Golf ball dimples defined by superposed curves

Abstract

The present invention is a golf ball which comprises dimples having a cross section defined by the superposition of two or more continuous and differentiable functions. Additionally, the dimples preferably have a circular boundary and maintain an axis coincident with the center of the circular boundary.

Claims

1. A golf ball having a surface with a plurality of recessed dimples thereon, wherein at least one of the dimples has a cross-section that can be defined by a function resulting from the sum of two or more different types of non-constant, non-linear continuous differentiable functions, y.sub.1(x) and y.sub.2(x).

2. The golf ball of claim 1, wherein y.sub.1(x) is a spherical function.

3. The golf ball of claim 1, wherein y.sub.1(x) is a cosine function.

4. The golf ball of claim 1, wherein y.sub.1(x) is a catenary function.

5. The golf ball of claim 1, wherein the dimple cross-section is defined by a function resulting from the sum of three or more different types of non-constant, non-linear continuous differentiable functions.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) These and other aspects of the present invention may be more fully understood with references to, but not limited by, the following drawings:

(2) FIG. 1 depicts spherical and cosine profile curves;

(3) FIG. 2 illustrates a dimple profile created from the superposing of the curves of FIG. 1;

(4) FIG. 3 illustrates an alternative dimple profile from superposing of another cosine profile curve with a spherical curve;

(5) FIG. 4 illustrates an alternative dimple profile from the superposing of another cosine profile with a spherical curve;

(6) FIG. 5 illustrates another alternative dimple profile from the superposing of yet another cosine profile with a spherical curve;

(7) FIG. 6 illustrates still yet another alternative dimple profile from the superposing of another cosine profile with a spherical curve;

(8) FIG. 7 depicts frequency and catenary profile curves;

(9) FIG. 8 illustrates a dimple profile created from the superposing of the curves of FIG. 7;

(10) FIG. 9 depicts frequency, catenary, and cosine profile curves;

(11) FIG. 10 illustrates a dimple profile created from the superposing of the curves of FIG. 9;

(12) FIG. 11 illustrates a dimple profile created from the superposing of a catenary curve with a cosine curve and a frequency curve;

(13) FIG. 12 illustrates a dimple profile created from the superposing of a catenary curve with a spherical curve;

(14) FIG. 13 illustrates a dimple profile created from the superposing of a catenary curve with a frequency curve;

(15) FIG. 14 illustrates a dimple profile created from the superposing of a plurality of different curves;

(16) FIG. 15 illustrates a dimple profile created from the superposing of a plurality of different curves; and

(17) FIG. 16 illustrates a dimple profile created from the superposing of a plurality of different curves.

DETAILED DESCRIPTION OF THE INVENTION

(18) The present invention is a golf ball which comprises dimples having a cross section defined by the superposition of two or more continuous and differentiable functions. Additionally, the dimples preferably have a circular boundary and maintain an axis coincident with the center of the circular boundary.

(19) Dimples that are defined by superposed curves provide greater opportunity to control the dimple cross-section and therefore, provide dimples that improve the flight characteristics of the golf ball. This method is capable of producing an unlimited number of unique dimple shapes produced using the superposition principle. Since the dimple shape is axially symmetric and maintains a circular boundary, hob, and cavity manufacture remains similar to those for conventionally shaped prior art dimple profiles.

(20) The Superposition Principle states that for linear homogenous ordinary differential equations, if y.sub.1(x) and y.sub.2(x) yield valid solutions, then the sum of y.sub.1(x) and y.sub.2(x) will also yield a valid solution. (Weisstein, Eric W. “Superposition Principle”) This allows the combination of equations that are continuous and differentiable, and combining their solutions creates unique dimple profiles.

(21) Several examples of dimple cross sections according to the present invention are illustrated by referencing FIGS. 1-6. For example, FIG. 1 displays two possible curves, a traditional spherical dimple curve 20 and a cosine curve 21. A phantom ball surface 22 is shown for reference. By using the superposition principle these curves 20 and 21 are combined to create an alternative dimple profile 23, which is illustrated in FIG. 2. The additional dimple shape parameters allow for greater flexibility in defining the final profile, including the dimple depth as defined by the distance from the center point of the dimple to the curved phantom surface and the edge angle as defined in U.S. Pat. No. 6,162,136, which is incorporated herein by reference. The depths of the dimples are preferably between about 0.002 inches and 0.02 inches. With the superposition of the functions as set forth in this invention, the range of potential edge angles of the dimple can be significantly wide. For example, the edge angle show in FIG. 1 is less than 0. However, edge angles of 0 degrees to 40 degrees are preferred.

(22) FIGS. 3 to 6 show alternative profiles from the manipulation of spherical curves 20 with cosine curves 21. Manipulation of both the frequency and the amplitude of the cosine function superposed with a prior art spherical profile produces an unlimited number of dimple profiles 23. Obviously, the permutations are endless. Preferably, the frequency of the cosine function is related to the dimple diameter such that the edges on opposite sides of the dimple are substantially equal and the dimple cross-section is symmetrical.

(23) Another example of a dimple profile is illustrated by reference to FIGS. 7 and 8, wherein a frequency curve is combined with a catenary profile. FIG. 7 displays a frequency curve 31 and a catenary curve 30 in relation to a golf ball phantom spherical surface 22. By using the superposition principle we can combine these curves to create an alternative dimple profile 33 shown in FIG. 8. Again, an infinite number of profiles exist based on the superposition of variations to these function families.

(24) Yet another example of the present invention is the superposition of more than 2 functions. For example, a frequency curve, catenary curve and cosine curve as shown in FIG. 9 can be combined to form the dimple profile in FIG. 10. FIG. 9 depicts three curves: a frequency curve 31, a catenary curve 30 and a cosine curve 21. By using the superposition principle we can combine these curves to create the alternative dimple profile curve 43 shown in FIG. 10. FIG. 11 is another such superimposition of functions. Again, the superposition of these curves greatly increases the possibilities of dimple depth and edge angles. Moreover, the edge angle and depth are not necessarily directly related as evidence from the vast differences between the dimple profiles 43 shown in FIGS. 10 and 11.

(25) Another example of the present invention is the combination of a catenary curve 30 and a spherical curve 21 to form the catenary-spherical curve dimple profile 53 shown in FIG. 12. Another dimple profile 58, shown in FIG. 13, is the combination of a catenary curve 30 with a frequency curve 31.

(26) FIG. 14 is an example of multiple equations being combined. A catenary curve 30, a cosine curve 21, a spherical curve 20, a frequency curve 31 and a linear function (or cone) 40 are superimposed to form the dimple profile 63 in FIG. 14. The linear function 40 is continuous from the dimple edge to the center and symmetrical, whereas the other functions are continuous through the entire dimple diameter, but also symmetrical about the center. Thus, the overall dimple profile 63 is similarly axial symmetric about the center of the dimple. Similarly, multiple functions are combined to form the dimple profile 73 in FIG. 15. The dimple profile 83 in FIG. 16 is formed by the superposition of a cosine curve 21, a spherical curve 20, a frequency curve 31, a Neile's parabola 81 and a conical curve 40.

(27) The simplicity of this method has the potential to generate dimple profiles that have not been utilized on prior art golf balls. Since the dimple boundaries of the golf ball are preferably circular, previously developed patterns can be utilized, refined and optimized for potentially improved distance and flight control. The visual appearance of golf balls produced from this method can be significantly different. The present invention may be used with any type of ball construction. For instance, the ball may have a 2-piece construction, a double cover or veneer cover construction or other multi-layer constructions depending on the type of performance desired of the ball. Examples of these and other types of ball constructions that may be used with the present invention include those described in U.S. Pat. Nos. 5,713,801, 5,803,831, 5,885,172, 5,919,100, 5,965,669, 5,981,654, 5,981,658, and 6,149,535, for example, the construction and materials disclosed in the patents being expressly incorporated herein. Different materials also 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 polyurethane, ionomer resin, balata or any other suitable cover material known to those skilled in the art. Different materials also may be used for forming core and intermediate layers of the ball.

(28) After selecting the desired ball construction, the flight performance of the golf ball can be adjusted according to the design, placement, and number of dimples on the ball. As explained above, the use of a variety of dimples, based on a superposition profile, provides a relatively effective way to modify the ball flight performance without significantly altering the dimple pattern. Thus, the use of dimples based on the superposition profile allows a golf ball designer to select flight characteristics of a golf ball in a similar way that different materials and ball constructions can be selected to achieve a desired performance.

(29) Each dimple of the present invention is part of a dimple pattern selected to achieve a particular desired lift coefficient. Dimple patterns that provide a high percentage of surface coverage are preferred, and are well known in the art. For example, U.S. Pat. Nos. 5,562,552, 5,575,477, 5,957,787, 5,249,804, and 4,925,193 disclose geometric patterns for positioning dimples on a golf ball. In one embodiment of the present invention, the dimple pattern is at least partially defined by phyllotaxis-based patterns, such as those described in co-pending U.S. patent application Ser. No. 09/418,003, which is incorporated by reference in its entirety. Preferably a dimple pattern that provides greater than about 70% surface coverage is selected. Even more preferably, the dimple pattern provides greater than about 80% surface coverage. Once the dimple pattern is selected, several alternative dimple profiles can be tested in a wind tunnel or indoor test range to empirically determine the properties of the profiles that provide the desired lift and drag coefficients at the desired launch conditions.

(30) While the invention has been described in conjunction with specific embodiments, it is evident that numerous alternatives, modifications, and variations will be apparent to those skilled in the art in light of the foregoing description.