U.S. patent number 3,633,007 [Application Number 05/001,188] was granted by the patent office on 1972-01-04 for golf game computer including improved drag circuit.
This patent grant is currently assigned to Brunswick Corporation. Invention is credited to James W. Sanders.
United States Patent |
3,633,007 |
Sanders |
January 4, 1972 |
GOLF GAME COMPUTER INCLUDING IMPROVED DRAG CIRCUIT
Abstract
A golf game computer including a circuit for computing the
instantaneous velocity of a golf ball hit from a tee and including
a circuit operative to receive a signal representative of the
initial velocity of a golf ball hit from a tee and apply thereto,
the effect of drag. In the exemplary embodiment of the invention, a
plurality of electrically parallel circuits, each having a switch
therein, are utilized to provide a signal proportional to the
mathematical square of the instantaneous velocity which is used in
computation.
Inventors: |
Sanders; James W. (Grand Haven,
MI) |
Assignee: |
Brunswick Corporation
(N/A)
|
Family
ID: |
26668691 |
Appl.
No.: |
05/001,188 |
Filed: |
January 7, 1970 |
Current U.S.
Class: |
473/199;
73/379.04; 708/808; 702/142 |
Current CPC
Class: |
G06G
7/48 (20130101) |
Current International
Class: |
G06G
7/48 (20060101); G06G 7/00 (20060101); G06f
015/44 (); G01l 005/02 () |
Field of
Search: |
;235/151,151.32,197
;273/184-185 ;73/13,379 |
References Cited
[Referenced By]
U.S. Patent Documents
Primary Examiner: Botz; Eugene G.
Assistant Examiner: Smith; Jerry
Claims
1. In a golf game including means for determining the initial
velocity of a golf ball hit from a tee and providing a signal
representative thereof, the combination comprising:
a first operational amplifier in an inverting circuit;
means for feeding said initial velocity signal to said operational
amplifier;
a plurality of electrically parallel circuits, at least one of
which consists of a resistance and the remainder each comprising a
serial combination of a resistance and a semiconductor having a
known breakover voltage;
a plurality of biasing circuits, one for each of said remaining
circuits and connected to its associated remaining circuit at the
junction of said resistance and said semiconductor, at least some
of said biasing circuits including temperature compensator means to
provide for temperature compensation for the parallel circuits;
means connecting an output of said first operational amplifier to
one side of each of said parallel circuits;
a second operational amplifier in an inverting circuit;
means connecting the opposite side of said parallel circuits to the
input of said second operational amplifier;
a first resistance shunting said second operational amplifier;
a second resistance shunting said second operational amplifier;
means for controlling the conduction of said second resistance
including a semiconductor having a predetermined breakover voltage
in series therewith and a biasing circuit including a variable
resistance connected to the junction of said last-named
semiconductor and said second resistance;
a potentiometer including a wiper connected to the output of said
second operational amplifier;
means defining a spin velocity function output terminal connected
to the output of said second operational amplifier;
a relay including normally open contacts adapted to be closed when
said relay is energized;
means conducting said potentiometer wiper to one side of said
contacts;
a third operational amplifier in an integrating circuit and
including a capacitor shunting said third operational
amplifier;
means connecting the other side of said contacts as an input to
said third operational amplifier;
said relay further including normally closed contacts shunting said
third operational amplifier whereby, when said relay is
deenergized, said capacitor will be discharged;
and means including a resistance connecting the output of said
third operational amplifier to the output of said first operational
amplifier to issue a signal proportional to the instantaneous
velocity of a golf ball
2. The combination of claim 1 further including a second relay
having normally open contacts and adapted to be energized when the
theoretical free flight trajectory of a golf ball contacts the
ground; means including a resistance interconnecting one side of
said second relay contacts to said one side of the normally open
contacts of said first-named relay; and means connecting the other
side of said second relay contacts at least partially in parallel
with said potentiometer whereby when the theoretical free flight of
a golf ball causes the same to contact the ground, an increase in
drag will be effected to increase the rate of decay of said
instantaneous velocity signal during the bouncing and/or rolling of
the ball on the ground.
Description
BACKGROUND OF THE INVENTION
The recent upsurge in the popularity of the game of golf has
resulted in severe overcrowding of existing facilities. As a
result, a number of proposals for indoor golf games which would
enable the golfer to play the game year around and which would
require much less space than outdoor courses have evolved.
A number of such proposals have been commercialized and of those
commercialized, some are extremely sophisticated and provide a
quite realistic simulation of the game of golf played on an outdoor
course. Of course, in order to effect a realistic simulation, a
variety of factors must be taken into consideration by the
computational systems employed. One such factor is the effect of
drag on a golf ball in flight.
One commercialized golf game includes means for considering the
effect of drag on a golf ball in flight in the course of
computation of a ball's theoretical trajectory. Specifically
employed is an analog circuit arranged to implement a mathematical
equation relating to the instantaneous velocity of a ball in flight
to the initial velocity and which requires a signal proportional to
the square of the instantaneous velocity. To provide such a signal,
a signal representing the instantaneous velocity was applied to a
voltage dependent resistor which permitted the current to pass
therethrough at a rate that was intended to approximate the square
of the voltage applied across the resistor.
While this circuit worked well for its intended purpose, a lack of
uniformity from one voltage dependent resistor to another resulted
in each computational system having quite different computational
characteristics from the others and which could not be predicted
with a reasonable degree of certainty in advance. Accordingly,
painstaking adjustment of the circuit was required for each such
computational system.
SUMMARY OF THE INVENTION
It is the principal object of the invention to provide a new and
improved golf game computer. More specifically, it is an object of
the invention to provide a golf game computational system including
an improved drag circuit which may be fabricated uniformly for each
computational system thereby obviating the need for extensive
adjustment of each system due to lack of uniformity of parts of the
circuit.
The exemplary embodiment of the invention accomplishes the
foregoing objects by means of a plurality of parallel circuits
which are impressed with a signal having a voltage proportional to
the instantaneous velocity of a golf ball at any time in flight.
Each circuit includes an impedance in the form of a resistor and a
switching means in the form of a semiconductor, and more
specifically, a diode, having a predetermined breakover voltage.
Biasing means are employed with each of the parallel circuits so as
to control the firing point of each diode in relation to the
voltage representing the instantaneous velocity and each of the
resistors are chosen to provide a particular linear rate of
increased current flow for a linear increase in the voltage
representing instantaneous velocity.
The combination of the parallel circuits operate in concert so that
for a low instantaneous velocity representing voltage, perhaps but
one circuit will be conducting and, as the voltage is increased,
additional circuits will sequentially begin to conduct. As more and
more of the circuits begin to conduct, the total current flow
through all circuits increases and by choosing the impedances
properly, a curve of the total current flow versus the
instantaneous velocity representing voltage may be made to
accurately approximate an exponential relation and specifically, a
mathematical square relation, to thereby provide a signal having a
characteristic representative of the square of the instantaneous
velocity.
Other objects and advantages will become apparent from the
following specification taken in conjunction with the accompanying
drawings.
DESCRIPTION OF THE DRAWINGS
FIG. 1 is a block diagram of a golf game computing system in which
an improved drag circuit made according to the invention may be
employed; and
FIG. 2 is comprised of FIGS. 2A and 2B with FIG. 2B being adapted
to be placed at the lower margin of FIG. 2A and illustrates a
preferred embodiment of the improved drag circuit.
DESCRIPTION OF THE PREFERRED EMBODIMENT
One form of golf game computer in which the inventive improvement
constituting this invention is susceptible to use is basically that
disclosed in the copending application of Russell et al., Ser. No.
588,922, filed Oct. 24, 1966, now U.S. Pat. No. 3,513,707, and
assigned to the same assignee as the instant application, the
details of which are incorporated herein by reference.
Before proceeding with the discussion of the basic operation of the
computer, it is to be understood that the same computes, throughout
the theoretical time of flight (including bouncing and rolling) of
the ball, three coordinates of the ball in space. The coordinates
represent the displacement of the ball in three directions from the
tee point and, as is known in the art, are referred to as the "X",
"Y" and "Z" directions. The Y-direction is vertical and thus, the
instantaneous Y-displacement represents the height of the ball in
flight above the ground. The Z-direction is horizontal and
straightaway from the tee point so that the instantaneous
Z-displacement represents the distance of the ball from the tee
point in a direction straightaway therefrom. The X-direction is
also horizontal and is transverse to the Z-direction. Thus, the
instantaneous X-displacement represents the location of the ball to
either side of the line defining the Z-direction. Further, since
the displacement can be to either side of the Z-direction, it may
be either positive or negative while the Y- and Z-displacements
will always be positive or zero.
The computer is illustrated in block form in FIG. 1 and includes a
tee trigger 10 which is adapted to sense when a ball has been hit
by a golfer from a tee area to start a binary counter 12. The
binary counter 12 is stopped when the ball has traveled a
predetermined distance from the tee by any suitable means. For
example, in the Russell et al., application, there is provided an
arcuate arrangement of photocells for sensing the initial angle of
elevation of the ball and when the ball passes through the
photocell matrix, a signal is generated thereby to stop the binary
counter. Alternatively, the predetermined distance may be set by
the location of a target for stopping the ball such as that
disclosed in the copending application of Conklin et al., Ser. No.
820,558, filed Apr. 30, 1969, now U.S. Pat. No. 3,591,184 and
assigned to the same assignee as the instant application, the
details of which are herein incorporated by reference. When the
latter system is used, the means contained within the target for
sensing elevation angle may also be used to stop the binary
counter.
In any event, elevation angle detecting means 14 are provided and
the same, in addition to detecting the initial angle of elevation
.theta. of a ball hit from the tee, are operative to stop the
binary counter 12.
The count contained in the binary counter 12 is inversely
representative of the initial velocity V.sub.o of the ball hit from
the tee. That is, the higher the count in the binary counter 12,
the longer it will have taken for the ball to pass the
predetermined distance from the tee point to the elevation angle
detecting means 14 and thus, the slower will be its velocity.
The count contained in the binary counter 12 is then decoded by a
digital to analog conversion matrix 16 which is operative to
convert and invert the digital time quantity contained in the
binary counter to an analog velocity quantity designated V.sub.o
for initial velocity. This information is then fed to a drag
circuit 18 which is operative to ascertain from the initial
velocity V.sub.o, the instantaneous velocity V.sub.i of the ball at
any point in its theoretical time of flight.
The digital to analog converter 16 also provides a second V.sub.o
(bounce) signal to the drag circuit 16 which is operative to
increase the drag or decay rate of the instantaneous velocity
V.sub.i after the free flight of the ball has terminated and the
same is bouncing or rolling on the ground.
Returning to the elevation angle detecting means, the same provides
a signal to an elevation trigonometry matrix 20 which has two
outputs. On one output, there is placed a signal having a magnitude
which is proportional to the product of the instantaneous velocity
V.sub.i and the cosine of the initial angle of elevation of the
shot, cos .theta., or V.sub.i cos .theta.. On the other output,
there is placed a signal having a magnitude proportional to the
product of the instantaneous velocity V.sub.i and the sine of the
initial angle of elevation of the shot, sin .theta., or V.sub.i sin
.theta..
The system also includes a azimuth angle detecting means 22 for
detecting the initial angle B of the shot with respect to the
azimuth. The azimuth angle detecting means 22 may be in the form of
the photocells disclosed by Russell et al. or incorporated in the
target in the manner disclosed by Conklin et al. The azimuth angle
information provided by the azimuth angle detecting means 22 is
then fed to an azimuth trigonometry matrix 24.
The V.sub.i cos .theta. output from the elevation trigonometry
matrix 20 is fed through an inverter 26 as an input to the azimuth
trigonometry matrix 24. The azimuth trigonometry matrix then
converts the signal to be proportional to the product of the
instantaneous velocity V.sub.i, the cosine of .theta., and the sine
of B, V.sub.i cos .theta. sin B, which, as will be appreciated from
the reading of the Russell et al. application, correspond to the
instantaneous velocity of the ball in the so-called X-direction
without regard to the effects of side spin.
The azimuth trigonometry matrix 24 also provides a second signal
which corresponds to the product of the instantaneous velocity
V.sub.i, the cosine of .theta. and the cosine of B, V.sub.i cos
.theta. cos B, which correspond to the instantaneous velocity of
the ball in the so-called Z-direction.
The V.sub.i cos .theta. cos B signal is then used as an input for
an integrating circuit 28 which provides as an output, a signal
proportional to the instantaneous displacement of the ball in the
Z-direction, S.sub.z. As shown in FIG. 1, such a signal is of
negative polarity and, for purposes explained in the Russell et al.
application, this signal is also fed to an inverter 30 which
provides as an output the same signal but with the opposite
polarity.
The V.sub.i cos .theta. sin B output of the azimuth trigonometry
matrix 24 is fed as an input to a first inverter 32 which, in turn,
provides an input to a second inverter 34. Shunting the inverter 34
is a pair of relay contacts 36 which are operative to cut the
inverter 34 in or out of the circuit.
As described in the Russell et al., application, the output of the
azimuth trigonometry matrix 24 is of the same polarity regardless
of whether the ball is traveling to the left or right in the
X-direction. However, means are also provided in association with
the matrix 24 for distinguishing whether the ball is traveling to
the left or the right and such means are employed to open or close
the contacts 36 appropriately. For example, if the polarity of the
output inverter 32 is arbitrarily such as to indicate that the ball
is traveling to the right and, in fact, the ball was sensed as
traveling to the left, the distinguishing means would leave the
contacts 36 open so that the inverter 34 would provide a signal
having an opposite polarity of that provided by the inverter 32
thereby indicating that the ball was in fact traveling to the left.
On the other hand, if the ball was in fact traveling to the right,
the distinguishing means would cause the contacts 36 to be closed
to thereby shunt the inverter 34 to provide a signal having a
polarity indicating that the ball was in fact traveling to the
right.
The parallel combination of the contacts 36 and the inverter 34 is
connected to a summing point 38 whereat the effect of side spin is
also considered in determining total velocity in the X-direction. A
second input to the summing point 38 is taken from the output of an
integrator 40 which has its input connected to a summing point 42.
The summing point 42 receives information from two sources.
Firstly, the same receives information from a hook-slice matrix 44
which in turn receives information from a spin detector 46 which
provides an indication of side spin on the ball. The spin detector
46 may be either of the forms disclosed by Russell et al. or that
disclosed by Conklin et al. The hook-slice matrix 44 also receives
an input from a circuit 48 which is representative of a power of
the instantaneous velocity V.sub.i received from the drag circuit
18.
The hook-slice matrix 44 also provides an output to the azimuth
trigonometry matrix 24 which inturn provides an output to an
inverter 50 which is connected to the summing point 42. The reasons
for the foregoing connections are not material to the invention but
are explained in detail in the Russell et al. application. For
purposes of this application, it is sufficient to note that at the
summing point 42, there will be a signal having a magnitude
indicative of spin force or spin acceleration.
This signal is then fed to the integrator 40 which provides an
output having a magnitude characteristic of the velocity in the
X-direction due to side spin which, in turn, is summed at the
summing point 38 with the velocity in the X-direction due to the
initial angle with respect to the azimuth B.
The resulting signal is then fed as an input to an integrator 52
which provides an output representative of the instantaneous
displacement in the X-direction or S.sub.x.
An output from the elevation trigonometry matrix having the signal
V.sub.i cos .theta. impressed thereon is utilized as an input to a
gravity and lift circuit 54. The gravity and lift circuit 54
provides an input to an integrator 56 which is representative of
the acceleration in the Y-direction due to the effects of lift and
gravity on the golf ball in flight. The integrator 56 in turn
converts this signal to a lift and gravity velocity signal which is
fed to a bounce circuit 58 which, by the means disclosed by Russell
et al., is ineffective while the ball is in free flight but comes
into play when the ball would begin its bouncing or rolling along
the ground.
The output of the bounce circuit 58 is in turn fed to a summing
point 60 which receives the V.sub.i sin .theta. output from the
elevation trigonometry matrix 20 which is representative of the
velocity in the Y-direction without regard to the effects of lift
and gravity. At the summing point 60, the two signals are combined
and the resulting signal is then fed as an input to an integrator
62 which provides an output representative of the instantaneous
displacement in the Y-direction, S.sub.y. Of course, when the ball
has encountered the ground for the first time, a bounce signal will
be impressed upon the summing point 60 by the bounce circuit 58 and
until such time as the ball would be motionless.
The signals representative of the displacements in the "X", "Y" and
"Z" directions, S.sub.x, S.sub.y and S.sub.z, may be used as inputs
to a display device such as a ball spot projector for displaying
the flight of the ball to the golfer.
The inventive improvement herein resides specifically in the drag
circuit 18 and may best be understood with reference to FIGS. 2A
and 2B. The computation to be effected is as follows.
As disclosed in the Russell et al. application, for a golf ball in
flight, it has been found that the instantaneous velocity bears the
following relation to the initial velocity.
where:
V.sub.i is the instantaneous velocity,
V.sub.o is the initial velocity, and
K is the drag coefficient.
Also as pointed out in the Russell et al. application, the value of
K changes depending upon the instantaneous velocity of the ball.
That is, for a ball at a high velocity, the airflow around the same
will be in a turbulent state and thus K will have a relatively low
value. However, when the instantaneous velocity is decreased due to
drag to the point where the airflow about the ball is in a laminar
state, the drag coefficient or K will have an increased value.
The means by which the computation is effected are as follows.
According to the exemplary embodiment of the invention, a signal
having a negative polarity whose voltage is proportional to the
initial velocity is fed from the digital to analog converter 16 to
the drag circuit including an operational amplifier 70 in an
inverting and summing circuit on a lead 72. The output of the
operational amplifier 70 is connected to a summing point 74 having
a lead 76 associated therewith. The lead 76 provides a positive
signal whose voltage is proportional to the instantaneous velocity
of the ball at any point in the theoretical flight thereof to the
remainder of the computer as indicated in FIG. 1.
The summing point 74 is also connected to a plurality of parallel
circuits 78, 79, 80, 81, 82, 83 and 84 of which the circuits 78-83
each include a resistor 85 in series with a solid state diode 86.
The circuit 84 merely consists of the resistor 85.
In the exemplary embodiment of the invention, the anode of each of
the diodes 86 is connected to a respective resistor 85 and this
junction is in turn connected through at least respective resistors
87 to a positive source of power. As illustrated in FIG. 2A,
certain of the resistors 87 are in series with potentiometers 88
and/or temperature dependent resistors 89 which provide for
temperature compensation of the overall circuit. The wipers of the
potentiometers 88, where used, are also connected to the positive
source of power.
The arrangement is such that the V.sub.i signal from the summing
point 74 is converted by the circuits 78-84 to a signal whose
current is proportional to the square of the instantaneous
velocity. This function is accomplished in the following manner.
Each of the diodes 86 has a predetermined forward breakover voltage
as is well known in the art. That is, a predetermined voltage
differential must exist between the cathode and the anode before
the diode 86 will conduct. Typically, this forward breakover
voltage is on the order of 0.6 volts.
The circuits 78-83 take advantage of this characteristic of the
semiconductor diodes 86 to utilize the same as switching devices
for respectively cutting in or cutting out one or more of the
circuits 78-83 from the overall circuit.
Accordingly, the resistors 87 and the resistors 88 (if present) are
selected so that the anode of the associated diode 86 is impressed
with a biasing potential that will preclude any of the diodes 86
from conducting when the summing point 74 is at zero volts. For a
positive voltage at the summing point 74, one or more of the diodes
86 may be caused to conduct. This will occur because, for a
positive potential at the summing point 74, the potential at the
junction between the anode of the diodes 86 and the associated
resistor 85 will become more positive than would be the case if the
summing point 74 were at zero volts.
When the resistive values indicated are used, the diodes 86 are
sequentially rendered conductive as the potential at the summing
point 74 goes increasingly positive. In the normal operation of the
circuit, the summing point 74 will initially be at some positive
potential dependent upon the initial velocity of the golf shot and
will gradually decrease thereby causing the circuits 78-83 to
sequentially cease conducting. Of course, the more of the legs
78-84 that are conducting, the higher will be the current level at
the common junction of the cathodes of the diodes 86.
The resistors 85, according to the exemplary embodiment, are
selected to essentially control the slope of the current flow
curve. That is, the amount of current passing through any given one
of the circuits 78-83 in proportion to voltage at the summing point
74 will be essentially determined by the value of the resistors
85.
The foregoing circuit including the circuits 78-84 is arranged so
that the total current flow at the common junction of the cathodes
of the diodes 86 and the line 92 connected thereto is proportional
to the square of the voltage at the summing point 74.
The circuit achieves this relation as follows. Starting with a zero
volt potential at the summing point 74, as the potential increases
at, for example, a linear rate, one of the diodes 86 will begin to
conduct and as the voltage increases, current flow will increase
according to Ohms law at a linear rate. At some predetermined
point, another one of the diodes 86 will begin to conduct and as a
result, the current flow on the line 92 will be the sum of the
current flow through the two circuit legs. While current flow in
each of the two now conducting circuits will be linear according to
voltage increase, total current flow would be represented by a
linear upswing starting at the point when the second circuit begins
to conduct and which would be equal to the sum of the current flow
through the two conducting legs. This procedure will continue on
until all of the circuits 78-83 are conducting.
A graph of the voltage to the summing point 74 versus total current
flow on the line 92 would result in a series of short, straight
line segments of differing slopes which would approximate an
exponential curve and, more specifically, one of the general form
of Y=x.sup.2. As a result, current flow along the line 92 will be
closely proportional to the square of the voltage at the summing
point 74.
The line 92 is connected as an input to an operational amplifier 94
in an inverting circuit as seen in FIG. 2B. The output signal of
the operational amplifier 94 is placed on a line 96, is negative in
polarity and its voltage is proportional to the square of the
instantaneous velocity of the ball.
Interconnecting the lines 92 and 96 are two parallel circuits 98
and 100 with the circuit 98 including a single resistor 102 and the
circuit 100 including a resistor 104 and a diode 106. The two
circuits 98 and 100 insert the K or drag coefficient into
computation.
Specifically, it will be seen that whenever there is a potential
difference between the lines 92 and 96, the circuit 98 will be
conducting while the circuit 100 may not be, depending upon whether
the forward breakover voltage of the diode 106 therein is
exceeded.
The foregoing interconnections of the line 92 ultimately to the
summing point 74 will result in the signal on the line 92 having a
voltage which will be related to the instantaneous velocity of the
ball. For high instantaneous velocities, the forward breakover
voltage of the diode 106 is exceeded and both the circuits 98 and
100 will be conducting and will result in a lesser rate of decay.
However, through a biasing circuit 107, the diode 106 may be biased
such that, when the instantaneous velocity of the ball falls to
that value wherein ball flight would be accompanied by air flow in
the laminar region, the diode 106 ceases conducting so that only
the circuit 98 would be interconnecting the lines 92 and 96 to
result in a higher rate of decay.
Returning to the line 96, the connection thereto may be utilized to
provide a signal proportional to the square of the instantaneous
velocity to the hook-slice matrix 44 as illustrated in FIG. 2B.
When such is done, the spin multiplier 48 may be eliminated.
Also, the line 96 is connected to ground through a potentiometer
108 which may have the position of its wiper changed to correctly
proportion the magnitude of the signal taken from the operational
amplifier 94. The signal picked off the wiper of the potentiometer
108 is then fed through a resistive circuit 110 to the normally
open contacts 112a of the relay 112. The relay 112 may be energized
through leads 113 and 114 which may be connected into the Russell
et al. computer in the manner described therein such that the relay
112 is energized when the computer initiates computation and is
deenergized when the computer is reset. Accordingly, when the
computer initiates computation, the relay 112 will be energized to
close the contacts 112a and ultimately apply the signal from the
potentiometer 108 as an input to an operational amplifier 115 in an
integrating circuit.
Included in the integrating circuit associated with the operational
amplifier 115 is an integrating capacitor 116 which has one lead
connected to the input to the operational amplifier 115 and one
lead connected to the output thereof. The relay 112 includes a pair
of normally closed contacts 112b which are connected through a load
resistor 118 to the input and the output of the operational
amplifier 115. When the computer is undergoing a computation cycle,
the contacts 112 will be opened due to the energization of the
relay 112. However, when computation is complete and the relay 112
deenergized, the contacts 112b will close thereby discharging the
capacitor 116 through the resistor 118 so as to effectively reset
the integrating circuit associated with the operational amplifier
115 to the next computation.
The output of the operational amplifier 115 is negative in polarity
and is fed on a line 120 to the summing point 74 through resistors
122 and 124.
As mentioned in the Russell et al. application, it is desirable to
increase the rate of drag when the ball is bouncing on the ground.
To this end, there is provided a resistor 126 which has one side
thereof connected to the input of the operational amplifier 115
during computation when the contacts 112a are closed and which has
its other side connected to normally open contacts 128a of a relay
128. The other side of the normally open contacts 128a is returned
by a line 130 to the line 96.
The relay 128 includes a pair of leads 132 and 134 which are
energized when the computer has determined that the ball touched
the ground for the first time and which are maintained energized
until the computer is reset. Suitable means for this purpose are
disclosed in the Russell et al. application. Thus, at the first
touch down of the ball, the relay 128 will be energized to thereby
close the contacts 128a and this action effectively puts the
resistor 126 in parallel with the resistor 108 to increase the rate
of decay thereby effecting increasing drag during the bouncing or
rolling of the ball on the ground.
Summarizing, a negative signal having a voltage proportional to the
initial velocity is inverted and provided to the summing point 74
by the operational amplifier 70. At the initiation of the flight of
the ball, the instantaneous velocity will equal the initial
velocity with the result being that the highest positive potential
for any given golf shot will be applied to the circuits 78, 79, 80,
81, 82, 83 and 84 which convert the signal to a signal proportional
to the square of the instantaneous velocity which is then fed to
the inverting operational amplifier 94. The operational amplifier
94 in turn provides a negative output signal having a voltage
proportional to the square of the instantaneous velocity and which
is diminished by the effect of the circuits 98 and 100 which
provide for the introduction of the drag coefficient. The negative
signal, as affected by drag, is then fed to the integrating
operational amplifier 115 which then provides an output signal that
is negative in polarity and proportional to the integral of the
instantaneous velocity squared to the summing point 74. Since the
initial velocity voltage at the summing point is positive, and the
voltage provided by the integrating operational amplifier 115,
which is representative of the term
is negative, subtraction will result so that the output on the lead
76 is a positive signal proportional to the instantaneous velocity
of the ball at any time in the theoretical flight thereof.
* * * * *