U.S. patent application number 11/828655 was filed with the patent office on 2008-01-24 for golfer's impact properties during a golf swing.
This patent application is currently assigned to CALLAWAY GOLF COMPANY. Invention is credited to SCOTT R. MANWARING.
Application Number | 20080020867 11/828655 |
Document ID | / |
Family ID | 38972109 |
Filed Date | 2008-01-24 |
United States Patent
Application |
20080020867 |
Kind Code |
A1 |
MANWARING; SCOTT R. |
January 24, 2008 |
GOLFER'S IMPACT PROPERTIES DURING A GOLF SWING
Abstract
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.
Inventors: |
MANWARING; SCOTT R.;
(CARLSBAD, CA) |
Correspondence
Address: |
CALLAWAY GOLF C0MPANY
2180 RUTHERFORD ROAD
CARLSBAD
CA
92008-7328
US
|
Assignee: |
CALLAWAY GOLF COMPANY
2180 RUTHERFORD ROAD
CARLSBAD
CA
92008-7328
|
Family ID: |
38972109 |
Appl. No.: |
11/828655 |
Filed: |
July 26, 2007 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
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10843782 |
May 11, 2004 |
|
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11828655 |
Jul 26, 2007 |
|
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60498796 |
Aug 28, 2003 |
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Current U.S.
Class: |
473/407 |
Current CPC
Class: |
A63B 2225/74 20200801;
A63B 2220/805 20130101; A63B 69/3632 20130101; A63B 71/06 20130101;
A63B 69/3658 20130101; A63B 2024/0031 20130101; A63B 2220/16
20130101; A63B 2220/35 20130101; A63B 2220/89 20130101; A63B
2220/24 20130101; A63B 24/0021 20130101; A63B 2220/05 20130101;
A63B 69/362 20200801; A63B 24/0003 20130101; A63B 2220/807
20130101; A63B 2220/30 20130101; A63B 69/3617 20130101 |
Class at
Publication: |
473/407 |
International
Class: |
A63B 57/00 20060101
A63B057/00 |
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.
Description
CROSS REFERENCES TO RELATED APPLICATIONS
[0001] 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 DEVELOPMENT
[0002] Not Applicable
BACKGROUND OF THE INVENTION
[0003] 1. Field of the Invention
[0004] 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.
[0005] 2. Description of the Related Art
[0006] 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.
[0007] 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.
[0008] 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.
[0009] 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.
[0010] 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.
[0011] 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 INVENTION
[0012] The 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.
[0013] 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.
[0014] 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
[0015] FIG. 1 is a flow chart of the general method of the present
invention.
[0016] FIG. 2 is a flow chart illustrating the inputs for the
measured values.
[0017] FIG. 3 is a flow chart illustrating the inputs for the golf
club swing properties.
[0018] FIG. 4 is a flow chart illustrating the inputs for the
measured golf ball inherent properties.
[0019] FIG. 5 is a flow chart illustrating the inputs for the
measured golf club head inherent properties.
[0020] FIG. 6 is a flow chart of the contents for the plurality of
actual ball launch parameters.
[0021] FIG. 7 is a flow chart of the contents for the plurality of
calculated ball launch parameters.
[0022] FIG. 8 is a flow chart of the inputs for the optimized
values.
[0023] FIG. 9 is a flow chart of the inputs for the optimized
values for the golf club head orientation.
[0024] FIG. 10 is a perspective view of a golf club head
illustrating the yaw, pitch and roll of the golf club head.
[0025] FIG. 11 is a flow chart for the verification of the ball
results.
[0026] FIG. 12 is a flow chart of the contents for the comparison
of the actual and calculated plurality of ball launch
parameters.
[0027] FIG. 13 is a flow chart of the contents for the weighting of
the absolute values of the differences between the actual and
calculated plurality of ball launch parameters.
[0028] FIG. 14 is a perspective view of the monitoring system of
the present invention.
[0029] FIG. 15 is a schematic representation of a full frame CMOS
sensor array.
[0030] FIG. 15A is a schematic representation of a field of
view.
[0031] FIG. 16 a schematic representation of a ROI within the CMOS
sensor array.
[0032] FIG. 17 a schematic representation of an object within the
field of view.
[0033] FIG. 18 a schematic representation of an object within the
field of view.
[0034] FIG. 19 a schematic representation of a ROI within the CMOS
sensor array.
[0035] FIG. 20 a schematic representation of an object within the
field of view.
[0036] FIG. 21 a schematic representation of a ROI within the CMOS
sensor array.
[0037] FIG. 22 a schematic representation of an object within the
field of view.
[0038] FIG. 23 a schematic representation of a ROI within the CMOS
sensor array.
[0039] FIG. 24 is a flow chart of a method of using the system of
the invention.
[0040] FIG. 25 is a flow chart of a method of using the system of
the invention.
[0041] FIG. 26 is a flow chart of a method of using the system of
the invention.
[0042] FIG. 27 is a flow chart of a method of using the system of
the invention.
[0043] FIG. 28 is a flow chart of a method of using the system of
the invention.
[0044] FIG. 29 is a schematic representation of the highly
reflective points of the golf club positioned in accordance with
the first, second and third exposures of the golf club.
[0045] FIG. 30 is an isolated view of a golf ball striped for
measurement.
[0046] FIG. 30A is an isolated view of a golf ball striped for
measurement using an image with a partial phantom of a prior image
with vector signs present to demonstrate calculation of angle
.theta..
[0047] FIG. 31 illustrates first, second and third images of the
connected highly reflective points on a golf club, and the teed
golf ball for the first find grouping of the highly reflective
points.
[0048] FIG. 31A illustrates first, second and third images of the
connected highly reflective points on a golf club, and the teed
golf ball for the first find grouping of the highly reflective
points.
[0049] FIG. 32 illustrates first, second and third images of the
connected highly reflective points on a golf club, and the teed
golf ball for the second find grouping of the highly reflective
points.
[0050] FIG. 33 illustrates first, second and third images of the
connected highly reflective points on a golf club, and the teed
golf ball for the second find grouping of the highly reflective
points.
[0051] FIG. 34 illustrates first, second and third images of the
connected highly reflective points on a golf club, and the teed
golf ball with repeated points eliminated and results of the find
displayed.
[0052] FIG. 35 illustrates first, second and third images of the
connected highly reflective points on a golf club, and the teed
golf ball with repeated points eliminated and results of the find
displayed.
[0053] FIG. 36 is a chart of the processed final pairs giving the
x, y and z coordinates.
[0054] FIG. 37 is an illustration of the thresholding of the images
for the golf ball in flight.
[0055] FIG. 38 is an isolated view of the golf ball to illustrate
determining the best ball center and radius.
[0056] FIG. 39 is a partial flow chart with images of golf balls
for stereo correlating two dimensional points.
[0057] FIG. 40 illustrates the teed golf ball and the first, second
third and fourth images of the golf ball after impact, along with
positioning information.
[0058] FIG. 41 is a flow chart of a method of predicting
performance using the impact location and golf club head
orientation values obtained through the optimization method.
[0059] FIG. 42 is a table of the golf club swing properties.
[0060] FIG. 43 is a table of the plurality of actual ball launch
parameters.
[0061] FIG. 44 is a table of the golf club head properties.
[0062] FIG. 45 is a table of the golf ball properties.
[0063] FIG. 46 is a table of a plurality of calculated ball launch
parameters.
[0064] FIG. 47 is a table of optimized values for the impact
location and golf club head orientation.
[0065] FIG. 48 is a table of the difference between the actual and
calculated plurality of ball launch parameters.
[0066] FIG. 49 is a table of the weighting of the absolute values
of the differences between the actual and calculated plurality of
ball launch parameters.
[0067] FIG. 50 a table of the error value.
DETAILED DESCRIPTION OF THE INVENTION
[0068] As shown in FIG. 1, a method for determining a golfer's
impact properties during a golf swing is generally designated 20.
The method 20 involves using measured dynamic properties for a
golfer during a golf swing and inherent properties of a golf ball
and golf club to determine through an optimization method the
impact location and the orientation of the golf club during the
golfer's swing. At block 22, the first optimized values for impact
location and the orientation of the golf club during the golfer's
swing are selected by an operator. These first optimized values are
speculative, and are probably not the true values for the impact
location and the orientation of the golf club during the golfer's
swing. However, these first optimized values 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 24, the measured
values are collected for input to determine through an optimization
method the impact location and the orientation of the golf club
during the golfer's swing.
[0069] 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.
[0070] 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.
[0071] FIG. 2 is a flow chart illustrating the inputs or content of
the measured values of block 24 of FIG. 1. Block 40 contains the
golf swing properties. Block 41 contains the measured golf ball
inherent properties. Block 42 contains the measured golf club
inherent properties.
[0072] FIG. 3 is a flow chart illustrating the inputs or content of
the golf club swing properties of block 40 of FIG. 2. The golf club
swing properties are obtained from the acquisition system as
disclosed 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.
[0073] FIG. 4 is a flow chart illustrating the inputs for the
measured golf ball inherent properties of block 41 of FIG. 2. The
measurement of the mass of the golf ball is collected at block 45.
The measurement of the radius of the golf ball is collected at
block 46. The measurement of the coefficient of restitution of the
golf ball is collected at block 47. The measurement of the moment
of inertia of the golf ball is collected at block 48. The data
collected at blocks 45-48 is inputted to create the measured golf
ball inherent properties at block 41 of FIG. 2.
[0074] 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.
[0075] FIG. 5 is a flow chart illustrating the inputs for the golf
club head properties of block 42 of FIG. 2. The measurements for
the face properties are collected at block 49. The face properties
include the face geometry, the face center, the bulge radius and
the roll radius. The measurements for the mass properties of the
golf club head are collected or recalled from a database at block
50. The mass properties include the inertia tensor, the mass of the
club head, and the center of gravity location. The measurement for
the coefficient of restitution ("COR") of the golf club head using
a specific golf ball is collected at block 51. The measurements for
the loft and lie angles of the golf club head are collected at
block 52. The data collected at blocks 49-52 is inputted to create
the golf club head properties at block 42 of FIG. 2.
[0076] 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.
[0077] 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.
[0078] FIG. 6 is a flow chart of the contents of the plurality of
actual ball launch parameters at block 30 of FIG. 1. The side spin
of the golf ball is measured at block 53. The back spin of the golf
ball is measured at block 54. The ball speed is measured at block
55. The side angle of the golf ball is measured at block 56. The
launch angle of the golf ball is measured at block 57. The
information from blocks 53-57 is inputted/contained as the measured
ball launch parameters or plurality of actual ball launch
parameters, at block 30 of FIG. 1.
[0079] FIG. 7 is a flow chart of the contents of the plurality of
calculated ball launch parameters at block 28 of FIG. 1. The side
spin of the golf ball is calculated at block 63. The back spin of
the golf ball is calculated at block 64. The ball speed is
calculated at block 65. The side angle of the golf ball is
calculated at block 66. The launch angle of the golf ball is
calculated at block 67. The information from blocks 63-67 is
inputted/contained as the calculated ball launch parameters or
plurality of calculated ball launch parameters, at block 28 of FIG.
1.
[0080] FIG. 8 is a flow chart of the optimization values of block
22 of FIG. 1. The impact location is selected at block 69. The golf
club head orientation is selected at block 70.
[0081] FIG. 9 is a flow chart of the inputs/contents of the
optimization values for the golf club head orientation of block 70
of FIG. 8. The pitch of the golf club head is selected at block 71.
The yaw of the golf club head is selected at block 72. The roll of
the golf club head is selected at block 73. FIG. 10 illustrates the
pitch, yaw and roll of a golf club head 133.
[0082] FIG. 11 is a flow chart of the verification step of block 32
of FIG. 1. At block 74, the information from block 28 (the
plurality of calculated ball launch parameters) and the information
from block 30 (the plurality of actual ball launch parameters) are
compared to each other, and the absolute value of the differences
is obtained for further processing at block 75. At block 75,
absolute values obtained at block 74 are weighted in accordance of
importance to determining the true values of the impact location
and the orientation of the golf club during the golfer's swing. At
block 76, the weighted values from block 75 are used in a
root-mean-sum equation to obtain an error check value. In such a
root-mean-sum calculation, the product of each of the weighted
absolute values to the second power are added together and the
square root of that addition value is the error value. In a
preferred example, if the error value is within 30, then the
optimization values are acceptable, and these values are accepted
as the true values of the impact location and the golf club head
orientation. If the error value is greater than 30, then the
optimized values are not accepted and new optimized values must be
used to calculate a new set of a plurality of calculated ball
launch parameters to verify against the plurality of actual ball
launch parameters.
[0083] FIG. 12 is a flow chart illustrating the comparison process
to obtain the absolute values for the plurality of ball launch
parameters. At block 77, the differences between the side spin of
the plurality of calculated ball launch parameters and the side
spin of the plurality of actual ball launch parameters is obtained
to determine the absolute value of the side spin for the ball
launch parameters. At block 78, the differences between the back
spin of the plurality of calculated ball launch parameters and the
back spin of the plurality of actual ball launch parameters is
obtained to determine the absolute value of the back spin for the
ball launch parameters. At block 79, the differences 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 the absolute value of the ball
speed for the ball launch parameters. At block 80, the differences
between the side angle of the plurality of calculated ball launch
parameters and the side angle of the plurality of actual ball
launch parameters is obtained to determine the absolute value of
the side angle for the ball launch parameters. At block 81, the
differences between the launch angle of the plurality of calculated
ball launch parameters and the launch angle of the plurality of
actual ball launch parameters is obtained to determine the absolute
value of the launch angle for the ball launch parameters.
[0084] FIG. 13 is a flow chart illustrating the weighting process
to obtain the weighted absolute values for the plurality of ball
launch parameters. At block 82, the absolute value for the side
spin is weighted to determine a weighted absolute value for the
side spin for the plurality of ball launch parameters. At block 83,
the absolute value for the back spin is weighted to determine a
weighted absolute value for the back spin for the plurality of ball
launch parameters. At block 84, the absolute value for the ball
speed is weighted to determine a weighted absolute value for the
ball speed for the plurality of ball launch parameters. At block
85, the absolute value for the side angle is weighted to determine
a weighted absolute value for the side angle for the plurality of
ball launch parameters. At block 86, the absolute value for the
launch angle is weighted to determine a weighted absolute value for
the launch angle for the plurality of ball launch parameters.
[0085] 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.
[0086] As shown in FIG. 14, the acquisition system 120 generally
includes a computer 122, a camera structure 124 with a first CMOS
camera unit 126, a second CMOS camera unit 128 and an optional
trigger device 130, a golf ball 132 and a golf club 133. The
acquisition system 120 is designed to operate on-course, at a
driving range, inside a retail store/showroom, or at similar
facilities.
[0087] 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.
[0088] 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.
[0089] As shown in FIG. 15, a CMOS sensor array 200 preferably has
one million active pixels 205. Each active pixel 205 is capable of
acting as a single camera to provide an image or a portion of an
image. As shown in FIG. 15A, the field of view 1000 corresponds to
the full frame sensor array 200, which preferably operates at a
minimum frame rate ranging from 250 to 500 frames per second,
however, it may have a frame rate as low as 30 frames per second.
At this frame rate, the CMOS sensor array is monitoring the field
of view at a rate of 250-500 times per second and is capable of
creating images at 250 to 500 times per second. The CMOS sensor
array 200 preferably has one thousand columns of active pixels 205
and one thousand rows of active pixels 205. In a preferred
embodiment, the field of view 1000 is large enough to capture
pre-impact golf club information and post-impact golf ball
information. However, those skilled in the pertinent art will
recognize that the field of view 1000 may be adjusted to focus on
any particular action by the golfer such as only pre-impact
information, putting information, and the like.
[0090] As shown in FIG. 16, an initial region of interest ("ROI")
210 is established at the edge 150 of the field of view 1000 or
CMOS sensor array 200. In a preferred embodiment, the initial ROI
210 extends along all of the rows of the sensor array 200 and from
10 to 100 columns of the CMOS sensor array 200 beginning with the
first column of active pixels 205 at the edge 150. In establishing
an ROI, only those pixels within the ROI are activated while the
pixels outside of the ROI are deactivated. Reducing the number of
active pixels 205 increases the frame rate in a pseudo-inverse
relationship. Thus, if only 25% of the active pixels of the CMOS
sensor array are activated, and the full frame rate of the CMOS
sensor array 200 is 500 frames per second. Then, the frame rate of
the ROI is 2000 frames per second. Thus, reducing the number of
active pixels 205 allows for the increased monitoring of a ROI
thereby providing increased information about an object entering
the ROI since an increased number of images may be obtained of the
object within the ROI.
[0091] 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. FIG. 17 illustrates the object or golf club, shown as
reflective dots 106a-c, as entering the field of view 100.
[0092] 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 FIG. 18, the golf club 133
(shown by the reflective dots 106a-c) has moved from its position
in FIG. 17. As shown in FIG. 19, a second ROI 215 is established
around the golf club 133. It is preferably to create an ROI having
a minimum size since the frame rate is increased as the number of
active pixels 205 is reduced. Some CMOS cameras only allow
reduction in the number of columns which would limit the frame
rate.
[0093] 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 FIG. 20, the current ROI 220 (shown by bold dashed
lines) overlaps the previous ROI 217 (shown by small dashed lines).
FIG. 21 illustrates the CMOS sensor array 200 for ROI 220.
[0094] FIGS. 22 and 23 illustrate the continued movement of the
object or golf club 133 through the field of view 1000 and the new
ROI 225 encompassing the current position of the golf club 133.
[0095] FIG. 24 is a flow chart of a method 300 of using the system
120 of the invention. At box 301, the full CMOS sensor array is
active similar to FIG. 15. At box 302, an object such as a golf
club 33 is detected within the field of view 1000. If analyzing a
golfer's swing, this first detection may be the golfer addressing
the golf ball 166. During this address of the golf ball, the system
120 may be gathering information concerning the orientation of the
club head to the golf ball as the golfer adjusts the position of
the golf club to strike the golf ball. The CMOS sensor array 200 is
operating at a minimum frame rate since all of the active pixels
205 are activated. However, since the movement of the golf club 133
is slow, this minimum frame rate is sufficient to gather the
necessary information.
[0096] 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.
[0097] FIG. 25 is a flow chart of a specific method 310 for
analysis of a golf club at address. At box 311, the CMOS sensor
array monitors the field of view 1000 at a minimum frame rate. At
box 312, the indication markers (reflective dots or other like
markers) on the golf club 133 are detected within the field of view
1000. At box 313, a ROI is created around the indication markers of
the golf club 133. At box 314, the golf club 133 is monitored at a
higher frame rate within the ROI. At box 315, the golf club 133 is
taken away from the field of view 1000.
[0098] FIG. 26 is a method 320 for using the system 120 to monitor
an object. At box 321, a portion of the field of view 1000 is
monitored at a maximum rate, similar to the ROI 210 established and
monitored in FIG. 16. At box 322, an object is detected within the
ROI. At box 323, a first ROI is created around the object. At box
324, a plurality of ROIs is created around the object as it tracks
through the field of view 1000. At box 325, information is provided
on the movement of the object through the field of view.
[0099] FIG. 27 is a flow chart of a method 330 for using the system
to monitor a golf club. At box 331, a portion of the field of view
1000 is monitored at a maximum rate, similar to the ROI 210
established and monitored in FIG. 16. At box 332, a golf club 133,
or more specifically the indication markers of the golf club 133,
is detected within the ROI. At box 333, a first ROI is created
around the indications markers on the golf club 133. At box 334, a
plurality of ROIs is created around the indication markers as the
golf club tracks through the field of view 1000. At box 335,
information is provided on the movement of the golf club through
the field of view to determine the swing properties of the
golfer.
[0100] FIG. 28 is a flow chart of a method 340 for using the system
to monitor a golf ball during launch. At box 341, an ROI is created
around the golf ball prior to impact with a golf club. At box 342,
movement of the golf ball 166 is detected by the system 120. At box
343, a plurality of ROIs is created around the golf ball during the
initial launch of the golf ball subsequent to impact with a golf
club. At box 344, the system analyzes the movement of the golf ball
to provide launch parameters of the golf ball 166.
[0101] 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.
[0102] 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.
[0103] 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.
[0104] As shown in FIG. 29, the first row of acquired highly
reflective points 106a (on the shaft) is designated series one, the
second row of acquired highly reflective points 106b (on the heel)
is designated series two, and the third row of acquired highly
reflective points 106c (on the toe) is designated series three. The
first row is the acquired highly reflective points 106a from the
shaft, the second row is the acquired highly reflective points 106a
from the heel, and the third row is the acquired highly reflective
points 106a from the toe. The following equation is used to acquire
the positioning information: d=[(Ptx-Pnx).sup.2+(Pty-Ptny).sup.2 .
. . ].sup.1/2
[0105] where d is the distance, Ptx is the position in the x
direction and Pty is the position in the y direction.
[0106] The system 120 may use a three point mode or a two point
mode to generate further information. The two point mode uses
V.sub.toe, V.sub.heel and V.sub.clubtop to calculate the head
speed.
V.sub.toe=[(Ptx.sub.3-Ptx.sub.1).sup.2+(Pty.sub.3-Pty.sub.1).sup.2+(Ptz.s-
ub.3-Ptz.sub.1).sup.2].sup.1/2[1/.delta.T]
V.sub.heel=[(Ptx.sub.3-Ptx.sub.1).sup.2+(Pty.sub.3-Pty.sub.1).sup.2+(Ptz.-
sub.3-Ptz.sub.1).sup.2].sup.1/2[1/.delta.T]
V.sub.clubtop=[V.sub.toe+V.sub.heel][1/2]
Vy=[(y.sub.3heel-y.sub.1heel).sup.2+(y.sub.3toe-y.sub.1toe).sup.2].sup.1/-
2[1/(2*.delta.T)]
Vz=[(z.sub.3heel-z.sub.1heel).sup.2+(z.sub.3toe-z.sub.1toe).sup.2].sup.1/-
2[1/(2*.delta.T)]
[0107] This information is then used to acquire the path angle and
attack angle of the golf club 133. The Path
angle=sin.sup.-1(Vy/[V]) where [V] is the magnitude of V.
[0108] The attack angle=sin.sup.-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.
[0109] 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:
V.sub.heel=[(Ptx.sub.3-Ptx.sub.1).sup.2+(Pty.sub.3-Pty.sub.1).sup.2+(Ptz.-
sub.3-Ptz.sub.1).sup.2].sup.1/2[1/.delta.T]
V.sub.shaft=[(Ptx.sub.3-Ptx.sub.1).sup.2+(Pty.sub.3-Pty.sub.1).sup.2+(Ptz-
.sub.3-Ptz.sub.1).sup.2].sup.1/2[1/.delta.T]
V.sub.center=1.02*(V.sub.shaft+V.sub.heel)
Vy=[(y.sub.3heel-y.sub.1heel).sup.2+(y.sub.3shaft-y.sub.1shaft).sup.2].su-
p.1/2[1/(2*.delta.T)]
Vz=[(z.sub.3heel-z.sub.1heel).sup.2+(z.sub.3shaft-z.sub.1shaft).sup.2].su-
p.1/2[1/(2*.delta.T)]
[0110] The Path angle=sin.sup.-1(Vy/[V]) where [V] is the magnitude
of V.
[0111] The attack angle=sin.sup.-1(Vz/[V]).
[0112] Using the toe highly reflective point 106c, the equations
are:
V.sub.toe=[(x.sub.3-x.sub.1).sup.2+(y.sub.3-y.sub.1).sup.2+(z.sub.3-z.sub-
.1).sup.2].sup.1/2[1/.delta.T]
V.sub.heel=[(x.sub.2-x.sub.1).sup.2+(y.sub.2-y.sub.1).sup.2+(z.sub.2-z.su-
b.1).sup.2].sup.1/2[1/.delta.T]
V.sub.clubtop=[V.sub.toe+V.sub.heel][1/2]
[0113] The path angle=sin.sup.-1(Vy.sub.clubtop/[V.sub.clubtop])
where [V.sub.clubtop] is the magnitude of V.sub.clubtop.
[0114] The attack angle=sin.sup.-1(Vz.sub.clubtop/[V.sub.clubtop])
where [V.sub.clubtop] is the magnitude of V.sub.clubtop.
[0115] 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.sup.-1(Vz/golf ball speed), and the spin
angle=sin.sup.-1(Vy/golf ball speed).
[0116] Next, the system 120 looks for the stripes 108a-b, as shown
in FIGS. 30 and 30A, on the golf ball 166 by using a random
transformation searching for the spot of greatest contrast. X, Y
and Z coordinates are used with the arc of stripe 108a and the arc
of stripe 108b to orient the arc on the golf ball. Then, the system
120 determines which arc is most normal using
(x.sup.2+y.sup.2).sup.1/2.
[0117] Next, the .theta. angle of the golf ball 166 is measured by
taking the first vector and the second vector and using the
equation: .theta.=cos.sup.-1 [(vector A1)(vector
A2)]/([V.sub.1][V.sub.2]) where [V.sub.1] is the magnitude of
V.sub.1 and [V.sub.2] is the magnitude of V.sub.2.
[0118] As the golf ball 166 rotates from the position shown in FIG.
30 to the position shown in FIG. 30A, the angle .theta. is
determined from the position of vector A at both rotation
positions. This allows for the spin to be determined. The back spin
is calculated and applied to the first set of axis with a tilt axis
of zero. The resultant vectors are compared to those of the next
image and a theta is calculated for each of the vectors. This is
done for each tilt axis until the Theta between the rotated first
set of axis and the second set of axis is minimized.
[0119] 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.
[0120] 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 FIGS. 31 and 31A. Then, the system 120 searches above and
below the three pairs for a second find, as shown in FIGS. 32 and
33. The repeated points 106 are eliminated and the results are
displayed from the find, as shown in FIGS. 34 and 35. The points of
the final pairs are processed by the computer 122 and displayed as
shown in FIG. 36.
[0121] Next the speed of the head of the golf club 133 is
determined by the system 120 using the equations discussed
above.
[0122] 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(.delta.z/.delta.x)
[0123] Where .delta.z is the z value of the midpoint between
106a.sub.1 and 106b.sub.1 minus the z value of the midpoint between
106a.sub.3 and 106b.sub.3. Where .delta.x is the x value of the
midpoint between 106a.sub.1 and 106b.sub.1 minus the x value of the
midpoint between 106a.sub.3 and 106b.sub.3.
[0124] The path angle is determined from the following equation:
path angle=-a tan(.delta.y/.delta.x)
[0125] Where .delta.y is the y value of the midpoint between
106a.sub.1 and 106b.sub.1 minus the y value of the midpoint between
106a.sub.3 and 106b.sub.3. Where .delta.x is the x value of the
midpoint between 106a.sub.1 and 106b.sub.1 minus the x value of the
midpoint between 106a.sub.3 and 106b.sub.3.
[0126] Next, the golf ball 166 data is determined b the system 120.
First, the thresholding of the image is established as shown in
FIG. 37, at a lower gray scale value, approximately 100 to 120, to
detect the golf ball 166. Next, well-known edge detection methods
are used to obtain the best golf ball 166 center and radius, as
shown in FIG. 38. Next, the stereo correlation of two dimensional
points on the golf ball 166 is performed by the system 120 as in
FIG. 39, which illustrates the images of the first camera 140 and
the second camera 144.
[0127] Next, as shown in FIG. 40, with the positioning information
provided therein, the speed of the golf ball 166, the launch angle
of the golf ball 166, and the side angle of the golf ball 166 is
determined by the system 120. The speed of the golf ball is
determined by the following equation: Golf ball
speed=[.delta.X.sup.2+.delta.Y.sup.2+.delta.Z.sup.2].sup.1/2/.delta.T.
For the information provided in FIG. 40, the speed of the golf
ball=[(-161.68+(-605.26)).sup.2+(-43.41+(-38.46)).sup.2+(-282.74+(-193.85-
)).sup.2].sup.1/2/(13127-5115), which is equal to 126 MPH once
converted from millimeters over microseconds.
[0128] The launch angle of the golf ball 166 is determined by the
following equation: Launch angle=sin.sup.-1(Vz/golf ball speed)
where Vz=.delta.Z/.delta.T. For the information provided in FIG.
40, Vz=[(-282.74+(-193.85)]/(13127-5115)=11.3 MPH. Then, the launch
angle=sin.sup.-1(11.3/126.3)=11.3 degrees.
[0129] The side angle of the golf ball 166 is determined by the
following equation: Side angle=sin.sup.-1(Vy/golf ball speed) where
Vy=.delta.Y/.delta.T. For the information provided in FIG. 40,
Vy=[(-43.41+(-38.46)]/(13127-5115)=1.4 MPH. Then, the side
angle=sin.sup.-1(1.4/126.3)=0.6 degrees.
[0130] 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:
.theta.=a cos((vectorA1 dot vector A2)/mag(v1)*mag(v2)) as
discussed above.
[0131] 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.
[0132] 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.
[0133] 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.
[0134] 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.
[0135] 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. [0136] The symbols are defined
as below: [0137] {right arrow over (i)}=(1 0 0), the unit vector in
the x-direction. [0138] {right arrow over (j)}=(0 1 0), the unit
vector in the y-direction. [0139] {right arrow over (k)}=(0 0 1),
the unit vector in the z-direction. [0140] m.sub.1, the mass of the
club head. [0141] m.sub.2, the mass of the golf ball. [ I ] 1 = [ I
xx , 1 - I xy , 1 - I xz , 1 - I xy , 1 I yy , 1 - I yz , 1 - I xz
, 1 - I yz , 1 I zz , 1 ] , ##EQU1## the inertia tensor of the club
head. [ I ] 2 = [ I xx , 2 - I xy , 2 - I xz , 2 - I xy , 2 I yy ,
2 - I yz , 2 - I xz , 2 - I yz , 2 I zz , 2 ] , .times. ##EQU2##
the inertia tensor of the golf ball. [0142] {right arrow over
(r)}.sub.1=(a.sub.1 b.sub.1 c.sub.1), the vector from point of
impact to the center of gravity of the club head. [0143] {right
arrow over (r)}.sub.2=(a.sub.2 b.sub.2 c.sub.2), the vector from
point of impact to the center of gravity of the golf ball. [0144]
{right arrow over (r)}.sub.3=-{right arrow over (r)}.sub.1+{right
arrow over (r)}.sub.2=(-a.sub.1+a.sub.2 -b.sub.1+b.sub.2
-c.sub.1+c.sub.2)=(a.sub.3 b.sub.3 c.sub.3), the vector from center
of gravity of club head to the center of gravity of the golf ball.
[0145] {right arrow over (v)}.sub.1,i=(v.sub.x,1,i v.sub.y,1,i
v.sub.z,1,i), the velocity of the club head before impact. [0146]
{right arrow over (v)}.sub.1,f=(v.sub.x,1,f v.sub.y,1,f
v.sub.z,1,f), the velocity of the club head after impact. [0147]
{right arrow over (v)}.sub.1,i=(v.sub.x,1,i v.sub.y,1,i
v.sub.z,1,i), the velocity of the golf ball before impact. [0148]
{right arrow over (v)}.sub.2,f=(v.sub.x,2,f v.sub.y,2,f
v.sub.z,2,f), the velocity of the golf ball after impact. [0149]
{right arrow over (.omega.)}.sub.1,i=(.omega..sub.x,1,i
.omega..sub.y,1,i .omega..sub.z,1,i), the angular velocity of the
club head before impact. [0150] {right arrow over
(.omega.)}.sub.1,f=(.omega..sub.x,1,f .omega..sub.y,1,f
.omega..sub.z,1,f), the angular velocity of the club head after
impact. [0151] {right arrow over
(.omega.)}.sub.2,i=(.omega..sub.x,2,i .omega..sub.y,2,i
.omega..sub.z,2,i), the angular velocity of the golf ball before
impact. [0152] {right arrow over
(.omega.)}.sub.2,f=(.omega..sub.x,2,f .omega..sub.y,2,f
.omega..sub.z,2,f), the angular velocity of the golf ball after
impact. [ e ] = [ e xx e xy e xz e xy e yy e yz e xz e yz e zz ] ,
##EQU3## the coefficient of restitution matrix. [0153] [L]=m{right
arrow over (v)}, definition of linear momentum. [0154]
[H]=[I]{right arrow over (.omega.)}, definition of angular
momentum. Conservation of linear momentum: m.sub.1{right arrow over
(v)}.sub.1,f+m.sub.2{right arrow over (v)}.sub.2,f=m.sub.1{right
arrow over (v)}.sub.1,i+m.sub.2{right arrow over (v)}.sub.2,i B1-B3
Conservation of angular momentum: [ I ] 1 .times. .omega. 1 , f + [
I ] 2 .times. .omega. 2 , f + m 1 .function. [ - c 1 .times. v y ,
1 , f + b 1 .times. v z , 1 , f c 1 .times. v x , 1 , f - a 1
.times. v z , 1 , f a 1 .times. v y , 1 , f - b 1 .times. v x , 1 ,
f ] + m 2 .function. [ - c 2 .times. v y , 2 , f + b 2 .times. v z
, 2 , f c 2 .times. v x , 2 , f - a 1 .times. v z , 2 , f a 2
.times. v y , 2 , f - b 1 .times. v x , 2 , f ] = [ I ] 1 .times.
.omega. 1 , i + [ I ] 2 .times. .omega. 2 , i + m 1 .function. [ -
c 1 .times. v y , 1 , i + b 1 .times. v z , 1 , i c 1 .times. v x ,
1 , i - a 1 .times. v z , 1 , i a 1 .times. v y , 1 , i - b 1
.times. v x , 1 , i ] + m 2 .function. [ - c 2 .times. v y , 2 , i
+ b 2 .times. v z , 2 , i c 2 .times. v x , 2 , i - a 2 .times. v z
, 2 , i a 2 .times. v y , 2 , i - b 2 .times. v x , 2 , i ] .times.
B4 .times. - .times. B6 ##EQU4## The definition of coefficients of
restitution: - [ e ] [ .times. ( v x , 2 , i + i ( .omega. 2 , i
.times. ( - r 2 ) ) ) - ( v x , 1 , i + i ( .omega. 1 , i .times. (
- r 1 ) ) ) ( v y , 2 , i + j ( .omega. 2 , i .times. ( - r 2 ) ) )
- ( v y , 1 , i + j ( .omega. 1 , i .times. ( - r 1 ) ) ) ( v z , 2
, i + k ( .omega. 2 , i .times. ( - r 2 ) ) ) - ( v z , 1 , i + k (
.omega. 1 , i .times. ( - r 1 ) ) ) ] = [ .times. ( v x , 2 , f + i
( .omega. 2 , f .times. ( - r 2 ) ) ) - ( v x , 1 , f + i ( .omega.
1 , f .times. ( - r 1 ) ) ) ( v y , 2 , f + j ( .omega. 2 , f
.times. ( - r 2 ) ) ) - ( v y , 1 , f + j ( .omega. 1 , f .times. (
- r 1 ) ) ) ( v z , 2 , f + k ( .omega. 2 , f .times. ( - r 2 ) ) )
- ( v z , 1 , f + k ( .omega. 1 , f .times. ( - r 1 ) ) ) ] .times.
.times. B7 .times. - .times. B9 ##EQU5## The tangential impulse on
the ball causes both rotation and translation: m 2 .function. [ c 2
.function. ( v y , 2 , f - v y , 2 , i ) - b 2 .function. ( v z , 2
, f - v z , 2 , i ) - c 2 .function. ( v x , 2 , f - v x , 2 , i )
+ a 2 .function. ( v z , 2 , f - v z , 2 , i ) b 2 .function. ( v x
, 2 , f - v x , 2 , i ) - a 2 .function. ( v y , 2 , f - v y , 2 ,
i ) ] = [ I ] 2 .function. [ .omega. x , 2 , f - .omega. x , 2 , i
.omega. y , 2 , f - .omega. y , 2 , i .omega. z , 2 , f - .omega. z
, 2 , i ] B10 .times. - .times. B12 ##EQU6## 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.
[0155] 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 F.sub.m, the maximum static friction force between the
golf ball 166 and the tee 168, is applied on the golf ball 166.
F.sub.m=.mu..sub.sN=.mu..sub.sm.sub.2g C1 .mu..sub.s , is the
static coefficient of friction and g is gravity. For a golf ball
166 with 45 grams of mass, and a .mu..sub.s of 0.3,
F.sub.m=.mu..sub.smg=(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)=0.0000662Ns 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. [ e
] = [ e xx e xy e xz e xy e yy e yz e xz e yz e zz ] .times.
##EQU7##
[0156] Each of the individual terms in the above matrix, e.sub.ij,
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 e.sub.zz includes all the
energy that is lost in the impact in the normal direction of
impact. e.sub.xx and e.sub.yy 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 e.sub.ij, where i.noteq.j, are equal to zero for
isotropic materials.
[0157] As shown in FIG. 41, a method for predicting a golfer's ball
striking performance is generally designated 90. A similar method
is disclosed in U.S. Pat. No. 6,506,124 for a Method For Predicting
A Golfer's Ball Striking Performance, assigned to Callaway Golf
Company (the Assignee of the present application) and hereby
incorporated by reference in its entirety. The method 90 commences
with inputting information on a specific golf club, specific golf
ball, and the swing characteristics of a golfer. At block 91, the
club head properties of the specific golf club are selected from a
database of stored and previously collected club head information.
The specific information for the club head properties is set forth
in greater detail above in reference to FIG. 5, specifically the
inputs to block 42. At block 92, the golf club swing properties of
the golfer are collected and stored in a database. The specific
information for the golfer's golf club swing properties includes
the true values for the impact location and the golf club head
orientation, which are obtained according to method 20 of FIG. 1.
Additionally, information from FIG. 3, specifically the inputs to
block 40, are part of the golf club swing properties. At block 93,
the golf ball properties of the specific golf ball are selected
from database of stored and previously collected golf ball
information. The specific information for the golf ball properties
is set forth in greater detail above in reference to FIG. 4,
specifically the inputs to block 41.
[0158] 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 FIG. 7, specifically the inputs for
block 28. At block 95, information concerning the atmospheric
conditions is selected from a database of stored atmospheric
conditions. At block 97, information concerning the lift and drag
properties of the golf ball are collected and stored. The lift and
drag properties of golf balls are measured using conventional
methods such as disclosed in U.S. Pat. No. 6,186,002, entitled
Method For Determining Coefficients Of Lift And Drag Of A Golf
Ball, which is hereby incorporated by reference in its entirety.
The lift and drag coefficients of a number of golf balls at
specific Reynolds numbers are disclosed in U.S. Pat. No. 6,224,499,
entitled A Golf Ball With Multiple Sets Of Dimples, which pertinent
parts are hereby incorporated by reference.
[0159] 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.
[0160] 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.
[0161] FIG. 42 is a table of the golf club swing properties of
block 40 for a six exemplary golf shots using a BIG BERTHA C4.RTM.
Driver available from Callaway Golf Company of Carlsbad, Calif.,
which is composed of a composite material.
[0162] FIG. 43 is a table of the plurality of actual ball launch
parameters of block 30 for the six exemplary golf shots using a
HX.RTM. RED Golf Ball available from Callaway Golf Company of
Carlsbad.
[0163] FIG. 44 is a table of the measured golf club inherent
properties of block 42 for a BIG BERTHA C4.RTM. Driver available
from Callaway Golf Company of Carlsbad, Calif., which is composed
of a composite material.
[0164] FIG. 45 is a table of the golf ball properties of block 41
for a HX.RTM. RED Golf Ball available from Callaway Golf Company of
Carlsbad.
[0165] FIG. 46 is a table of the plurality of calculated ball
launch parameters of block 28 generated by the rigid body code for
six exemplary shots. The table includes an example of information
for blocks 63-67 of FIG. 7.
[0166] FIG. 47 is a table of the plurality of optimized values for
the impact location and orientation of the golf club head of block
69 and 70 for the six exemplary shots.
[0167] FIG. 48 is a table of differences between the actual and
calculated plurality of ball launch parameters of 74 for the six
exemplary shots. The table includes an example of information for
blocks 77-81 of FIG. 12.
[0168] FIG. 49 is a table of the weighting values for absolute
values of the differences between the actual and calculated
plurality of ball launch parameters of 75 for the six exemplary
shots. The table includes an example of information for blocks
82-86 of FIG. 13.
[0169] FIG. 50 is a table of the error value of block 76 for the
six exemplary shots.
[0170] 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.
* * * * *
References