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Description  |
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BACKGROUND OF THE INVENTION
Athletes, and particularly golfers, are interested in improving their game
performance. One of the elements in golf performance in the
through-the-air carry distance and the directional accuracy resulting from
the golf drive.
As disclosed in U.S. Patent application Ser. No. 626,712 filed Oct. 29,
1975 now U.S. Pat. No. 4,063,259, owned by the assignee of the present
invention, applicants have discovered through wind-tunnel tests and
controlled mechanical driving of golf balls that they can predict the
landing point of a driven golf ball with great accuracy if they are given
the values of ball velocity, flight direction and ball spin in the
immediate post-launch time period. In addition, applicants can diagnose
problems in the golfer's swing if they are given the velocity, direction
and rotary motions of the golf club head in the immediate pre-launch time
period.
There are known monitoring devices for determining the position of a
plurality of points on a moving object at two closely spaced points in
time which can advantageously be used in the present invention to provide
the required velocity and rotation data useable in making such performance
predictions.
SUMMARY OF THE INVENTION
The present invention suitably uses at least two electro-optical kinematic
monitors to detect the apparent positions of at least three non-collinear
spots on an object at two closely spaced points in time. If the object
being monitored is a golf club head, the two time points immediately
precede impact of the club with the ball. If the object is a golf ball the
two time points closely follow the impact of the golf club. It will be
understood that only one time point is necessary if the original
orientation of the ball on the tee is known. It will be appreciated that
in certain instances where the object is of the proper geometry, notably
spherical, one of the "spots" can be the whole object image in which case
it is only necessary to have two non-collinear spots added to the object
itself.
At each electro-optical sensing location, an accurate bi-angular
measurement is made of spots on the ball or club. A vector can then be
defined from each sensor passing through the spot which it detects. Given
the knowledge of the geometric relationships of the two electro-optical
sensors and the location of the monitored spots on the surface of the
object being monitored, the object center and angular orientation are
uniquely and accurately determined at each of the two time points.
A displacement calculator in the present invention determines the direction
in which the monitored object moved between time points and calculates the
object's speed and direction. A spin calculator determines how much the
object has rotated between time points and calculates the rotation rate,
W, of the object. The rotation rate W may conveniently be described in
terms of vector spin components about three mutually orthogonal spin axes,
conventionally I, J and K, or may be described in polar form as a single
magnitude and a resultant spin axis.
The above information about the launch of a golf ball, coupled with
knowledge of the type of golf ball used, is sufficient for applicants to
accurately predict the flight trajectory and point of landing of the golf
ball. Similarly, information of this nature about the golf club enables
applicants to diagnose problems in the golfer's swing preparatory to
making recommendations for their correction.
Although the preceding has treated impact monitoring of the golf club and
launch monitoring of the golf ball as separate processes, nothing in the
foregoing should be taken to exclude combined impact and launch monitoring
during a single golf swing. Combined monitoring may utilize some or all of
the same electro-optical sensors.
The geometric calculations performed may be adapted to different surface
shapes of club head and golf ball. Therefore the golfer's own clubs and/or
balls may be used if desired provided, of course, the spots are added as
discussed hereinbefore.
Additional useful data may be obtained by monitoring the club head at the
instant of impact with the golf ball and at one or more points in time
thereafter in addition to the two pre-impact or post-impact monitoring
time points described in the preceding. Therefore, the present invention
may conveniently extend the number and spacing of time points for
monitoring the club head to include the moment of impact and one or more
time points following impact.
While golf is certainly the primary application of the present invention,
it may also advantageously be used to monitor other types of sports
devices. For example, other ball-and-implement games such as baseball,
tennis, and the like; non-ball games such as hockey; and ball-only games
such as football, basketball and bowling may be advantageously monitored
using the present invention.
BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 shows an overall block diagram of the impact/launch monitor.
FIG. 2 shows a closeup of a ball being monitored by three electro-optical
sensors.
FIG. 3 shows an orthogonal spin axis system.
DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT
Referring to FIG. 1, there is shown a golfer 10 holding a golf club 11 for
hitting a golf ball 30. The golf club 11 occupies positions 18 and 20 at
two closely spaced points in time before it strikes the ball 30. The golf
ball occupies positions 14 and 16 at two closely spaced points in time
after being struck by the golf club 11.
At least one optically enhanced spot 22 on the object being monitored is
visible to each electro-optical launch/impact position sensor 24, 26, 28.
In FIG. 1, the optically enhanced spot 22 is assumed to be the one visible
to impact/launch position sensor A 24. Similar optically enhanced spots,
not shown, are visible to impact/launch position sensor B 26 and to
impact/launch position sensor C 28. The three impact/launch position
sensors 24, 26 and 28 freeze the point on the object which they monitor at
a minimum of two points in time and generate digital numbers indicative of
the apparent position of the spot at each time point.
In the preferred embodiment, the optically enhanced spot 22 is
retroreflective material. Although retroreflective techniques simplify the
pattern recognition problem considerably by improving the optical
contrast, the target spot may in general be a dot of a first optical
reflectivity on a ball of different optical reflectivity. More complicated
processing could extract the ball orientation information from low
contrast targets. The golf ball dimples themselves may be considered of
sufficiently different optical reflectivity from the ball surface to be
marginally adequate indicators of ball orientation.
Referring momentarily to FIG. 2, the ball 30 having its center of gravity
at 32 is viewed by the three impact/launch position sensors 24, 26 and 28.
Assume, for purposes of description, that FIG. 2 is a plan view. Each
impact/launch position sensor 24, 26, 28 develops one of its two outputs
in sensor coordinates X.sub.A, X.sub.B, X.sub.C. Each X coordinate is
related in a known manner to the angular displacement .theta..sub.A of the
spot from the sensor axis. For example, the sensor coordinate X.sub.A from
sensor 24 is related to angle .theta..sub.A from the sensor 24 axis to the
spot 22. The second set of outputs Y.sub.A, Y.sub.B and Y.sub.C in sensor
coordinates are generated in a similar manner using the angles
.phi..sub.A, .phi..sub.B and .phi..sub.C (not shown) which can
conveniently be normal to the plane defined by angles .theta..sub.A,
.theta..sub.B and .theta..sub.C.
The displacement of the center of gravity 32 between time points defines
the object velocity. Given the angle information in sensor coordinates,
shown in FIG. 1, and knowing .theta..sub.A, .theta..sub.B and
.theta..sub.C, the location of the spots on the ball 30, and its geometry,
two dimensions of the center of gravity 32 of the ball 30 in unified
coordinates can be uniquely calculated. Similarly, the third dimension can
be uniquely calculated in unified coordinates using the normal angles
.phi..sub.A, .phi..sub.B and .phi..sub.C. Unified coordinates as used in
the foregoing is to be taken to mean any single common coordinate system
determined by resolution of the individual data items in sensor
coordinates into the common coordinate system. For example, a
three-dimensional, cartesian coordinate system X', Y', Z' could be defined
with its origin at impact/launch monitor sensor 24. Only the X' and Y'
axes are shown. The Z' axis is assumed to be normal to the page. All
measurements from impact/launch position sensors 26 and 28 would be
resolved into the X', Y', Z' coordinate system using the known distances
and angles between impact/launch position sensors 24, 26 and 28. Thus the
position of the center of gravity 32 would be determined in coordinates
X', Y' and Z' at the two time points.
Referring again to FIG. 1, the target center triangulation calculator 34
performs the resolution of the sensor-coordinate measurements into unified
coordinates and calculates the coordinates of the center of gravity 32 X,
Y and Z.
The coordinates of the center of gravity 32, X, Y, Z are connected to an
initial velocity and angle calculator 36 and a spin calculator 38. The
spin calculator 38 also receives spot-position data indicating the
positions of the spots 20, 20b and 20c on the surface of the ball 30. The
spot-position data can be in sensor coordinates (X.sub.A, Y.sub.A),
(X.sub.B, Y.sub.B) and (X.sub.C, Y.sub.C) or they may be in unified
coordinates X', Y', Z' developed in the manner previously described. If
the angle .gamma. in an arbitrary coordinate system changes by an amount
.DELTA. .gamma. in the time .DELTA. T, between time points, the ratio
.DELTA. .gamma./.DELTA. T is approximately equal to d .gamma./d t when the
time points are close enough together. For the purposes of the present
invention, .DELTA. .gamma./.DELTA. T is a sufficiently accurate measure of
d .gamma./d T when .DELTA. T between time points is less than about a
tenth of a second.
Spin denoted by W is a vector quantity having both a scalar magnitude and
direction. A single spin vector can be resolved into spin components,
conventionally taken to be along three mutually orthogonal axes. FIG. 3
illustrates an orthogonal spin axis system having axes J, K and L.
Conventionally, axis J is aligned with the X axis, K with the Y axis and L
with the Z axis in a cartesian coordinate system. W.sub.J, for example, is
the vector component of spin about the J spin axis. The spin of a
projectile moving through a resisting medium, a golf ball through air for
example, develops lift. The magnitude and direction of the lift depends on
the magnitude of the spin, the orientation of the spin with respect to the
relative air flow and the nature of the projectile-medium interface. The
dimples at the ball-air interface of a golf ball are purposely provided to
achieve desired values of lift.
Referring again to FIG. 1, the spin calculator 38 calculates the value of
spin W. The calculated spin may be either as a single resultant spin W or
as orthogonal spin components W.sub.J, W.sub.K and W.sub.L. The calculated
initial spin is then made available to external devices (not shown).
The initial velocity and angle calculator 36 receives the two values of the
ball centroid coordinates (X, Y, Z). The component of displacement along
each axis is the difference in the magnitude of the components along each
axis occurring between the two time points. For example the X component of
displacement is .DELTA.X = X.sub.2 - X.sub.1 ; where
X.sub.1 = first measured X
X.sub.2 = second measured X
The total displacement is .sqroot..DELTA.X.sup.2 + .DELTA.Y.sup.2 +
.DELTA.Z.sup.2
The magnitude of the total initial velocity is thus
V = .sqroot..DELTA.X.sup.2 + .DELTA.Y.sup.2 + .DELTA.Z.sup.2 /.DELTA.T
Velocity V is also a vector quantity and can be resolved into components,
conventionally along mutually orthogonal axes which lie along the X', Y'
and Z' axes. The angle which one component of velocity makes with the
plane defined by the axes of the other two components can be determined
from the individual displacement components. For example,
the total loft angle = arctan (.DELTA.Z/.sqroot..DELTA.X.sup.2 +
.DELTA.Y.sup.2)
By calculations similar to those described, the components of velocity and
loft angle along the coordinate axes may also be calculated.
The values of initial velocity and angles are connected from the initial
velocity and angle calculator to external devices (not shown).
It will be understood that the claims are intended to cover all changes and
modifications of the preferred embodiments of the invention, herein chosen
for the purpose of illustration which do not constitute departures from
the spirit and scope of the invention.
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