All About Spines

What spine is -- and isn't

Definitions

• 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.

The mechanics of bend

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.

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: The spines (directions of maximum stiffness) are two in number and 180º apart from each other. The NBPs (directions of minimum stiffness) are two in number and 180º apart from each other. The NBPs are 90º 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

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 25º-55º for a driver, and about 5º 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.