Torque is the amount of "twisting force" applied to a body, to turn it
around some axis or fulcrum.

You may remember it from high school physics as the "moment"
of a force
on a lever. In the lever example (which we'll use for a bit here), the
fixed axis is called the lever's "fulcrum". The torque (twisting force,
remember?) produced by any force that acts on the lever is the force times
the distance from the force to the fulcrum.

For instance...

Suppose I put a 200-gram weight on a lever, at a point
12 inches to the right of the fulcrum. Then the weight will try to turn
the lever clockwise (right side down) with a torque
of 2400 inch-grams
(200 * 12). Putting more weight on the lever will certainly increase
the
torque, but so will moving the original 200 grams further from the
fulcrum.
If we moved it out another 12 inches, its clockwise torque would be
4800
inch-grams. Coloquially, we've increase the "leverage" of the force.

How about a little exercise to really feel what we're talking
about
here.

Lay one of your clubs on (or preferably across) a table or workbench,
with
the entire grip (and nothing else) hanging over the edge.

Put your finger on the grip near the butt, and press down
until you lift
the clubhead free of the bench. Note what the force you apply feels
like.

Now repeat, but press on the grip about an inch or two from
the edge of
the bench. Note how much harder you have to press.

What's going on here is that it takes a certain amount of torque
to turn
the club about the fulcrum (the edge of the bench) and lift the
clubhead.
Remember that torque is force times distance from
the fulcrum. You can
apply that torque by either a small force at the butt or by a much
larger
force much closer to the fulcrum.

Torque has a number of interesting applications in golf club
design:

Of course, we're used to reading about the "torque" of a shaft,
which is
a complete misnomer. Actually, that rating is an angle (say, 3.5
degrees),
not a torque. It is the amount a shaft twists when a given amount of
torque
is applied to it, trying to twist the shaft around its long axis. The
smaller
the number, the stiffer the shaft in resisting
torque.

The Center of Gravity (CG) of any body
is informally defined as the "balance
point" of the body. A more quantitative definition is that axis about
which
the clockwise and counterclockwise torques (due to the body's own
weight)
balance exactly. The informal definition is easier to measure
in
a finished club, but the formal definition is the way you compute
the CG of something you're designing.

Swingweight is a torque, too. It's the
torque provided by the weight of
the whole club, about an axis 14 inches from the grip. As such, it
measures how much
pressure (counter-torque) you have to apply to the grip to swing (turn)
the club about the axis. Note that, since the head is further from the
grip than the shaft, a gram of head weight contributes more to
swingweight
(torque) than a gram of shaft weight.

Ironic, isn't it, that the only example that calls itself "torque"
isn't
really torque at all, but rather the twisting motion resulting from
torque.
(Scientists and engineers call that "torsion", not torque).

Moment of Inertia

When you hit something on its CG, you move it straight away from the
point
where you hit it. But if you hit it off its CG, it will twist. Let's
verify
that with another little experiment:

Hang a wire hanger from a finger of your left hand. Its CG will be
right
below the finger from which it's hanging.

Tap it with a finger of your right hand, on the middle of
the long horizontal
wire (i.e.- right beneath the CG). Note that it swings back and forth,
but it doesn't turn about its vertical axis.

Stop it from swinging. Now tap it with the same finger, but
at the end
of the hanger. Note how most of the energy from the tap goes into
turning
the hanger rather than swinging it.

The reason for the behavior stems from Newton's original observation
that
"a mass at rest tends to remain at rest." In particular, the center of
mass (another name for the CG) tends to remain in one place unless
prodded.
If you hit it with a force that doesn't go through the CG, the body
will
turn, allowing it to respond to the force without moving the CG any
more
than it has to.

Remember torque? Think of the wire hanger as a lever. The CG,
which
wants to remain in one place, is the fulcrum for that brief dynamic
moment
before anything moves. And therefore the force applied when you tap the
hanger is a torque around that fulcrum. The farther from the fulcrum
(CG)
you tap it, the more it wants to twist (rather than swing).

OK, so how much will the hanger twist in response to an
off-center tap?
We know mass has an "inertia" that makes it resist a force that wants
to
move it. (The famous equation "F=ma" means that the higher the mass the
more force it will take to accelerate it a certain amount.) Well mass
has
a "rotational inertia" as well; the higher this rotational inertia, the
more torque it will take to produce a certain amount of rotational (or
"angular") acceleration. The rotational inertia is called the "Moment
of
Inertia". (For mnemonic purposes, it is called "MOI" in these notes,
which is how the golf community abbreviates it. Physics textbooks
usually refer to it as I;
golf is the only context in which I have seen it as MOI.)

As you might expect, the further we place the mass from the CG
the more
effective it is in resisting torque. If your intuition doesn't tell you
this, it's time for another experiment.

Get two identical wire hangers and four identical "weights" (small
objects
considerably heavier than the hangers, but still light enough so you
can
attach them to the hangers with, say, masking tape).

On hanger #1, tape two weights to the horizontal wire as
close to the center
as possible.

On hanger #2, tape two weights to the horizontal wire, as
far from the
center as possible. One weight should be near each tip.

Repeat the previous experiment with both hangers, but note
how "enthusiastically"
each hanger swings or turns in response to the same strength of tap.

The
videos here repeat that experiment, but on steroids. We have made a
short
barbell with
steel weight plates and PVC pipe, and hung it so it can turn. If you
don't want to do the experiment yourself, you can see what happened
when I did it
with the short barbell.

The two barbells (like the two hangers) are exactly the same mass, and
they should swing identically
in response to tapping the center of the barbell. But, in response
to an off-center tap, barbell #1 will turn much faster than barbell #2.
That's because the weights far from the axis of rotation contribute a
lot
more to the moment of inertia than do weights near the axis. Moreover,
#1's motion seems to be all rotation, while #2 swings a little as well,
indicating that the object's mass is getting into the act, not just its
moment of inertia.

Quantitatively, the distance between weight and the axis of
rotation
is even more significant in computing moment of inertia than it was in
computing torque. Whereas the torque of each force is the force times
the
distance to the axis, the moment of inertia of each grain of mass is
its
mass times the square of the distance to the axis.

Application to golf

OK,
time for a few golf applications of Moment of Inertia. We will take a
look at how moment of inertia can make a clubhead more forgiving, and
how it can control the timing of the club's release during the swing.

To evaluate the forgivingness of a clubhead to off-center
hits, we use the Clubhead MOI.
Specifically, we use the moment of inertia of the clubhead as we try to
rotate it around its center of gravity.

Here are the things you need to
understand for this; they may be counterintuitive, but a lot about golf
is counterintuitive:

During impact, the club rotates around its center of gravity, not
the shaft or hosel. Most people (including me) start out by believing
that the hosel is the stationary point around which the clubhead
rotates, but it isn't. The duration of impact is so short (1/2000 of a
second) and the forces of impact so great (up to 2000 pounds) that any
force the shaft could exert is only a tiny fraction of what is going
on. So the shaft plays no more part in impact than if it were a string.
(We'll see this more mathematically as we get deeper into the e-book.)

The
higher the MOI, the less the clubhead will twist during impact; that is
the fundamental property of MOI, and I hope that part is not
counterintuitive. But if the clubhead doesn't twist as much but the
force is still as high, then something else must be resisting the
force. And that is the mass of the clubhead itself, resisting as F=ma.
So the more MOI prevents the clubhead from twisting, the more of the
clubhead's force can be exerted on accelerating the golf ball.

The other picture shows the entire club trying to rotate
around the butt of the club. This Whole-club MOI is
the moment of inertia that resists
turning the club at our wrist hinge.

Forgiving clubheads:
Consider two putter heads with identical
weights and blade lengths. Head #1 is a simple uniform blade, while
head
#2 has all its weight at the heel and toe.

Head #2 has a much higher moment of inertia than head #1, because all
its
weight is as far as it can get from the CG. In fact, the moment of
inertia
of a pure heel-toe weighted putter is three times that of a blade, even
though their total weight is the same.

Roughly speaking, the CG is the "sweet spot" of the head.
Hit the ball
there and you get a nice straight putt.

If you hit the ball off-center, the putter will twist and
your putt
will
go off-line; it also won't go as far, because the clubhead is twisting
away from the ball. The higher the moment of inertia of the putter
head, the less
it will twist so the closer to the intended line your putt will go, and
the more nearly it will achieve the distance you intended.

Conclusion: a heel-toe weighted putter head with its higher moment of
inertia
is more forgiving of off-center hits than a blade. Another way of
saying
this is that head #2 has a "larger sweet spot".

Now let's talk about cavity-back irons. Clubhead manufacturers
talk
about the cavity making the sweet spot bigger. Now we're in a position
to understand what's really going on. It's not that
the cavity is magic,
but that it allows all the weight of the clubhead to be moved to the
edge
of the face. This is called "peripheral weighting", and (just as we saw
with the putters) it increases the moment of inertia of
the
head. And just as with the putters, this means that the head twists
less
when you don't meet the ball right on the sweet spot. That's why the
club
is more forgiving of off-center hits. It ain't the cavity at all; it's
all the steel they dug out of the cavity and moved to the edge of the clubhead.

This also explains why metalwoods are more forgiving than
wooden woods
of the same weight. The woods have their mass distributed more or less
uniformly throughout the head, while the metalwoods are hollow shells
(because
steel is much heavier than wood). Can you say "peripheral weighting"? I
knew you could.

Release of the club: MOI Matching:

The goals of a good golf swing are to have the clubhead traveling at
its maximum speed at impact, with full extension to the ball so that
impact occurs at the middle of the clubface. At impact, the hands have
slowed considerably, so most of that clubhead speed comes from the club
rotating around the hands. (For most golfers this is somewhere near the
wrist hinge, but I have seen estimates that put the center of rotation
anywhere from 5 inches below the butt to 8 inches above. Our assumption
will be rotation around the butt.)

This rotation is created by the swing. Resisting the rotation is the Whole-club
MOI. One goal of clubfitting is to find the right
whole-club moment of inertia so that the club is fully extended when
the head reaches the ball. Too much MOI, and the club will not be fully
released. Too little MOI, and the clubhead will have passed the hands,
causing all sorts of ugly things to happen.

Selecting this whole-club MOI to control release is what is
meant by the term "MOI matching". We'll see it in much more
detail in the chapter on
heft matching.

Last modified May 25, 2017

Copyright Dave Tutelman
2020 -- All rights reserved