JP2005278882A - Individual optimal design method of inertia characteristic of golf club - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide an individual optimal design method of inertia characteristics of a club for every golfer using a statistical method. <P>SOLUTION: This individual optimal design method of the golf club inertia characteristics is provided with a step of preparing basic clubs having independently and randomly dispersed three elements out of eight types of club inertia characteristic specifications, a step of actually driving balls with the basic clubs, and creating a multiple regression formula using the ball initial speed measured then as a dependent variable and the three elements as independent variables and including a secondary term in the independent variable, a step of calculating a stationary point as a provisional optimal specifications from the multiple regression formula and a step of rationally selecting an improvement degrees of the ball initial speed and a deviance from a high precision using an index based on the stationary point. <P>COPYRIGHT: (C)2006,JPO&NCIPI

Description

  According to the present invention, the optimum golf club specification for the player is determined based on the correlation between the initial ball speed and the club spec when the target player hits a plurality of golf clubs (hereinafter referred to as clubs) having known specifications. It relates to the design method to be determined.

In the golf club, a head portion that directly hits a ball, a grip portion that a player holds, and a shaft portion that supports both of them are integrally connected. Also, a golf club set usually includes 9 to 10 iron clubs and several wood clubs. These clubs have different club lengths, loft angles, head masses, and the like according to purposes such as a hitting distance and a hitting angle.
Club makers have repeatedly improved so that a large hitting distance can be obtained with a small amount of work, and the probability that the direction of the hitting ball matches the target direction is high.
In addition, club makers design and manufacture general-purpose clubs for the majority of players. Recently, so-called custom designs for individual players have been widely implemented.
The club design for individual players usually has a grip thickness that matches the size of the player's hand, a bending rigidity distribution of the shaft that matches the flexure of the shaft, and a head that matches the hitting position on the head face. It is implemented only for limited elements such as the center of gravity position.

The major requirements of players are “improving accuracy” and “improving initial ball speed”, but at present, an effective design method that satisfies the requirements of the target player has not been established.
Based on the general club mass and club length, only minor adjustments are made, such as weight reduction for beginners and lengthening if flight distance is important. Further, a balance standard called 14-inch balance is used, and the shaft mass and the head mass are almost automatically determined by the club mass and the club length. However, this is only an empirical balance standard.
In order to improve the initial ball speed, a swing that achieves a high head speed and a head with a large mass are indispensable. In order to improve accuracy, the reproducibility of the swing must be high. These conditions are physically contradictory, such that if the head mass is increased, it becomes difficult to swing. Therefore, it is extremely difficult to achieve all the conditions in a balanced manner.

In order to solve these design problems, research has been promoted and numerous reports have been made. For example, see Non-Patent Document 1 and Non-Patent Document 2.
According to these research results, it can be seen that the inertia characteristic specifications of the club greatly influence the determination of the swing. The club inertia characteristic specifications are mainly classified into the following 8 types.
Club length (Lc): Distance from the closest point on the shaft axis of the center of gravity of the head to the grip end Club mass (Mc)
Head mass (Mh): Mass of head unit center of gravity position (R); Distance from the center of gravity of the club on the shaft axis to the grip end. Moment of inertia around the center of gravity (Ig)
Moment of inertia around grip end (I); Ig + Mc × R ²
First moment around grip end (McR); Mc × R
Grip end equivalent end pendulum length (Lp); I ÷ McR
However, each spec is closely related, as the club length increases and the club mass and the moment of inertia around the grip end automatically increase. If the three types are determined, the other specifications are almost determined. In other words, it can be said that the degree of freedom in designing the inertia characteristic of the club is 3.

According to the above research, the influence of the club inertia characteristics on the golfer's swing and the initial ball speed at the time of hitting is as follows. That is,
I: Load on shoulder joint in general down swing McR: Load on shoulder joint after cock release Lp: Load on wrist joint M: Impact on joint torque is small. The larger M is, the trunk-driven swing becomes and the cock opening is delayed a little.

Further, as found in Non-Patent Document 3, the ball hitting of the head can be regarded as a collision phenomenon between the single head and the ball. That is, the rigidity of the shaft and the restraining force of the grip portion by the golfer's hand are not affected, and it can be said that the initial ball speed is determined only by Mh (head mass) and the coefficient of restitution.
That is, since the load on the body changes due to the change in the inertia characteristic of the club, the swing changes and the head speed at the time of hitting the ball also changes. If the head speed is determined, the initial ball speed is automatically determined from the head mass at that time. Therefore, it can be said that “improvement of the ball initial velocity” is closely influenced by the club inertia characteristic specifications.
In addition, since the stability of the swing is indispensable for “improving accuracy”, it can be said that the club inertia characteristic specifications are also influential.

Recently, an attempt has been made to develop a design method using these research results.
Many of them involve simulating a golfer's movement on a computer, and changing the inertia characteristics of the club at this time to find a pattern that maximizes the ball initial speed, for example. However, golfers actually change their swings almost unconsciously in response to changes in the inertia characteristics of the club. It is very difficult to simulate this change on a computer. Simulation with a simulated golfer cannot be expected to improve design accuracy unless physiological information such as musculoskeletal mechanical characteristics and muscle contraction control characteristics are included. In other words, optimal design by dynamic simulation has not yet been put into practical use.

As another design method, Patent Document 1 is known as a method for selecting a golf club that matches a golfer based on the natural frequency of the golf club.
According to the above document, sex, age, golf calendar, number of rounds, number of exercises, sport calendar, height, weight, grip strength, handicap, head speed, round stroke, driver flight distance, flight distance of 5 iron and ball muscle The swing characteristics can be analyzed based on at least one of the items, and the golf club suitable for the golfer can be selected, the flight distance can be increased, and the miss shot can be eliminated.
However, in the conventional golf club selection method of Document 1, even if an appropriate shaft rigidity can be selected for a specific club length and club mass, the inertia characteristics such as the club length and club mass that should be originally selected are However, there is a problem that it must be determined in advance, and the selection is extremely limited.
These efforts are vacant, and players are currently forced to use a reliable but labor-intensive method of choosing the ones that have produced the best results using the clubs of choice. Furthermore, it has not been possible to examine the possibility that there is an optimum design value other than the hit club.

JP-A-1-285276 Proceedings of the Japan Opportunity Society [No99-41] Symposium 2A05 Contribution of Joint Torque to Golf Club Movement Keisen Kaneko (Mizuno Co., Ltd.) The Society of Instrument and Control Engineers Measurement and Control Vol. 38 No. 4 April 1999 Measurement and Control of Golf Swing Motion in Golf Club Development Keisen Kaneko (Mizuno Co., Ltd.) Iwata, M., Okuto, N .; , Satoh, F. “Designing of golf club heads by Finite Element Method (FEM) analysis”, in Cochran, A .; J. et al. (Ed.), Science and Golf, Chapman and Hall: London, 1990. pp. 274-279.

Accordingly, the present invention has been made to solve the above-described problems.
An object of the present invention is to provide a method for optimally designing the inertia characteristics of a club individually for each golfer using a statistical method.

  In order to achieve the object of the present invention, the invention according to claim 1 uses a basic club having a known specification value of the inertia characteristic of a golf club, and the "improved accuracy" A provisional optimum spec golf club satisfying the above, comprising preparing the basic club in which three of the eight inertia characteristic specs of the club vary independently of each other, and A step of creating a multiple regression equation in which a basic club is hit and the initial ball velocity measured at that time is a dependent variable and the three elements are independent variables, and the independent variable includes a quadratic term; And a step of calculating the three-element value indicating a stopping point which is a provisional optimum specification.

  The invention according to claim 2 is the individual optimum design method of the golf club inertial characteristics according to claim 1, and can be converted by the distance from the stop point in the relationship of the multiple regression equation with the provisional optimum specification as a reference. 2. The golf club inertia characteristic individual optimum design method according to claim 1, wherein a final specification is selected with reference to numerical values of a degree of deviation from a degree of improvement in ball initial speed and high accuracy.

  According to the method of the present invention, it is possible to digitally infer the “temporary optimal specification” of the club inertia characteristic that realizes “improvement of accuracy”, and further, “risk” and “gain” are used as the reference to “improve the initial ball speed” The advantage is that it is possible to select a specification of a club inertia characteristic that achieves “balanced”.

Hereinafter, the individual optimum design method of the golf club inertia characteristic according to the embodiment of the present invention will be described.
The present invention is a method of statistically estimating the club specifications most effective for the player from the value of the initial velocity of the ball when the player actually hits a plurality of golf clubs having known specifications. The method of the present invention will be described based on an example in which a golf club having an optimum specification for an arbitrary player is estimated.
The method of the present invention comprises the following steps.

(Step 1)
First, prepare a basic club. The number of basic clubs is preferably as many as possible in order to improve the statistical accuracy, but it is sufficient that the number of clubs is at least the minimum number. The minimum number is the number that can calculate the multiple regression equation described later. Since the number of coefficients of the regression equation that can be obtained by partial differentiation to obtain the value of the stopping point is at least 6, the minimum number of basic clubs is 7. It is necessary to prepare the minimum number by adding one to the number of coefficients of the regression equation to be adopted.

In addition, the basic club must be a group of clubs whose inertia characteristics are randomly different beyond the range of clubs that are usually on the market. In particular, among the eight elements of the inertia characteristic, the three elements of Lc (club length), Mc (club mass), and Mh (head mass), which are often adopted as actual design values and are familiar to general players, are provided. Randomly different club groups are desirable.
“Randomly different” means that there are three or more factors having an eigenvalue of 1 or more when principal component analysis is performed on the eight types of inertia characteristic specifications of the basic club. At that time, in each factor, it is desirable that elements having a maximum factor load or a size close thereto are Lc (club length), Mc (club mass), and Mh (head mass), respectively.
At this time, all clubs are unified with respect to the grip, the rigidity distribution of the shaft, and the head type (loft angle) preferred by the golfer. This is to eliminate influences other than the inertia characteristics of the club.
In this example, the following 11 clubs were used.

  When the principal component analysis is performed on the 11 pieces in Table 1 using the inertia characteristic specifications of 8 types of clubs, the results shown in Table 2 are obtained.

From the results of Table 2, the eigenvalues of the first factor to the third factor are 1 or more, and the factors having the maximum or near factor loading amount of each factor are Lc (club length), Mc ( Club mass) and Mh (head mass). Therefore, it can be confirmed that three types of the inertia characteristic specifications of the club vary randomly.
As described above, at least three types of club inertia characteristics may be determined in the design, but in this embodiment, Lc (club length) and Mc (club mass) which randomly vary among the three types. ) And Mh (head mass) were selected.

(Step 2)
Next, the golfer's initial ball speed is measured.
A golf player hits 11 prepared basic clubs, and the head speed Vh (immediately before impact) and the initial ball speed Vb (immediately after impact) are measured. In the embodiment, measurement of 11 types × 6 balls = 66 balls is performed, and the average value of each is used.
In the measurement, the measurement is performed using an apparatus disclosed in Japanese Patent Application Laid-Open No. 2003-117064.
That is, a striking speed detecting means for irradiating laser light at two locations in a direction intersecting the passing direction of the hitting tool, and detecting the hitting speed of the hitting tool according to the time during which each laser light is blocked by the passing of the hitting tool; The shot speed information and the ball image information obtained by shooting with the camera device capable of shooting the ball at the front and rear two points corresponding to the hit speed by the hit speed detecting means are taken in, and the flying direction and the ball direction are calculated by calculation based on the ball speed and rotation. It is an apparatus provided with a hit ball state calculation means 11 for determining a flight distance and an output means for outputting a calculation result.

・・・・・式（１）

・ ・ ・ ・ ・ Formula (1)

When the ball mass is Mb and the coefficient of restitution is e, Equation (1) is obtained from the momentum conservation law.
From the average value of the measured Vh (head speed) and Vb ′ (ball initial speed), the Mh (head mass) of each club and the ball mass of 45.5 g according to the above equation (1), the coefficient of restitution (net) Can be obtained. When this net coefficient of restitution is averaged, e ′ = 0.711. This e ′ is unified, and the initial ball speed is obtained again from the head speed using the law of conservation of momentum, and this is set as the net initial ball speed Vb. Vb can be said to be a pure ball initial speed in which variations due to mistakes at impact are removed.

  In this example, the net initial ball speed shown in Table 3 was obtained. If the spin amount and the launch angle of the ball are constant, it is possible to compare the flight distance at this net initial ball speed.

(Step 3)
Next, although not necessary for the present embodiment, the following regression equation was created for the explanation of the present invention. That is, when linear multiple regression analysis is performed with Vb as a dependent variable and Lc, Mh, and Mc as independent variables, the following regression equation is obtained.

・・・・・式（２）

・ ・ ・ ・ ・ Formula (2)

According to Equation (2), the ball initial velocity of the target player can be calculated by substituting the values of the three types of inertia characteristic specifications.
However, it does not match the actual measurement value so much (adjusted R ² = 0.656), and the combination of design elements satisfying the optimum condition cannot be obtained by the linear expression. In other words, since it is a linear relational expression, it is found that the longer the club length, the larger the head mass, the smaller the club mass, the faster the ball initial velocity.
In the present invention, the purpose is not to determine a mere trend but to determine a combination of optimum values. For this purpose, the following measures have been taken.
That is, multiple regression analysis was similarly performed using the independent variable as a coefficient of a biquadratic equation, and a regression equation was obtained. At this time, the degree of matching with the actually measured value is also high (adjusted R ² = 0.981).

・・・・・式（３）

・ ・ ・ ・ ・ Formula (3)

Since Equation (3) is a quadratic equation, the stopping point of Vb can be obtained unlike Equation (2). That is, it is possible to obtain a combination of variables that are partially differentiated by three variables and become equal 0. However, equation (3) has as many as nine coefficients, and it is not certain whether all the coefficients are effective.
Therefore, we decided to select the coefficients to be adopted.
By adopting at least one of Lc ² , Mh ² , and Mc ² and combining LcMh, LcMc, MhMc, Lc, Mh, and Mc as appropriate, 441 coefficient patterns can be formed. The same multiple regression analysis is performed using each pattern as an independent variable, and 441 regression equations can be obtained. Observing each of the 441 correlation coefficients and residuals, despite the small number of coefficients, the adjusted R ² = 0.990, and the standard error of the estimated value is 0.110, which is very good. A high regression equation can be found. This is the following equation (4).

・・・・・式（４）

・ ・ ・ ・ ・ Formula (4)

(Step 4)
Find the provisional optimum spec value.
When partial differentiation is performed on Lc, Mh, and Mc in Equation (4) and simultaneous equations are calculated with = 0, the values of the stopping points of Lc, Mh, and Mc can be obtained.
The obtained stop point values are as follows.

・・・・・（式５）

... (Formula 5)

From the above equation (5), Lc = 1.117, Mh = 0.2038, Mc = 0.528
It becomes.
This combination of values is referred to as a “provisional optimum spec pattern”.
The provisional optimum specification pattern is a stop point (saddle point) of the equation (4). That is, it is the center value of the pattern in which the value of Vb does not change greatly even if Lc, Mh, Mc changes slightly.
Therefore, the provisional optimum spec pattern can be estimated to be a spec that enables the most stable or reproducible swing when the player swings. Therefore, it can be said that this provisional optimum specification pattern is a provisional optimum specification pattern that achieves “improvement of accuracy” to the maximum extent among the target “improvement of initial ball speed” and “improvement of accuracy”.

(Step 5)
Next, based on the provisional optimum specifications that achieve "improving accuracy", in order to select the specifications that achieve "improving initial ball speed", two indicators are defined and used to The balance between “Improvement” and “Improved initial ball speed”.
“GN: gain (%)” is used as an index for increasing the initial ball speed of the club based on the provisional optimum spec pattern.
Regarding Expression (5), when Lc, Mh, and Mc are changed from the provisional optimum specifications, the value of Vb naturally also changes.
The rate of change with respect to the Vb value (63.75 (m / s) in this embodiment) in the provisional optimum specification pattern is defined as GN. The definition of GN is as follows.

・・・・・（式６）

... (Formula 6)

(Lc, Mh, and Mc changed into Expression (5) are substituted, and the obtained Vb is defined as Vb ′)
(Substituting the provisional optimum specification pattern into the equation (5) and let Vb obtained be Vb)
In order to increase GN, the values of Lc, Mh, and Mc must be greatly changed from the provisional optimal specification pattern.
The larger the amount of change in Lc, Mh, and Mc (the distance from the provisional optimum spec pattern in the relationship of Expression (4)), the more stable the swing becomes. This is because it can be estimated that the swing becomes unstable because the initial velocity of the ball changes greatly with a small amount of change in inertia characteristic specifications. Therefore, while evaluating “maximizing the initial ball speed” using GN, an index indicating the risk of improper load on the swing according to the amount of change (distance) from the provisional optimal specification pattern of Lc, Mh, and Mc “RK: Risk (%)” is used.
“RK: Risk (%)”, which is the distance from the provisional optimum specification, is defined as in Expression (7).

・・・・・式（７）

..... Formula (7)

(The provisional optimum spec pattern is Lc, Mh, Mc)
(Lc, Mh, and Mc changed to Lc ′, Mh ′, and Mc ′)
Therefore, using GN and RK, the degree of improvement in the initial ball speed from the provisional optimal spec pattern and the degree of deviation from the high accuracy can be compared and judged numerically. It is possible to select specifications that are compatible with each other at a high level, and the player's requirements can be achieved efficiently.

Specifically, the final optimum specification pattern is selected based on the provisional optimum specification pattern.
For example, if an RK of 9 (%) is allowed, a specification pattern of <Lc = 43.0 (inch), Mh = 190 (g), Mc = 330 (g)> is recommended.
In this case, GN is increased by 9 (%).
By the way, the specifications of the reference club I with the largest Vb in the actual hitting measurement values shown in Table 3 for the basic club are as large as 6 (%) for GN, but as 15.9 (%) for RK. You can't expect a bigger, very stable swing.
It can also be seen that among the 11 types of trial hit clubs, the F club is balanced with GN 3% and RK 5%. However, it is difficult to say that RK exceeds GN and is not optimal. In other words, there was no optimal spec for the target player in the reference club. However, this design method makes it possible to rationally select the optimum spec pattern.

As described above, by using the method of the present invention, it is possible to accurately select a club specification that can achieve “improved initial ball speed” and “improved accuracy” in a well-balanced manner for individual players. .

Claims (2)

A method for identifying a golf club having a provisional optimal specification that satisfies the "improving accuracy" from the initial velocity of the ball when a player to be designed uses a basic club whose specification value of inertia characteristics of the golf club is known. ,
A step of preparing the basic club in which three of the eight inertia characteristic specifications of the club vary independently at random;
Hitting the basic club, creating a multiple regression equation in which the independent initial variable includes a quadratic term, with the initial ball velocity measured as a dependent variable and the three elements as independent variables;
And a step of calculating the three-element value indicating a stopping point, which is a provisional optimum specification, from the multiple regression equation. With reference to the provisional optimum specification, the final specification can be selected by referring to the numerical value of the degree of improvement in the initial velocity of the ball and the degree of deviation from the high accuracy, which can be converted by the distance from the stopping point in the relationship of the multiple regression equation. 2. The method for individually designing golf club inertia characteristics according to claim 1, wherein: