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:
  1. 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.
  2. 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.


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

Total shaft length
Clamp length
Beam length (total length - clamped length
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.

full length
NF4 beam length
Trim sensitivity conversion
(in Kg per cpm) 1
Graph useful for conversion 2
Click here
Click here
Frequency to Load
.0356 F - 4.87
.0224 F -2.39
.047 F - 7.22
.0322 F - 4.55
Load to Frequency
28.1 L + 137
44.6 L + 107
21.3 L + 154
31.1 L + 141
(goodness of fit) 3

  1. 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.
  2. These are larger copies of the graphs, complete with gridlines, to use in converting between frequency and NF4 load.
  3. 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