Patent Grant
10532250
The present invention relates to golf ball dimples having a non-isodiametrical, curvilinear plan shape defined by circular arcs. In particular, the present invention relates to golf ball dimples having plan shapes defined by a number of convex or concave arcs derived from a regular n-sided polygon. When utilized on golf balls, the golf ball dimples of the present invention provide surface textures with unique appearances, while maintaining desirable aerodynamic characteristics.
Golf balls generally include a spherical outer surface with a plurality of dimples formed thereon. The dimples on a golf ball improve the aerodynamic characteristics of a golf ball and, therefore, golf ball manufacturers have researched dimple patterns, shape, volume, and cross-section in order to improve the aerodynamic performance of a golf ball. Determining specific dimple arrangements and dimple shapes that result in an aerodynamic advantage requires an understanding of how a golf ball travels through air.
Aerodynamic forces acting on a golf ball are typically resolved into orthogonal components of lift (FL) and drag (FD). Lift is defined as the aerodynamic force component acting perpendicular to the flight path. It results from a difference in pressure that is created by a distortion in the air flow that results from the back spin of the ball. Due to the back spin, the top of the ball moves with the air flow, which delays the separation to a point further aft. Conversely, the bottom of the ball moves against the air flow, moving the separation point forward. This asymmetrical separation creates an arch in the flow pattern, requiring the air over the top of the ball to move faster, and thus have lower pressure than the air underneath the ball.
Drag is defined as the aerodynamic force component acting opposite to the ball flight direction. As the ball travels through the air, the air surrounding the ball has different velocities and, thus, different pressures. The air exerts maximum pressure at the stagnation point on the front of the ball. The air then flows over the sides of the ball and has increased velocity and reduced pressure. The air separates from the surface of the ball, leaving a large turbulent flow area with low pressure, i.e., the wake. The difference between the high pressure in front of the ball and the low pressure behind the ball reduces the ball speed and acts as the primary source of drag.
Lift and drag, among other aerodynamic characteristics of a golf ball, are influenced by the external surface geometry of the ball, which includes the dimples thereon. As such, the dimples on a golf ball play an important role in controlling those parameters.
Recently, a number of golf ball products in the market place have been introduced with golf ball surfaces featuring visually distinct dimple patterns. Golf balls featuring these visually distinct dimple patterns are most prevalent in the premium distance category. Existing examples of such golf balls include, but are not limited to, the Dunlop XXiO XD Aero, the Bridgestone Tourstage PHYZ, and the Saso Kaede. While these golf ball designs possess a unique visual appearance, the dimple patterns utilized on the golf balls, when compared to conventional dimple patterns, are less aerodynamically efficient.
Other unique dimple designs have also been introduced. For example, isodiametrical dimples, such as those disclosed in U.S. Pat. No. 5,377,989, provide for visually distinct dimple shapes. However, due to the nature of the curvatures in forming the isodiametric shape, these dimples limit surface coverage uniformity and packing efficiency when utilized on golf balls. Accordingly, there remains a need for a dimple geometry that provides a visually distinct golf ball surface texture, while providing improved aerodynamic characteristics and maximized packing efficiency.
The present invention is directed to a golf ball having a substantially spherical surface, including a plurality of dimples on the spherical surface, wherein at least a portion of the plurality of dimples, for example, about 50 percent or more, include a curvilinear plan shape defined by at least 3 circular arcs, wherein each circular arc includes two endpoints that define adjacent vertices of a regular polygon. In one embodiment, the curvilinear plan shape is defined by 3 to 12 circular arcs. In another embodiment, the regular polygon is an equilateral polygon comprising from 3 to 12 sides. In still another embodiment, the number of circular arcs is equivalent to the number of sides of the regular polygon. The circular arcs may include concave arcs, convex arcs, or combinations thereof. For example, the plan shape may be defined by an even number of alternating convex and concave circular arcs less than or equal to 12. In yet another embodiment, the portion of the plurality of dimples has a plan shape area ratio of about 0.35 to about 1.75.
The present invention is also directed to a golf ball having a substantially spherical surface, including a plurality of dimples on the spherical surface, wherein at least a portion of the plurality of dimples, for example, about 70 percent or more, include a curvilinear plan shape defined by a plurality of arc segments having endpoints that define adjacent vertices of a polygon including n sides, wherein each arc segment includes an arc center outside of the polygon, and wherein the plurality of arc segments is equal to n. In one embodiment, n ranges from 3 to 12, and more preferably, from 3 to 8. In another embodiment, the plurality of arc segments has identical lengths and radii. Conversely, the arc segments may each have a different length and radius. In still another embodiment, the plurality of arc segments includes both concave and convex circular arcs. For example, the plan shape may be defined by alternating convex and concave circular arcs. In yet another embodiment, the portion of the plurality of dimples has a plan shape perimeter ratio of less than 1.10.
The present invention is further directed to a golf ball dimple having a perimeter defined by a plurality of convex or concave circular arcs having identical lengths and radii, wherein each circular arc has two endpoints that define consecutive vertices of a regular n-sided polygon. In one embodiment, the perimeter of the dimple is defined by at least 3 circular arcs, for example, 3 to 12 circular arcs. In this aspect, the perimeter may be defined by a plurality of concave circular arcs and a plurality of convex circular arcs. In another embodiment, the regular n-sided polygon is selected from the group consisting of triangles, squares, pentagons, hexagons, heptagons, octagons, nonagons, decagons, hendecagons, and dodecagons.
The present invention may also be directed to a golf ball having a substantially spherical surface, including a plurality of dimples on the spherical surface, wherein at least a portion of the plurality of dimples include a convex curvilinear plan shape defined by circular arcs, wherein each circular arc comprises two endpoints that define adjacent vertices of a regular polygon having three or four sides, for example, an equilateral triangle or a square, wherein each vertex of the regular polygon has an arc vertex angle θv defined by the following equation:
wherein n is the number of sides of the regular polygon and R is about 5 to 35. In one embodiment, each circular arc comprises an arc center outside of the regular polygon. In another embodiment, each side of the regular polygon is about 0.085 inches to about 0.350 inches in length. In still another embodiment, the regular polygon has an inradius of about 0.025 inches to about 0.100 inches and a circumradius of about 0.050 inches to about 0.200 inches.
The present invention is further directed to a golf ball having a substantially spherical surface, including a plurality of dimples on the spherical surface, wherein at least a portion of the plurality of dimples include one or more non-isodiametrical plan shapes, wherein each non-isodiametrical plan shape is defined by a plurality of convex are segments having endpoints that define adjacent vertices of a regular polygon comprising n sides, wherein the plurality of arc segments is equal to n, wherein n is three or four, wherein each vertex of the regular polygon has an arc vertex angle θv defined by the following equation:
where n is the number of sides of the regular polygon and R is about 5 to 35, and wherein each arc segment includes an arc center outside of the regular polygon. In one embodiment, each dimple has a plan shape perimeter ratio of less than 1.10. In another embodiment, in the portion of the plurality of dimples, each dimple has a plan shape area of about 0.0025 in2 to about 0.045 in2. In still another embodiment, in the portion of the plurality of dimples, each dimple has a plan shape area ratio of greater than 1 and less than 1.75. In yet another embodiment, in the portion of the plurality of dimples, each dimple has a maximum absolute distance of about 0.0005 inches to about 0.040 inches. In another embodiment, in the portion of the plurality of dimples, a first number of dimples include a non-isodiametrical plan shape defined by a plurality of convex arc segments having endpoints that define adjacent vertices of a polygon including three sides and a second number of dimples include a non-isodiametrical plan shape defined by a plurality of convex arc segments having endpoints that define adjacent vertices of a polygon including four sides. In this aspect, the first number of dimples and the second number of dimples may have different plan shape perimeter ratios and different plan shape areas. In yet another embodiment, each arc segment has the same radius.
The present invention may also be directed to a golf ball dimple having a non-isodiametrical plan shape defined by a plurality of convex circular arcs, wherein each circular arc has a pair of endpoints that define consecutive vertices of a regular three-sided or four-sided polygon, wherein each circular arc includes an arc center outside of the polygon, wherein each pair of endpoints define consecutive vertices on the same polygon, and wherein each vertex of the polygon has an arc vertex angle θv defined by the following equation:
where n is the number of sides of the regular polygon and R is about 5 to 35. In one embodiment, the golf ball dimple has an equivalent dimple diameter of about 0.080 inches to about 0.220 inches. In another embodiment, the golf ball dimple has a plan shape area of about 0.005 in2 to about 0.035 in2. In still another embodiment, the golf ball dimple has a dimple surface volume of about 0.5×10−4 in3 to about 3.0×10−4 in3. In yet another embodiment, the regular polygon has a circumradius and an inradius, and wherein each circular arc has a radius at least twice the circumradius of the regular polygon. In still another embodiment, the regular polygon has an inradius of about 0.025 inches to about 0.100 inches and a circumradius of about 0.050 inches to about 0.200 inches.
The present invention is also directed to a golf ball having a substantially spherical surface, including a plurality of dimples on the spherical surface, wherein at least a portion of the plurality of dimples include a non-isodiametrical plan shape defined by at least three circular arcs, wherein each circular arc defines an edge of the dimple and includes two discontinuous endpoints that define adjacent vertices of a base polygon, wherein at least one dimple pair in the portion of the plurality of dimples includes a first dimple having a first edge and a second dimple having a second edge that is adjacent to the first edge, and wherein the first edge is defined by a concave circular arc and the second edge is defined by a convex circular arc, and the maximum integration distance between the first edge and the second edge is about 0.020 inches or less. In another embodiment, the first edge and the second edge have substantially equal arc edge radii. In still another embodiment, the first edge and the second edge each have a maximum distance between the circular arc and the base polygon of about 0.005 inches to about 0.030 inches. In one embodiment, the first edge and the second edge have the same maximum distances. In another embodiment, the first edge has a first maximum distance, the second edge has a second maximum distance, and the difference between the first maximum distance and the second maximum distance is less than or equal to about 0.01 inches. In yet another embodiment, the maximum integration distance between the first edge and the second edge is about 0.010 inches or less. In another embodiment, the at least a portion of the plurality of dimples include a non-isodiametrical plan shape defined by three or four circular arcs.
The present invention is further directed to a golf ball having a substantially spherical surface, including a plurality of dimples on the spherical surface, wherein at least a portion of the plurality of dimples include a non-isodiametrical plan shape defined by at least three circular arcs, wherein each circular arc defines an edge of the dimple and includes two discontinuous endpoints that define adjacent vertices of a regular polygon, wherein at least one dimple in the portion of the plurality of dimples includes at least one edge that is adjacent to a respective edge of at least one other dimple in the portion of the plurality of dimples, wherein the at least one edge has a first concavity, the respective edge has a second concavity, and the first concavity is different from the second concavity, wherein the maximum integration distance between the at least one edge and the respective edge is about 0.020 inches or less, and wherein the at least one edge and the respective edge are unified. In one embodiment, the at least one edge and the respective edge have substantially equal arc edge radii. In another embodiment, the first concavity and the second concavity are selected from concave-in or concave-out. For example, the first concavity may be concave-in and the second concavity may be concave-out. In still another embodiment, the maximum integration distance between the first edge and the second edge is about 0.010 inches or less, for instance, about 0.005 inches or less. In yet another embodiment, at least about 25 percent, for example, at least about 50 percent, of the dimples on the golf ball include at least one unified edge.
The present invention may also be directed to a golf ball having a substantially spherical surface, including a plurality of dimples on the spherical surface, wherein at least a portion of the plurality of dimples include a non-isodiametrical plan shape defined by at least three circular arcs, wherein each circular arc defines an edge of the dimple and includes two discontinuous endpoints that define adjacent vertices of a regular polygon, wherein at least one dimple in the portion of the plurality of dimples includes at least two edges that are adjacent to respective edges of at least two other dimples in the portion of the plurality of dimples, wherein the at least two edges each have a first concavity, the respective edges of the at least two other dimples each have a second concavity, and the first concavity is different from the second concavity, wherein the maximum integration distance between each of the at least two edges and the respective edges is about 0.010 inches or less, and wherein the at least two edges and the respective edges are unified. In this aspect, the first concavity and the second concavity are selected from concave-in or concave-out. In another embodiment, at least about 50 percent of the dimples on the golf ball include at least two unified edges. In yet another embodiment, at least about 10 percent, for instance, at least about 50 percent, of the edges defined by circular arcs are unified.
Further features and advantages of the invention can be ascertained from the following detailed description that is provided in connection with the drawings described below:
The present invention is directed to golf balls having surface textures with unique appearances and improved aerodynamic characteristics due, at least in part, to the use of noncircular dimple plan shapes. In particular, the present invention is directed to a golf ball that includes at least a portion of its dimples having a curvilinear plan shape defined by a number of convex or concave arcs that are derived from a regular n-sided polygon.
Advantageously, in one embodiment, golf balls including dimple plan shapes produced in accordance with the present invention have visually distinct surface textures. Indeed, the dimple plan shapes of the present invention possess a unique visual appearance. In another embodiment, the dimple plan shapes of the present invention allow the dimples to be arranged according to spherically tiled dimple designs. The spherical tiling layouts utilizing the dimple plan shapes of the present invention provide improved symmetry including multiple axes of symmetry on each golf ball. As a result, golf balls including the dimple plan shapes of the present invention exhibit improved aerodynamic performance in addition to providing visually distinct dimple patterns.
Dimple Plan Shane
A dimple plan shape, as used herein, refers to the perimeter of the dimple as seen from a top view of the dimple, or the demarcation between the dimple and the outer surface of the golf ball or fret surface. The present invention contemplates dimples having a curvilinear plan shape.
The present invention contemplates curvilinear dimple plan shapes defined by circular arcs that form a simple closed path. A “simple closed path,” as used herein, includes a curve that starts and ends at the same point without traversing any defining point or edge along the path more than once. In particular, the dimple plan shapes of the present invention include a number of convex or concave circular arcs having endpoints that define the vertices of a regular n-sided polygon. That is, the plan shapes of the present invention are defined by arc segments created from a regular n-sided polygon. Indeed, the present invention contemplates non-smooth plan shapes having discontinuities at the endpoints of each arc segment. As used herein, a plan shape has “discontinuities at the endpoints” or “discontinuous endpoints” if two dimple edges meet at a point making the plan shape non-differentiable at that point.
The present invention contemplates plan shapes defined by a plurality of arc segments that are derived from the sides of a regular n-sided polygon. In one embodiment, the arc segments are created by arcs of circles centered outside of a regular polygon. As discussed in greater detail below, the location of the centers of the circles is dependent on whether the number of sides of the polygon is odd or even. For example, when the number of sides of the polygon is even, the centers of the circles lie on an axis defined by the center of the polygonal inradius and the side mid-point. In another embodiment, when the number of sides of the polygon is odd, the centers of the circles lie on an axis defined by the center of the polygonal inradius and the vertex. Indeed, the circular arcs are designed to sweep the sides of the regular polygon such that arc segments are created between each vertex of the regular polygon in a convex or concave manner.
In one embodiment, the plan shape may be defined by a plurality of convex arcs. For example, the plan shape may include a plurality of arc segments that curve in an outwardly direction. In another embodiment, the plan shape may be defined by a plurality of concave arcs. For example, the plan shape may include a plurality of arc segments that curve in an inwardly direction.
In still another embodiment, the plan shape may be defined by a combination of convex and concave arcs. For example, the plan shape may include one or more convex arcs and one or more concave arcs such that each arc segment is created between each vertex of the regular polygon in a concave or convex manner.
In yet another embodiment, the plan shape may be defined by alternating convex and concave arcs. For example, the plan shape may include a plurality of arc segments that alternate between convex arcs and concave arcs. In this embodiment, the number of sides of the polygon is even.
The number of arc segments is equivalent to the number of sides of the regular polygon. For example, a plan shape including three arc segments may correspond to a three-sided polygon or a triangle. In another embodiment, a plan shape including four arc segments may correspond to a four-sided polygon or a square. In still another embodiment, a plan shape including five arc segments may correspond to a five-sided polygon or a pentagon. In yet another embodiment, a plan shape including six arc segments may correspond to a six-sided polygon or a hexagon.
In this aspect, the present invention contemplates the use of any regular n-sided polygon. By the term, “regular n-sided polygon,” it is meant a polygon that is equiangular (i.e., all angles are equal in measure) and equilateral (i.e., all sides have the same length). In one embodiment, the present invention contemplates regular n-sided polygons, where n is equal to or greater than 3. Indeed, the present invention contemplates regular polygons having at least 3 or more equal length sides. While polygons having a higher number of sides may be employed, increasing the number of sides produces plan shapes which closely approximate a circular perimeter. Thus, it is preferable to utilize polygons having smaller values of n.
For example, the present invention contemplates the use of regular n-sided polygons having from 3 to about 50 equal length sides. In another embodiment, the polygon of the present invention has from 3 to about 26 equal length sides. In still another embodiment, the polygon of the present invention has from 3 to about 12 equal length sides. In yet another embodiment, the polygon of the present invention has from 3 to about 8 equal length sides. For example, the polygon may have 4 equal length sides.
Suitable examples of regular n-sided polygons contemplated by the present invention include, but are not limited to, triangles, squares, pentagons, hexagons, heptagons, octagons, nonagons, decagons, hendecagons, and dodecagons. In one embodiment, the regular n-sided polygon is a triangle. In another embodiment, the regular n-sided polygon is a square.
The overall dimensions of the regular n-sided polygon may vary. In this aspect, the dimensions of the polygon may be defined by the length of the sides of the polygon. As noted above, the polygons of the present invention are equilateral (i.e., all sides have the same length). In this aspect, the length of each side of the polygon may be at least about 0.085 inches. In one embodiment, the length of each side of the polygon is about 0.350 inches or less. For example, the length of each side of the polygon may range from about 0.085 inches to about 0.350 inches. In another embodiment, the length of each side of the polygon ranges from about 0.085 inches to about 0.260 inches. For example, the length of each side may range from about 0.100 inches to about 0.250 inches. In another embodiment, the length of each side may range from about 0.125 inches to about 0.225 inches. In still another embodiment, the length of each side may range from about 0.150 inches to about 0.200 inches.
In another embodiment, the dimensions of the polygon may be defined by the inradius of the regular polygon. For purposes of the present invention, the term, “inradius,” refers to the radius of a polygon's incircle, or the radius of the largest circle that fits inside of the polygon and is tangent to each side. The inradius of a regular polygon with n sides and side length a is given by equation (1), denoted below:
In this aspect, the present invention contemplates regular polygons having an inradius of at least about 0.020 inches. In one embodiment, the inradius is about 0.175 inches or less. In another embodiment, the inradius is about 0.125 inches or less. In yet another embodiment, the inradius is about 0.115 inches or less. In still another embodiment, the inradius is about 0.010 inches or less. For example, the inradius may range from about 0.025 inches to about 0.150 inches. In one embodiment, the polygon of the present invention has an inradius of about 0.050 inches to about 0.125 inches. In another embodiment, the polygon of the present invention has an inradius of about 0.075 inches to about 0.115 inches. In still another embodiment, the polygon of the present invention has an inradius of about 0.080 inches to about 0.100 inches. For example, the polygon of the present invention may have an inradius of about 0.025 inches to about 0.100 inches.
In still another embodiment, the dimensions of the polygon may be defined by the circumradius of the regular polygon. For purposes of the present invention, the term, “circumradius,” refers to the radius of the polygon's circumcircle, or the radius of the circle that passes through each vertex of the regular polygon. Indeed, the circumradius will approach the inradius as n approaches infinity. For example, when n=3, the circumradius is twice the inradius.
In this aspect, the present invention contemplates regular polygons having a circumradius of at least about 0.05 inches. Likewise, the circumradius may be about 0.300 inches or less. In one embodiment, the circumradius ranges from about 0.050 inches to about 0.300 inches. For example, the polygon of the present invention may have a circumradius of about 0.075 inches to about 0.275 inches. In another embodiment, the polygon of the present invention may have a circumradius of about 0.100 inches to about 0.250 inches. In still another embodiment, the polygon of the present invention may have a circumradius of about 0.125 inches to about 0.225 inches. In yet another embodiment, the polygon of the present invention may have a circumradius of about 0.150 inches to about 0.200 inches. For example, the polygon of the present invention may have a circumradius of about 0.050 inches to about 0.200 inches.
The length and radii of the curvature of each arc segment will vary based on the selected dimensions of the regular n-sided polygon. However, in one embodiment, the arc segments of the plan shape have equal curvatures. That is, each arc segment of the plan shape has an identical length and radii. In another embodiment, the arc segments of the plan shape have different lengths and radii. For instance, each arc segment may have a different radii. In still another embodiment, at least one of the arc segments may have different radii.
Once the base polygon is chosen, each arc segment is constructed. According to the present invention, the number of arc segments is equivalent to the number of sides of the regular polygon. For example, if the regular polygon has four sides, the plan shape of the present invention will be defined by four arc segments. To construct the first arc segment, an arc center is determined (step 102). The arc center, C, may be defined as any point lying outside the polygonal boundary. Indeed, each arc center should lie outside the convex hull of the base polygon.
In this aspect, the location of the arc center, C, will vary depending on the number of sides of the polygon. In one embodiment, when the number of sides of the polygon is even, the arc center lies on an axis that extends radially from the inradius center and bisects the opposing side of the polygon. In another embodiment, when the number of sides of the polygon is odd, the arc center lies on an axis that extends radially from the inradius center and through the opposing vertex. For example, if the polygon is a triangle, the arc centers lie on axes defined by the inradius center and the opposing vertex. In contrast, if the polygon is a square, the arc centers lie on axes defined by the inradius center and the opposing side mid-point.
After the arc center has been defined, at step 103, an arc is swept around the arc center to create a circle. In one embodiment, the circle should sweep one side of the regular polygon such that an arc segment is defined having endpoints at two consecutive vertices of the polygon. In this regard, to ensure that the circle sweeps the interior or exterior of a side of the polygon, the radius, r, of the circle should, at a minimum, be greater than twice the circumradius, rc, of the selected polygon. For example, the radius, r, of the circle should satisfy the following inequality, denoted as equation (2) below:
where constants, α and β, define the upper bound on the radius. In one embodiment, α is a value between about 50 and about 100, while β is a value between about 2 and about 4. For example, α may be between about 60 and about 90. In one embodiment, α is between about 75 and about 85. In another embodiment, α is between about 50 and 65. In yet another embodiment, α is between about 85 and 100.
Steps 102 and 103, as described above, are repeated for each arc segment of the plan shape (step 104). Indeed, an arc segment should be constructed for each side of the selected regular polygon. In this aspect, the remaining arc centers should be defined around the regular polygon such that each side of the polygon is utilized in constructing an arc segment.
For example,
Similarly, the arc center, C3, is defined as a point lying outside the boundary of the square polygon. The radius, r3, of the circle, A3, is determined such that the radius is at least twice the circumradius of the square 5 and satisfies the inequality of equation (2). The circle, A3, is swept around the arc center, C3, to define arc segment, S3, having endpoints at consecutive vertices, V3 and V4, of the square.
Further, arc center, C4, is defined as a point lying outside the boundary of the square polygon. The radius, r4, of the circle, A4, is determined such that the radius is at least twice the circumradius of the square 5 and satisfies the inequality of equation (2). The circle, A4, is swept around the arc center, C4, to define arc segment, S4, having endpoints at consecutive vertices, V4 and V1, of the square. In this embodiment, the circles, the radii, the arc segments, and the Euclidean distance of the arc centers from the incenter of the polygon, are equivalent.
As discussed briefly above, the arc segments of the present invention may be convex or concave. In this aspect of the invention, the location of the arc center relative to the arc will determine whether the arc segment is convex or concave. For example, when forming a convex arc, the arc center should lie on the side opposite to the side of the polygon where the convex arc segment is formed. Conversely, when forming a concave arc, the arc center should lie on the same side as the side of the polygon where the concave arc segment is formed.
After each of the arc segments are constructed, the dimple plan shape of the present invention is generated (step 105).
In certain embodiments, the present invention contemplates dimple plan shapes defined by convex arc segments and created from a square, such as the plan shape depicted in
The dimple plan shapes of the present invention also maintain a maximum absolute distance or sagitta. For example, the square and triangular convex dimple plan shapes maintain a maximum absolute distance or sagitta. As used herein, the “maximum absolute distance” or “sagitta” is defined as the maximum distance between any point on the plan shape and the base polygon.
d=√{square root over ((xpolygon−xplan)2+(ypolygon−yplan)2])}
The maximum value, the sagitta, for all sides of the polygon is the maximum absolute distance dmax. In one embodiment, dmax is at least about 0.0005 inches. In another embodiment, dmax is at least about 0.001 inches. In yet another embodiment, dmax is at least about 0.003 inches. In still another embodiment, dmax is about 0.040 inches or less. In yet another embodiment, dmax is about 0.03 inches or less. In still another embodiment, dmax is about 0.020 inches or less. For example, the maximum absolute distance, dmax, or sagitta, may range from about 0.0005 inches to about 0.040 inches. In another embodiment, the maximum absolute distance, dmax, or sagitta, ranges from about 0.001 inches to about 0.030 inches. In still another embodiment, the maximum absolute distance, dmax, or sagitta, ranges from about 0.003 inches to about 0.020 inches.
Furthermore, the convex dimple plan shapes of the present invention include an arc vertex angle. For instance, each of the square and triangular convex dimple plan shapes constructed in accordance with the present invention includes an arc vertex angle. As used herein, “arc vertex angle,” is defined as the angle formed by tangent lines drawn through the shared vertex of adjacent arc segments of the plan shape. For instance, as shown in
where n is the number of sides of the regular polygon, R is a constant, and θv is the arc vertex angle. In one embodiment, R has a value of about 5 to 35, for example, about 5 to 30, about 10 to 25, about 10 to 20, and about 15 to 20. In this aspect, the arc vertex angle for a triangle may range from greater than 60° to less than 95°, for instance, from 65° to 85° or from 70° to 80°. Similarly, the arc vertex angle for a square may range from greater than 90° to less than 125°, for example, from 95° to 120° or from 100° to 115°.
The process described above in
As discussed above, step 101 includes selecting the regular polygon and its overall dimensions, and defining the regular polygon in a two-dimensional plane. For illustrative purposes, the square 5 having four equal sides that meet at four vertices, V1, V2, V3, and V4 (as shown in
To construct the first arc segment, an arc center is determined (step 102). In this embodiment, since the number of sides of the polygon is even, the arc center should lie on an axis that extends radially from the polygonal incenter and through the vertex. Additionally, because a concave arc segment is contemplated, the arc center should lie on the same side as the side of the polygon where the concave arc segment is formed. For example, as shown in
Steps 102 and 103, as described above, are repeated for each arc segment of the plan shape (step 104). Indeed, an arc segment should be constructed for each side of the selected regular polygon. In this aspect, the remaining arc centers should be defined around the regular polygon such that each side of the polygon is utilized in constructing an arc segment. For example,
Similarly, the arc center, C3, is defined as a point lying outside the boundary of the square polygon, but located on the same side as S3. The radius, r3, of the circle, A3, is determined such that the radius is at least twice the circumradius of the square 5 and satisfies the inequality of equation (2). The circle, A3, is swept around the arc center, C3, to define arc segment, S3, having endpoints at consecutive vertices, V3 and V4, of the square.
Further, arc center, C4, is defined as a point lying outside the boundary of the square polygon, but located on the same side as S4. The radius, r4, of the circle, A4, is determined such that the radius is at least twice the circumradius of the square 5 and satisfies the inequality of equation (2). The circle, A4, is swept around the arc center, C4, to define arc segment, S4, having endpoints at consecutive vertices, V4 and V1, of the square.
After each of the arc segments are constructed, the dimple plan shape of the present invention is generated (step 105).
In still another embodiment, the process described above in
After the dimple plan shape has been generated, at step 106, the plan shape can be used in designing geometries for dimple patterns of a golf ball. For example, the plan shapes generated in accordance with the present invention can be imported into a CAD program and used to define dimple geometries and tool paths for fabricating tooling for golf ball manufacture. The various dimple geometries can then be used in constructing dimple patterns that provide surface textures with unique appearances and improved aerodynamic characteristics.
At step 107, the resulting dimple pattern can be transformed to the outer surface of a golf ball. Similarly, the negative of the resulting dimple pattern may be used to form the interior surface of the cavity of a golf ball mold. For example, the negative of the resulting golf ball dimple pattern can be applied to the interior of a golf ball mold, which can then be used in an injection molding, compression molding, or casting process to form a cover layer comprising the golf ball dimple pattern.
Dimple Patterns & Packing
The golf ball dimples of the present invention may be tailored to maximize surface coverage uniformity and packing efficiency by altering the plan shape of the dimple. For example, in one embodiment, the convex and concave edges of the dimple plan shapes according to the present invention can be designed such that the dimples are packed more closely together to reduce the width of the land portions adjacent to each dimple. In this aspect, each individual dimple may have a different plan shape so that the space between each dimple can be reduced. Thus, the surface edges of the dimples of the present invention allow for maximizing the dimple coverage on the surface of a golf ball by reducing the land portion located between adjacent dimples.
In another embodiment, the golf ball dimple plan shapes of the present invention can be tailored to maximize surface coverage uniformity and packing efficiency by selecting a regular n-sided polygon having a number of sides that is equivalent to the number of neighboring dimples. For example, if the dimple plan shape is constructed using a regular polygon having 5 sides, the present invention contemplates that the dimple will be surrounded by 5 neighboring dimples. In another embodiment, the number of sides of the regular polygon is a scalar multiple of the number of neighboring dimples. For example, if the number of neighboring dimples is 4, the present invention contemplates a dimple plan shape created from a regular polygon having 8 or 12 sides.
As discussed above, the present invention contemplates dimple plan shapes defined by convex arc segments and created from a three- or four-sided polygon, e.g., a triangle or a square. Such convex dimple plan shapes of the present invention may be utilized in various dimple patterns. For example, in some embodiments, the dimple patterns of the present invention may utilize only square convex dimple plan shapes. In other embodiments, the dimple patterns of the present invention may utilize only triangular convex dimple plan shapes. In other embodiments, the dimple patterns may utilize a combination of square and triangular convex dimple plan shapes. In this aspect, the dimple patterns may include about 1 to about 99 percent of the dimples created from square convex dimple plan shapes with the remainder of the dimples created from triangle convex dimple plan shapes. For example, a suitable dimple pattern may include about 10 to about 90 percent of the dimples created from square convex dimple plan shapes with the remainder of the dimples created from triangle convex dimple plan shapes.
In this aspect, the opposing hemispheres of the golf balls may have the same or different dimple patterns/layouts. The specific arrangement or packing of the dimples within the hemispheres may vary. For example, each hemisphere may include a base pattern that is rotated about the polar axis and which forms the overall dimple pattern. In other embodiments, each hemisphere may be composed of a single base pattern that is not rotated about the polar axis. The dimples arranged in each hemisphere may be of varying designs and dimensions. For example, each hemisphere may be composed of dimples having square and triangular convex plan shapes and varying profile shapes, dimple diameters, plan shape perimeter ratios, plan shape area ratios, and maximum absolute distances (sagittas).
In some embodiments, the dimple patterns of the present invention may be composed of dimples having the same plan shape type and having identical or differing dimensions. For instance, the dimple patterns may be composed of a number of triangular convex plan shapes having varying or identical equivalent dimple diameters (as defined below), depths, plan shape perimeter ratios, plan shape area ratios, and maximum absolute distances (sagittas). In another embodiment, the dimple patterns of the present invention may be composed of dimples having different plan shape types, where each plan shape type has identical or differing dimensions.
While the dimple plan shapes of the present invention may be used for at least a portion of the dimples on a golf ball, it is not necessary that the dimple plan shapes be used on every dimple of a golf ball. In general, it is preferred that a sufficient number of dimples on the ball are constructed in accordance with the present invention so that the aerodynamic characteristics of the ball may be altered. For example, at least about 30 percent of the dimples on a golf ball include plan shapes according to the present invention. In another embodiment, at least about 50 percent of the dimples on a golf ball include plan shapes according to the present invention. In still another embodiment, at least about 70 percent of the dimples on a golf ball include plan shapes according to the present invention. In yet another embodiment, at least about 90 percent of the dimples on a golf ball include the plan shapes of the present invention. Indeed, 100 percent of the dimples on a golf ball may include the plan shapes of the present invention.
While the present invention is not limited by any particular dimple pattern, dimples having plan shapes according to the present invention are arranged preferably along parting lines or equatorial lines, in proximity to the poles, or along the outlines of a geodesic or polyhedron pattern. Conventional dimples, or those dimples that do not include the plan shapes of the present invention, may occupy the remaining spaces. The reverse arrangement is also suitable.
In addition, the dimples in each hemisphere should be packed such that the golf ball does not have any dimple free great circles. As will be apparent to those of ordinary skill in the art, a golf ball having no “dimple free great circles” refers to a golf ball having an outer surface that does not contain a great circle which is free of dimples.
Suitable dimple patterns include, but are not limited to, polyhedron-based patterns (e.g., tetrahedron, icosahedron, octahedron, dodecahedron, icosidodecahedron, cuboctahedron, and triangular dipyramid), phyllotaxis-based patterns, spherical tiling patterns, and random arrangements. In one embodiment, the dimples are arranged according to a spherical tiling pattern. For example, the dimples of the present invention may be arranged according to spherical tiling patterns described in U.S. Pat. No. 8,029,388 and U.S. Publication No. 2013/0065708, the entire disclosures of which are incorporated by reference herein.
The dimple patterns of the present invention may be of any count. In one embodiment, the dimple count ranges from about 300 to about 400. In another embodiment, the dimple count is about 312. In still another embodiment, the dimple count is about 330, for example, about 332. In yet another embodiment, the dimple count is about 392. In addition, the dimple pattern may include any number of dimple sizes. In one embodiment, the number of dimple sizes range from about 1 to about 30. In another embodiment, the number of dimple sizes range from about 5 to about 20.
Dimple Patterns Having Cohesively Integrated Dimples
The present invention also contemplates dimple patterns composed of cohesively integrated dimples having the disclosed plan shapes. As discussed above, the dimples of the present invention have a curvilinear plan shape defined by at least three convex and/or concave arcs. The term, “cohesively integrated dimples,” refers to an arrangement of adjacent dimples having the disclosed plan shapes where at least one arc edge of the plan shape of a first dimple is adjacent to an arc edge of the plan shape of a second dimple and the two adjacent arc edges are unified. In other words, the two adjacent arc edges are substantially equal in radius, have opposite concavity, and maintain a pre-determined maximum integration distance. The cohesively integrated dimples of the present invention provide improved packing efficiency. For example, the unified edges of the dimple plan shapes according to the present invention provide integrated or opposing concavity, which allows for the dimples to be packed more closely together to reduce the width of the land portions adjacent to each dimple.
In one embodiment, the cohesively integrated dimples of the present invention include adjacent edges that are unified. In this aspect, to be considered “unified,” the adjacent edges have opposite concavity. That is, one of the adjacent arc edges curves inward while the opposing adjacent arc edge curve outwards. For example, if the dimple edge of the first dimple is a concave arc, the adjacent dimple edge of the second dimple should be a convex arc. Similarly, if the dimple edge of the first dimple is a convex arc, the adjacent dimple edge of the second dimple should be a concave arc. The concavity of the arcs may also be referred to as “concave-in” (which is intended to refer to concave arcs) and “concave-out” (which is intended to refer to convex arcs). In this aspect, the concavity of the dimple edge of the first dimple is different from the concavity of the adjacent dimple edge of the second dimple.
In another embodiment, to be considered “unified,” the two adjacent edges must have a pre-determined maximum integration distance (“MID”). The MID represents the maximum distance between the two adjacent edges (i.e., the dimple edge of the first dimple and the adjacent dimple edge of the second dimple). To determine the MID between the two adjacent edges, the center of the arc forming the concave edge is identified. For instance, in the pair of adjacent edges shown in
Upon determination of the location of the center of the arc forming the concave edge, three reference lines are drawn that are utilized in calculating the MID. In one embodiment, the first reference line is drawn from the center of the concave arc (as determined from above) to the center point on the concave edge. In this aspect, the first reference line should intersect the adjacent convex edge of the opposing dimple without intersecting any other dimple edges first. For instance, as shown in
The MID between the two adjacent edges (i.e., the dimple edge of the first dimple and the adjacent dimple edge of the second dimple) is determined from the reference lines. In one embodiment, if the adjacent convex edge of the opposing dimple only intersects the first reference line, the MID between the two adjacent edges is the distance between the center point on the concave edge and the point of intersection between the first reference line and the adjacent convex edge of the opposing dimple. While the adjacent convex edge 152 in
In another embodiment, if the adjacent convex edge of the opposing dimple intersects the first reference line in addition to the second reference line and/or the third reference line, the MID between the two adjacent edges is the largest of the following three distances:
In this aspect, to consider the two adjacent edges unified, the MID between the two adjacent edges (i.e., the concave dimple edge and the adjacent convex dimple edge) is less than or equal to about 0.020 inches. In another embodiment, the MID between the unified adjacent edges is less than or equal to about 0.010 inches. In still another embodiment, the MID between the unified adjacent edges is less than or equal to about 0.005 inches. In yet another embodiment, the MID between the unified adjacent edges is less than or equal to about 0.0025 inches. However, as will be apparent to one of ordinary skill in the art, the MID must be greater than zero. In another embodiment, the MID between the unified adjacent edges ranges from about 0.0025 inches to about 0.020 inches. For example, the MID between the unified adjacent edges ranges from about 0.005 inches to about 0.010 inches.
In another embodiment, the adjacent edges have substantially equal arc edge radii. The term, “arc edge radius,” refers to the radius of each of the arc edges of the disclosed curvilinear plan shapes. For example, each adjacent edge may have an arc edge radius that is greater than twice the inradius of the base polygon and less than five times the inradius of the base polygon. In another embodiment, each adjacent edge may have an arc edge radius that is greater than three times the inradius of the base polygon and less than five times the inradius of the base polygon.
As used herein, “substantially equal arc edge radii” means each radius measurement differs by less than 0.10 inches. In another embodiment, “substantially equal arc edge radii” means each radius measurement differs by less than about 0.08 inches. In still another embodiment, “substantially equal are edge radii” means each radius measurement differs by less than about 0.05 inches. In yet another embodiment, “substantially equal arc edge radii” means each radius measurement differs by less than about 0.01 inches. In another embodiment, the adjacent edges have identical radii.
In still another embodiment, each of the adjacent edges maintains a maximum absolute distance or sagitta. The maximum absolute distance (“dmax”), as defined above, represents the maximum distance between the circular arc and the base polygon. Each of the unified adjacent edges has a dmax of about 0.005 inches to about 0.030 inches. In another embodiment, each of the unified adjacent edges has a dmax of about 0.010 inches to about 0.025 inches. In yet another embodiment, each of the unified adjacent edges has a dmax of about 0.015 inches to about 0.020 inches.
In one embodiment, the unified adjacent edges have the same maximum absolute distance. In another embodiment, the unified adjacent edges have different maximum absolute distances. In this aspect, the difference between the maximum absolute distances of each of the two adjacent edges should be less than or equal to about 0.01 inches. In another embodiment, the difference between the maximum absolute distances of each of the two adjacent edges should be less than or equal to about 0.005 inches. In still another embodiment, the difference between the maximum absolute distances of each of the two adjacent edges should be less than or equal to about 0.0025 inches. In yet another embodiment, the difference between the maximum absolute distances of each of the two adjacent edges should be less than or equal to about 0.0015 inches.
Any of the disclosed dimple plan shapes may have unified adjacent edges as discussed above. That is, cohesively integrated dimples of the present invention may include any of the disclosed dimples having a curvilinear plan shape defined by at least three convex and/or concave arcs. For example, in one embodiment, the cohesively integrated dimples may include dimples having a curvilinear plan shape defined by three convex and/or concave arcs. In another embodiment, the cohesively integrated dimples may include dimples having a curvilinear plan shape defined by four convex and/or concave arcs. In still another embodiment, the cohesively integrated dimples may include dimples having a curvilinear plan shape defined by five convex and/or concave arcs. In yet another embodiment, the cohesively integrated dimples may include dimples having a curvilinear plan shape defined by six or more convex and/or concave arcs.
In another embodiment, the cohesively integrated dimples may include combinations of dimples having varying curvilinear plan shapes. For example, the cohesively integrated dimples may be arranged such that a dimple having a curvilinear plan shape defined by three concave arcs has an edge that is unified with an adjacent edge of a curvilinear plan shape defined by four convex arcs.
In one embodiment, each cohesively integrated dimple may include more than one edge that has unified arcs. For instance, a first cohesively integrated dimple may include a first edge that is unified with an adjacent edge of a second dimple and the first dimple may include a second edge that is unified with an adjacent edge of a third dimple. In one embodiment, the cohesively integrated dimple may include at least two edges that have unified arcs (for example, at least two unified edges). In another embodiment, the cohesively integrated dimple may include at least three edges that have unified arcs (for example, at least three unified edges). In still another embodiment, the cohesively integrated dimple may include at least four edges that have unified arcs (for example, at least four unified edges).
While at least a portion of the dimples on a golf ball are cohesively integrated, it is not necessary that every dimple on the golf ball be cohesively integrated. In one embodiment, less than about 10 percent of the dimples on a golf ball having the disclosed curvilinear plan shapes include at least one edge that has unified arcs (for example, unified edges). In another embodiment, more than about 10 percent of the dimples on a golf ball having the disclosed curvilinear plan shapes may include at least one edge that has unified arcs (for example, unified edges). For instance, at least about 25 percent of the dimples on a golf ball having the disclosed curvilinear plan shapes include at least one edge that has unified arcs (for example, unified edges). In another embodiment, at least about 50 percent of the dimples on a golf ball having the disclosed curvilinear plan shapes include at least one unified edge. In still another embodiment, at least about 75 percent of the dimples on a golf ball having the disclosed curvilinear plan shapes include at least one unified edge. In yet another embodiment, at least about 90 percent of the dimples on a golf ball having the disclosed curvilinear plan shapes include at least one unified edge. Indeed, 100 percent of the dimples on a golf ball having the disclosed curvilinear plan shapes may include at least one unified edge.
In this aspect, the present invention contemplates dimple patterns composed of dimples having the disclosed curvilinear plan shapes where at least about 10 percent of all edges defined by circular arcs are unified. In another embodiment, the present invention contemplates dimple patterns composed of dimples having the disclosed curvilinear plan shapes where at least about 25 percent of all edges defined by circular arcs are unified. In still another embodiment, the present invention contemplates dimple patterns composed of dimples having the disclosed curvilinear plan shapes where at least about 50 percent of all edges defined by circular arcs are unified. In yet another embodiment, the present invention contemplates dimple patterns composed of dimples having the disclosed curvilinear plan shapes where at least about 75 percent of all edges defined by circular arcs are unified. In another embodiment, the present invention contemplates dimple patterns composed of dimples having the disclosed curvilinear plan shapes where at least about 90 percent of all edges defined by circular arcs are unified.
Dimple Dimensions
The dimples on the golf balls of the present invention may comprise any width, depth, depth profile, edge angle, or edge radius and the patterns may comprise multitudes of dimples having different widths, depths, depth profiles, edge angles, or edge radii. Since the plan shape perimeters of the present invention are noncircular, the plan shapes are defined by an effective dimple diameter which is twice the average radial dimension of the set of points defining the plan shape from the plan shape centroid. For example, in one embodiment, dimples according to the present invention have an effective dimple diameter within a range of about 0.050 inches to about 0.300 inches. In another embodiment, the dimples have an effective dimple diameter of about 0.100 inches to about 0.250 inches. In still another embodiment, the dimples have an effective dimple diameter of about 0.110 inches to about 0.225 inches. In yet another embodiment, the dimples have an effective dimple diameter of about 0.125 inches to about 0.200 inches.
The dimples of the present invention also have an equivalent dimple diameter. As used herein, “equivalent dimple diameter” is defined as the equivalent circular spherical dimple diameter equal to the specific curvilinear dimple plan shape area. The equivalent dimple diameter may be calculated according to the following formula:
where de is the equivalent dimple diameter and A is the plan shape area of the curvilinear dimple. In one embodiment, the equivalent dimple diameter is at least about 0.08 inches, about 0.09 inches, about 0.010 inches, or about 0.110 inches. In another embodiment, the equivalent dimple diameter is about 0.22 inches or less, about 0.21 inches or less, about 0.20 inches or less, or about 0.19 inches or less. For example, when the dimples have square and triangular convex dimple plan shapes, the dimples may have equivalent dimple diameters ranging from about 0.080 inches to about 0.220 inches. In another embodiment, the dimples may have equivalent dimple diameters ranging from about 0.090 inches to about 0.210 inches. In still another embodiment, the dimples may have equivalent dimple diameters ranging from about 0.100 inches to about 0.200 inches. In yet another embodiment, the dimples may have equivalent dimple diameters ranging from about 0.110 inches to about 0.190 inches.
The surface depth for dimples of the present invention is within a range of about 0.003 inches to about 0.025 inches. In one embodiment, the surface depth is about 0.005 inches to about 0.020 inches. In another embodiment, the surface depth is about 0.006 inches to about 0.017 inches.
The dimples of the present invention have a plan shape perimeter ratio. The plan shape perimeter ratio is defined as the ratio of the plan shape perimeter to that of the regular n-sided polygon perimeter. The perimeter is defined as the distance around a two-dimensional shape, and thus, the length of the boundary line defining the plan shape. In one embodiment, dimples of the present invention have a plan shape perimeter ratio of less than 1.10. In another embodiment, the dimples of the present invention have a plan shape perimeter ratio of less than 1.07. In still another embodiment, the dimples of the present invention have a plan shape perimeter ratio of less than 1.05.
For example, when the dimples have triangular convex dimple plan shapes, the dimples may have a plan shape perimeter ratio of less than 1.10, less than 1.05, or less than 1.01. Similarly, when the dimples have square convex dimple plan shapes, the dimples may have a plan shape perimeter ratio of less than 1.10, less than 1.05, or less than 1.01.
The dimples of the present invention also have a plan shape area. By the term, “plan shape area,” it is meant the area based on a planar view of the dimple plan shape, such that the viewing plane is normal to an axis connecting the center of the golf ball to the point of the calculated surface depth. In one embodiment, dimples of the present invention have a plan shape area ranging from about 0.0025 in2 to about 0.045 in2. In another embodiment, dimples of the present invention have a plan shape area ranging from about 0.005 in2 to about 0.035 in2. In still another embodiment, dimples of the present invention have a plan shape area ranging from about 0.010 in2 to about 0.030 in2.
The dimples of the present invention are further defined to have a plan shape area ratio. The plan shape area ratio is defined as the ratio of the plan shape area to that of the regular n-sided polygon area. In one embodiment, dimples of the present invention have a plan shape area ratio ranging from about 0.35 to about 1.75. In another embodiment, the plan shape area ratio ranges from about 0.40 to about 1.65. In still another embodiment, the plan shape perimeter ratio ranges from about 0.45 to about 1.55.
For example, when the dimples have triangular convex dimple plan shapes, the dimples may have a plan shape area ratio of greater than 1.0. In one embodiment, when the dimples have triangular convex dimple plan shapes, the dimples may have a plan shape area ratio of equal to or less than 1.75. In another embodiment, the dimples having triangular convex dimple plan shapes may have a plan shape area ratio of equal to or less than 1.65. In still another embodiment, the dimples having triangular convex dimple plan shapes may have a plan shape area ratio of equal to or less than 1.55. In one embodiment, the plan shape area ratio is between 1.0 and 1.75, 1.0 and 1.65, or 1.0 and 1.55.
Similarly, when the dimples have square convex dimple plan shapes, the dimples may have a plan shape area ratio of greater than 1.0. In one embodiment, the dimples having square convex dimple plan shapes have a plan shape area ratio of 1.75 or less, 1.65 or less, or 1.55 or less. For example, the dimples having square convex dimple plan shapes may have a plan shape area ratio of more than 1.0, but no more than 1.75.
Further, dimples of the present invention have a dimple surface volume. By the term, “dimple surface volume,” it is meant the total volume encompassed by the dimple shape and the surface of the golf ball.
In another embodiment, dimples produced in accordance with the present invention have a plan shape area and dimple surface volume falling within the ranges shown in
In still another embodiment, when the dimples have square or triangular convex dimple plan shapes, the dimples may have a plan shape area and dimple surface volume falling within the ranges show in
Vs=−0.0464A2+0.0135A−1.00×10−5
and greater than the lower limit calculated by
Vs=0.0703A2+0.0016A−3.00×10−6,
where A is the dimple plan shape area. In one embodiment, the dimple plan shape area (A) may range from 0.0025 in2 to 0.045 in2. In another embodiment, the dimple plan shape area (A) may range from 0.0050 in2 to 0.035 in2. In yet another embodiment, the dimple plan shape area (A) may range from 0.0050 in2 to 0.030 in2. In still another embodiment, the dimple plan shape area (A) may range from 0.0075 in2 to 0.020 in2. In yet another embodiment, the dimple plan shape area (A) may range from 0.010 in2 to 0.015 in2. In still another embodiment, the dimple plan shape area (A) may range from 0.010 in2 to 0.030 in2.
Based on the above equations and the contemplated dimple plan shape areas, the surface volumes of dimples having square or triangular convex dimple plan shapes may range from about 0.014×10−4 in3 to about 5.035×10−4 in3. In another embodiment, the surface volumes may range from about 0.50×10−4 in3 to about 4.50×10−4 in3. For example, the surface volume may range from about 0.50×10−4 in3 to about 3.0×10−4 in3 or about 0.50×10−4 in3 to about 2.0×10−4 in3. In still another embodiment, the surface volumes may range from about 1.5×10−4 in3 to about 4.0×10−4 in3. In yet another embodiment, the surface volumes may range from about 2.0×10−4 in3 to about 3.5×10−4 in3.
Dimple Profile
In addition to varying the size of the dimples, the cross-sectional profile of the dimples may be varied. The cross-sectional profile of the dimples according to the present invention may be based on any known dimple profile shape. In one embodiment, the profile of the dimples corresponds to a curve. For example, the dimples of the present invention may be defined by the revolution of a catenary curve about an axis, such as that disclosed in U.S. Pat. Nos. 6,796,912 and 6,729,976, the entire disclosures of which are incorporated by reference herein. In another embodiment, the dimple profiles correspond to polynomial curves, ellipses, spherical curves, saucer-shapes, truncated cones, trigonometric, exponential, frequency, or logarithmic curves and flattened trapezoids. In still another embodiment, the dimples of the present invention may have dimple profiles that are conical. In yet another embodiment, the dimple profiles may be created from a set of mathematical functions including polynomial, exponential, and trigonometric functions or combinations thereof.
The profile of the dimple may also aid in the design of the aerodynamics of the golf ball. For example, shallow dimple depths, such as those in U.S. Pat. No. 5,566,943, the entire disclosure of which is incorporated by reference herein, may be used to obtain a golf ball with high lift and low drag coefficients. Conversely, a relatively deep dimple depth may aid in obtaining a golf ball with low lift and low drag coefficients.
The dimple profile may also be defined by combining a spherical curve and a different curve, such as a cosine curve, a frequency curve or a catenary curve, as disclosed in U.S. Patent Publication No. 2012/0165130, which is incorporated in its entirety by reference herein. In another embodiment, the dimple profile can result from the superposition of three or more different curves. In still another embodiment, one or more of the superposed curves can be a functionally weighted curve, as disclosed in U.S. Patent Publication No. 2013/0172123, which is incorporated in its entirety by reference herein.
Golf Ball Construction
The dimples of the present invention may be used with practically any type of ball construction. For instance, the golf ball may have a two-piece design, a double cover, or two-component dual core construction depending on the type of performance desired of the ball. Other suitable golf ball constructions include solid, wound, liquid-filled, and/or dual cores, and multiple intermediate layers.
Different materials may be used in the construction of the golf balls made with the present invention. For example, the cover of the ball may be made of a thermoset or thermoplastic, a castable or non-castable polyurethane and polyurea, an ionomer resin, balata, or any other suitable cover material known to those skilled in the art. Conventional and non-conventional materials may be used for forming core and intermediate layers of the ball including polybutadiene and other rubber-based core formulations, ionomer resins, highly neutralized polymers, and the like.
The following non-limiting examples demonstrate golf ball dimple plan shapes made in accordance with the present invention. The examples are merely illustrative of the preferred embodiments of the present invention, and are not to be construed as limiting the invention, the scope of which is defined by the appended claims.
Examples 1-5 demonstrate various curvilinear dimple plan shapes defined by circular arcs that are derived from regular n-sided polygons. As demonstrated by the following examples, the present invention provides for a number of different visually distinct dimple plan shapes and surface textures.
The following example illustrates a golf ball dimple plan shape produced in accordance with the present invention. In particular,
The following example illustrates a golf ball dimple plan shape produced in accordance with the present invention. In particular,
The following example illustrates a golf ball dimple plan shape produced in accordance with the present invention. In particular,
The following example illustrates a golf ball dimple plan shape produced in accordance with the present invention. In particular,
The following example illustrates a golf ball dimple plan shape produced in accordance with the present invention. In particular,
The following example illustrates a golf ball dimple pattern contemplated by the present invention. More particularly, the following example illustrates a dimple base pattern utilizing square and triangular convex plan shapes of varying sizes.
Referring to
The dimples having plan shapes created from four circular arcs or the square convex plan shapes are represented by letter ID: F. Dimples F have a plan shape perimeter ratio of 1.0170 and a plan shape area ratio of 1.2144 with an equivalent dimple diameter of about 0.210 inches. In addition, dimples F have a maximum absolute distance, or sagitta, of about 0.013 inches.
Although any dimple profile or profiles can be used, as discussed above, the ideal dimple volumes should remain within the preferred range defined in
The following example illustrates another golf ball dimple pattern contemplated by the present invention. In particular, the following example illustrates a dimple base pattern utilizing square convex plan shapes.
Referring to
Although any dimple profile or profiles can be used, as discussed above, the ideal dimple volumes should remain within the preferred range defined in
The following example illustrates a dimple pattern of the present invention having cohesively integrated dimples.
When determining the maximum integration distance (MID) in this example, the center of the arc forming the concave edge is identified. In
As can be seen in
The following example illustrates an arrangement of cohesively integrated dimples according to the present invention.
When determining the maximum integration distance (MID) in this example, the center of the are forming the concave edge is identified. In
As can be seen in
The following example illustrates a dimple pattern of the present invention having cohesively integrated dimples.
Notwithstanding that the numerical ranges and parameters setting forth the broad scope of the invention are approximations, the numerical values set forth in the specific examples are reported as precisely as possible. Any numerical value, however, inherently contain certain errors necessarily resulting from the standard deviation found in their respective testing measurements. Furthermore, when numerical ranges of varying scope are set forth herein, it is contemplated that any combination of these values inclusive of the recited values may be used.
The invention described and claimed herein is not to be limited in scope by the specific embodiments herein disclosed, since these embodiments are intended as illustrations of several aspects of the invention. Any equivalent embodiments are intended to be within the scope of this invention. Indeed, various modifications of the invention in addition to those shown and described herein will become apparent to those skilled in the art from the foregoing description. Such modifications are also intended to fall within the scope of the appended claims. All patents and patent applications cited in the foregoing text are expressly incorporated herein by reference in their entirety.
| Number | Name | Date | Kind |
|---|---|---|---|
| 20030158002 | Morgan | Aug 2003 | A1 |
| 20050239579 | Sato | Oct 2005 | A1 |
| 20060089211 | Sato | Apr 2006 | A1 |
| 20080004136 | Kasashima | Jan 2008 | A1 |
| Number | Date | Country | |
|---|---|---|---|
| 20180272193 A1 | Sep 2018 | US |
| Number | Date | Country | |
|---|---|---|---|
| Parent | 15726615 | Oct 2017 | US |
| Child | 15849932 | US | |
| Parent | 14941916 | Nov 2015 | US |
| Child | 15726615 | US |
