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 YoungHoo 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
twodimensional." (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 outofplane motion, then
you obviously need a 3D model. But if you are only worried about
inplane 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 outofplane wobbles.
 If the plane of the analysis is the "functional swing
plane", then nonplanar 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 1cos(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 inplane, 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 followup,
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,
YoungHoo 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 threedimensional 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 inplane model used by
Nesbit & McGinnis, saying:
The 2D 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 3D inverse dynamics method that I use has been used in
biomechanics for centuries so it is a wellestablished 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 2D model and my general 3D 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 kilowatthours. 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 freebody 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_{x}V_{x}
+ F_{y}V_{y}. If
we were doing it in three dimensions, we'd add in an F_{z}V_{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 "overarrow" means the quantity is a multidimensional
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_{x}V_{x}
+ F_{y}V_{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.
.

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 lefthand 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
pushpull of the two hands against each other creates a couple that is
positive almost to impact, but goes negative about 3050msec 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 colorcoded 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 lessskilled 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
