Finding Spines with a Non-Differential Instrument

Dave Tutelman -- Feburary 5, 2011

This 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 deflection.

This 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.)

His note 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.

The theory says that, going around the shaft, you see spine-NBP-spine-NBP at 90 intervals. The stiffness profile looks like a sine wave where a full rotation of the shaft gives two cycles of the sine wave.
Hans' measurements, shown 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.
Then it 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 it are:
  • 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:
  • A spine at about 30.
  • An NBP at about 130.
  • A spine at about 220.
  • An NBP at about 310.
A perfect spine profile (that is, exactly 90 between "singularities") would differ only in that the first spine should be at 40 instead of 30. 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.)

It is worth dwelling on this graph for a bit. Points to ponder:
  1. This alternative method of doing differential deflection is very effective. It doesn't lose anything by not having an instrument designed for the purpose.
  2. 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.
  3. 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.
  4. 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.
My 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.

The Procedure

  1. Set 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.
  2. Measure the load at intervals around the shaft. (I prefer a 10 interval. Hans chose a 20 interval, which is not too bad.) Record all the measurements.
  3. 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.
  4. Repeat step #2, taking and recording all measurements around the shaft. The measurements should be at the same stations you measured in step #2.
  5. For each station around the shaft, subtract the small load reading from the large one.
  6. Plot 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 Points

I 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.

Hans' 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.

Finally, 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