All About Spines

What spine is -- and isn't

Definitions

Let's start by an explicit definition of what spine is -- and a careful statement of some things it is not. Here is my definition:
Generically, spine in golf club shafts is the directional variation of stiffness.
More specifically, the spine is the direction of greatest stiffness of the shaft.


Since shafts cannot be built perfectly symmetrically, every shaft will be stiffer (more resistant to bending) in some directions than in others. This difference may be too small to be measured, or -- even if detected -- too small to make a practical difference. But, given imperfect fabrication, the difference will exist.

That does not sound like a very radical definition. But the ramifications that follow from it were widely misinterpreted. Because of the way the spine's direction was typically determined, the discussion of shaft spines since the 1990s has been loaded with misconceptions. For instance, Bill Day has done a terrific job in codifying the description and terminology of measured spine in a shaft. Unfortunately, almost everything in the document is based on notions drawn from experience with instruments that do not properly measure the spine. So it turns out that most of Bill's document is unnecessary. All shafts, if they are measured for true spine as I defined it above, are what Bill calls "Type 2" shafts. But most of the document deals with characterization of things only found in Type 1 and Type 3 shafts -- which are artifacts of a common but generally incorrect measurement technique.[1] This will be explained in more detail later, where we compare the spine found by feel finders with those found by FLO.

Having said that, it is important to note what spine is not:
  • It is not some obvious physical characteristic, like welded seam of steel shaft. Actually, the name "spine" originally came from the belief that, since most steel shafts were welded tubes, the seam created an asymmetry in stiffness. But the welding seam isn't the only cause of spine, nor even the major cause. We won't worry yet about what causes it. First, let's concern ourselves with the implications of the fact that shafts have spine. That is the important thing for clubfitters, not how the shaft got that way. But later we'll briefly look at the cause of spines in shafts.
  • It is not residual bend. Just as it is impossible to manufacture a perfectly symmetrical shaft, it is impossible to manufacture a perfectly straight shaft. Some shafts are straighter than others, just as some shafts are more symmetrical in stiffness than others. The bend of the shaft at rest -- with no flex forces on it -- is called the "residual bend". Why do we worry about this? Because much of what is widely believed about spine is due to measuring instruments that misinterpret residual bend as spine. We'll see this in a later section. And we will spend a lot of time discussing how Day's various shaft type nomenclature is really a distinction based on residual bend more than spine.
Since Bill Day did such a good job of creating terminology, let's adopt another of his terms. (Actually, we're adapting rather than adopting. Our definition is in the spirit of his, but not based on the misleading instrument that measured it.)
Natural Bending Position (NBP) is the direction of least stiffness of the shaft.

So we are left with the term "spine" for the stiff direction and "NBP" for the flexible direction of a shaft.

Let's finish with a definition of the size of the spine. Remarkably little of the discussion of spine alignment addresses the fact that there are big, serious spines and then there are spines that are probably too small to matter.
The size of the spine in a shaft is a measure of the difference between the stiffness at the spine and the stiffness at the NBP. It can be measured in CPM or in percentage difference of spring constant, depending on whether your measuring instruments use frequency or deflection.

1cpm of frequency or 1% of spring constant is a small or even negligible spine. 10cpm or 8% is a rather large spine. The work has not been done to quantify where, between these numbers, is the "threshold" of spine importance, but it makes no sense to talk about aligning spine without also talking about the size of the spine.

The mechanics of bend

Spine is about stiffness. And stiffness is about bend. If the shaft isn't bending, then the spine is having no effect on anything.

So we need to understand what happens in a shaft when it bends. The field of Engineering Mechanics deals with bending and flex. The golf shaft is a beam, flexing in response to forces imposed on it at the grip (forces and torques transmitted from the hands to the grip) and the tip (inertial forces from the clubhead). The result is a "bending moment" that will try to curve the shaft in one direction or another.

When a bending moment causes a beam to bend, the edge of the beam at the outside of the curve is stretched a little longer, and the inside edge is squeezed a little shorter. Since shaft materials are "elastic" (technical terminology that means they act as a spring), the material at the outside edge is in tension (just as if you were pulling on the shaft) and the inside edge is in compression. Looking in a little more detail...

Almost all the material in the beam gets some stress (internal force) from the bend. There can only be one plane through the beam that isn't either longer or shorter than it was before the bend. Engineers call that the "neutral plane"[2]. Every fiber of material above the neutral plane in the diagram (that is, toward the outside of the bend) is longer than it was at rest, and is therefore in tension. Below the neutral plane, the material is in compression.

Quantitatively, the further from the neutral plane we get, the greater the tension and compression. The blue triangle represents the amount of  tension at various distances from the neutral plane, and the red triangle the amount of compression. The shape is a triangle because the amount of elongation or shortening is directly proportional to the distance from the neutral plane; that's just geometry.

The sizes of the triangles keep the tension and compression in balance.They have to stay in balance if the shaft is not to come apart into a lot of little pieces. The forces and moments of tension, through the cross section, have to equal those of compression.

This description works just fine if the beam has a symmetrical cross-section, like a perfect golf shaft. But this article is about spine, which is what happens if the symmetry is not perfect. What happens then?

Let's take an extreme example, shown in the diagram. Suppose the old Apollo advertising campaign had been correct, and a welded shaft had a big extra "bead" of steel down seam on the inside of the shaft. How would a shaft like that react to bend?

Most people's first intuition says that the shaft just became a lot stiffer if you try to bend it downward, away from the added stiffening material. On the other hand it would only be very slightly stiffer than it was before if you bend it upward. The result is a serious spine, with the shaft much stiffer to bend downward than upward.

That is certainly what I would have thought before I took an Engineering Mechanics course, and it is the immediate reaction of most clubmakers I have talked to.

But that is not what actually happens. Not even close.

What happens is the neutral plane moves. It repositions itself so that the material is better balanced on either side of it. In the picture, the shaft is bending downward. The tension triangle is smaller and the compressive triangle larger. But, since there is more material above the neutral plane than below, we don't need as much tension in each grain of the shaft in order to give a total force balance above and below.

And suppose we bent the asymmetrical shaft upwards? The neutral plane stays in the same place as it did with the downward bend, but the red and blue triangles exchange colors. The small triangle on top is compression and the larger triangle on the bottom is tension.

What this means is the stiffness is exactly the same whether we bend it upwards or downwards. The welding bead will make the shaft stiffer overall in the up/down plane than it was before, but it is just as stiff upwards as it is downwards. True, we have introduced a spine.We have made up/down stiffer than right/left. But we have not made down stiffer than up or vice versa.

This brings us to a few rules for how the spine and NBP distribute themselves in a shaft. These rules come from engineering textbooks[3] that have been around a long time. The rules work just fine on the worst-spine golf shaft you will ever find; in fact, they work on much more asymmetrical beams than any golf shaft.

The stiffness of the shaft in any direction can be represented as an ellipse. (No, the shaft cross section does not have to be an ellipse. It can be anything at all. The stiffness curve is an ellipse.) This leads us to the rules, which apply as long as the shaft has enough asymmetry that you can measure spine at all:
  1. The spines (directions of maximum stiffness) are two in number and 180 apart from each other.
  2. The NBPs (directions of minimum stiffness) are two in number and 180 apart from each other.
  3. The NBPs are 90 away from the spines.
This is a remarkable result -- and very different from the measurements that led to Bill Day's terminology article. This says that every shaft is a Type 2 shaft. If your measurement tools tell you differently, then your measurement tools are wrong. (We'll see later why they are wrong.)

How golf shafts bend during a swing

Once again, let's remind ourselves that spine only means something if the shaft is bending. When the shaft is straight, the spine has no effect on anything. We just looked at what happens inside the shaft when it bends. Now let's look at the bend behavior of the shaft during a swing.

First off, the shaft bends in different planes. Part of the reason for that is that the swing plane (which is ideally a slanted version of the "target plane") is not the same as the reference planes of the club. The club has a heel-toe plane which is perpendicular to the "face-back" plane. In fact, the club planes and the swing plane change their relationship completely during the downswing.

A few pictures (from Jack Nicklaus' book "Golf My Way") to show what I mean...

At the start of the downswing, the club's heel-toe plane (green line) is aligned in the same direction as the swing plane (blue line).

At the moment of impact, the clubface has squared and the face-back direction is aligned with the swing plane.

With all this complication, how can we possibly characterize enough about shaft bend to be useful? An instrument called ShaftLab can be used to measure the actual shaft bend in the club-referenced planes during the downswing. For instance, here is a "polar" trace showing the direction and magnitude of the shaft bend during Greg Norman's driver swing (circa the late 1990s). The blue numbers at each data point on the curve refer to the number of milliseconds before impact of clubhead and ball.

It turns out, of course, that everyone's swing is different. But here are some worthwhile generalities about shaft bend during the swing:
  • The largest bend occurs while the wrists are just beginning to uncock. Most of this bending occurs while the heel-to plane is still fairly well aligned with the swing plane, so this maximum bend is not far from the direction of the heel-toe plane.
  • In the vicinity of impact, the bend is a lot less less. That means that any spine effects are likely to be greater earlier in the downswing, unless there is some physical reason to assign more importance to proximity to impact.
  • Near impact, much of the bend is out of swing plane. Much of the reason for this is "toe droop". Bend near impact is a combination of toe droop (out-of-plane) and in-plane "rebound" from the early in-plane bend. The angle of the total bend from in-plane depends on the golfer. Tour pro swings exhibit angles of 25-55 for a driver, and about 5 more for an iron.

This is still too vague, and too variable from golfer to golfer, to support a detailed analysis of how spine affects the golf swing and vice versa. But it is enough to at least evaluate the plausibility of the various theories of shaft behavior. And we will do that later.


Notes:

  1. In February 2008, Bill posted on the Spinetalker's forum, "For the moment, I find Dave's article misleading, and it contains several errors. Dave, I can use this forum or private e-mail to discuss the errors that need correction, but at the moment I would suggest that you remove the article from your web site until corrections have been made." Bill and I exchanged more than a dozen emails over the following five days, and found ourselves no closer to agreement. Most of our disagreements stem from two very fundamentally different beliefs:
    1. Bill believes that every shaft needs to be spine-aligned, no matter how small the spine. I do not.
    2. I believe that just about every shaft that does not behave as "Type 2" (in Bill's nomenclature) can be explained by residual bend. Bill does not.
    Both these controversies will become more clear later in this article. Since I do not agree with the fundamentals underlying Bill's views, I cannot call them "errors" and will not withdraw the article.
  2. Please don't confuse "neutral plane" with NBP, which stands for "natural bending position". I have seen NBP called "neutral position" or even "neutral bending plane". Regardless of what you call it, it has absolutely nothing to do with the neutral plane. Neutral plane and NBP are competely unrelated concepts. Neutral plane is the plane inside the shaft where the tension and compression cancel to zero. NBP is the direction of least stiffness when you bend the shaft.
    And please don't blame me for the confusion. NBP is relatively new terminology, around since about 2000. Neutral plane has been in engineering texts since well before I went to college in 1958.
  3. I have seen this proved mathematically in S. Timoshenko's classic 1930 engineering text, "Strength of Materials - Part 1" Van Nostrand, 1930. See Appendix V for the proof. If you want something more recent, try R. C. Hibbeler, "Engineering Mechanics: Statics and Dynamics", Macmillan, 1983. See Sec. 10.7 - Principal Moments of Inertia.
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Last modified -- 2/23/2008