## 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, constant-frequency and sloped-frequency.

### Constant Frequency Matching

(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 single-frequency matching of golf clubs. He reports having done preference testing with golfers of varying skill levels. He had them pick their favorite 2-iron, 5-iron, 7-iron, and 9-iron, from a flex-varied 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 single-frequency 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 25-30 cpm lower than the irons.

### Sloped Frequency Matching

(I'd like to thank Dave Ouellette of Brunswick Golf and Mark Merritt for supplying this material.)

Brunswick Golf has the best-known system for frequency-matching 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 flex-designating "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
Brunswick
Driver
Freq
5-iron
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 tip-trimming 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 constant-frequency match. The frequencies are based on a Brunswick 5.5 iron shaft for the Brunswick match, and the same stiffness 5-iron in the constant-frequency 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 R-flex to S-flex) is a 10- to 13-cpm difference. The Brunswick system has almost a 30-cpm 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.

1. All clubs are swung at the same speed
2. .

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 heft-match 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.

3. The longer clubs are swung with longer swings
4. .

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 swingweight-matched 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 longer-duration 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 two-hour segment of ordinary videotape of a golf tournament. Whenever one of the players took a full swing, I stopped the VCR and single-stepped 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 constant-frequency 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 high-speed 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 swingweight-scale dispute arose from the question whether duffers could swing a set that was heft-matched for a pro.

5. The shorter clubs require more accuracy and the longer clubs more distance
6. .

Therefore, the shorter clubs should be an exactly matched flex, while the longer clubs should be high-risk, high-yield 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 sloped-frequency 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 frequency-match 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 frequency-match 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 frequency-matched shafts is Brunswick; so if you order them matched, you'll get a slope-matched set at about 4.2 cpm per club.

But remember that all shaft manufacturers have some frequency-matching pattern in mind. If you follow the tip-trim 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.)
• "Sheet-wrapped" 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.
• "Filament-wound" graphite can be made almost as uniform as steel.
While low-end graphite shafts are likely to be sheet-wrapped, it doesn't follow that more expensive shafts are filament-wound. Summitt and Wishon's book contains data that shows:
• The Aldila HM-40, a very popular high-performance shaft, is sheet-wrapped 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 filament-wound shaft, showed similar sample uniformity to the steel shafts in the study (3cpm).
The HM-40 costs over \$50, while the Fibrematch costs \$35.

I have done an analytical study, and now know how to vary the tip-trim 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 tip-trimming 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.