NF4 Load Reading and
Frequency
Dave Tutelman -- March 19,
2006
Executive Summary
The stiffness of a golf shaft can be represented as:
- A spring constant (the load required to produce a
deflection divided by the size of the deflection) , or
- A frequency (the rate of oscillation when the shaft is
clamped, then plucked with a mass on the tip).
For most of the past decade, clubmakers have used frequency
to talk
about the stiffness of a shaft. In the last couple of years,
instruments have become available to measure the deflection spring
constant instead. The
NeuFinder 4 (NF4) is one such instrument. Others
include the GolfMechanix
Auditor, the MCC/Apache Multi-Match,
and the Flexmaster. With the
advent of these machines, there is a need to be able to relate the
flex readings to the more traditional frequency numbers.
This article is an estimate of the relation between the reading of an
NF4 and the butt frequency of a shaft, based on measurement of quite a
few shafts. The frequency was measured as a butt frequency in cycles
per minute (cpm), using a 5" clamp and a tip mass of 205 grams for
woods and 255 grams for irons. The NF4 readings were taken at the
conventional settings for matching clubs: 38" for woods and 32" for
irons.
The important results are:
- The relationship between a Kg change
in NF4 reading and a cpm change in frequency. One
cpm difference in stiffness corresponds to a change of:
- 0.036Kg on the NF4 for woods.
- 0.047Kg
on the NF4 for irons.
- An
estimator to convert between frequency and NF4 reading. This
is provided both as equations and graphically, which are not being made
availabe in the summary. You are going to have to read the details for
that, because you need to know the limitations and proper use of this
conversion.
Details
A number of shafts were measured using both the NF4 and a frequency
meter. The sample was larger than the seven wood shafts and eleven iron
shafts used for the data. But many of the shafts were the same model
and same nominal flex, and I didn't want small numbers of nominally
identical shafts dominating the data. So one or a few representative
shafts from each of these identical populations were used to obtain the
results. (When I get data from more diverse shafts, I will update these
results as needed.)
Frequency was measured at full length. The specifics are
given in the
table below. Wood shafts were assumed to be 46" full length, and iron
shafts 41". Where shaft samples did not meet these specifications, they
were clamped so that the beam lengths were as indicated in the table.
(For instance, a 40" iron shaft would have been clamped for only 4" of
its butt, so it would still be measured at a 36" beam length.)
Frequency
Measurement Parameters
|
Woods
|
Irons
| Total shaft length
|
46"
|
41"
|
Clamp
length
| 5"
| 5"
|
Beam
length (total length - clamped length
| 41"
|
36"
|
Tip
weight
| 205 grams
| 255 grams
|
NF4 load was measured at the normal beam
length for matching clubs: 38"
for woods and 32" for irons. Therefore, the measurement represented
more of the upper midsection of the shaft, and less of the butt, than
the frequency measurements.  The
results for the wood shafts are shown to the right, in the form of both
raw data points and a straight-line estimator. A few notes about the
graph:
- The straight line was computed
to give a least-square-error fit to the data.
- I
used Excel '97 to do the computations and generate the
graphs. Its graphing capability seems to require that zero be in the
graph for each axis. In order to keep the size up on the part of the
graph we are using, I started frequency at 200cpm and flex at 2Kg.
- The estimator is not terribly good, in that the data points
may lie some distance from the straight line. For instance, more than
one point lies 10cpm from the line.
- On the other
hand, the slope of the line is pretty robust. The standard error for
the slope was quite small.
What can we learn from this? The slope, which is a good estimator, is
really the number that does us the most good. We may need it in order
to set a tip trim load interval for the NF4. We also need it in order
to compare the accuracy of our readings to those of a frequency meter.
So we have a good estimator for our most important needs.
| But
what if we need to estimate the actual
frequency from our NF4? Is there any way we can do that? Since the
first step to fixing a problem is understanding it, let's see if we can
figure out why the straight-line estimator is not very good.
As mentioned before, the frequency is taken with most of the
contribution coming near the end of the clamp, at 41" from the tip. The
NF4, on the other hand, is measured at a beam length of 38", with most
of its contribution coming 30-34" from the tip. So it is measuring more
of the upper middle of the shaft, compared to the frequency meter's
butt measurement. Since different model shafts have different profiles,
measuring the same stiffness at 31" will not assure that the shafts
have the same stiffness at 41". So we would expect a 31" reading to be
only somewhat related to a 41" reading, rather than being tightly
locked in their relationship. We might hope for a tighter best-fit line
for samples of a single model of shaft, or for shafts with a similar
profile. And, based on a small experiment involving samples of the same
model in different flexes, we see that result.
 Which is better,
the butt frequency or the upper-mid flex? A good argument can be made
for either. But suppose we really need to estimate the shaft's butt
frequency, and all we have is an NF4. Can we get a more reliable
estimate?
The answer is yes. If the problem is that we are measuring too far from
the butt, the NF4 can measure much closer to the butt of the shaft. It
can get to a beam length of 44" on most raw stock wood shafts, which is
6" closer to the butt. The graph on the right shows the same shafts,
also measured with the toggle board in matching position but now with a
beam length of 44". (The new measurements are the purple data.) Note
that the longer beam gives a closer estimator, with all the data points
within 5cpm of the line.
So, if you really need to estimate the butt frequency of a shaft using
your NF4, take a reading at a longer-than-normal beam length and use
that reading for estimating frequency.
|
 Here
is the comparable graph for iron shafts, showing the same effect. But
the effect is not as pronounced; the estimators are a better fit to the
data than the the wood shafts were. That is probably because there is
less variety of profile shape in iron shafts than wood shafts.
|
Now that you have seen enough so you know how to interpret the results
-- and how you could get into trouble using them blindly -- here is a
table of all the statistical analysis.
|
Woods
| Irons
| matching
length
| full
length
| matching
length
| full length
| NF4
beam length
| 38"
| 44"
|
32"
|
39"
|
Trim
sensitivity conversion
(in Kg per cpm) 1
|
.036
|
.022
|
.047
|
.032
|
Graph useful
for conversion 2
| | |
Formula:
Frequency to Load
| .0356 F -
4.87
| .0224 F -2.39
|
.047 F
- 7.22
| .0322 F - 4.55
|
Formula:
Load to Frequency
| 28.1 L + 137
| 44.6
L + 107
| 21.3 L + 154
|
31.1 L
+ 141
| R-squared
(goodness of fit) 3
|
0.84
|
0.93
|
0.92
|
0.98
|
Notes:
- The slopes differ depending on the beam length.
This means that,
if you decide to do shaft matching at something other than the nominal
beam length, you will need to adjust your load slope.
- These are larger copies of the graphs, complete with
gridlines, to use in converting between frequency and NF4 load.
- The R-squared value measures how well the straight-line
estimator
matches the data. A perfect match is 1.0, and a useless estimator is
0.0. Note that our full-length estimators are more than twice as close
to perfection as the matching-length estimators. That is a strong hint
to measure at full length if you want to convert to frequency.
Here's another important caveat for using these results.You
can't just use these numbers to map frequency to NF4 readings in order
to trim a set of irons. The data here refers to raw shafts (their
original length) with constant tip weights. It's what you might do
(with a frequency meter) to evaluate the shafts before you start to trim. Think of it as what you do with your NF4 to evaluate the shafts and decide which shaft to assign to which iron.
Remember that frequency readings can serve two very different purposes.
It is a way of numerically quantifying a shaft's stiffness.
Alternatively, it is a way of quantifying a club's stiffness. Those two
goals, though related, are not the same!
This article deals with the first purpose. If you try to use these
estimators for the second purpose, you will probably come to grief.
Last modified -- 1/27/2016
|
