JP2005319304A - Method for determining impact characteristics of golfer during swing - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a method for determining the direction of a golf club head swung by a golfer and the impact position. <P>SOLUTION: The method includes the step of inputting optimum values of the direction of a golf club head and the impact position, a plurality of swing characteristics of a golfer, a plurality of mass characteristics of a first golf club, and a plurality of mass characteristics of a first golf ball to a rigid body code. A plurality of ball stroking parameters computed are generated from the rigid body code and compared with a plurality of actual ball stroking parameters. The ball stroking parameters are compared with each other to validate the optimum values. If the validation is not within a prescribed value, new optimum values are selected for this method. The method is repeated until the validation becomes a prescribed value. <P>COPYRIGHT: (C)2006,JPO&NCIPI

Description

  The present invention relates to a method for determining the impact characteristics of a golfer for a golf swing. More specifically, the present invention relates to a method for determining the orientation and impact position of a golf club head on a golf swing.

  For over 20 years, high speed cameras have been used to collect information on golfer swings. This information varies from simple club head speeds to spins after impact by a golf club. Over the years, it has nurtured many improvements in golf clubs and golf balls, and has helped golfers choose golf clubs and golf balls to improve the game. Furthermore, systems incorporating such high speed cameras have been used to teach how to improve swing when using golf clubs provided to golfers.

  An example of such a system is Lynch et al., U.S. Pat. No. 4,063,259, filed in 1975, “Method for Adapting a Golf Ball, Golf Club, or Playstyle to a Golfer”. Lynch provides a measurement of golf ball hits using a shuttered camera, which operates when the light beam that activates the light source flash is interrupted, and causes the club head and golf ball to rest on the camera film. Give an image. Includes initial velocity, initial spin and launch angle derived by Lynch.

  Another example is Sullivan, US Pat. No. 4,136,387, filed in 1977, “Golf Club Impact and Golf Ball Launch Monitoring System”. Sullivan not only discloses golf ball launch measurements, but also provides measurements for golf clubs.

  Further examples include Gobush et al., US Pat. No. 4,136,387, filed Sep. 30, 1994, and 5,501,463, filed Feb. 24, 1994, 1995. There are patent families of 5,575,719 filed on August 1, 1996 and 5,803,823 filed on November 18, 1996. This patent family discloses a system having two camera angles that are angled to each other, a golf ball having a reflective mark, a golf club having a reflective mark, and a computer. This system makes it possible to plot points and measure a golf club or golf ball separately.

  Another example is US Pat. No. 6,042,483 “Golf Ball Motion Measuring Device”. This patent uses three cameras, optical sensors and strobes to obtain information about golf clubs and golf balls.

  However, this prior art disclosure and most launch monitors have not succeeded in determining the impact location and golf club orientation during a golfer's swing.

  The present invention makes it possible to determine the impact position and golf club head orientation during a golfer's swing based on the information obtained during the golfer's swing and the unique characteristics of the measured golf ball and golf club. Is the method. The present invention uses an optimization method, such as the Powell optimization method or the Nerder & Mead Simplex optimization method, to obtain impact position and golf club head orientation. .

  One aspect of the present invention is a method for determining the impact characteristics of a golfer during a golf swing. The method includes a first optimum including a plurality of characteristics of the golf club head, a plurality of characteristics of the golf ball, a direction of the golf club head during impact with the golf ball, and a position at which the golf ball impacts the golf club head. Including giving a value. The method also includes measuring the angular velocity and linear velocity during the swing of the golf club and the actual launch parameters of the ball. The method also includes a first optimum value for the plurality of golf club characteristics, the plurality of golf ball characteristics, the angular velocity of the golf club, the linear velocity of the golf club, and a rigid body code. The method also includes generating a plurality of ball launch parameters calculated from the rigid body code. The method also includes verifying the accuracy of the calculated plurality of ball launch parameters.

  Another aspect of the present invention is to use impact characteristics obtained through an optimization method to predict a golfer's hitting behavior. The method includes a plurality of golf club head characteristics for the first golf club, a plurality of golf ball characteristics for the first golf ball, a golf club head orientation during impact with the golf ball, and the golf ball Providing a first optimum value including the location of the impact on the golf club head. The method also includes measuring the golf club head angular velocity and linear velocity during the golfer's swing and a plurality of actual launch parameters. The method also includes inputting a plurality of golf club characteristics, a plurality of golf ball characteristics, a golf club angular velocity, a golf club linear velocity, and a first optimum value for the rigid body code. The method also includes generating a first plurality of ball launch parameters from the rigid body code for the first golf ball. The method also includes inputting the first plurality of ball launch parameters, the plurality of atmospheric conditions, and the first golf ball's lift and drag characteristics into the ballistic code. The method also includes generating performance from the ballistic code of the golf ball when the golfer hits the first golf club at a plurality of atmospheric conditions. The method also includes the plurality of mass characteristics of the second golf club, the mass characteristics of the first golf ball, the angular velocity of the golf club, the linear velocity of the golf club, and the golf club when impacted. And inputting an impact position of the golf ball on the golf club into the rigid body code. The method also includes generating a second plurality of ball launch parameters from the rigid body code. The method also includes inputting a second plurality of ball launch parameters, a plurality of atmospheric conditions, a first golf ball lift, and resistance characteristics into the ballistic code. The method also includes generating performance from the ballistic cord of the first golf ball when struck by a golfer by a second golf club under a first atmospheric condition. The method also includes a plurality of mass characteristics of the first golf club, a plurality of mass characteristics of the second golf ball, an angular velocity of the golf club, a linear velocity of the golf club, and an impact with the golf ball. Inputting the orientation of the golf club head and the impact position of the golf ball on the golf club head into the rigid body code. The method also includes generating a third plurality of ball launch parameters from the rigid body code. The method also includes inputting a plurality of third ball launch parameters, a plurality of atmospheric conditions, and lift and resistance characteristics for the second golf ball into the ballistic code. The method also includes generating performance from the ballistic code of the second golf ball when struck by a golfer with the first golf club under the atmospheric conditions.

  As shown in FIG. 1, a method for determining the impact characteristics of a golfer during a golf swing is indicated generally at 20. This method 20 uses the measured motion characteristics during the golfer's golf swing and the unique characteristics of the golf ball and golf club to determine the impact position and golf club orientation during the golfer's swing through an optimization method. Including that. At block 22, an optimum value for the impact position and golf club orientation during the golf swing of the golfer is selected by the operator. These first optimum values are speculative and probably do not indicate the true impact position and golf club orientation during the golfer's swing. However, these first optimum values must be used to obtain the golfer's true impact position and golf club orientation during the golf swing. At block 24, the measured values are collected for input to determine the golfer's impact location and golf club orientation during the golf swing through an optimization method.

In block 26, the information from blocks 22 and 24 is input into the rigid body code.
This rigid body code is shown in equations B1-B13 below and will be described in detail below. In block 28, the rigid body code generates a plurality of calculated ball launch parameters. At block 30, a plurality of actual ball launch parameters are collected from the acquisition system described below. At block 32, a plurality of calculated ball launch parameters are verified as described in more detail below. In block 34, if the value obtained in the verification step of block 32 is within the error range, the impact position and golf club orientation values during the golfer's swing are corrected, and the impact value during the true golfer's swing is corrected. The location and golf club orientation are selected. In block 36, if the value obtained in the verification step of block 32 is outside the error range, the selected value of the golfer's swing impact position and golf club orientation is not corrected and the golfer's An optimization method must be used to obtain the true value of the position of the impact during the swing and the orientation of the golf club.

  At block 38, the optimization method selects a new value for the location of the golfer's swing impact and golf club orientation to enter the rigid code of block 26. A preferred optimization method is the Powell optimization method, which is described in Chapter 10 of Numeric Recipes in C: The Art Of Scientific Computing, Cambridge University Press (1988-1992), which is incorporated herein by reference. An alternative optimization method is the Nelder & Simplex optimization method. Those skilled in the art will appreciate that other optimization methods may be used without departing from the spirit and scope of the present invention. This method is repeated with the new optimal value while the value obtained in the verification step of block 32 is in the error range, thereby obtaining a true value for the impact position and golf club orientation during the golfer's swing. .

  FIG. 2 is a flow chart showing the measured input or content of block 24 of FIG. Block 40 shows the characteristics of the golf swing. Block 41 includes the measured golf ball specific characteristics. Block 42 includes the measured golf club specific characteristics.

  FIG. 3 is a flowchart showing the input or content of the golf club swing characteristics of block 40 of FIG. Golf club swing characteristics are obtained from the acquisition system described below. Block 43 contains the linear velocity of the golf club during the golfer's swing. Block 44 contains the angular velocity of the golf club during the golfer's swing.

  FIG. 4 shows the inputs for the measured golf ball specific characteristics of block 41 of FIG. A measurement of the mass of the golf ball is obtained at block 45. Golf ball radius measurements are collected at block 46. Golf ball restitution coefficients are collected at block 47. The golf ball's moment of inertia is collected at block 48. The data collected at blocks 45-48 is input to generate the golf ball specific characteristics measured at block 41 of FIG.

  The golf ball properties of the stored and collected block 41 are: golf ball mass (limited to 45 g or less according to the golf rules established by USGA and R & A), golf ball radius (golf rules have a diameter of At least 1.68 inches are required), including golf ball COR and golf ball MOI. The MOI of a golf ball is determined using methods well known in the art. One such method is disclosed in US Pat. No. 5,899,822, which is hereby incorporated by reference. The COR is determined using a method such as that disclosed in US Pat. No. 6,443,858 “Golf Ball with High Restitution” granted to the applicant's Callaway Golf Company, which is incorporated herein by reference. The

  FIG. 5 is a flowchart showing the input of the golf club head characteristics in block 42 of FIG. Measurements for face characteristics are collected at block 49. Face characteristics include face shape, face center, bulge radius and roll radius. Measurements of the golf ball's mass properties are collected or recalled from a database at block 50. Mass properties include inertia tensor, club head mass, and center of gravity. Golf club head coefficient of restitution (“COR”) measurements are collected at block 51. Golf club head loft and lie angle measurements are collected at block 52. The data collected at blocks 49-52 is input to generate golf club head characteristics at block 42 of FIG.

  The mass, bulge and roll radius, loft and lie angle, face shape and face center are determined using conventional methods well known in the golf industry. The inertia tensor is: x-axis, moment of inertia around Ixx, y-axis, moment of inertia around Iyy, z-axis, moment of inertia around Izz, product of inertia Ixy, product of inertia Izy, product of inertia Calculated using Izx. The club head's CG and MOI are in accordance with what is described in Patent No. 6,607,452, "Composite Golf Club with High Moment of Inertia", which is incorporated herein by reference and is assigned to the applicant's Callaway Golf Company. It is determined. The products of inertia moments Ixv, Ixz, Izy are in accordance with the contents of Patent No. 6425832 “Driver head with large volume with high moment of inertia” granted to Callaway Golf Company, the assignee of the present application incorporated herein by reference. It is determined.

  The golf club head COR is used by the United States Golf Association ("USGA"), www. usga. org, disclosed in US Pat. No. 6,585,605, “Measurement of the coefficient of restitution of a golf club,” issued to Callaway Golf Company, the assignee of the present application, which is incorporated herein by reference. Determined according to the method and content. However, the COR of a golf club head depends on the golf ball and varies depending on the type of golf ball.

  FIG. 6 is a flowchart of the contents of a plurality of actual ball launch parameters in block 30 of FIG. The side spin of the golf ball is measured at block 53. The backspin of the golf ball is measured at block 54. The launch angle of the golf ball is measured at block 57. Information from blocks 53-57 is entered / stored as launch parameters measured in block 30 of FIG. 1 or as a plurality of actual launch parameters.

  FIG. 7 is a flowchart of the contents of a plurality of calculated launch parameters in block 28 of FIG. The side spin of the golf ball is calculated at block 63. The golf ball's backspin is calculated at block 64. Ball speed is measured at block 65. The lateral angle of the golf ball is calculated at block 66. A golf ball launch angle is calculated at block 67. Information from blocks 63-67 is entered / stored as a calculated ball launch parameter or as a plurality of calculated ball launch parameters in block 28 of FIG.

  FIG. 8 is a flowchart of the optimum value of block 22 in FIG. The impact position is selected at block 69. The orientation of the golf club head is selected at block 70.

  FIG. 9 is a flowchart showing the input / content of the optimum value of the orientation of the golf club head in block 70 of FIG. The pitch of the golf club head is selected at block 71. Golf club head yaw is selected at block 72. A roll of golf club head is selected at block 73. FIG. 10 shows the pitch, yaw and roll of the golf club head 133.

  FIG. 11 is a flowchart of the verification step of block 32 of FIG. In block 74, the information from block 28 (calculated ball launch parameters) and the information from block 30 (plural actual ball launch parameters) are compared with each other, and the absolute value of the difference is shown in block 75. Is operated on. In block 75, the absolute values obtained in block 74 are weighted according to their importance to determine the true impact position and golf club orientation values during the golfer's swing. At block 76, the weighted value from block 75 is used to obtain an error check value using an average sum-square-root equation. In such calculation of the average sum square square root, the squares of the weighted values are added, and the square root of the total value becomes an error value. In the preferred embodiment, if the error value is within 30, optimum values are acceptable, and these values are accepted as true values for impact position and golf club head orientation. If the error value is 30 or more, the optimal value is not accepted and is verified against multiple actual ball launch parameters and a new optimal value is calculated to calculate a new set of ball launch parameters Must be used.

  FIG. 12 is a flowchart showing a comparison process for obtaining absolute values for a plurality of ball launch parameters. At block 77, the difference between the side spin of the plurality of calculated ball launch parameters and the side spin of the actual ball launch parameters is obtained to obtain the absolute value of the side spin of the ball launch parameters. At block 78, the difference between the backspin of the plurality of calculated ball launch parameters and the backspin of the plurality of actual ball launch parameters is earned to determine the absolute value of the backspin of the ball launch parameters. At block 79, the difference between the ball speed of the plurality of calculated ball launch parameters and the ball speed of the plurality of actual ball launch parameters is obtained to determine an absolute value of the ball speed of the ball launch parameters. . In block 80, the difference between the lateral angle of the plurality of calculated ball launch parameters and the lateral angle of the plurality of actual ball launch parameters determines the absolute value of the lateral angle of the ball launch parameters. Earned. In block 81, the difference between the launch angle of the plurality of calculated ball launch parameters and the launch angle of the plurality of actual ball launch parameters determines the absolute value of the launch angle of the ball launch parameters. To be acquired.

  FIG. 13 is a flowchart showing a weighting process for obtaining a weighted absolute value of a plurality of ball launch parameters. In block 82, the absolute value of the side spin is weighted to obtain a weighted absolute value of the side spin for a plurality of ball launch parameters. At block 83, the absolute value of the backspin is weighted to obtain a weighted absolute value of the backspin for a plurality of ball launch parameters. At block 84, the absolute value of the ball speed is weighted to obtain a weighted absolute value of the ball speed of a plurality of ball launch parameters. At block 85, the absolute value of the lateral angle is weighted to obtain a weighted absolute value of the lateral angle of the plurality of ball launch parameters. At block 86, the absolute value of the launch angle is weighted to obtain a weighted absolute value of the launch angle of the plurality of ball launch parameters.

  This acquisition system used to measure a golfer's dynamic swing characteristics and multiple actual ball launch parameters is given to Applicant's Callaway Golf Company, which is hereby incorporated by reference in its entirety. Such a system as disclosed in U.S. Pat. No. 6,431,1990. However, those skilled in the art will appreciate that other acquisition systems can be used to determine the pre-impact swing characteristics.

  As shown in FIG. 14, the acquisition system 120 generally includes a computer 122, a camera mechanism 124 having a first camera unit 126, a second camera unit 128, a trigger device 132, and a golf ball 133. The acquisition system 120 is designed to be operated on a course, in a driving range, at a dealer, showroom, or other similar facility.

  The first camera unit 126 includes a first camera 140 and flash units 142a and 142b. The second camera unit 128 includes a second camera 144 and flash units 146a and 146b. A preferred camera is a charge coupled device (“CCD”) camera available from Wintis Engineering, Calif. Under the trade name OPSIS 1300.

The trigger device 130 includes a receiver 148 and a transmitter 160. The transmitter 160 is preferably attached to the frame 134 at a predetermined distance from the camera units 126, 128. A preferred trigger device is a laser device that emits a laser beam from transmitter 160 to receiver 148 and is triggered when interrupted by a club that is swung toward golf ball 132. The golf ball 132 placed on the tee includes a golf ball 166 and a tee 168. Other trigger devices such as optical detectors and acoustic measuring devices can also be used in the present invention. Golf ball 132 teed is the predetermined distance _{L 1} away from the frame 134. The length is preferably 38.5 inches. However, those skilled in the art will appreciate that this length will vary depending on the position and placement of the first and second camera units 126,128. Transmitter 160 is preferably 10 to 14 inches away from cameras 140 and 144. The receiver 148 and transmitter 160, and thus the laser beam, trigger the trigger device before the club swings the beam and impacts the ball on the tee. As will be described in more detail below, the trigger of the trigger device 130 generates instructions to shoot the golf club 133 before impacting the golf ball 132 on the tee to the first and second camera units 126, 128. . The collected data is sent via a cable 162 to a computer 122 to which a receiver 148 and first and second camera units 126 and 128 are connected. The computer 122 includes a monitor 164 that displays image frames that are photographed by the first and second camera units 126 and 128 and generated by exposure.

  The first golf club 133 is preferably prepared for use in the system 120 for determining pre-impact characteristics. Typically, the acquisition system 120 takes an average of 10 swings of a single golfer to determine the pre-impact characteristics. As shown in FIG. 15, the golf club 133 has a club head 150, a shaft 152 (FIG. 15), a face 154, a score line 156, a toe end 158, and a heel end 159. A plurality of markers are preferably placed on the golf club 133 so that a specific position of the golf club 133 is conspicuous. Only three markers are required on the golf club. A preferred embodiment is shown in FIG. However, the acquisition system 12 can use special features of the golf club 133, such as score lines, without using markers. The first marker 301 is placed at the tip of the shaft 152. The second marker 302 is placed at the tip of the shaft at a lower position than the first marker 301. The third marker 303 is placed at the high toe end of the club head 150.

  FIG. 15 shows four exposure image frames before the impact of the swing of the golf club 133. The golf club 133 is shown before the first exposure 702a, the second exposure 702b, the third exposure 702c, and the fourth exposure 704d impact the golf ball 166. Markers 301-303 are located in two dimensions and then correlated in three dimensions. Marker 303 is correlated to markers 301 and 302 on shaft 152. The position of the face 154 before impact and the ball 132 on the tee are reconstructed and input to determine pre-impact characteristics.

  The rigid body code uses linear and angular moment conservation to solve the impact problem, which gives complete motion of the two rigid bodies. The impulse is calculated using the impulse definition and the mathematical formula is shown below. The coordinate system used in the impulse equation is shown below. The impulse-moment method does not consider the time course of impact events. Collisions are only explained at the moment before and after the collision. The force transmitted from the club head to the ball is only equal and opposite in direction to the force transmitted from the ball to the club head. These forces are summed over a predetermined time when two objects are in contact, which are called linear and angular impulses.

  The rigid cord is such that the golf club head 150 is clearly connected to the shaft 152 and the ball 166 is not floating in the air when impacting the golf club head 150, but both the ball 166 and the golf club head 150 are non- Based on the assumption that it is a rigid body of constraints. For the golf club head 150, this unconstrained rigid body assumption is that the impact with the golf ball 166 occurs within a very short time frame (microseconds) and only a small tip of the shaft 152 contributes to the impact. . For a golf ball 166, the impulse due to friction between it and the surface (eg, tee, mat or ground) on which it is placed is very small compared to the magnitude of the impulse based on the impulse with the golf club head 150. Thus, friction is negligible in this calculation.

  In addition to the normal restitution coefficient that governs the normal velocity component during impact, there is a restitution coefficient that governs the tangential component of velocity. This additional coefficient of restitution is determined experimentally.

  An absolute performance number is defined in the global coordinate system, i.e. the global frame. The coordinate system includes a third point perpendicular to both the origin at the center of the ball, one axis indicating the final direction of the shot, one axis above the atmosphere, and the first two axes. With an axis. This global coordinate system preferably follows the right-hand rule.

  The coordinate system used for this analysis is called the impact coordinate system or impact frame. This frame is defined in relation to the global frame for complete analysis of the golf shot. The impact frame is defined by a vertical plane at the impact position of the golf club head 150. The positive z-direction is defined as the vertical direction outward from the golf club head 150. The tangent to the point of impact includes both the x-axis and the y-axis. For ease of calculation, the x-axis is arbitrarily chosen to be parallel to the global ground, and therefore the yz-plane is perpendicular to ground. The impact frame incorporates the club head loft, bulge and roll, and includes the net result of the golf swing. Dynamic loft, open or closed to face, and toe down are all measured for impact frames. The motion in the impact frame is converted to the global coordinate system since the global coordinate system and the impact coordinate system are known. The post-impact movement of the golf ball 166 is used to enter the ballistic code, and the shot distance and deviation are calculated by the present invention.

  The sign is defined below:

ｍ１，クラブヘッドの質量
ｍ２，ゴルフボールの質量

m1, club head mass m2, golf ball mass

リニアモメンタムの変換：

Linear momentum conversion:

角モメンタムの変換：

Angular momentum conversion:

反発係数の定義：

Definition of coefficient of restitution:

ゴルフボールにかかる接線方向インパルスは回転と並進移動の両方を生じさせる：

Tangential impulses on the golf ball cause both rotation and translation:

式Ｂ１−Ｂ１２は式のリニア数式システムを形成するために結合することができる：
［Ａ］｛ｘ｝＝｛Ｂ｝ Ｂ１３
ここで、［Ａ］、および｛Ｂ｝はインパクト前の既知の速度、ゴルフボール１６６とクラブヘッド１５０の質量特性、ゴルフボール１６６とクラブヘッド１５０の重心に対するインパクト位置、インパクト位置における垂直面から決定される。｛ｘ｝は全てのインパクト後の速度（リニアおよび角度）を含み、また、｛Ｂ｝と［Ａ］の逆数の積により解かれるか、又は他の線形代数における方程式の解析システムにより解析される。

Equations B1-B12 can be combined to form a linear equation system of equations:
[A] {x} = {B} B13
Here, [A] and {B} are determined from the known speed before impact, the mass characteristics of the golf ball 166 and the club head 150, the impact position with respect to the center of gravity of the golf ball 166 and the club head 150, and the vertical plane at the impact position. Is done. {X} includes all post-impact velocities (linear and angle) and is solved by the product of the reciprocal of {B} and [A] or analyzed by an analysis system of equations in other linear algebra .

When the golf ball 166 is placed on the tee 168, it is in equilibrium. The golf ball 166 does not move until F _m , the maximum static friction force between the golf ball 166 and the tee 168, and the above force is applied to the golf ball 166.

F _m = μ _s N = μm ₂ g C1
μ _s is a static friction coefficient, and g is gravity.

For a golf ball 166 with a mass of 45 grams and a _μs of 0.3,
F _m = μ _s mg = (0.3) (0.045) (9.81) = 0.132N
Assuming that this force acts on the golf ball 166 for 0.0005 seconds (a setting greater than the actual impulse), the impulse (impulse) L for the golf ball 166 is:
L = (0.132) (0.005) = 0.0000662 N · s
The impulse L moves the golf ball 166 at 0.00147 m / s (or 0.00483 ft / sec) and rotates it at 8.08 rad / sec (77.1 rpm). Both of these numbers are relatively smaller than those found in normal irons and wood. If the rigid cord of the present invention can be applied to a putter, it is preferable to include friction between the green and the golf ball for analysis.

上記のマトリックスの各項、ｅ_ｉｊ、ここでｉ＝ｘ，ｙ，ｚ及びｊ＝ｘ，ｙ，ｚ、はｊ−方向に対するｉ−方向の測度である。ダイアゴナル（主対角線）ターム、ここでｉ＝ｊ，はインパクトの前及び後の一つの軸の測度ｘ，ｙ，ｚを示す。項ｅ_ｚｚはインパクトの垂直方向における全てのエネルギーの損失を示す。ｅ_ｘｘ及びｅ_ｙｙは、最終結果をアドレスすることにより、接線面におけるゴルフボール１６６とクラブヘッド１５０との間の複雑な相互作用のためのアカウントである。通常、オフダイアゴナル項ｅ_ｉｊ、ここでｉ≠ｙ，は等方性材料についてはゼロに等しい。

Each term of the above matrix, e _ij , where i = x, y, z and j = x, y, z are measures of the i-direction relative to the j-direction. A diagonal (main diagonal) term, where i = j, represents the measure x, y, z of one axis before and after impact. The term e _zz represents the loss of all energy in the vertical direction of impact. e _xx and e _yy are accounts for complex interactions between the golf ball 166 and the club head 150 in the tangential plane by addressing the final result. Normally, the off diagonal term e _ij , where i ≠ y, is equal to zero for isotropic materials.

  As shown in FIG. 16, a method for predicting a golfer's ball striking motion is indicated generally at 90. A similar method is described in US Pat. No. 6,506,124, “Method for Predicting the Strike Motion of a Golf Ball,” issued to Callaway Golf Company, the assignee of the present application, hereby incorporated by reference in its entirety. The method 90 begins by entering the swing characteristics of a particular golf club, a particular golf ball, and a golfer. At block 91, the club head characteristics for a particular golf club are selected from the accumulated database and the club head characteristics already collected. Specific information for club head characteristics is described in more detail above as input to block 42 with reference to FIG. At block 92, the golfer's golf club swing characteristics are collected and stored in a database. The specific information of the golfer's golf swing characteristics includes the true value of impact position and golf club orientation, which are obtained according to the method 20 of FIG. Further, the information from FIG. 3, particularly the input to block 40, becomes part of the golf club characteristics. At block 93, the golf ball characteristics of a particular golf ball are selected from a stored database and information already collected. The specific information of the golf ball characteristics has been previously described in more detail with reference to FIG.

  In block 94, the information from blocks 91, 92, and 93 is input to the rigid body code. The rigid body code has already been described in detail. In block 94, the rigid body code is used to generate a plurality of ball launch parameters, as already described with reference to FIG. At block 95, atmospheric information is selected from a stored database of atmospheric conditions. At block 97, the lift and resistance characteristics of the golf ball are determined by conventional methods as described in US Pat. No. 6,186,002, “Method for Determining the Lift and Resistance Coefficient of a Golf Ball”, which is incorporated herein by reference. Measured. The lift and drag coefficients of many golf balls of a particular Reynolds number are described in US Pat. No. 6,224,499, incorporated herein by reference.

  At block 98, ball launch parameters, atmospheric conditions, and lift / drag characteristics are entered into the ballistic code. At block 99, the ballistic code is used to predict the golfer's motion when a particular golfer swings in a particular atmospheric condition using a particular golf club. Ballistic cords are well known in the art, and one such cord is described in the aforementioned US Pat. No. 6,186,002. USGA has such a ballistic code and can be purchased.

  When predicting the ball striking motion by a golfer using a specific golf club in a given atmospheric condition, the operator may choose to enter the center of the face as the impact position, regardless of the true position of the impact Can do. This enables prediction of the motion of the golf club 133 for toe shots, heel shots, and center shots. Golf ball type can be selected, golf club type can be selected, atmospheric pressure, temperature and ground conditions are selected by the operator, and the golfer's motion using these input parameters according to the pre-impact swing characteristics for the golfer Can be predicted.

  FIG. 17 is a table of golf club swing characteristics of block 40 for six trial golf shots using a BIG BERTHA C4® driver made of composite material obtained from Carlsbad, Golfway Golf Company, California.

  FIG. 18 is a table of actual multiple ball launch parameters for a block 30 of six trial golf shots using an HX® RED golf ball obtained from Carlsbad Golf Company, Carlsbad, California.

  FIG. 19 is a table of measured golf club intrinsic properties of a BIG BERTHA C4® driver made of a composite material obtained from Carlsbad Callaway Golf Company, California.

  FIG. 20 is a golf ball characteristic of an HX® RED golf ball obtained from Carlsbad Callaway Golf Company, California.

  FIG. 21 is a table of a plurality of calculated ball launch parameters for block 28 generated by the rigid body code for six trial shots. This table contains information for the example of blocks 63-67 of FIG.

  FIG. 22 is a table of a plurality of optimum values for the impact position and orientation of the golf club heads at blocks 69 and 70 for six trial shots.

  FIG. 23 is a table of differences between actually measured values and calculated values of a plurality of ball launch parameters for six test shots. This table contains an example of the information in blocks 77-81 of FIG.

  FIG. 24 is a table of weights of absolute values of differences between actually measured values and calculated values of the ball launch parameters of the block 75 of six trial shots. This table contains example information for blocks 82-86 of FIG.

  FIG. 25 is a table of error values for block 76 of six trial shots.

  From the foregoing, those skilled in the art will recognize the advantages of the invention and the invention has been described with reference to the preferred and other embodiments with reference to the drawings, while numerous modifications and improvements, It will be understood that equivalent substitutions may be made without departing from the scope and spirit of the invention which is not limited by the foregoing description as set forth in the following claims.

2 is a flowchart of the overall method of the present invention. It is a flowchart which shows the input for a measured value. It is a flowchart which shows the input for a golf club swing characteristic. 6 is a flowchart illustrating inputs for measured golf ball specific characteristics. 6 is a flowchart illustrating inputs for measured golf club head specific characteristics. It is a flowchart of the content of the actual ball launch parameters. It is a flowchart of the content of several calculated ball | bowl launch parameters. It is a flowchart of the input of an optimal value. It is a flowchart of the input of the optimal value of direction of a golf club head. 1 is a perspective view of a golf club showing yaw, pitch and roll of the golf club. It is a flowchart for verification of the result of a ball. It is a flowchart of the content for the comparison with the actual thing and the calculated thing of several ball | bowl launch parameters. It is a flowchart of the content for weighting the absolute value of the difference of the actual thing and the calculated thing of several ball | bowl launch parameters. It is a perspective view of the monitoring system of this invention. It is an image frame of a golfer's swing consisting of a plurality of screens before impact. It is a flowchart of the method of estimating performance using the impact position and direction of a golf club head obtained by the optimization method. It is a table | surface the characteristic of a golf club swing. It is a table | surface of several actual ball | bowl launch parameters. It is a table | surface of a golf club head characteristic. It is a table | surface of a golf ball characteristic. 4 is a table of a plurality of calculated ball launch parameters. It is a table | surface of the optimal value of an impact position and direction of a golf club head. FIG. 6 is a table of differences between calculated and actual multiple bar launch parameters. FIG. It is a table | surface which weights the absolute value of the difference of an actual and calculated several ball | bowl launch parameter. It is a table of error values.

Explanation of symbols

120 Acquisition System 122 Computer 124 Camera Mechanism 126 First Camera Unit 128 Second Camera Unit 140 Camera Flash Unit 142a, 142b Flash Unit 144 Second Camera 146a, 146b Flash Unit 130 Trigger Device 148 Receiver 160 Transmitter 133 Golf Club 168 Tee 166 Golf Ball

Claims (20)

Providing multiple golf club head characteristics for a golf club;
Provide multiple golf ball characteristics for the golf ball;
Providing a first optimal value comprising the orientation of the golf club during impact with the golf ball and the location of the impact on the golf club head;
Measuring the angular velocity of the golf club and the linear velocity of the golf club during the golfer's swing;
Measure several actual ball launch parameters;
Inputting the plurality of golf club characteristics, the plurality of golf ball characteristics, the angular velocity of the golf club, the linear velocity of the golf club, and the first optimum value into a rigid body code,
Generating a plurality of calculated ball launch parameters from the rigid body code;
Verifying the accuracy of the calculated ball launch parameters;
A method for determining the impact characteristics of a golfer during a golf swing.   The golf club head characteristics include: golf club head mass, golf club head center of gravity position relative to golf ball impact position, golf club head inertia tensor, golf club head face geometry, golf club 2. The method of claim 1 comprising a bulge and roll radius of the head, a golf club head loft and a golf club head face center location.   The method of claim 1, wherein the plurality of golf ball characteristics comprises a golf ball mass, a first golf ball coefficient of restitution at a speed of 143 feet per second, a golf ball moment of inertia, and a golf ball radius. .   2. The plurality of actual ball launch parameters include a golf ball launch angle, a golf ball lateral angle, a golf ball speed, a golf ball side spin, and a golf ball back spin. The method described in 1.   2. The plurality of actual ball launch parameters include a golf ball launch angle, a golf ball lateral angle, a golf ball speed, a golf ball side spin, and a golf ball back spin. The method described in 1.   The method of claim 2, wherein the plurality of golf club head characteristics further comprises a coefficient of restitution of the golf club head when the golf ball is hit and a spin coefficient of restitution of the golf club head when the golf ball is hit. a) giving an optimum value consisting of the orientation of the golf club during impact with the golf ball and the location of the impact on the golf club head;
b) measuring the angular velocity and linear velocity of the golf club during the golfer's swing;
c) measuring a plurality of actual ball launch parameters;
d) providing a plurality of golf club head characteristics for the golf club;
e) providing multiple golf ball characteristics for the golf ball;
f) inputting a plurality of golf club characteristics, a plurality of golf ball characteristics, an angular velocity of the golf club, a linear velocity and an optimum value of the golf club into the rigid body code;
g) generating a plurality of calculated ball launch parameters from the rigid body code;
h) verifying the accuracy of the plurality of calculated ball launch parameters;
i) repeating the steps d-h with different optimal values until the plurality of calculated ball launch parameters are verified;
A method for determining the impact characteristics of a golfer during a golf swing. Verification of the accuracy of the calculated ball launch parameters is:
Obtaining a plurality of absolute values of differences between each ball launch parameter of the plurality of calculated ball launch parameters and the plurality of actual ball launch parameters;
Weighting a plurality of absolute values of the difference to generate a plurality of weighted values;
Obtaining an error from an average sum square root of the plurality of weighted values;
The method of claim 7 comprising:   8. The method of claim 7, wherein the optimum value of golf club head orientation comprises a golf club head yaw, golf club head pitch and golf club head roll relative to the ground.   8. The method of claim 7, wherein the optimum impact position of the golf ball with the golf club head comprises an X-coordinate relative to the center of the golf club head face and a Y-coordinate relative to the golf club head face center.   The method of claim 7, wherein the optimal value is generated from a non-linear optimization method.   The method of claim 7, wherein the optimal value is generated by a Powell nonlinear optimization method.   The plurality of golf club head characteristics include a golf club head mass, a golf club head center of gravity position relative to a golf ball impact position, a golf club head inertia tensor, a golf club head geometry, and a golf club. 8. The method of claim 7, comprising a bulge and roll radius of the head face, a loft of the golf club head, and a center position of the golf club head face.   8. The method of claim 7, wherein the plurality of golf ball characteristics comprises a golf ball mass, a first golf ball coefficient of restitution at a speed of 143 feet per second, a golf ball moment of inertia, and a golf ball radius. .   The plurality of actual ball launch parameters include a launch ball launch angle, a golf ball lateral angle, a golf ball speed, a golf ball side spin, and a golf ball back spin. The method described.   The plurality of calculated ball launch parameters include a golf ball launch angle, a golf ball lateral angle, a golf ball speed, a golf ball side spin, and a golf ball back spin. 8. The method according to 7. A plurality of golf club characteristics, a plurality of golf ball characteristics, an angular velocity of the golf club, a linear velocity of the golf ball, and an optimum value are input to the rigid body code;
Generating a plurality of calculated ball launch parameters from the rigid body code;
Verifying the accuracy of the plurality of calculated ball launch parameters;
A method for determining the impact characteristics of a golfer during a golf swing.   The method of claim 17, wherein the optimum value comprises a golf ball orientation during impact with the golf ball and a position of the golf ball on the golf club head.   The method of claim 17, wherein the optimal value is generated from a non-linear optimization method.   The method of claim 17, wherein the optimal value is generated from a Powell nonlinear optimization method.

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