Abstract:
A golf ball which reduces frictional resistance against air travels further. The golf ball includes a surface configured to have convex dimples arranged on the surface. Relative roughness of the golf ball having the convex dimples is maintained to be similar to that of a golf ball having concave dimples, thereby ensuring stability of carry of the golf ball.

Description:
CROSS-REFERENCE TO RELATED APPLICATION(S) 
       [0001]    This application claims the benefit under 35 U.S.C. §119(a) of Korean Utility Model Application No. 20-2010-0001004, filed on Jan. 28, 2010, in the Korean Intellectual Property Office, the entire disclosure of which is incorporated herein by reference for all purposes. 
       BACKGROUND 
       [0002]    1. Field 
         [0003]    The following delineates a golf ball, and more particularly, a golf ball with a surface having convex dimples. 
         [0004]    2. Description of the Related Art 
         [0005]    Originally, a golf ball had a smooth surface like any other kinds of balls. As a golf ball with a smooth surface is hit more and more, the ball is worn and its surface becomes rougher. Golfers learned from experiences that a golf ball with a rough surface travelled farther than a new golf ball. Hence, numerous small grooves were made on a ball to increase carry. Such small concave portions on a golf ball are referred to as “dimples.” Dimples reduce frictional resistance against the air, allowing the golf ball to fly further. 
         [0006]    It was found that when dimples are covered on about 50% of a surface of a golf ball and dimples on upper side and lower side are deeper than those on the equator of the golf ball, backspin is generated and the golf ball is prevented from bouncing right and left, so that the golf ball can travel in a linear direction further. 
         [0007]    Golf balls in recent use have various shapes of dimples such as a pentagon, a rectangle, a circle, etc. The shape, number, depth, and diameter of the dimples may influence the carry of the golf ball. In this regards, design of the golf ball has continuously changed, and to regulate such change, Rules of Golf have been introduced which provide detailed regulations for five s items including a diameter, a weight, symmetry, initial velocity and the overall flight distance of a golf ball. The recent golf ball has generally about 200 to 500 dimples, and a golf ball having nearly 400 dimples is most widely used. 
       SUMMARY 
       [0008]    The focal points of a golf ball which has convex dimples are as follows. 
         [0009]    The golf ball having convex dimples has turbulent flow in a forward side of the ball as in a general golf ball having concave dimples. Thus, mixing of air takes place in the forward side due to the turbulent flow, and change of airflow only occurs in a backward side of the ball. That is, while frictional resistance generated in the forward side of the ball increases, form resistance generated in the backward side decreases significantly, resulting in increase of carry of the ball. In other words, the concave dimples and the convex dimples play the same role in terms of aerodynamics of the ball, allowing the ball to travel further. 
         [0010]    In this case, relative roughness (standard deviation with respect to a center) of a golf ball with convex dimples may be maintained similar to relative roughness of a golf ball with concave dimples, such that stability of carry of the golf ball is ensured. 
         [0011]    In addition, due to the convex dimples which may possibly trigger more augmented, frictional power with respected to a golf club, backspin can easily take place on the ball with convex dimples; hence, more accurate control of the ball could be enabled when the ball is hit. 
         [0012]    Moreover, the convex dimples of the golf ball enlarge the area of contact with a putt, so that the golf ball can be more accurately directed in a hitting direction. 
         [0013]    Furthermore, the golf ball with convex dimples is much easier to be manufactured compared to a golf ball with concave dimples since the molding process is easier, and thus various shapes of dimples can be molded with ease and reduction of manufacturing cost can be realized. 
         [0014]    Other features and aspects may be apparent from the following detailed explanation with the drawings, and the claims. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0015]      FIG. 1  is a diagram illustrating an example of a form of a golf ball and various shapes of dimples. 
           [0016]      FIG. 2  is a graph showing a relationship between Reynolds number and drag coefficients according to relative roughness. 
           [0017]    Throughout the drawings and the detailed description, unless otherwise described, the same drawing reference numerals will be understood to refer to the same elements, features, and structures. The relative size and depiction of these elements may be exaggerated for clarity, illustration, and convenience. 
       
    
    
     DETAILED DESCRIPTION 
       [0018]    The following detailed description is provided to assist the reader in gaining a comprehensive understanding of the methods, apparatuses and/or systems described herein. Various changes, modifications, and equivalents of the systems, apparatuses and/or methods described herein will suggest themselves to those of ordinary skill in the art. Descriptions of well-known functions and structures are omitted to enhance clarity and conciseness. 
         [0019]    In the following description, a detailed description of known functions and configurations incorporated herein will be omitted when it may obscure the subject matter with unnecessary detail. 
         [0020]    Before describing the exemplary embodiments, terms used throughout this specification are defined. These terms are defined in consideration of functions according to exemplary embodiments, and can be varied according to a purpose of a user or manager, or precedent and so on. Therefore, definitions of the terms should be made on the basis of the overall context. 
         [0021]      FIG. 1  illustrates an example of a golf ball and various shapes of dimples of the golf ball. 
         [0022]    The golf ball has a surface with a plurality of dimples. On the surface of the golf ball, the dimples may be arranged in a regular pattern or in an irregular pattern. The number of dimples may be about 300 to 500. 
         [0023]    A shape of the dimple will be described as follows. 
         [0024]      FIG. 1(   a ) illustrates an example of concave dimples of a general golf ball. 
         [0025]      FIG. 1(   b ) illustrates an example of convex dimples corresponding to the general concave dimples. 
         [0026]      FIG. 1(   c ) illustrates an example of convex dimples having more protruding tops than the convex dimples shown in  FIG. 1(   b ). 
         [0027]      FIG. 1(   d ) illustrates an example of convex dimples having rather flat tops along a curved surface of the golf ball. 
         [0028]      FIG. 1(   e ) illustrates an example of small convex dimples, the number of which is greater than that of the dimples illustrated in  FIGS. 1(   b ) to  1 ( d ). 
         [0029]    As another example, the dimples may be in combination of the shapes shown in  FIGS. 1(   b ) to  1 ( e ). 
         [0030]    Factors that affect a relationship between a shape of a golf ball and the carry will be described. From an aerodynamic view, if the influence of the airflow over a golf ball in flight is neglected, dynamical conditions of the golf ball hit by a golf club determine the carry, and the dynamical conditions include an angle of the golf ball with respect to the ground when impact takes place and an initial velocity of the golf ball. Thus, if the golf ball is to be hit at an angle of 45 degrees, in consideration of the influence of the air, a launch angle of the golf ball may be required to be in practice smaller than 45 degrees. This is because the golf ball flies higher than an ideal parabolic trajectory due to backspin. 
         [0031]    In this case, the carry increases as the golf ball flies farther and a head speed increases. Lift due to backspin will now be discussed as a factor produced while the golf ball is flying in the air. Due to backspin on the golf ball, fluid increases in its speed on an upstream side of the golf ball in flight on which a velocity direction and a fluid direction are identical, that is, the upstream airflow is faster than the downstream airflow, a pressure on a downside of the golf ball is higher than a pressure of the upside, and thus a lift force is generated. As a result, the golf ball is lifted up and a duration of the flight is lengthened. That is, the carry increases. 
         [0032]    Air resistance prevents the golf ball from flying infinitely. There are two types of air resistance: one is form resistance which is produced by a difference between pressures applied on a forward-moving side and a backward-moving side of a ball, and which varies with the form of the golf ball, and the other is frictional resistance which is produced by friction between the air and the golf ball. The main cause of the resistance on the golf ball is the form resistance, and thus reduction in form resistance enables the golf ball to travel farther. 
         [0033]    Airflow is generated around a surface of the golf ball when the golf ball is flying. As the velocity of the golf ball increases, from the middle of the golf ball, the airflow starts far away from the surface. Then, the velocity of air is rapidly reduced from the middle of the golf ball, and thus a direction of the airflow is altered, resulting in lowering the air pressure in the backward side of the golf ball. Accordingly, the air pressure increases on the forward side of the golf ball and the air pressure decreases on the backward side, preventing the golf ball from flying further. 
         [0034]    Projections on the surface of the golf ball creates turbulence on a forward surface, which mixes the air actively, and thus the change of airflow takes place only on the backward side of the golf ball. At this time, the frictional resistance increases, but the form resistance can be substantially decreased. (while the effect by the frictional resistance (frictional drag) is only less than 10%, the effect by the pressure resistance (pressure drag) is 90%.) 
         [0035]    Therefore, if the surface of the golf ball is made uneven, the surface on which a low pressure is produced is reduced, so that the reduction in the form resistance of the golf ball is achieved, which causes the ball to travel further. 
         [0036]    Laminar flow refers to a fluid flowing in layers, and when the fluid flows slowly or even rather fast, viscosity of the fluid is so great that the fluid flows in layers. 
         [0037]    Turbulence occurs when fluid particles are mixing together and flowing chaotically. 
         [0038]    When Reynolds number Re (Re=(density of fluid*fluid velocity*linear dimension)/dynamic viscosity of fluid) is smaller than or equal to 2300, the fluid is defined as laminar flow, and otherwise, the fluid is defined as turbulent flow. 
         [0039]    Swirl refers to a flow of liquid or gas flowing in a spinning fashion. 
         [0040]    Experiments to distinguish laminar flow and turbulent flow were conducted by Osborne Reynolds in 1883. In the experiments, different colors of inks were dropped in water flowing in a pipe to show distinctly laminar flow and turbulent flow, and suggested definite variables that define two flows. The variables are referred to as “Reynolds number” in memory of his achievement. 
         [0041]    In order to reduce the form resistance, the air needs to flow smoothly along the surface of a ball. However, with the increase of velocity, the air cannot flow smoothly along the surface of the ball, and the airflow becomes farther from the surface from the middle of the ball. At this time, from the middle of the ball, the air velocity is dynamically decreased and the direction of airflow is changed. 
         [0042]    As such, if the airflow in the backward side of a blunt object is changed, the pressure at the corresponding position drops abruptly. Thus, a high pressure applied on a forward-moving side of the object and a low pressure applied on a backward-moving side may create a large form resistance, which prevents a ball from flying farther. In this case, if the surface of the ball is made slightly rough, turbulent flow is produced on the forward surface of the ball. The turbulent flow promotes mixing between fluid streams, and thus the change of airflow occurs only in the backward side of the ball. Accordingly, the area of the surface of the ball having a lower pressure is reduced, resulting in reduction in form resistance. The golf ball employs the above two types of principles. Namely, by providing small projections on a surface of the ball, the golf ball can travel two times farther than a golf ball without projections. 
         [0043]    Although objects are designed to have projections on their surface, some objects enjoy reduced residence, whereas the others do not, in accordance with their size and velocity. The possibility of reduction in resistance may be determined based on Reynolds number. 
         [0044]    Fluid flow is categorized into laminar flow and turbulent flow according to Reynolds number. At Reynolds number between about 40,000 and 400,000, form resistance is reduced by forming projections on an object. 
         [0045]    If Reynolds number is out of the range of 40,000 to 400,000, the overall resistance rather increases. Since Reynolds number of a golf ball in flight is about 50,000 to 150,000, form resistance may be reduced by forming projections on a surface of the golf ball. 
         [0046]    Since Reynolds number of a ping-pong ball is smaller than 40,000, a surface of the ping-pong ball is intentionally made smooth. Reynolds number of a base ball thrown by a major league pitcher, Chan Ho Park whose fastball reaches 150 km per hour, is about 300,000. For a ball as fast as or slower than 150 km/h, stitches on the ball may play a significant role in reducing resistance. On the other hand, since Reynolds number for a bullet is much greater than 400,000, a bullet with a rough surface decreases in its shot distance. 
         [0047]      FIG. 2  illustrates a graph showing an example of a relationship between Reynolds number and drag coefficients according to relative roughness. 
         [0048]    A diameter of a golf ball is 1.69 inches, and its weight is 0.0992 lb. In this example it is assumed that the golf ball is hit by a tee and flies at 200 ft/s. Reynolds number is obtained as a characteristic velocity of fluid (U)*a characteristic length of fluid (D)/kinematic viscosity is coefficient (v). The kinematic viscosity of the air is 1.57*10 −4  ft 2 /s. 
         [0049]    That is, Re=UD/v=(200 ft/s)(1.69/12 ft)/1.57*10 −4  ft 2 /s. A drag coefficient C D  is represented by a function of Reynolds number and relative roughness. A drag coefficient C D  of a golf ball with dimples is 0.25 and a drag coefficient C D  of a golf ball with a smooth surface is 0.51. In the case of Reynolds number of 5*10 4  to 3*10 5 , the drag coefficient of the dimpled golf ball is a half of the drag coefficient of a golf ball with a smooth surface. 
         [0050]    Reviewing again the definition of Reynolds number (Re), the same balls have the same characteristic length, and the kinematic viscosity of fluid is the same as the kinematic viscosity of the air at the same position and at the nearly same time. There is only a difference in characteristic velocity. That is, Reynolds number varies only with the velocity at which the ball is flying in the air. Generally, it is considered that carry of a driver is two times longer than carry of an iron  9 . Thus, the characteristic velocity is different by 2 1/2  times, and a characteristic velocity of the iron  9  may be defined as U=140 ft/s. Hence, if Reynolds number (Re D ) of the driver is Re D =1.79*10 5 , Reynolds number (Re I ) of the iron  9  is Re I =1.26*10 5 . 
         [0051]    The above example will be described in conjunction with  FIG. 2 . In the case of the first curve of the golf ball, the golf ball draws a stable curve while maintaining a drag resistance a half of that of a golf ball drawing a similar curve when Reynolds number is between about 0.8*10 5  to 3.0*10 5 . 
         [0052]    In case of a golf ball with a less rough middle curve and with a relative roughness of 5*10 3 , Reynolds number abruptly decreases from 1.0*10 5  to 2.0*10 5 , and C D  value is lowered and reaches the minimum value at 1.4*10 5  and rises again. When Reynolds number is greater than 2.0*10 5 , C D  of the golf ball with a less rough surface becomes greater than C D  of a general golf ball. 
         [0053]    Therefore, a golf ball having relative roughness smaller than 5*10 3  may be allowed to is have a longer carry. However, the stable carry of each type of golf club cannot be ensured within a Reynolds number range between 1.0*10 5  and 1.3*10 5 , and thus carry differences between golf clubs change abruptly. Furthermore, at Reynolds number greater than 1.3*10 5 , carry of a golf ball is shorter than that of the golf ball with manipulated relative roughness. 
         [0054]    In addition, in view of shapes and drag coefficients of dimples, relative roughness is a mean value of deviation between convex portions and concave portions out of an average line of a surface of a golf ball. Thus, the convex and concave portions do not have significant difference therebetween. The relative roughness of an object in flight is a mean value, and a drag coefficient may be obtained from the experimentally achieved graph illustrated in  FIG. 2 . Carry of golf balls having the same relative roughness is determined only by the initial velocity, and the carry is unrelated to the shape of dimples. Flight forms of balls having partially different relative roughness due to a diameter and shape of a dimple may be identified by experiments. The symmetry of the ball affects the stable flight of the ball. The symmetry is a degree of how symmetrical relative roughness is with respect to a center point of the ball according to the shapes and diameters of dimples on a partial area. 
         [0055]    The purpose of the research and development of a golf ball is to increase carry. However, a golf ball is supposed to undergo tests which are conducted in accordance with international standard rules before the ball is to be used. 
         [0056]    The diameter of the ball must not be less than 1.680 inches (42.67 mm). This specification will be satisfied if, under its own weight, a ball falls through a 1.680 inches diameter ring gauge in fewer than 25 out of 100 randomly selected positions, the test being carried out at a temperature of 23+/−1° C. 
         [0057]    A golf ball must weigh no more than 45.93 g (1.620 oz). 
         [0058]    The ball must not be designed, manufactured or intentionally modified to have properties which differ from those of a spherically symmetrical ball. 
         [0059]    The flight velocity must be no more than 76.2 m/s (250 ft/s) as measured on the R&amp;A equipment. The maximum error tolerance is 2%, and a temperature for the test is 23±1 ° C. 
         [0060]    The combined carry and roll of the ball, when tested on an apparatus approved by the R&amp;A, must not exceed the distance (256 m, i.e., 280 yd) specified under the conditions (error tolerance of 6%) set forth in the Overall Distance Standard for golf balls on file with the R&amp;A. 
         [0061]    The current standard rules for a golf ball are as described above, and this indicates the carry is regulated. An upper limit on repulsive forces of a ball and a golf club at a time of impact is imposed by regulating the flight velocity of the golf ball to have an initial velocity of 76.2 m/s (250 ft/s) within an error tolerance of 2%, and by regulating the combined carry and roll of the ball not to exceed 256 m (280 yd) within an error tolerance of 6%. In other words, the carry is regulated not by human capability but by development and design of equipment. Even though it appears that golf balls and golf clubs are developed separately, due to the restricted range by the regulations, there must be correlation between the golf balls and the golf clubs in terms of development. 
         [0062]    For example, in the case of a driver shot at 250 ft/s (the flight velocity is predicted as 200 ft/s in consideration of air resistance), Reynolds number is about 1.8*10 5 , and Reynolds number is zero if a ball is not hit at a time of pitch shot. Reynolds number may be about 5*10 4  to 2*10 5  when a ball is normally hit even in consideration of individuals&#39; capabilities. Referring to the graph illustrated in  FIG. 2 , drag coefficients change abruptly between 4.0*10 4  and 8*10 4 , but if the ball is hit by a half swing or as a control shot, a drag coefficient is increased and the carry is advantageously decreased. In addition, between 8*10 4  and 3*10 5 , the drag coefficients are constant, and thus the carries between golf clubs can be maintained equally. 
         [0063]    Relative roughness of golf balls in recent use conform to standard rules that regulate the current golf courses, golf clubs and golf equipment, and changes between concave or convex patterns of dimples do not affect the relative roughness. 
         [0064]    A number of examples have been described above. Nevertheless, it should be understood that various modifications could be made. For example, suitable results may be achieved if the described techniques are performed in a different order and/or if components in a described system, architecture, device, or circuit are combined in a different manner and/or replaced or supplemented by other components or their equivalents. Thus, other implementations are within the scope of the following claims.