Finding Spines with a Non-Differential
Dave Tutelman -- Feburary 5, 2011
article describes a
way to accurately find the spine of a shaft, using instruments like the
GolfMechanix Auditor, the NeuFinder 2, or the Apache Multi-Match, which
were never designed to do differential deflection.
In everything I have written on the subject for more than a dozen
years, I have cautioned that the usual instructions for finding spines
will generally give bad answers, and aligning shafts to these bad
answers will not be helpful. Specifically, bearing-based spine finders
give bad answers, as do even well-made and precise deflection meters, unless
the process used involves differential deflection. Rather
than rehash what that means here, let me refer you to my article "All About Spines",
especially the chapters on bearing-based
spine finders and differential
morning I received email from Hans Brunner, a retired Swiss engineer
turned clubmaker. He has a GolfMechanix Auditor
that he uses
to characterize shaft flex. (That's a picture of the Auditor at the
left. Ironically, it is the same picture that I used in the article on
spines, where I cited it as an example of an instrument that gives wrong answers.)
asked why the spine he found did not match what the theory demanded. He
said he used differential deflection, blocking the bearing wheels so
they acted more as a V-block, thus holding the shaft at the rotation he set.
Then he inserted spacers so that the deflection differences would be
the same at each angle. He even measured twice, once with a small (4mm)
spacer and again with a larger (10.5mm) one. Let's look at the result.
theory says that, going around the shaft, you see spine-NBP-spine-NBP
at 90º intervals. The stiffness profile looks like a sine wave where a
full rotation of the shaft gives two cycles of the sine wave.
in the graph at the right, were roughly sinusoidal, but only one cycle of the sine wave through the full shaft rotation.
I immediately wrote back that the curves look like:
- The measurements were not done with differential
deflection. That is, the shaft was not preloaded and tared before
inserting the spacer. That would cause the measurements to revert back
to a naive feel-finder-plus-load-cell. It may be numerically precise, but it does
not give a reasonable position for the spine unless the shaft is very
straight -- no residual bend at all.
- This shaft had enough residual bend to completely
swamp out any spine that existed. The single-cycle behavior is what Bill
Day calls "Type 1", and is entirely an artifact of the shaft's residual
bend. In this case, it totally masked any actual spine in the shaft.
occurred to me that there is probably enough information in the data he
sent (in the form of an Excel spreadsheet) to do a differential
deflection analysis and find the spine. The reason is that he
had taken two passes. Each was a naive pass (that is, not
differential), but there are two, comparable passes. Suppose we use the
small-spacer curve as a "tare" and subtract it from the large-spacer
curve? If we do that, here is what we get.
The green curve is the result of subtraction. The things to note about
- There is very little variation. That means that the
actual spine is quite small.
- What variation there is seems to be a double cycle
rather than a single cycle of a sine wave. It looks like we should expect
a spine profile to look.
Let's "magnify" the variation of the green curve by subtracting out its
average value and plotting it again. The result is below.
This is what a spine profile should look like. Visually, we have:
perfect spine profile (that is, exactly 90º between "singularities")
would differ only in that the first spine should be at 40º instead of
30º. This is truly remarkable fidelity to the theory, considering that
subtraction of measured data tends to be a very "noisy" process. (That
is, it magnifies any errors in the measurement.)
- A spine at about 30º.
- An NBP at about 130º.
- A spine at about 220º.
- An NBP at about 310º.
It is worth dwelling on this graph for a bit. Points to ponder:
conclusion is that it is important to learn this procedure if you
intend to use your deflection instrument to find spine. Not doing so
will tell you that you have a much bigger spine than the shaft actually
has, and will give you an orientation quite different from the
shaft's actual spine. So using the naive procedure instead of this one
is worse than useless. Trusting a wrong answer is almost always worse
than knowing you have no answer.
alternative method of doing differential deflection is very effective.
It doesn't lose anything by not having an instrument designed for the
- The only drawback is effort. You must record all the
readings and then do arithmetic, instead of using a zero-tare button to
eliminate half the readings and all the calculations.
- The shaft
in question has a relatively small spine. Measured in deflection, the spine is
only 2% of the total deflection. (Peak to peak 40 grams out of a load of about 2000g.) That would be comparable to about 3cpm of
frequency, if you are used to thinking about spine magnitudes in cpm.
- On the other hand, the residual deflection of the shaft -- which is not spine and should not be aligned -- masquerades as a very large spine. It looks like 7% of the deflection for the large spacer, and 15% for the small spacer.
your instrument (Auditor, Multi-Match, etc) to a substantial
deflection, so you get a good, solid load reading. This exact
deflection should be used for all the measurements taken in step #2; do
not touch the deflection again until step #3.
the load at intervals around the shaft. (I prefer a 10º interval. Hans
chose a 20º interval, which is not too bad.) Record all the
- Now reduce the deflection on the instrument to give about 20% of the original load. The exact amount is not critical, but this same deflection should be used for all the measurements taken in
step #4; do not touch the deflection again.
step #2, taking and recording all measurements around the shaft. The
measurements should be at the same stations you measured in step #2.
- For each station around the shaft, subtract the small load reading from the large one.
the results from step #5. Looking at the graph should tell you where
the spine and NBP is. The peaks are spines and the valleys are NBPs.
A Few Final PointsI
have prepared an Excel spreadsheet to do the calculations. All you have
to do is enter the large-load and small-load readings. To download the
spreadsheet, click here.
data is an excellent test of the method. However, I took it upon myself
to test a couple of the shafts in the original article on spines. (I
used my NF4 in "naive mode"', not bothering to pre-load and
tare.) The method and the
spreadsheet worked very well for them, too.
let me remind you that, although you can now use differential
deflection to find the spine, such naively designed instruments are
still subject to errors in measuring overall flex (for shaft trimming)
and flex profiles (for shaft selection). Those errors are not a problem
for an instrument that does differential deflection by design, like the
NeuFinder-4 and -9, and the FlexMaster. Such problems, caused by
residual bend, shaft tapering, shaft steps, and grips on completed
clubs, are not readily solved by instruments like the Auditor or the
Multi-Match, but are handled automatically by differential deflection
on the NeuFinder-4 and -9.
Last modified -- 2/7/2011