JP2007190365A - Method for acquiring optimal aerodynamic characteristic of golf ball, and custom-made system for golf ball dimple using the method - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To acquire the drag coefficient Cd and lift coefficient Cl of the golf ball optimal for the hitting initial conditions of each golf ball and the taste of each golfer, and to allow a golf ball to be made to order, which has dimples optimally designed for each golfer. <P>SOLUTION: A ball speed in hitting the golf ball, a back spin amount, and a hitting angle are defined as the initial conditions. An aerodynamic coefficient composed of the drag coefficient and lift coefficient of the golf ball is defined as a design variable number. The carry of the ball when the ball falls on the ground, a fall speed, and a fall angle, or/and the spin amount at the fall are defined as target functions. The design variable number for obtaining the optimal target function with respect to the initial conditions is obtained and a method for acquiring the optimal aerodynamic characteristic of the golf ball is used, so that the golf ball dimple optimal for the initial conditions and taste of the golfer is made to order. <P>COPYRIGHT: (C)2007,JPO&INPIT

Description

  The present invention relates to a method for obtaining an optimum aerodynamic characteristic of a golf ball and a custom-made system for a golf ball using the method. Specifically, the method differs depending on a golfer's impact and a golf club shaft (hereinafter abbreviated as a club) to be used. The golf ball dimple having the aerodynamic characteristics corresponding to the golf ball's launch characteristics and golfer's preference using the acquisition method while acquiring the optimum aerodynamic characteristics of the golf ball with respect to the initial launch conditions of the golf ball. It provides a system that can be customized.

Conventionally, it has been known that the golfer's hitting form, the initial launch conditions (initial speed, spin rate, launch angle, etc.) according to the golfer's club and the aerodynamic characteristics of the golf ball affect the flight distance. It has been.
It is generally said that the smaller the drag coefficient (Cd) of the aerodynamic characteristics of the golf ball, the better when trying to fly the golf ball far away. Depending on the type of club to be used, the aerodynamic characteristics of golf balls that are ideal for different launch initial conditions have not been sufficiently researched and clear knowledge has not been made.

In order to obtain this knowledge, the actual trajectory test is performed with a golf ball having various aerodynamic characteristics under various initial launch conditions, or what trajectory is obtained by using a trajectory equation whose accuracy is sufficiently confirmed. Only a method of predicting this by calculation is employed.
However, the former method requires actual tests at random, and the conventional calculation method used for prediction by the latter ballistic calculation not only takes time and effort. There is a high possibility that the optimal solution cannot be reached.
Therefore, of course, based on the initial launch conditions of the golfer, scientifically know what dimples are suitable in relation to the flight performance that the golfer emphasizes and recommend it to the golfer. The system is not built.

  As described above, a high-precision analysis method has not been obtained for the relationship between the initial conditions at launch and the aerodynamic characteristics of the golf ball, but optimal dimples were provided according to the initial launch conditions and preferred flight characteristics of each golfer. In order to provide a golf ball, it is desired to establish a method capable of acquiring the aerodynamic characteristics of a golf ball having dimples that are optimal for the initial launch conditions.

  In relation to this, as a conventional method for measuring the aerodynamic characteristics of a golf ball or designing a golf ball, JP 2004-184236 A (Patent Document 1) and JP 2005-103127 A (Patent Document 2) are disclosed. Proposed.

Patent Document 1 proposes a method for measuring the rotation characteristics and flight characteristics of a sphere, and as shown in FIG. 8, a rotating sphere with a mark on the surface is photographed by the CCD camera 2 and the micro flash 3 of the measuring apparatus 1. At the same time, a virtual sphere is created by the computer 4, the virtual sphere is subjected to posture displacement operation so that the two-dimensional virtual mark coordinates of the virtual sphere coincide with the photographed two-dimensional video mark coordinates, and the posture displacement operation amount is referred to as a genetic algorithm. It is obtained by calculation according to the optimization method, and the rotational characteristics and flight characteristics of the sphere are measured in a short time.
However, Patent Document 1 does not measure the rotational characteristics and flight characteristics of the golf ball according to the initial launch conditions of the golf ball, and until a golf ball having rotational characteristics and flight characteristics suitable for the initial launch conditions can be found. In addition, no specific guidelines for golf ball design have been presented.

In Patent Document 2, as shown in FIG. 9, the head speed is maximized by using the ratio between the first time T1 from the start of backswing to the top state and the second time T2 from the top state to hitting. And calculating an optimum value of the vibration frequency of the vibration form, selecting a golf club model based on the calculated value, and calculating a swing behavior for the selected golf club model.
However, in the method of designing a golf club or golf ball in Patent Document 2, it is necessary to design an optimal golf ball and golf club for each golfer, and there is a problem that it takes time and cost.

JP 2004-184236 A JP 2005-103127 A

  The present invention has been made in view of the above problems, and analyzes and acquires the optimal aerodynamic characteristics of each golf ball for each golfer's strike and the initial launch condition of the golf ball that is biased by the club to be used. It is an object to provide a golf ball having a dimple that is optimal for a golfer's unique launch initial condition and a golfer's preference using a method of obtaining the golf ball.

In order to solve the above-mentioned problems, first, as a first invention, a method for obtaining an optimum aerodynamic characteristic of a golf ball is provided.
That is, as the first invention,
The initial conditions are the ball speed (initial speed), backspin amount, and launch angle when launching a golf ball.
The design coefficient is the aerodynamic coefficient that consists of the drag coefficient and lift coefficient of the golf ball.
The objective function is the ball flight distance, drop speed, drop angle, or / and spin amount when falling on the ground,
There is provided a method for obtaining an optimum aerodynamic characteristic of a golf ball, wherein the design variable for obtaining an optimum objective function with respect to the initial condition is obtained.

  Specifically, for example, the Reynolds number and spin rate of the golf ball are obtained from the initial conditions, a neural network is constructed between the Reynolds number and spin rate, and the drag coefficient and lift coefficient. The objective function is obtained using a ballistic equation from the drag coefficient and lift coefficient related to the Reynolds number and spin rate, and the initial condition.

  In addition, the objective function obtained using the ballistic equation is provided with target values for the ball flight distance, drop speed, drop angle, and spin amount at the time of fall. It is preferable to set a simple objective function and search for the design variable that becomes the optimal objective function by using a genetic algorithm from the objective function obtained by the ballistic equation.

For example, the Reynolds number and spin rate of the hit golf ball are calculated or measured in advance under various launch initial conditions in which the golf ball is hit with a club made of iron, wood, and wood edge. The golf ball Reynolds number and spin rate that change according to the initial launch conditions are combined with the drag coefficient and lift coefficient of the golf ball that change depending on the dimple pattern, size, depth, etc. The fall angle and the spin amount at the time of fall are calculated, and the drag coefficient and lift coefficient at which this calculated value (objective function) is optimal are obtained.
That is, by obtaining the optimum aerodynamic characteristics of the golf ball corresponding to each initial launch condition, the golf ball dimple having the aerodynamic characteristics is designed to provide a golf ball suitable for each golfer. .
Similarly, by determining the Reynolds number and spin rate of the golf ball in advance as the initial launch condition corresponding to the golfer's handicap, physical strength, etc., according to the characteristics of the golfer such as the golfer's handicap in the same manner as described above. A golf ball having optimal dimples can be provided. In addition, although conditions, such as this golfer's handicap and physical strength, can also be set for every golfer, the conditions may be grouped and the average condition in the group may be set for every group. .

As described above, there are a number of initial launch conditions depending on the type of club used and the golfer's own conditions. Accordingly, there are many types of combinations of Reynolds number and spin rate corresponding to each launch initial condition. On the other hand, the drag coefficient and lift coefficient of a golf ball are various depending on the dimple pattern, size, depth, etc. of the golf ball.
As described above, when the various types of conditions combined with the Reynolds number and the spin rate number and the various types of conditions combined with the drag coefficient and the lift coefficient are further combined, the combination pattern becomes enormous.
Therefore, according to the present invention, as described above, a neural network is constructed between the condition combining the Reynolds number and the spin rate and the condition combining the drag coefficient and the lift coefficient.

Neural networks are engineered with clever and diverse information processing functions in living organisms. Learning functions, control functions, signal processing functions, pattern estimation functions, diagnostic functions, and optimization that closely resemble the human brain It is constructed as a network having functions.
A neural network (neural circuit) is a network that connects nerve cells (neurons), and the neurons have a function of receiving signals from other neurons, integrating those signals, and transmitting them to other neurons. A connection point between neurons is called a synapse, and one neuron transmits signals to other neurons via a large number of synapses.
This neural network is provided with a plurality of layers to which a plurality of neurons are input, and the neurons of these layers are combined in a one-to-one relationship via the neural network to obtain output data, which is used as a learning sample for other neurons. The learning sample is learned by a combination of. This learning method is a learning using back-propagation, and the structure of the system transforms in response to input from the outside world. In the biological nervous system, synaptic connections between neurons It is understood that learning is performed by changing the strength of.
Therefore, in the theory of neural networks, learning means that the connection load value (load matrix) between synapses is changed according to the input.

In the present invention, the “Reynolds number and spin rate” corresponding to the initial launch condition are input to the input layer of the neural network, and the “drag coefficient and lift coefficient” of the golf ball as design variables are input via the neurons in the intermediate layer. Output to the output layer. That is, the neural network is used as a function for combining the “reynolds number and spin rate” of the input layer and the “drag coefficient and lift coefficient” of the output layer with the neurons of the intermediate layer.
For example, once the learning system that outputs one condition in the input layer combined with all the neurons in the intermediate layer is finished, the neuron obtained in the previous learning for any other condition in the next input layer A system that outputs in accordance with the combination of is constructed by the learning function.

  The number of neurons in the intermediate layer between the input layer and the output layer is preferably 2 or more and 20 or less, particularly preferably 3 to 5. If the number of neurons is too small, the response to sudden changes becomes worse, so it becomes difficult to express non-linearity. If the number is too large, the computational burden for learning increases. There is no synaptic connection between neurons in the same layer.

  In the present invention, a neural network is provided between the input layer and the output layer. However, the number of layers may be increased by adding layers for inputting other conditions. The number of layers to be added is preferably from 1 to 10 layers. In particular, about 2 to 4 layers are preferable.

  From the “drag coefficient and lift coefficient” of the golf ball combined with the “Reynolds number and spin rate” by a neural network and the initial launch conditions (initial velocity, launch angle, spin rate), the ballistic equation is expressed as described above. The golf ball flight distance, drop speed, drop angle, spin amount at the time of fall, etc., which are the objective functions, are calculated.

  At that time, as described above, since the objective function is a ball flight distance, a falling speed, a falling angle, and a spin amount at the time of falling, a target value of each objective function is set in advance, A single optimal objective function that combines the objective values of the objective function is set, and a genetic algorithm that is less likely to fall into a local optimal solution is selected from the various objective functions obtained by the ballistic equation. It is preferable to search for the optimum value.

For example, the maximum target value (AT) of the flying distance is 300 yards, the minimum target value (BT) of the falling angle is 10 degrees, the maximum target value (CT) of the falling angle speed is 40 m / s, and the minimum target of the spin rate at the time of falling The value (DT) is 100 rpm, and the total optimum objective function X is X = aA ′ + bB ′ + cC ′ + dD ′.
The a, b, c, and d are relative weights, for example, a = 1.0, b = 0.2, c = 0.3, and d = 0.4.
A ′ is A / AT, B ′ is B / BT, C ′ is C / CT, and D ′ is D / DT.

Until each objective function calculated using the ballistic equation reaches the target value, it repeats using the ballistic equation from the “drag coefficient and lift coefficient” combined with the “Reynolds number and spin rate” and the neural network and the initial conditions. The objective function is acquired. If the target value is not reached even after the predetermined number of times, the calculation is terminated.
The optimal objective function X is searched using the genetic algorithm as described above from the large number of objective functions thus obtained.

As is well known, genetic algorithms are variously modified by reproduction, selection and mutation, and are applied to the solution of optimization problems by applying the evolutionary process of genetic programs of living organisms to be passed on to the next generation. Algorithm.
In the present invention, the optimal drag function and lift coefficient of the optimum golf ball corresponding to the initial launch condition are accurately acquired by searching the optimal objective function from a large number of objective functions acquired by ballistic calculation using a genetic algorithm. .

It is preferable that the drag coefficient and lift coefficient of the golf ball as the design variables are obtained in advance for each dimple pattern of the golf ball.
In the present invention, the dimple pattern refers to the overall configuration of dimples provided on one golf ball having various conditions such as the arrangement of dimples, the size of each dimple, and the depth of each dimple.
The drag coefficient and lift coefficient, which are the aerodynamic characteristics of a golf ball, greatly depend on the dimple pattern when the composition and the overall layer structure of the golf ball are the same. Therefore, experimental data on aerodynamic characteristics consisting of drag coefficient and lift coefficient of golf balls with various dimple patterns were hit or simulated with golf balls having various types of dimple patterns in advance. If measured, it is possible to recommend a golf ball having a dimple pattern having an optimum aerodynamic characteristic corresponding to a golfer's hitting characteristic.

  A golf ball having a dimple pattern having a golf player's hitting form and a flight characteristic required by the golfer is used as the golf ball's order as a second invention, in the method for obtaining the optimum aerodynamic characteristic of the golf ball of the first invention. A custom made golf ball dimple system that can be provided based on

That is, as a second invention, using the method for obtaining the optimum aerodynamic characteristics of the golf ball of the first invention,
Information including the initial conditions consisting of the initial velocity, launch angle, left / right swing angle, backspin amount, and side spin amount of the golf ball unique to the golfer, and weighting functions set according to the requirements regarding the flight characteristics of each golfer are input. Input means having a function to
A dimple pattern of a plurality of dimples of the golf ball, and storage means for storing a drag coefficient and a lift coefficient of the dimple pattern;
Based on the information received from the input means, the design variable that optimizes the objective function is obtained by an optimization method, and a dimple pattern having a drag coefficient and a lift coefficient that are the design variables is stored in the storage means. Arithmetic processing means for selecting from the dimple pattern
Display means for presenting the optimum dimple pattern obtained by the arithmetic processing means;
A custom-made system for golf ball dimples is provided.

That is, in the input means, the golfer actually hits the ball and measures in advance initial conditions unique to each golfer such as the initial velocity of the ball so that different initial conditions can be input for each golfer. A request (that is, a preference) relating to a flight characteristic of a golfer can be inputted by weighting.
The weight function is scored in the order of emphasis on the relationship between carry, run, total flight distance, against and follow, iron and wood, golf club count, hook and slice. The configuration is such that input is possible. More specifically, whether the focus is on run, carry, or total flight distance, whether to focus on the against or follow conditions, whether to strike on the iron or on the driver, etc. It is filled in with a formula, and weights are scored in 1 to 5 steps in the order of importance so that they can be input.
Thus, for example, when emphasizing the total flight distance when hitting under a follow condition using dimples and wood, which is suitable when placing importance on the total flight distance when hitting under an against condition using an iron Suitable dimples can be provided.

In the present system, according to the input conditions by the input means, in the arithmetic processing means, the objective function f _i a distance under different conditions, by setting the weight value w _i golfer purposes A drag coefficient and a lift coefficient are obtained by maximizing a linear weighted sum of the function f _i and the weight value w _i . Further, the dimple closest to the obtained drag coefficient and lift coefficient is selected from the storage means.
A golf ball is manufactured using a dimple mold that forms the selected dimple pattern, and is provided to the golfer, thereby reflecting the golfer's initial conditions and the flight characteristics required by the golfer. Can be provided.

Thus, by providing the input means with a weighting function that can be set by each golfer according to his / her preference, it is possible to provide the golfer with a golf ball that fits the golfer's own hitting form and considers the golfer's preference.
Therefore, a golfer can obtain a custom-made golf ball with a dimple pattern, for example, a golfer can use a custom-made golf ball according to the course of the golf course and the weather at the time of golf. Become.

The weighting function set by the input means is preferably specified by specifying the type and count of the golf club.
That is, the golfer's launch initial conditions that are input differ depending on the type of club divided by the structure of the club that hits the golf ball, and the same type depending on the iron, wood, count, and the like. Therefore, by specifying the club, it is possible to select dimples that match the golfer's initial launch conditions and the golfer's preference with higher accuracy.

It is preferable to use data measured by a golfer's golf ball hitting measurement device as an initial condition input to the input means.
If the golf ball hitting measurement device and the custom-made system device of the present invention are installed in the same place, the golfer measures his / her hitting with the golf ball hitting measuring device when custom-made, and this measurement is performed. Using the data, it is possible to customize a golf ball that is suitable for its own hitting form and has a favorite dimple pattern.

The input means of the system of the present invention is preferably provided on a golf shop, a driving range, a terminal device installed on a golf course, or a homepage on the Internet.
With the above configuration, the golfer can input initial conditions and weighting functions directly into the input means, and in particular, by providing an input means on a homepage on the Internet, it is easy even without going to a golf course or a golf shop. A golf ball having suitable dimples can be made to order, which is highly convenient for golfers.

  As described above, according to the method for obtaining the optimum aerodynamic characteristics of the golf ball of the first invention, the initial three elements of the golf ball differing according to the type of club used when hitting golf, the handicap of the golfer, etc. In other words, for the initial conditions consisting of initial velocity, backspin amount and launch angle, the golf ball's inherent drag coefficient and lift coefficient are combined as design variables, and the ballistic formula is used to calculate the flight distance and fall of the golf ball as objective functions. The drag coefficient and lift coefficient of the golf ball, which are the optimal objective function for the initial launch conditions, are obtained by repeatedly acquiring the objective function by changing the design variables by acquiring the speed, the falling angle, and the spin amount at the time of falling. Can be obtained.

In the method for obtaining the optimum aerodynamic characteristics of the golf ball of the present invention, the Reynolds number and spin rate of the golf ball corresponding to the initial launch condition are obtained in advance, and the Reynolds number and spin rate are determined as the drag coefficient of the golf ball. A genetic algorithm is used as a method of combining with a lift coefficient, sequentially performing this combination using a neural network, and obtaining an optimal objective function from a large number of objective functions acquired according to these combinations.
In this way, in combination with the initial launch conditions, the drag coefficient and lift coefficient of the golf ball, and using the ballistic equation to find the objective function, the neural network method and the genetic algorithm method are used in combination. Thus, the calculation can be performed efficiently and the optimum objective function can be obtained with high accuracy.

  According to the present invention consisting of the above technique, it is possible to know the aerodynamic characteristics of the optimal golf ball according to the handy of the club or golfer to be used, which could not be known conventionally, and as a result, for example, by club, by handy, A golf ball having optimum dimples can be provided.

According to the second-order golf ball dimple customization system of the second invention, the method for obtaining the optimum aerodynamic characteristics of the golf ball is used, and a dimple pattern having the optimum drag coefficient and lift coefficient is obtained in advance. The optimal dimple pattern in consideration of the golfer's request can be obtained by setting the requirement regarding the golfer's flight characteristics, that is, the preference as the input condition.
Therefore, by using this system, it is possible to provide a golf ball having a dimple pattern in consideration of a golfer's hitting form and a golfer's preference based on the golfer's order.

  In addition, when the input means is provided on a golf shop, golf driving range, terminal equipment installed at a golf course, or on a homepage on the Internet, the golfer simply inputs initial conditions and weighting functions directly to the input means. A golf ball having dimples can be ordered, and a custom-made golf ball can be obtained. In particular, when an input means is used on a homepage on the Internet, a golf ball can be easily made without going to a golf course or a golf shop, which is convenient for golfers.

Hereinafter, embodiments of the present invention will be described with reference to the drawings.
First, a first embodiment of a method for obtaining optimum aerodynamic characteristics of a golf ball according to a first aspect of the invention will be described with reference to FIGS.
In the present invention, the optimum drag coefficient and lift coefficient of the golf ball according to the initial three conditions including the initial velocity of the ball, the back spin amount, and the launch angle are obtained by measurement by a computer.

Experiments were conducted in advance on the golf ball Reynolds number Re, the drag coefficient Cd and the lift coefficient Cl of the spin rate SR corresponding to each initial condition, from a number of initial conditions corresponding to the ball speed, backspin amount, and launch angle at the time of ball launch. Etc.
On the other hand, the drag coefficient Cd and the lift coefficient Cl of a large number of golf balls are obtained in advance based on differences in dimple pattern, shape, size, depth, and the like of the golf ball.

As shown in FIG. 1, “Reynolds number Re and spin rate SR obtained as initial variables 11 corresponding to the initial condition 11 are used as design variables, and the objective function 14 is the flight distance until the golf ball falls on the ground, the fall speed, the fall A system that clarifies “drag coefficient Cd and lift coefficient Cl” in “Reynolds number Re and spin rate SR” that can be maximized (or minimized) with respect to the angle and the spin amount at the time of fall is established. . The drag coefficient and lift coefficient of the golf ball, which are the design variables, are obtained in advance based on each dimple pattern having various conditions such as the arrangement, size, and depth of the dimples of the golf ball.
The ball speed, the backspin amount, and the launch angle at the time of launching the ball must be given as the initial condition 11, and these can be freely set.
Various methods can be employed as the optimization method, but a genetic algorithm method that does not end the optimization process with the local optimal solution is most preferably used.

In order to optimize, it is necessary to calculate the flight distance, drop speed, drop angle, and spin amount during the fall under the initial conditions set by ballistic calculation. It is necessary to accurately derive “drag coefficient Cd and lift coefficient Cl” in “Reynolds number Re and spin rate SR” that change every moment. In order to carry out this process at high speed and with high accuracy, a neural network shown in FIG. 1B is used.
As the conditions, the Reynolds number Re and the spin rate SR were given to the input layer 12 of the neural network, and one neural network was prepared for each of the drag coefficient Cd and the lift coefficient Cl as one layer. As shown in FIG. 1C, the output layer 13 may be two layers (13A, 13B), the drag coefficient Cd and the lift coefficient Cl may be set, and only one neural network may be constructed.
Two or more intermediate layers 18 are provided between the input layer 12 and the output layer 13, and the input layer 12 and the output layer 13 are variously combined by changing the neurons 18 a of the intermediate layer 18.

  The neural network N comprises the network shown in FIG. 2, and the drag coefficient Cd and lift coefficient Cl for the Reynolds number Re and spin rate SR are constructed from prior experimental data. The condition number of Reynolds number Re, spin rate SR, drag coefficient Cd, and lift coefficient Cl for constructing the neural network N is set to 15 in this embodiment in order to maintain accuracy, but it may be 10 or more and 100 or less.

The target values of the flight distance, the falling speed, the falling angle, and the spin amount at the time of falling are set in advance as the objective function 14.
For example, the maximum target value (AT) of the flying distance is 300 yards, the minimum target value (BT) of the falling angle is 10 degrees, the maximum target value (CT) of the falling angle speed is 40 m / s, and the minimum target of the spin rate at the time of falling The value (DT) is 100 rpm.
Furthermore, since these many objective functions become many, the optimal objective function X which calculated | required the target value of many objective functions is calculated | required.
In the optimum objective function, X is X = aA ′ + bB ′ + cC ′ + dD ′.
In the above formula, a, b, c, and d are relative weights, for example, a = 1.0, b = 0.2, c = 0.3, and d = 0.4.
A ′ is A / AT, B ′ is B / BT, C ′ is C / CT, and D ′ is D / DT.

The objective function 14 is calculated based on the ballistic equation described later from the initial condition 11 (a1), the drag coefficient CD, and the lift coefficient Cl.
As shown in FIG. 3, when the target value of the objective function 14 is reached, the optimization calculation is terminated. If the optimum value is not reached even when the number of repetitions reaches the specified number of times, the process ends with the number of repetitions set in advance.
Thus the optimal objective function X from the objective function 14 obtained in _{(d 1, d 2, d} 3 ... d n) to the searched using the genetic algorithm, the optimal (drag coefficient with respect to the initial conditions 11 Cd and lift coefficient Cl).

Next, the optimization calculation of the present invention will be described in detail.
First, the ball speed (v _{x (0)} , v _{y (0)} , v _{z (0)} ) and the backspin amount (ω _{x (0)} , ω _{y (0)} , ω _{z (0)} ) at the time of launch An initial condition 11 (a ₁ , a ₂ , a ₃ ...) Is obtained.
(V _{x (0)} ) is the x component of the initial velocity of the ball (v _{y (0)} ) is the y component of the initial velocity of the ball (v _{z (0)} ) is the z component of the initial velocity of the ball ω _{x (0)} is x Spin ω _{y (0)} around the axis is spin ω _{z (0)} around the y axis.
From the initial condition 11 (a ₁ , a ₂ , a ₃ ...), The Reynolds number Re ₍₀₎ and the spin rate SR ₍₀₎ are calculated from the following formula 1.
R is the radius of the ball, p is the kinematic viscosity of air, and ω is the angular velocity of the ball.

As described above, the Reynolds number Re and spin rate SR of the input layer 12 obtained from Expression 1 and the drag coefficient Cd and lift coefficient Cl of the output layer 13 are related by the neural network N shown in FIG.
The relationship between the Reynolds number Re and the spin rate SR, the drag coefficient Cd, and the lift coefficient Cl in the neural network N is constructed based on previous experimental data as described above.
As a method for constructing the neural network N, a back propagation method (Back-propagation) is used, and the coupling load value is changed according to the input.
Only the Reynolds number Re and the spin rate SR of the input layer 12 of the neural network may be used as conditions, but SR ^{2 and the} like may also be used as conditions.

The Reynolds number Re and spin rate SR of the input layer 12 of the neural network N obtained from the initial condition 11 (a ₁ , a ₂ , a ₃ ... A _n ), the drag coefficient Cd and the lift coefficient Cl of the output layer 13 are obtained. When the combined learning is completed, a system for calculating by combining the input layer 12 and the output layer 13 corresponding to other initial conditions corresponding to the input layer 12 is constructed.
Using the neural network N constructed in this way, a drag coefficient Cd and a lift coefficient Cl combined with the initial condition 11a (Reynolds number Re and spin rate SR) are derived.
In the neural network, since the Reynolds number Re and the spin rate SR of the input layer 12 preferably have values between −1 and 1, scaling is performed.

Next, ballistic calculation is performed from the derived drag coefficient Cd _(0), lift coefficient Cl _(0), and initial condition 11a ₍₀₎ using the ballistic equation expressed by the following formula 2.
a _{x (0)} is the x component of the initial acceleration of the ball,
a _{y (0)} is the y component of the initial acceleration of the ball,
a _{z (0)} is the z component of the initial acceleration of the ball,
r is the density of the air,
d is the diameter of the golf ball,
m is the weight of the golf ball.

Equation 2 is a ballistic equation in the initial state (n = 0).

As shown in FIG. 4A, the fall information at the fall point of the objective function 14, that is, the flight distance to the fall point, the fall speed, the fall angle, and the fall spin amount, is y = 0 in the xy coordinate system. Therefore, substituting ω _x = 0, ω _y = 0, g _x = 0, g _y = 9.8, and g _z = 0 into Equation 2, the following Equations 3-1 to 3-1 It becomes like 3-3.

Substituting the initial condition a, the drag coefficient Cd _(0), and the lift coefficient Cl ₍₀₎ into the equations 3-1 to 3-2, the ball initial acceleration (ax ₍₀₎ , a _{y (0)} , a _{z ( 0)} ) is required.
Since the initial ball coordinates are (x, y) = (0, 0), and the initial ball velocity (v _{x (0)} , v _{y (0)} , v _{z (0)} ) is known in the initial condition, Ball coordinates (x ₍₁₎ , y ₍₁₎ , z ₍₁₎ ) of n = 1 can be obtained.
It is assumed that the acceleration does not change between n = 0 and 1. The ball speed (v _{x (1)} , v _{y (1)} , v _{z (1)} ) is the ball initial acceleration (a _{x (0)} , a _{y (0)} , a _{z (0)} ) and the ball initial speed (vx ₍₀₎ , vy ₍₀₎ , _{vz (0)} ) can be calculated using a fourth-order Runge-Kutta method.
The fourth-order Runge-Kutta method will be described below.

The fourth-order Runge-Kutta method does not require any future (n + 1) information, and can predict (n + 1) information after one step from only the current (n) information.
Differential equation dy / dt = f (x, y) When the _relation of _{y n + 1} and _{y n} is expressed by the following equation.
_{Therefore, y n + 1} can be obtained from the _{y n} and dy _n / dt.

  As shown in FIG. 4B, h represents a time from n to n + 1, and h = 0.001 (s) to 0.01 (s) is desirable. The smaller h is, the better the accuracy is, but the memory capacity is required and the CPU load increases.

The above-described Runge-Kutta method is used in Equations 3-1, 3-2, and 3-3.
In the case of Equation 3-2, if the differential equation is d ² y / dt ₂ = f (v _x , v _y ), the relationship between _{vy (n + 1)} and vy _(n) is as follows.

Accordingly, since the ball speed vy _{(n + 1)} can be obtained from the ball acceleration _{ay (n)} and the ball speed vy _(n) , vy ₍₁₎ becomes _{ay (0)} and vy _(0). It can be obtained more.
The differential equation d ² x / dt ₂ = f (v _x , v _y ) in Expression 3-1 can be similarly expressed.
Thus, since ball speed _{v x (n + 1)} can be obtained from the ball acceleration _{a x (n)} and ball speed _{v x (n), a x} (0) and _{v x (0)} from _{v x} a ₍₁₎ Can be sought.
In the case of the differential equation d ² z / dt ₂ = f (v _z ) in Expression 3-3, the relational expression between v _{z (1)} and v _{z (n)} can be expressed as the following expression.
Thus, since ball speed _{v z (n + 1)} can be obtained from the ball acceleration _{a z (n)} and ball speed _{v z (n), a z} (0) and _{v z (0)} from _{v z: (1)} Can be sought.

In addition, it is necessary to consider spin decay, and ω _{(n) in} Expressions 3-1 to 3-3 is expressed by the following expression using ω _(n−1) . Here, R ₁ = 0.00002.

From the above, using the Runge-Kutta method, the ball initial acceleration (ax _{x (0)} , a _{y (0)} , a _{z (0)} ) and the ball initial velocity (v _{x (0)} , vy ₍₀₎ , v _{z (0)} ), the ball velocity (v _{x (1)} , vy ₍₁₎ , v _{z (1)} ) of n = 1 can be obtained, and the initial ball velocity (v _{x (0)} , vy _{( 0)} , v _{z (0)} ) and n = 1 ball coordinates (x ₍₁₎ , y ₍₁₎ , z ₍₁₎ ) and the ball acceleration using equations 3-1 to 3-3. (A _{x (1)} , a _{y (1)} , a _{z (1)} can be obtained.
In this manner, the ballistic calculation of Equations 3-1 to 3-3 is repeated in the same manner for n = 2 and thereafter, and the ball coordinates (x _(t) , y _{( t)} , z _(t) ), ball speed (vx _(t) , vy _(t) , _{vz (t)} ), and spin amount ω _(t) at fall.
Therefore, the values of the flight distance x _(t) , the falling speed v _{x (t)} , vy _(t) , and the spin amount ω _(t) at the time of falling can be obtained. Moreover, the drop angle θ is obtained by calculating the following equation.
Incidentally, since the Reynolds number Re and the spin rate SR will change with time, the Re a _(n) and _{SR (n)} for Cd _(n) and _{Cl (n)} in advance built in every step Neural The trajectory calculation is carried out using the obtained Cd _(n) and Cl _(n) .

Flight distance A, fall angle B, fall speed C, fall spin amount D, target flight distance AT (300 yards), target fall angle BT (10 degrees), target fall speed CT obtained from the above ballistic calculation From (40 m / s) and the target spin amount DT (100 rpm), A / AT = A ′, B / BT = B ′, C / CT = C ′, and D / DT = D ′ are obtained.
The optimal objective function X is set by a linear sum with weighting factors a to d as shown in the following formula 9, and the process ends when the optimal target value X is reached.
If the optimum target value X is not reached, the drag coefficient Cd and the lift coefficient Cl are reset. The target function does not need to calculate a linear sum for all items, and may calculate a linear sum only for items to be evaluated.

The end condition of the optimization calculation is the case where the number of iterations reaches the specified number unless the target value is reached, and a given Reynolds number Re is obtained from the obtained objective function using a genetic algorithm. The optimum drag coefficient Cd and lift coefficient Cl are searched for the spin rate SR.
The conditions for optimization using the genetic algorithm (GA) of this embodiment are shown below.
In the optimization by GA, it is necessary to code the design variable, and the code is obtained by converting each variable (real value) of the drag coefficient Cd and the lift coefficient Cl into a 10-bit binary system.
The basic setting values for optimization by the genetic algorithm are shown below.
Number of design variables: 2 variables x number of conditions (15) = 30 Chromosome length: 10 bits x number of design variables (30) = 300 bits Termination condition: Golf ball that reaches the target value or reaches the number of iterations The golf ball's drag coefficient Cd and lift coefficient Cl under the initial conditions are used as design variables, and the golf ball's motion state and spatial position during the fall, such as the flight distance, fall speed, fall angle, and fall spin amount of the golf ball. Information is the objective function 14.

(Example)
The optimum drag coefficient and lift coefficient of the golf ball according to the following initial launch conditions of the golf ball were determined.
The initial conditions of the golf ball were an initial ball speed of 58 m / s, a back spin of 2400 rpm, and a launch angle of 12 degrees.
As shown in Table 1 below, arbitrary design variables within the range of drag coefficient Cd _(Min) -Cd _(Max) and lift coefficient Cl _(Min) -Cl _(Max) under 15 conditions are input to the computer, The relationship of (Cd, Cl) = f (Re, SR) was constructed as a neural network model using the values as teacher data.
Enter the initial ball velocity, backspin amount and launch angle of the initial conditions obtained in advance, and use the ballistic equation and the neural network built in advance, the ball flight distance to the objective function, the angle of fall The falling speed and the spin amount at the time of falling were determined.

The target values of the objective function were a target maximum flight distance AT = 300 yards, a target minimum fall angle BT = 10 degrees, a target maximum fall speed CT = 40 m / s, and a target minimum fall spin DT = 100 rpm.
Since there are a plurality of objective functions, the objective function X = aA ′ + bB ′ + cC ′ + dD ′.
The coefficients a, b, c, and d are weighted and replaced with the problem of maximizing X. In the embodiment, the optimization problem of maximizing X was set by setting the coefficients as a = 1.0, b = −0.2, c = 0.3, and d = −0.4, respectively.
A ′ = A / AT, B ′ = B / BT, C ′ = C / CT, D ′ = D / DT

  Table 1 shows conditions 1 to 15 as the maximum value and minimum value of (Re, SR) of the input layer 12 and the maximum value and minimum value of (Cd, Cl) of the output layer 13 constituting the neural network. Indicates that it is set. For example, when the condition 1 of the input layer and the condition 5 of the output layer c are combined by the neural network, the objective function is calculated from the ballistic equation from the known initial condition a and the Cd and Cl of the condition 5. Distance, drop angle, drop speed, and spin at fall were calculated.

  Next, a second embodiment of a customized golf ball dimple system using the method for obtaining the optimum aerodynamic characteristics of the golf ball of the second invention will be described with reference to FIGS.

  As shown in the block diagram of FIG. 5, the customized system of the present invention includes an input means 30 for inputting information of each golfer, a number of existing dimple patterns, and a drag coefficient and lift force of a golf ball having these dimple patterns. Storage means 31 storing aerodynamic characteristics based on a coefficient, and storage means for calculating an aerodynamic characteristic based on information of each golfer received from the input means 30 and storing an optimum golf ball dimple pattern having the aerodynamic characteristics An arithmetic processing means 32 for selecting from 31 and a display means 33 for presenting an optimal dimple pattern of the golf ball obtained by the arithmetic processing means 32 are provided.

Specifically, the input means 30 includes a terminal device such as a personal computer, an input screen is displayed on the terminal device, and a user who customizes a golf ball having a required dimple pattern based on the display (hereinafter, referred to as a user interface). A golfer) performs an input operation using a keyboard or the like.
The display screen includes the initial condition 11 including the initial velocity, launch angle, left / right deflection angle, back spin amount, and side spin amount of a golf ball unique to the golfer, and flight characteristics desired by each golfer (hereinafter referred to as preference). Is set by weighting 20 by the number of points.

The input means 30 is provided on a golf shop, a golf driving range, a terminal device installed on a golf course, or a homepage on the Internet. The golfer's preference may be input by the golfer himself according to the input screen input, or an attendant may perform an input operation based on the following questionnaire.
The golfer's launch initial condition is such that data measured by a golf ball hitting measuring device (measuring device) attached to the place where the input means is installed is automatically input.
If the golf ball hitting device is not attached and the data measured by the golf ball hitting measuring device attached at another place is possessed, the golfer himself or a staff member inputs the data.

The weighting 20 according to the golfer's preference input by the input means 30 is important in the relationship between carry and run and total flight distance, against and follow, iron and wood, golf club count, hook and slice. It is set to be able to input by scoring in five-step evaluation in order. Specifically, a questionnaire with questions 1 to 5 in FIG. 6 is presented so that the golfer responds.
In the case of Question 1, when the driver and the iron place importance on the flight distance with the driver, the number is 1, while the case where the flight distance with the iron is important is set to 5, depending on which one is more important. Select a number. If the golfer chooses 2, the golfer places more importance on the distance traveled by the driver than the distance traveled by the iron.

  The storage means 31 includes information on a number of dimple patterns having various conditions such as the arrangement relation, size, and depth of existing dimples of the golf ball, and a drag coefficient Cd and lift force of the golf ball having each dimple pattern. Information on the coefficient Cl is recorded. The drag coefficient Cd and the lift coefficient Cl of the golf ball having each dimple pattern are obtained by measuring in advance.

  The arithmetic processing means 32 is connected to the input means 30 and the storage means 31, and is a design variable (lift coefficient Cl, drag coefficient) that obtains an objective function 14 that is optimal for the initial condition 11 and weighting 20 received from the input means 30. Cd) is obtained by the optimization calculation described in the method for obtaining the optimum aerodynamic characteristic of the golf ball of the first embodiment, and the golf ball has a drag coefficient Cd and a lift coefficient Cl obtained by the process. It has a function of selecting a dimple pattern from the storage means 31.

The display means 33 includes a display for displaying the dimple pattern obtained by the arithmetic processing means 32. In addition, the display means 33 displays the carry when the golf ball having the displayed dimple pattern is hit and the total flight distance.
Further, whether or not to order a golf ball having the displayed dimple pattern is also displayed.

  When an order is received from a golfer, a custom-made golf ball is manufactured by forming a dimple pattern on the ball surface using a dimple mold for forming each dimple pattern.

Next, a custom-made procedure for golf ball dimples according to the present system will be described with reference to the flowchart of FIG.
In step S1, the golfer launch initial conditions are automatically input to the input means 30 from the measuring device.
In step S2, a golfer's preference weight is input.
Steps S3 and S4 are performed by the arithmetic processing means 32.

The arithmetic processing means 32 uses the design variables (the lift coefficient Cl and the drag coefficient Cd) for obtaining the objective function 14 that is optimum for the initial condition 11 and the weighting 20 received from the input means 30 as the optimum aerodynamic characteristics of the golf ball. Obtained by the optimization calculation described in the acquisition method.
First, the weighting function w _i for each of the following objective functions f _i (f _{1 to} f ₁₂ ) is determined in accordance with the weighting input by the input means 30. The objective function 14 is set from each objective function f _i and the weighting function w _i .

f ₁ = Driver carry f ₂ = Driver's total flight distance f ₃ = Iron's carry f ₄ = Iron's total flight distance f ₅ = Driver carry in the against condition f ₆ = Driver's total flight distance in the against condition f ₇ = Iron carry under the Against condition f ₈ = Total iron carry distance under the Against condition f ₉ = Driver carry under the follow condition f ₁₀ = Total carry distance of the driver under the following condition f ₁₁ = Follow condition Iron carry f12 at ₁₂ = Total iron travel distance under follow conditions

In the case of question 1 in FIG. 6, since this golfer places more importance on the flight distance of the driver than the flight distance of the iron, the weighting of f ₁ , f ₂ , f ₅ , f ₆ , f ₉ , and f ₁₀ is performed. the function _{w i} plus _4, the f _{3, f 4, f 7,} weighting function f _{11, f 12 w i} adds 2. In this way, each weighting function w _i is determined as described above from the weighting 20 set by the golfer.

Next, using the optimization calculation described in the first embodiment, design variables (lift coefficient Cl and drag coefficient Cd) in which the objective function 14 set from each objective function f _i and weighting function w _i is optimal are shown. Ask for.
That is, the lift coefficient Cl and the drag coefficient Cd are obtained from the initial condition 11 obtained from the input means 30 using the neural network N under the 15 conditions defined in Table 1.
Each objective function f _i in each initial condition 11 is obtained from the lift coefficient Cl and the drag coefficient Cd using a ballistic equation, and is linearly added as shown in the following Expression 10 to obtain a single objective function 14. .
A lift coefficient Cl ₀ and a drag coefficient Cd ₀ that maximize the objective function 14 are obtained. In Expression 10, p is the number of questionnaire items, and in this case, p = 12.

Next, a dimple of the golf ball that matches the lift coefficient Cl ₀ and the drag coefficient Cd ₀ is selected from the dimple pattern stored in the storage means 31.
This selection approach, the lift and drag coefficients in specified conditions 15 conditions in Table 1 in the dimple pattern is recorded in the storage unit 31 Cl _n, and Cd _n.
From Equation 11 of the formula, from lift and drag coefficients _Cl n, lift coefficient Cl ₀ and drag coefficient Cd ₀ Metropolitan obtained with Cd _n, obtains the evaluation function H1.
M in the following expression 11 is the condition number, which is 15 in this case.

The arithmetic processing means 32 selects from the data stored in the storage means 31 a dimple pattern having the lift coefficient Cl _n and the drag coefficient Cdn _where the evaluation function H1 is minimized.
In another method for selecting a dimple pattern, among the 15 conditions in Table 1, there are conditions that are not relevant to the golfer, so each condition of the 15 conditions in Table 1 is represented by Equation 12 below. A weighting function w _{t is performed} for each.

The weighting function w _t performs the ballistic calculation from the initial condition 11 of the ball, confirms how the ball speed and the spin amount change during the flight, and the condition closer to the value of the ball speed and the spin amount. The value of the weighting function w _t is increased.
The weighting function w _t is obtained by the following calculation.

Assuming that the velocity of the golf ball hit by a specific golfer changes during the flight v _(t) and the backspin amount is r _(t) , the spin rate Sp _(t) is Sp _(t) = r _(t) / v _(T) .
If the speed in each of the 15 conditions in Table 1 is vi _(m) and the backspin is ri _(m) , then Sp _(m) = ri _(m) / vi _(m) .
The minimum difference between the spin rate in each of the 15 conditions and the spin rate in flight is represented by min (Sp _(m) -Sp _(t) ), and min (Sp _(m) -Sp _(t) ) is expressed as the weighting function w. _{Let t} .
Processing means 32 selects the dimples having a lift coefficient Cl _n and the drag coefficient Cd _n evaluation function H2, stored in the storage unit 31 is minimized from the data storage means 31.

As described above, after the steps S3 and S4 are performed by the arithmetic processing unit 32 and the optimum golf ball dimple is selected from the storage unit 31, the dimple pattern suitable for the golfer's hitting form and the golfer's preference is displayed by the display unit 33 in step S5. Is displayed.
In addition, the carry distance, total flight distance, and the like when the golf ball with the proposed dimple pattern is hit are displayed in step S6, and as shown in step S7, it is asked whether or not they are satisfied.
If the golfer is satisfied, the process ends. Further, although not shown, the golf ball having the proposed dimple pattern is inquired as to whether or not to order (ordered). Manufacture golf balls and send them to golfers. If the golf ball having the dimple pattern is a ready-made product, the golf ball is sent to the golfer.
When the golfer responds that he is not satisfied in step S7, he / she further performs weighting 20 for each item and presents a golf ball dimple that the golfer satisfies.

  A golf ball with an ordered dimple pattern can be easily manufactured by changing the dimple pattern in the golf ball manufacturing process by preparing a dimple mold, making it easy for golfers to make a custom-made golf ball. Can be provided.

(A) is explanatory drawing which shows the whole 1st Embodiment of the method of this invention, (B) (C) is drawing which shows the relationship of a neural network. 4 is a graph showing the construction of a neural network according to an embodiment of the present invention. It is a flowchart which shows optimization calculation. (A) is a diagram showing the trajectory of a ball in xy coordinates, and (B) is a relationship diagram between h, n, and n + 1. It is a block diagram which shows the custom-made system of the golf ball dimple of this invention. It is an example of the questionnaire paper which describes a golfer's preference. It is a flowchart which shows the custom-made system of the golf ball dimple of 2nd Embodiment. It is a figure of a prior art example. It is a figure of another prior art example.

Explanation of symbols

11 Initial condition 12 Input layer 13 Output layer 14 Objective function N Neural network 30 Input means 31 Storage means 32 Arithmetic processing means 33 Display means

Claims (9)

The initial conditions are the ball speed, backspin amount, and launch angle when launching a golf ball.
The design coefficient is the aerodynamic coefficient that consists of the drag coefficient and lift coefficient of the golf ball.
The objective function is the ball flight distance, drop speed, drop angle, or / and spin amount when falling on the ground,
A method for obtaining an optimum aerodynamic characteristic of a golf ball, wherein the design variable that obtains an optimum objective function with respect to the initial condition is obtained.   The Reynolds number and spin rate of the golf ball are obtained from the initial conditions, a neural network is constructed between the Reynolds number and spin rate, and the drag coefficient and lift coefficient, and the neural network is related to the Reynolds number and spin rate. 2. The method for obtaining optimum aerodynamic characteristics of a golf ball according to claim 1, wherein the objective function is obtained using a ballistic equation from the drag coefficient and lift coefficient applied and the initial condition.   The objective function obtained using the ballistic equation is provided with target values for the ball flight distance, drop speed, drop angle, and spin amount at the time of fall, and one optimum objective that combines the target values of these many objective functions. 3. The method for obtaining optimum aerodynamic characteristics of a golf ball according to claim 2, wherein a function is set, and the design variable that becomes the optimum objective function is searched using a genetic algorithm from the objective function obtained by the ballistic equation.   4. The optimum aerodynamic characteristics of the golf ball according to claim 1, wherein the drag coefficient and lift coefficient of the golf ball that are the design variables are obtained in advance for each dimple pattern of the golf ball. 5. Acquisition method. A golf ball dimple custom-made system using the method for obtaining optimum aerodynamic characteristics of a golf ball according to claim 4,
Information including the initial conditions consisting of the initial velocity, launch angle, left / right swing angle, backspin amount, and side spin amount of the golf ball unique to the golfer, and weighting functions set according to the requirements regarding the flight characteristics of each golfer are input. Input means having a function to
A dimple pattern of a plurality of dimples of the golf ball, and storage means for storing a drag coefficient and a lift coefficient of the dimple pattern;
Based on the information received from the input means, the design variable that optimizes the objective function is obtained by an optimization method, and a dimple pattern having a drag coefficient and a lift coefficient that are the design variables is stored in the storage means. Arithmetic processing means for selecting from the dimple pattern
Display means for presenting the optimum dimple pattern obtained by the arithmetic processing means;
A custom-made system for golf ball dimples.   The weighting function is scored in the order of emphasis on the relationship between carry and run and total flight distance, against and follow, iron and wood, golf club count, hook and slice. 2. The golf ball dimple custom-made system according to claim 1, which is configured to be input.   6. The golf ball dimple customization system according to claim 5, wherein the weighting function set by the input means is made by specifying the type and count of the golf club.   8. The golf ball dimple custom-made system according to claim 5, wherein data measured by a golfer's golf ball hitting measurement device is used as an initial condition input to the input means. 9.   The golf ball dimple according to any one of claims 5 to 8, wherein at least the input means is provided on a terminal device installed in a golf shop, a golf driving range, a golf course, or a homepage on the Internet. Customized system.