Golf Ball Dimple Profile Defined by Piecewise Function

The present application is a continuation application of U.S. Non-Provisional patent application Ser. No. 18/236,180, filed on Aug. 21, 2023, the entire disclosure of which is hereby incorporated herein by reference.

The present invention relates to a golf ball dimple profile, and more particularly relates to the contour of the dimple surface being defined by juxtaposed curves.

Golf balls were originally made with smooth outer surfaces. In the late nineteenth century, players observed that the gutta-percha golf balls traveled further as they got older and more gouged up. The players then began to roughen the surface of new golf balls with a hammer to increase flight distance. Manufacturers soon caught on and began molding non-smooth outer surfaces on golf balls.

By the mid-1900s, almost every golf ball being made 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 had 384 dimples that were arranged in an icosahedral pattern. About 76 percent of its outer surface was covered with dimples and the golf ball exhibited improved aerodynamic performance. Today, dimpled golf balls travel nearly two times farther than a similar ball without dimples.

The dimples on a golf ball are important in reducing drag and increasing lift. Drag is the air resistance that acts on the golf ball in the opposite direction from 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. At some point air separates from the surface of the ball, leaving a large turbulent flow area called the wake that has low pressure. The difference in the high pressure in front of the ball and the low pressure behind the ball slows the ball down. This is the primary source of drag for a golf ball.

The dimples on the ball create a turbulent boundary layer around the ball, i.e., a thin layer of air adjacent to the ball flows in a turbulent manner. The turbulence energizes the boundary layer of air around the ball and helps the air stay attached further around the ball to reduce the area of the wake. This greatly increases the pressure behind the ball and substantially reduces the drag. Lift is the upward force on the ball that is created from a difference in pressure on the top of the ball to the bottom of the ball. The difference in pressure is created by a warpage in the air flow resulting from the ball's back spin. 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.

Golf ball manufacturers extensively study the effect of dimple shape, volume, and cross-section on overall flight performance of the ball. Golf ball dimples having two different spherical radii with an inflection point where the two curves meet are known. In most cases, however, the cross-sectional profiles of dimples in prior art golf balls are parabolic curves, ellipses, semi-spherical curves, saucer-shaped, a sine curve, a truncated cone, or a flattened trapezoid. One disadvantage of these shapes is that they can sharply intrude into the surface of the ball, which may cause the drag to become greater than the lift. As a result, the ball may not make best use of momentum initially imparted thereto, resulting in an insufficient carry of the ball.

It would generally be desirable to provide a golf ball dimple profile that is comprised of at least two different or distinct curves or functions having a seamless transition to provide additional capabilities for high performing aerodynamic golf balls.

In one example, a golf ball having a plurality of dimples on a surface thereof is disclosed herein. At least a first group of the plurality of dimples has a cross-sectional profile (i.e. a cross-sectional dimple profile) defined by x-y coordinates, wherein x=0 corresponds to a central axis of the cross-sectional profile (i.e., at a centroid of the golf ball dimple profile), and y=0 corresponds to a maximum depth of the cross-sectional profile which is defined at the central axis of the cross-sectional profile or the centroid of the golf ball dimple profile. The cross-sectional profile can be symmetrical about the central axis, such that the cross-sectional profile is comprised of a cross-sectional half profile that is rotated about x=0. The cross-sectional half profile can be defined by a piecewise function (y) comprised of a first function (y) and a second function (y), and the piecewise function (y) can be rotated about x=0 to define the full cross-sectional profile of the dimple. Accordingly, the full cross-sectional profile of the dimple is also defined by the piecewise function (y) with the inclusion of negative x values and equivalent inequality boundaries, as understood by one with ordinary skill in the art. These first and second functions (y, y) can be referred to as sub-functions.

The first function (y) and the second function (y) can intersect at at least one intersection point (x, y) such that:

Rotation of the piecewise function (y) about the central axis of x=0, i.e., the centroid of the golf ball dimple profile, generates the full or entire cross-sectional golf ball dimple profile. Accordingly, the first function (y) and the second function (y) can intersect at least one intersection point (−x, y) such that:

The first function (y) and the second function (y) can have opposing directions of concavity. One of ordinary skill in the art would understand that the entire golf ball dimple profile consists of a golf ball dimple half profile, which is defined by the piecewise function (y), that is rotated about the central axis to define the entire or full cross-sectional dimple profile. At least one of the first function (y) or the second function (y) can have a non-constant radius of curvature. Both of the first and second functions (y, y) can have a non-constant radius of curvature.

The first function (y) can be defined by:

where SF is a shape factor, and the shape factor (SF) is within the following range: 1≤SF≤1,000.

The second function (y) can be defined by:

where HF is a horn factor, and the horn factor (HF) is defined by:

A dimple diameter (d) of the plurality of dimples can be within the following range: 0.100 inches≤d≤0.200 inches. A chord depth (c) of the plurality of dimples can be within the following range: 0.001 inches≤c≤0.010 inches.

A y-coordinate of the intersection point (y) can be defined by the following equation:

where θ is a fraction of a total chord depth (in inches) that is contributed by the first function (y), and where cis a chord depth (in inches) of the plurality of dimples. Accordingly, κ is referred to herein as a chord depth-contribution factor.

An x-coordinate of the intersection point (x) can be defined by the following equation:

where the shape factor (SF) is within the following range: 1≤SF≤1,000.

The following equation can be used to define the chord depth-contribution factor (K):

The plurality of the dimples can include at least 50% of the plurality of dimples. In another example, the plurality of the dimples can include 100% of the plurality of dimples.

The first function (y) can be defined by a catenary function, and the second function (y) can be defined by a Gabriel's horn function. One of ordinary skill in the art would understand that other functions can be used to define the golf ball dimple profile.

In another example, a golf ball having a plurality of dimples on a surface thereof is provided. At least a first group of the plurality of dimples has a cross-sectional profile defined by x-y coordinates, where x=0 corresponds to a central axis of the cross-sectional profile, y=0 corresponds to a maximum depth of the cross-sectional profile, and the cross-sectional profile is symmetrical about the central axis.

The cross-sectional half profile can be comprised of a piecewise function (y) defined by a first function (y) and a second function (y). The first function (y) and the second function (y) intersect at at least one intersection point (x, y) such that:

The first function (y) can be defined by a catenary function, and the second function (y) can be defined by a Gabriel's horn function.

The first function (y) and the second function (y) can have opposing directions of concavity, and at least one of the first function (y) or the second function (y) can have a non-constant radius of curvature.

In this example, the first function (y) and the second function (y) can be defined by:

where the shape factor (SF) is within the following range: 1≤SF≤1,000, and where the horn factor (HF) is defined by:

In yet another example, a golf ball having a plurality of dimples on a surface thereof is provided. At least a first group of the plurality of dimples has a cross-sectional profile defined by x-y coordinates, where x=0 corresponds to a central axis of the cross-sectional profile, y=0 corresponds to a maximum depth of the cross-sectional profile, and the cross-sectional profile is symmetrical about the central axis.

The cross-sectional half profile can be comprised of a piecewise function (y) defined by a first function (y) and a second function (y). The first function (y) and the second function (y) can intersect at an intersection point (x, y), and the first function (y) and the second function (y) are smooth, continuous, and tangential at the intersection point (x, y). The first function (y) can be defined by a catenary function, and the second function (y) can be defined by a Gabriel's horn function. The y-coordinate of the intersection point (y) can be defined by the following equation:

In some embodiments, it is preferred that all of the dimple profiles on the golf ball are similar. However, in other embodiments, the profiles can be varied over the surface of the golf ball and the dimples can have different dimple diameters and depths.

According to one aspect, the present disclosure is directed to a golf ball having at least one dimple cross-sectional half profile using at least two curves with a smooth transition between the curving functions, at least one of the two curves having a non-constant radius of curvature (i.e., at least one curve is not circular), and concavities among the at least two curves are opposite from each other.

Several examples of golf ball dimple profiles according to the present disclosure are illustrated in.illustrates the golf ball dimple half profile associated with the golf ball dimple profile of.

illustrates a golf ball dimple profiledefined by at least two curves (y) and (y) that intersect at at least one intersection point (−x, y; x, y). The golf ball dimple profileis defined as being recessed relative to a golf ball landing surfacesurrounding the golf ball dimple. A phantom surface (P) for the golf ball surface is also shown in.

As shown in, the golf ball dimple has a diameter (d) and a chord depth (Ca). The diameter (d) of the golf ball dimple can be 0.100 inches-0.200 inches, in some examples. In other examples, the diameter (d) of the golf ball dimple can be 0.050 inches-0.300 inches. The chord depth (c) can be 0.001 inches-0.010 inches, in some examples. In other examples, the chord depth (c) can be 0.0005 inches-0.020 inches. One of ordinary skill in the art would understand that the diameter (d) and the chord depth (c) of the golf ball dimple profile can vary.

The present golf ball dimple profile can be used for all of the dimples on a golf ball surface in one example. In another example, the present golf ball dimple profile can be used for at least 50% of the golf ball dimples on a golf ball surface. In another example, the present golf ball dimple profile can be used for no more than 50% of the golf ball dimples on a golf ball surface. In another example, the present golf ball dimple profile can be used for at least 75% of the golf ball dimples on a golf ball surface. For those dimples having a profile shape different from the profile illustrated in, that profile may be spherical, catenary, saucer, conical, or other similarly known profiles. One of ordinary skill in the art understands multiple types of the profiles may also be used in concert.