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.

## 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.)

 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

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:
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.