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Nesbit or Kwon or MacKenzie?

Dave Tutelman -- October 24, 2018

I really believe it's Jacobs and Manzella vs the bulk of the biomechanics research world. Jacobs and Manzella are backed by Steven Nesbit, but Nesbit hasn't participated in the debate. Here are the technical issues as I see them.

My favorite swing modelers are Doctors Young-Hoo Kwon, Sasho MacKenzie, and Steven Nesbit. All three are college professors, Kwon and MacKenzie in biomechanics and Nesbit in mechanical engineering. I have huge respect for all three.

So it pains me a bit to see a rather fundamental technical issue where they are on opposite sides of the question. Let me detail what the dispute is, and present where I stand on it and why.

The papers

The main sources of information in the discussion are three papers, two published papers by Nesbit and one tutorial posted on social media by Kwon. The links may or may not work by the time you get to try them. I have had links to some of these papers fail in the past, and I had to find them again under new links. I will quote sections of the papers and use pictures from them, but by all means use the links if you want to see them in context.

Nesbit - Work and Power

Steven M Nesbit & Monika Serrano, Work and Power Analysis of the Golf Swing, Journal of Sports Science and Medicine, Dec 2005.

This paper is focused more on the mechanical work done to the club than on the equations of motion. It is an inverse dynamics study of the swings of four golfers. Of course, the equations of motion must be invoked on a body model in order to get the forces and torques needed to calculate work. But very little of that is reported in the paper; the results tend to be the work and the power. (Power is the first derivative of work.)

But there is a graph of torque in the paper. It plots "alpha swing torque" against time for each of the four golfers. What does that mean?

Torque is a term from physics indicating an angular (or twisting) "force". I'll assume here you know what a torque is, or can look it up in a physics tutorial.
Alpha refers to the club's motion in the swing plane. By comparison, "beta" is angular motion perpendicular to the plane, and gamma is rotation of the club about the shaft axis. (Some refer to these colloquially as "in, out, and about" respectively.)
Swing torque is not defined in this paper, and that is a part of the difficulty here. Not the biggest nor most important part, but significant enough.

Nesbit - Swing Hub Path

Steven M. Nesbit & Ryan McGinnis, Kinematic Analyses of the Golf Swing Hub Path and its Role in Golfer/Club Kinetic Transfers, Journal of Science and Sports Medicine, Jun 2009.

In this paper, Nesbit and McGinnis explore the effect of the hand path on the ability to generate clubhead speed. This is one of the earlier papers to advocate "pull up and in, 'go normal'" to maximize clubhead speed. (Though not the first. The earliest one I know of is K. Miura, Parametric acceleration -- the effect of inward pull of the golf club at impact stage, Sports Engineering, 2001.)

Nesbit & McGinnis start off with a diagram and derive from it the classic equations of motion.

These three equations are pretty standard stuff. Equations (1) and (2) are F=ma in the X and Y directions. And Equation (3) is the angular analogy to F=ma, which is written τ=Iα. The equations and the explanatory text are screenshots from the paper, but I have highlighted some things to facilitate the discussion below.

One of the things we can get out of this is Nesbit's definition of "swing torque" -- and hope it is the same definition that he uses in "Power and Work". In this diagram, it is the "twist" that the hands apply directly to the grip of the club, shown as T in the diagram and the equations. Why is this an issue? Because equation (3) shows that there is a lot more to torque than just T. The torques one can talk about in just this one equation are:

T, Nesbit's "swing torque", which I have highlighted yellow. Physicists refer to this as a "couple", and so will I for the rest of this article. But Nesbit is hardly the only engineer to make up his own term for it. I'm guilty of that myself; plenty of my articles refer to it as "wrist torque".
The "moment of the force F" is just as much a torque as T. I have highlighted it in green.
The right side of the equation is the "total torque", the sum of couple T and the moment of force F. The total torque is highlighted in blue, and also bracketed in blue on the left side of the equation.

This set of eqations does a few worthwhile things for the discussion. It shows that Nesbit is using the same equations of motion as everybody else; any differences can't be due to that. And it very clearly defines what he means by "swing torque".

I have heard at least a few people dismiss this paper as, "Oh that's just two-dimensional." (The people I have in mind are Jacobs and Manzella, who apparently want to limit all discussion of Nesbit to "Work and Power".) What's wrong with 2D, if it's appropriate to the problem? The two dimensions are clearly intended (and even stated) to be the swing plane. Not vertical and not horizontal. If it were just a vertical plane, I'd also question its value, but a swing plane model is not to be easily dismissed. A few points here:

If the objective is to quantify out-of-plane motion, then you obviously need a 3D model. But if you are only worried about in-plane motion -- like clubhead speed at impact, or alpha torques -- then you're only interested in a 2D model, provided it doesn't have large errors due to out-of-plane wobbles.
If the plane of the analysis is the "functional swing plane", then non-planar behavior during the downswing does not affect it much. Any motion out of this plane by an error of e degrees introduces an error of only 1-cos(e). Things would have to get to 8° out of plane before the error in the analysis got to even 1%.
There is an error in the equations Nesbit has set up. I noticed it, and the fix is pretty easy. (Kwon also noticed it, and suggested the same fix.) The mg term in equation (2) should be mg sin(d), where d is the angle of the swing plane from horizontal. That is because the mg force is at an angle to the plane, not in-plane, unless the swing plane is a perfectly vertical 90°. Since gravity contributes only a small amount to the result, we can probably ignore this error for qualitative purposes.
Clearly Nesbit didn't think there was a problem with 2D models, even several years after he did the 3D "Work and Power" study. He and McGinnis did a follow-up, featuring optimization of the hand path, in 2014 -- long after the 3D "Work and Power" paper. See Kinetic Constrained Optimization of the Golf Swing Hub Path, Dec 2014. It sets up the same, identical equations of motion in two dimensions. Think about it; he did several 3D papers (not just "Work and Power") in 2005, then several 2D papers in 2009 and 2014.

Kwon - Tutorial from a Facebook discussion

There was a brisk discussion of a seemingly strange torque result, in the Facebook group for Golf Biomechanists. As part of the discussion, Young-Hoo Kwon posted a tutorial on the equations of motion and the result of their solution. He did it as a 3D model, with the diagram and equations shown here.

He set it up with three-dimensional vector notation. None of his primary planes is the swing plane. They are the ground plane and two vertical planes, one on the target line and the other perpendicular to the previous two. Note that gravity g is not just a scalar number, but a vector pointing straight down.

About the quantities in the dot notation... p is the linear momentum. Momentum is mv. Mass is constant and the first derivative (the "dot") of velocity is acceleration. So p dot is the same as ma. H is angular momentum, and the same argument holds about the dot.

While Kwon uses 3D equations of motion, he does not see a problem with the 2D in-plane model used by Nesbit & McGinnis, saying:

The 2-D model presented in the Nesbit & McGinnis paper is perfectly fine except the minor glitch in Eq. 2. But since the actual acceleration of the club is substantially larger than the gravitational acceleration, it won't make a huge difference and can be ignored.

The 3-D inverse dynamics method that I use has been used in biomechanics for centuries so it is a well-established method. There is nothing special or fancy about it. My Kwon3D software was first developed in 1990 and has been validated by many colleagues sufficiently. Both N&M's 2-D model and my general 3-D model yielded almost identical results. So the model is good.

"Almost identical results." The issue hangs on the "almost".

The issue

Well, what is the issue?

Swing modelers since Alastair Cochran in 1968 (The Search for the Perfect Swing) have concluded that a positive couple coming into impact is not helpful; in fact, it reduces the clubhead speed. Theodore Jorgenson (The Physics of Golf) further concluded that negative couple could increase clubhead speed. More recent modelers, notably Doctors Kwon and MacKenzie, have identified a negative torque when they modeled the full swings of good golfers.

Looking at the torque graph from "Work & Power", we see a torque that can go either way. Of the four golfers, two have a positive torque, one a negative, and one just about zero. Actually it is slightly positive, but might just as well be zero. Jacobs has said once (quite a few years ago; I don't know if it is still his position) that a positive torque is more usual than negative.

Something "does not compute" here.

Terminology

My guess was that there was a disconnect about what Nesbit meant by "torque" in Figure 11 of "Work and Power". That is because the torque curves looked about right for total torque. Remember, his definition of "swing torque" is in a different paper altogether. I had assurances several times from Brian Manzella that Nesbit was using the term identically in both papers. What finally convinced me he was right was something he said that initially made no sense at all to me. It was in answer to a question asked by Michael Finney (I will paraphrase to keep the terminology as consistent as possible), "If by torque he means the couple, then what is the moment of the force doing?" Manzella read the answer that Nesbit had emailed him as, "It's in the linear." My reaction was, "Huh?!? What does that mean?" Finney, whose audio was still on, asked essentially the same thing. The best Manzella could respond was to point to the email and say, "He says it right here!" Obviously none of us had a clue what Nesbit was actually saying.

Let me digress a moment to explain why this should not make sense. Torque is about angular, and is measured in things like degrees, radians, etc. Linear is measured in things like inches, meters, etc. You can't convert one to the other, because they are units of different things, just like there is no factor to convert grams to miles. So it makes no sense to say that the torque (angular) was absorbed in the linear. Maybe force? Maybe distance? What? And how?

But when I thought about that answer for a bit, something occurred to me. The paper in question is about work. Energy! Measured in Joules, or BTUs, or kilowatt-hours. And energy can be linear (a force times a distance) or angular (a torque times an angle), both measured in the same units. He probably meant that the energy represented by the force, including the moment of the force, was included in the linear energy -- which is measured in the same units as angular energy.

Let me bring back Nesbit's free-body diagram from the hand path paper and make a few changes to it. (My changes are in color so you can keep track of them.)

I have added the velocity vector V and its x and y components V_x and V_y. I have also highlighted points A and G. We'll see why below.

There is a practical difference between computing motion and work:

When computing motion, it is most convenient to measure everything at the center of mass (which engineers typically call the center of gravity, or CG). That is the point G, shaded green in my modified diagram.
When computing work, it is most convenient to measure everything where the force or torque is being applied. In this case, that is the handle of the club, point A, shaded red in my modified diagram.

The energy is the power accumulated over time -- integrated over time, if you understand calculus. And the powers are computed at point A as follows:

Linear power is F_xV_x + F_yV_y. If we were doing it in three dimensions, we'd add in an F_zV_z term.
Angular power is Tω, where ω is the angular velocity, which can also be represented by ɣ dot (which is how Nesbit shows it in the diagram).

That is what equation (3) in "Work and Power" is about. Here I have slightly simplified and annotated it, so you can see how it aligns with the explanation. Of course it is written very compactly, using vector notation. The "over-arrow" means the quantity is a multi-dimensional vector (three dimensional in the case at hand). The "dot product" means you multiply together the components of the vectors that lie in the same dimension, then you add everything together. That is what we did with F_xV_x + F_yV_y above.

So you can add together angular and linear, if they are both powers or both energies. And, if you do that, anything having to do with a force through the handle will be computed as part of the linear energy. The only torque that is interesting in this computation is what the hands apply to the handle of the club -- the couple.

So Nesbit's answer does in fact make sense. It explains why the moment of force is not interesting in computing work.

That is what convinced me that Manzella's interpretation of torque was exactly what Nesbit meant. My apologies for doubting you, Brian.

Unfortunately, that does not solve the dispute. It pushes it from a failure to communicate (different terminology) to a failure to get the same results.

A substantive issue: here's the beef

The problem is that other swing modelers found that all golfers tested exhibited significant negative couple at impact. Figure 11 from "Work and Power" show only one out of the four golfers with a negative couple. We have now determined that it isn't just a problem of terminology; it is a real difference between the results.

For instance, Kwon's tutorial includes a plot of the three kinds of torque for an inverse dynamic model of a real golfer with a driver. What we see in this graph is:

The moment of force (Tf, red) takes over from the couple (T, blue) about 25msec before impact, and the couple goes steeply negative from there. By impact, it is significantly negative and the moment is significantly positive.
The sum of these two trends is very much in the middle. The total torque (Ttotal, green), while trending downward, is pretty close to zero. It could go either way, as it crosses zero perhaps 12msec before impact. That is why I thought Nesbit's torques were more likely total torque. I was used to seeing this sort of torque plot from biomechanics studies.

I said "studies" -- plural. To give another example, here is a Sasho MacKenzie video animating the same three torques. The video also explains very well what they are. It represents data from a real golfer. Actually, he shows plots from two golfers, one of them a multiple major winner. Both plots look very much like Dr Kwon's for the last 100 milliseconds. The total torque is somewhat positive for one and negative for the other, but the couple is very negative for both.

So this is a very real difference. On Oct 21, 2018, Tom Rezendes asked on Facebook, "Looking for a yes or no answer... Sasho Mackenzie. Then maybe we can move this thing forward."

MacKenzie replied, "I have not seen a positive couple at impact with a full swing (like how you would hit a full 5 iron or driver). It usually goes negative about 0.04 s before. I frequently see the total torque (moment of force + couple) stay positive up until impact with full swings. This is the same answer I had 4 years ago on a Friday."

Manzella commented later in the same thread, "Thanks for your answer, Sasho. "Owning such a assertion—especially one that is in direct contrast to Dr. Steven Nesbit—is laudable.

"We 100% disagree with your position, as we see both inputs as in Dr. Nesbit's "Work & Power" paper which has three positive torques and one negative torque at impact. 'Torque' is Dr. Steven Nesbit's preferred tern for the twisting action independent from any 'angular response' (also his preferred term).

"We see no resolution to this fundamental disagreement and we considered this matter closed."

One more thing worth mentioning. Manzella and Jacobs keep making fun of any 2D model (including their own expert's recent 2D work). But this difference is not a 2D vs 3D thing. Doctors Kwon and MacKenzie have 3D models, and they still come out with a negative couple at impact every time

What I would really like to see is a comparable plot of all three torques from Dr Nesbit's tests, to see if there is a good reason they are so different. Given that Manzella "considers the matter closed," I doubt this will happen. I'll speculate below what might cause the difference, but I don't have a lot of confidence in the conjecture. In fact, on the next page I present what I really think is the difference.
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Where I come out on all of this

I firmly believe the results of Kwon, MacKenzie, and the others who have done the work and revealed their methods. Science moves forward by giving others enough information to repeat the experiment. Those who have repeated the experiment have come up with a negative torque at impact.

Jacobs and Manzella refuse to reveal their methods on the paranoid assumption that others want to steal their program. Whether or not their fear is justified (personally I doubt it, but give them the benefit of that doubt), what they are doing is not science. It is commerce.

But there are other reasons for not believing the Nesbit side of this argument. Reasons that are less concerned with process or people, and more concerned with evidence that didn't come up on the Facebook discussion. The reasons:

Actual measurement of hand forces during the swing say couple at impact is negative.
Shaft bend is tightly tied to hand couple, and shaft bend says the couple at impact is negative.
Even Nesbit says a good swing has negative couple at impact.

Let's discuss these in more detail.

Instrumented Grip

Something that could answer a lot of questions -- not just this one but likely also the infamous "closed loop problem" -- would be a study using a club with an instrumented grip. Put strain gauges in the handle, and measure what forces the hands actually apply to the club. What a concept! No inverse dynamics, in fact no modeling at all. Measure the forces on the handle directly and compute the torques directly.

Turns out there is more than one such study. The first I know about was published in 2006. (S. Koike, H. Iida, H, Shiraki, M. Ae, An Instrumented Grip Handle for Golf Clubs to Measure Forces and Moments Exerted by Each Hand During the Swing Motion, Engineering and Sport 6, 2006.) From the abstract:

An instrumented grip handle was designed to simultaneously measure the forces and moments exerted by each hand on the handle during golf swing. Eleven pairs of strain gages were attached on the surface of an aluminum bar inserted under separated grip covers... A professional golf player participated in this study and performed golf swings with several clubs.

Here are two graphs from that paper. The image quality is poor because I was only able to get a scanned copy of the paper.

Graph (a) shows the force across the shaft by each hand individually, the pull by the left hand and push by the right hand. (Actually, it's measured as a push either way; the mostly negative dotted curve says the left hand force is a pull until almost impact.) They are nearly equal the whole duration of the downswing, and comprise a couple almost perfectly. The forces cross about 20% of the downswing time before impact, and form a negative couple of about 10 Nm at impact.
Graph (c) shows the couple produced by each hand individually. For instance the dotted curve shows the left-hand couple; the left thumb is pushing and the left pinky is pulling. Similarly for the right hand and the solid curve. By the time you get to impact, the right hand provides only a tiny couple, perhaps fractionally positive, and the left is negative about 10 Nm.

These results firmly place the couple as negative at impact. Specifically:

The push-pull of the two hands against each other creates a couple that is positive almost to impact, but goes negative about 30-50msec before impact.
The left hand loses its ability to keep up with the club's rotation fairly early in the release, 40 or 50msec before impact.
The right hand never torques torques the club in a positive direction, and has recovered roughly to zero torque by impact.

Koike did another, similar study with similar results in 2016. That couple at impact is not as strongly negative, but still unambiguously negative.

Direct measurement may be the best reason for believing the couple is negative at impact, and perhaps the strongest reason. But there are more.

Shaft bend says something else

There is a serious inconsistency in the "Work and Power" paper regarding torque at impact. We know what the graph shows. But in the text, Nesbit writes:

The angular power peaks prior to the linear power for each subject. Because the wrist joints cannot keep up with the angular speed of the club, they actually retard the angular motion of the club just prior to impact resulting in the straightening of the club and the release of its stored strain energy.

Think about that! The wrist joints "actually retard the angular motion of the club just prior to impact resulting in the straightening of the club". That certainly sounds like negative couple to me.

The reason this text jumped off the page at me is that I come at this from a background in clubfitting, not golf instruction. I know that the shaft is always bent forward coming into impact. I have never experienced, nor heard of another clubfitter who experienced, a backward bend coming into impact for a decent full swing. (That is, a full swing meant to hit the ball the "stock" distance or more for that club, and not distorted by a skilled golfer trying to do something specific with torque to make a point -- something different from what they would do if playing golf.)

What does this have to do with the question? Here is a diagram from another of my articles (only slightly modified to conform to the terminology we're using now). It was drawn in 2010, before this debate started. (Nesbit had just published "Work and Power" at the time, and I didn't even know about it for another year or so.) So I didn't do this work for this debate; it has been my opinion predating the dispute.

My position is that, if the shaft is bent forward, then the couple must be negative. A positive couple is accompanied by a backward shaft bend. And a backward shaft bend coming into impact simply does not occur in real life.

Nesbit knows this too, and remarked on it in "Work and Power". Those remarks are at odds with the graph of Figure 11.

As usual, Nesbit remains silent about this, and allows Manzella and Jacobs to do his talking. They remind us that Nesbit is an expert in shaft bending, having published on the subject. On the next page of this article, I will discuss his publication on shaft bend. Not only does it not shake my faith in this explanation, it explains how his results come out different from everybody else's. It is due to several assumptions at the beginning of his analysis, assumptions contrary to fact.

What should we be teaching?

Ultimately, the most important question from the whole discussion is not who is right and who is wrong, but what should we be teaching golfers about the swing. Should we teach them to twist the handle just before impact? (That is, apply couple torque late in the downswing.) Should we teach them to "hold the lag"? Should we teach them to relax the hands through the downswing and just let them be a hinge? The technical discussion we are having bears directly on this question of what we should teach.

I remember seeing a Manzella instructional video a year or two ago urging golfers to torque the handle coming into impact. (I was unable to find it while I was writing this. Perhaps it has been withdrawn.) If you believe that a positive couple near impact is both possible and a good thing, that might be good instructional advice. Let me take a contrary position.

My first arguing point will be to bring back Figure 11 of "Work and Power". This time, I have color-coded the impact couple to tie it to the subject. Remember, Nesbit had four subjects. Two points to note:

The one golfer with negative couple (and it is substantially negative) is the scratch golfer, the best in the sample population.
The highest positive couple belongs to the highest handicap golfer.

I know what that tells me about what we should teach, if indeed we are looking at teachable cause and effect. It is possible we are not; correlation is not necessarily causation. But in this case, I am pretty sure that one of the things that makes the scratch golfer so good is a swing that happens to produce a negative impact couple. What would this mysterious something be? A moment of force through the last 100msec of downswing that accelerates the club so effectively that the wrists can't keep up when approaching impact.

Nesbit would seem to think so as well. Toward the end of his paper, he singles out the scratch golfer for further analysis. He finds several things to praise. Let me single out one.

All the torque components pass through zero before impact causing the rotational work to be maximized then decrease by impact. It is at this point that the wrists approximate a 'free hinge' configuration as the golfer merely holds on to the club as its momentum carries it to impact. By the time impact is reached, all torque components are reversed thus doing negative work simply because the wrists cannot keep up with the rotational speed of the club at this time in the downswing. The club head does not slow down however, as the straightening of the shaft continues to accelerate the club head. The club head deflection passed through zero at impact releasing about half of the shaft stored strain energy, and resulting in the club head velocity peaking exactly at impact.

So there you have Nesbit's own opinion of where the couple ought to be and why.

I promised a speculative guess at why Nesbit had more variation of couple at impact than Kwon, MacKenzie, and other swing model researchers. Perhaps he was working with worse golfers. When you do a study with a single golfer, you want it to be a good golfer, and that is a reasonable wish. By including less-skilled golfers in the study, perhaps Nesbit allows in some swings that were bad enough to exhibit a positive couple at impact.

I don't believe this to be true, but let me at least put it out there as a possibility. My reason for not believing it is the accumulated experience of clubfitters, fitting even high handicappers. They never encounter a shaft bent backwards at impact, and shaft bend is tied tightly to the couple.

Since I wrote that speculation, I have a better idea of where the difference comes from, the difference between Nesbit's results and much of the rest of the biomechanics community. I explore that on the next page.

If you read the article I originally posted in October 2018 and just want to know what is new in this version, I have a summary of the new insights here. If you want the whole story, continue on to the next page.

Last modified -- Mar 3, 2019