JP4190971B2 - Method for evaluating dimple effect of golf ball and golf ball - Google Patents

Description

  The present invention relates to a method for evaluating a dimple effect of a golf ball and a golf ball. More specifically, the present invention relates to a method for simply evaluating air resistance when a golf ball having dimples on the surface flies in space.

Conventionally, various analysis methods have been proposed in order to know the aerodynamic characteristics of objects such as golf balls and baseballs. Particularly, in golf balls, a large number of dimples (recesses) provided on the surface are large in the aerodynamic characteristics of the balls. Because of the influence, the determination of the dimple shape and the like is an important matter.
The dimple shape of a golf ball is evaluated for its air resistance, etc. by making a prototype of a golf ball or a model with the dimple and performing a flight test or a wind tunnel experiment. In recent years, the aerodynamic characteristics of a golf ball have been evaluated by fluid simulation using a computer because it consumes time and money.

For example, in Japanese Patent Laid-Open No. 2002-250739 and Japanese Patent Laid-Open No. 2002-358473, a golf ball on which a dimple to be evaluated is formed is formed on a computer, and the air flow around the ball is simulated and the resistance of the entire sphere The coefficient and lift coefficient are calculated to evaluate the aerodynamic characteristics of the ball.
In JP-A-2002-340735, a cylindrical model having a groove is formed on a computer, and a dimple of a golf ball is regarded as a groove, and a surrounding object such as a sphere having the same cross-sectional shape as the cut surface of the cylindrical model is used. It is applied to the analysis of gas flow.

However, according to each of the above patent documents, the aerodynamic characteristics of a ball as a whole ball provided with a plurality of dimples are evaluated macroscopically, but not with dimples alone. In these methods, since the entire ball is reproduced on a computer, a large calculation cost is required, which is a serious problem in product development of golf balls.
In order to avoid this problem, even if the dimple is evaluated alone, the evaluation index for the dimple alone has not been established, and it can be understood what evaluation of the dimple would lead to the evaluation of the aerodynamic characteristics of the entire ball. The situation is not.
JP 2002-250739 A JP 2002-358473 A JP 2002-340735 A

  The present invention has been made in view of the above problems, and an object of the present invention is to propose a method for evaluating the aerodynamic characteristics of a golf ball having dimples on the surface with a single dimple.

In order to solve the above-mentioned problems, the present invention is to fly the strength of a longitudinal vortex having a vortex main axis in the same direction as the air flow direction among the vortices generated by dimples on the surface of the golf ball, while reducing the air resistance against the golf ball. As a standard to enhance the characteristics ,
The strength of the longitudinal vortex is such that the flow direction of the gas flowing on the dimple is the Y direction, the direction perpendicular to the normal direction of the dimple position and the direction perpendicular to the gas flow direction is the X direction, and the Y direction The X direction distribution of the flow velocity is sampled and evaluated by the speed difference between the maximum speed and the minimum speed among the sampled Y direction speeds. The greater the speed difference, the greater the strength of the longitudinal vortex flow, and the above air resistance. It provides an evaluation method of the dimple effect of the golf ball that has been evaluated and is reduced.

As will be described later, the present inventor observes the vortex structure around the dimples (concave portions) of the golf ball in detail to generate a spiral longitudinal vortex having a main axis in the same direction as the air flow direction. I found out. Therefore, when the longitudinal vortex swirling in the shear direction of the flow is generated more strongly due to the dimple effect, the energy of the gas flow becomes higher, the separation point of the boundary layer flow moves backward, and the resistance coefficient of the golf ball Can be determined to be small.
Therefore, according to the above method, it is possible to easily evaluate the air resistance of the golf ball simply by evaluating the strength of the vertical vortex of the golf ball dimple alone. As a result, it is possible to easily perform dimple design of a golf ball with low air resistance in a short time.

The strength of the longitudinal vortex is such that the flow direction of the gas flowing on the dimple is the Y direction, the direction perpendicular to the normal direction of the dimple position and the direction perpendicular to the gas flow direction is the X direction, and the Y direction The X direction distribution of the flow velocity is sampled and evaluated by the speed difference between the maximum speed and the minimum speed among the sampled Y direction speeds. The greater the speed difference, the greater the strength of the longitudinal vortex flow, and the above air resistance. it is evaluated and becomes smaller.

In the X-direction distribution of the Y-direction velocity of the gas flowing on the dimples of the golf ball, if the velocity difference between the maximum velocity and the minimum velocity among these increases, the shear force of the flow increases, so there is an axis in the Y-direction. It can be said that the longitudinal vortex is strongly generated. If the vertical vortex is strongly generated, it can be determined that the separation point of the boundary layer flow on the surface of the golf ball transitions to the wake side, and the resistance coefficient of the golf ball to the gas becomes small.
Therefore, it is possible to easily evaluate the air resistance of the golf ball simply by evaluating the gas velocity on the dimple alone of the golf ball.
Note that the above evaluation method may be applied to computer simulation, or may be performed by experimentation.

The dimple has a symmetrical shape with respect to the central axis in the Y direction, and the X direction distribution of the Y velocity of the gas is sampled in a half region of the dimple divided by the central axis.
That is, when the dimple shape is symmetric with respect to the gas flow direction, it is only necessary to determine the speed difference between the maximum speed and the minimum speed of each Y-direction speed distributed in the X direction of the gas only in one half region. .

One dimples form a golf ball having a surface on the computer, to form a limited space around the dimples of the golf ball, a large number to form a cell partitioned dividing the limited space,
Gas is introduced from one side of the finite space along the dimple surface of the golf ball , and is allowed to flow through the finite space and flow out from the other side to calculate the gas velocity for each cell in the finite space. The intensity of the longitudinal vortex is evaluated by simulating the velocity distribution of the gas around the dimple.

Thus, by calculating the velocity distribution of the flow around the dimples of the golf ball by simulation on a computer, the velocity difference between the maximum velocity and the minimum velocity of each Y-direction velocity distributed in the X direction can be easily calculated. And the time required for analysis can be greatly reduced .

  The simulation is performed on a computer while changing the shape, area, depth, cross-sectional shape and / or volume condition of the dimple of the golf ball, and the shape, area, depth, cross-sectional shape and / or volume of the dimple are The correlation with the strength of the longitudinal vortex is evaluated.

  By doing the above, by simulating by changing each condition of the shape, area, depth, cross-sectional shape, and volume, which are factors determining the dimples of the golf ball, and evaluating the speed of the calculation results, The correlation between the longitudinal vortex flow and each of the above factors can be easily obtained.

Further, the present invention is based on the method for evaluating the dimple effect of the golf ball, wherein the dimple shape, area, depth, cross-sectional shape and / or volume are set so as to enhance the longitudinal vortex Offering a ball.
That is, a golf ball having a low air resistance can be provided by adopting the shape, area, depth, cross-sectional shape and / or volume of a dimple that generates a strong longitudinal vortex determined by the above evaluation method. it can.

As is clear from the above description, according to the present invention, the energy of the gas flow is higher when the longitudinal vortex swirling in the shear direction of the flow is generated more strongly in the dimples of the golf ball, and the boundary layer flow is separated. It can be evaluated that the point moves backward and the air resistance against the golf ball becomes small.
Specifically, it is possible to evaluate the air resistance of a golf ball having dimples only by evaluating the speed difference between the maximum speed and the minimum speed among the Y-direction speeds distributed in the X direction of the gas flowing on the dimples. it can. That is, since the shear force of the flow increases as the speed difference increases, it can be determined that a longitudinal vortex having an axis in the Y direction is strongly generated and the resistance coefficient of the golf ball is reduced. If this evaluation method is used for computer simulation, the air resistance of a golf ball can be easily evaluated by simply evaluating the gas velocity on the dimples, for example, in designing a golf ball, without using a prototype ball. It is possible to improve design efficiency.

First, before describing the embodiment of the present invention, a vertical vortex structure generated in a dimple of a golf ball found by the present inventor will be described.
As shown in FIG. 1, the gas flowing on the surface of the golf ball G having the dimple D flows at a high flow rate without being affected by the dimple D while the gas flowing away from the surface flows. In the boundary layer flowing in the vicinity of the surface, a phenomenon that the flow path rapidly expands in the dimple D portion occurs, so that the flow velocity becomes slow. This is the same principle as the flow deceleration phenomenon in a generally known rapid expansion pipe.

Considering the above phenomenon from above the dimple D, as shown in FIG. 2A, the gas flowing in in a uniform flow is a point A → B point → C because the dimple D is circular. The speed starts decreasing in the order of the points. That is, looking at the velocity distribution in the shear direction at point C, a velocity difference is generated such that the velocity on the center side is small and the velocity on both sides is large.
When a velocity difference in the shearing direction is generated with respect to the flow in this way, a shearing force is generated in the gas flow, and the gas is twisted. As shown in FIGS. 2B and 2C, the same direction as the gas flow direction is obtained. A spiral longitudinal vortex V having a main axis is generated.

  In general, in a gas flow around an object, generating a strong vortex increases the boundary layer energy, and the separation point of the boundary layer from the object can be moved backward to reduce the resistance coefficient. I know that. Therefore, it can be paraphrased that if the dimple that strongly generates the longitudinal vortex V is formed, the resistance coefficient of the golf ball can be reduced, that is, a dimple having a large velocity difference in gas flow velocity distributed in the shear direction. It can be said that the more the golf ball has, the better the flight characteristics with less air resistance.

Hereinafter, embodiments of the present invention will be described with reference to the drawings.
FIG. 3 shows a flowchart of a simulation method using a program to which the dimple effect evaluation method of the present invention is applied.

  First, as a simulation preparation stage, a hemisphere 10 having one dimple 10a having a circular arc cross section as shown in FIG. It is created three-dimensionally in the virtual space of the computer. Next, in order to model a space to be simulated for gas flow, as shown in FIG. 4A, in the space around the spherical surface side of the hemisphere 10, a finite space 20 is formed by dividing it into blocks. Yes. At this time, as shown in FIG. 4C, the dimple 10a of the hemisphere 10 is arranged at a position of 90 ° with respect to the Y direction which is the flow direction.

  Here, the target object is not a sphere but a hemisphere, and the finite space 20 is formed only on the spherical surface side of the hemisphere 10 because the sphere is set on the center line of the flow space and the whole is not calculated. In both cases, the sphere has a symmetrical shape, and the phenomenon can be grasped by calculating only the half side with respect to the flow direction. Therefore, the calculation time is reduced only for the half side.

  At this time, the length L1 of the finite space 20 is not less than 15 times the depth of the dimple 10a so that the state of change in the velocity of the gas flow caused by the dimple 10a on the surface of the hemisphere 10 can be sufficiently evaluated in consideration of the calculation efficiency. 1000 times or less, or 3 times or more of the diameter of the hemisphere 10 and 200 times or less. The width L2 is 10 times to 500 times the depth of the dimple 10a, or 2 times to 100 times the diameter of the hemisphere 10. The height L3 is set to be not less than 10 times and not more than 500 times the depth of the dimple 10a, or not less than 2 times the diameter of the hemisphere 10 and not more than 100 times.

  Such a finite space 20 is partitioned and divided into a lattice shape so as to include the surface of the hemisphere 10 to form a large number of cells 20a. In order to set the size of the cell 20a to be divided to be sufficiently smaller than the fluctuation scale of the gas flow, the calculation accuracy is improved by dividing the cell 20a around the hemisphere 10 and, in particular, in the downstream region by small cells. The part away from the body 10 is devised to increase the cell size to shorten the calculation time.

  The shape of each cell 20a is a hexahedron and is defined as a hexahedron, and in order to define the position coordinates of the cell node 20b, the gas flow direction in the finite space 20 is the Y direction, and the normal direction to the dimple 10a of the hemisphere 10 is Z. The direction perpendicular to the direction and the Y / Z direction is the X direction. The shape of the cell 20a can be formed in a shape such as a triangular pyramid, a quadrangular pyramid, a triangular prism, etc., in addition to a hexahedron, which is a hexahedron. I do not care.

  After performing the modeling as described above, the simulation program causes a uniform flow of gas (air) to flow from one surface side of the finite space 20 as shown in FIG. It passes through the inside and flows out from the other side. The governing equation relating to such a gas flow uses the following three-dimensional compressible Navier-Stokes equation.

  Here, Q represents a variable vector, and F (Q) and G (Q) represent inviscid and viscous flux vectors, respectively. n is an outward unit normal vector on the boundary surface ∂Ω of the inspection volume Ω. This governing equation is discretized by the cell nodal finite volume method as shown below, and the air flow is calculated and analyzed for each cell 20a in the finite space 20.

Here, ΔS _ij is the area of the inspection volume boundary surface with respect to the side consisting of the lattice points i and j, V _i represents the volume of the inspection volume Ω _i , and h is the inviscid numerical flux perpendicular to the inspection volume boundary surface Q _ij ⁺ and Q _ij ⁻ are values on both sides of the examination volume boundary surface.
Note that the simulation method may be performed by appropriately selecting a finite difference method, a finite element method, a boundary element method, or the like in addition to the finite volume method in consideration of simulation conditions and the like. Moreover, you may use a turbulent flow model for the said simulation method.

  If the finite volume method is used, the calculation by the discretized equation is performed by approximating the balance of physical quantities at the boundary of the cell 20a, and the gas velocity, which is a motion element related to the gas flow at a specific time, The movement of the gas flow in the entire finite space 20 is quantified by obtaining the flow direction and the gas pressure on the surface of the hemisphere, and combining the calculation results of these cells 20a. This is calculated every minute time dt, and the movement of the gas flow in each time zone is digitized.

Next, the strength of the generation of the vertical vortex in the dimple 10a of the hemisphere 10 is evaluated using these calculation results.
At a position separated from the upstream end of the dimple 10a by a distance of 0% to 50% of the diameter in the Y direction, the X direction has the same width as the dimple 10a and has a height 100 times the dimple depth in the Z direction. The X-direction distribution of the Y-direction velocity of the gas in the sampling cross section within the rectangular region is extracted. At this time, since the dimple 10a is symmetric with respect to the Y direction, sampling is performed only in one half region of the dimple 10a with respect to the Y direction. The number of sampling points is preferably 5 or more in consideration of accuracy, and 1000 or less is preferable in consideration of calculation time.

Among the speeds in the Y direction distributed in the sampling section, the speed difference between the maximum speed and the minimum speed is calculated. It is determined that the larger the speed difference, the stronger the vertical vortex having an axis in the Y direction, and the lower the air resistance of the hemisphere 10.
Then, by changing the shape, area, depth, cross-sectional shape, and volume conditions of the dimple 10a and performing the above simulation under various conditions, the optimum dimple shape, area, depth, and cross-sectional shape with low air resistance are obtained. Find the volume.

  As described above, if the simulation using the evaluation method of the present invention is performed, the resistance coefficient of the golf ball can be easily evaluated by merely evaluating the gas velocity in the dimple without making a trial golf ball. This makes it possible to dramatically improve design efficiency.

  Note that the present invention is not limited to the above-described embodiment, and the calculation target can be appropriately increased or decreased from an object having only one dimple to an object having a plurality of dimples. In addition, when a rotating sphere is to be a simulation target, the tangential direction component of the sphere surface is calculated as the velocity on the sphere surface by the rotation speed of the sphere, instead of making the velocity of the sphere surface zero. Good. Furthermore, in addition to the uniform flow of the gas inflow and outflow into the finite space, a velocity distribution or a turbulence condition of the airflow may be added to the inflow velocity as a component according to the simulation conditions.

Hereinafter, specific examples of the embodiment will be described.
(Example 1)
In the case of simulating a change in air resistance due to dimples provided on the golf ball, in Example 1, the diameter of the hemisphere 10 is 42.7 mm, the length L1 of the finite space 20 is 2500 mm, the width L2 is 500 mm, The height L3 is set to 1000 mm. The hemispherical body 10 is provided with only one dimple 10a which is a substantially hemispherical depression. The circular dimple 10a has a diameter of 3.8 mm, a depth of 0.15 mm, a cross-sectional shape of a single radius, a top surface, and a top surface. The visual area is 11.34 mm ² , and the volume in the dimple is 0.852 mm ³ .

  In the present example, assuming that the golf ball flies in the air at a speed of 50 m / s, a simulation was performed by flowing a gas from one side of the finite space 20 in a uniform flow of 50 m / s. In addition, the velocity component on the surface of the hemisphere 10 was set to zero with the surface of the hemisphere 10 not slipping.

A simulation is performed under the above conditions, and a sampling cross section is set at a position 15% away from the upstream end of the dimple 10a in the Y direction. The sampling cross section has the same width as the dimple 10a at the 15% position in the X direction and a height of 4d from the bottom of the dimple 10a when the depth at the 15% position is d in the Z direction. A rectangular region having a thickness is used. The X-direction distribution of the Y-direction velocity of the gas in the sampling section was extracted at an arbitrary time. Of the speeds distributed in the sampling section, the difference between the maximum speed and the minimum speed was calculated to be about 20 m / s.
When the velocity distribution is visualized, it becomes as shown in FIG. Visualization of the gas velocity is performed by inputting the calculated value by the above simulation into commercially available visualization software (FIELD VIEW: manufactured by Intelligent Light, USA). FIG. 6A shows that the longer the vector, the faster the air velocity. The speed can also be recognized by the color of the vector, blue is 0 to 7.5 m / s, green is 7.5 to 15 m / s, yellow is 15 to 22.5 m / s, and red is 22. 5 to 30 m / s.

(Example 2)
In the second embodiment, the hemisphere 10 is provided with only one dimple 10a, which is a substantially hemispherical depression. The dimple 10a has a diameter of 3.9 mm, a depth of 0.1 mm, a cross-sectional shape of a single radius, and an upper surface. The visual area is 11.94 mm ² and the volume in the dimple is 0.598 mm ³ . Other conditions are the same as in the first embodiment.
Visualizing the velocity distribution of each velocity in the Y direction of the gas distributed in the X direction in the sampling cross section is as shown in FIG. The speed difference between the maximum speed and the minimum speed among the speeds distributed in the sampling cross section was calculated to be about 13 m / s.

(Evaluation)
Comparing Example 1 and Example 2 above, Example 1 has a greater difference in flow velocity in the shear direction than Example 2. Therefore, Example 1 has a stronger shear force against the gas flow on the dimple 10a. It can be said that vertical vortices are generated. That is, it can be evaluated that Example 1 is a dimple excellent in flight characteristics because the separation point is retracted to the wake side and air resistance is reduced.

  Next, as support for the simulation results of Example 1 and Example 2, 198 dimples similar to Example 1 were arranged on the surface of a golf ball having a diameter of 42.7 mm at equal intervals, and Example 2 198 similar dimples were arranged on the surface of a golf ball having a diameter of 42.7 mm at equal intervals, and flight experiments were conducted. The conditions of the flight experiment were a launch speed of 50 m / s, a launch angle of 20 °, and a ball spin of 2500 rpm.

As a result, the flight distance of the golf ball corresponding to Example 1 was 221 years, and the flight distance of the golf ball corresponding to Example 2 was 213 years.
That is, similar to the simulation results, it was confirmed that the use of the dimples of Example 1 had less air resistance and better flight characteristics, and that this evaluation method was correct.

It is the schematic showing the gas flow around a dimple. (A) is a plan view showing a velocity distribution on a dimple, (B) is a plan view showing generation of a vertical vortex, and (C) is a cross-sectional view showing generation of a vertical vortex. It is a flowchart of the simulation using the evaluation method of the dimple effect of this invention. (A) The schematic perspective view showing the lattice division of a finite space, (B) is the schematic perspective view showing the lattice division of a hemisphere, (C) is explanatory drawing which shows arrangement | positioning of the hemisphere in a finite space. It is the schematic showing the lattice point of the lattice division used as the operation object by the finite volume method. FIG. 3 is a visual diagram of speed and direction on a dimple according to the first embodiment. FIG. 6 is a visual diagram of speed and direction on a dimple of Example 2.

Explanation of symbols

10 hemisphere 10a dimple 20 finite space 20a cell

Claims (5)

Of the vortex generated by the dimples on the surface of the golf ball, the strength of the longitudinal vortex having the vortex main axis in the same direction as the air flow direction is used as a standard for improving the flight characteristics by reducing the air resistance to the golf ball,
The strength of the longitudinal vortex is such that the flow direction of the gas flowing on the dimple is the Y direction, the direction perpendicular to the normal direction of the dimple position and the direction perpendicular to the gas flow direction is the X direction, and the Y direction The X direction distribution of the flow velocity is sampled and evaluated by the speed difference between the maximum speed and the minimum speed among the sampled Y direction speeds. The greater the speed difference, the greater the strength of the longitudinal vortex flow, and the above air resistance. A method for evaluating the dimple effect of a golf ball that is evaluated to be small.   2. The dimple has a symmetrical shape with respect to a central axis in the Y direction, and an X-direction distribution of the velocity in the Y direction of the gas is sampled in a half region of the dimple divided by the central axis. Of evaluating the dimple effect of a golf ball. One dimples form a golf ball having a surface on a computer,
A finite space is formed around the dimples of the golf ball, and the finite space is partitioned to form a large number of cells.
Gas is introduced from one side of the finite space along the surface of the dimple of the golf ball , and is allowed to pass through the finite space and flow out from the other side, and the gas velocity is adjusted for each cell in the finite space. Calculate and simulate the velocity distribution of the gas around the dimple,
Of the vortex generated by the dimple, the dimple effect of the golf ball is evaluated based on the strength of the longitudinal vortex having the vortex principal axis in the same direction as the air flow direction as a criterion for improving the flight characteristics by reducing the air resistance against the golf ball. Evaluation method. One dimples form a golf ball having a surface on a computer,
Change one or more conditions of the shape, area, depth, cross-sectional shape, and volume of the dimple,
A finite space is formed around the dimples of the golf ball, and the finite space is partitioned to form a large number of cells.
Gas is introduced from one side of the finite space along the surface of the dimple of the golf ball , and is allowed to pass through the finite space and flow out from the other side, and the gas velocity is adjusted for each cell in the finite space. Calculate and simulate the velocity distribution of the gas around the dimple,
Of the eddy currents generated by the dimples, the strength of the longitudinal eddy current having the vortex main axis in the same direction as the air flow direction is used as a standard for improving the flight characteristics by reducing the air resistance to the golf ball,
A method for evaluating the dimple effect of a golf ball, wherein the correlation between the shape, area, depth, cross-sectional shape, and volume of the dimple and the strength of the longitudinal vortex generated by the dimple is evaluated.   The dimple shape, area, depth, cross-sectional shape and / or volume are set so as to strengthen the longitudinal vortex based on the golf ball dimple effect evaluation method according to claim 1. Golf ball.

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