Golf ball dimple profile

Abstract

The present invention concerns a golf ball having dimples with a cross-sectional profile comprising a conical top portion and a non-conical bottom portion. More particularly, the profiles of the present invention are defined by three independent parameters: dimple diameter (D.sub.D), edge angle (Φ.sub.EDGE), and saucer ratio (S.sub.r). These parameters fully define the dimple shape and allow for greater flexibility in constructing a dimple profile versus conventional spherical dimples. Further, conical dimples provide a unique dimple cross-section which is visually distinct.

Claims

1. A golf ball having a generally spherical surface and comprising a plurality of dimples separated by a land area formed on the surface, wherein at least of portion of the dimples consist of a top conical sidewall and a bottom portion and have a saucer ratio (S.sub.r), defined as the ratio of the bottom portion diameter (D.sub.S) to the dimple diameter (D.sub.D), of from about 0.05 to about 0.75, and an edge angle (Φ.sub.EDGE) defined by
1.33(S.sub.r).sup.2−0.39(S.sub.r)+10.40≦Φ.sub.EDGE≦2.85(S.sub.r).sup.2−1.12(S.sub.r)+13.49 wherein the bottom portion is defined by a function rotated about a central axis, and wherein the function is selected from the group consisting of polynomial, trigonometric, hyperbolic, exponential functions, and the superposition of two or more thereof, excluding linear functions and functions that result in a cone or sphere.

2. The golf ball of claim 1, wherein the difference between the slope of the conical sidewall and the slope of the bottom portion at a defined point of intersection between the top conical sidewall and the bottom portion is less than about 2°.

3. The golf ball of claim 2, wherein the difference between the slope of the conical sidewall and the slope of the bottom portion at the point of intersection is less than about 1°.

4. The golf ball of claim 2, wherein the slope of the conical sidewall and the slope of the bottom portion at the point of intersection is equal.

5. The golf ball of claim 1, wherein the saucer ratio is from about 0.10 to about 0.70.

6. The golf ball of claim 1, wherein the saucer ratio is from about 0.20 to about 0.60.

7. The golf ball of claim 1, wherein the saucer ratio is from about 0.25 to about 0.55.

8. The golf ball of claim 1, wherein the saucer ratio is from about 0.30 to about 0.50.

9. The golf ball of claim 1, wherein the saucer ratio is from about 0.35 to about 0.45.

10. A golf ball having a generally spherical surface and comprising a plurality of dimples separated by a land area formed on the surface, wherein at least of portion of the dimples consist of a top conical sidewall and a bottom portion and have a saucer ratio (S.sub.r), defined as the ratio of the bottom portion diameter (D.sub.S) to the dimple diameter (D.sub.D), of from about 0.05 to about 0.75, and a chord depth (d.sub.CHORD) defined by
0.0009(S.sub.r).sup.2−0.0035(S.sub.r)+0.0062≦d.sub.CHORD≦0.0030(S.sub.r).sup.2−0.0069(S.sub.r)+0.0113, wherein the bottom portion is defined by a function rotated about a central axis, and wherein the function is selected from the group consisting of polynomial, trigonometric, hyperbolic, exponential functions, and the superposition of two or more thereof, excluding linear functions and functions that result in a cone or sphere.

11. The golf ball of claim 10, wherein the difference between the slope of the conical sidewall and the slope of the bottom portion at a defined point of intersection between the top conical sidewall and the bottom portion is less than about 2°.

12. The golf ball of claim 11, wherein the difference between the slope of the conical sidewall and the slope of the bottom portion at the point of intersection is less than about 1°.

13. The golf ball of claim 11, wherein the slope of the conical sidewall and the slope of the bottom portion at the point of intersection is equal.

14. The golf ball of claim 10, wherein the saucer ratio is from about 0.10 to about 0.70.

15. The golf ball of claim 10, wherein the saucer ratio is from about 0.20 to about 0.60.

16. The golf ball of claim 10, wherein the saucer ratio is from about 0.25 to about 0.55.

17. The golf ball of claim 10, wherein the saucer ratio is from about 0.30 to about 0.50.

18. The golf ball of claim 10, wherein the saucer ratio is from about 0.35 to about 0.45.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) In the accompanying drawings which form a part of the specification and are to be read in conjunction therewith and in which like reference numerals are used to indicate like parts in the various views:

(2) FIG. 1 is a schematic diagram illustrating a dimple profile according to this invention;

(3) FIG. 2 is a schematic diagram illustrating a method for measuring the edge angle of a dimple;

(4) FIG. 3 is a schematic diagram illustrating a method for measuring the chord depth of a dimple;

(5) FIG. 4 is a schematic diagram illustrating another dimple profile according to this invention;

(6) FIG. 5 is a schematic diagram illustrating another dimple profile according to this invention;

(7) FIG. 6 shows a dimple cross-sectional shape according to an embodiment of the present invention;

(8) FIG. 7 shows a dimple cross-sectional shape according to another embodiment of the present invention;

(9) FIG. 8 shows a dimple cross-sectional shape according to another embodiment of the present invention;

(10) FIG. 9A is a schematic diagram illustrating a dimple profile according to an embodiment of the present invention;

(11) FIG. 9B is a schematic diagram illustrating a dimple profile according to an embodiment of the present invention;

(12) FIG. 9C is a schematic diagram illustrating two dimple profiles according to embodiments of the present invention;

(13) FIG. 10 is a graphical representation of the relationship between saucer ratio and edge angle according to an embodiment of the present invention;

(14) FIG. 11 is a graphical representation of the relationship between saucer ratio and chord depth according to an embodiment of the present invention; and

(15) FIG. 12 is a graphical representation of the relationship between dimple volume and plan shape area according to an embodiment of the present invention.

DETAILED DESCRIPTION

(16) The present invention concerns a golf ball with dimples consisting of a top conical sidewall and a non-conical bottom portion. In one embodiment, the bottom portion is a spherical cap with a prescribed point of tangency to the conical sidewall. In another embodiment, the bottom portion is defined by a function selected from the group consisting of polynomial, trigonometric, hyperbolic, exponential functions, and the superposition of two or more thereof, excluding linear functions and functions that result in a cone or sphere when rotated about a central axis. Functions resulting from the superposition of two or more different functions, and the use thereof for dimple profiles, are further disclosed, for example, in U.S. Patent Application Publication No. 2012/0165130 to Madson et al. and U.S. Patent Application Publication No. 2013/0172125 to Nardacci et al., the entire disclosures of which are hereby incorporated herein by reference.

(17) The profiles of the present invention are further defined by three parameters: dimple diameter (D.sub.D), edge angle (Φ.sub.EDGE), and saucer ratio (S.sub.r). These parameters fully define the dimple shape and allow for greater flexibility in constructing a dimple profile versus conventional spherical dimples. Further, conical dimples provide a unique dimple cross-section which is visually distinct.

(18) FIG. 1 is a cross-sectional view illustrating a dimple 10 on a golf ball 20 having an outer spherical surface with a phantom portion 30 and an undimpled land area 40. A rotational axis 50 vertically traverses the center of dimple 10. The dimple 10 comprises a top conical edge 12 (an edge with no radius) and a bottom spherical cap 14. More particularly, the dimple diameter (D.sub.D) that defines the phantom spherical outer surface 30 acts as the base of a right circular cone. From that base, a conical edge 12 forms the top portion of the dimple 10. The bottom of dimple 10 is defined by a spherical cap 14. The diameter of the bottom spherical cap 14 is also referred to as the saucer diameter (D.sub.S) and is preferably concentric with the dimple diameter (D.sub.D).

(19) In one innovative aspect of the present invention, dimple 10 has a defined tangent point 16, wherein the straight conical edge 12 meets the spherical bottom cap 14. The tangent point 16 is determined by the saucer diameter (D.sub.S) and the edge angle (Φ.sub.EDGE) of the dimple, which is defined below. At the defined tangent point 16, the difference in the slope of the straight conical edge 12 and the slope of the spherical arcuate cap 14, which is the slope of a line tangent to cap 14 at point 16, will be less than 2°, preferably less than 1°, and more preferably the slopes will be about equal at that connection to ensure tangency at that location.

(20) The ultimate shape of dimple 10 is defined by three parameters. The first of these parameters is the dimple diameter (D.sub.D), and the second of these parameters is the saucer ratio (S.sub.r), which is defined by equation (1):
S.sub.r=D.sub.S/D.sub.D   (1)
If S.sub.r=0, then the dimple would be a cone with no spherical bottom radius, and if S.sub.r=1, then the dimple is spherical. For the purpose of this invention, the value of S.sub.r preferably falls in the range of about 0.05≦S.sub.r≦0.75, preferably about 0.10≦S.sub.r≦0.70, more preferably about 0.15≦S.sub.r≦0.65, more preferably about 0.20≦S.sub.r≦0.60, more preferably about 0.25≦S.sub.r≦0.55, more preferably about 0.30≦S.sub.r≦0.50, and more preferably about 0.35≦S.sub.r≦0.45. If S.sub.r is less than 0.05 then the manufacturing of dimple 10 becomes more difficult, and the sharp point at the bottom of the dimple can diminish the aerodynamic qualities of golf ball 20 and is susceptible to paint flooding. If S.sub.r is greater than 0.75 then it too closely resembles the shape of a spherical dimple and the qualities of conical dimples to adjust the flight performance of the golf ball 20 is diminished.

(21) The third parameter to adjust the dimple shape can either be the edge angle (Φ.sub.EDGE) or the chord depth (d.sub.CHORD). Both parameters are dependent upon one another. The edge angle (Φ.sub.EDGE) is defined as the angle between a first tangent line T1 and a second tangent line T2, which can be measured as shown in FIG. 2. Generally, it may be difficult to define and measure an edge angle (Φ.sub.EDGE) due to the indistinct nature of the boundary dividing the dimple 10 from the ball's undisturbed land surface 40. Due to the effects of the paint and/or the dimple design itself, the junction between the land surface and dimple is not a sharp corner and is therefore indistinct. This can make the measurement of a dimple's edge angle (Φ.sub.EDGE) and radius (R.sub.D) somewhat ambiguous. Thus, as shown in FIG. 2, to resolve this problem, a ball phantom surface 30 is constructed above the dimple 10 as a continuation of land surface 40.

(22) In FIG. 2, first tangent line T1 is a line that is tangent to conical edge 12 at a point P2 that is spaced about 0.0030 inches radially inward from the phantom surface 30. T1 intersects phantom surface 30 at a point P1, which defines a nominal edge position. The second tangent line T2 is constructed as being tangent to the phantom surface 30 at P1. The edge angle is the angle between T1 and T2. The point P1 can also be used to measure the dimple radius (R.sub.D) to be the distance from P1 to the rotational axis 50.

(23) FIG. 10 is a graphical representation of the relationship between saucer ratio and edge angle according to an embodiment of the present invention. In a particular embodiment, dimples of the present invention have an edge angle (Φ.sub.EDGE) defined by
1.33(S.sub.r).sup.2−0.39(S.sub.r)+10.40≦Φ.sub.EDGE≦2.85(S.sub.r).sup.2−1.12(S.sub.r)+13.49

(24) FIG. 3 illustrates a method of measuring the chord depth (d.sub.CHORD). As illustrated therein, the chord depth (d.sub.CHORD) is measured as the distance from the theoretical cone base, denoted by the line marking dimple diameter (D.sub.D), to the bottom of the dimple.

(25) With a desired chord depth (d.sub.CHORD), the edge angle (Φ.sub.EDGE) can be calculated by equation (2):
Φ.sub.EDGE=Φ.sub.CAP+Φ.sub.CHORD   (2)

(26) Where: Φ.sub.CAP=sin.sup.−1(D.sub.D/D.sub.B)
Φ.sub.CHORD=tan.sup.−1{(d.sub.CHORD−d.sub.SAUCER)÷(R.sub.D−R.sub.S)}

(27) And: D.sub.B=Diameter of the golf ball R.sub.D=Dimple radius, (D.sub.D/2) R.sub.S=Saucer radius, (D.sub.S/2)
d.sub.SAUCER=saucer depth=r.sub.APEX−√(r.sub.APEX.sup.2−R.sub.S.sup.2)
r.sub.APEX=R.sub.S/sin (Φ.sub.CHORD)
Alternatively, if the edge angle (Φ.sub.EDGE) is known then the chord depth (d.sub.CHORD) can be calculated by equation (3):
d.sub.CHORD=d.sub.SAUCER+(R.sub.D−R.sub.S)×tan [Φ.sub.EDGE−{cos.sup.−1(D.sub.D/D.sub.B)}]  (3)

(28) FIG. 11 is a graphical representation of the relationship between saucer ratio and chord depth according to an embodiment of the present invention. In a particular embodiment, dimples of the present invention have a chord depth (d.sub.CHORD) defined by
0.0009(S.sub.r).sup.2−0.0035(S.sub.r)+0.0062≦d.sub.CHORD≦0.0030(S.sub.r).sup.2−0.0069(S.sub.r)+0.0113.

(29) The dimple 10 also has a volume ratio (V.sub.R), which is the ratio between the dimple volume (V.sub.D) and the theoretical cylindrical volume (V.sub.C). In other words, V.sub.R=V.sub.D:V.sub.C. The volume ratio (V.sub.R) preferably falls in the range of about 1/3≦V.sub.R≦1/2. The dimple volume (V.sub.D) can be calculated by equation (4):
V.sub.D=[1/3πR.sub.D.sup.2(d.sub.CHORD)]−[1/3πR.sub.S.sup.2(d.sub.SAUCER)]+[π(d.sub.SAUCER)(3R.sub.S.sup.2+d.sub.SAUCER.sup.2)÷6]  (4)
The theoretical cylindrical volume (V.sub.C) is the volume of a theoretical cylinder having a base diameter equal to that of the dimple diameter (D.sub.D) and a height equal to the chord depth (d.sub.CHORD) such that V.sub.C is calculated by equation (5):
V.sub.C=πR.sub.D.sup.2 (d.sub.CHORD)   (5)

(30) FIG. 12 is a graphical representation of the relationship between dimple volume and plan shape area according to an embodiment of the present invention. For purposes of the present invention, the plan shape area is calculated as π(D.sub.D/2).sup.2. In a particular embodiment, dimples produced in accordance with the present invention have a plan shape area and dimple volume within a range having a lower limit and an upper limit selected from the values within region 1 of FIG. 12. In another embodiment, dimples produced in accordance with the present invention have a plan shape area and dimple volume within a range having a lower limit and an upper limit selected from the values within region 2 of FIG. 12.

(31) FIGS. 4 and 5 are illustrative examples of different dimple shapes 10′ and 10″, respectively, in accordance with the present invention, wherein the saucer ratio (S.sub.r) is changed but the edge angle (Φ.sub.EDGE) remains constant at a value of about 16°. More particularly, in FIG. 4, dimple 10′ has a saucer ratio (S.sub.r) of about 0.05, a chord depth (d.sub.CHORD) of about 0.0152 in., and a volume ratio (V.sub.R) of about 0.341. By way of comparison, FIG. 5 illustrates a dimple 10″ with a saucer ratio (S.sub.r) of about 0.75, a chord depth (d.sub.CHORD) of about 0.0097 in, and a volume ratio (V.sub.R) of about 0.403.

(32) FIG. 9A is an illustrative example of dimple shape 60, according to an embodiment of the present invention, having a top conical edge and a bottom portion defined by a polynomial function. Dimple shape 60 has a dimple diameter (D.sub.d), a saucer diameter (Ds.sub.1), an edge angle (θ.sub.1), and a chord depth (d.sub.c1). The saucer ratio of dimple shape 60, defined by D.sub.S1/D.sub.d, of dimple shape 60 is about 0.05.

(33) FIG. 9B is an illustrative example of dimple shape 65, according to an embodiment of the present invention, having a top conical edge and a bottom portion defined by a polynomial function. Dimple shape 65 has a dimple diameter (D.sub.d), a saucer diameter (Ds.sub.2), an edge angle (θ.sub.2), and a chord depth (d.sub.c2). The saucer ratio of dimple shape 65, defined by D.sub.S2/D.sub.d, of dimple shape 65 is about 0.75.

(34) FIG. 9C shows an overlay of the dimple shape 60 of FIG. 9A and the dimple shape 65 of FIG. 9B to illustrate the effect that a change in saucer ratio may have on edge angle and chord depth, particularly showing that θ.sub.1<θ.sub.2 and d.sub.c1>d.sub.c2.

(35) FIGS. 6-8 show various dimple cross-sectional shapes having a base portion defined by a simple plane curve, such as a polynomial, trigonometric, hyperbolic, or exponential function. To define the base portion according to such functions, it should be taken into account that the chord plane of the dimple represents y=0 and the vertical axis in the center of the dimple represents x=0.

(36) FIG. 6 illustrates a dimple profile resulting from a combination of a conical top portion and a base portion defined by a polynomial function: y(x)=ax.sup.2+bx+c. The profile is then rotated 360° about the Y (vertical) axis to define the dimple surface. The highest order of the polynomial will dictate the overall shape of the base curve and the constants a, b, and c are used to modify the curvature intensity of the base curve. While FIG. 6 illustrates a base portion defined by a 2.sup.nd order polynomial, it should be understood that a polynomial of any order and containing any number terms may be used.

(37) FIG. 7 illustrates a dimple profile resulting from a combination of a conical top portion and a base portion defined by a trigonometric function: y(x)=a sin(bx″). The profile is then rotated 360° about the Y (vertical) axis to define the dimple surface. While FIG. 7 illustrates a base portion defined by a sine function, it should be understood that any trigonometric or hyperbolic function may be used.

(38) FIG. 8 illustrates a dimple profile resulting from a combination of a conical top portion and a base portion defined by an exponential function: y(x)=ce.sup.x.sup.n. The profile is then rotated 360° about the Y (vertical) axis to define the dimple surface. While FIG. 8 illustrates a base portion defined by a specific exponential function, it should be understood that any exponential function may be used.

(39) While it is apparent that the illustrative embodiments of the invention disclosed herein fulfill the objectives of the present invention, it is appreciated that numerous modifications and other embodiments may be devised by those skilled in the art. Additionally, feature(s) and/or element(s) from any embodiment may be used singly or in combination with other embodiment(s) and steps or elements from methods in accordance with the present invention can be executed or performed in any suitable order. Therefore, it will be understood that the appended claims are intended to cover all such modifications and embodiments, which would come within the spirit and scope of the present invention.