstream end of a club head's cross-sectional area is reduced to approximately fifty percent of the club head's maximum cross section. This drag may be mitigated by shearing off or removing the too-short tapered downstream end of the club head, rather than maintaining the too-short tapered end. It is this relatively abrupt cut off of the tapered end that is referred to as the Kammback feature 23.
During a significant portion of the golfer's downswing, as discussed above, the heel 24 and/or the hosel region 26 lead the swing. During these portions of the downswing, either the toe 20, portion of the toe 20, the intersection of the toe 20 with the back 22, and/or portions of the back 22 form the downstream or trailing end of the club head 14 (see, e.g.,
Further, during the last approximately 20° of the golfer's downswing prior to impact with the golf ball, as the ball striking face 17 begins to lead the swing, the back 22 of the club head 14 becomes aligned with the downstream direction of the airflow. Thus, the Kammback feature 23, when positioned along the back 22 of club head 14, is expected to reduce turbulent flow, and therefore reduce drag due to turbulence, most significantly during the last approximately 20° of the golfer's downswing.
According to certain aspects, the Kammback feature 23 may include a continuous groove 29 formed about a portion of a periphery of club head 14. As illustrated in
In the illustrated embodiment of
As air flows over crown 18 and sole 28 of body member 15 of club head 14, it tends to separate, which causes increased drag. Groove 29 may serve to reduce the tendency of the air to separate, thereby reducing drag and improving the aerodynamics of club head 14, which in turn increases club head speed and the distance that the ball will travel after being struck. Having groove 29 extend along toe 20 may be particularly advantageous, since for the majority of the swing path of golf club head 14, the leading portion of club head 14 is heel 24 with the trailing edge of club head 14 being toe 20, as noted above. Thus, the aerodynamic advantage provided by groove 29 along toe 20 is realized during the majority of the swing path. The portion of groove 29 that extends along the back 22 may provide an aerodynamic advantage at the point of impact of club head 14 with the ball.
An example of the reduction in drag during the swing provided by groove 29 is illustrated in the table below. This table is based on a computer fluid dynamic (CFD) model for the embodiment of club head 14 as shown in
From the results of the computer model, it can be seen that at the point of impact, where the yaw angle is 0°, the drag force for the square club head with groove 29 is approximately 48.2% (4.01/8.32) of that of the square club head. However, an integration of the total drag during the entire swing for the square club head provides a total drag work of 544.39, while the total drag work for the square club head with groove 29 is 216.75. Thus the total drag work for the square club head with groove 29 is approximately 39.8% (216.75/544.39) of that of the square club head. Thus, integrating the drag force throughout the swing can produce a very different result than calculating the drag force at the point of impact only.
Referring to
One or more of the drag-reducing structures, such as the streamlined portion 100 of the heel 24, the diffuser 36 of the sole 28, and/or the Kammback feature 23, may be provided on the club head 14 in order to reduce the drag on the club head during a user's golf swing from the end of a user's backswing throughout the downswing to the ball impact location. Specifically, the streamlined portion 100 of the heel 24, the diffuser 36, and the Kammback feature 23 may be provided to reduce the drag on the club head 14 primarily when the heel 24 and/or the hosel region 26 of the club head 14 are generally leading the swing. The Kammback feature 23, especially when positioned within the back 22 of the club head 14, may also be provided to reduce the drag on the club head 14 when the ball striking face 17 is generally leading the swing.
Different golf clubs are designed for the different skills that a player brings to the game. For example, professional players may opt for clubs that are highly efficient at transforming the energy developed during the swing into the energy driving the golf ball over a very small sweet spot. In contrast, weekend players may opt for clubs designed to forgive less-than-perfect placement of the club's sweet spot relative to the struck golf ball. In order to provide these differing club characteristics, clubs may be provided with club heads having any of various weights, volumes, moments-of-inertias, center-of-gravity placements, stiffnesses, face (i.e., ball-striking surface) heights, widths and/or areas, etc.
The club heads of typical modern drivers may be provided with a volume that ranges from approximately 420 cc to approximately 470 cc. Club head volumes, as presented herein, are as measured using the USGA “Procedure for Measuring the Club Head Size of Wood Clubs” (Nov. 21, 2003). The club head weight for a typical driver may range from approximately 190 g to approximately 220 g. Referring to
The above-presented values for certain characteristic parameters of the club heads of typical modern drivers are not meant to be limiting. Thus, for example, for certain embodiments, club head volumes may exceed 470 cc or club head weights may exceed 220 g. For certain embodiments, the moment-of-inertia at the center-of-gravity around an axis parallel to the X0-axis may exceed 3200 g-cm2. For example, the moment-of-inertia at the center-of-gravity around an axis parallel to the X0-axis may be range up to 3400 g-cm2, up to 3600 g-cm2, or even up to or over 4000 g-cm2. Similarly, for certain embodiments, the moment-of-inertia at the center-of-gravity around an axis parallel to the Z0-axis may exceed 5500 g-cm2. For example, the moment-of-inertia at the center-of-gravity around an axis parallel to the Z0-axis may be range up to 5700 g-cm2, up to 5800 g-cm2, or even up to 6000 g-cm2.
The design of any given golf club always involves a series of tradeoffs or compromises. The following disclosed embodiments illustrate some of these tradeoffs.
In a first example, a representative embodiment of a club head as shown in
In addition, the club head of this first example embodiment may have a weight that ranges from approximately 200 g to approximately 210 g. Referring again to
For this example club head, Table I provides a set of nominal spline point coordinates for the upper curve 113 and lower curve 114 of cross-section 110. As discussed, these nominal spline point coordinates may vary, in some instances, within a range of ±10%.
Alternatively, for this example club head, the Bézier equations (1a) and (1b) presented above may be used to obtain, respectively, the x- and z-coordinates of the upper curve 113 of cross-section 110 as follows:
x
U=3(17)(1−t)t2+(48)t3 Equ. (113a)
z
U=3(10)(1−t)2t+3(26)(1−t)t2+(26)t3 Equ. (113b)
Thus, for this particular curve 113, the Bézier control points for the x-coordinates have been defined as: Pxu0=0, Pxu1=0, Pxu2=17 and Pxu3=48, and the Bézier control points for the z-coordinates have been defined as: Pzu0=0, Pzu1=10, Pzu2=26 and Pzu3=26. As discussed, these z-coordinates may vary, in some instances, within a range of ±10%.
Similarly, for this example club head, the Bézier equations (2a) and (2b) may be used to obtain, respectively, the x- and z-coordinates of the lower curve 114 of cross-section 110 as follows:
x
L=3(11)(1−t)t2+(48)t3 Equ. (114a)
z
L=3(−10)(1−t)2t+3(−26)(1−t)t2+(−32)t3 Equ. (114b)
Thus, for this particular curve 114, the Bézier control points for the x-coordinates have been defined as: P
It can be seen from an examination of the data and the figures that the upper, crown-side curve 113 differs from the lower, sole-side curve 114. For example, at 3 mm along the x-axis from the apex point 112, the lower curve 114 has a z-coordinate value that is approximately 40% greater than the z-coordinate value of the upper curve 113. This introduces an initial asymmetry into the curves, i.e., lower curve 114 starts out deeper than upper curve 113. However, from 3 mm to 24 mm along the x-axis, the upper curve 113 and the lower curve 114 both extend away from the x-axis by an additional 15 mm (i.e., the ΔzU=22−7=15 mm and the ΔzL=25−10=15 mm). And, from 3 mm to 36 mm along the x-axis, the upper curve 113 and the lower curve 114 extend away from the x-axis by an additional 18 mm and 19 mm, respectively—a difference of less than 10%. In other words, from 3 mm to 36 mm along the x-axis, the curvatures of the upper curve 113 and the lower curve 114 are approximately the same.
As with curves 113 and 114 discussed above with respect to
Alternatively, for this example club head, the Bézier equations (1a) and (1b) presented above may be used to obtain, respectively, the x- and z-coordinates of the upper curve 123 of cross-section 120 as follows:
x
U=3(19)(1−t)t2+(48)t3 Equ. (123a)
z
U=3(10)(1−t)2t+3(25)(1−t)t2+(25)t3 Equ. (123b)
Thus, it can be seen that for this particular curve 123, the Bézier control points for the x-coordinates have been defined as: Pxu0=0, Pxu1=0, Pxu2=19 and Pxu3=48, and the Bézier control points for the z-coordinates have been defined as: Pzu0=0, Pzu1=10, Pzu2=25 and Pzu3=25.
As above, for this example club head, the Bézier equations (2a) and (2b) may be used to obtain, respectively, the x- and z-coordinates of the lower curve 124 of cross-section 120 as follows:
x
L=3(13)(1−t)t2+(48)t3 Equ. (124a)
z
L=3(−10)(1−t)2t+3(−26)(1−t)t2+(−30)t3 Equ. (124b)
Thus, for this particular curve 124, the Bézier control points for the x-coordinates have been defined as: P
It can be seen from an examination of the data and the figures that the upper, crown-side curve 123 differs from the lower, sole-side curve 124. For example, at 3 mm along the x-axis from the apex point 112, the lower curve 124 has a z-coordinate value that is approximately 30% greater than the z-coordinate value of the upper curve 123. This introduces an initial asymmetry into the curves. However, from 3 mm to 18 mm along the x-axis, the upper curve 123 and the lower curve 124 both extend away from the x-axis by an additional 12 mm (i.e., the ΔzU=19−7=12 mm and the ΔzL=21−9=12 mm). And, from 3 mm to 24 mm along the x-axis, the upper curve 123 and the lower curve 124 extend away from the x-axis by an additional 14 mm and 15 mm, respectively—a difference of less than 10%. In other words, from 3 mm to 24 mm along the x-axis, the curvatures of the upper curve 123 and the lower curve 124 are approximately the same.
Again, as with surfaces 113 and 114 discussed above, the upper and lower curves 133 and 134 may be characterized by curves presented as a table of spline points. Table III provides a set of spline point coordinates for the cross-section 130 for Example (1). For purposes of this table, all of the coordinates of the spline points are defined relative to the apex point 112. The zU-coordinates are associated with the upper curve 133; the zL-coordinates are associated with the lower curve 134.
Alternatively, for this example club head, the Bézier equations (1a) and (1b) presented above may be used to obtain, respectively, the x- and z-coordinates of the upper curve 133 of cross-section 130 as follows:
x
U=3(25)(1−t)t2+(48)t3 Equ. (133a)
z
U=3(10)(1−t)2t+3(21)(1−t)t2+(18)t3 Equ. (133b)
Thus, for this particular curve 133, the Bézier control points for the x-coordinates have been defined as: Pxu0=0, Pxu1=0, Pxu2=25 and Pxu3=48, and the Bézier control points for the z-coordinates have been defined as: Pzu0=0, Pzu1=10, Pzu2=21 and Pzu3=18.
As above, for this example club head, the Bézier equations (2a) and (2b) may be used to obtain, respectively, the x- and z-coordinates of the lower curve 134 of cross-section 130 as follows:
x
L=3(12)(1−t)t2+(48)t3 Equ. (134a)
z
L=3(−10)(1−t)2t+3(−22)(1−t)t2+(−29)t3 Equ. (134b)
Thus, for this particular curve 134, the Bézier control points for the x-coordinates have been defined as: P
An analysis of the data for this Example (1) embodiment at cross-section 130 shows that at 3 mm along the x-axis from the apex point 112 the lower, sole-side curve 134 has a z-coordinate value that is approximately 30% greater than the z-coordinate value of the upper, crown-side curve 133. This introduces an initial asymmetry into the curves. From 3 mm to 18 mm along the x-axis, the upper curve 133 and the lower curve 134 extend away from the x-axis by an additional 9 mm and 12 mm, respectively. In fact, from 3 mm to 12 mm along the x-axis, the upper curve 133 and the lower curve 134 extend away from the x-axis by an additional 6 mm and 8 mm, respectively—a difference of greater than 10%. In other words, the curvatures of the upper curve 133 and the lower curve 134 for this Example (1) embodiment are significantly different over the range of interest. And it can be seen, by looking at
Further, when the curves of the cross-section 110 (i.e., the cross-section oriented at 90 degrees from the centerline) are compared to the curves of the cross-section 120 (i.e., the cross-section oriented at 70 degrees from the centerline), it can be seen that they are very similar. Specifically, the values of the z-coordinates for the upper curve 113 are the same as the values of the z-coordinates for the upper curve 123 at the x-coordinates of 3 mm, 6 mm, 12 mm and 18 mm, and thereafter, the values for the z-coordinates of the upper curves 113 and 123 depart from each other by less than 10%. With respect to the lower curves 114 and 124 for the cross-sections 110 and 120, respectively, the values of the z-coordinates depart from each other by 10% or less over the x-coordinate range from 0 mm to 48 mm, with the lower curve 124 being slightly smaller than the lower curve 114. When the curves of the cross-section 110 (i.e., the cross-section oriented at 90 degrees from the centerline) are compared to the curves of the cross-section 130 (i.e., the cross-section oriented at 45 degrees from the centerline), it can be seen that the values of the z-coordinates for the lower curve 134 of the cross-section 130 differ from the values of the z-coordinates for the lower curve 114 of the cross-section 110 by a fairly constant amount—either 2 mm or 3 mm—over the x-coordinate range of 0 mm to 48 mm. On the other hand, it can be seen that the difference in the values of the z-coordinates for the upper curve 133 of the cross-section 130 from the values of the z-coordinates for the upper curve 113 of the cross-section 110 increases over the x-coordinate range of 0 mm to 48 mm. In other words, the curvature of the upper curve 133 significantly departs from curvature of the upper curve 113, with upper curve 133 being significantly flatter than upper curve 113. This can also be appreciated by comparing curve 113 in
In a second example, a representative embodiment of a club head as shown in
In addition, the club head of this second example embodiment may have a weight that ranges from approximately 197 g to approximately 207 g. Referring again to
For this Example (2) club head, Table IV provides a set of nominal spline point coordinates for the upper and lower curves of cross-section 110. As previously discussed, these nominal spline point coordinates may vary, in some instances, within a range of ±10%.
Alternatively, for this example club head, the Bézier equations (1a) and (1b) presented above may be used to obtain, respectively, the x- and z-coordinates of the upper curve 113 of cross-section 110 as follows:
x
U=3(22)(1−t)t2+(48)t3 Equ. (213a)
z
U=3(8)(1−t)2t+3(23)(1−t)t2+(23)t3 Equ. (213b)
Thus, for this particular curve 113, the Bézier control points for the x-coordinates have been defined as: Pxu0=0, Pxu1=0, Pxu2=22 and Pxu3=48, and the Bézier control points for the z-coordinates have been defined as: Pzu0=0, Pzu1=8, Pzu2=23 and Pzu3=23. As discussed, these z-coordinates may vary, in some instances, within a range of ±10%.
Similarly, for this example club head, the Bézier equations (2a) and (2b) may be used to obtain, respectively, the x- and z-coordinates of the lower curve 114 of cross-section 110 as follows:
x
L=3(18)(1−t)t2+(48)t3 Equ. (214a)
z
L=3(−12)(1−t)2t+3(−25)(1−t)t2+(−33)t3 Equ. (214b)
Thus, for this particular curve 114, the Bézier control points for the x-coordinates have been defined as: P
It can be seen from an examination of the data of this Example (2) embodiment at cross-section 110 that at 3 mm along the x-axis from the apex point 112, the lower curve 114 has a z-coordinate value that is 50% greater than the z-coordinate value of the upper curve 113. This introduces an initial asymmetry into the curves. However, from 3 mm to 24 mm along the x-axis, the upper curve 113 extends away from the x-axis by an additional 13 mm (i.e., ΔzU=19−6=13 mm) and the lower curve 114 extends away from the x-axis by an additional 15 mm (i.e., ΔzL=24−9=15 mm). And, from 3 mm to 36 mm along the x-axis, the upper curve 113 and the lower curve 114 extend away from the x-axis by an additional 16 mm and 21 mm, respectively. In other words, from 3 mm to 36 mm along the x-axis, the upper curve 113 is flatter than the lower curve 114.
As with curves 113 and 114 discussed above with respect to
Alternatively, for this example club head, the Bézier equations (1a) and (1b) presented above may be used to obtain, respectively, the x- and z-coordinates of the upper curve 123 of cross-section 120 as follows:
x
U=3(28)(1−t)t2+(48)t3 Equ. (223a)
z
U=3(9)(1−t)2t+3(22)(1−t)t2+(21)t3 Equ. (223b)
Thus, it can be sent that for this particular curve 123, the Bézier control points for the x-coordinates have been defined as: Pxu0=0, Pxu1=0, Pxu2=28 and Pxu3=48, and the Bézier control points for the z-coordinates have been defined as: Pzu0=0, Pzu1=9, Pzu2=22 and Pzu3=21.
As above, for this example club head, the Bézier equations (2a) and (2b) may be used to obtain, respectively, the x- and z-coordinates of the lower curve 124 of cross-section 120 as follows:
x
L=3(13)(1−t)t2+(48)t3 Equ. (224a)
z
L=3(−11)(1−t)2t+3(−22)(1−t)t2+(−33)t3 Equ. (224b)
Thus, for this particular curve 124, the Bézier control points for the x-coordinates have been defined as: P
At cross-section 120 at 3 mm along the x-axis from the apex point 112, the lower curve 124 has a z-coordinate value that is 50% greater than the z-coordinate value of the upper curve 123. This introduces an initial asymmetry into the curves. However, from 3 mm to 24 mm along the x-axis, the upper curve 123 extends away from the x-axis by an additional 11 mm (i.e., ΔzU=17−6=11 mm) and the lower curve 124 extends away from the x-axis by an additional 15 mm (i.e., ΔzL=24−9=15 mm). And, from 3 mm to 36 mm along the x-axis, the upper curve 123 and the lower curve 124 extend away from the x-axis by an additional 14 mm and 20 mm, respectively. In other words, similar to the curves of cross-section 110, from 3 mm to 36 mm along the x-axis, the upper curve 123 is flatter than the lower curve 124.
As with surfaces 113 and 114 discussed above, the upper and lower curves 133 and 134 may be characterized by curves presented as a table of spline points. Table VI provides a set of spline point coordinates for the cross-section 130 for Example (2). For purposes of this table, all of the coordinates of the spline points are defined relative to the apex point 112. The zU-coordinates are associated with the upper curve 133; the zL-coordinates are associated with the lower curve 134.
Alternatively, for this example club head, the Bézier equations (1a) and (1b) presented above may be used to obtain, respectively, the x- and z-coordinates of the upper curve 133 of cross-section 130 as follows:
x
U=3(26)(1−t)t2+(48)t3 Equ. (233a)
z
U=3(9)(1−t)2t+3(14)(1−t)t2+(13)t3 Equ. (233b)
Thus, for this particular curve 133, the Bézier control points for the x-coordinates have been defined as: Pxu0=0, Pxu1=0, Pxu2=26 and Pxu3=48, and the Bézier control points for the z-coordinates have been defined as: Pzu0=0, Pzu1=9, Pzu2=14 and Pzu3=13.
As above, for this example club head, the Bézier equations (2a) and (2b) may be used to obtain, respectively, the x- and z-coordinates of the lower curve 134 of cross-section 130 as follows:
x
L=3(18)(1−t)t2+(48)t3 Equ. (234a)
z
L=3(−7)(1−t)2t+3(−23)(1−t)t2+(−30)t3 Equ. (234b)
Thus, for this particular curve 134, the Bézier control points for the x-coordinates have been defined as: P
At cross-section 130, at 3 mm along the x-axis from the apex point 112, the lower curve 134 has a z-coordinate value that is only 20% greater than the z-coordinate value of the upper curve 133. This introduces an initial asymmetry into the curves. From 3 mm to 24 mm along the x-axis, the upper curve 133 extends away from the x-axis by an additional 7 mm (i.e., ΔzU=12−5=7 mm) and the lower curve 134 extends away from the x-axis by an additional 15 mm (i.e., ΔzL=21−6=15 mm). And, from 3 mm to 36 mm along the x-axis, the upper curve 133 and the lower curve 134 extend away from the x-axis by an additional 8 mm and 20 mm, respectively. In other words, from 3 mm to 36 mm along the x-axis, the upper curve 133 is significantly flatter than the lower curve 134.
Further, for this Example (2) embodiment, when the curves of the cross-section 110 (i.e., the cross-section oriented at 90 degrees from the centerline) are compared to the curves of the cross-section 120 (i.e., the cross-section oriented at 70 degrees from the centerline), it can be seen that they are similar. Specifically, the values of the z-coordinates for the upper curve 113 vary from the values of the z-coordinates for the upper curve 123 by approximately 10% or less. With respect to the lower curves 114 and 124 for the cross-sections 110 and 120, respectively, the values of the z-coordinates depart from each other by less than 10% over the x-coordinate range from 0 mm to 48 mm, with the lower curve 124 being slightly smaller than the lower curve 114. When the curves for this Example (2) embodiment of the cross-section 110 (i.e., the cross-section oriented at 90 degrees from the centerline) are compared to the curves of the cross-section 130 (i.e., the cross-section oriented at 45 degrees from the centerline), it can be seen that the values of the z-coordinates for the lower curve 134 of the cross-section 130 differ from the values of the z-coordinates for the lower curve 114 of the cross-section 110 by a fairly constant amount—either 3 mm or 4 mm—over the x-coordinate range of 0 mm to 48 mm. On the other hand, it can be seen that the difference in the values of the z-coordinates for the upper curve 133 of the cross-section 130 from the values of the z-coordinates for the upper curve 113 of the cross-section 110 steadily increases over the x-coordinate range of 0 mm to 48 mm. In other words, the curvature of the upper curve 133 significantly departs from curvature of the upper curve 113, with upper curve 133 being significantly flatter than upper curve 113.
In a third example, a representative embodiment of a club head as shown in
This third example club head may also be provided with a weight that may range from approximately 200 g to approximately 210 g. Referring to
For this Example (3) club head, Table VII provides a set of nominal spline point coordinates for the upper and lower curves of cross-section 110. As previously discussed, these nominal spline point coordinates may vary, in some instances, within a range of ±10%.
Alternatively, for this example club head, the Bézier equations (1a) and (1b) presented above may be used to obtain, respectively, the x- and z-coordinates of the upper curve 113 of cross-section 110 as follows:
x
U=3(17)(1−t)t2+(48)t3 Equ. (313a)
z
U=3(5)(1−t)2t+3(12)(1-t)t2+(11)t3 Equ. (313b)
Thus, for this particular curve 113, the Bézier control points for the x-coordinates have been defined as: Pxu0=0, Pxu1=0, Pxu2=17 and Pxu3=48, and the Bézier control points for the z-coordinates have been defined as: Pzu0=0, Pzu1=5, Pzu2=12 and Pzu3=11. As discussed, these z-coordinates may vary, in some instances, within a range of ±10%.
Similarly, for this example club head, the Bézier equations (2a) and (2b) may be used to obtain, respectively, the x- and z-coordinates of the lower curve 114 of cross-section 110 as follows:
x
L=3(7)(1−t)t2+(48)t3 Equ. (314a)
z
L=3(−15)(1−t)2t+3(−32)(1−t)t2+(−44)t3 Equ. (314b)
Thus, for this particular curve 114, the Bézier control points for the x-coordinates have been defined as: P
It can be seen from an examination of the data of this Example (3) embodiment at cross-section 110 that at 3 mm along the x-axis from the apex point 112, the lower curve 114 has a z-coordinate value that is 275% greater than the z-coordinate value of the upper curve 113. This introduces an initial asymmetry into the curves. From 3 mm to 24 mm along the x-axis, the upper curve 113 extends away from the x-axis by an additional 6 mm (i.e., ΔzU=10−4=6 mm) and the lower curve 114 extends away from the x-axis by an additional 19 mm (i.e., ΔzL=34−15=19 mm). And, from 3 mm to 36 mm along the x-axis, the upper curve 113 and the lower curve 114 extend away from the x-axis by an additional 7 mm and 25 mm, respectively. In other words, from 3 mm to 36 mm along the x-axis, the upper curve 113 is significantly flatter than the lower curve 114.
As with curves 113 and 114 discussed above with respect to
Alternatively, for this Example (3) club head, the Bézier equations (1a) and (1b) presented above may be used to obtain, respectively, the x- and z-coordinates of the upper curve 123 of cross-section 120 as follows:
x
U=3(21)(1−t)t2+(48)t3 Equ. (323a)
z
U=3(5)(1−t)2t+3(7)(1−t)t2+(7)t3 Equ. (323b)
Thus, it can be seen that for this particular curve 123, the Bézier control points for the x-coordinates have been defined as: Pxu0=0, Pxu1=0, Pxu2=21 and Pxu3=48, and the Bézier control points for the z-coordinates have been defined as: Pzu0=0, Pzu1=5, Pzu2=7 and Pzu3=7.
As above, for this example club head, the Bézier equations (2a) and (2b) may be used to obtain, respectively, the x- and z-coordinates of the lower curve 124 of cross-section 120 as follows:
x
L=3(13)(1−t)t2+(48)t3 Equ. (324a)
z
L=3(−18)(1−t)2t+3(−34)(1−t)t2+(−43)t3 Equ. (324b)
Thus, for this particular curve 124, the Bézier control points for the x-coordinates have been defined as: P
At cross-section 120 for Example (3) at 3 mm along the x-axis from the apex point 112, the lower curve 124 has a z-coordinate value that is 250% greater than the z-coordinate value of the upper curve 123. This introduces an initial asymmetry into the curves. From 3 mm to 24 mm along the x-axis, the upper curve 123 extends away from the x-axis by an additional 3 mm (i.e., ΔzU=7−4=3 mm) and the lower curve 124 extends away from the x-axis by an additional 20 mm (i.e., ΔzL=34−14=20 mm). And, from 3 mm to 36 mm along the x-axis, the upper curve 123 and the lower curve 124 extend away from the x-axis by an additional 3 mm and 25 mm, respectively. In other words, similar to the curves of cross-section 110, from 3 mm to 36 mm along the x-axis, the upper curve 123 is significantly flatter than the lower curve 124. In fact, from 24 mm to 48 mm, the upper curve 123 maintains a constant distance from the x-axis, while the lower curve 124 over this same range departs by an additional 9 mm.
As with surfaces 113 and 114 discussed above, the upper and lower curves 133 and 134 may be characterized by curves presented as a table of spline points. Table IX provides a set of spline point coordinates for the cross-section 130 for Example (3). For purposes of this table, all of the coordinates of the spline points are defined relative to the apex point 112. The zU-coordinates are associated with the upper curve 133; the zL-coordinates are associated with the lower curve 134.
Alternatively, for this example club head, the Bézier equations (1a) and (1b) presented above may be used to obtain, respectively, the x- and z-coordinates of the upper curve 133 of cross-section 130 as follows:
x
U=3(5)(1−t)t2+(48)t3 Equ. (333a)
z
U=3(6)(1−t)2t+3(5)(1−t)t2+(−2)t3 Equ. (333b)
Thus, for this particular curve 133, the Bézier control points for the x-coordinates have been defined as: Pxu0=0, Pxu1=0, Pxu2=5 and Pxu3=48, and the Bézier control points for the z-coordinates have been defined as: Pzu0=0, Pzu1=6, Pzu2=5 and Pzu3=−2.
As above, for this Example (3) club head, the Bézier equations (2a) and (2b) may be used to obtain, respectively, the x- and z-coordinates of the lower curve 134 of cross-section 130 as follows:
x
L=3(18)(1−t)t2+(48)t3 Equ. (334a)
z
L=3(−15)(1−t)2t+3(−32)(1−t)t2+(−41)t3 Equ. (334b)
Thus, for this particular curve 134, the Bézier control points for the x-coordinates have been defined as: P
At cross-section 130 for Example (3), at 3 mm along the x-axis from the apex point 112, the lower curve 134 has a z-coordinate value that is 175% greater than the z-coordinate value of the upper curve 133. This introduces an initial asymmetry into the curves. From 3 mm to 24 mm along the x-axis, the upper curve 133 extends away from the x-axis by −2 mm (i.e., ΔzU=2−4=−2 mm). In other words, the upper curve 133 has actually approached the x-axis over this range. On the other hand, the lower curve 134 extends away from the x-axis by an additional 19 mm (i.e., ΔzL=30−11=19 mm). And, from 3 mm to 36 mm along the x-axis, the upper curve 133 and the lower curve 134 extend away from the x-axis by an additional−4 mm and 26 mm, respectively. In other words, from 3 mm to 36 mm along the x-axis, the upper curve 133 is significantly flatter than the lower curve 134.
Further, for this Example (3) embodiment, when the curves of the cross-section 110 (i.e., the cross-section oriented at 90 degrees from the centerline) are compared to the curves of the cross-section 120 (i.e., the cross-section oriented at 70 degrees from the centerline), it can be seen that the upper curves vary significantly, while the lower curves are very similar. Specifically, the values of the z-coordinates for the upper curve 113 vary from the values of the z-coordinates for the upper curve 123 by up to 57% (relative to upper curve 123). Upper curve 123 is significantly flatter than upper curve 113. With respect to the lower curves 114 and 124 for the cross-sections 110 and 120, respectively, the values of the z-coordinates depart from each other by less than 10% over the x-coordinate range from 0 mm to 48 mm, with the lower curve 124 being slightly smaller than the lower curve 114. When the curves for this Example (3) embodiment of the cross-section 110 (i.e., the cross-section oriented at 90 degrees from the centerline) are compared to the curves of the cross-section 130 (i.e., the cross-section oriented at 45 degrees from the centerline), it can be seen that the values of the z-coordinates for the lower curve 134 of the cross-section 130 differ from the values of the z-coordinates for the lower curve 114 of the cross-section 110 by a fairly constant amount—either 3 mm or 4 mm—over the x-coordinate range of 0 mm to 48 mm. Thus, the curvature of lower curve 134 is approximately the same as the curvature of lower curve 114, with respect to the x-axis, over the x-coordinate range of 0 mm to 48 mm. On the other hand, it can be seen that the difference in the values of the z-coordinates for the upper curve 133 of the cross-section 130 from the values of the z-coordinates for the upper curve 113 of the cross-section 110 steadily increases over the x-coordinate range of 0 mm to 48 mm. In other words, the curvature of the upper curve 133 significantly departs from curvature of the upper curve 113, with upper curve 133 being significantly flatter than upper curve 113.
In a fourth example, a representative embodiment of a club head as shown in
Additionally, this fourth example club head is provided with a weight that may range from approximately 200 g to approximately 210 g. Referring to
For this Example (4) club head, Table×provides a set of nominal spline point coordinates for the heel side of cross-section 110. These spline point coordinates are provided as absolute values. As discussed, these nominal spline point coordinates may vary, in some instances, within a range of ±10%.
Alternatively, for this Example (4) club head, the Bézier equations (1a) and (1b) presented above may be used to obtain, respectively, the x- and z-coordinates of the upper curve 113 of cross-section 110 as follows:
x
U=3(31)(1−t)t2+(48)t3 Equ. (413a)
z
U=3(9)(1−t)2t+3(21)(1−t)t2+(20)t3 Equ. (413b)
Thus, for this particular curve 113, the Bézier control points for the x-coordinates have been defined as: Pxu0=0, Pxu1=0, Pxu2=31 and Pxu3=48, and the Bézier control points for the z-coordinates have been defined as: Pzu0=0, Pzu1=9, Pzu2=21 and Pzu3=20. As discussed, these z-coordinates may vary, in some instances, within a range of ±10%.
Similarly, for this example club head, the Bézier equations (2a) and (2b) may be used to obtain, respectively, the x- and z-coordinates of the lower curve 114 of cross-section 110 as follows:
x
L=3(30)(1−t)t2+(48)t3 Equ. (414a)
z
L=3(−17)(1−t)2t+3(−37)(1−t)t2+(−40)t3 Equ. (414b)
Thus, for this particular curve 114, the Bézier control points for the x-coordinates have been defined as: P
It can be seen from an examination of the data of this Example (4) embodiment at cross-section 110 that at 3 mm along the x-axis from the apex point 112, the lower curve 114 has a z-coordinate value that is 100% greater than the z-coordinate value of the upper curve 113. This introduces an initial asymmetry into the curves. From 3 mm to 24 mm along the x-axis, the upper curve 113 extends away from the x-axis by an additional 11 mm (i.e., ΔzU=16−5=11 mm) and the lower curve 114 extends away from the x-axis by an additional 20 mm (i.e., ΔzL=30−10=20 mm). And, from 3 mm to 36 mm along the x-axis, the upper curve 113 and the lower curve 114 extend away from the x-axis by an additional 14 mm and 26 mm, respectively. In other words, from 3 mm to 36 mm along the x-axis, the upper curve 113 is significantly flatter than the lower curve 114.
As with curves 113 and 114 discussed above with respect to
Alternatively, for this Example (4) club head, the Bézier equations (1a) and (1b) presented above may be used to obtain, respectively, the x- and z-coordinates of the upper curve 123 of cross-section 120 as follows:
x
U=3(25)(1−t)t2+(48)t3 Equ. (423a)
z
U=3(4)(1−t)2t+3(16)(1−t)t2+(14)t3 Equ. (423b)
Thus, it can be seen that for this particular curve 123, the Bézier control points for the x-coordinates have been defined as: Pxu0=0, Pxu1=0, Pxu2=25 and Pxu3=48, and the Bézier control points for the z-coordinates have been defined as: Pzu0=0, Pzu1=4, Pzu2=16 and Pzu3=14.
As above, for this example club head, the Bézier equations (2a) and (2b) may be used to obtain, respectively, the x- and z-coordinates of the lower curve 124 of cross-section 120 as follows:
x
L=3(26)(1−t)t2+(48)t3 Equ. (424a)
z
L=3(−18)(1−t)2t+3(−36)(1−t)t2+(−41)t3 Equ. (424b)
Thus, for this particular curve 124, the Bézier control points for the x-coordinates have been defined as: P
At cross-section 120 for Example (4) at 3 mm along the x-axis from the apex point 112, the lower curve 124 has a z-coordinate value that is 175% greater than the z-coordinate value of the upper curve 123. This introduces an initial asymmetry into the curves. From 3 mm to 24 mm along the x-axis, the upper curve 123 extends away from the x-axis by an additional 8 mm (i.e., ΔzU=12−4=8 mm) and the lower curve 124 extends away from the x-axis by an additional 20 mm (i.e., ΔzL=31−11=20 mm). And, from 3 mm to 36 mm along the x-axis, the upper curve 123 and the lower curve 124 extend away from the x-axis by an additional 10 mm and 26 mm, respectively. In other words, similar to the curves of cross-section 110, from 3 mm to 36 mm along the x-axis, the upper curve 123 is significantly flatter than the lower curve 124.
As with surfaces 113 and 114 discussed above, the upper and lower curves 133 and 134 may be characterized by curves presented as a table of spline points. Table XII provides a set of spline point coordinates for the cross-section 130 for Example (4). For purposes of this table, all of the coordinates of the spline points are defined relative to the apex point 112. The zU-coordinates are associated with the upper curve 133; the zL-coordinates are associated with the lower curve 134.
Alternatively, for this example club head, the Bézier equations (1a) and (1b) presented above may be used to obtain, respectively, the x- and z-coordinates of the upper curve 133 of cross-section 130 as follows:
x
U=3(35)(1−t)t2+(48)t3 Equ. (433a)
z
U=3(6)(1−t)2t+3(9)(1−t)t2+(5)t3 Equ. (433b)
Thus, for this particular curve 133, the Bézier control points for the x-coordinates have been defined as: Pxu0=0, Pxu1=0, Pxu2=35 and Pxu3=48, and the Bézier control points for the z-coordinates have been defined as: Pzu0=0, Pzu1=6, Pzu2=9 and Pzu3=5.
As above, for this Example (4) club head, the Bézier equations (2a) and (2b) may be used to obtain, respectively, the x- and z-coordinates of the lower curve 134 of cross-section 130 as follows:
x
L=3(40)(1−t)t2+(48)t3 Equ. (434a)
z
L=3(−17)(1−t)2t+3(−35)(1−t)t2+(−37)t3 Equ. (434b)
Thus, for this particular curve 134, the Bézier control points for the x-coordinates have been defined as: P
At cross-section 130 for Example (4), at 3 mm along the x-axis from the apex point 112, the lower curve 134 has a z-coordinate value that is 100% greater than the z-coordinate value of the upper curve 133. This introduces an initial asymmetry into the curves. From 3 mm to 24 mm along the x-axis, the upper curve 133 extends away from the x-axis by 3 mm (i.e., ΔzU=7−4=3 mm). The lower curve 134 extends away from the x-axis by an additional 18 mm (i.e., ΔzL=26−8=18 mm). And, from 3 mm to 36 mm along the x-axis, the upper curve 133 and the lower curve 134 extend away from the x-axis by an additional 3 mm and 24 mm, respectively. In other words, from 3 mm to 36 mm along the x-axis, the upper curve 133 is significantly flatter than the lower curve 134.
Further, for this Example (4) embodiment, when the curves of the cross-section 110 (i.e., the cross-section oriented at 90 degrees from the centerline) are compared to the curves of the cross-section 120 (i.e., the cross-section oriented at 70 degrees from the centerline), it can be seen that the upper curves vary significantly, while the lower curves are very similar. Specifically, the values of the z-coordinates for the upper curve 113 vary from the values of the z-coordinates for the upper curve 123 by up to 43% (relative to upper curve 123). Upper curve 123 is significantly flatter than upper curve 113. With respect to the lower curves 114 and 124 for the cross-sections 110 and 120, respectively, the values of the z-coordinates depart from each other by less than 10% over the x-coordinate range from 0 mm to 48 mm, with the lower curve 124 being slightly smaller than the lower curve 114. When the curves for this Example (4) embodiment of the cross-section 110 (i.e., the cross-section oriented at 90 degrees from the centerline) are compared to the curves of the cross-section 130 (i.e., the cross-section oriented at 45 degrees from the centerline), it can be seen that the values of the z-coordinates for the lower curve 134 of the cross-section 130 differ from the values of the z-coordinates for the lower curve 114 of the cross-section 110 by over a range of 2 mm to 4 mm—over the x-coordinate range of 0 mm to 48 mm. Thus, for the Example (4) embodiment, the curvature of lower curve 134 varies somewhat from the curvature of lower curve 114. On the other hand, it can be seen that the difference in the values of the z-coordinates for the upper curve 133 of the cross-section 130 from the values of the z-coordinates for the upper curve 113 of the cross-section 110 steadily increases from a difference of 1 mm to a difference of 15 mm over the x-coordinate range of 0 mm to 48 mm. In other words, the curvature of the upper curve 133 significantly departs from curvature of the upper curve 113, with upper curve 133 being significantly flatter than upper curve 113.
It would be apparent to persons of ordinary skill in the art, given the benefit of this disclosure, that a streamlined region 100 similarly proportioned to the cross-sections 110, 120, 130 would achieve the same drag reduction benefits as the specific cross-sections 110, 120, 130 defined by Tables I-XII. Thus, the cross-sections 110, 120, 130 presented in Tables I-XII may be enlarged or reduced to accommodate club heads of various sizes. Additionally, it would be apparent to persons of ordinary skill in the art, given the benefit of this disclosure, that a streamlined region 100 having upper and lower curves that substantially accord with those defined by Tables I-XII would also generally achieve the same drag reduction benefits as the specific upper and lower curves presented in Tables I-XII. Thus, for example, the z-coordinate values may vary from those presented in Tables I-XII by up to ±5%, up to ±10%, or even in some instances, up to ±15%.
While there have been shown, described, and pointed out fundamental novel features of various embodiments, it will be understood that various omissions, substitutions, and changes in the form and details of the devices illustrated, and in their operation, may be made by those skilled in the art without departing from the spirit and scope of the invention. For example, the golf club head may be any driver, wood, or the like. Further, it is expressly intended that all combinations of those elements which perform substantially the same function, in substantially the same way, to achieve the same results are within the scope of the invention. Substitutions of elements from one described embodiment to another are also fully intended and contemplated. It is the intention, therefore, to be limited only as indicated by the scope of the claims appended hereto.
The present patent application is a continuation of U.S. patent application Ser. No. 14/472,917, filed Aug. 29, 2014, entitled “Golf Club Assembly and Golf Club With Aerodynamic Features,” and naming Gary Tavares, et al. as inventors, which is a continuation of U.S. patent application Ser. No. 13/740,394, filed Jan. 14, 2013, now U.S. Pat. No. 8,821,311 entitled “Golf Club Assembly and Golf Club With Aerodynamic Features,” and naming Gary Tavares, et al. as inventors, which is a continuation of U.S. patent application Ser. No. 12/779,669, filed May 13, 2010, now U.S. Pat. No. 8,366,565, entitled “Golf Club Assembly and Golf Club With Aerodynamic Features,” and naming Gary Tavares, et al. as inventors, which is a continuation-in-part of U.S. patent application Ser. No. 12/465,164, filed May 13, 2009, now U.S. Pat. No. 8,162,775, entitled “Golf Club Assembly and Golf Club With Aerodynamic Features,” and naming Gary Tavares, et al. as inventors, and which claims the benefit of priority of Provisional Application No. 61/298,742, filed Jan. 27, 2010, entitled “Golf Club Assembly and Golf Club With Aerodynamic Features,” and naming Gary Tavares, et al. as inventors. Each of these earlier filed applications is incorporated herein by reference in its entirety.
| Number | Date | Country | |
|---|---|---|---|
| 61298742 | Jan 2010 | US |
| Number | Date | Country | |
|---|---|---|---|
| Parent | 14472917 | Aug 2014 | US |
| Child | 15155520 | US | |
| Parent | 13740394 | Jan 2013 | US |
| Child | 14472917 | US | |
| Parent | 12779669 | May 2010 | US |
| Child | 13740394 | US |
| Number | Date | Country | |
|---|---|---|---|
| Parent | 12465164 | May 2009 | US |
| Child | 12779669 | US |
