Frequency Matching
We've noted several times already that there are two major dimensions
to the
"feel" of a club: heft feel and flex feel. In the chapter on
swingweight, we
saw how to get your set to match in heft feel by matching either the
swingweight or the moment of inertia across the set. Now we'll talk a
little
about a much younger technology, matching the flex feel across the set.
Everyone agrees that the key quantity to matching flex
feel is the vibration
frequency of the club. But there's substantial disagreement as to what
it
means to match a set for frequency. There are a few who feel that all
the
clubs should vibrate at the same frequency. But that's not the only way
of
defining "matched", and frankly not even the most popular. The options
for
matching are:
First, let's look at a representative system for each of the schools of
thought, constantfrequency and slopedfrequency.
(I'd like to thank D.B. Miko of
Mac Shack Golf for supplying this material.)
Eric Cook of IsoVibe is one of the major proponents of
singlefrequency
matching of golf clubs. He reports having done preference testing with
golfers of varying skill levels. He had them pick their favorite
2iron,
5iron, 7iron, and 9iron, from a flexvaried collection of each. Most
picked 3 out of 4 clubs within 5 cpm of one another. This is strong
evidence
that the best match of "flex feel" for these golfers is provided by a
constant frequency over the set.
The singlefrequency matching systems I've seen aren't
quite pure, in that
they "match" the woods to a lower frequency than the irons. The woods
are set
to a frequency 2530 cpm lower than the irons.
(I'd like to thank Dave
Ouellette of Brunswick Golf and Mark Merritt for
supplying this material.)
Brunswick Golf has the bestknown system for
frequencymatching clubs, but
they do it on a slope. Interpolating from their curves, they make the
club
vibrate 8.5 cpm faster for every inch shorter the club is. (That
equates to a
slope 4.2 cpm per club in the irons, where the length of the clubs is
stepped
by 1/2".)
The Brunswick system is defined by a set of diagonal
lines on a graph of
frequency vs. club length. Each line is labeled with a flexdesignating
"name", like "5.5" or "6.5". (By now, we should recognize these as the
Brunswick equivalent of "R" and "S".) The "5.5" line, for instance,
would
have a frequency of 255 cpm at a length of 43" (the standard length for
a
driver). It would slope upward at 8.5 cpm for each inch reduction in
length.
To find the Brunswick stiffness of a club:
 First measure the club's frequency and length.
 Plot the frequency and length on a graph containing
the Brunswick diagonal lines.
 Look to see where it is within the diagonal lines.
For instance, if it's between the 6.0 and 6.5 lines and a little closer
to 6.0, then the club is a 6.2 stiffness on the Brunswick scale.
The table below shows how this sloped scale tends to map to other
scales and
measurements.
Nominal
Grade 
Brunswick
Grade 
Driver
Freq 
5iron
Freq 
L 
3.5 
235 
282 
A 
4.5 
245 
292 
R 
5.5 
255 
302 
S 
6.5 
265 
312 
X 
7.5 
275 
322 
That's the theory anyway. The DSFI book shows the
Brunswick FCM iron
shafts
to measure out about 10 cpm stiffer than the table (or the graphs) say
they
should be, while the driver shafts are right on the curves. I have no
explanation for the discontinuity, but 10 cpm is a full flex grade; you
WILL
feel it.
The other major shaft manufacturers also use a sloped
frequency match, mostly
pretty similar to Brunswick's. But their systems are implicit in the
tiptrimming instructions they recommend with their shafts. I've done
some
calculations indicating that they are, for the most part, sloped
slightly
steeper than Brunswick, at about 5 cpm per club.
Comparison of the Methods
Let's look at the frequencies of two different sets of irons: one using
a
Brunswick slope and the other a constantfrequency match. The
frequencies are
based on a Brunswick 5.5 iron shaft for the Brunswick match, and the
same
stiffness 5iron in the constantfrequency set.
Club 
Brunswick
Frequency 
Constant
Frequency 
2I 
289 
302 
3I 
293 
302 
4I 
297 
302 
5I 
302 
302 
6I 
306 
302 
7I 
310 
302 
8I 
314 
302 
9I 
318 
302 
It is generally agreed that most golfers can feel a
cpm difference
when
they swing a club. A whole "flex grade" (say Rflex to Sflex) is a 10
to
13cpm difference. The Brunswick system has almost a 30cpm difference
across
the set, and the difference between the two systems is over a dozen cpm
at
each end of the scale. So why isn't there a definitive answer to the
question, "Which is RIGHT?"
I wish I knew.
There are smart people on both sides of the question.
There are companies
with the resources to have experimented extensively on both sides of
the
question. But so far, nobody seems to be sharing their raw data, which
is the
essence of science, and they claim results that are fundamentally in
conflict.
Without a body of convincing literature to consult, I
tried out all the
rationales I could for either system. I was able to come up with three
possible arguments; they are presented below, together with what I know
so
far to support each. I hope to be able to say more in a future edition
of
these notes.
 All clubs are swung at the same speed
.
Therefore, all clubs take the same amount of time to
go from the top of the backswing to impact. Therefore, all clubs should
vibrate at the same frequency.
This makes a certain amount of sense. Frequency is
the inverse of the time response of the club. If you want it to be at
the same point of its "unloading" at impact for each club, then you
want the frequency to be inversely proportional to the time duration
from the beginning of loading to impact. So if the duration of the
downswing is the same for all clubs, then it would follow that all
clubs should have the same frequency.
While it isn't in the IsoVibe literature, it's a fact
that they also heftmatch their clubs by moment of inertia rather than
swingweight. This suggests to me that they work from this rationale;
all the clubs have the same dynamic heft, and therefore are swung at
the same speed.
This is a consistent argument, which they claim is
backed by subjective testing. But a lot of their data is held as
proprietary; they claim it as their competitive advantage.
 The longer clubs are swung with longer swings
.
Therefore, the longer clubs take a longer time to go
from the top of the backswing to impact. Therefore, the longer clubs
should vibrate at lower frequencies.
This is the flip side of rationale #1. If the time
duration from loading to impact varies with the club, then the
frequency should vary too; otherwise, not all clubs will unload to the
same stage at impact.
 Consider:
 in a swingweightmatched set, the long clubs have a
heavier MOI than the short clubs. If MOI is the determinant of the
speed of the swing, then longer clubs WILL have a longerduration
downswing. I computed how much of an effect this would contribute, and
was unable to justify a slope much bigger than 1/2 cpm per club. This
is nowhere near as big as the common OEM slopes of 4 to 5 cpm per club.
 Well then, consider:
 Players frequently use shorter backswings with the
shorter clubs, and longer, fuller backswings with the longer clubs.
This might have an effect on the downswing duration suggesting a sloped
frequency.
To test this out, I viewed a twohour segment of
ordinary videotape of a golf tournament. Whenever one of the players
took a full swing, I stopped the VCR and singlestepped through the
downswing. I measured the downswing duration as a count of the total
number of frames in the downswing. (I believe I was able to estimate to
about a half a frame.)
The results indicate different strokes for
different folks. I was able to time enough swings to see a trend
for only four golfers, but there was enough variation among them to see
that it would be hard to generalize. The results show that:
 Corey Pavin has absolutely the same duration
downswing no matter what club he picks up. It was uncanny. If ever
there were a candidate for a constantfrequency set, it's Pavin.
 Mark O'Meara is almost as constant as Pavin, to
the limits I could measure.
 Ben Crenshaw and especially Nick Faldo have a
noticeably longer downswing as the clubs get longer. The slope of their
downswing durations imply a frequency slope of 2.5 (Crenshaw) to 3.5
(Faldo) cpm per club. Faldo is within experimental error of a Brunswick
slope.
I don't know if a highspeed video camera should be part of a
clubfitter's tools, but this data suggests it might be useful to choose
a slope (or lack of slope) for frequency matching.
By the way, I have no idea whether data drawn from
PGA pros at the top of their game is useful for designing clubs for
weekend hackers. Remember that part of the swingweightscale dispute
arose from the question whether duffers could swing a set that was
heftmatched for a pro.
 The shorter clubs require more accuracy and
the longer clubs more distance
.
Therefore, the shorter clubs should be an exactly
matched flex, while the longer clubs should be highrisk, highyield
flex. Therefore, the longer clubs should vibrate at lower frequencies.
Jack Nicklaus describes this rationale in his 1964
book, "My 55 Ways to Lower Your Golf Score." This predates using
frequency to rate the stiffness of shafts, and possibly predates
"sloping" the stiffness with the club. Jack attributes it to his
college coach, Bob Kepler, who reshafted the team's clubs with stiff
shafts in the short irons, regulars in the middle irons, and whippy in
the long irons.
But recently, short game guru Dave Pelz has begun
arguing that the short irons and wedges should be more flexible than
the world has been making them. Since the vast majority of OEM clubs
are based on a slopedfrequency system, Pelz might be interpreted as
calling for less of a slope, and perhaps a constant frequency.
Each of these is a valid argument, if you accept the premise. I'm still
not
sure which premise I believe.
Doing the Matching
Of course, the most reliable way to frequencymatch is with a meter.
But I'll assume that, if you have a meter, you know how to do it
already.
I didn't have a frequency meter myself until quite
recently. So, out of necessity, I put a lot of analysis and
experimentation into
figuring out how to match shafts without a meter.
The second most reliable way to frequencymatch is to
order a matched set from the
manufacturer. If you order a matched set, you "buy into" the matching
system
endorsed by that manufacturer. The only manufacturer (as of 1995) who
sells
frequencymatched shafts is Brunswick; so if you order them matched,
you'll
get a slopematched set at about 4.2 cpm per club.
But remember that all shaft manufacturers have some
frequencymatching
pattern in mind. If you follow the tiptrim instructions that came with
the
shaft, you'll get an approximation of the matching pattern endorsed by
your
shaft manufacturer. How good an approximation? It depends on the
uniformity
of the shafts supplied by the manufacturer. Price isn't necessarily a
good
guide here; material and construction method tell the story.
 Steel shafts are probably the most uniform. (There's
no difference between welded and seamless tubing, advertising slogans
notwithstanding.)
 "Sheetwrapped" graphite is the least uniform, and
can vary by as much as a full flex grade (10 cpm) between different
samples of the same model.
 "Filamentwound" graphite can be made almost as
uniform as steel.
While lowend graphite shafts are likely to be sheetwrapped, it
doesn't
follow that more expensive shafts are filamentwound. Summitt and
Wishon's
book contains data that shows:
 The Aldila HM40, a very popular highperformance
shaft, is sheetwrapped and shows all the uniformity problems of the
breed. To Aldila's credit, they continue to improve the process.
Between 1989 and 1992, the frequency spread in a sample batch went from
26cpm (almost three flex grades) to 9cpm (one flex grade). But it still
shows the basic limitations of the process.
 The Brunswick Fibrematch, a filamentwound shaft,
showed similar sample uniformity to the steel shafts in the study
(3cpm).
The HM40 costs over $50, while the Fibrematch costs $35.
I have done an analytical study, and now know how to
vary the tiptrim to
get slopes other than the one intended by the manufacturer. Of course,
to get ANY consistent slope without a meter requires the same
predictability
of the manufactured shafts that I discussed above.
Before I leave the subject, let me share a hint suggested by Paul
Nickles of
Raven Golf. Take most commercial shafts and, instead of tiptrimming
according to the instructions, trim THE SAME amount from each tip. This
will
give you a modest slope, somewhere between the manufacturer's slope and
a
constant frequency. (I've done some calculations that show it to be
just under 2 cpm per club.) He says, and I concur in principle (I
haven't tried it yet),
that this is a conservative choice for someone who doesn't know which
side to
believe.
Last modified Dec 4, 1998
