How Shafts Bend

Dave Tutelman -- January 25, 2014

This is just the beginning of a long article I have in the works on shaft bend. I hope to complete it sometime in 2014. But let's start it with a little-known fact about shaft behavior.

The Question[s]

When I started looking at ShaftLab traces fifteen years ago, a question occurred to me that bothered me for months -- probably a year. It seems a bit too abstract to be interesting when stated straight out: When a flexed golf shaft rotates around its axis, does the bend rotate with it?

But it's really not abstract at all if you are trying to understand how a shaft reacts to a swing. Let's look at a swing and see why it is interesting. Here is a ShaftLab trace for a representative professional swing.

The exact shape is a "signature" for the swing, but some features are shared by all good golf swings:
  1. For the first half of the downswing, the shaft exhibits a toe-up bend. I admit I chose this particular swing for purity of the toe-up bend. But all the professional swings I've seen have a large, predominantly toe-up bend for the first half or more of the downswing.
  2. At impact, the shaft is bent toe-down ("D" on the graph).
  3. At impact, the shaft is bent in lead ("C" on the graph).
Other stuff happens between the midpoint of the downswing and impact, but #1, #2, and #3 are all pretty unmistakeable in all decent golf swings.

Now a question: Which bend at impact might be due to rebound from the large toe-up bend: the toe-down bend or the clubhead lead? Most people faced with this question feel that toe-down is the rebound from toe-up. How could lead-lag bend possibly be involved?

Before answering the question, allow me to point out that the two highlighted questions above are the same. Remember, the shaft rotates 90 from the top of the backswing to impact. That means while the early toe-up bend was in the swing plane, the toe-down bend at impact is across the swing plane -- and the clubhead lead is in the swing plane. Therefore:
  • If the flex rotates with the shaft, then toe-down bend might be a rebound from toe-up bend.
  • If the flex stays in the same plane no matter how the shaft rotates, then leading bend might be a rebound from toe-up bend.
Note: I have been careful to say "might"! I don't know if either #2 or #3 actually is a rebound effect. That's a question for another day.

The Answer

Sometimes analysis is the way to answer a physics question. When I first thought about the question, I tried thinking analytically. It took a while -- months, in fact -- to convince myself. I did come up with the correct answer.

But sometimes a good old experiment will do the job better, more easily, and more convincingly. So let's make this a lab course. Here's a video of the experiment I did in my basement.

This demonstrates pretty conclusively that the shaft flex remains in the plane it was, rather than rotating with the shaft.

The obvious corollary is that the lead bend at impact might be due to rebound from the toe-up bend, but the toe-down bend cannot be. That is because the lead bend is in the same plane as the toe-up bend, even though the shaft has rotated 90 in the interim.

Sidelight: I realized I would need some sort of indicator to show rotation on the video; the shaft and the chuck were circular in section and polished, so you could not see rotation. I had trouble finding the drinking straws in the kitchen, and asked my wife where they were. She said, "Well you don't drink with them. Are you doing some sort of science experiment?" I guess after 47 years living together, people get to know one another.

The Explanation

For readers who are analytically inclined, Here is my cut at why shafts behave this way.

 When the shaft is flexed, what is holding it in position are inertial forces (the weight at the tip and the hands or a clamp at the butt) countered by spring forces in the shaft itself. None of the shaft bend is a permanent deformation; it is simply a spring reaction to the inertia of the mass at the tip.

When the shaft is rotated, it obviously rotates the mass at the tip. (See Figure A.) The rotation at the butt exerts torque on the shaft, which is transmitted the length of the shaft and rotates the weight.

But can the shaft exert a force to move the mass laterally around the butt's axis, so the bend itself rotates? (See Figure B.) Well, it could if it were permanently bent, but it is not. As noted above, it is held in bend by spring forces and inertia of the tip weight. The mass wants to say where it is, or move in the direction it is already moving. The spring force simply wants to restore the shaft to straight along the butt axis. In order for the bend to rotate, there would have to be a considerable force (labeled "???" in Figure B) perpendicular to the plane of the bend -- and around the butt axis. I can't think of a single mechanism to transmit that sort of force down the shaft.

Even if you don't accept this explanation, there is no arguing with the answer to the original question. That has been shown unequivocally in the lab.

Last modified -- Jan 26, 2014