U.S. patent application number 10/589833 was filed with the patent office on 2007-07-19 for method and systems using prediction of outcome for launched objects.
Invention is credited to Norman Matheson Lindsay.
Application Number | 20070167247 10/589833 |
Document ID | / |
Family ID | 34426974 |
Filed Date | 2007-07-19 |
United States Patent
Application |
20070167247 |
Kind Code |
A1 |
Lindsay; Norman Matheson |
July 19, 2007 |
Method and systems using prediction of outcome for launched
objects
Abstract
Each golfer (1-3) on a golf range (4) has an individual display
(12-14) showing at least a predicted outcome of each of his/her
shots, and a launch-analyser (6-8) to measure velocity vectors of
the ball and/or club at strike for central-computation (9) of the
prediction. Vibration and piezo-cable sensors (54,55;68,69) at
instrumented targets (5;41-45,47) distributed throughout the range
(4), detect the presence of balls arriving in their respective
locations for matching with launched balls using the computed
predictions and probability; active or passive radio-frequency
identification and location of balls may also be used. Where a
match is found, error between predicted and actual outcome is
applied to adaptive correction of the prediction-computing process,
and the actual outcome is displayed to the golfer instead of the
prediction. Ball and/or club velocity vectors, and ball spin, at
launch are measured from light changes occurring in detection
planes (96,97;105;114-117;134;144-146) defined by slit apertures
(94,95;104), and resulting from retro-reflection from ball
(91;110;131) and/or club (130).
Inventors: |
Lindsay; Norman Matheson;
(Buckinghamshire, GB) |
Correspondence
Address: |
DAVIS & BUJOLD, P.L.L.C.
112 PLEASANT STREET
CONCORD
NH
03301
US
|
Family ID: |
34426974 |
Appl. No.: |
10/589833 |
Filed: |
February 18, 2005 |
PCT Filed: |
February 18, 2005 |
PCT NO: |
PCT/GB05/00611 |
371 Date: |
August 17, 2006 |
Current U.S.
Class: |
473/131 |
Current CPC
Class: |
G01S 17/86 20200101;
G01S 17/74 20130101; A63B 69/3658 20130101; G01S 17/58 20130101;
A63B 69/002 20130101; G01S 17/88 20130101; A63B 43/00 20130101;
G01S 17/875 20130101; A63B 2024/0031 20130101; A63B 24/0021
20130101; A63B 2225/54 20130101; G01S 17/89 20130101; A63B
2024/0037 20130101; G01S 17/66 20130101; A63B 2243/0066 20130101;
A63B 2225/30 20130101 |
Class at
Publication: |
473/131 |
International
Class: |
A63B 69/36 20060101
A63B069/36 |
Foreign Application Data
Date |
Code |
Application Number |
Feb 18, 2004 |
GB |
0403561.4 |
Jun 5, 2004 |
GB |
0412583.7 |
Jun 23, 2004 |
GB |
0414028.1 |
Oct 22, 2004 |
GB |
0423500.8 |
Claims
1.-32. (canceled)
33. A method for deriving representations of the individual
outcomes of launching objects into an area that contains a
plurality of mutually-spaced object-sensing means, wherein each
sensing means detects the presence of any of the launched objects
that arrive in the location of that respective sensing means, a
prediction of the outcome of the launching of each individual
object is computed in dependence upon measurements of velocity
vectors of that object at launch, the prediction is used to provide
representation of the outcome of the launch of that respective
object in the event that the presence as aforesaid of that object
is not detected by the sensing means, and the computation process
by which the predictions are computed is subject to adaptive
correction in dependence upon error between the outcome predicted
and the actual outcome realised in respect of individual objects
for which the presence as aforesaid is detected by any of the
sensing means.
34. The method according to claim 33, wherein the representation
provided in respect of the individual objects for which the
presence as aforesaid is detected by any of the sensing means, is
of the actual outcome realised.
35. The method according to claim 33, wherein the measurements of
velocity vectors of each object at launch are derived by detecting
light-change resulting from passage of that object through
detection planes defined by respective slit-apertures.
36. The method according to claim 35, wherein each detection plane
involves means for emitting light as a beam through the respective
slit-aperture and means for sensing light from the beam reflected
back through that same slit-aperture.
37. The method according to claim 36, wherein each object carries
at least one retro-reflective element for reflecting light from the
beam back to the light-sensing means.
38. The method according to claim 33, wherein the sensing means
each detect the presence as aforesaid of each said object by impact
of that object within the respective location.
39. The method according to claim 38, wherein each sensing means
involves piezo-electric cabling for sensing impact.
40. The method according to claim 39, wherein each sensing means
includes a plurality of piezo-electric cables, and the position of
the impact within the location of the respective sensing means is
derived from electric signals produced in the respective cables in
response to the impact.
41. The method according to claim 33, wherein each said object
carries a radio-frequency identification tag and the sensing means
each include radio-frequency means for detecting the presence as
aforesaid of each said object.
42. The method according to claim 33, wherein the derived
representions are provided in the form of video display.
43. The method according to claim 33, wherein the objects are golf
balls that are launched by a golfer in successive strikes.
44. The method according to claim 43, wherein the prediction of the
outcome of launching of each individual ball is computed in
accordance with velocity and spin vectors of the ball at
launch.
45. The method according to claim 43, wherein the predicted outcome
is represented in terms of the location the ball is predicted to
reach within the area.
46. The method according to claim 43, wherein the area is a golf
range used by a plurality of golfers, and each golfer is provided
individually with a representation of the outcome of his/her
strikes.
47. The method according to claim 46, wherein possible ambiguity in
relating actual outcome with predicted outcome in respect of balls
from different golfers is resolved on the basis of a probability
assessment.
48. A system for deriving representations of the individual
outcomes of launching objects into a defined area, comprising a
plurality of mutually-spaced object-sensing means within the
defined area, each of the sensing means being operative to detect
the presence of any of the launched objects that arrive in the
location of that respective sensing means, launch-analyser means
for deriving measurements of the launch velocity vectors of each of
the objects individually, computer means for computing in
dependence upon these measurements a prediction for the respective
object of the outcome of its launch, and means for providing
representation of the computed prediction in the event that the
presence as aforesaid of the respective object is not detected by
the sensing means, and wherein the computation process by which the
predictions are computed by the computer means is subject to
adaptive correction in dependence upon error between the outcome
predicted and the actual outcome realised in respect of individual
objects for which the presence as aforesaid is detected by any of
the sensing means.
49. The system according to claim 48, wherein the representation
provided in respect of the individual objects for which the
presence as aforesaid is detected by any of the sensing means, is
of the actual outcome realised.
50. The system according to claim 48, wherein the measurements of
velocity vectors of each object at launch are derived by detecting
light-change resulting from passage of that object through
detection planes defined by respective slit-apertures.
51. The system according to claim 50, wherein each detection plane
involves means for emitting light as a beam through the respective
slit-aperture and means for sensing light from the beam reflected
back through that same slit-aperture.
52. The system according to claim 51, wherein each object carries
at least one retro-reflective element for reflecting light from the
beam back to the light-sensing means.
53. The system according to claim 50, wherein the sensing means
each detect the presence as aforesaid of each said object by impact
of that object within the respective location.
54. The system according to claim 53, wherein each sensing means
involves piezo-electric cabling for sensing impact.
55. The system according to claim 54, wherein each sensing means
includes a plurality of piezo-electric cables, and the position of
the impact within the location of the respective sensing means is
derived from electric signals produced in the respective cables in
response to the impact.
56. The system according to claim 48, wherein each said object
carries a radio-frequency identification tag and the sensing means
each include radio-frequency means for detecting the presence as
aforesaid of each said object.
57. The system according to claim 48, wherein the derived
representions are provided in the form of video display.
58. The system according to claim 48, wherein the objects are golf
balls that are launched by a golfer in successive strikes.
59. The system according to claim 58, wherein the prediction of the
outcome of launching of each individual ball is computed in
accordance with velocity and spin vectors of the ball at
launch.
60. The system according to claim 58, wherein the predicted outcome
is represented in terms of the location the ball is predicted to
reach within the area.
61. The system according to claim 58, wherein the area is a golf
range having a plurality of bays for occupation by a plurality of
golfers respectively, and each bay has means for providing a
representation of the outcome of strikes from that bay.
62. The system according to claim 61, wherein possible ambiguity in
relating actual outcome with predicted outcome in respect of balls
from different golfers is resolved on the basis of a probability
assessment made by the computer means.
Description
[0001] This application is a national stage completion of
PCT/GB2005/000611 filed Feb. 18, 2005 which claims priority from
British Application Serial No. 0423500.8 filed Oct. 22, 2004, which
claims priority from British Application Serial No. 0414028.1 filed
Jun. 23, 2004, which claims priority from British Application
Serial No. 0412583.7 filed Jun. 5, 2004, which claims priority from
British Application Serial No. 0403561.4 filed Feb. 18, 2004.
FIELD OF THE INVENTION
[0002] This invention relates to methods and systems using
prediction of outcome for launched objects.
BACKGROUND OF THE INVENTION
[0003] According to one aspect of the present invention there is
provided a method for deriving representations of the individual
outcomes of launching objects into an area that contains a
plurality of mutually-spaced object-sensing means, wherein each
sensing means detects the presence of any of the launched objects
that arrive in the location of that respective sensing means, a
prediction of the outcome of the launching of each individual
object is computed in dependence upon measurements of velocity
vectors of that object at launch, the prediction is used to provide
representation of the outcome of the launch of that respective
object in the event that the presence as aforesaid of that object
is not detected by the sensing means, and the computation process
by which the predictions are computed is subject to adaptive
correction in dependence upon error between the outcome predicted
and the actual outcome realised in respect of individual objects
for which the presence as aforesaid is detected by any of the
sensing means.
[0004] According to another aspect of the invention there is
provided a system for deriving representations of the individual
outcomes of launching objects into a defined area, comprising a
plurality of mutually-spaced object-sensing means within the
defined area, each of the sensing means being operative to detect
the presence of any of the launched objects that arrive in the
location of that respective sensing means, launch-analyser means
for deriving measurements of the launch velocity vectors of each of
the objects individually, computer means for computing in
dependence upon these measurements a prediction for the respective
object of the outcome of its launch, and means for providing
representation of the computed prediction in the event that the
presence as aforesaid of the respective object is not detected by
the sensing means, and wherein the computation process by which the
predictions are computed by the computer means is subject to
adaptive correction in dependence upon error between the outcome
predicted and the actual outcome realised in respect of individual
objects for which the presence as aforesaid is detected by any of
the sensing means.
[0005] With the method and system of the invention, the
representation provided in respect of the individual objects for
which the presence as aforesaid is detected by any of the sensing
means, may be the actual outcome realised.
SUMMARY OF THE INVENTION
[0006] The method and system of the invention is especially
applicable to providing representations of the outcome of
successive strikes of a golf ball, for example in the context of a
golf range. In this respect, measurements of the launch velocity
and spin vectors of a ball can be used to predict its ensuing
flight-carry and -duration, its landing speed, landing backspin,
angle of descent and subsequent bounce and roll. However, the
accuracy of such prediction is very prone to errors arising from
inaccuracies in the flight model, the bounce and roll model and the
launch measurements and also variations in atmospheric conditions
(e.g. wind speed, rain, temperature and pressure) and also in the
rebound and friction properties of the landing terrain. The method
and system of the present invention enable a significant
improvement in prediction accuracy to be achieved by sensing the
actual outcomes realised in relation to some shots and from the way
in which these differ from the predicted outcomes computed for
those same shots, correct the computation process adaptively to
reduce error.
[0007] The "end-of-flight" parameters may be predicted and
measured, namely, the carry-length, the direction and the flight
duration. One possible means of achieving the measurement of actual
carry distance and deviation and the flight duration is disclosed
in WO-A-9201494 which describes the use of geophones distributed
around a reception area to sense the impact of the ball as it
lands. Signals corresponding to the time of arrival of the impact
vibration at proximate geophones are recorded and, by analysing the
time differences in these signals at different geophones, the
position and time of impact can be accurately measured.
[0008] As an alternative, passive or active radio-frequency
identification ("RFID") tags may be embedded in each golf ball and
used for identifying the final position of the ball. A system that
employs passive RFID tags to locate the final positions of golf
balls is described in US-B-6,607,123. In the present case, balls
may be first identified at the tee and then at instrumented target
areas on the driving range outfield where means is provided to
interrogate the tags, dependent on ball position. This in turn
provides data on the final outcomes of a proportion of golf shots
and such measurements may be used to correct the ball launch
calibration parameters and the prediction of ball carry, bounce and
roll, taking into account prevailing atmospheric conditions and
prevailing bounce and roll characteristics of the terrain.
[0009] The measurement of velocity vectors and/or other parameters
of a launched ball or other object may be carried out for the
method and system of the present invention by detecting
light-change resulting from passage of that object through
detection planes defined by respective slit-apertures. Each
detection plane may involve means for emitting light as a beam
through the respective slit-aperture and means for sensing light
from the beam reflected back through that same slit-aperture from
the object. The angle subtended at the object by the light-emitting
means and the light-sensing means is preferably less than 3
degrees, in these circumstances. More particularly, the subtended
angle (identified as the "observation angle") is preferably less
than 1 degree, and more desirably less than 0.5 degree or even 0.2
degree.
[0010] The light-emitting means and its co-acting light sensing
means (referred to collectively as a "TXRX pair") preferably
operate in the infrared or near-infrared spectrum as this
suppresses interference from extraneous daylight sources and is
invisible to the user; however, other light wavelengths may be
used. Furthermore, the light emitted may be continuous or pulsed.
For example, low duty-cycle pulsed emissions with a repetition
frequency in the range 10 kHz to 100 kHz may be used with
measurements coinciding with each pulse. This corresponds to
providing measurements of club-head and ball positions at intervals
of a few millimeters to a fraction of a millimeter. (In a `full
swing` golf shot the club head speed at impact is typically in the
range 25 meters per second to 55 meters per seconds, and ball
launch speeds are typically 30% to 60% greater). For applications
where the movement of a golf putter is to be measured, the
repetition frequency can be much lower (e.g. about 1 kHz).
[0011] The light emission may be square-wave or sinusoidal
modulated or the like, with high modulation frequency (e.g. 50 to
100 kHz or higher), and the received signal highly amplified and
narrow-band filtered (preferably with a phase sensitive detector)
so that very weak signals from retro-reflectors can be detected.
This embodiment can be arranged to read identifying codes, such as
dot-codes, on more slowly moving objects and/or on larger
retro-reflectors with long-range and large capture-window
applications.
[0012] A detection plane may be established as indicated above by
arranging the active elements in a TXRX pair in close proximity
(e.g. 2 to 10 millimeters apart, but not limited to this range) and
some distance behind a slit-aperture. The width of the
slit-aperture may nominally equal the distance between the emitting
means and the light-sensing means in the TXRX pair ("the TXRX
separation"), with the length axis of the aperture perpendicular to
the axis that is co-linear with the centre of the light emitting
means and the centre of the light-sensing means in the TXRX pair
("the TXRX axis"). Neglecting the finite size of the active areas
in the TXRX pair and diffraction effects at the edges of the
aperture, the width of the detection plane in this arrangement is
nearly constant throughout the useful extent of the detection plane
and is equal to the TXRX separation (typically 3 to 4 millimeters).
This controlled-width detection plane is advantageously used in
conjunction with retro-reflectors that have much greater reflective
efficiency than diffuse reflectors, with the efficiency increasing
with smaller observation angles. This increased efficiency helps to
compensate for spreading losses at increasing range (and thus
decreasing observation angle). When the detection plane is not more
than x millimeters in width (where x can be any number, but
typically 3 to 4 millimeters), different features in the shape or
pattern of the reflector can be detected provided that these
features are separated by at least x millimeters. By providing a
line array of light emitters and light sensors with adjacent
elements in the array forming a TXRX pair and with the array axis
normal to the length axis of the slit-aperture, the position of the
detection plane can be altered, depending on which TXRX pair is
selected or made active. In this arrangement, each TXRX axis is
co-linear with the array axis.
[0013] Another way of creating a detection plane is to arrange that
the TXRX axis is parallel to the length axis of the slit-aperture.
Provided the TXRX separation is small compared to the length of the
slit-aperture, the fields of view for the light emitting means and
light-sensing means are nearly identical. The detection plane thus
formed comprises the common field of view. An advantage of this
type of detection plane compared with that previously described, is
that more light is emitted into the detection plane and more light
is reflected back from the detection plane because the entire field
of view is used. However, the width of the detection plane
increases with range as it spreads out into a wedge shaped volume.
This can be corrected using a cylindrical lens, so that the
detection plane is again of uniform thickness (equal to the width
of the slit-aperture) or nearly so. This method of forming the
detection plane improves its sensitivity and operating range.
[0014] It is sometimes desirable to use a diffuse reflector (e.g.
one side of the surface of a golf ball). Because diffuse reflection
is inefficient, the method of creating detection planes described
in the immediately-previous paragraph is preferred for diffuse
reflection. In this case it is sometimes advantageous to have
larger TXRX separation (giving greater observation angles) to
suppress retro-reflection relative to diffuse or spectral
reflection from the golf ball or other object.
[0015] The golf ball or other object may carry one or more
reflectors. A single reflector comprising an area of reflective
surface of distinctive shape, such as a triangle or rectangle, may
be used. Alternatively, two or more separate reflective surfaces
may be used in a defined pattern, such as circular dots arranged
along a line, a barcode pattern, or three dots on the corners of a
triangle. Although diffuse reflection may be used, there are
advantages to be achieved using retro-reflective elements. These
later elements are preferably, but not necessarily, of the
corner-cube or prism type, and may be provided with special prism
structures with biased and/or variable tilt axes in orderto
orientate the maximum reflectivity at an incidence angle other than
90 degrees, and/or to make the reflectivity more uniform over a
range of incidence angles. In the case of a golf ball, it may have
just one retro-reflector with the remainder of the ball surface
providing a diffuse reflector, but preferably it carries a
plurality of retro-reflective dots arranged in a spherically
symmetric orientation on the ball. The golf club used may also
carry at least one retro-reflector preferably on the club-head
and/or on the lower end of the shaft, above the club-head.
[0016] Means may be provided to enhance the detection of a
retro-reflector in the presence of unwanted reflections from other
parts of the moving article by placing a first light polarizing
filter in front of the light emitter and a second light polarizing
filter in front of the co-acting light sensor. Light reflected from
the retro-reflector has its plane of polarization rotated 90
degrees (or theoretically so). The two filters are oriented so that
the planes of polarization are at 90 degrees to one another (or at
optimum cross orientation), so only the polarized target-reflected
light is allowed to pass through the said second polarizing filter
and into the light sensor. When the polarized emitted light strikes
other (non-retro-reflective) surfaces of the object being detected
or internal surfaces in the measurement apparatus, its plane of
polarization is not rotated, and the returned beam is blocked from
entering the sensor. A second co-acting light sensor may be
provided on the obverse side of the light emitter with a polarized
filter aligned with the plane of polarisation of the emitted light.
This is insensitive to reflected light from retro-reflective
surfaces but sensitive to other reflective surfaces, and provides
two signals, for example, one responsive to retro-reflective dots
on the surface of a golf ball and the second responsive to
reflections from the ball surface alone.
[0017] Various types of polarizing filters may be used such as
Rochon, Brewster or dichroic polarizers. One type of dichroic
polarizer that is advantageously useful at infrared wavelengths is
the wire-grid polarizer. Wire-grid polarizers are very expensive to
manufacture compared to the much more common sheet polarizers
(based on modified polyvinyl alcohol iodine) but, in the present
context, the dimensions of the filters are exceptionally small so
it is economic to use wire-grids. Since both the emitter and sensor
devices in a TXRX pair share a common focusing lens and/or
slit-aperture, the filters are preferably fabricated on or very
close to the active areas of these devices. The active areas are
very small (e.g. 0.1 to 1.0 square millimeters) so the polarizing
filters are also very small. Judicious design of the wire-grids and
associated conductors can also help to reduce radio frequency
interference in the sensor signals generated by the relatively high
power emitter drive signals. Anticipating future developments in
light emitter and sensor devices, the emitter and/or sensor may
transmivrespond in one plane of polarization without need of
additional filters.
[0018] Preferred shapes for the reflectors have simple geometries
such as circular, hemispherical (i.e. a golf ball surface),
triangular or quadrilateral. However, any shape that can be defined
mathematically may be used. In one preferred embodiment, the shape
comprises one or more small circular dots having diameters of
similar sizes as the width of a detection plane and arranged in
known relative positions on a golf club, golf ball or other object
to be measured. The detection planes are preferably arranged to
traverse the path of a reflector at various positions along the
path and at various angles thereto. As a reflector travels through
the various detection planes, data capture circuits record the
corresponding time and amplitude response. These data are used to
compute the speed, position and direction of the reflector and thus
determine the ball and/or club head motion. A powerful technique
for extracting accurate three-dimensional data of the motion of a
reflector as it passes through an array of detection planes is the
Levenberg-Marquardt method for non-linear estimation. This, and
alternative estimation algorithms, require a fairly representative
mathematical model of the measurement system and to this end it is
advantageous that the reflectors have basic geometries that can be
described in simple mathematical terms.
[0019] The object-sensing means, which may for example utilise
optical, acoustic, electromagnetic, electromechanical, or
radio-frequency sensing, may be utilised in the context of golf
shots for example, to detect the outcome of the ball flight (i.e.
the carry distance and deviation and the duration of flight), or of
the entire travel of the ball to where it comes to rest. The
vibration created by the impact of the ball on landing may be
detected, and data derived from the position and time of impact for
a proportion of balls may be utilised with data comprising the
carry distance, deviation and duration of flight, to correct the
ball launch calibration parameters and/or the ball flight model
parameters. Optionally, the position and/or timing of a second
impact of a ball (i.e. after bouncing off the ground) may be
measured to determine the final direction, descent speed and other
end-of-flight parameters.
[0020] The vibration sensing means may be single devices, each
attached, for example, to an individual panel that vibrates on
impact so as to indicate the landing of a ball on the panel, and/or
may involve a distributed array of geophones to sense ground
transmitted vibrations or the like. One preferred geophone
arrangement uses buried piezoelectric cables near the perimeter of
a sensing zone and/or arranged along grid lines distributed across
the sensing zone.
BRIEF DESCRIPTION OF THE DRAWINGS
[0021] Methods and systems in accordance with the present invention
will now be described, by way of example, with reference to the
accompanying drawings, in which:
[0022] FIG. 1 is a logic block diagram of a system according to the
invention for use in providing a golf-range facility;
[0023] FIG. 2 is a flowchart showing the main computation and
decision routines used in the system of FIG. 1;
[0024] FIGS. 3(a) and 3(b) illustrate two scenarios of actual and
predicted golf shots;
[0025] FIG. 4 is a diagrammatic plan view of the outfield of the
driving-range facility;
[0026] FIGS. 5(a) and 5(b) are a plan view and a sectional side
view of a short-range target of the driving-range facility of FIG.
4;
[0027] FIGS. 6(a) and 6(b) are a plan view and a sectional side
view of a distance-range target of the driving-range facility of
FIG. 4;
[0028] FIG. 7 is a flowchart showing main computation and decision
routines used in the system of FIG. 1 as an alternative to the
computation and decision routines of FIG. 2;
[0029] FIGS. 8(a) and 8(b) are a plan view and a sectional side
view of an instrumented target that uses radio-frequency
identification to detect balls on the target;
[0030] FIG. 9(a) and 9(b) are schematic diagrams showing a launch
analyser for use in the system of FIG. 1, together with a golf ball
prior to its launch;
[0031] FIG. 10(a) and 10(b) are schematic views illustrating the
establishment of detection planes corresponding to those of the
launch analyser of FIGS. 9(a) and 9(b);
[0032] FIGS. 11(a) and 11(b) are diagrammatic plan and side views
of a golf ball passing through detection planes corresponding to
those of the launch analyser of FIGS. 9(a) and 9(b);
[0033] FIG. 12 shows time-dependent waveforms representing sensor
signals generated from the detection planes of FIGS. 11(a) and
11(b);
[0034] FIG. 13 is a plan view of a launch analyser which is
responsive to movement of the golf-club head as well as of the golf
ball during launch of the ball, and which may be used as an
alternative to the launch analyser of FIGS. 9(a) and 9(b) in the
system of FIG. 1;
[0035] FIG. 14 is a side view illustrative of operation of the
launch analyser of FIG. 13; and
[0036] FIG. 15 shows time-dependent amplitude waveforms generated
illustrating signal responses generated from detection planes shown
in FIG. 14.
DETAILED DESCRIPTION OF THE INVENTION
[0037] Reference axes X, Y and Z are shown for convenience in
conveying orientation, where this is appropriate in certain of the
figures to which reference is made in the following description. In
this respect, the Z-axis is vertical and points upwards, the Y-axis
is horizontal and points downrange (i.e. along the general line of
flight of a golf shot), and the X-axis is orthogonal to the Y- and
Z-axes and points in the general `heel-to-toe` direction of a club
head at ball address.
[0038] The block diagram of FIG. 1 outlines the top level system
for a golf range facility where several golfers hit golf balls into
the same general area. Blocks representing first, second and Nth
golfers using the range are show as 1, 2 and 3 respectively. The
golfers launch golf balls downrange onto the outfield 4 at random
times and with random distances and direction, and some of the
balls land on instrumented targets 5. In a first version of the
instrumented target, the "end of flight" or "end of carry" position
and time of balls can be measured from vibrations caused by the
balls hitting the surface of an instrumented target as they first
land at high speed on the outfield, with means provided to locate
the radiation centre of these vibrations and the point in time of
their occurrence. In a second version of instrumented target, the
"end of run" positions of balls can be measured using a passive or
active RFID tag embedded in each ball to uniquely identify all
balls in the driving range and means are provided in the
instrumented targets to read tag identifying codes on any ball that
runs or bounces onto that target. If required, a driving range with
the second version of instrumented targets can additionally be
provided with ball landing impact sensors (similar to the sensors
in the first version of instrumented target) to enhance the quality
of data for actual shot outcomes. Preferably, all the golf balls
used in the facility are of similar external construction with
nominally equal weight and diameter (which is true by default for
all standard golf balls), and of closely similar impact and
aerodynamic properties, which again is easily achieved.
[0039] The golfers 1, 2 and 3 are provided with individual launch
analysers 6, 7 and 8, and balls are dispensed to them at or near
the tee, or at a central dispensing station. The launch analysers
6, 7 and 8 measure the initial speed, spin and launch angles of
driven balls and from these measurements predict the flight or the
flight and run of the balls. If balls with embedded RFID tags are
used, the launch analysers also register a golfer- or user-code by
means of a key- or card-reader. Each golfer is in this case issued
with an individually-coded key or card for use in registering
his/her code at the allotted launch analyser, and the same key or
card is used for the allocation to him/her of RFID-tagged balls, so
that the unique codes of all balls dispensed to the individual
golfer can be identified with the launch analyser where they are to
be used. Two or more golfers may share one key or card and select
their name on a touch-screen or by other selection means when
taking turn to play.
[0040] The data from the launch analysers at each driving bay are
transmitted to a central computer 9. The computer 9 matches balls
that are detected on any instrumented target with the golfer who
hit that ball, and computes the error between the predicted outcome
for that golfer's shot (based on launch analyser measurements) and
the actual outcome.
[0041] In one form of RFID tagged ball each ball is provided with
an active RF transmitter, preferably using an internal
re-chargeable power source. Typically, the power source may have
capacity of a few milliamp-seconds or less (e.g. from charge stored
in a high-value multi-layer ceramic capacitor or the like). The
power source may be charged through a connector but preferably
charge is provided from an inductively coupled external field prior
to hitting the ball off the tee. The balls may be activated to
transmit their unique code by an RF field that is local to each
target area. The position of a stationary ball on a target area can
then be sensed either by buried loops within operating range of the
tag transponders or by directional scanning antennas located in the
vicinity of each target area.
[0042] In one arrangement, the RFID reader at each target area is
provided with a plurality of buried loops or antenna and receiver
channels configured such that at least one can receive
transmissions from the golf-ball active tag dependent on its
orientation. The RFID tags may be programmed to be normally in
standby (low-power mode) and momentarily power-up at two to three
second intervals or other intervals so that if it is in radio range
with at least one antenna/receiver circuit it can indicate its
presence. The interrogation (i.e. radio communication between
reader and tag) is then performed using the in-range channel. This
means that only one channel performs the interrogation, and that
transmit-power is required of the reader only when a ball first
lands on a target area. Preferably, means may be provided on each
tag to sense the high energy impact of the golf shot and initiate
power-up only after impact and optionally shut down after the tag
code is successfully transmitted to the target area receiver.
[0043] In a second and preferred form of RFID tagged ball, the
embedded RFID devices are passive. This requires that balls that
roll or bounce onto an instrumented target subsequently roll back
into a collecting channel or duct or the like where they come in
close proximity to a RFID reader. Preferably, instrumented targets
that sense passive RFID balls are fairly small in diameter or span
compared with their individual distances from the driving bays.
Thus a passive RFID type target at 100 meters range could be
typically ten meters in diameter (if circular), which would then
have a measurement resolution of .+-.5%; this assumes that there is
only one passive RFID reader per target area. Numerous such targets
would be provided on the outfield to ensure a reasonably high
success rate of shots landing on targets. Although the resolution
is only .+-.5% (or some other percentage), the system is still able
to minimise systematic errors to nearly zero, since very large
numbers of balls are sampled and the average of all measurements is
sensitive to small systematic discrepancies.
[0044] Instrumented targets of either RFID mode are more akin to
"real golf" than targets that detect impact, in that the equivalent
to the target in real golf is the green with a hole and a flag and
the aim on "approach shots" is to strike the ball so that it flies,
bounces and finally rolls to a stop close to the flag--or better
still, drops into the hole. With RFID instrumented targets, each
target can be provided with a regulation size hole and a
traditional flag. The target surface emulates the surface of a
traditional green and the hole is provided with a RFID reader to
register "hole-in-one" shots. The chances of achieving a
hole-in-one on a driving range according to this embodiment of the
invention are similar to the chances of achieving a hole-in-one on
a traditional golf course.
[0045] The instrumented target areas comprise a fraction of the
total outfield area so a proportion of balls may land in
intermediate areas between the target areas. In these instances,
the outcome of a golf shot is interpolated using computer
prediction of the outcome based on accurately measured ball launch
parameters. The instrumented target measured data is used to apply
corrections to the data generated in each of the launch analysers
6, 7 and 8 and to update the golf shot prediction model so that the
interpolation of shot outcomes is accurate. The above corrections
are generated using iterative algorithms that test where and how
much correction is appropriate so after a few results from each
launch analyser the predicted and actual data converge (to within
very small tolerance). The correction process continues as long as
golfers hit balls onto the instrumented target areas and adapts to
environmental changes on an hour-to-hour and day-to-day basis. The
computer can also monitor long-term calibration drift in each
launch analyser and apply appropriate correction, or report that
specific components of the facility require maintenance. A weather
monitor 11 positioned downrange, measures wind speed and direction
and air density and signals the results to the central computer to
assist the prediction process. In consequence, each video display
unit 12, 13 and 14 provides the relevant golfer with a reliable
representation of great precision, of the outcome of each of
his/her shots.
[0046] For one shot per bay, the average number M of balls detected
within an instrumented range may be considerably less than the
number of bays in use N. In a busy 50-bay driving range, about 6000
balls per hour are hit during peak usage. It is only necessary to
have a few hundred results per hour to obtain very good feedback
for adaptive correction purposes. Thus, in a driving range
according to the invention, it is only necessary to measure the
actual outcome of a fraction of the total of driven balls in order
to provide accurate prediction of all balls hit. Furthermore,
because golfers have an incentive to land their balls on a target,
the density (i.e. number per unit area) of balls landing on
instrumented targets is relatively high compared with the density
elsewhere, so the total area of instrumented targets dispersed
around the outfield as a ratio of the overall area of the outfield
is significantly less than the ratio M/N. Thus, in a driving range
according to the present invention, the area occupied by all the
instrumented targets as a percentage of the total available area of
the outfield may be less than 10% or even less than 2%. This very
low coverage of outfield sensors provides significant cost
advantages compared with ranges where most of the outfield is
populated with landing sensors or the like.
[0047] The launch analyser apparatus may be provided with a
card-reader or other key device that may be mechanical or
electronic. The code contained in such device can be used to
provide membership account data, membership expiry date (if
required) and credit amount for future playing time. In the case of
a range using RFID tagged balls, the code contained in such device
can be additionally used to identify which balls are dispensed to
one or more players in each bay. Additional data such as a
customer's e-mail address can be used to relay the results of a
practice or game session directly to the customer's home PC.
Alternatively, data from individual customers could be
automatically posted on a website and each customer provided with a
unique password to allow private access to their results.
[0048] FIG. 2 is a flowchart showing the main computation and
decision routines required for the system of FIG. 1 when the
adaptive correction is provided by impact vibration sensors that
detect when and where balls land on the outfield. In FIG. 2, the
decision block 20 sorts the predicted data into two streams
depending on whether the data has or has not an acceptable chance
of hitting an instrumented target, where the acceptable chance is
defined as the probability that the prediction is within six-sigma
meters of a target (i.e. six-sigma meters from any landing sensor).
This criterion gives a very high confidence that virtually all
possible chances are included and obviously may be modified in
practice to less than six-sigma meters if desired. The predicted
results for shots expected to land out of range of any target are
displayed without further processing (routine 27) and these
typically form the majority of all golf shots in the driving range,
whereas the remaining predictions are included as candidates for
matching with balls that land on any of the landing sensors.
[0049] In routine 21, each ball detected by the landing sensors is
assigned to the most probable prediction. The probability that a
ball is correctly assigned to a given shot prediction can be
calculated from the ratios of the errors in predicted carry length,
carry deviation and flight duration to the respective standard
deviations of errors in these three parameters. It is thus very
desirable to frequently monitor and update the values of standard
deviation in prediction errors and assign each prediction with the
best current estimate of the applicable standard deviations. For
example, standard deviations in the predicted outcome for short
chip shots will be very small compared to those for a long drive.
The chip shot is nearly unaffected by wind and ball spin, whereas
the drive is very sensitive to these factors.
[0050] Occasionally golf shots will land on the same target nearly
simultaneously, or will be predicted to do so. In these
circumstances it is desirable to hold the incoming data (routine
22) until such time that any possible confusion between two actual
shots is resolved. Decision routine 23 checks whether there is any
confusion, that is, whether the process tries to assign two actual
shots to one golfer. When this happens, a second predicted shot
must exist so that for every two actual shots there are two
predicted shots, but sometimes the allocation is wrong. In these
circumstances, routine 24 computes the combined probability of both
combinations in order to choose which is the most likely. That is
the probability that A matches with B AND C matches with D is found
and then the probability that A matches with D AND C matches with B
is found and the combination with higher probability is chosen. The
process can then be repeated and expanded if yet another ball lands
at nearly the same time and in close proximity.
[0051] For the above process to be meaningful, it is important that
reliable values of standard deviations in the various error
parameters are obtained. Typical values for standard deviations in
predicted carry distances and flight duration are published (see
Quintavalla, S. J. 2002 "A generally Applicable Model for the
Aerodynamic Behaviour of Golf Balls", In Science and Golf IV, ed.
E. Thain, p. 346, London: Routledge). Values of 1.65 meters
standard deviation in ball carry of 240 meters (average) and 100
milliseconds standard deviation in flight time (estimated to be
about 7 seconds) were reported.
[0052] The timeout routine 25 stops the holding process (routine
22) when the probability of new (future) data from the landing
sensors matching with held predictions becomes diminishingly small.
For example, the standard deviation of errors in flight time
prediction for a certain type of shot may be 100 milliseconds.
[0053] If such a predicted shot has a chance of hitting a landing
sensor (detected in routine 20) it should be held until such time
that the actual shot detected on the landing sensor is registered.
But if this does not happen after six-sigma seconds (i.e. 600
milliseconds) there is negligible chance of it ever happening. The
data that is released from the "hold" state is then checked in
routine 26 to see whether it is actual and matched or only
predicted. In the event that the released data is a predicted
outcome that is not matched, it is displayed to the appropriate
golfer via step 27. However, in the event that the released data is
an actual outcome that has been matched to a prediction, this
actual outcome is displayed to the golfer via step 28, and the
error of the prediction from the actual, realised outcome is
analysed in routine 29 for adaptive correction of the prediction
process in the computer 9. Over a long period of time, thousands or
even millions of matched results can be recorded and analysed to
give adaptive correction. This will allow very sensitive control
and detection of non-random errors. For example, fuzzy logic or
other algorithms can be used to correlate changes in wind speed and
direction with shot outcome and anticipate the corrections
required.
[0054] FIGS. 3(a) and 3(b) illustrate two scenarios where ambiguity
or confusion between shots occurs. In FIG. 3(a) two actual shots
31, 32 and two corresponding predicted shots 33, 34 are shown where
the errors in predicted carry length are much exaggerated. Actual
shot 31 lands first at point A1 and since this is closer to P2, the
predicted point landing of shot 32, the process will first match A1
with P2 instead of P1. However, a few milliseconds later, actual
shot 32 lands at point A2 and the process will then assign A2 to P2
and thus the prediction P2 is assigned to both A1 and A2. The
process must then select a second prediction (P1) and it will find
that the probability of A2 being matched to P1 is very small indeed
and will reject this in favour of the correct assignments, namely
A1 to P1 and A2 to P2.
[0055] The carry errors illustrated in FIG. 3(a) are typical of
those produced by a gust of head wind, where the carry lengths of
both shots are reduced. In general, errors in the same direction
will not cause the system to finally match predicted and actual
shots incorrectly. A second error scenario is illustrated in FIG.
3(b) where the predicted shots 35 and 36 have large errors in
opposite directions with P2 being predicted to be much shorter than
A2 and P1 predicted to be much longer than A1. In this case the
system will fail to finally match actual and predicted correctly.
This scenario could arise if two launch analysers are used
simultaneously to measure very similar shots on the same target and
one analyser "reads high", while the other "reads low". This
occurrence will be very rare and is limited to instances where two
balls land very close together, at nearly the same time and
significant length or line prediction errors in opposite directions
cause the predictions to "cross over".
[0056] The predicted carry length, deviation and duration may be
found using the following equations:
dv.sub.x/dt=-Bv(C.sub.Dv.sub.x+C.sub.Lv.sub.y sin a) (1)
dv.sub.y/dt=-Bv[C.sub.Dv.sub.y-C.sub.L(v.sub.x sin a-v.sub.z cos
a)] (2) dv.sub.z/dt=-g-Bv(C.sub.Dv.sub.z-C.sub.Lv.sub.y cos a) (3)
[0057] where; B=nA/2m [0058] g is the acceleration due to gravity
[0059] n is the density of air [0060] m and A are the mass and
cross-sectional area of a golf ball
[0061] Equations 1 to 3 are a simplified form of the trajectory
equations for a golf ball, assuming that the ball spins about an
axis in the XZ plane at angle a to the horizontal, i.e. it does not
have "rifling spin". When a is zero, the ball has no sidespin but
only backspin. If required, additional terms to account for rifling
spin can be added, but in practice these make very little
difference to the predictions.
[0062] The trajectory equations give the rate of change of the
three vector components v.sub.x, v.sub.y and v.sub.z of the
trajectory velocity v of the ball after impact, so knowing the
initial velocity vectors (i.e. the velocities in the X, Y and Z
directions) and other parameters in the equations, the flight path
and duration can be calculated. C.sub.D and C.sub.L are the
applicable drag and lift coefficients, which are dependent on the
ball dimple pattern and the linear and angular velocity of the ball
relative to the surrounding air. These dependencies are in general
highly non-linear and difficult to predict analytically for all
possible golf shots. However, according to the present invention,
the adaptive correction process allows the system to learn fairly
precisely how C.sub.D and C.sub.L vary under virtually all possible
golf shot conditions and also adapt to changes in environment such
as air pressure, and temperature (which affect n). Thus, after an
initial learning period, the prediction of shots becomes very
accurate and the remaining errors are predominantly random with
very small standard deviations, or due to changes in ambient
conditions. It should be realised that the bulk of the said
learning period is a "once off" occurrence. That is, once a first
system has been built and commissioned, the initial learning
process for one type of ball and one type of launch analyser will
be the same for the same type of ball and launch analyser in other
sites.
[0063] The flight prediction yields information on the landing
velocity and final backspin rate of a ball. After initial
touch-down, a ball typically bounces a few times and then rolls to
a halt. The duration and length of the bounce and roll phase can be
estimated approximately with appropriate formulae involving the
ball landing data and bounce and roll coefficients for the landing
surface. Again, feedback of actual results (e.g. from known
outcomes of RFID tagged balls) allow the system to learn accurate
relationships between ball landing parameters and subsequent bounce
and roll behaviour across the entire outfield.
[0064] FIG. 4 is a diagrammatic plan view of the outfield, purely
exemplary of a driving range according to the invention with
tee-off bays (not shown) disposed along curved line 40. Five
distance targets 41 to 45 are distributed beyond a barrier 46 and a
plurality of short range targets 47 are disposed between the
barrier 46 and the tee line 40. Arrows 48 indicate the straight
ahead aiming directions for the two bays at the ends of the tee
line 40. The centres of all the distance targets 41 to 45 are
arranged to be within .+-.20 degrees of the direction of the arrows
48 and are also within .+-.20 degrees of the straight-ahead
direction of all other bays. The sum of distances from any one bay
to all the five distance targets average out to about the same
total by virtue of the curvature of the tee line 40. Thus, each bay
provides approximately the same degree of difficulty to
successfully hit all targets. One short range target 47 is provided
for a small group of bays so that again the degree of difficulty to
hit a short range target is approximately the same, irrespective of
bay position.
[0065] The barrier 46 is an optional feature, which may extend
across the outfield or part thereof at about 40 to 50 meters (or at
other distances) from the tee-off bays. It may be 0.5 to 1.0 meters
high (or higher) and may comprise separate, spaced apart barriers.
Its purpose is to provide a simple and easy test for beginners or
very young players that also may form part of a points-scoring
game. For example, hitting the barrier "on the fly" (i.e. without
the ball rolling or bouncing before reaching the barrier) may score
one point, whereas balls that carry over and beyond the barrier
score two points. Distributed vibration sensors, for example a
piezoelectric cable, built into the barrier or barriers sense when
it is hit by a ball and the launch analysers confirm the bay from
which any successful shot is made. The barrier thus provides a test
of initial ability to at least hit a ball off the ground and carry
some distance down a fairway, but ability to hit straight is not
required.
[0066] A second stage of ability is provided by the short range
targets 47, which require some degree of both distance and
direction control. These targets are typically set at 20 to 25
meters range and provide an attainable goal for the weakest players
but also a facility for higher-ability golfers to practice their
short game with precise feedback.
[0067] FIGS. 5 (a) and 5 (b) are a plan view and a sectional side
view of a possible design for a short range target. The target 47
is typically circular in plan view, but may be otherwise shaped,
and comprises a generally dome-shaped outer shell with a lid 50 and
a skirt 51. The lid 50 attaches to the skirt 51 via a shock
absorbent mounting 52 so that vibrations from impact on the skirt
do not transmit readily to the top. The shell may be supported
slightly above ground level by a shock absorbing mounting 53, which
may extend throughout the full perimeter of the lower lip of the
skirt 51. A ball landing directly on the outer shell 50,51 creates
an impact noise that is detected by a microphone 54 inside the
shell. The microphone 54 may be designed to reject far-field noise
and signal processing can be provided to distinguish between the
sound of ball impact and other sounds such as wind, rain or
thunder. A vibration sensor 55 attached to the lid 50 also senses
impacts that land on the lid 50 but not on the skirt 51 and thus
provides feedback to the central computer to distinguish between
impacts on the skirt 51 and impacts on the lid 50. Once ball impact
is detected, a processor 56 sends a signal to the central computer
9 (FIG. 1) to indicate a successful shot and record the precise
time of the impact. Balls that roll along the ground towards the
target 47, hit the shock absorbing mounting 53, but such impact
generates insufficient sound intensity for detection. It may be
preferable to provide some degree of damping on the shell 50,51 to
limit the amount of rebound and/or impact sound intensity.
[0068] Typically, the overall diameter of the target 47 is 10% to
20% of its distance from the tee line 40 so as to provide a fairly
easy target. The lid 50 typically has a diameter of only 20% to 50%
of the overall target diameter and is thus much more difficult to
hit directly with a golf shot. Optionally, the shell 50,51 can be
formed as one piece and a microphone used to detect impacts on any
part of the shell (i.e. providing no distinction between impacts on
the lid 50 and skirt 51). The slope of the skirt 51 should not be
steeper than 45 degrees on any part facing the bays, since
otherwise there is a danger of a very hard hit, low trajectory ball
rebounding back towards the bays. Optionally, the central top part
may be provided with a layer of high friction and/or softer
material so that balls landing with high backspin can be observed
in the way they bounce upwards or backwards.
[0069] Preferably the ground surrounding a target 47 is fairly soft
so that nearby missed shots do not rebound high off the ground and
subsequently land on the target. However, on the rare occasions
this does happen, the launch sensing and flight prediction system
accurately distinguishes between direct hits and hits off a
ground-bounce so that such shots are not rewarded a game score. It
should be noted that for very short distance shots (up to 30 meters
or so) the ball flight is almost purely ballistic and not
significantly affected by aerodynamic effects due to ball spin
and/or wind. This is because the aerodynamic lift and drag forces
on a ball are proportional to the square of its absolute velocity
through the air. This being the case, extremely accurate
predictions of landing positions and landing times are obtained
from the flight prediction system for short, low velocity shots.
These predictions can be calculated very quickly, so that the
result is computed before the ball finishes its flight of 1 to 2
seconds through the air.
[0070] To enhance the fun aspect of the driving range, visual
and/or auditory feedback may be provided on the targets 47. For
example, at least part of the shell may be fabricated from a
material that is translucent but impact resistant, and a high
intensity lamp 57 may be provided inside the shell to be switched
on at the instant a validated shot hits the target. The light
intensity can then be controlled to dim gradually, reducing to zero
intensity over a few seconds, unless another ball hits the target
in which case the transient light process is repeated. The
intensity of the light can also be adjusted to be much greater
during sunlight-conditions as compared with night-time or
low-daylight conditions. This provides a golfer with highly visible
and instant feedback of success and in addition three points (say)
can be added to his or her game score. In this regard, a message
such as "3 POINTS!" can be reverse printed on the inside of the
skirt 51 in an opaque colour that matches the colour of the shell
50,51, so that it is visible (as illustrated in FIG. 5(a)) through
the translucent skirt 51 as a dark symbol against an illuminated
background, when the internal lamp 57 is switched on. Various other
lighting and colour effects can be provided. Additionally or
alternatively, the sound of a ball impacting a short range target
may provide auditory feedback and optionally this can be amplified
and relayed to a speaker system local to the bay from which the
ball was launched. This latter option can be arranged so as to
confine the auditory response principally to just the one
appropriate bay.
[0071] FIGS. 6(a) and 6(b) show a plan view and a side sectional
view of a distance range target typical of the targets 41 to 45.
Here, the ground forming the target is contoured. The central and
intermediate zones form a dome or hillock 60 with preferably a
uniform slope from top to bottom to ensure that balls are not able
to come to rest on the hillock 60 but instead roll down and into a
trench 61. The outer zone of the target is sloped into a conical
dish 62 so that again balls do not rest but instead roll into the
trench 61. The trench is itself sloped so that balls rolling into
the trench continue to roll (from left to right in the diagram of
FIG. 6(b)) and then down a drain pipe 63 and finally into a
collection sump 64 from which they are periodically collected and
returned to a washing and dispensing machine in the bay area. The
floor of the trench 61 is preferably lined with a layer of low
rolling friction material so that the balls roll easily down the
trench and into the drain pipe 63, which has an internal surface
with very low rolling friction. Similarly, the surface of the
target is preferably artificial turf with low rolling friction. By
this means, only small gradients are required to ensure that balls
continue rolling from any part of the target and into the sump 64.
However, it is also preferable that any area on which a ball might
land (i.e. the target surface or the trench floor) should also have
low rebound coefficient so that most of the kinetic energy of the
ball is absorbed on first impact on the target.
[0072] To enhance the visibility of the target, especially at
night-time, the perimeter of the target is marked out with
retro-reflective reflectors 65. These are arranged on an outer bank
66 with the reflectors 65 nearest the golfers (on the left-hand
side in FIG. 6(b) positioned near the bottom of the bank 66, and
the reflectors 65 furthest from the golfers on the top, or even
above, the bank 66. Thus, a circle of reflectors 65 is formed,
which is slightly tilted up and towards the golfers so as to be in
good view. A central flag and flag-pole 67 may also be
retro-reflective. However, it may prove preferable to use high
efficiency, coloured LEDs.
[0073] Two separate, concentric piezoelectric cables 68 are buried
a few centimeters below the target surface and adjacent to the
perimeter circle of reflectors 65. These cables 68 are connected to
a differential amplifier (not shown) so that common-mode noise
(i.e. noise from distant sources such as road traffic, wind, etc.)
is rejected and only vibrations caused by impacts close to the
cables 68 (e.g. golf-ball landing impacts) are sensed. This
arrangement detects very precisely whether a ball lands inside or
outside the perimeter circle. A second set of piezoelectric cables
69 are arranged in a grid formation covering the surface of the
target inside the perimeter circle. Each of the cables 69 (of which
only eight are shown) is connected to an individual amplifier (not
shown), and is preferably buried somewhat deeper than cables 68.
The cables 69 detect balls landing on any part of the target inside
the perimeter circle to provide measurements of landing position
and landing time.
[0074] Preferably, a local signal conditioning and processing unit
(not shown) is provided at each target 41 to 45. This analyses the
raw data, rejects far-field impacts and computes the co-ordinates
of the first (and optionally second) impact of balls landing within
a given radius of the target centre. This processing unit will also
communicate with the central computer 9 (FIG. 1) and with any
peripheral equipment. Power and communications lines may be
provided by underground cables, but optionally cables will only be
used to connect the target sub-system components. The powering of
the sub-system, including of radio communications to the central
computer, can be from rechargeable battery and/or a local solar
power generator.
[0075] As with the short range targets 47 (FIG. 4), it is desirable
to provide optional special effects when golfers successfully hit
the target to enhance the "fun" aspect of the facility. This can be
limited to only a central zone of each distance target and may be
provided with high pressure water jets to form transient fountains
on each (fairly rare) occasion that a ball carries to a central
zone. Each distance target 41 to 45 would be provided with one such
water jet situated near the centre of the target and controlled to
operate for a few seconds each time a ball lands on its central
zone. Since the ball flight to distance targets is always a few
seconds duration, the prediction that a ball will land may be
computed before it actually does, so the response time (ball
landing to jet operation) can be nearly instantaneous. To enable
various other custom special effects, a general purpose control
interface can be provided. This would provide multiple triggering
signals to operate such devices as balloon releases, display
rockets or other fireworks or the like that would be
operated/ignited in synchronism with balls landing near the centres
of targets.
[0076] Other designs of target, which may include traditional
landscaped greens, bunkers and water features, etc., may be
provided instead of, or in addition to, the distance targets
described above.
[0077] FIG. 7 is a flowchart showing the main computation and
decision routines required for the system of FIG. 1 when the
adaptive correction is provided by RFID readers that identify
"captured" balls, that is to say, balls landing on outfield
targets. The readers and central computer 9 identify each captured
ball with the bay from which it was hit. The code for each
individual ball as it is dispensed to the golfer (routine 70) and
the system also identifies which golfer plays from which launch
analyser. The balls may be dispensed into a bucket at a central
location or by other means. Thus the launch point (i.e. driving
bay) of every captured ball is known. The launch analysers measure
the velocity vectors and preferably also the spin vectors of balls
as they are hit and these measurements are then used to compute
predicted flight and run of the balls (routine 71). Optionally, the
system can then display the predicted flight and run of a ball
before the run actually ends (routine 72) and thereafter display
final information and score points after the run is complete. A
decision routine 73 sorts predictions into those that have at least
a small chance of "capture" (i.e. landing on a target and being
recognised by a RFID reader) and those that do not. The outcome and
"score" of a ball with virtually no chance of capture is displayed
(routine 77) without further processing but this final display is
preferably timed to occur at the approximate end of the actual run
for that ball. Prediction data for balls that appear to have some
chance of capture are held in a register (routine 74) until such
time that a matching code in a captured ball is obtained (routine
75) or until a timeout occurs (routine 76). The timeout may be
separately calculated for each prediction and chosen to be a few
seconds longer than the predicted time to capture. For captured
balls, the final outcome with confirmation of landing on a target
is displayed (routine 78).
[0078] In routine 79 the captured ball data is analysed to quantify
errors and apply adaptive correction. Routine 79 performs a similar
function to routine 29 in FIG. 2 but a significant difference in
FIG. 7 is that for a given target there are only two outcome values
for each ball, namely it is either captured or not captured.
However, there are preferably numerous targets distributed over the
outfield. (Optionally, targets may be divided into different
segments so that more than two outcomes are available.) In
contrast, the actual data in routine 29 (FIG. 2) can have an
infinite variety of positions within each target. Nevertheless, the
captured ball data and the almost-captured ball data (i.e. all
balls predicted to be within range of a target) can be used to
analyse range and direction errors and minimise systematic errors
because the very large volume of data builds up an accurate picture
of which predicted shots enter the target and which do not. The
"capture zone" is similar to the "sink zone" for putted balls
described in Tierney, D. E. and Coop, R. H. 1999, "A Bivariate
Probability Model for Putting Proficiency", Science and Golf III,
ed. A. J. Cochran and M. R. Farrally, pp. 387-389, United Kingdom:
Human Kinetics. In the present invention, the capture zone is
mainly dependent on ball horizontal velocity and direction but
descent trajectory and backspin also affect the capture.
[0079] FIGS. 8(a) and 8(b) are a plan view and a side section view
of an instrumented target that uses RFID reader apparatus to detect
balls on the target. Balls hit from the driving bays travel in a
general left to right direction in FIGS. 8(a) and 8(b). Most of the
area of the instrumented target comprises a top sloping surface 80.
A re-entrant channel or trench 81 borders the front lip of the
sloping surface 80 such that balls landing on the surface roll into
the trench 81 where their identifying codes are recorded by at
least one RFID reader (not shown). More than one RFID reader may be
provided or a distributed reader arrangement may be used such that
balls rolling into the trench 81 are read very soon after they roll
in. One or more down-pipes 82 lead from the trench to a collecting
sump 83.
[0080] The trench is sloped to cause balls to roll into the
down-pipe or down-pipes and constant or periodic water-flushing
(not shown) may be employed to ensure that the trench 81 is kept
clear and balls readily collect in the sump 83. To this end, it may
be advantageous to use balls that are slightly less dense than
water. A flag-pole sits in a regulation size golf hole 84 and a
RFID reader (not shown) identifies any ball that enters this hole
to record a "hole-in-one" shot. Floodlights (not shown) may be
provided inside the re-entrant trench 81 to illuminate the sloping
surface 80 and the flag-pole during night-time and other periods of
low visibility.
[0081] Balls travel at various speed towards the target. In most
cases, balls roll onto the target over the upper surface of the
re-entrant trench 81 and up the top sloping surface 80 where they
slow down and eventually either roll back to fall into the trench
81, or, occasionally, into the hole 84. In other cases, especially
with a high pitch shot, the ball may land directly onto the top
sloping surface 80 and roll forward into the hole 84 or, more
usually, roll part way up the slope and then roll back, into the
trench 81. Other balls that approach at high speed will roll or
bounce off the top sloping surface 80 and not be captured. The top
sloping surface 80 has a tendency to slow down the run of a ball
and return it so that it falls into the trench 81 and eventually
into the sump 83. In other words, the target captures balls that
would roll onto its surface and also some way beyond if it were
flat. This is shown in FIG. 8(a) where arrow 85 indicates one
possible approach direction and dotted line 86 represents the
boundary of the capture zone for all balls approaching the target
in the direction of arrow 85 (the "capture zone" is the area where
balls would come to rest if the target were completely flat with an
unbroken surface). A different capture zone boundary will obtain
for different directions of arrow 85. To a first approximation the
shape and extent of the capture zone boundary 86 is dependent on
just the horizontal velocity of the ball at landing and the amount
by which the path of the ball is offset from the centre of the
target. Both these parameters can be predicted accurately from
launch analyser measurements. Secondary factors such as descent
trajectory, backspin, variations in ground bounce and undulations
in terrain will affect the shape and extent of the capture zone
boundary but with a large volume of data an accurate knowledge of
the boundary for each approach direction can be built up. By this
means, the outcome of balls that do not get captured can be
predicted accurately by interpolation of the results for captured
balls at several instrumented target locations distributed over the
outfield.
[0082] For balls that carry further than 50 meters or so, the
spin-rate and spin-axis tilt of the ball at launch, as well as its
linear velocity vectors, are critical to its eventual carry
distance, carry deviation and flight duration. In order to predict
reliably where and when a ball lands on the outfield for reliably
matching landing-data with launch-data, it is essential that the
spin imparted on a ball at impact is measured as precisely as
possible as well as launch angle and linear speed. This is
especially the case at peak usage in large driving ranges when the
likelihood of shots from different bays landing at nearly the same
spot at the same time is most frequent. Ideally, the predicted-shot
outcomes and actual-shot outcomes should match to accuracies that
are equal to, or better than, a golfer can be reasonably expected
to observe. This would then ensure that the matching process works
with complete integrity and credibility no matter how many balls
land on any given target in any time slot. It is thus an aim of the
invention to provide apparatus that measures ball launch velocity
and spin vectors to a very high degree of precision.
[0083] In FIGS. 9(a) and 9(b), a launch analyser 90 is positioned
generally forward of the pre-impact position of a golf ball 91 and
parallel but offset from the expected straight-ahead launch
trajectory of the ball (shown by arrow 92). In practice, the launch
trajectory will have elevation angle typically in the range 5
degrees (as in a low trajectory drive shot) to 30 degrees or more
(as in a 9-iron shot) and may diverge from the straight-ahead
direction by .+-.25 degrees or more in azimuth. The golf ball
surface is provided with retro-reflective elements 93 comprising
small dots of retro-reflective material. A plurality of detection
planes emanate from upper slit-apertures 94 and lower
slit-apertures 95. The detection planes contain beams of light that
are focussed into thin sheets which traverse the path of the ball
91 during part of its initial few centimeters of flight (e.g. from
10 to 50 centimeters or so). Dotted lines 96 indicate the vertical
extent of one of the detection planes emanating from an upper
slit-aperture 94, whereas dotted lines 97 indicate the vertical
extent of one of the detection planes emanating from a lower
slit-aperture 95. These detection planes are very thin (for example
in the range 2 to 5 millimeters) measured transverse to the plane
of the slit-aperture, with very small or zero divergence
angles.
[0084] FIGS. 10(a) and 10(b) are more detailed views of a
detection-plane arrangement in FIGS. 9(a) and 9(b). A TXRX pair 100
comprises a light emitter device (LED) 101 and light sensor 102. A
cylindrical lens 103 and a slit-aperture 104 are arranged with the
TXRX axis, the length axes of the lens, and the length axis of the
slit-aperture parallel and coplanar. The TXRX pair 100 is disposed
on the principal focal line of the cylindrical lens such that
parallel rays (show as dashed lines 105 in FIG. 10(b)) converge to
a line focus on the TXRX axis. With this arrangement, the field of
view of the sensor 102 and the irradiation field of the LED 101
coalesce to form a detection plane with nominally uniform thickness
106 equal to the width (for example, in the range 2 to 5
millimeters) of the slit-aperture and with angular extent 107
determined by the length of the slit-aperture and the distance of
the TXRX pair behind the aperture. The detection plane formed by
the arrangement of FIGS. 10(a) and 10(b) is parallel to the Y=0
plane, but in general the launch analyser apparatus requires other
detection planes that are rotated about the X and/or Z axes. In
practice, it is difficult to ensure that the TXRX pair 100 is
exactly placed on the principal focal line of the cylindrical lens
103. Small errors in positioning result in the detection plane
either converging or diverging, so that the thickness reduces or
increases slightly with increasing range. These variations can be
accommodated in the data processing.
[0085] The detection plane arrangement of FIGS. 10(a) and 10(b) may
be used in other applications where it is desirable to detect
information from a moving object and from a distance. For example
an arrangement of detection planes may be used to detect vehicle
information provided as a retro-reflective dot code or bar code on
the inside front windscreen of a vehicle (e.g. on a tax disc).
Since the windscreen is kept clean to give the driver good
visibility, the retro-reflective code is also kept visible and
protected from weather and grime.
[0086] FIGS. 11(a) and 11(b) show a diagrammatic plan view and side
view of a golf ball 110 in a first position y1 just after impact
and the same ball 110 in a second position y2, two milliseconds
later passing through detection planes shown by dashed lines 114,
115, 116 and 117. The ball diameter is 42.7 millimeters and (purely
for example) travels at 64 m/s so the distance between y1 and y2 is
very nearly three ball diameters. The ball 110 has, by way of
example, a regular octahedron dimple pattern and is provided with a
spherically symmetric arrangement of eight retro-reflective
elements comprising two elements 111 and 112 that are in most
direct detection view of the lower slit-apertures 65 and six other
elements 113, some of which are below the ball (FIG. 11(a)) or
behind the ball (FIG. 11(b)). The retro-reflective elements 111
through 113 are positioned on the centres of each facet of the
octahedron. The eight elements thus form the corners of a
hypothetical cube with sides 24.6 millimeters square, and this
provides a simple model of their relative spatial positions and
orientations.
[0087] Retro-reflective material has significant thickness because
the light-reflecting surfaces of it are arranged in a
three-dimensional shape, such as a prism. For example, a preferred
high-grade retro-reflective material is 0.4 millimeters thick.
However, golf-ball dimples are typically only 0.2 millimeters deep
so attaching reflecting material of this kind to a golf ball has an
unbalancing effect on its aerodynamic properties unless a suitable
number of reflectors are arranged to be part of the spherically
symmetric dimple pattern of the ball.
[0088] Typically, each retro-reflective element is inserted as a
separate element within the area of one large dimple on the ball
surface. These elements may be small circular discs of micro-prism
retro-reflective material, or may be single corner-cube prisms,
"cat's eye" lenses or the like. Alternatively, retro-reflective
elements may be directly fabricated or painted on the surface of a
golf ball and individual areas may occupy more than one dimple.
[0089] It is necessary that the means of attachment of the elements
to the golf ball surface is robust and withstands the high impact
forces and significant ball deformation during a golf shot as well
as the cleaning and scrubbing operations after collection from the
outfield. A large measure of protection can be afforded by having
the retro-reflective element recessed slightly below the outermost
surface of a golf ball (as in a dimple). Acrylic corner-cube
reflectors with a glass layer or other scratch-resistant surface
may be used. In one preferred construction the retro-reflective
part has a tough, scratch resistant protective surface and is
ruggedly attached onto a short cylindrical pellet that is inserted
into cylindrical cavities formed in the ball during moulding, and
is slightly recessed. The depth of the pellet may extend beyond a
thin outer casing (which is often about 2 millimeters thick in a
two-piece ball construction) and into the inner rubber core. Thus,
the pellet is encased in a resilient and protective housing and may
be prevented from dislodging by barbs on the pellet surface and/or
adhesive bonding. The entire surface of the ball may be encased in
a transparent outer cover.
[0090] The retro-reflective elements provide suitable reference
marks from which the spin rate and spin axis as well as the linear
velocity components of the ball can be detected. Advantageously,
this arrangement can be used to measure the velocity and spin
components of the ball with any arbitrary initial orientation prior
to impact. Not only is the spin rate and spin axis orientation
measured, but the orientation of the octahedron dimple pattern
relative to the spin axis can be determined, which can provide
superior characterisation in a ball flight prediction model. The
spin and velocity measurement means may employ high speed,
time-elapsed camera images, but preferably the measurement is
provided using an array of detection planes. In alternative
arrangements, six retro-reflective elements may be positioned on
the vertices of an octahedron pattern or twelve such elements on
the facets of a dodecahedron and so on. The methods described above
can be adapted for spot-kicks on a soccer or rugby ball to measure
the resultant velocity and spin components. In this case the widths
of the slit-apertures could be larger than those required for
golf-ball measurements.
[0091] A significant advantage of providing a ball with
retro-reflective parts on its surface is that it can be much more
visible as it flies through the air during night-time or other
periods of low ambient lighting. The higher visibility is provided
by illumination from flood-lights mounted near each bay, which also
illuminate the distance targets 41 to 45. As a ball flies down
range, the observation angle (i.e. the angle subtended at the golf
ball between the golfer's eyes and the local light source)
gradually decreases, and consequently the reflectivity increases
and partly compensates for the weaker illumination at greater
range. The visibility can be increased by providing more of the
surface of the ball with retro-reflective surface. For example,
instead of one retro-reflective dot on each facet of a ball there
may be a symmetrical arrangement of more than one, e.g. three in
the centre of a triangular facet.
[0092] Preferably, each bay is fitted with a separate relatively
low-power flood light positioned just above head-height but forward
of the golfer so that there is ample head-room above and around the
golfer to swing a driver or other club. This construction minimises
the said observation angle, especially for balls with steep
trajectories, and so enhances reflectivity off the ball. With this
arrangement and judicious use of side-lighting and/or ground
mounted lights, the total lighting power requirements can be
significantly reduced compared to a driving range using standard
golf balls and non-reflecting targets. This in turn minimises
glare, sky glow and other light pollution problems as well as
saving energy.
[0093] The ball of FIGS. 11(a) and 11(b) may be used in combination
with portable apparatus adapted to assist location of the ball on a
golf course.
[0094] The ball passes through the four detection planes 114, 115,
116 and 117, which all emanate from lower slit-apertures 65 so the
associated light sensors detect the reflections of associated light
emissions off the side of the golf ball 110. Other detection planes
(not shown) emanate from upper slit-apertures 94 and from other
lower slit-apertures. The detection planes that emanate from upper
slit-apertures sense reflections from a different angle, directed
downwards by typically 40 to 60 degrees. Also, detection planes
emanating from either upper or lower slit-apertures (94 and/or 95)
may be rotated about the Z-axis so as to be partly directed
forwards or backwards along the Y-axis. Thus, as it passes through
a plurality of detection planes, the ball and the retro-reflective
elements thereon are detected from a multiplicity of angles and at
various intervals along its initial trajectory so that plentiful
data are available from which the velocity and spin vectors of the
ball can be accurately computed.
[0095] FIG. 12 shows the time dependant voltage signals Va, Vb, Vc
and Vd corresponding to the golf ball 110 passing through detection
planes 114, 115, 116 and 117 respectively. The four voltage
waveforms each contain two pulses 121 and 122, of short duration
and high amplitude which correspond to the passage of the two
retro-reflective elements 111 and 112 respectively through
detection planes 114 to 117. For simplicity, we ignore the presence
of the other six elements, some of which may be marginally within
detection view. In addition to pulses 121 and 122, each waveform
also shows a subsidiary pulse 123 of lower amplitude and longer
duration coincident with both 121 and 122 and corresponding to the
slower amplitude rise and fall of sensor signals due to reflection
off the ball surface as it enters and exits each detection plane in
turn. By analysing the voltage signals the four instants in time
t1, t2, t3 and t4 when the ball passed through detection planes
114, 115, 116 and 117 respectively, can be determined.
[0096] Detection planes 114 and 117 are vertical and normal to the
azimuth direction of the ball. The ball velocity Vy parallel to the
Y-axis is given by the distance between detection planes 114 and
117 divided by (t4-t1). Detection plane 115 is also vertical but is
rotated about the Z-axis as shown. Consequently the displacement ax
(see FIG. 11) is equal to Vy.times.(t2-t1)/tan e; where e is the
angle of inclination between detection planes 114 and 115. Thus,
the XY coordinates of the ball and the retro-reflective elements
can be found from analysis of the time delay between corresponding
signals. Similarly, the elevation angle of the ball is obtained
from time delay (t4-t3), its speed and the geometry of detection
planes 116 and 117.
[0097] In the arrangement of FIG. 11 the reflector pattern repeats
every 90 degrees so care is required to ensure that high spin rates
are accurately recorded by providing suitable spacing between at
least two detection planes. Low elevation angle shots (i.e. drives)
tend to have low spin rates whereas high elevation angle shots
(i.e. pitching irons) have high spin rates; where spin rate is
defined as the ratio of the peripheral speed due to spin of the
ball divided by its linear or translational velocity. Thus, it is
advantageous to provide at least two detection planes with small
separation distance for high elevation angles and larger separation
distance for low elevation angles and this is provided by detection
planes 116 and 117.
[0098] The qualitative features of the signal waveforms of FIG. 12
are evident, but it is not so obvious how to extract precise data
from such waveforms. The preferred method is to use a guess of the
motion of the ball and the retro-reflective elements and apply this
to a mathematical model of the array of detection planes and their
response to reflections from a ball and from those retro-reflective
elements that are detectable by the detection planes. The main
features of the waveforms allow an initial approximate guess of the
ball velocity, trajectory and spin from which model data are
generated. The model data and real data are compared and the
differences are used to obtain an improved guess (i.e. an improved
estimate). We repeat this process until the model data converges to
nearly the same as the real data. The above is a simplified
description of non-linear minimisation or non-linear estimation
which are well-known techniques in engineering. One preferred
mathematical technique for solving the estimation is the
Levenberg-Marquardt method. In FIG. 12, the waveforms are shown as
continuous traces, but in practice it is preferable that the TXRX
pairs are operated in pulse-multiplexed mode and the data is
acquired as a sequence of digital samples (from a sampling
analogue-to-digital converter), which are then used as input data
in a mathematical model of the detection planes array and probable
ball launch parameters. A non-linear estimation such as the
Levenberg-Marquardt method then extracts accurate estimations of
the true launch velocity and spin vectors of the ball.
[0099] FIG. 13 is the plan view of an alternative ball launch
analyser where the velocity vectors and certain orientations and
positions of a club head 130 are sensed prior to impact with a golf
ball 131 and only the velocity vectors of the ball are sensed. A
sensor enclosure 132 has a detection plane window face 133
generally parallel but offset from the golf swing and ball
trajectory paths and provides a number of detection planes 134
crossing the path of the club head and golf ball in the pre-impact
and post impact region of a golf shot. The detection planes
comprise a mixture of normal, angled, narrow width and expanded
width types to fully detect the approach direction (in azimuth and
elevation), speed, dynamic loft and offset (in vertical and
horizontal sense) of the club head 130 and the launch velocity
vectors of the ball. This gives sufficient data to determine the
spin vectors of the ball as well as its velocity vectors. From
this, a prediction of the subsequent ball flight can be made.
Errors in measurement will degrade the accuracy of the flight
prediction, but these errors are mainly systematic, especially if
known types of club and a known type of ball are used. It is thus
possible to correct systematic errors by applying feedback of the
actual flight outcome measured by accurate means.
[0100] FIG. 14 shows a side view of the club head 130 and ball 131
as "seen" by the detection plane array. The motion of the club head
is sensed by tracking three retro-reflective elements in the form
of small, circular, retro-reflective dots, 141, 142 and 143
attached to the club head. The positions of the centre-planes of
three detection planes are shown by dotted lines 144, 145 and 146,
where the planes are normal to the page in FIG. 14. The diameter of
the retro-reflective dots are preferably nearly the same as the
width of the detection planes so that the signal pulse generated
when a retro-reflective dot passes through a detection plane has a
well defined peak. By this means the point in time when the dot is
exactly central in a detection plane can be accurately estimated.
The diameter of the retro-reflective dots may however be larger or
smaller than the detection plane widths. Larger dots give higher
signal magnitude but have flatter peak waveforms (though good
estimation of the centre of the peak is still possible) and can be
less convenient to attach to the club head.
[0101] The contrast of the retro-reflective elements 141, 142 and
143 against reflections from the body of the club head can be
enhanced by using filters to polarize the transmitted light from
each TXRX pair in one direction and a second filter (for each TXRX
pair) to polarize the received light at 90 degrees to the emitted
light. In one possible arrangement, the ambient signal amplitude is
measured just before and/or just after a (pulsed) light emission
and the reflected plus ambient signal amplitude is measured during
the TXRX pulsed emission. Since these two measurements (or three
measurements in the case of measurement before and after the pulsed
emission) occur at nearly the same time so the club head position
and orientation change very little during these measurements, the
amplitude response to light reflected exclusively from the
retro-reflective elements can be found very precisely (assuming the
above polarising filtering arrangement removes most of the unwanted
reflections). In general, it is preferred to use infrared TXRX
pairs as these generate light outside the visible spectrum, but
other light wavelengths such as visible red light may be preferable
since some polarising filters are more readily available at these
wavelengths. If necessary, a mixture of light wavelengths can be
used to eliminate visible disturbance prior to impact and enhance
performance during the impact phase only. Also, the club head body
can be sprayed with non-reflective coating prior to attaching its
retro-reflective element.
[0102] FIG. 15 shows the time dependant amplitude waveforms of the
three retro-reflective elements of FIG. 14 as they pass through the
three detection planes. The three waveforms each contain three
pulses. In waveform 151, consecutive pulses 152, 153 and 154
correspond to the passage of the retro-reflective dots 141, 142 and
143 respectively through detection plane 144. In waveform 155,
consecutive pulses 156, 157 and 158 correspond to the passage of
the dots 141, 142 and 143 respectively through detection plane 145.
Detection planes 144 and 145 are parallel and it can be seen that
waveform 155 is a time-delayed replica of waveform 151. The speed
of the club head can be found from the duration of the time delay
and the distance between detection planes 144 and 145. In waveform
159, pulses 201, 202 and 203 correspond to the passage of the dots
141, 142 and 143 respectively through detection plane 146, but in
this case pulse 202 precedes pulse 201 because, due to the
inclination of detection plane 146 from the vertical,
retro-reflective dot 142 is the first to pass through.
[0103] In FIG. 15, the waveforms are shown as continuous traces,
but in practice it is preferable that the TXRX pairs are operated
in pulse-multiplexed mode and the data is acquired as a sequence of
digital samples (from a sampling analogue-to-digital converter). In
one preferred but not limiting method of data analysis, the true
centres of the pulses on the time axis are found by quadratic
interpolation of three data points nearest each apparent peak to
yield nine precise points in time (in the example of FIGS. 14 and
15), which are then used as input data in a mathematical model of
the detection planes array and club head motion. A non-linear
estimation such as the Levenberg-Marquardt method then extracts
accurate swing parameters of the club head.
[0104] In purpose-built clubs, the retro-reflective dots 141, 142
and 143 are preferably inserted into shallow circular recesses that
are formed at manufacture. The exact location of the centres of the
retro-reflective elements relative to the club-face are then known
very accurately. It is also desirable to provide a similar
retro-reflective arrangement on other makes of golf clubs. For
example, retro-reflective dots 142 and 143 can be provided on a
single strip of self-adhesive sticker, which is attached to the toe
of the club head with the edge of the sticker aligned with the edge
of the club-face as shown. This ensures that the centres of dots
142 and 143 are on a line parallel to the loft angle of the
club-face. The self-adhesive sticker preferably forms a low
reflectivity substrate to enhance the contrast of the
retro-reflective dots. The dot 141 can also be mounted on a low
reflectivity sticker; the position of dot 141 is less critical as
its chief purpose is to provide an approximate indication of lie
angle (i.e. the amount by which the heel-toe axis tilts relative to
the horizontal). The retro-reflective dots are typically all the
same nominal size, but a mixture of different sizes can be used to
provide a code to differentiate between different club-head
characteristics. For wood clubs, a preferred position of
retro-reflector dots 142 and 143 are on the centre of the crown
(i.e. the top surface of the club-head) and aligned front to back
(substantially along the Y-axis). As these crown-mounted dots face
upwards they need to be detected by a downwardly-oriented detection
plane such as detection plane 96 in FIG. 9(b).
* * * * *