GOLFER'S IMPACT PROPERTIES DURING A GOLF SWING
A method for determining a golfer's golf club head orientation and impact location for a golf swing is disclosed herein. The method inputs the optimized values for the golf club head orientation and impact location, a plurality of golf swing properties of a golfer, a plurality of mass properties of a first golf club, and a plurality of mass properties of a first golf ball into a rigid body code. A plurality of calculated ball launch parameters is generated from the rigid body, which are compared to a plurality of actual ball launch parameters measured using a CMOS imaging system. The ball launch parameters are compared to each other to verify the optimized values. If the verification is not within a predetermined value, new optimized values are selected for the method. The method is repeated until the verification is within the value.
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The present application is a continuation application of U.S. patent application Ser. No. 10/843,782, filed on May 11, 2004, which claims priority to U.S. Provisional Application No. 60/498,796, filed on Aug. 28, 2003.
STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENTNot Applicable
BACKGROUND OF THE INVENTION1. Field of the Invention
The present invention relates to a method for determining a golfer's impact properties for a golf swing. More specifically, the present invention relates to a method for determining a golfer's golf club head orientation and impact location for a golf swing.
2. Description of the Related Art
For over twenty-five years, high speed camera technology has been used for gathering information on a golfer's swing. The information has varied from simple club head speed to the spin of the golf ball after impact with a certain golf club. Over the years, this information has fostered numerous improvements in golf clubs and golf balls, and assisted golfers in choosing golf clubs and golf balls that improve their game. Additionally, systems incorporating such high speed camera technology have been used in teaching golfers how to improve their swing when using a given golf club.
An example of such a system is U.S. Pat. No. 4,063,259 to Lynch et al., for a Method Of Matching Golfer With Golf Ball, Golf Club, Or Style Of Play, which was filed in 1975. Lynch discloses a system that provides golf ball launch measurements through use of a shuttered camera that is activated when a club head breaks a beam of light that activates the flashing of a light source to provide stop action of the club head and golf ball on a camera film. The golf ball launch measurements retrieved by the Lynch system include initial velocity, initial spin velocity and launch angle.
Another example is U.S. Pat. No. 4,136,387 to Sullivan, et al., for a Golf Club Impact And Golf Ball Launching Monitoring System, which was filed in 1977. Sullivan discloses a system that not only provides golf ball launch measurements, it also provides measurements on the golf club.
Yet another example is a family of patents to Gobush et al.,: U.S. Pat. No. 5,471,383 filed on Sep. 30, 1994; U.S. Pat. No. 5,501,463 filed on Feb. 24, 1994; U.S. Pat. No. 5,575,719 filed on Aug. 1, 1995; and U.S. Pat. No. 5,803,823 filed on Nov. 18, 1996. This family of patents discloses a system that has two cameras angled toward each other, a golf ball with reflective markers, a golf club with reflective markers thereon and a computer. The system allows for measurement of the golf club or golf ball separately, based on the plotting of points.
Yet another example is U.S. Pat. No. 6,042,483 for a Method Of Measuring Motion Of A Golf Ball. The patent discloses a system that uses three cameras, an optical sensor means, and strobes to obtain golf club and golf ball information.
The prior disclosures and most launch monitors, however, fail to disclose a system and method that determine the impact location and golf club head orientation during a golfer's swing.
BRIEF SUMMARY OF THE INVENTIONThe present invention is a method that allows for determining the impact location and golf club head orientation during a golfer's swing based on information obtained during a golfer's swing and measured inherent properties of a golf ball and golf club. The present invention uses an optimization method such as the Powell Optimization method or the Nelder & Mead Simplex optimization method to obtain the impact location and golf club head orientation.
One aspect of the present invention is a method for determining a golfer's impact properties during a golf swing. The method includes providing a plurality of golf club head properties for a golf club, a plurality of golf ball properties for a golf ball, and a first optimization value including an orientation of the golf club head during impact with a golf ball and an impact location of the golf ball on the golf club head. The method also includes measuring an angular velocity of the golf club and the linear velocity of the golf club during the golfer's swing, and a plurality of actual ball launch parameters. The method also includes inputting the plurality of golf club properties, the plurality of golf ball properties, the angular velocity of the golf club, the linear velocity of the golf club, and the first optimization value into a rigid body code. The method also includes generating a plurality of calculated ball launch parameters from the rigid body code. The method also includes verifying the accuracy of the plurality of calculated ball launch parameters.
Another aspect of the present invention is using the impact properties obtained through an optimization method to predict a golfer's ball striking performance. The method includes providing a plurality of golf club head properties for a first golf club, a plurality of golf ball properties for a first golf ball, and a first optimization value including an orientation of the golf club head during impact with a golf ball and an impact location of the golf ball on the golf club head. The method also includes measuring an angular velocity of the golf club and the linear velocity of the golf club during the golfer's swing, and a plurality of actual ball launch parameters. The method also includes inputting the plurality of golf club properties, the plurality of golf ball properties, the angular velocity of the golf club, the linear velocity of the golf club, and the first optimization value into a 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, a plurality of atmospheric conditions and a plurality of lift and drag properties for the first golf ball into a trajectory code. The method also includes generating the performance from the trajectory code of the first golf ball if struck by the golfer with the first golf club under the plurality of atmospheric conditions. The method also includes inputting a plurality of mass properties of a second golf club, the plurality of mass properties of the first golf ball, the angular velocity of the golf club, the linear velocity of the golf club, orientation of the golf club head during impact with a golf ball, and the impact location of a golf ball on the golf club head 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 the second plurality of ball launch parameters, the plurality of atmospheric conditions and the plurality of lift and drag properties for the first golf ball into the trajectory code. The method also includes generating the performance from the trajectory code of the first golf ball if struck by the golfer with the second golf club under the first atmospheric conditions. The method also includes inputting the plurality of mass properties of the first golf club, a plurality of mass properties of a second golf ball the angular velocity of the golf club, the linear velocity of the golf club, orientation of the golf club head during impact with a golf ball, and the impact location of a 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 the third plurality of ball launch parameters, the plurality of atmospheric conditions and a plurality of lift and drag properties for the second golf ball into the trajectory code. The method also includes generating the performance from the trajectory code of the second golf ball if struck by the golfer with the first golf club under the atmospheric conditions.
BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS
As shown in
At block 26, information from blocks 22 and 24 are inputted into a rigid body code. The rigid body code is set forth in equations B1-B13 below, and explained in further detail below. At block 28, the rigid body code generates a plurality of calculated ball launch parameters. At block 30, a plurality of actual ball launch parameters is collected from an acquisition system as discussed below. At block 32, the plurality of calculated ball launch parameters is verified by comparison to the plurality of actual ball launch parameters, as discussed in greater detail below. At block 34, if the value obtained during the verification step of block 32 is within an error value, then the values selected for the impact location and the orientation of the golf club during the golfer's swing are correct and the true values for the impact location and the orientation of the golf club during the golfer's swing. At block 36, if the value obtained during the verification step of block 32 is outside of the error value, then the values selected for the impact location and the orientation of the golf club during the golfer's swing is not correct and an optimization method must be used to obtain the true values for the impact location and the orientation of the golf club during the golfer's swing.
At block 38, the optimization method selects new values for the impact location and the orientation of the golf club during the golfer's swing for input into the rigid body code at block 26. A preferred optimization method is the Powell Optimization method, which is disclosed in Chapter 10 of Numerical Recipes in C: The Art Of Scientific Computing, Cambridge University Press (1988-1992), which pertinent parts are hereby incorporated by reference. An alternative optimization method is the Nelder & Mead Simplex optimization method. Those skilled in the relevant art will recognize that other optimization methods may be used with the method without departing from the scope and spirit of the present invention. The method is repeated with new optimization values until the value obtained during the verification step of block 32 is within an error value thereby indicating that the true values for the impact location and the orientation of the golf club during the golfer's swing have been determined by the method.
The golf ball properties of block 41 that are stored and collected include the mass of the golf ball (the Rules of Golf, as set forth by the USGA and the R&A, limit the mass to 45 grains or less), the radius of the golf ball (the Rules of Golf require a diameter of at least 1.68 inches), the COR of the golf ball and the MOI of the golf ball. The MOI of the golf ball may be determined using method well known in the industry. One such method is disclosed in U.S. Pat. No. 5,899,822, which pertinent parts are hereby incorporated by reference. The COR is determined using a method such as disclosed in U.S. Pat. No. 6,443,858, entitled Golf Ball With A High Coefficient Of Restitution, assigned to Callaway Golf Company, the assignee of the present application, and which pertinent parts are hereby incorporated by reference.
The mass, bulge and roll radii, loft and lie angles, face geometry and face center are determined using conventional methods well known in the golf industry. The inertia tensor is calculated using: the moment of inertia about the x-axis, Ixx; the moment of inertia about the y-axis, Iyy; the moment of inertia about the z-axis, Izz; the product of inertia Ixy; the product of inertia Izy; and the product of inertia Izx. The CG and the MOI of the club head are determined according to the teachings of U.S. Pat. No. 6,607,452, entitled High Moment of Inertia Composite Golf Club, assigned to Callaway Golf Company, the assignee of the present application, and hereby incorporated by reference in its entirety. The products of inertia Ixy, Ixz and Izy are determined according to the teachings of U.S. Pat. No. 6,425,832, entitled Golf Club Head That Optimizes Products Of Inertia, assigned to Callaway Golf Company, the assignee of the present application, and hereby incorporated by reference in its entirety.
The COR of the golf club head is determined using a method used by the United States Golf Association (“USGA”) and disclosed at www.usga.org, or using the method and system disclosed in U.S. Pat. No. 6,585,605, entitled Measurement Of The Coefficient Of Restitution Of A Golf Club, assigned to Callaway Golf Company, the assignee of the present application, and hereby incorporated by reference in its entirety. However, the COR of the golf club head is predicated on the golf ball, and will vary for different types of golf balls.
The acquisition system used to measure the dynamic swing properties of the golfer and the plurality of actual ball launch parameters is a system that captures and analyzes golf club information and golf ball information during and after a golfer's swing. The golf club information includes golf club head orientation, golf club head velocity, and golf club spin. The golf club head orientation includes dynamic lie, loft and face angle of the golf club head. The golf club head velocity includes path of the golf club head and attack of the golf club head. The golf ball information includes golf ball velocity, golf ball launch angle, golf ball side angle, golf ball speed and golf ball orientation. The golf ball orientation includes the true spin of the golf ball, and the tilt axis of the golf ball which entails the back spin and the side spin of the golf ball. The various measurements will be described in greater detail below.
As shown in
The first camera unit 126 preferably includes a first camera 140 and optional flash units 142a and 142b. The second camera unit 128 preferably includes a second camera 44 and optional flash units 146a and 146b. A preferred camera is a complementary metal oxide semiconductor (“CMOS”) camera with active pixel technology and a full frame rate ranging from 250 to 500 frames per second.
The field of view of the cameras 140 and 144 corresponds to the CMOS sensor array 200. In a preferred embodiment, the CMOS sensor array 200 is at least one megapixel in size having one thousand rows of pixels and one thousand columns of pixels for a total of one million pixels.
As shown in
As shown in
The establishment of an ROI 210 at the edge 150′ allows for “through the lens” triggering of the system 20. The through the lens triggering is a substitute for the triggering device 30. The system 20 is monitoring the ROI 210 at a very high frame rate, 1000 to 4000 frames per second, to detect any activity, or the appearance of the golf club 133. The system 120 can be instructed to monitor the ROI 210 for a certain brightness provided by the reflected dots 106a-c. Once the system 20 detects the object in the ROI 210, the cameras are instructed to gather information on the object.
As the golf club 133 tracks through the field of view 1000, the CMOS sensor array 200 creates new ROIs the encompass the reflective dots 106a-c. As shown in
As the object or golf club 133 moves through the field of view 1000, the current ROI preferably overlaps the previous ROI in order to better track the movement of the object or golf club 33. As shown in
At box 303, a ROI is created around the object. At box 304, the objected is monitored at a higher frame rate. At box 305, the object is removed from the field of view. If the golf club 133 is monitored during address at box 304, increased information is provided until the golf club is taken away for a swing. Alternatively, if a golf ball 166 is monitored at prior to impact, at impact and post impact, then the ROI is created around the golf ball 166 until it leaves the field of view 1000.
The CMOS sensor array 200 can operate at frames rates 4000 frames per second for a very small ROI. However, processing time between images or frames requires preferably less than 500 microseconds, and preferably less than 250 microseconds. The processing time is needed to analyze the image to determine if an object is detected and if the object is moving.
The system 120 may be calibrated using many techniques known to those skilled in the pertinent art. One such technique is disclosed in U.S. Pat. No. 5,803,823, which is hereby incorporated by reference. The system 120 is calibrated when first activated, and then may operate to analyze golf swings for golfers until deactivated.
As mentioned above, the system 120 captures and analyzes golf club information and golf ball information during and after a golfer's swing. The system 120 uses the images and other information to generate the information on the golfer's swing. The golf club 133 has at least two, but preferably three highly reflective points 106a-c preferably positioned on the shaft, heel and toe of the golf club 133. The highly reflective points 106a-c may be inherent with the golf club design, or each may be composed of a highly reflective material that is adhesively attached to the desired positions of the golf club 133. The points 106a-c are preferably highly reflective since the cameras 140 and 144 are preferably programmed to search for two or three points that have a certain brightness such as 200 out of a gray scale of 0-255. The cameras 140 and 144 search for point pairs that have approximately one inch separation, and in this manner, the detection of the golf club 133 is acquired by the cameras for data acquisition.
As shown in
d=[(Ptx−Pnx)2+(Pty−Ptny)2 . . . ]1/2
where d is the distance, Ptx is the position in the x direction and Pty is the position in the y direction.
The system 120 may use a three point mode or a two point mode to generate further information. The two point mode uses Vtoe, Vheel and Vclubtop to calculate the head speed.
Vtoe=[(Ptx3−Ptx1)2+(Pty3−Pty1)2+(Ptz3−Ptz1)2]1/2[1/δT]
Vheel=[(Ptx3−Ptx1)2+(Pty3−Pty1)2+(Ptz3−Ptz1)2]1/2[1/δT]
Vclubtop=[Vtoe+Vheel][1/2]
Vy=[(y3heel−y1heel)2+(y3toe−y1toe)2]1/2[1/(2*δT)]
Vz=[(z3heel−z1heel)2+(z3toe−z1toe)2]1/2[1/(2*δT)]
This information is then used to acquire the path angle and attack angle of the golf club 133. The Path angle=sin−1(Vy/[V]) where [V] is the magnitude of V.
The attack angle=sin−1(Vz/[V]), and the dynamic loft and dynamic lie are obtained by using Series one and Series two to project the loft and lie onto the vertical and horizontal planes.
The two point mode uses the shaft highly reflective point 106a or the toe highly reflective point 106c along with the heel highly reflective point 106b to calculate the head speed of the golf club, the path angle and the attack angle. Using the shaft highly reflective point 106a, the equations are:
Vheel=[(Ptx3−Ptx1)2+(Pty3−Pty1)2+(Ptz3−Ptz1)2]1/2[1/δT]
Vshaft=[(Ptx3−Ptx1)2+(Pty3−Pty1)2+(Ptz3−Ptz1)2]1/2[1/δT]
Vcenter=1.02*(Vshaft+Vheel)
Vy=[(y3heel−y1heel)2+(y3shaft−y1shaft)2]1/2[1/(2*δT)]
Vz=[(z3heel−z1heel)2+(z3shaft−z1shaft)2]1/2[1/(2*δT)]
The Path angle=sin−1(Vy/[V]) where [V] is the magnitude of V.
The attack angle=sin−1(Vz/[V]).
Using the toe highly reflective point 106c, the equations are:
Vtoe=[(x3−x1)2+(y3−y1)2+(z3−z1)2]1/2[1/δT]
Vheel=[(x2−x1)2+(y2−y1)2+(z2−z1)2]1/2[1/δT]
Vclubtop=[Vtoe+Vheel][1/2]
The path angle=sin−1(Vyclubtop/[Vclubtop]) where [Vclubtop] is the magnitude of Vclubtop.
The attack angle=sin−1(Vzclubtop/[Vclubtop]) where [Vclubtop] is the magnitude of Vclubtop.
The golf ball 166 information is mostly obtained from images of the golf ball post impact. First, the best radius and position of the two dimensional areas of interest are determined from the images. Next, all of the combinations of the golf ball 166 centers in the images are matched and passed through a calibration model to obtain the X, Y, and Z coordinates of the golf ball 166. The system 120 removes the pairs with an error value greater then 5 millimeters to get acceptable X, Y, Z coordinates. Next, the velocity of the golf ball 166 is obtained from Vx, Vy and Vz using a linear approximation. Next the golf ball speed is obtained by calculating the magnitude of Vx, Vy and Vz.
The launch angle=sin−1(Vz/golf ball speed),
and the spin angle=sin−1(Vy/golf ball speed).
Next, the system 120 looks for the stripes 108a-b, as shown in
Next, the θ angle of the golf ball 166 is measured by taking the first vector and the second vector and using the equation:
θ=cos−1 [(vector A1)(vector A2)]/([V1][V2]) where [V1] is the magnitude of V1 and [V2] is the magnitude of V2.
As the golf ball 166 rotates from the position shown in
The following is an example of how the system captures and analyzes golf club information and golf ball information during and after a golfer's swing. The golf club information includes golf club head orientation, golf club head velocity, and golf club spin. The golf club head orientation includes dynamic lie, loft and face angle of the golf club head. The golf club head velocity includes path of the golf club head, attack of the golf club head and downrange information. The golf ball information includes golf ball velocity, golf ball launch angle, golf ball side angle, golf ball speed manipulation and golf ball orientation. The golf ball orientation includes the true spin of the golf ball, and the tilt axis of the golf ball which entails the back spin and the side spin of the golf ball.
The system 120 pairs the points 106a-c, verifying size, separation, orientation and attack angle. Then, the system 120 captures a set of six points (three pairs) from a first find as shown in
Next the speed of the head of the golf club 133 is determined by the system 120 using the equations discussed above.
Next the path angle and the attack angle of the golf club 133 is determined by the system 120. Using the methods previously described, the attack angle is determined from the following equation:
Attack angle=−a tan(δz/δx)
Where δz is the z value of the midpoint between 106a1 and 106b1 minus the z value of the midpoint between 106a3 and 106b3. Where δx is the x value of the midpoint between 106a1 and 106b1 minus the x value of the midpoint between 106a3 and 106b3.
The path angle is determined from the following equation:
path angle=−a tan(δy/δx)
Where δy is the y value of the midpoint between 106a1 and 106b1 minus the y value of the midpoint between 106a3 and 106b3. Where δx is the x value of the midpoint between 106a1 and 106b1 minus the x value of the midpoint between 106a3 and 106b3.
Next, the golf ball 166 data is determined b the system 120. First, the thresholding of the image is established as shown in
Next, as shown in
Golf ball speed=[δX2+δY2+δZ2]1/2/δT. For the information provided in FIG. 40, the speed of the golf ball=[(−161.68+(−605.26))2+(−43.41+(−38.46))2+(−282.74+(−193.85))2]1/2/(13127−5115), which is equal to 126 MPH once converted from millimeters over microseconds.
The launch angle of the golf ball 166 is determined by the following equation:
Launch angle=sin−1(Vz/golf ball speed) where Vz=δZ/δT.
For the information provided in
Then, the launch angle=sin−1(11.3/126.3)=11.3 degrees.
The side angle of the golf ball 166 is determined by the following equation:
Side angle=sin−1(Vy/golf ball speed) where Vy=δY/δT. For the information provided in FIG. 40, Vy=[(−43.41+(−38.46)]/(13127−5115)=1.4 MPH.
Then, the side angle=sin−1(1.4/126.3)=0.6 degrees.
The ball spin is calculated by determining the location of the three striped on each of the acquired golf balls. Matching each axis in the field of view and determine which of the axis is orthogonal to the vertical plane. The spin is then calculated by:
θ=a cos((vectorA1 dot vector A2)/mag(v1)*mag(v2)) as discussed above.
The rigid body code solves the impact problem using conservation of linear and angular momentum, which gives the complete motion of the two rigid bodies. The impulses are calculated using the definition of impulse, and the equations are set forth below. The coordinate system used for the impulse equations is set forth below. The impulse-momentum method does not take in account the time history of the impact event. The collision is described at only the instant before contact and the instant after contact. The force transmitted from the club head to the ball is equal and opposite to the force transmitted from the ball to the club head. These forces are conveniently summed up over the period of time in which the two objects are in contact, and they are called the linear and angular impulses.
The rigid body code assumes that both the golf ball 166 and the golf club head 150 are unconstrained rigid bodies, even though the golf club head 150 is obviously connected to the shaft 152, and the ball 166 is not floating in air upon impact with the golf club head 150. For the golf club head 150, the assumption of an unconstrained rigid body is that the impact with the golf ball 166 occurs within a very short time frame (microseconds), that only a small portion of the tip of the shaft 152 contributes to the impact. For the golf ball 166, the impulse due to friction between itself and the surface it is placed upon (e.g. tee, mat or ground) is very small in magnitude relative to the impulse due to the impact with the golf club head 150, and thus this friction is ignored in the calculations.
In addition to the normal coefficient of restitution, which governs the normal component of velocity during the impact, there are coefficients of restitution that govern the tangential components of velocity. The additional coefficients of restitution are determined experimentally.
The absolute performance numbers are defined in the global coordinate system, or the global frame. This coordinate system has the origin at the center of the golf ball, one axis points toward the intended final destination of the shot, one axis points straight up into the air, and the third axis is normal to both of the first two axis. The global coordinate system preferably follows the right hand rule.
The coordinate system used for the analysis is referred to as the impact coordinate system, or the impact frame. This frame is defined relative to the global frame for complete analysis of a golf shot. The impact frame is determined by the surface normal at the impact location on the golf club head 150. The positive z-direction is defined as the normal outward from the golf club head 150. The plane tangent to the point of impact contains 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 plane, and thus the yz-plane is normal to the ground plane. The impact frame incorporates the loft, bulge and roll of a club head, and also includes the net result of the golf swing. Dynamic loft, open or close to the face, and toe down all measured for definition of the impact frame. Motion in the impact frame is converted to equivalent motion in the global frame since the relationship between the global coordinate system and the impact coordinate system is known. The post impact motion of the golf ball 166 is used as inputs in the Trajectory Code, and the distance and deviation of the shot is calculated by the present invention.
- The symbols are defined as below:
- {right arrow over (i)}=(1 0 0), the unit vector in the x-direction.
- {right arrow over (j)}=(0 1 0), the unit vector in the y-direction.
- {right arrow over (k)}=(0 0 1), the unit vector in the z-direction.
- m1, the mass of the club head.
- m2, the mass of the golf ball.
the inertia tensor of the club head.
the inertia tensor of the golf ball. - {right arrow over (r)}1=(a1 b1 c1), the vector from point of impact to the center of gravity of the club head.
- {right arrow over (r)}2=(a2 b2 c2), the vector from point of impact to the center of gravity of the golf ball.
- {right arrow over (r)}3=−{right arrow over (r)}1+{right arrow over (r)}2=(−a1+a2 −b1+b2 −c1+c2)=(a3 b3 c3), the vector from center of gravity of club head to the center of gravity of the golf ball.
- {right arrow over (v)}1,i=(vx,1,i vy,1,i vz,1,i), the velocity of the club head before impact.
- {right arrow over (v)}1,f=(vx,1,f vy,1,f vz,1,f), the velocity of the club head after impact.
- {right arrow over (v)}1,i=(vx,1,i vy,1,i vz,1,i), the velocity of the golf ball before impact.
- {right arrow over (v)}2,f=(vx,2,f vy,2,f vz,2,f), the velocity of the golf ball after impact.
- {right arrow over (ω)}1,i=(ωx,1,i ωy,1,i ωz,1,i), the angular velocity of the club head before impact.
- {right arrow over (ω)}1,f=(ωx,1,f ωy,1,f ωz,1,f), the angular velocity of the club head after impact.
- {right arrow over (ω)}2,i=(ωx,2,i ωy,2,i ωz,2,i), the angular velocity of the golf ball before impact.
- {right arrow over (ω)}2,f=(ωx,2,f ωy,2,f ωz,2,f), the angular velocity of the golf ball after impact.
the coefficient of restitution matrix. - [L]=m{right arrow over (v)}, definition of linear momentum.
- [H]=[I]{right arrow over (ω)}, definition of angular momentum.
Conservation of linear momentum:
m1{right arrow over (v)}1,f+m2{right arrow over (v)}2,f=m1{right arrow over (v)}1,i+m2{right arrow over (v)}2,i B1-B3
Conservation of angular momentum:
The definition of coefficients of restitution:
The tangential impulse on the ball causes both rotation and translation:
Equations B1-B12 can be combined to form a system of linear equations of the form:
[A]{x}={B} B13
where [A], and {B} are determined from the known velocities before the impact, the mass properties of the golf ball 166 and golf club head 150, the impact location relative to the center of gravity of the golf ball 166 and the golf club head 150, and the surface normal at the point of impact. {x} contains all the post impact velocities (linear and angular), and is solved by pre-multiplying {B} by the inverse of [A], or any other method in solving system of equations in linear algebra.
When the golf ball 166 is sitting on the tee 168, it is in equilibrium. The golf ball 166 will not move until a force that's greater than Fm, the maximum static friction force between the golf ball 166 and the tee 168, is applied on the golf ball 166.
Fm=μsN=μsm2g C1
μs , is the static coefficient of friction and g is gravity.
For a golf ball 166 with 45 grams of mass, and a μs of 0.3,
Fm=μsmg=(0.3)(0.045)(9.81)=0.132N
Assume this force is applied on the golf ball 166 for the duration of an impact of 0.0005 sec (which is an overestimation of the actual impulse), then the impulse, L, on the golf ball 166 is:
L=(0.132)(0.0005)=0.0000662N·s
This impulse, L, would cause the golf ball 166 to move at 0.00147 m/s (or 0.00483 ft/sec), and rotate at 8.08 rad/sec (or 77.1 rpm). Both of these numbers are small relative to the range of numbers normally seen for irons and woods. If the rigid body code of the present invention were to be applied to putters, then it would be preferable to include the friction force between the green and the golf ball 166 for the analysis.
Each of the individual terms in the above matrix, eij, where i=x, y, z, and j =x, y, z, relates the velocity in the i-direction to the j-direction. Each of the diagonal terms, where i=j, indicate the relationship in velocity of one of the axis, x, y, or z, before and after the impact. Let x, y, z be the axis defined in the impact frame. The term ezz includes all the energy that is lost in the impact in the normal direction of impact. exx and eyy are account for the complicated interaction between the golf ball 166 and the golf club head 150 in the tangential plane by addressing the end result. In general, the off diagonal terms eij, where i≠j, are equal to zero for isotropic materials.
As shown in
At block 94, the information from blocks 91, 92 and 93 are inputted into a rigid body code. The rigid body code is explained in greater detail above. At block 94, the rigid body code is used to generate a plurality of ball launch parameters, such as disclosed above in reference to
At block 98, the ball launch parameters, the atmospheric conditions and the lift and drag properties are inputted into a trajectory code. At block 99, the trajectory code is utilized to predict the performance of the golfer when swinging the specific golf club, with the specific golf ball under the specific atmospheric conditions. Trajectory codes are known in the industry, and one such code is disclosed in the afore-mentioned U.S. Pat. No. 6,186,002. The USGA has such a trajectory code available for purchase.
In predicting the performance of a golf ball struck by a golfer with a specific golf club under predetermined atmospheric conditions, an operator has the option of inputting an impact of the face at a certain location regardless of the true location of impact. This allows for prediction of the performance of the golf club 133 for toe shots, heel shots and center shots. The type of golf ball may be selected, the type of golf club may be selected, the atmospheric conditions including wind speed, direction, relative humidity, air pressure, temperature and the terrain may be selected by the operator to predict a golfer's performance using these input parameters along with the pre-impact swing properties for the golfer.
From the foregoing it is believed that those skilled in the pertinent art will recognize the meritorious advancement of this invention and will readily understand that while the present invention has been described in association with a preferred embodiment thereof, and other embodiments illustrated in the accompanying drawings, numerous changes, modifications and substitutions of equivalents may be made therein without departing from the spirit and scope of this invention which is intended to be unlimited by the foregoing except as may appear in the following appended claims. Therefore, the embodiments of the invention in which an exclusive property or privilege is claimed are defined in the following appended claims.
Claims
1. A method for determining a golfer's impact properties during impact of a golf club with a golf ball, the method comprising:
- obtaining a first optimization value, the first optimization value comprising an orientation of a golf club head of the golf club during impact with a golf ball and an impact location of the golf ball on a face of the golf club head;
- measuring an angular velocity of the golf club and a linear velocity of the golf club during the golfer's swing using a CMOS imaging system, the CMOS imaging system having a sensor array with at least one megapixel in size, wherein the CMOS imaging system forms a region of interest operating at a frame rate of 1000 to 4000 frames per second prior to the golf club entering the field of view and then forms subsequent regions of interest as the golf club travels through the field of view;
- measuring a plurality of actual ball launch parameters using the CMOS imaging system;
- inputting a plurality of golf club properties, a plurality of golf ball properties, the angular velocity of the golf club, the linear velocity of the golf club, and the first optimization value into a rigid body code;
- generating a plurality of calculated ball launch parameters from the rigid body code; and
- verifying the accuracy of the plurality of calculated ball launch parameters to actual ball parameters by obtaining a plurality of absolute values of the differences between each of the ball launch parameters of the plurality of calculated ball launch parameters and the plurality of actual ball launch parameters, weighting each of the plurality of absolute values of the differences to create a plurality of weighted values, and obtaining an error value from the root-mean-sum of the plurality of weighted values.
2. The method according to claim 1 wherein the plurality of golf club head properties comprises the mass of the golf club head, the location of the center of gravity of the golf club head relative to the impact location of the golf ball, the inertia tensor of the golf club head, the geometry of the face of the golf club head, the bulge and roll radii of the face of the golf club head, the loft of the golf club head and the face center location of the golf club head.
3. The method according to claim 1 wherein the plurality of golf ball properties comprises the mass of the golf ball, the coefficient of restitution of the first golf ball at a speed of 143 feet per second, the moment of inertia of the golf ball and the radius of the golf ball.
4. The method according to claim 1 wherein the plurality of actual ball launch parameters comprises a launch angle of the golf ball, a side angle of the golf ball, a golf ball speed, a side spin of the golf ball and a back spin of the golf ball.
5. The method according to claim 1 wherein the plurality of calculated ball launch parameters comprises a launch angle of the golf ball, a side angle of the golf ball, a golf ball speed, a side spin of the golf ball and a back spin of the golf ball.
6. The method according to claim 2 wherein the plurality of golf club head properties further comprises the coefficient of restitution of the golf club head when striking the golf ball, and a spin coefficient of restitution of the golf club head when striking the golf ball.
7. A method for determining a golfer's impact properties during impact of a golf club with a golf ball, the method comprising:
- a) providing an optimization value, the optimization value comprising an orientation of a golf club head of the golf club during impact with the golf ball and an impact location of the golf ball on a face of the golf club head;
- b) measuring an angular velocity of the golf club and a linear velocity of the golf club during the golfer's swing using a CMOS imaging system, the CMOS imaging system having a sensor array with at least one megapixel in size, wherein the CMOS imaging system forms a region of interest operating at a frame rate of 1000 to 4000 frames per second prior to the golf club entering the field of view and then forms subsequent regions of interest as the golf club travels through the field of view during the golfer's swing;
- c) measuring a plurality of actual ball launch parameters using the CMOS imaging system;
- d) providing a plurality of golf club head properties for the golf club;
- e) providing a plurality of golf ball properties for the golf ball;
- f) inputting the plurality of golf club properties, the plurality of golf ball properties, the angular velocity of the golf club, the linear velocity of the golf club, and the optimization value into a 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 to actual ball parameters by obtaining a plurality of absolute values of the differences between each of the ball launch parameters of the plurality of calculated ball launch parameters and the plurality of actual ball launch parameters, weighting each of the plurality of absolute values of the differences to create a plurality of weighted values, and obtaining an error value from the root-mean-sum of the plurality of weighted values;
- i) repeating steps d-h with different optimization values using non-linear optimization methods until the accuracy of the plurality of calculated ball launch parameters is verified to measurements in step c.
8. The method according to claim 7 wherein the optimization value for the orientation of the golf club head comprises the yaw of the golf club head, the pitch of the golf club head and the roll of the golf club head, all relative to the ground.
9. The method according to claim 7 wherein the optimization value for the impact location of the golf ball with the golf club head comprises a X-coordinate relative to the center of a face of the golf club head and a Y-coordinate relative to the center of the face of the golf club head.
10. The method according to claim 7 wherein the optimization values are generated from the Powell non-linear optimization method.
11. The method according to claim 7 wherein the plurality of golf club head properties comprises the mass of the golf club head, the location of the center of gravity of the golf club head relative to the impact location of the golf ball, the inertia tensor of the golf club head, the geometry of the face of the golf club head, the bulge and roll radii of the face of the golf club head, the loft of the golf club head and the face center location of the golf club head.
12. The method according to claim 7 wherein the plurality of golf ball properties comprises the mass of the golf ball, the coefficient of restitution of the first golf ball at a speed of 143 feet per second, the moment of inertia of the golf ball and the radius of the golf ball.
13. The method according to claim 7 wherein the plurality of actual ball launch parameters comprises a launch angle of the golf ball, a side angle of the golf ball, a golf ball speed, a side spin of the golf ball and a back spin of the golf ball.
14. The method according to claim 7 wherein the plurality of calculated ball launch parameters comprises a launch angle of the golf ball, a side angle of the golf ball, a golf ball speed, a side spin of the golf ball and a back spin of the golf ball.
15. A method for determining a golfer's impact properties during a golf swing, the method comprising:
- inputting a plurality of golf club properties, a plurality of golf ball properties, an angular velocity of a golf club, a linear velocity of the golf club, and an optimization value into a rigid body code, wherein the optimization value is generated from a Powell non-linear optimization method;
- generating a plurality of calculated ball launch parameters from the rigid body code; and
- verifying the accuracy of the plurality of calculated ball launch parameters against a plurality of actual ball launch parameters measured using a CMOS imaging system, the CMOS imaging system having a sensor array with at least one megapixel in size, wherein the CMOS imaging system forms a region of interest operating at a frame rate of 1000 to 4000 frames per second prior to a golf ball entering the field of view and then forms subsequent regions of interest as the golf ball travels through the field of view.
16. The method according to claim 15 wherein the optimization value comprises an orientation of the golf club head during impact with a golf ball and an impact location of the golf ball on the golf club head.
17. A method for determining a golfer's impact properties during a golf swing, the method comprising:
- providing a plurality of golf club head properties for a golf club;
- providing a plurality of golf ball properties for a golf ball;
- providing a first optimization value, the first optimization value comprising an orientation of the golf club head during impact with a golf ball and an impact location of the golf ball on the golf club head;
- measuring an angular velocity of the golf club and the linear velocity of the golf club during the golfer's swing;
- measuring a plurality of actual ball launch parameters;
- inputting the plurality of golf club properties, the plurality of golf ball properties, the angular velocity of the golf club, the linear velocity of the golf club, and the first optimization value into a rigid body code;
- generating a plurality of calculated ball launch parameters from the rigid body code; and
- verifying the accuracy of the plurality of calculated ball launch parameters.
18. The method according to claim 17 wherein the plurality of golf club head properties comprises the mass of the golf club head, the location of the center of gravity of the golf club head relative to the impact location of the golf ball, the inertia tensor of the golf club head, the geometry of the face of the golf club head, the bulge and roll radii of the face of the golf club head, the loft of the golf club head and the face center location of the golf club head.
19. The method according to claim 17 wherein the plurality of golf ball properties comprises the mass of the golf ball, the coefficient of restitution of the first golf ball at a speed of 143 feet per second, the moment of inertia of the golf ball and the radius of the golf ball.
20. The method according to claim 17 wherein the plurality of actual ball launch parameters comprises a launch angle of the golf ball, a side angle of the golf ball, a golf ball speed, a side spin of the golf ball and a back spin of the golf ball.
21. The method according to claim 17 wherein the plurality of calculated ball launch parameters comprises a launch angle of the golf ball, a side angle of the golf ball, a golf ball speed, a side spin of the golf ball and a back spin of the golf ball.
22. A method for determining a golfer's impact properties during a golf swing, the method comprising:
- b) providing an optimization value, the optimization value comprising an orientation of the golf club head during impact with a golf ball and an impact location of the golf ball on the golf club head;
- b) measuring an angular velocity of the golf club and the linear velocity of the golf club during the golfer's swing;
- c) measuring a plurality of actual ball launch parameters, wherein the plurality of actual ball launch parameters comprises a launch angle of the golf ball, a side angle of the golf ball, a golf ball speed, a side spin of the golf ball and a back spin of the golf ball;
- d) providing a plurality of golf club head properties for a golf club, wherein the plurality of golf club head properties comprises a mass of the golf club head, a location of the center of gravity of the golf club head relative to the impact location of the golf ball, an inertia tensor of the golf club head, the geometry of the face of the golf club head, a bulge and roll radii of the face of the golf club head, a loft of the golf club head and a face center location of the golf club head;
- e) providing a plurality of golf ball properties for a golf ball, wherein the plurality of golf ball properties comprises a mass of the golf ball, a coefficient of restitution of the first golf ball at a speed of 143 feet per second, a moment of inertia of the golf ball and a radius of the golf ball;
- f) inputting the plurality of golf club properties, the plurality of golf ball properties, the angular velocity of the golf club, the linear velocity of the golf club, and the optimization value into a rigid body code;
- g) generating a plurality of calculated ball launch parameters from the rigid body code, wherein the plurality of calculated ball launch parameters comprises a launch angle of the golf ball, a side angle of the golf ball, a golf ball speed, a side spin of the golf ball and a back spin of the golf ball;
- h) verifying the accuracy of the plurality of calculated ball launch parameters;
- i) repeating steps d-h with different optimization values until the accuracy of the plurality of calculated ball launch parameters is verified.
23. The method according to claim 22 wherein the verifying the accuracy of the plurality of calculated ball launch parameters comprises:
- obtaining a plurality of absolute values of the differences between each of the ball launch parameters of the plurality of calculated ball launch parameters and the plurality of actual ball launch parameters;
- weighting each of the plurality of absolute values of the differences to create a plurality of weighted values; and
- obtaining an error value from the root-mean-sum of the plurality of weighted values.
24. The method according to claim 22 wherein the optimization value for the orientation of the golf club head comprises the yaw of the golf club head, the pitch of the golf club head and the roll of the golf club head, all relative to the ground.
25. The method according to claim 22 wherein the optimization value for the impact location of the golf ball with the golf club head comprises a X-coordinate relative to the center of a face of the golf club head and a Y-coordinate relative to the center of the face of the golf club head.
Type: Application
Filed: Jul 26, 2007
Publication Date: Jan 24, 2008
Applicant: CALLAWAY GOLF COMPANY (CARLSBAD, CA)
Inventor: SCOTT MANWARING (CARLSBAD, CA)
Application Number: 11/828,655
International Classification: A63B 57/00 (20060101);