Tutelman -- August 31, 2004
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
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
a variety of shafts. Among the important lessons we learned were:
- The NF4 is a very effective way to take shaft
- There are ways to process and
display the data that make shaft
differences stand out very visibly.
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
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.
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
drove to Charlie Badami's house. (He is currently
the clubmaker for Virtual Dunes and the Metedeconk National Golf Club,
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
three driver shafts he wanted to profile:
- Harmon Tour Design HTD CB-60.350 (S flex)
- Apache/MCC MFS-65 (R3 flex)
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". |
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.
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
|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. |
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
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."
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.
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
(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
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. |
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
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
3.1 - A few interesting shafts
This plot shows a few things:
- I had an MFS-65 (R3 flex) in my own basement. I
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
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 manufactureOne
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
"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
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
all other measurements I took). The wildest data points were only 2%
differences, and only at two points. All the other data points were
identical, given the measurement precision of the NF4.
3.3 - Different models from the same manufacturerAgain
looking at Mercury shafts, I profiled three
different models of driver shafts. Mercury characterizes them as
I had already done some golfer testing to compare 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
difference in results.
- The Performance is an "entry level" shaft.
- The Savage is an ultralight, low-torque shaft.
Pro-Kevlar has a kevlar-stabilized tip; it's the one their
long-drive tour guys use.
The graph tells the story. Starting with the same butt
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
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
is fairly similar to the Pro-Kevlar in profile, though the Pro-Kevlar
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
frequency profiling beam length. They are similar but not the same,
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
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
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:
757 Regular: 180 210 242 290
365 508 855
Regular : 176 196 233 285 362 515
Stiff : 185 207 241 296 384 545
ahead and made up a spreadsheet with these
numbers. Here is the resulting graph.
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
finally -- this way of reducing and displaying the data is
as useful for a frequency profile as for a deflection profile.
4.2 - Sources of errorFrequency and deflection are somewhat different in the way
to the stiffness of the shaft. Most notably:
The consequence is that deflection shows twice the variation
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:
- Deflection is inversely proportional to shaft
- Frequency is proportional to the
square root of stiffness.
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.
- For iron shafts (~300cpm), a 1cpm difference
corresponds to a
0.7% difference in stiffness or in deflection measurement.
driver shafts (~250cpm), a 1cpm difference corresponds to a
0.8% difference in stiffness or in deflection measurement.
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
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.
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
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
Future work includes:
Those who wish
to help in these
efforts are most welcome.
- Choosing a baseline shaft profile for a "neutral
- Relating NF4 beam lengths and
frequency beam lengths.
- Lots of actual profiling.
- Making available a profile library or data base.
Appendix A - Normalization formula
The normalization formula is actually pretty easy, and easy to
implement in a spreadsheet. In the equations that follow:
The computation for the spreadsheet consists of two stages:
then from B[i,x]
is an index for the shafts being profiled. The "standard" shaft is i=0, and it
by one for each successive shaft.
is the position along the shaft. For the NF4 profiles in this article,
x ranged from 19" to 44" at 5" intervals.
is a raw reading.
is a reading normalized to assume the same butt stiffness for all
shafts being compared.
is the high-information reading that we graph as "the profile".
= A[i,x] / A[i,butt]And that's all there is to it.
B[i,x] / B[0,x] ) - 1
B - Excel
You can download your own copy of the spreadsheet to play with. Just
click on this link.
- 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.
can enter the names for your shafts in the first table, and
they will show up in the other tables and the graph.
are updated as you enter the data.