Identification and use of golf club selectivity

The selectivity or the damping factor or the bandwith of a golf club can be determined by stimulating a club and measuring the rate of decay of the displacement, velocity, or acceleration. The resulting information provides a measure of the risk of off-speed swings from using a particular golf club and enables a better fit to be accomplished between a golf club and a player.

BACKGROUND OF THE INVENTION 
Many golfers have one or two favorite clubs, which they refer over the rest 
of the clubs in their set. The favorite club(s) usually feels and performs 
better for the golfer. If the golfer could duplicate the performance of 
this favorite club and make each of the clubs in his set feel and perform 
like his favorite club, the golfer could improve his game. 
That a golfer finds a difference in behavior of one club from another in a 
set is not surprising due predominantly to normal shaft manufacturing 
tolerances. Shafts made from the same die can vary substantially. For 
example, steel shafts of a leading manufacturer are permitted to vary by 
up to .+-.2.5% in stiffness and still be within tolerance. With the 
difference between "regular" and "stiff" shafts or "stiff" and "extra 
stiff" being only about 2.5%, a shaft within a set can vary all the way 
from "regular" to "extra stiff" even though all the shafts in the set were 
made from a "stiff" die. 
Attempts at duplication of a golf club to copy a single golf club or to 
produce a matched set of clubs are well known in the art. A variety of 
different methods have been proposed to accomplish these difficult tasks. 
One of the most popular techniques involves the determination of and then 
matching the natural frequency of the clubs or, in some instances, the 
club shafts. U.S. Pat. Nos. 3,395,571; 4,070,022; 4,122,593; 4,555,112; 
and 4,736,093 and U.K. Application No. 2,223,951 each disclose methods of 
duplicating golf clubs and/or producing matched golf club sets by means of 
club or shaft natural frequency matching. 
U.S. Pat. No. 3,698,239 discloses a method of producing a dynamically 
matched set of clubs by starting with a favorite club, determining its 
moment of inertia of mass for a selected swinging axis by calculation from 
its length and weight, and producing the remaining set to have the same 
moment of inertia, by calculation. The use of the moment of inertia in the 
duplication of golf clubs is also disclosed in U.S. Pat. No. 4,128,242. 
U.S. Pat. No. 4,175,440 discloses dynamic testing and matching of clubs by 
measuring the angular velocity and centrifugal force along the axis of the 
club shaft as the club is swung on an arcuate path using an adjustable 
power rotational drive means. 
Overall mass matching is used in U.S. Pat. No. 4,415,156 to produce a 
matched set of clubs. 
In U.S. Pat. No. 4,900,025 a correlated set of clubs is made by matching 
the shaft flexure characteristics such that the deflection of a reference 
point is substantially uniform when a given torque is applied at the 
point. 
None of these techniques, however, have developed enough or in some cases 
the right information about a particular club to enable one to accurately 
and completely duplicate the club so that the duplicate club performs and 
feels like the club being duplicated. 
Also, none of these techniques have developed enough or in some cases the 
right information about a particular club to enable one to accurately and 
completely match other clubs in a set so that matched club(s) perform and 
feel like the first club. 
Particularly, the prior art has not recognized that club or shaft 
selectivity (or damping factor or bandwidth) are important to the proper 
selection of a club for a particular player. The art has not related a 
golf club's ability to perform to its capacity to forgive off-speed 
swings. 
Moreover, the art has not adequately addressed the issue of how to select a 
"pattern" club so as to produce a set of clubs appropriate for a 
particular individual. It has been left up to a player or his teacher or 
clubfitter to attempt to select an initial club for replication throughout 
a set of golf clubs. 
Accordingly, it is an object of the present invention to develop a method 
and device to either duplicate a golf club or to produce a matched set of 
clubs so that the golfer using the produced clubs can not tell the 
difference between the clubs. 
It is a further object to differentiate golf clubs based upon their 
selectivity for forgiving off-speed swings. 
It is a still further object to scientifically determine which golf club of 
a series has the appropriate selectivity for a particular golfer. 
It is another object of this invention to alter a golf club's selectivity 
by selection of shaft material and shaft construction methods and to alter 
Q of existing clubs by changing clubhead weight and grip hardness. 
It is an object of this invention to measure a golfer's swing speeds with a 
multiplicity of test clubs and to perform statistical calculations and a 
device for measuring, storing, calculating and displaying swing speed 
characteristics such as mean speed for swings taken with each test club 
and the statistical variation, sigma, of a normal distribution of the same 
swings. The optimum test club frequency is revealed by these statistics: 
the best club is associated with the highest average swing speed of each 
sample and the lowest sigma. 
SUMMARY OF THE INVENTION 
The present invention is directed to a method of duplicating a single golf 
club, a method of producing a matched set of golf clubs, and a device for 
carrying out the duplication or matching process. As used herein, the term 
"duplicating" means producing a golf club which feels and performs 
substantially the same as the golf club being duplicated when used in the 
same manner. 
The duplicating or matching process generally comprises attaching a golf 
club to be duplicated or matched to an oscillating means at the club's 
grip end, oscillating the golf club over a range of frequencies, measuring 
at each frequency the excursion of the golf club head from a stationary 
position, and thereafter plotting the excursion versus the frequency of 
the club head to form a curve which is defined herein as a "spectral 
response curve." The curve formed by such plotting normally has a 
distinctive peak that appears at about the natural frequency of the golf 
club. The natural frequency is the frequency at which the maximum 
excursion occurs. Once a spectral response curve for the golf club to be 
duplicated or matched has been measured and plotted, a golf club shaft 
having substantially the same spectral response curve, at least at about 
the portions of the curve near the natural frequency of the club, is 
selected. 
Preferably a multiplicity of golf club shafts are pretested to determine 
their spectral response curves by oscillating each shaft with dummy club 
heads attached thereto. Thus, when it is time to select an appropriate 
shaft, all that needs to be done is to select a shaft having a spectral 
response curve that is substantially the same as the spectral response 
curve of the club to be duplicated at least at about the portion of the 
curve corresponding to the natural frequency of the club. This comparison 
process may be carried out in any suitable manner including manually by 
using transparent overlays and electronically by using an appropriate 
computer program. 
After an appropriate shaft of the same length is located, a club head of 
the same weight, size, loft, and lie as the head on the club being 
duplicated is attached to the new shaft. 
Other properties and dimensions of the golf club which con-tribute to 
producing a duplicate of a golf club or a matched set of clubs include: 
the club swing weight and the overall weight of the club, the torque of 
the shaft, the flex point of the shaft, and the grip diameter of the grip 
end of the club. In duplicating a golf club or matching a set of golf 
clubs these properties and dimensions may also be duplicated or matched to 
produce the new club. 
The present invention is further directed to a method of measuring a golf 
club's selectivity, Q, a device for so doing, a method for quantifying Q, 
and a golf club having its selectivity indicated thereon. To determine Q 
for a golf club, a club clamped by its grip in a stationary vise is 
induced to oscillate by pulling the club head back several inches from its 
normal resting position and releasing it. Q is calculated by measuring the 
rate of decay of the displacement, velocity, or acceleration of the club 
head and then utilizing well known second order differential equations 
that describe damped harmonic motion.

DETAILED DESCRIPTION OF THE INVENTION 
As shown in the drawings, a golf club 10 comprises a shaft 12 having at one 
end a grip portion 14 and at the other end a club head 16. As is well 
known in the art, the club head may be either a "wood" head or an "iron" 
head. The term wood head refers to a particular type of club well known in 
the art used to drive golf balls longer distances than irons. It may be 
manufactured from a variety of conventional materials including metal, 
wood, graphite, and polycarbonate. Iron heads are generally made of 
materials such as cast or malleable iron or plastic composites and are 
generally used to drive golf balls shorter distances in comparison to the 
woods. The shaft may be made of any of a variety of conventional materials 
including steel, aluminum, graphite, or fiber-filled polycarbonate. A set 
of golf clubs generally comprises iron wedges such as the sand and 
pitching wedges, short irons (7-9 irons), long irons (2-6 irons), short 
woods (3-5 woods), and long woods (1-2 woods), though more or less clubs 
may be in an actual set. 
According to the present invention, any golf club, whether it be a wood or 
an iron and notwithstanding the construction of the shaft or the materials 
used to form the shaft or head, may have its performance duplicated by the 
method herein. 
The method according to the present invention comprises attaching the golf 
club to be duplicated or matched at its grip end to an oscillating means 
such as an oscillating motor and oscillating the club over a range of 
frequencies. Other oscillating means which may be employed include a 
linear motor attached to the grip end of the club, a servo motor 
programmed to oscillate back and forth, and a magnetically induced 
oscillating motor. While the specific frequency range used for the 
oscillations will depend upon the particular club and materials used to 
make the club, the range of frequencies used is generally from about 200 
RPM to 800 RPM, preferably from about 225 RPM to 375 RPM. At each 
frequency, the excursion of the club head from its stationary position is 
measured. The excursion may be measured by any suitable means including a 
visual scale such as a ruler or the like or an optical sensor array. It is 
presently preferred to measure the excursion by a sensor array so that the 
phase angle, a parameter discussed hereinafter, may also be measured. If a 
visual scale such as a ruler is used, the phase angle measurement is not 
possible. According to an embodiment of the present invention and best 
shown in FIG. 2 to 3, a rotating motor 22 connected to an oscillating arm 
24 by means of a pin 26 mounted on the outer edge of a disk 25 which is 
attached to the motor shaft 27. The pin 26 fits into a slot 28 in the 
oscillating arm 24. It is presently preferred to employ a rotating 
synchronous AC motor driven by a variable frequency controller which can 
hold a set point of speed at .+-.1 RPM. By this arrangement, the 
rotational movement of the motor is translated into oscillating movement 
in the oscillation arm 24, which is attached to surface 29 by means of a 
pin 31 so as to form a pivot at the grip end of the club. Attached to the 
oscillating arm 24 is a vise 30 used to hold the golf club 10 at its grip 
end 14. A screw 32 is used to tighten and loosen the vise. A tachometer 33 
which is electrically connected to the motor is used to measure the speed 
of the motor. In this embodiment, an optical sensor array 34 arranged in a 
semi-circular path is used to measure the excursion of the club head. As 
shown, a set of light emitting diodes (LED's) are arranged in a 
semi-circle under the path that the clubhead subscribes with a sinusoidal 
generator (not shown) whose output magnitude is proportional to the 
highest order LED covered by the clubhead as it swings at each frequency. 
As an alternative to the optical sensor array, a strain gauge placed on 
the shaft of the club near the clubhead with an analog output could be 
employed. The analog output is a continuous voltage which is roughly 
proportional to the displacement of the clubhead. Still another measuring 
technique which could be employed is to use a strain gauge to measure the 
phase angle (hereinafter discussed) and an optical sensor with a short 
term memory to scan the LED's to sense the highest order LED intercepted 
by the clubhead. As shown, when the oscillating means is operating, the 
club head oscillates from one position shown at X to another position 
shown at Y. These X and Y points will change as the frequency of the motor 
is varied. The excursion of the club head is shown in FIG. 2 as the 
distance "d" which will also change as the frequency changes. 
The frequency and excursion measurements are then used to plot a curve, 
defined herein as a "spectral response curve." FIG. 4 shows such a curve 
20 for a golf club. As shown, the spectral response curve has a 
distinctive peak. The peak is at the natural frequency (f.sub.o) of the 
club. The shape of the curve at about the natural frequency of the club 
(the portion generally extending from the beginning of the upward slope 
and the ending of the downward slope shown as W in FIG. 4) provides 
important information about the performance of the club. Both the height 
of the peak at f.sub.o and the width of the peak at various percentages of 
the heights of the curve at f.sub.o are useful parameters in the process 
of duplicating or matching a golf club. 
As shown in FIG. 4, the width of the spectral response measured at about 
70% of the height "h" of the peak at f.sub.o, shown as Q, represents the 
ability of the club to forgive offspeed swings. It also is a measure of 
mechanical gain which is in conflict with forgiveness; i.e. narrow peaked 
shafts result in high mechanical gain and non-forgiving clubs. Only 
players with very repetitive swings or those who hope to achieve distance 
at the expense of accuracy should play with narrow peaked shafts. When 
determining the characteristics of a club to produce a matched set of 
clubs therefrom, the width of the peak Q is important to consider. Width 
measurement of the curve at other points such as about 10% and 70% of the 
height of the peak at f.sub.o may also be used in matching the spectral 
response curve of the club to be duplicated or matched. 
Once the spectral response curve for the golf club whose performance is to 
be duplicated is determined, the next step in the process is the selection 
of a club shaft which, when a club head substantially equal in weight to 
the club head being duplicated is attached thereto, has substantially the 
same spectral response curve as the golf club that is being duplicated or 
matched, at least at about the portions of the curve corresponding to the 
natural frequency of the golf club. As used herein, "substantially the 
same spectral response curve" means that the amplitudes of the two curves 
at the portions of the curves at about the f.sub.o peaks are within about 
.+-.10%, more preferably within about .+-.6%, and most preferably within 
about +3%, and at other frequencies of the curves being matched within 
about .+-.15%, more preferably within about .+-.10% and most preferably 
within about +7%. Preferably, the natural frequencies f.sub.o, at which 
the peaks occur, are within +1%, preferably .+-.0.5%, and most preferably 
.+-.0.1% The spectral response curve for a suitable new club is shown, by 
means of example only, in FIG. 4 as a dotted line 23. 
To obtain a more precise duplication, the spectral response curves of the 
club being duplicated can be matched with the new club over the same and 
entire frequency range measured. 
Since the spectral response curves for various golf clubs may vary 
significantly from one golf club to another due to shaft design and shaft 
manufacturing tolerances, it is presently preferred to measure the 
spectral response curves for a large variety of shafts with various golf 
club heads or dummy heads simulating a golf club head attached thereto. 
Such spectral response curves can then be placed on file and matched to 
the spectral response curve of a golf shaft to be used to construct a golf 
club which a customer desires to duplicate or to which other clubs in a 
set are to be matched. The matching of the spectral response curves may be 
accomplished by any suitable means including using transparent overlays to 
match up the curves or using conventional electronic means such as a 
computer with appropriate programming to match the curves. 
To make the duplication process more precise, two other parameters not 
directly associated with the spectral response curve may be measured and 
matched. Those two parameters are the flex point and the torque of the 
club shaft. The flex point is determined by oscillating the club as 
described above at a frequency of 2f.sub.o and observing and identifying 
the point on the club shaft which is substantially stationary while the 
remainder of the club oscillates. This point is approximately two thirds 
of the distance from the grip end of the club to the club head. Two clubs 
having shafts of identical longitudinal stiffness but differing flex 
points may present a detectable "feel" variation to the golfer. Thus the 
flex points should be matched to more precisely duplicate the golf club. 
When the flex point of two clubs is being matched it should be at the same 
distance from the grip end of the club .+-. about 0.5 inches, more 
preferably .+-. about 0.25 inches, and most preferably .+-. about 0.1 
inches. 
The torque of the club is generally defined as the resistance to twisting 
of the club shaft. As shown in FIG. 5, it is measured by marking the sole 
plate 42 on club head 44 of the club 46 being duplicated with chalk or 
other suitable mark 48 and using a synchronized strobe light (not shown) 
to read the angle of deflection (D) when the club is oscillated at its 
natural frequency (f.sub.o) using a suitable oscillating means 45 such as 
the device shown in FIG. 2. This deflection is caused by the center of 
gravity of the club head being located off the center of the shaft. The 
torque of the duplicate or matched club should generally be about equal to 
or stiffer than the club being duplicated, which translates into an angle 
D for the duplicate club of about equal to or less than the angle D 
possessed by the club being duplicated. 
One method according to the present invention of obtaining a fairly precise 
duplication is to match each of the following parameters: (1) the natural 
frequency f.sub.o (.+-. about 0.1%); (2) the height of the peak at the 
natural frequency f.sub.o (.+-. about 1.0 inch); (3) the width of the peak 
Q at 70% of the height of the peak measured from the bottom of the curve 
at the natural frequency (+ about 2.0 CPM); (4) the width of the peak at 
10% of the height of the peak measured from the bottom of the curve at the 
natural frequency (.+-.4.0 about CPM); (5) the flex point (.+-. about 0.5 
inch); and (6) the torque (an angle about equal to or less than D of the 
club to be duplicated.) This method will result in matching the curves at 
about the natural frequency of the two clubs within the tolerances recited 
hereinabove. 
Once the curves and any other desired parameters are matched and the 
appropriate new shafts thereby determined, the shaft is cut to an 
appropriate length. The length for the duplication of a golf club is 
substantially the same as the length of the initial golf club. A club head 
substantially the same as the club head of the golf club being duplicated 
is then attached thereto. A club head which is substantially the same 
should be of the same weight .+-. about 2.0 grams, more preferably .+-. 
about 1.0 grams, and also have the same lie .+-. about 0.5.degree., more 
preferably .+-. about 0.2.degree.. It is not necessary, however, that the 
club head be made of the same materials as the head of the club being 
duplicated. The lie of the club head is the angle .alpha. shown in FIG. 
1(a). The loft is the angle .beta. shown in FIG. 1(b). The loft is more 
conventionally represented by the club number, e.g. 5 iron, 3 wood. Thus, 
two 7 irons will generally have substantially the same loft. The 
variations of loft and lie angles between successive clubs in a set are 
well known. 
To complete the duplication of the club, the new club shaft should 
preferably have substantially the same grip diameter as the club being 
duplicated. The grip diameter should generally not vary from the original 
by more than about .+-.1/32 inch, more preferably by not more than about 
1/64 inch. In addition, the new club should have a swing weight (described 
below) within about .+-.1, more preferable about .+-.1/2, swing weights of 
the club being duplicated. The overall weight of the two clubs should be 
within about .+-.9 grams, more preferably .+-. about 4 grams, most 
preferably .+-. about 2 grams. 
FIG. 6 shows one method for the measurement of the swing weight of a club. 
A club 50 is placed on a counterbalanced scale 52 on a flat surface 54 and 
is balanced on the fulcrum 56 using a sliding counterweight 58. A swing 
weight is a scale factor defined when an increment of weight is added to 
the club head such that the counterbalance is moved one scale increment. 
The scale that is used is arbitrary. It is important, however, that the 
same scale be used in measuring the swing weight for the club being 
duplicated and the new matching club. 
While not necessary to duplicate a club, a parameter defined herein as the 
"phase angle" may be duplicated to obtain very precise duplication. As 
described previously, the motor used to oscillate the club during the 
duplication process is an AC driven motor. An AC voltage used to drive the 
motor produces a sine wave when displayed on an oscilloscope- Such a sine 
wave has a magnitude and a phase angle. The optical sensor array, which 
may be used to measure the club head excursion, produces a voltage which 
exhibits a sine wave. As shown in FIG. 7, the sine wave 60 of the motor 
and the sine wave 62 of the optical sensor may be displayed on a dual 
trace oscilloscope 66. The phase angle h of the golf club is measured as 
shown. In order to match phase angles of two different shafts for the 
purposes of duplicating a club, the phase angles of the two clubs should 
be within the range of about .+-.5 degrees, more preferably within about 
.+-.2 degrees, of each other. 
Once the spectral response curve of a particular club has been determined 
or a particular club has been duplicated, an entire set of clubs or any 
subset thereof may be made having analogous characteristics to the 
particular club. Generally, each number club differs from the next 
numbered club by about 1/2 inch in shaft length. For example, a 5 iron is 
normally about 1/2 inch shorter than a 4 iron which is normally about 1/2 
inch shorter than a 3 iron, etc. In order to manufacture a set or subset 
of golf clubs having the same performance characteristics, the spectral 
response curve for a single club is determined in the manner described 
above. While the single club (or clubs) to which other clubs in a set is 
to be matched will preferably be the user's favorite club, other 
techniques for identifying the appropriate starting club may be utilized. 
For instance, a player can evaluate on a practice tee a calibrated 
selection of test clubs to identify the club which he prefers. Or a 
player's swing can be videotaped and superimposed upon images of other 
player's swings (for which a preferred club is known) until a match is 
found and then producing clubs of the same spectral response curve as 
those of the known player. 
Thereafter, the remaining clubs are produced by selecting shafts and 
appropriate club heads which have substantially the same spectral response 
curve as the favorite club's curve excepting that the spectral response 
curve is shifted. In a plot of the relationship of length of club 
(directly proportional to the club number with the driver or 1 wood being 
the longest and the wedges the shortest) versus the natural frequency (in 
cpm) the shift in the spectral response curve when going from one club to 
the next higher or lower club produces a backward "S" curve such as the 
one shown in FIG. 8. As shown, the curve becomes convex between about the 
eight iron and sand wedge (SW) and concave between about the four wood and 
the driver. The curve between the 8 iron and the 4 wood is less severe, 
but is not a constant slope. FIG. 8 shows a backward "S" curve for shafts 
having an inherent gradient (slope) of 10 cpm/inch. Each golf shaft model 
has a specific inherent gradient which usually ranges from about 8 to 
about 15 cpm/inch. As a result of this variation, the specific shape of 
the backwards "S" curve and the increments between successive clubs in a 
set produced in accordance with the present invention will vary, depending 
upon the shaft model selected. The shaft model to be selected will depend 
upon obtaining the best match of spectral response curves. 
Table 1 provides appropriate approximate frequency increments between 
successive clubs for inherent shaft gradients of 8, 10, 12 and 14 
cpm/inch. The frequency increment for shaft models having a gradient of 10 
cpm/inch between the driver and 2 wood is 2.2 cpm, between 2 wood and 3 
wood 2.8 cpm, etc. 
TABLE I 
______________________________________ 
Frequency Increments Be- 
Length of tween Successive Clubs 
Standard at Various Gradients (CPM) 
Club Club 8 10 12 14 
______________________________________ 
Driver 43" 
&gt;1.0 &gt;2.0 &gt;3.0 &gt;4.0 
2 Wood 421/2 
&gt;2.0 &gt;2.5 &gt;3.7 &gt;4.5 
3 Wood 42 
&gt;2.3 &gt;3.5 &gt;4.3 &gt;5.6 
4 Wood 411/2 
&gt;3.0 &gt;4.0 &gt;5.2 &gt;6.0 
5 Wood 41 
&gt;3.4 &gt;4.3 &gt;5.4 &gt;6.4 
6 Wood 401/2 
&gt;3.5 &gt;4.4 &gt;5.5 &gt;6.5 
1 iron 40 
&gt;3.6 &gt;4.7 &gt;5.6 &gt;6.6 
2 iron 391/2 
&gt;3.8 &gt;4.8 &gt;5.7 &gt;6.7 
3 iron 39 
&gt;3.9 &gt;4.9 &gt;5.9 &gt;6.8 
4 iron 381/2 
&gt;3.8 &gt;5.0 &gt;5.7 &gt;7.0 
5 iron 38 
&gt;3.6 &gt;4.5 &gt;5.4 &gt;6.5 
6 iron 371/2 
&gt;3.3 &gt;3.5 &gt;5.2 &gt;6.3 
7 iron 37 
&gt;3.1 &gt;2.0 &gt;4.5 &gt;6.0 
8 iron 361/2 
&gt;1.0 &gt;0 &gt;2.0 &gt;4.0 
9 iron 36 
&gt;-5.0 &gt;-4.8 &gt;-4.0 &gt;-2.0 
PW 351/2 
&gt;-5.0 &gt;-4.5 &gt;-4.0 &gt;-3.5 
SW 351/2 
______________________________________ 
The increments shown in Table 1 are appropriate for duplicating shafts 
with nominal inherent gradients (slopes) of 8, 10, 12, and 14 cpm/inch. 
Other shafts, for example those with a 13 cpm/inch, require extrapolation 
of the increments shown in Table 1. As the inherent cpm/inch value for 
shaft model shifts, the increments must be adjusted accordingly. In all 
cases a plot of the relationship of length of club versus the natural 
frequency of a set of clubs produces the backward "S" curve relationship. 
In this manner an entire set of clubs can be manufactured with each club 
having the same performance characteristics as a single specific club. 
An alternative and the presently preferred method for measuring both 
selectivity Q and natural frequency f.sub.o is best described with 
reference to FIG. 10. As shown, a club 12 is clamped in a stationary vise 
51 mounted on a support surface (not shown), tightened in place by a screw 
or lever 53 and excited into oscillation by preferably manually pulling 
the club to one side a few inches and then releasing it so that it 
vibrates in a plane that causes the shaft to pass repeatedly over a box 61 
that contains the electronics comprising the circuitry shown in FIG. 11. 
The term "golf club" is defined herein and includes complete golf clubs as 
well as shafts to which a dead weight is attached as well as clubs or 
shafts which do not have actual grips thereon. The degree of tightening of 
a club within the vise should be as uniform from club to club so that the 
results of the determinations are properly comparable. 
As shown, a source of infrared (IR) power 64 drives an IR emitter 55 which 
emits IR energy, preferably not in the human visible spectrum. The IR 
energy reflects off the club shaft 12 and the reflection is received by 
the appropriate IR detector 59 or 57 as the club passes alternatively back 
and forth above them. Stable high frequency, e. g. 4 megahertz, clock 
pulses from a crystal oscillator 73 are gated into both timer/gates 65 and 
67 started and stopped by low frequency, e.g. 3 to 7, pulses per second 
from detectors 59 and 57, respectively. 
FIG. 12 is a plot of a club head displacement versus time. t.sub.1 is the 
time for one complete cycle of the club head, i.e. the time between two 
successive appearances of the club head above a single sensor. t.sub.2 is 
the time for the club head to pass from above one sensor to above the 
second sensor. p is the distance between the sensors. The dotted lines are 
the decay envelope for the velocity as the club head slows. 
The club frequency, f.sub.o, is computed in microprocessor 69 by inverting 
the count of timer/gate 65 and multiplying by the clock rate of the 
crystal oscillator and times 60 to convert from seconds to minutes so that 
the output is provided in cycles per minute (CPM). The value is held until 
reset by the display driver/memory 71. To increase accuracy, the results 
of several successive determinations are accumulated and averaged. 
Velocity of the golf club during each excursion is calculated by starting 
timer/gate 67 with a pulse from sensor 59 and stopping the timer/gate 67 
with a pulse from sensor 57. Pulses from the crystal oscillator 73 are 
accumulated during the interval so defined and shown in FIG. 12 as t.sub.2 
and transmitted to the microprocessor after each club oscillation. By 
comparing cycle to cycle velocity calculations, the rate of decay of the 
velocity contained in the exponent of the standard velocity equation: 
EQU V=e.sup.-.alpha.t sin(2.pi.f.sub.o t) 
provides a value of Q after only about 10 to 20 cycles which occurs in 
about 4 seconds. In this equation, .alpha. is the damping factor and t is 
the elapsed time. Further details about the conventional mathematics 
utilized herein may be found in such as Introductory Circuit Theory, E. A. 
Gilliman, John Wiley, NY (1953). Q is then equal to 2.alpha.. 
After the computation is made in the microprocessor 69, the result is shown 
on display 68 driven by display driver/memory 72 and retained until reset. 
This method of measuring Q is much faster than the method discussed in the 
embodiment of FIGS. 1-4. The equipment used in the circuitry of FIG. 11 is 
commercially available. 
The rate of decay of the velocity of oscillation is determined by 
mathematical means described herein to be related to the damping factor 
which is proportional to the selectivity by well known second order 
differential equations that describes damped harmonic motion. 
Alternatively, the rate of decay of club head or shaft displacement can be 
measured and the same selectivity, damping factor, or bandwidth 
calculation made. Another alternative is to measure acceleration of the 
clubhead or shaft of an oscillating club and derive the same parameters. 
One application of the selectivity measurement Q is made by marking it on 
clubs (or shafts) so that a golfer can rate the relative risk factor 
associated with an off-speed swing of each club so designated even without 
the golfer having had determined variations in his swing speeds. The 
higher the value of Q, the more intolerant a club is to off-speed swings 
and the greater the risk of a bad shot. 
To make the best use of club selectivity as obtained above by either 
method, the preferred embodiment is to derive swing statistics from a 
players's swings of the club having the best shaft flex for him. In this 
method, a player swings each of several calibrated test clubs many times 
until the sigma, i.e. the standard deviation of a normal distribution 
which contains the results of 2/3 of all swings recorded with that club, 
as shown in FIG. 14, and which is displayed on display 88 in Fig. 13, no 
longer increases. The preferred method of measuring a golfer's swing speed 
and variations therein is performed by having a golfer swing a club 10 
repeatedly in close proximity to a commercially available club speed 
measuring device 84. Preferably, a magnetic sensor 81 is used to sense 
club head motion, sometimes with the aid of a piece of metal tape 80 added 
to the club head 16, and the speeds of the swings taken since the device 
has been cleared by manually depressing CLEAR button 91 whenever a 
different test club is selected are used to form a best-fit normal 
distribution curve. Mean swing speed for that test club and sigma are 
displayed on display 83 and 88 respectively. 
The club registering the largest f.sub.o and the smallest sigma is the 
optimum for him and that club is the one which should be used to assign a 
value of sigma and f.sub.o to that player. 
It is currently believed that conservative golfers should utilize a golf 
club having a selectivity Q essentially equal to their sigma, when both 
are measured in the same units, e.g. miles per hour. Risk takers, on the 
other hand, could use golf clubs having a much higher Q rating, especially 
if driving distance is more important than accuracy because a higher Q 
will produce greater distance while sacrificing accuracy. 
Selectivity Q of existing clubs can be altered by modification of the 
hardness of the grip by changing grips or by using underlistings of 
different hardnesses. Softer grips lower the selectivity Q and harder 
grips raise it. Grips designed specifically to raise or lower selectivity 
Q are part of this invention. 
Another way to raise of lower selectivity while keeping the frequency 
f.sub.o constant involves the selection of shafts known to exhibit a value 
of Q as required in a specific application. Since the value of Q is found 
to vary more by shaft model than within editions of the same model, target 
selectivities are achieved by choosing the shaft model shown by 
experimentation to offer the range of Q needed in an analogous way that 
shaft frequency targets are achieved. 
Shafts can be designed with target values of selectivity Q in mind. Also, 
some shaft designs that exhibit values of Q combined with other factors 
could be eliminated as undesirable. Conversely, very high Q shafts could 
be desirable for golfer's with consistent swing speeds desiring to trade 
accuracy for added distance. 
The following Example illustrate the duplication of a single golf club and 
preparing other clubs therefrom. It is illustrative of the invention and 
should not be considered as limiting the invention. 
EXAMPLE 
A driver (1 wood) was oscillated using an oscillating means as shown in 
FIG. 2 except a ruler was used instead of an optical sensor array to 
measure the excursion of the club head. The frequency and excursion 
measurements were taken over a range of frequencies of from 200 to 800 
cycles per minute (CPM). The frequency and excursion measurements were 
then plotted to form a spectral response curve unique to the club. The 
curve is shown in FIG. 9 as a solid line. From a stock of other shafts 
with predetermined spectral response curves a shaft having substantially 
the same spectral response curve was selected and a dummy head having 
approximately the same weight as the head of the club being duplicated was 
attached. Its curve is shown as the dotted line in FIG. 9. As can be seen 
from FIG. 9, the frequencies of the two curves were within about .+-.2 CPM 
at all points, the height of the peak at the natural frequency of the club 
being copied was 1.0 inch higher than the height of the f.sub.o peak of 
the new club. The width of the peak at 50% of the height of the peak for 
the master club was 22 CPM and the width of the peak at 50% of the height 
of the peak for the new club was 24 CPM, giving a difference of 2 CPM. At 
70% of the maximum heights, i.e. Q, the difference is even less. The new 
club was then provided with a club head of the same loft and lie as the 
master club and a grip diameter substantially the same as that of the 
master club. The club head and grip were selected to appear the same as on 
the master club. When used on a driving range, a player could not 
distinguish between them. 
A 5-iron is prepared to match the characteristics of the above driver 
(which had been prepared from a shaft having an inherent gradient of 10 
cpm/inch). In accordance with Table I and FIG. 8, 5-iron is produced 
having (i) a length 5 inches shorter than the driver, (ii) a natural 
frequency of 300 cpm, i.e. 40.1 cpm greater than that of the driver, and 
(iii) a spectral response curve having a maximum height of 13.4 inches and 
a width Q of 23 cpm. The 5-iron is produced by selecting a commercially 
available shaft of the same shaft model and having the desired spectral 
response curve, cutting that shaft to the appropriate length, and 
attaching a 5-iron head and grip. When used on a driving range by the 
player for whom the driver was prepared, the 5-iron feels substantially 
the same.