Shaft Deflection Profiling

Dave Tutelman -- August 31, 2004

To date, much of the publicly-available information on shaft profiling involves frequency profiling. But the industry "buzz" is that the shaft manufacturers themselves use deflection profiling in their design and quality control. This article describes some experience in profiling shafts using a NeuFinder 4 to plot deflection profiles.

In the summer of 2004, one of my projects has been the building and testing of the NeuFinder 4. The NF4 was designed with shaft profiling in mind, and that was a primary interest for me. The device is able to measure a shaft at a beam length of as little as 19", which is almost a pure tip measurement.

This article describes some early experiences using the NF4 to profile a variety of shafts. Among the important lessons we learned were:
  • The NF4 is a very effective way to take shaft profile data.
  • There are ways to process and display the data that make shaft profile differences stand out very visibly.
  • This processing is simple enough to be easily incorporated into a spreadsheet, and plotted automatically for a graphic display of the flex "shape" of the shaft.

1. Description of the equipment

(Click on the thumbnails to see larger pictures.)
Dan Neubecker designed the original NeuFinder, and the NF2. In the case of the NF4, Dan was still the chief designer, but I provided a lot of engineering input so I feel it was very much a joint project. During the development Dan built a couple of prototypes, and I built the first test model from the resulting plans.

The NF4 is basically an inverted deflection board. It creates a known deflection in a shaft, and measures the load created by the bending of the shaft. The bigger the load, the stiffer the shaft.

In use, a shaft is placed unloaded into the three sets of bearings. (The original NeuFinder was a bearing-based spine-finder, and it still shows its roots.) Then a toggle clamp drives the tip bearing to a "preload" position, and the digital scale is zeroed out ("tared", in measurement parlance). Then the toggle clamp loads the tip by a known, calibrated distance, and the shaft attempts to turn the board that carries the other two sets of bearings. The digital scale reads the force it must exert to keep the board from turning, which is a measure of the shaft stiffness.

The ability to profile shafts was designed in. Profiling a shaft involves measuring the stiffness at various beam lengths, where beam length is defined for the NF4 as the distance between the middle of the tip bearing set and the middle of the furthest bearing set from the tip. Profiling is done with the tip close to the tip bearing at all beam lengths; there is a tip stop attached to the tip bearing assembly to hold this small distance constant. In this sense, profiling with the NF4 is comparable to profiling with a frequency meter, where there is a fixed weight at a fixed position at the tip of the shaft, and the unsupported beam length is varied by moving the clamp down the shaft.

The beam length can be varied from as much as 48 inches to as little as 19 inches. This allows a good sampling of shaft stiffness at a wide variety of stations from the butt to the tip.

Evolution of the design has resulted in a way of sliding the shaft quickly and easily from station to station for profiling. A 46" shaft for woods can be profiled at six stations in less than three minutes, taking care to do everything right and no rushing. That includes loading the shaft originally, changing the beam length from station to station, waiting for the scale to settle, and even writing the results. If two readings are taken at each station (as an extra-care sanity check), the procedure is still under four minutes.

2. How to display the data?

2.1 - Tables of numbers

For my first profiling experience, I loaded the NF4 into the car and drove to Charlie Badami's house. (He is currently the clubmaker for Virtual Dunes and the Metedeconk National Golf Club, but his workshop is his basement.) Charlie's main, almost sole, interest in the NF4 is profiling. This was the first NeuFinder he had seen in the flesh, and he was impressed.

Anyway, when I arrived at Charlie's, he was ready for the exercise with three driver shafts he wanted to profile:
  • Harmon Tour Design HTD CB-60.350 (S flex)
  • Apache/MCC MFS-65 (R3 flex)
  • Graphite Design YS-6 (S flex)
We took a profile for each shaft, that consisted of readings at 5" intervals of beam length. We wanted one reading to be as close to the tip as possible, so the measurements were at 19" (the shortest possible beam length with the NF4), 24", 29", 34", 39", and 44".

The result was this table of raw readings. Charlie and I looked at them, and had trouble drawing any conclusions about the shafts. It occurred to me that the reason we couldn't see anything useful about the shape was that the numbers in the table reflected both shape and magnitude. The shafts all had different flexes, as measured by butt frequency and confirmed by the 44" stiffness reading. So it was hard to tell much about which had a relatively softer tip if the entire shaft was softer or stiffer.

This suggested "normalizing" the data, so the butt stiffness of all the shafts was the same. So I calculated a new table, formed by dividing each reading by the butt reading for that shaft. This was a lot more telling, once you got used to looking at the numbers. In fact, Charlie got pretty excited about it, so excited that he pulled out another shaft and said, "Here, measure this!"

The shaft was a Fujikura VistaPro 80 (S flex). Charlie didn't say why he wanted me to measure this in particular; we just did it.
Adding the row to the table, it looked like this. We "eyeballed" the data, and saw something interesting. I pointed out that at the tip (19"), the Fuji was the stiffest of the shafts; however, in the middle (29" to 39"), it was the most flexible. In fact, at 34" it was the most flexible by a lot.

Charlie just grinned and said, "Dave, I talked to a Fujikura engineer who told me that the VistaPro 80 is tip-stiff but soft in the middle. Sounded like gobbledygook to me, but I wanted to see what he might have been saying. And what do you know? It is tip-stiff but soft in the middle, compared to these other shafts."

2.2 - Graphical display

With the numbers normalized to butt stiffness, you could tell some interesting things about the shape of a shaft's profile by looking at the table. But the very word "shape" connotes something visible or graphical, not an array of numbers. So when I got the data home, I plotted it to see what the "shape" actually looked like.

I used Excel, because it is a natural for graphing tabular data; the capability is built in. Of course, the fact that it is a spreadsheet also made it a natural for doing the normalizing -- and any other data reduction processing I might want to do. I could just enter the raw NF4 readings, and direct the spreadsheet to do both the processing and the graphing. Here's what I got...

This plot shows the Fujikura shaft (the blue line) has the stiffest tip (about as stiff as the YS-6) and, by quite a bit, the softest middle. The Harmon and the Apache (black and red lines) are fairly similar in profile through most of their length, but the Harmon has a much softer tip than any of the others.

This interesting display still leaves the eyeball a little unsatisfied, because the curves are so close together on the scale. The biggest difference among the shafts is less than 15% of the scale reading, and most of the differences are in the 5% range. It's hard to show these in a way that jumps off the page at you -- unless.....

2.3 - Normalizing the difference

Suppose we plotted the data as a percentage difference among the shafts. That would create a graph of differences, which is what we are really trying to see. We are not interested in the absolute stiffness of the shaft; in fact, we normalized that away with our very first data reduction. We are interested in seeing how the shape of the shafts' profile differs from shaft to shaft.

In order to show the differences, we have to decide, "Different from what?" This implies a "baseline", a shaft of zero difference. We must choose a "standard" shaft -- or at least a standard profile -- against which the others will be compared.

While the logic requires this, we don't have enough data yet to know what that "standard" should be. In fact, it needn't be a real shaft at all, just a set of profile numbers that we agree is a "middling" or "neutral" profile, not particularly stiff nor flexible at any point along the shaft. We are probably not far from suggesting such a set of numbers, but I'm not ready to do it in this article.

Anyway, here is the graph that Excel plotted from the data that Charlie and I took. Note that the differences in shape are quite clearly visible, almost highlighted. For instance, it is very obvious from this what "tip-stiff but soft middle" means, when you look at the shape of the Fujikura shaft.

In this case, we used the Harmon as the "standard shaft". That was just an arbitrary choice; I set up the spreadsheet so that the first row of data would be the benchmark. I don't think the HTD is a good standard; it is quite tip-soft, and we need a more "middling" profile as the standard.

3. More shafts, more profiling adventures

Once I had a spreadsheet set up for reducing and displaying shaft profiles, I experimented with profiling, going through a variety of shafts in my own basement. Here are a few of the more interesting comparisons.

3.1 - A few interesting shafts

This plot shows a few things:
  • I had an MFS-65 (R3 flex) in my own basement. I decided to compare the two shafts (Charlie's and mine) to see how consistent Apache/MCC is in the profile of their shafts (not just the butt stiffness). This shows that they are quite consistent indeed, showing a "noise" of only about .02 (or 2%). Bearing in mind that the measurement precision of the NF4 itself is almost 1%, that means that the two Apache shafts were less than 2% apart everywhere along their profile.
  • I also have a plot here of the TrueTemper EI-70. It seems to be exactly the opposite of the Fujikura, in that it is quite stiff in the midsection and soft in the tip. We know that the EI-70 has its fans and its detractors; almost nobody is lukewarm about it, they either love it or hate it. It would be interesting to do subjective and/or robot testing to see if the EI-70 and the VistaPro 80 really have precisely opposite feel and trajectory. If not, then one must question the value of shaft profiling.

3.2 - Checking consistency of shaft manufacture

One of my recent activities has been testing shafts for Mercury Golf. I was very impressed with the consistency of their shafts in parameters like weight and butt frequency. Now I had an opportunity to see if the consistency of stiffness applied to the entire shaft profile and not just the butt measurement.

I had three stepless steel Savage shafts left over from a batch that I tested. I had made the rest into a set of irons; these remaining three were the "culls". In other words, they were the outliers on either frequency or weight (these happened to be weight; there were no frequency outliers). So I anticipated that these would be a worst-case comparison, because they were the data wild cards -- or at least as wild as Mercury makes, which is never very wild at all.

Since these are iron shafts, the 44" beam length measurement was not taken. The data points are there because my spreadsheet template has them, but only the data at 39" and below is meaningful.

These shafts proved to be very consistent in profile (as they were in all other measurements I took). The wildest data points were only 2% differences, and only at two points. All the other data points were essentially identical, given the measurement precision of the NF4.

3.3 - Different models from the same manufacturer

Again looking at Mercury shafts, I profiled three different models of driver shafts. Mercury characterizes them as follows:
  • The Performance is an "entry level" shaft.
  • The Savage is an ultralight, low-torque shaft.
  • The Pro-Kevlar has a kevlar-stabilized tip; it's the one their long-drive tour guys use.
I had already done some golfer testing to compare the Pro-Kevlar and the Performance. (Two different golfers, same head, different model shaft at the same butt frequency.) There is a big difference in trajectory; the Pro-Kevlar is several degrees lower than the Performance. So it would be interesting to see whether their profiles differ enough to explain the difference in results.

The graph tells the story. Starting with the same butt stiffness (the normalization would do this even if the shafts weren't the same), the Performance gets progressively softer compared to the Pro-Kevlar. By the time we reach the tip, the Performance is fully 25% softer. So we know how to get a high trajectory.

This strongly suggests that the Savage would have an extremely low trajectory. I have not done the golfer testing to confirm this, but a query to Mercury brought the answer that the trajectory would be similar to the Pro-Kevlar.

By the way, I used the MFS-65 as the benchmark shaft for this plot. It is fairly similar to the Pro-Kevlar in profile, though the Pro-Kevlar gets almost 7% stiffer in the high-middle portion.

4. Comparison with frequency profiling

There are quite a few efforts underway to understand and even standardize profiling using "zone" frequencies as the stiffness measurement. This is done by putting a weight on the tip, and measuring the frequency with the clamp in different positions along the shaft. The result is a profile of frequency vs beam length. The beam length measure is the unsupported length between the front of the clamp and the tip of the shaft. This is quite analogous to the NF4 profiles above, which are plots of stiffness in deflection vs beam length.

Work is currently under way to relate the NF4 beam length to the frequency profiling beam length. They are similar but not the same, because frequency is measured with the shaft cantilevered rigidly in a clamp, while the NF4 has effectively point loads separated by 9.4". Initial work suggests that the NF4's minimum beam length of 19" corresponds to a frequency measurement with a beam length of 12" to 15".

4.1 - Representation and display

Regardless of whether the measurements are frequency- or deflection-based, the analysis of the profiles can be done similarly. In particular, the data reduction and the plotting of normalized differences are as useful for frequency profiling as for NF4 profiling. Here is a good example.

Tom Wishon Golf Technology is one of the leaders in publicly using profiling to characterize shaft performance. They are pioneers in the use of frequency profiling. On July 28, 2004, Matt Mohi of Wishon Golf posted on their web forum:

Ok, just got done with this little project. Long story short, the SL-5 in a Regular Flex has a very similar profile to the Speeder 757. I think that if you tipped it about 1/3 of an inch it would be really good in the upper 2/3rds of the shaft and slightly stiffer in the tip section. Below are the numbers:

Speeder 757 Regular: 180 210 242 290 365 508 855
SL-5 Regular : 176 196 233 285 362 515 915
SL-5 Stiff : 185 207 241 296 384 545 955

I went ahead and made up a spreadsheet with these numbers. Here is the resulting graph.

What this graph tells me is:
  • As Matt says, the tip of the SL5 is stiffer (relative to butt stiffness) than that of the Speeder.
  • If we assume that the Speeder is true to its Fujikura heritage, then it will be soft in the middle and stiff at the tip. This graph uses the Speeder as the baseline shaft, so the SL5 is even softer in the middle and stiffer in the tip. Whatever Fujikura is doing, Wishon is doing more of it.
  • Wishon's design remains true across flex. Since the normalization takes out the effect of base stiffness, we would hope that the R-flex and S-flex have the same shape. This graph shows that they track one another extremely well, which speaks well of both the design and the quality control.
  • And finally -- this way of reducing and displaying the data is just as useful for a frequency profile as for a deflection profile.

4.2 - Sources of error

Frequency and deflection are somewhat different in the way they relate to the stiffness of the shaft. Most notably:
  • Deflection is inversely proportional to shaft stiffness.
  • Frequency is proportional to the square root of stiffness.
The consequence is that deflection shows twice the variation as does frequency for a given measurement. For instance, if two shafts vary from one another by 2% in stiffness, they will differ by 2% measured by deflection, and will differ by 1% measured by frequency. Another way of saying this is:
  • For iron shafts (~300cpm), a 1cpm difference corresponds to a 0.7% difference in stiffness or in deflection measurement.
  • For driver shafts (~250cpm), a 1cpm difference corresponds to a 0.8% difference in stiffness or in deflection measurement.
Most frequency-measurement systems for clubmaking are precise to one or two cpm. So, if a deflection measurement system has a 1% tolerance, it is comparable in precision to the frequency meters you are likely to encounter. The NF4 measures to within 1%, so it is comparable to a frequency setup with a precision of 1cpm.

But there is another source of error in frequency measurements that is not present in the NF4. Frequency is sensitive to the weight of the shaft itself. The equation for frequency has a factor of (M + 0.24m), where M is the head or tip mass, and m is the mass of the shaft. The NF4 eliminates shaft weight by setting a zero reading with the shaft already slightly flexed. This "taring" removes any effect that shaft weight has on deflection.

How big is the frequency error due to shaft weight? Consider two shafts of identical stiffness but different weights. One is a steel shaft of 120 grams, while the other is a graphite shaft of 60 grams. The table below shows the differences in reading.

Tip mass=
Tip mass=
Tip mass=
% difference in frequency
% difference in effective stiffness

Those who do frequency profiling use much heavier tip weights than the standard 205g normally used to measure a shaft's overall stiffness. The main reason they do this is to keep the frequency from going offscale when reading tip frequencies; most clubmaking frequency meters top off at 999cpm. But this plot shows a distinct accuracy advantage as well. Even so, this inherent source of error assures that NF4 profiles (with accuracy approximately 1% of stiffness) are going to be at least as accurate as frequency profiles.


The NF4 is an extremely effective tool for profiling the stiffness of golf shafts. It does the job at least as accurately as frequency profiling, and very quickly and easily.

A most effective way to analyze profiles is by normalized differences. It gives a much more visually comprehensible display than a simple graph of frequency or deflection, or even normalized frequency or deflection. An Excel spreadsheet is available for free download to plot normalized differences.

Future work includes:
  • Choosing a baseline shaft profile for a "neutral profile standard".
  • Relating NF4 beam lengths and frequency beam lengths.
  • Lots of actual profiling.
  • Making available a profile library or data base.
Those who wish to help in these efforts are most welcome.


Appendix A - Normalization formula

The normalization formula is actually pretty easy, and easy to implement in a spreadsheet. In the equations that follow:
  • i is an index for the shafts being profiled. The "standard" shaft is i=0, and it increases by one for each successive shaft.
  • x is the position along the shaft. For the NF4 profiles in this article, x ranged from 19" to 44" at 5" intervals.
  • A[i,x] is a raw reading.
  • B[i,x] is a reading normalized to assume the same butt stiffness for all shafts being compared.
  • C[i,x] is the high-information reading that we graph as "the profile".
The computation for the spreadsheet consists of two stages: converting from A[i,x] to B[i,x], then from B[i,x] to C[i,x].

B[i,x] = A[i,x] / A[i,butt]

C[i,x] = ( B[i,x] / B[0,x] ) - 1

And that's all there is to it.

Appendix B - Excel spreadsheet

You can download your own copy of the spreadsheet to play with. Just click on this link.

Note that:
  • You enter readings in the first table, which is the raw data.
  • If you are using some other set of beam lengths, you can enter them in the first table. There is room in the spreadsheet for up to seven measurements per profile.
  • You can enter the names for your shafts in the first table, and they will show up in the other tables and the graph.
  • Graphs are updated as you enter the data.