Modeling the Swing  Executive Summary
Dave Tutelman
 January 16, 2012
This executive summary serves two
purposes:
 An introduction to the notion of modeling a golf swing 
what a
swing model is and why we would want one.
 A summary of the models studied and the lessons learned
from them.
What is a model of the
golf swing?
The picture
at the right shows two models of a
rearpaddlewheel boat. Which one is better?
The answer: It
depends!
Specifically, it depends what you want to do with the model.
 If you want the model to look good on your mantel or
in a
museum, then clearly the choice is A.
 If you want to use the model to investigate how a
paddlewheel boat works, then equally clearly the choice is B.
A
is a "scale model". The objective for a scale model is to capture as
much detail  to look as much as possible like the real world  as
possible. It doesn't matter if the model doesn't do anything; the
important thing is the fidelity of the appearance.^{[1]
}
B is a
working model. The
objective is to use it to mimic the operation of a paddlewheeler. Why
mimic the operation? There are a couple of reasons to want to. The boat
in the picture is a toy; it is fun to play with working model boats.
But you can also use the model to learn about paddlewheeler operation.
Let's look at the second motive: learning from the model. Suppose you
want to learn how a paddlewheeler works, and what changes might make
it work better. Then you want a model that
contains the important elements that you want to investigate, but it
doesn't need to contain any more elements. If the goal is to relate
paddle speed to boat speed, you need a paddle and hull of the
appropriate shape and weight  and that is all. It doesn't matter how
many windows the boat
has on each deck, or whether there is a pilot house or smokestack;
those features of a model are completely irrelevant to the purpose.
Moreover, they are expensive to include in the model, and may even get
in the way of the
researcher.
Important
point: there is a third kind of model, whose only purpose
is
for
learning about operation.
C is a
mathematical
model. If you come up with a bareminimumsimple working
model (say,
model B
without
the racing stripes), you probably have a system simple enough that it
can be described by equations well known to physicists and engineers.
At that point, you don't have to get your hands wet to answer the
questions a working model could answer; you can let a computer crank
through the equations and answer the questions for you.

Now, just
to see if you've been paying attention, at the left are two models of a
golf swing. Which one is better?
The answer is the
same as above, and for all the same reasons. That goes for
(A) the scale model, (B) the working model, and (C) the mathematical
model (not in the picture).
In this article, we are tracing the most important developments (in my
opinion, of course) in models of the golf swing. In each case, there is
a mathematical model; there may also be a physical working model
to demonstrate the principles. We will look at swing models starting
with the simplest (the double pendulum model), and work towards more
complex models. Each of the models answers some questions about the
golf swing, but the model does not include the detail to answer other
questions. For instance, even the fullbody model  which simulates 14
joints  cannot address which fingers should be the "pressure points"
for the swing; individual fingers are more detail than the model
contains.
Let's finish this introduction to models by reminding ourselves what
a swing model is NOT:
A
swing model is not the same as a model swing!
When most people hear "model swing", they think of a perfect swing, one
to be emulated when making your own swing. That is a correct
interpretation, but it is not what a "swing model" is about. A
swing model is a simplified representation of a swing (either
mechanical or mathematical) that you can "play with" to learn more
about what works in a golf swing and what doesn't.
A
swing model is not an actual, human golf swing! This
should go without saying, but too often it doesn't. A model is a simplification
of a golf swing. In any simplification, details are left out. Those
details may be important or not, depending on what questions we are
trying to answer using the model. For instance, the Iron Byron  the
swing robot in picture B  teaches us a lot about the left arm, the
wrists, and the shoulder turn. But it does not
teach us anything about how the torso or hips or legs create
the body rotation, just what the body rotation does to the arms and
club. You need a model that has a representation of torso, hips, and
legs to answer that question.

Lessons from the
models
Here is a simple description of each of the models, and the lessons to
be learned from the model. For details about a model or a lesson, click
on the button
next to it. You can use this summary in at least three ways:
 Just read it and assume you know what the article says.
(You'll
probably be wrong about that, but you'll know where to turn when you
really need to know.)
 Use it as a table of contents, so you can dive into the
specific
lessons you find of interest.
 Use it as an introduction to tell you what to expect, then
go
ahead and read the whole article.
Whichever you choose... Enjoy!
Model

Lessons

Double
Pendulum
Two rigid pendulum members. The inner member represents the golfer's
straight left arm, and the outer represents the club. A torque (which
can be a function of time) may be applied at each of the pivot joints.
All hinging is done in the same plane, so the model is twodimensional.

Increasing the initial
wrist cock angle
significantly increases the clubhead speed at impact.

Increasing the initial
shoulder turn only
increases clubhead speed at impact by a little. 
Increasing
the strength of the shoulder torque (the torque representing body
rotation) increases the clubhead speed at impact, though not in
proportion to the increase in torque. 
Increasing
the initial shoulder turn allows a more complete release of the wrist
cock. Increasing it too much ("overswinging") turns this release into a
cupped wrist.

The
longer into the downswing you maintain a large wrist cock ("clubhead
lag"), the more the clubhead speed at impact. This is the
most
important lesson from the double pendulum, and leads to the surprising
result...

Simply
allowing the wrists to hinge effortlessly gives a higher clubhead speed
at impact than does applying wrist torque to help release.

Gravity accounts for about
8% of the
clubhead speed at impact.

We
lose something important by holding the inner pivot in a fixed
position. If we approximate the movement of the left shoulder by
shifting the pivot forward during the downswing, we gain about 9%
more clubhead speed at impact.

ThreeDimensional Triple
Pendulum
Added to the double pendulum model is a third
element, a
shoulder. It is another member, from the spine at the base of the neck
to the shoulder joint. In addition, this model is no longer restricted
to two dimensions. The axis of the spine pivot and the axis of the
shoulder joint are not in the same plane. In addition, the leftarm
member can rotate around its own axis. So, instead of two torques there
are four, and none of those four axes are parallel to another.

In
a good swing, the club releases from the inside out: first torso turn,
then the arm moves away from the chest, then the wrist uncocks. As a
consequence...

Clubhead lag is a major
factor in clubhead
speed, just as we learned with the double pendulum model.

A "blip" of wrist torque
at the correct
moment will increase the
clubhead speed at impact. But most of the work is done by torso and
shoulder torque,
and very little wrist torque is employed for most of a proper downswing. 
The
angle of the clubface to the target plane (clubface squaring) roughly
tracks
the wrist cock angle. That is, the clubface lies in the target plane
early in the downswing while the wrist cock is about 90º; at impact,
the wrist cock is 0º and the clubface is perpendicular to the target
plane. In between, they track closely enough to use for approximate
studies.

Even the best swings are
pretty far from a
single plane. The plane of the left arm varies by 25º
over the course of the downswing, for MacKenzie's optimized model.
Similar variations are observed in other studies that MacKenzie cites. 
The right arm "pistoning"
(right elbow in
extension) helps to create maximum distance. 
FullBody Model
A model with 16 elements (if you include the golf club) and 14 joints.
Each joint is a ball joint that can turn in three dimensions. Torques
are applied to the joints, and "tuned" until the motion of the model
matches that of a good golfer. (Or a notsogood golfer; that is one
way to look at the model's output and see what the good golfer does
differently from the high handicapper.) While this is much closer to a
working scale model than the others, its complexity taxes both the
computer's abilities to simulate it and the researcher's abilities to
properly formulate questions of the model.

In
the best swings, the lion's share of the work is done by the right hip,
the muscles in the lumbar region, and the muscles in the thorax. The
next most important muscles are those driving the left hip and
extending the right elbow. The other muscles play a relatively small
role; in fact, the left ankle and left knee add nothing.

In
the best swings, the work starts at the bottom and works its way up:
first ankles, then knees, hips, lumbar, thorax, and shoulders in that
order. 
On
a finer grain level, the left side fires before the right side. That
is, the left knee before the right knee, the left hip before the right
hip, etc. 
When
things get to the arms (that is, wrist and elbow joints), the sequence
seems to make less difference. All four of these joints peak in the
last 15 milliseconds of the swing  almost simultaneously and almost
at impact.

Wrist cock is vital to
clubhead speed. The
clubhead speed with a good wrist cock is 4070% higher than with no
wrist cock.

A good swing just allows
the wrists to
uncock, rather rather than encouraging the uncock using wrist torque.
In fact, by
the time impact is reached, the wrists cannot keep up with the
rotational speed of the club. 
Better
golfers enhance centrifugal release by controlling the path of their
hands  specifically, the curvature of that path. Their hands move
more in a straight line early in the downswing, and a tighter curve
just before impact.

Exercise programs for golf
should focus on
flexibility, not just strength.

Notes:
 Of course
there are counterexamples, working
scale models. For instance, model railroading is a hobby where accuracy
of both appearance and operation is important. But that is not what we
are talking about here.
Last
modified  March 6, 2012
