Patent Application
20170319908
The present invention relates to golf balls with symmetric flight performance due to volumetric equivalence in the dimples on opposing hemispheres on the ball. In particular, golf balls according to the present invention achieve flight symmetry and overall satisfactory flight performance due to a dimple surface volume ratio that is equivalent between opposing hemispheres despite the use of different dimple geometry, different dimple arrangements, and/or different dimple counts on the opposing hemispheres.
Golf balls were originally made with smooth outer surfaces. However, in the late nineteenth century, players observed that gutta-percha golf balls traveled further as they aged and their surfaces were roughened. As a result, players began roughening the surfaces of new golf balls to increase flight distance; and manufacturers began molding non-smooth outer surfaces on golf balls.
By the mid 1900's almost every manufactured golf ball had 336 dimples arranged in an octahedral pattern. Generally, these balls had about 60 percent of their outer surface covered by dimples. Over time, improvements in ball performance were developed by utilizing different dimple patterns. In 1983, for instance, Titleist introduced the TITLEIST 384, which, not surprisingly, had 384 dimples that were arranged in an icosahedral pattern. With about 76 percent of its outer surface covered with dimples, the TITLEIST 384 exhibited improved aerodynamic performance. Today, dimpled golf balls travel nearly two times farther than similar balls without dimples.
The dimples on a golf ball play an important role in reducing drag and increasing lift. More specifically, the dimples on a golf ball create a turbulent boundary layer around the ball, i.e., a thin layer of air adjacent to the ball that flows in a turbulent manner. The turbulent nature of the boundary layer of air around the ball energizes the boundary layer, and helps the air flow stay attached farther around the ball. The prolonged attachment of the air flow around the surface of the ball reduces the area of the wake behind the ball, effectively yielding an increase in pressure behind the ball, thereby substantially reducing drag and increasing lift on the ball during flight.
As such, manufacturers continually experiment with different dimple shapes and patterns in an effort to improve the aerodynamic forces exerted on golf balls, with the goal of increasing travel distances of the balls. However, the United States Golf Association (USGA) requires that a ball must not be designed, manufactured, or intentionally modified to have properties that differ from those of a spherically symmetric ball. In other words, manufacturers who desire to better aerodynamic performance of a golf ball are also required to conform with the overall distance and symmetry requirements of the USGA. In particular, a golf ball is considered to achieve flight symmetry when it is found, under calibrated testing conditions, to fly at substantially the same height and distance, and remain in flight for substantially the same period of time, regardless of how it is placed on the tee. The testing conditions for assessing flight symmetry of a golf ball are provided in USGA-TPX3006, Revision 2.0.0, “Actual Launch Conditions Overall Distance and Symmetry Test Procedure (Phase II)”. Accordingly, conventional golf balls typically remain hemispherically identical with regard to the dimples thereon in order to maintain the required flight symmetry and performance.
As such, there has been little to no focus on the use of differing dimple geometry, dimple arrangements, and/or dimple counts on the opposing hemispheres of a golf ball-likely due to the previous inability to achieve volumetric equivalence between the opposing hemispheres and, thus, flight symmetry. Accordingly, there remains a need in the art for a golf ball that has opposing hemispheres that differ from one another in that the dimple shapes, dimple profiles, dimple arrangements, and/or dimple counts are not identical on both hemispheres, while still achieving flight symmetry and overall satisfactory flight performance.
The present invention relates to a golf ball including: a first hemisphere comprising a plurality of dimples; and a second hemisphere comprising a plurality of dimples, wherein a first dimple in the first hemisphere comprises a first plan shape, a first profile, and a first geometric center, the first geometric center being located at a position defined by a first polar angle θN measured from a pole of the first hemisphere; a second dimple in the second hemisphere comprises a second plan shape, a second profile shape, and a second geometric center, the second geometric center being located at a position defined by a second polar angle θS measured from a pole of the second hemisphere, wherein the first polar angle θN differs from the second polar angle θS by no more than 3°, the first dimple differs from the second dimple by at least one of (i) the first plan shape differing from the second plan shape and (ii) the first profile differing from the second profile; and the first dimple and the second dimple have substantially identical surface volumes.
In one embodiment, the first plan shape differs from the second plan shape. In another embodiment, the first profile shape differs from the second profile shape. In still another embodiment, the first plan shape includes a first shape of a first size, the second plan shape includes a second shape of a second size, and the first size is different from the second size.
In this aspect of the invention, the first profile may differ from the second profile. In one embodiment, the geometric center of the first dimple is separated from the geometric center of the second dimple by an offset angle γ. In another embodiment, a third dimple in the first hemisphere includes a third plan shape, a third profile, and a third geometric center, the third geometric center being located at a position defined by a third polar angle θN′ measured from the pole of the first hemisphere. In yet another embodiment, a fourth dimple in the second hemisphere includes a fourth plan shape, a fourth profile, and a fourth geometric center, the fourth geometric center being located at a position defined by a fourth polar angle θS′ measured from the pole of the second hemisphere. The third polar angle θN′ may differ from the fourth polar angle θS′ by no more than 3°. In another embodiment, the third dimple differs from the fourth dimple by at least one of: (i) the third plan shape differing from the fourth plan shape; (ii) the third profile differing from the fourth profile shape; and the third dimple and the fourth dimple have substantially identical surface volumes.
The geometric center of the first dimple may be separated from the geometric center of the second dimple by an offset angle γ, the geometric center of the third dimple is separated from the geometric center of the fourth dimple by an offset angle γ, and the offset angle γ between the geometric centers of the first and second dimples differs from the offset angle γ between the geometric centers of the third and fourth dimples by no more than 3.
In one embodiment, the first plan shape includes a first shape at a first size, the second plan shape includes a second shape at a second size, the third plan shape includes a third shape at a third size, the fourth plan shape includes a fourth shape at a fourth size, the first shape is the same as the third shape, and the second shape is the same as the fourth shape. In another embodiment, the first shape is different from the second shape.
The present invention also relates to a golf ball including first and second hemispheres each including a plurality of dimples, wherein each dimple in the first hemisphere has a respective geometric center located at a position defined by a respective polar angle θN measured from a pole of the first hemisphere, wherein each dimple in the second hemisphere has a respective geometric center located at a position defined by a respective polar angle θS measured from a pole of the second hemisphere, wherein each dimple in the first hemisphere corresponds with a dimple in the second hemisphere, with the dimples in each pair of corresponding dimples satisfying a relationship whereby the polar angle θN of the dimple in the first hemisphere is substantially equal to the polar angle θS of the dimple in the second hemisphere, and wherein (i) in each pair of corresponding dimples, the geometric center of the dimple in the first hemisphere is separated from the geometric center of the dimple in the second hemisphere by an offset angle γ, with the offset angle γ being the same in all pairs of corresponding dimples, (ii) in each pair of corresponding dimples, the dimple in the first hemisphere differs from the dimple in the second hemisphere by at least one of (i) a difference in plan shape and (ii) a difference in profile, and (iii) the first hemisphere and the second hemisphere have substantially equivalent surface volumes.
In one embodiment, in each pair of corresponding dimples, the dimple in the first hemisphere differs from the dimple in the second hemisphere in that the two dimples have different plan shapes. In another embodiment, in each pair of corresponding dimples, the dimple in the first hemisphere differs from the dimple in the second hemisphere in that the two dimples have different profiles.
The present invention also relates to a golf ball including a first hemisphere including a first plurality of dimples and a second hemisphere including a second plurality of dimples, wherein each dimple in the first plurality of dimples has a corresponding dimple in the second plurality of dimples, wherein a dimple in the first hemisphere differs from a corresponding dimple in the second hemisphere by at least one of (i) a difference in plan shapes and (ii) a difference in profile shapes.
In one embodiment, the dimple in the first hemisphere differs from the corresponding dimple in the second hemisphere in that the two dimples have different plan shapes. In another embodiment, the dimple in the first hemisphere has a first shape at a first size; the corresponding dimple in the second hemisphere has a second shape at a second size, wherein the first size is different than the second size. In yet another embodiment, the dimple in the first hemisphere has a first shape at a first size, the corresponding dimple in the second hemisphere has a second shape at a second size, the shape of the dimple in the first hemisphere is the same shape as the shape of the dimple in the second hemisphere, and the first size differs from the second size. In this aspect of the invention, the dimple in the first hemisphere may differ from the corresponding dimple in the second hemisphere in that the two dimples have different profiles. In addition, the dimple in the first hemisphere may differ from the corresponding dimple in the second hemisphere in that the two dimples have different profiles and different plan shapes.
The present invention is also directed to a golf ball including a first hemisphere including a first plurality of dimples; and a second hemisphere including a second plurality of dimples, wherein each hemisphere is rotational symmetric about a polar axis, the first hemisphere has a first number of axes of symmetry about the polar axis, the second hemisphere has a second number of axes of symmetry about the polar axis, the first number of axes of symmetry is different from the second number of axes of symmetry, and the first plurality of dimples and the second plurality of dimples have substantially equivalent surface volumes. In this aspect, the first and second number of axes of symmetry may range from two to seven. In another embodiment, the first number of axes of symmetry is five or greater and the second number of axes of symmetry is four or less.
In still another embodiment, the first hemisphere may further include a third plurality of dimples adjacent to an equatorial axis of the golf ball; the second hemisphere further include a fourth plurality of dimples adjacent to the equatorial axis of the golf ball; each of the third plurality of dimples has a rotational angle φN and a polar angle θN; each of the fourth plurality of dimples has a rotational angle φS and a polar angle θS; wherein the difference in rotational angle φN or polar angle θN of each of the third plurality of dimples and the rotational angle φS or polar angle θS of each of the fourth plurality of dimples is at most 3°. In yet another embodiment, at least a portion of the first plurality of dimples has a different plan shape than a portion of the second plurality of dimples or at least a portion of the first plurality of dimples has a different profile shape than a portion of the second plurality of dimples. Furthermore, the golf ball includes a spherical outer surface, wherein the outer surface of the golf ball does not contain a great circle which is free of dimples.
The present invention is further directed to a golf ball, including a first hemisphere including a first plurality of dimples having a first average dimple surface volume; and a second hemisphere including a second plurality of dimples having a second average dimple surface volume, wherein the first hemisphere has a first number of axes of symmetry about the pole of the first hemisphere, the second hemisphere has a second number of axes of symmetry about the pole of the second hemisphere, the first number of axes of symmetry is the same as the second number of axes of symmetry, a portion of the first plurality of dimples has a rotational angle φN and a polar angle θN, a portion of the second plurality of dimples has a rotational angle φS and a polar angle θS, each respective rotational angle φN or polar angle θN differs from each respective rotational angle φS or polar angle θS by at least 30, for example, by at least 50, and the absolute difference between the first average dimple surface volume and the second average dimple surface volume is less than 3.5×10−6. In this aspect, the first and second number of axes of symmetry may range from two to seven, for example, from three to six. In another embodiment, the golf ball includes a spherical outer surface, wherein the outer surface of the golf ball does not contain a great circle which is free of dimples. In still another embodiment, at least a portion of the first plurality of dimples differ from a portion of the second plurality of dimples in plan shape, profile shape, or both. In yet another embodiment, the portion of the first plurality of dimples is at least 25 percent of the first plurality of dimples and the portion of the second plurality of dimples is at least 25 percent of the second plurality of dimples.
Moreover, the present invention is directed to a golf ball having a spherical outer surface, including a first hemisphere including a first number of dimples having a first average dimple surface volume; a second hemisphere including a second number of dimples having a second average dimple surface volume; wherein the first number of dimples differs from the second number of dimples by at least two; the absolute difference between the first average dimple surface volume and the second average dimple surface volume is less than 3.5×10−6; and the outer surface of the golf ball does not contain a great circle which is free of dimples. In this aspect, the first hemisphere has a first number of axes of symmetry about a polar axis; the second hemisphere has a second number of axes of symmetry about the polar axis; and the first number of axes of symmetry may be different from the second number of axes of symmetry. In another embodiment, the difference in the first number of dimples and the second number of dimples is greater than two and less than 100. In yet another embodiment, the difference in the first number of dimples and the second number of dimples is from 5 to 90. In still another embodiment, the absolute difference between the first average dimple surface volume and the second average dimple surface volume is less than 2.5×10−6. In another embodiment, at least a portion of the first number of dimples differ from a portion of the second number of dimples in plan shape, profile shape, or both.
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 provides golf balls with opposing hemispheres that differ from one another, e.g., by having different dimple plan shapes or profiles, different dimple arrangements, and/or different dimple counts, while also achieving flight symmetry and overall satisfactory flight performance. In this aspect, the present invention provides golf balls that permit a multitude of unique appearances, while also conforming to the USGA's requirements for overall distance and flight symmetry. The present invention is also directed to methods of developing the dimple geometries and arrangements applied to the opposing hemispheres, as well as methods of making the finished golf balls with the inventive dimple patterns applied thereto.
In particular, finished golf balls according to the present invention have opposing hemispheres with dimple geometries that differ from one another in that the dimples on one hemisphere have different plan shapes (the shape of the dimple in a plan view), different profile shapes (the shape of the dimple cross-section, as seen in a profile view of a plane extending transverse to the center of the golf ball and through the geometric center of the dimple), or a combination thereof, as compared to dimples on an opposing hemisphere. In another embodiment, the finished golf balls according to the present invention may have opposing hemispheres with dimple arrangements that differ from one another. In still another embodiment, the finished golf balls according to the present invention may have opposing hemispheres with differing dimple counts. Despite the difference in dimple geometry, dimple arrangement, and/or dimple count, the dimples on one hemisphere have dimple surface volumes that are substantially similar to the dimple surface volumes on an opposing hemisphere.
As discussed above, the opposing hemispheres of the golf balls contemplated by the present invention may have the same dimple arrangement or differing dimple arrangements. In one embodiment, when the dimple geometry on the opposing hemispheres are designed to differ in that the plan shape and/or profile shape of the dimples in one hemisphere are different from the plan shape and/or profile shape of the dimples in another hemisphere, the hemispheres may have the same dimple arrangement or pattern. In other words, the dimples in one hemisphere are positioned such that the locations of their geometric centers are substantially identical to the locations of the geometric centers of the dimples in the other hemisphere in terms of polar angles θ (measuring the rotational offset of an individual dimple from the polar axis of its respective hemisphere) and offset angles γ (measuring the rotational offset between two corresponding dimples, as rotated around the equator of the golf ball).
A non-limiting example of suitable dimple geometries for use on a golf ball according to the present invention is shown in
For example, as shown in
As shown in
As discussed below, at least one of the corresponding dimple pairs from the plurality of corresponding dimples on each hemisphere differ in plan shape, profile, or a combination thereof. In other words, as shown in
In another embodiment, the opposing hemispheres may have differing dimple arrangements or patterns. In this aspect, the dimples in one hemisphere are positioned such that the locations of their geometric centers are substantially different from the locations of the geometric centers of the dimples in the other hemisphere. This may be achieved by designing the opposing hemispheres such that each hemisphere is rotational symmetric about the polar axis and each hemisphere has different symmetry about the polar axis. By designing the hemispheres such that opposing hemispheres have different levels of symmetry about the polar axis, there are minimal, if any, corresponding/matching dimple pairs (i.e., the locations of the dimples in each hemisphere are substantially different).
More specifically, the locations of the geometric centers of dimples in one hemisphere are considered to be substantially different from the locations of the geometric centers of dimples in the other hemisphere when each hemisphere has a different order of rotational symmetry. In one embodiment, the order of symmetry may be described in terms of symmetry about the polar axis (i.e., how many times the base pattern is rotated about the polar axis). In this aspect, the number of axes of symmetry may range from two to seven. In another embodiment, the number of axes of symmetry may range from two to six. In still another embodiment, the number of axes of symmetry may range from three to six. For example, one hemisphere may include six axes of symmetry (i.e., the base pattern was rotated six times about the polar axis) and the other hemisphere may include four axes of symmetry (i.e., the base pattern was rotated four times about the polar axis). When a first hemisphere has a different number of axes of symmetry about the polar axis than the opposing hemisphere, the location of the dimples on the first hemisphere are considered to be substantially different than the location of the dimples on the opposing hemisphere.
Similarly, the order of symmetry may be described in terms of the dimple patterns utilized in each hemisphere. That is, the dimples in each hemisphere may be based on different dimple patterns. In this aspect, the dimples in each hemisphere may be based on polyhedron-based patterns (e.g., icosahedron, tetrahedron, octahedron, dodecahedron, icosidodecahedron, cuboctahedron, and triangular dipyramid, hexagonal dipyramid), phyllotaxis-based patterns, spherical tiling patterns, and random arrangements. For instance, the dimples in one hemisphere may be arranged based on a tetrahedron pattern and the dimples in the opposing hemisphere may be arranged based on an octahedron pattern. When the arrangement of dimples in a first hemisphere is based on a different dimple pattern than the arrangement of dimples in the opposing hemisphere, the locations of the dimples in the first hemisphere are considered to be substantially different than the locations of the dimples in the opposing hemisphere.
When each of the opposing hemispheres have the same order of symmetry as defined above, the locations of the geometric centers of dimples in one hemisphere may nonetheless still be considered substantially different from the locations of the geometric centers of dimples in the other hemisphere. In this aspect, when each of the opposing hemispheres have the same order of symmetry/dimple pattern, the location of a dimple in a base pattern of a first hemisphere may be considered substantially different from the location of a dimple in the base pattern of the second hemisphere if the difference in polar angles (θN, θS) or rotational angles (φN, φS) of the two dimples is greater than 3°. The polar angles (θN, θS) of the two dimples may be determined using the method described above. The rotational angle (φ) is defined as the angle between the dimple center and the edge of the base pattern. As shown in
In another embodiment, when each of the opposing hemispheres have the same order of symmetry/dimple pattern, the location of a dimple in a base pattern of a first hemisphere may be considered substantially different from the location of a dimple in the base pattern of the second hemisphere if the difference in polar angles (θN, θS) or rotational angles (φN, φS) of the two dimples is greater than 5°. In still another embodiment, the location of a dimple in a base pattern of a first hemisphere may be considered substantially different from the location of a dimple in the base pattern of the second hemisphere if the difference in polar angles (θN, θS) or rotational angles (φN, φS) of the two dimples is greater than 70. In yet another embodiment, the location of a dimple in a base pattern of a first hemisphere may be considered substantially different from the location of a dimple in the base pattern of the second hemisphere if the difference in polar angles (θN, θS) or rotational angles (φN, φS) of the two dimples is greater than 12°.
In this aspect of the invention, when the opposing hemispheres have differing dimple arrangements, at least a plurality of dimples in each hemisphere should have differing locations. In other words, some dimples in each hemisphere may have differing locations, whereas others may not. For instance, in one embodiment, the dimples in the first hemisphere that are directly adjacent to the equator may have the same dimple locations as the dimples in the second hemisphere that are directly adjacent to the equator. That is, the difference in polar angle (θN) or rotational angle (φN) of the dimples in the first hemisphere that are directly adjacent to the equator and polar angle (θS) or rotational angle (φS) of the dimples in the second hemisphere that are directly adjacent to the equator is at most 3°. Alternatively, the dimples in the first hemisphere that are directly adjacent to the equator may have different locations from the dimples in the second hemisphere that are directly adjacent to the equator. In this aspect, the difference in polar angle (θN) or rotational angle (φN) of the dimples in the first hemisphere that are directly adjacent to the equator and polar angle (θS) or rotational angle (φS) of the dimples in the second hemisphere that are directly adjacent to the equator is greater than 3°.
In one embodiment, the locations of the dimples on the first hemisphere are substantially different from the locations of the dimples on the second hemisphere for at least about 10 percent of the dimples on the golf ball. In another embodiment, the locations of the dimples on the first hemisphere are substantially different from the locations of the dimples on the second hemisphere for at least about 25 percent of the dimples on the golf ball. In still another embodiment, the locations of the dimples on the first hemisphere are substantially different from the locations of the dimples on the second hemisphere for at least about 50 percent of the dimples on the golf ball. In yet another embodiment, the locations of the dimples on the first hemisphere are substantially different from the locations of the dimples on the second hemisphere for at least about 75 percent of the dimples on the golf ball. In another embodiment, the locations of the dimples on the first hemisphere are substantially different from the locations of the dimples on the second hemisphere for at least about 90 percent of the dimples on the golf ball.
As explained above, the opposing hemispheres of the golf balls may have different dimple patterns/layouts. In this aspect, each hemispherical dimple pattern/layout includes a base pattern. The base pattern is an arrangement of dimples that is rotated about the polar axis and which forms the overall dimple pattern. For instance, as explained above, if a first hemisphere includes six axes of symmetry, the base pattern is rotated six times about the polar axis such that the overall dimple pattern of the first hemisphere includes six base patterns. If a second hemisphere has three axes of symmetry, the base pattern is rotated three times about the polar axis such that the overall dimple pattern of the second hemisphere includes three base patterns.
The specific arrangement or packing of the dimples within the base patterns utilized in each hemisphere may vary so long as (i) a plurality of dimples in one hemisphere are positioned such that the locations of their geometric centers are substantially different from the locations of the geometric centers of a plurality of dimples in the other hemisphere, and (ii) the shape and dimensions of the dimples within each base pattern are chosen such that an appropriate degree of volumetric equivalence is maintained between the two hemispheres. As long as the above two conditions are met, each base pattern may include dimples of varying designs and dimensions. For example, each base pattern may be composed of dimples having varying plan shapes, profile shapes, dimple diameters, dimple edge angles, and dimple surface volumes. While each base pattern may be packed with various dimple types and sizes, at least one different dimple diameter should be utilized within each base pattern. In another embodiment, at least two different dimple diameters should be utilized within each base pattern. In still another embodiment, at least three different dimple diameters should be utilized within each base pattern. 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. In other words, the dimples are arranged such that the golf ball does not have any great circles. In this aspect, the golf balls contemplated by the present invention may have a staggered wave parting line.
The opposing hemispheres of the golf balls contemplated by the present invention may have the same dimple count or differing dimple counts. As used herein, the “dimple count” of a golf ball refers to how many dimples are present on the golf ball. The present invention contemplates golf balls having a dimple count of 250 to 400, and preferably 300 to 400. In this aspect, each hemisphere of the golf ball may have 75 to 250 dimples. In another embodiment, each hemisphere of the golf ball may have 125 to 200 dimples.
In one embodiment, each opposing hemisphere has the same dimple count. This means that each hemisphere includes the same number of dimples. In this aspect, the number of dimples in each hemisphere may vary so long as the number is the same for each of the opposing hemispheres and the total number of dimples is greater than 250 and less than 400. For instance, the first and second hemispheres may each have 168 dimples. Alternatively, the first and second hemispheres may each have 125 dimples.
In another embodiment, the opposing hemispheres may have differing dimple counts. In other words, one hemisphere may have a greater number of dimples than the opposing hemisphere. In this aspect, when the opposing hemispheres have differing dimple counts, the difference in the number of dimples on the opposing hemispheres is greater than one. In another embodiment, when the opposing hemispheres have differing dimple counts, the difference in the number of dimples on the opposing hemispheres is greater than one and less than 100. In still another embodiment, the difference in the number of dimples on the opposing hemispheres may range from 5 to 90. In yet another embodiment, the difference in the number of dimples on the opposing hemispheres may range from 10 to 75. In another embodiment, the difference in the number of dimples on the opposing hemispheres may range from 15 to 60. For instance, with a first and second hemisphere each having 6-way symmetry about the polar axis, the first hemisphere may have 169 dimples and the second hemisphere may have 163 dimples. In other words, the first hemisphere includes an additional dimple in each of the six base patterns, which means that the difference in the number of dimples on the opposing hemispheres is 6.
Regardless of whether each hemisphere has the same dimple count or differing dimple counts, the underlying dimple pattern in each hemisphere may be the same or different. For example, a golf ball may have opposing hemispheres having the same dimple count but differing dimple patterns. Similarly, a golf ball may have opposing hemispheres having different dimple counts but having the same underlying dimple pattern.
One way to achieve differing dimple geometries with the same or different dimple arrangement on opposing hemispheres in accordance with the present invention is to include corresponding dimples that differ in plan shape. Thus, in one aspect of the present invention, the dimples in two hemispheres are considered different from one another if, in a given pair of corresponding dimples, a dimple in one hemisphere has a different plan shape than the plan shape of the corresponding dimple in the other hemisphere. In another aspect of the present invention, the dimples in two hemispheres are considered different from one another if, in a given pair of corresponding dimples, a dimple in one hemisphere has a different plan shape orientation than the plan shape orientation of the corresponding dimple in the other hemisphere. However, in still another aspect of the present invention, the dimple plan shapes or plan shape orientations in opposing hemispheres may not be different. That is, when the opposing hemispheres have different dimple arrangements and/or dimple counts, the dimples on the first and second hemispheres may not have different plan shapes or plan shapes orientations.
When differing plan shapes or plan shape orientations are utilized, at least about 25 percent of the corresponding dimples in the opposing hemispheres may have different plan shapes. In another embodiment, at least about 50 percent of the corresponding dimples in the opposing hemispheres have different plan shapes. In yet another embodiment, at least about 75 percent of the corresponding dimples in the opposing hemispheres have different plan shapes. In still another embodiment, all of the corresponding dimples in the opposing hemispheres have different plan shapes.
The plan shapes (or plan shape orientations) of two dimples are considered different from one another if a comparison of the overlaid dimples yields a mean absolute residual
In order to make the overlaying comparison, dimples in a pair of corresponding dimples must be aligned with one another. For example, the dimple in the southern hemisphere is transformed γ degrees about the polar axis such that the centroid of the southern hemisphere dimple lies in a common plane (P) as the centroid of the northern hemisphere dimple and the golf ball centroid. The southern hemisphere dimple is then transformed by an angle of [2*(90−θ)] degrees about an axis that is normal to plane P and passes though the golf ball centroid. The plan shape is then rotated by 180 degrees about an axis connecting the dimple centroid to the golf ball centroid. These transformations will result in the plan shapes of the southern and northern dimples, in a pair of corresponding dimples, to be properly oriented in the same plane such that differences between their plan shape and plan shape orientation can be determined by calculating the absolute residual. In another example, where the plan shapes of the dimples are not axially symmetric, the dimples may be aligned with one another by positioning the two dimples relative to one another such that a single axis passes through the centroid of each plan shape.
An absolute residual r is determined by overlaying the plan shapes of two dimples 100/200 with the geometric centers 101/201 of the two plan shapes aligned with one another, as shown in
A mean absolute residual
A residual standard deviation S, is calculated for the group of (n) residuals r, via the following equation:
A t-statistic (tj) is then calculated according to the following equation:
The calculated t-statistic (tj) is compared to a critical t value from a t-distribution with (n−1) degrees of freedom and an alpha value of 0.05, via the following equation:
t
j
>t
α,n-1
If the foregoing equation comparing t and t is logically true, then the overlaid plan shapes are considered different.
The foregoing procedure may be repeated for any dimple pair on the ball that could be considered different. However, as one of ordinary skill in the art would readily understand, and because not all dimple pairs on the ball will have different shapes, the foregoing procedure would only be applied to dimple pairs with a different plan shape. In one embodiment, the foregoing procedure is performed only until dimples in a single pair of corresponding dimples are determined to be different, with the understanding that identification of different dimples within even a single pair of corresponding dimples is sufficient to conclude that the two hemispheres on which the dimples are located have different dimple geometries.
The plan shape of each dimple in a corresponding dimple pair may be any shape within the context of the above disclosure. In one embodiment, the plan shape may be any one of a circle, square, triangle, rectangle, oval, or other geometric or non-geometric shape providing that the corresponding dimple in another hemisphere differs. By way of example, in a pair of corresponding dimples, the dimple in the first hemisphere may be a circle and the corresponding dimple in the second hemisphere may be a square (as generally shown in
Another way to achieve differing dimple geometries with the same or different dimple arrangement on opposing hemispheres in accordance with the present invention is to include corresponding dimples that differ in profile shape. Thus, in another embodiment, the dimples on opposing hemispheres are considered different from one another if, in a pair of corresponding dimples, the profile shapes of the corresponding dimples differ from one another. The profile shapes of two dimples are considered different from one another if an overlaying comparison of the profile shapes of the two dimples yields a mean absolute residual
When differing dimple profile shapes are utilized, at least about 25 percent of the corresponding dimples in the opposing hemispheres have different profile shapes. In another embodiment, at least about 50 percent of the corresponding dimples in the opposing hemispheres have different profile shapes. In yet another embodiment, at least about 75 percent of the corresponding dimples in the opposing hemispheres have different profile shapes. In still another embodiment, all of the corresponding dimples in the opposing hemispheres have different profile shapes.
An absolute residual r is determined by overlaying the profile shapes of two dimples 100/200, as shown in
The dimple profile shapes are overlaid with one another such that the geometric centers 101/201 of the two dimples 100/200 are aligned on a common vertical axis Y-Y, and such that the peripheral edges 105/205 of the two profile shapes (i.e., the edges of the dimple perimeter that intersect the outer surface of the golf ball 1) are aligned on a common horizontal axis X-X, as shown in
A mean absolute residual r is calculated by calculating an absolute residual r over a number (n+1) of equally spaced intersection lines 400/400′, and averaging the separately calculated absolute residuals r.
A residual standard deviation S, is calculated for the group of (n+1) residuals r, via the following equation:
A t-statistic (tj) is calculated according to the following equation:
The calculated t-statistic (tj) is compared to a critical t value from a t-distribution with ((n+1)−1) degrees of freedom and an alpha value of 0.05, via the following equation:
t
j
>t
α,n
If the foregoing equation comparing t and t is logically true, then the overlaid profile shapes are considered different.
The foregoing procedure may be repeated for any dimple pair on the ball that could be considered to have different profile shapes. However, as one of ordinary skill in the art would appreciate, and because not all dimple pairs on the ball will have different profile shapes, the foregoing procedure would only be applied to dimple pairs with a different profile shape. In one embodiment, the foregoing procedure is performed only until dimples in a single pair of corresponding dimples are determined to be different (in plan and/or profile shape), with the understanding that identification of different dimples within even a single pair of corresponding dimples is sufficient to conclude that the two hemispheres on which the dimples are located have different dimple geometries.
The cross-sectional profile of the dimples according to the present invention may be based on any known dimple profile shape that works within the context of the above disclosure. 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 parabolic curves, ellipses, spherical curves, saucer-shapes, truncated cones, and flattened trapezoids.
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. Similarly, the dimple profile may be defined by the superposition of two or more curves defined by continuous and differentiable functions that have valid solutions. For example, in one embodiment, the dimple profile is defined by combining a spherical curve and a different curve. In another embodiment, the dimple profile is defined by combining a cosine curve and a different curve. In still another embodiment, the dimple profile is defined by the superposition of a frequency curve and a different curve. In yet another embodiment, the dimple profile is defined by the superposition of a catenary curve and different curve.
In one embodiment, when differing profile shapes and plan shapes are utilized, at least about 25 percent of the corresponding dimples in the opposing hemispheres have different profile shapes and different plan shapes. In another embodiment, at least about 50 percent of the corresponding dimples in the opposing hemispheres have different profile shapes and different plan shapes. In yet another embodiment, at least about 75 percent of the corresponding dimples in the opposing hemispheres have different profile shapes and different plan shapes. In still another embodiment, all of the corresponding dimples in the opposing hemispheres have different profile shapes and different plan shapes.
As discussed above, even though the dimple geometries, dimple arrangements, and/or dimple counts in the opposing hemispheres may differ, an appropriate degree of volumetric equivalence is maintained between the two hemispheres. In this aspect of the invention, the dimples in one hemisphere have dimple surface volumes similar to the dimple surface volumes of the dimples in the other hemisphere.
In one embodiment, when the opposing hemispheres have the same dimple arrangement/dimple count (and merely differing plan and/or profile shapes), volumetric equivalence of two hemispheres of a golf ball may be assessed via a regression analysis of dimple surface volumes. This may be done by calculating the surface volumes of the two dimples in a pair of corresponding dimples 100/200, and plotting the calculated surface volumes of the two dimples against one another. An example of a surface volume plotting is shown in
After the surface volumes for all pairs of corresponding dimples 100/200 have been calculated and plotted, linear regression analysis is performed on the data to yield coefficients in the form y=α+βx. It should be understood by one of ordinary skill in the art the linear function y uses least squares regression to determine the slope β and the y-intercept α, where x represents the surface volume from the dimple on the first hemisphere and y represents the surface volume of the dimple on the second hemisphere. Two hemispheres are considered to have volumetric equivalence when two conditions are met. First, the coefficient β must be about one—which is to say that the coefficient β must be within a range from about 0.90 to about 1.10; preferably from about 0.95 to about 1.05. Second, a coefficient of determination R2 must be about one—which is to say that the coefficient of determination R2 must be greater than about 0.90; preferably greater than about 0.95. In order to satisfy the requirement of volumetric equivalence both of these conditions must be met. Thus, a suitable dimple pattern has a coefficient β that ranges from about 0.90 to about 1.10 and a coefficient of determination R2 greater than about 0.90.
In another embodiment, when the hemispheres have differing dimple arrangements and/or dimple counts, the volumetric equivalence of two hemispheres of a golf ball may be assessed by calculating the average hemispherical dimple surface volume. This may be done by first calculating the volume of each dimple in the first hemisphere and the volume of each dimple in the second hemisphere. Then, the average of the dimple surface volumes of the first hemisphere and the average of the dimple surface volumes of the second hemisphere are determined. As known to those of ordinary skill in the art, the average may be determined by summing up all of the dimple surface volumes in each hemisphere and dividing by the number of dimple surface volumes counted in the sum. Once the average of the dimple surface volumes in the first and second hemispheres is determined, the absolute difference between the two averages is calculated. The resulting absolute difference is the absolute value of the average dimple surface volume difference. For example, if the first hemisphere has an average dimple surface volume of 1.15922×104 and the second hemisphere has an average dimple surface volume of 1.16507×104, the resulting absolute difference, i.e., the average dimple surface volume difference between the two hemispheres, is 5.85×10−7.
In this aspect, two hemispheres are considered to have volumetric equivalence when the average dimple surface volume difference is less than a certain value. More specifically, in order for the hemispheres to show volumetric equivalence, the average dimple surface volume difference should be less than 3.5×10−6. In another embodiment, two hemispheres are considered to have volumetric equivalence when the average dimple surface volume difference is less than 3.0×10−6. In still another embodiment, two hemispheres are considered to have volumetric equivalence when the average dimple surface volume difference is less than 2.5×10−6. In yet another embodiment, two hemispheres are considered to have volumetric equivalence when the average dimple surface volume difference is less than 2.0×10−6.
The dimples on golf balls according to the present invention may comprise any width, depth, and edge angle; and the dimple patterns may comprise multitudes of dimples having different widths, depths, and edge angles. In this aspect, the width (i.e., dimple diameter) and the dimple edge angle may be adjusted to achieve volumetric equivalence between the two hemispheres. For instance, if the dimples on one hemisphere have a smaller average diameter, the edge angle of the dimples in that hemisphere may be adjusted, for example, may be increased, to allow for volumetric equivalence between the two hemispheres. Alternatively, if the dimples on one hemisphere have a larger average diameter, the edge angle of the dimples in that hemisphere may be adjusted, for example, may be decreased, to allow for volumetric equivalence between the two hemispheres.
In one embodiment, the surface volume of dimples in a golf ball according to the present invention is within a range of about 0.000001 in3 to about 0.0005 in3. In one embodiment, the surface volume is about 0.00003 in3 to about 0.0005 in3. In another embodiment, the surface volume is about 0.00003 in3 to about 0.00035 in3.
Dimple patterns according to 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 veneer cover 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 golf balls according to 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 dimple patterns that may be 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. In fact, it will be appreciated by those skilled in the art that golf balls according to the present invention may take on a number of permutations, provided volumetric equivalence between the two hemispheres is achieved. Again, volumetric equivalence between two hemispheres may be achieved by adapting the surface volumes of the dimples in the two separate hemispheres to yield substantially identical hemispherical volumes, in accord with the discussion above.
Golf Ball with Dimple Patterns Having Differing Plan Shapes
Golf Ball with Dimple Patterns Having Differing Profiles
Golf Ball with Dimple Patterns Having Differing Plan and Profile Shapes
Golf Ball with Differing Dimple Arrangements
As can be seen from Tables 2 and 3, the dimples in the second hemisphere 20 have a smaller average diameter. In order to compensate for the smaller average diameter, the edge angle of the dimples in the second hemisphere 20 is 2.5° deeper than the dimples of the first hemisphere 10 to allow for volumetric equivalence. This results in an average dimple surface volume difference between the two hemispheres of 1.0×106, which is an appropriate degree of volumetric equivalence between the two hemispheres.
Golf Ball with Differing Dimple Counts
As can be seen from Tables 4 and 5, the dimples in the second hemisphere 20 have a larger average diameter. In order to compensate for the larger average diameter, the edge angle of the dimples in the second hemisphere 20 is 0.5° shallower than the dimples of the first hemisphere 10 to allow for volumetric equivalence. This results in an average surface volume difference between the two hemispheres of 5.6×10−7, which is an appropriate degree of volumetric equivalence between the two hemispheres.
Although the present invention is described with reference to particular embodiments, it will be understood to those skilled in the art that the foregoing disclosure addresses exemplary embodiments only; that the scope of the invention is not limited to the disclosed embodiments; and that the scope of the invention may encompass additional embodiments embracing various changes and modifications relative to the examples disclosed herein without departing from the scope of the invention as defined in the appended claims and equivalents thereto.
To the extent necessary to understand or complete the disclosure of the present invention, all publications, patents, and patent applications mentioned herein are expressly incorporated by reference herein to the same extent as though each were individually so incorporated. No license, express or implied, is granted to any patent incorporated herein. Ranges expressed in the disclosure include the endpoints of each range, all values in between the endpoints, and all intermediate ranges subsumed by the endpoints.
The present invention is not limited to the exemplary embodiments illustrated herein, but is instead characterized by the appended claims.
| Number | Date | Country | |
|---|---|---|---|
| Parent | 14985743 | Dec 2015 | US |
| Child | 15651244 | US |
