Is Frequency Matching Meaningless?

[BC MIST]

I measured the frequency of 9 graphite wood shafts today, at 5" intervals from the tip, starting at 10", and using a 550 g tip weight(a drill chuck).

Two shafts, the SK Fiber Lite Revolution S and the Aldila One, Low launch S 75, produced some interesting numbers.

Both shafts had almost exactly the same frequency at the butt end. Logically then it would seem that both shafts would be suitable for a golfer(me), whose swing speed was fast enough for that flex of shaft. However, when measuring the frequency of the tip end, the difference in frequency was almost 200 cpm. The Aldila One is so stiff at the end that it is almost "brittle." I can hit and use the Lite Revolution, whereas, when I tried the Aldila One, it was the worst performing shaft that I had ever used.

Now when I can figure out what to do with all these numbers I might be able deteremine what kind of ball flight pattern occurs with shafts of varying frequencies, at different points along the shaft. Always something to unlearn first, and then learn the truth.

[jvincent]

BC, Not sure if you check out the Wishon golf forums on a regular basis but he is apparently working on a different way of profiling / analysing shafts. I remember someone asking him if he was in tune with what Dave Tutelman was doing WRT the NF4 and profiling but I don't remember his answer.

I'm pretty sure he's said that matching based on butt frequency is a waste of time.

All of the shaft manufacturers now have the technology to create pretty much any stiffness profile they want. The hard part will be figuring out which one is best for you.

[Chieflongtee]

JVincent. Tom has been using the shaft profiling method described by BC for quite some time. That topic has been discussed at length on the Spinetalkers forum.

[BC MIST]

BC, Not sure if you check out the Wishon golf forums on a regular basis but he is apparently working on a different way of profiling / analysing shafts. I remember someone asking him if he was in tune with what Dave Tutelman was doing WRT the NF4 and profiling but I don't remember his answer.

I'm pretty sure he's said that matching based on butt frequency is a waste of time.

All of the shaft manufacturers now have the technology to create pretty much any stiffness profile they want. The hard part will be figuring out which one is best for you.

Regardless of the flex profile of a shaft, when it comes to actually doing the trimming, I will trust my FA over "trim .25" from each tip for the next shortest club in the set." Of course, this assumes that I have been able to select an appropriate shaft for the golfer, so use of frequency is not quite yet obsolete. However, selecting a shaft solely based on its butt frequency, is a waste of time.

How they are going to eventually figure out what shaft profile will suit any particular golfer's swing characteristics, will be fascinating.

One interesting thing about the testing that I did above was that an SK Fiber Lite Revolution "S" shaft was stiffer in the butt section compared to the corresponding "R" shaft, and yet the "R" shaft was stiffer in the tip section. Now which one is actually going to "play" stiffer. The "S" will feel stiffer, but will it actually play stiffer? So much yet to figure out.

[jvincent]

How they are going to eventually figure out what shaft profile will suit any particular golfer's swing characteristics, will be fascinating.

Then there's also the "feel" question to take into account. And people wonder why I've got a half dozen or so used driver shafts in the "spare shaft" box.

[BC MIST]

Then there's also the "feel" question to take into account. And people wonder why I've got a half dozen or so used driver shafts in the "spare shaft" box.

Only 6. You should come out here.

[jvincent]

Only 6. You should come out here.

Give me time. I'm still relatively young.

[Chieflongtee]

I measured the frequency of 9 graphite wood shafts today, at 5" intervals from the tip, starting at 10", and using a 550 g tip weight(a drill chuck).

Two shafts, the SK Fiber Lite Revolution S and the Aldila One, Low launch S 75, produced some interesting numbers.

Both shafts had almost exactly the same frequency at the butt end. Logically then it would seem that both shafts would be suitable for a golfer(me), whose swing speed was fast enough for that flex of shaft. However, when measuring the frequency of the tip end, the difference in frequency was almost 200 cpm. The Aldila One is so stiff at the end that it is almost "brittle." I can hit and use the Lite Revolution, whereas, when I tried the Aldila One, it was the worst performing shaft that I had ever used.

Now when I can figure out what to do with all these numbers I might be able deteremine what kind of ball flight pattern occurs with shafts of varying frequencies, at different points along the shaft. Always something to unlearn first, and then learn the truth.

BC. Profling is good but you'll still have to through a bunch of shafts to get it right. See the following:
http://www.freegolfinfo.com/forums/tm.aspx?m=1996790

[Started2k3]

BC is there any chance you could post your test results on the 9 shafts?

[downhillslider]

Only 6. You should come out here.

Ditto on that one !

[BC MIST]

BC is there any chance you could post your test results on the 9 shafts?

Aldila One Low Launch 75 S 735 539 366 261 205 173 155
Mercury Savage S 709 456 335 263 217 180 155
Aldila NV S 679 434 318 248 206 179 158
Harrisson 2.5 Titanium 60 S 672 421 308 244 200 175 160
Mercury Savage R 669 426 315 248 207 172 147
Graffaloy ProLite 35 S 623 422 325 264 219 188 162
SK Fiber Lite Revolution R 616 383 284 230 195 170 152
TT Dynamic Gold S300 Steel S 615 388 281 232 197 173 153
SK Fiber Lite Revolution S 608 404 301 244 209 180 163
UST Proforce 55 A 596 376 269 215 182 158 142
Accuflex Vision 55 S 594 383 285 228 189 168 151
SK Fiber Pure Energy S 590 387 293 237 202 177 159
Mercury Pro Kevlar S 579 418 318 258 219 186 160
Mercury Pro Kevlar R 575 395 301 247 209 179 156
Mercury Perefromance Plus R 557 366 276 224 187 165 148
Average 628 413 305 243 203 175 155

[Started2k3]

Aldila One Low Launch 75 S 735 539 366 261 205 173 155
Mercury Savage S 709 456 335 263 217 180 155
...

Thank you. Wonderful data.

I am working on a shaft profiling theory and these helped to illustrate what you are talking about in your first thread.

But I would like to have some additional data, and unfortunately I don't have the equipment for empirical test so:

This is a call out to any clubmakers who are willing to participate. If you are making a club that requires tip trimming and you have a frequency analyzer. Could you please post the frequency profile of the raw shaft and then the frequency profile of the tip trimmed shaft, as well as shaft model and how much was trimmed.

Thank you.
Charles

[Chieflongtee]

This is a call out to any clubmakers who are willing to participate. If you are making a club that requires tip trimming and you have a frequency analyzer. Could you please post the frequency profile of the raw shaft and then the frequency profile of the tip trimmed shaft, as well as shaft model and how much was trimmed.

Thank you.
Charles

Charles. You probably saw this but just in case:
http://tutelman.com/golfclubs/frequency.php?ref=

Also I think you should be a little more specific with your request.
Do you want the actual data with the actual clubhead(dry fit) or a tip weight? Also depending on the fm used you might end up with the wrong data(ex 2.5 clamp or 5 inch clamp)

[Started2k3]

Charles. You probably saw this but just in case:
http://tutelman.com/golfclubs/frequency.php?ref=

I had forgotten about that page, thanks for the reminder. It is probably sufficient to illustrate my point which I will post later (hopefully today).

Also I think you should be a little more specific with your request.
Do you want the actual data with the actual clubhead(dry fit) or a tip weight? Also depending on the fm used you might end up with the wrong data(ex 2.5 clamp or 5 inch clamp)

Actually so long as the same equipment is used (tip weight, clamp, etc) then the results would be what I wanted. I am looking for the relationship between the a raw shaft and a tip trimmed shaft, which would be a single pair of data.

The real worry would be if after tip trimming the shaft cannot be profiled at the 10" to 20" range because it has stiffened up beyond the range of the FA. But this shouldn't be a problem with high tip weights, like BC uses (550g).

[Started2k3]

This has been a fun journey and I hope you will enjoy the ride. I suspect it is not over.

I have not had a chance to review all available published material on frequency profiling (nor is it likely that I will). Thus far I have not found anything on the web that compares or is similar to the following (but then again it may just be where I am looking). Note that may of the concepts are defined in terms of frequency profiling but they are also relevant and translatable to deflection profiling.

Lyle (aka BC MIST) provided my first glimpse at a frequency profile. Like many others I found this fascinating. I immediately entered the data in excel for graphing, and observed the obvious non-linear relationship between frequency and length that kind of looks like a shaft bending.

Non-linear relationships are generally more difficult to deal with than a linear relationship, so I looked to see if it could be “linearized”. The first attempt was to take the natural log of the frequency, no luck. The second attempt was to take the inverse of the frequency, which seemed to work quite well. From physics we know that the inverse of the frequency (f) is the period (T=1/f). [Note that the formula I used to get the period in this analysis was actually: T = 1000/f so the units would be minutes per 1000 cycles. This was done so that the period numbers weren’t ridiculously small values.] There appeared to be quite a linear relationship between the period and beam length (L), with the best relationship occurring over the middle zone of the shaft.

Figure 1: Frequency versus Beam Length and Period versus Beam Length
This is not new but I have not seen anybody else compare the period to beam length.


My belief from this was that it would be possible to come up with a linear equation that would relate T and L to describe a particular shaft. This way the equation could be manipulated (head weight and tip trimming) to obtain desired flex characteristics. Unfortunately, at the time I only had two profiles to test, but these seemed to work quite well. However, a single equation for the entire shaft was not possible so I thought maybe use three equations, one for each zone. The idea would be that you could relate the quantifiable slope of the equation with a common flex designation (L,A,R,S,X). But this left me wondering what the intersection of the equations meant, if it meant anything. I needed more data, but I didn’t have the means to get it.

When Lyle profiled nine shafts and made the results available online, I was able to resurrect my previous analysis. This seemed to work great for some shafts (ie ) but failed miserably with other shafts (ie ).

Back to basics so I looked at the common equation used for frequency analysis of golf shafts. Reprinted below:
f = 1/(2*pi)*sqrt ((3*E*I)/((H+.23*s)*L^3))
Where:
H = head mass
s = shaft mass
L = beam length
E = modulus of elasticity
I = Geometry stiffness

I then graphed three shafts: one that showed a linear relationship between T and L (Graffaloy ProLite 35 S), one that was very non-linear in T and L (Aldila One Low Launch 75 S), and a final shaft that is described by the formula above (inverse of the function to get period).

Figure2: Three shafts, period versus beam length
Note that none of shafts are really comparable.

The graph reminded me that the geometry stiffness (I) is variable over most of the length of the shaft. Also that the formula above is used to describe what the frequency would be if a “uniform rod” was used. So the tapering or stepping of the shaft was causing the period profile to “straighten out”.

This was the spark that gave me the idea of having an “ideal R flex shaft”. The properties of the shaft would be that the butt frequency, and subsequently the butt period, would be fixed (ie 255 CPM) and it would have an intercept in the T vs L graph at {0,0}. Keeping the intercept the same but increasing or decreasing the butt frequency by a set amount (ie 12 CPM) we could then obtain a “set of ideal shafts”.

Figure 3: Set of Ideal Shafts: frequency vs beam length & period vs beam length
Shows how the frequency profiles compare for the set of ideal shafts.

Using the “set of ideal shafts” we can now compare an individual shaft frequency profile against the set to get an idea of its characteristics over different zones of the shaft.

Figure 4: Two examples of shafts compared to the set of ideal shafts, frequency
Here we can see how an actual profile would compare and can be analyzed when displayed against the set of ideal shafts. Note that the Mercury shaft slowly drifts to in between an L and A flex, but the Aldila actually really stiffens up at the 10” measurement it would be considered 3X but around the 15” measurement it is between 5X and 6X. Hence the “brittleness” feel that Lyle had mentioned in the original post.

One of the characteristics of the set of ideal shafts is that the CPM “gap” between ideal shafts is symmetric at each measurement point (ie 12 CPM gap at the butt and 48 CPM gap at the 10” measurement).

As far as how the frequency measurements should be made there appears to be a strengthening consensus that a butt measurement of 255 CPM is a R flex (for a wood shaft) and this is done with a 205g head weight and a 5” clamp at 40”. Also there is a 10 CPM gap between flexes at the butt measurement. The consensus is also building for iron shafts (note that these may be different for each club, but this may depend on what frequency slope you prefer – flat line or sloped frequency irons) but a consensus 5-iron flex could probably be agreed upon with reasonable ease.

Another neat thing about the “set of ideal shafts” is that it does not require that the shaft exists, because it is purely a construct for comparison. This means that no individual company can be thought of as having the base to which everybody else compares to … little bit of politics off the table.

Comments?

[TourIQ]

One interesting thing about the testing that I did above was that an SK Fiber Lite Revolution "S" shaft was stiffer in the butt section compared to the corresponding "R" shaft, and yet the "R" shaft was stiffer in the tip section. Now which one is actually going to "play" stiffer. The "S" will feel stiffer, but will it actually play stiffer? So much yet to figure out.

Hi BC MIST

This will add to the confusion ...

Here's Tim's post from MyOstrichGolf:
http://groups.yahoo.com/group/shoptalk/message/72385
As you get more and more into shaft profiling, you'll also find that there are shafts with identical bend profiles that feel and play nothing like one another ... It's a fun part of trying to understand the golf shaft. There is one problem with the data set - at least the last time I saw
it - shafts are profiled in very small "sets" and generally from the same run from the manufacturer. I have 50 different shafts profiled in the same model and flex from a very well known shaft company. These shafts were purchased from different sources, a just a few at a time. They profile into nearly 6 different shafts - very, VERY different shaft profiles. You can't even average them, and the profile in the database is not really representative of the shafts that I have either. Consistency or a very large sample size are needed to get a picture of how weak or poor a shaft profile may be as a representation of a particular shaft model and flex.

[rhh7]

"...Granted, I do believe that in the long run, electronic deflection would
be a better way to do bend profile analysis because of the difficulty in
making the counting protocol of a good frequency analyzer to be able to
be a little more repeatable for short beam length measurements.

But since virtually no Clubmakers own a proper electronic deflection
machine, this sort of makes bend profile analysis impossible for each
clubmaker who is interested to do on his/her own. Thus for now, I plan
to stay with CPM bend profile measurement because it becomes a little
more possible for more Clubmakers with their FQ analyzers to participate
themselves. But if this gets to be more and more difficult to wrap our
arms around, we may have to make the switch some day to deflection.

IN the meantime, hope this helps a little,

TOM WISHON"

[Chieflongtee]

Geez Robert. You scared me. For a while I thought you had suddenly turned into a guru Then I saw TW's name at the bottom of the quote and I was releieved . One guy sorts all his shafts in what he calls zone c and picks the ones closest to one another to build his sets. On another note I asked if a large spine could affect the profiling but no one answered. If let's say a you have a butt frequency that varies from 12 cpms from the spine and the NBP it is bound to make a difference in profiling especially in the tip portion. Is spining considered when zone profiling ?

[Chieflongtee]

"...Granted, I do believe that in the long run, electronic deflection would
be a better way to do bend profile analysis because of the difficulty in
making the counting protocol of a good frequency analyzer to be able to
be a little more repeatable for short beam length measurements.

But since virtually no Clubmakers own a proper electronic deflection
machine, this sort of makes bend profile analysis impossible for each
clubmaker who is interested to do on his/her own. Thus for now, I plan
to stay with CPM bend profile measurement because it becomes a little
more possible for more Clubmakers with their FQ analyzers to participate
themselves. But if this gets to be more and more difficult to wrap our
arms around, we may have to make the switch some day to deflection.

IN the meantime, hope this helps a little,

TOM WISHON"

THe NF4 does differential deflection and takes residual bend out of the equation.

[Started2k3]

Geez Robert. You scared me. For a while I thought you had suddenly turned into a guru Then I saw TW's name at the bottom of the quote and I was releieved . One guy sorts all his shafts in what he calls zone c and picks the ones closest to one another to build his sets. On another note I asked if a large spine could affect the profiling but no one answered. If let's say a you have a butt frequency that varies from 12 cpms from the spine and the NBP it is bound to make a difference in profiling especially in the tip portion. Is spining considered when zone profiling ?

If you check Kaufman's site you will find that he has used FA to find the spine, in one of the technotes, by testing - turning 22.5° - testing - repeat to 360° - plot and the spine is pretty obvious. But it it probably quicker and easier to use a mechanical setup.

I would think that you have to take the spine into consideration when zone profiling, AND trying to match shafts for a set.

One thing that I have not seen online is a discussion of whether or not the spine is straight along the entire length of the shaft or does it spiral around the shaft, or even worse oscillate down the shaft in an irregular pattern. This I think could most easily be tested by the kaufman method at each of the measurement points.

[Started2k3]

I have asked for some expert opinion and review, so I went to one of the main sources … Dave Tutelman. Reprinted with permission below is the email dialogue between myself and Dave. Dave thank you, your input will always be welcome.
- Charles


Started2k3 wrote:
I realize that you are busy but I was wondering if you could provide some feedback on what I wrote (on another forum)?

Here is the link:
http://forum.ottawagolf.com/showthread.php?t=6186
post #15



Dave Tutelman wrote:
Hi,

As I suspected (and said so in my last post) this is the same thing
that Jay Messner noticed about two years ago. He put it differently,
but I can show you that the math is the same:

Jay said that frequency F times beam length L is roughly a flat line.
Mathematically, that can be put as:

FL = const

or, since F = 1/T

L/T = constant

You said that period vs beam length is roughly a straight line. If
that straight line is through the origin, then your statement can be
put mathematically as

L/T = constant

Same thing!

You mention the classic EI equation for frequency, but I'm not sure
why. You never use it in the rest of what you do. You don't plot it
to compare with your ad hoc model (which, I agree, works a lot better
in practice). And, in fact, it's pretty useless for real shafts,
because I (and sometimes E) varies considerably over the length of
the shaft. The equation doesn't have anything to do with an "ideal"
shaft, just a shaft of uniform EI over its length.

Cheers!
DaveT





Interleaved S2k3 and Dave T email dialogue:


S2k3: Any idea where I can get some of Jay Messner's earlier work? Online?

Dave T: In my prior email to you, I included his post on the subject to the Wishon forum. That's the only public disclosure of his work that I've seen. I've exchanged an email with him but (a) I don't know if I'm at liberty to disclose it, and (b) there wasn't much of substance there.

S2k3: The reason why I was looking at it was because I keep reading on many of the
forums that the terms for flex (ie L, A, R, S, X) are meaningless or that
OEM's lie .

Dave T: That's certainly true.

S2k3: I was seeing if there was a way to come up with a method that
brings meaning back into the flex designations.

Dave T: The PCS has a kit that it sells (for a small fee to its members and a large fee to non-members) that includes relating butt frequencies to LARSX. That particular piece of the "kit" seems to be public knowledge; you can probably find the chart on the net if you look hard. It is very similar to the "Brunswick chart" that justified the Rifle ratings. It has sloped lines on a graph of frequency vs club length. But instead of the sloped lines being designated 6.5 or 4.0, they are LARSX. (Actually, I'm not sure that the PCS chart labels the lines LARSX, but I certainly have seen charts that do.)

If you are going to propose an LARSX based on full profile rather than butt frequency, then how do you describe it? What do you call a shaft that is an "ideal R" at the butt, an "ideal S+" in the midsection, and an "ideal X-" in the tip. (I'm not making this up; I profiled a friend's driver today, and that's what came out of it.)

Personally, I think that we should continue to use either butt frequency or some other SINGLE, AGREED station frequency to designate LARSX. The rest of the profile should be a SHAPE, not a stiffness designation. That's why I propose the sort of normalization that I do in my first article.

S2k3: I actually used the classic equation for frequency to produce the plot of
the "formula" line in one of the figures. Used to demonstrate how different
actual shafts can be from the uniform rod equation, but remember in a
frequency plot they may look quite similar because of the non-linearity of
both lines.

Dave T: Again, that's why normalization and differencing is important. Without it, the naive viewer will just see the similarity when the differences are really very large.

S2k3: The classical equation, I believe, still holds when talking
about what happens to the frequency as trimming and different head weights
are used.

Dave T: Trimming? No. Head weight? Probably. And you can do something empirical with trimming that looks like the equation -- but really doesn't come from it. For instance, you can see how I finessed it in my article at http://www.tutelman.com/golfclubs/frequency.php

S2k3: May I have permission to post your email response on the forum?

Dave T: You may use this email. You may use everything in the previous email

[rhh7]

Geez Robert. You scared me. For a while I thought you had suddenly turned into a guru ...

When I was younger, I thought I knew almost everything. Now, at age 60, I realize that I know almost nothing. But my mind is like a thirsty sponge, I want to soak up knowledge, and I am running out of time!

I have learned so much in such a short time on this forum, both from the threads posted here, and from the links so generously provided. Thanks, everyone!