Heft of the club: Swingweight & MOI
What Is It, And Why Do We Care?
Swingweight is an attempt to reflect a couple of important properties
of the club:
Feel: specifically, how head-heavy is the club?
Together, these constitute the "heft" of the club.
Performance: specifically, how does the placement of mass affect the timing of the release?
Q. Now that doesn't sound so hard. Why not just make all the clubs the same weight?
A. Well, you can do that and still have major differences in the
balance point. Total weight alone doesn't reflect what the golfer feels
nor what the club does.
Q. OK, then. Make all the clubs with the same head weight, and
the same shaft weight, and the same grip weight. That should do it.
A. Well, it would if all clubs were the same length. The real problem is that there is a length progression across the set. As you make the club longer, it will feel more head-heavy and will release differently.
Q. Oh! Well then, how about making the head lighter as the club gets longer.
A. Exactly! But how much lighter? That is the subject of this section...
Swingweight is an attempt to quantify the heft of a golf club, as it
affects both the feel and the physics. Let me emphasize the word attempt! Swingweight
not a magic quantity that can be shown by physical laws to have
whatsoever to do with the things it would like to measure. It is,
an empirical approximation with an interesting history over a century
old. Because it is so important to understand that swingweight doesn't
represent anything really fundamental, let's start by reviewing that
Once upon a time...
First, a big thank you to D.B. Miko of Mac Shack Golf, for
providing me with a number of references on this subject.
By the early 1900s, clubmakers for professional golfers were already
using mathematical formulas for matching their pros' clubs for heft
across the set. The formula they used was to match the product of
the head weight and the square of the length. Thus the longer the
club, the lighter the head had to be, by about twice the percentage
increase in length.
Let's take an example. Consider a 5-iron of the time: 37.5" long
with a 255g head. If we made the club 1" longer (that's 2.7% longer),
we would need to make the head 14g lighter (that's twice 2.7% of 255g).
So, for each inch longer or shorter in the vicinity of a 5-iron, we'd
need to vary the head weight by 14g. Since, for a normal set of irons,
the club spacing is a half inch, the progression of head weight from
each club to the next is a half of 14g, or 7 grams. Does that sound familiar? Now you know where it comes from.
At that time, clubs were made with hickory
shafts and wound leather grips. There wasn't much you could do to
change their weights, once the length and stiffness were determined. So
none of the matching formulas included shaft or grip
weight, because for all practical purposes they were fixed.
Now, think about the physics of such matching. Back in the chapter on Physics: moment of inertia, we saw that "the moment of inertia of each grain of mass is its
mass times the square of the distance to the axis."
variation in shafts and grips could be neglected, then this formula
made sure that the set matched for all clubs' moments of inertia about
their butts. The clubmakers of
a century ago were building moment-of-inertia matched sets. (Well, almost. See note  below.)
Now, at that point, there was no such thing as swingweight; neither
the measure nor the word was invented yet. But something was needed
because the math was a little tedious. Remember, no electronic calculators or computers back then.
the early 1930s, a clubmaker named Robert Adams invented the
swingweight scale. It was a balance that measured the amount of torque
the weight of the club exerted about a pivoting fulcrum. The
diagram shows a modern swingweight scale taken from the 2006 Golfsmith
catalog, but it is basically the same instrument that Adams used alnost
years earlier. The weight of the club exerts a counterclockwise torque
on the beam, because the center of gravity of the club is to the left
of the fulcrum. The clubfitter moves the sliding weight until its
clockwise torque balances the torque from the weight of the club. The
position of the sliding weight then gives the "swingweight" of the
club. Notice from the picture below (a scan from Adams' original
patent), how little the design has changed over three quarters of a
After much experimenting, Adams concluded that a
fulcrum 14" from the butt seemed to give the "best" match, in a
subjective sense, for
the pros he worked for. Why 14"? Did that correspond to some sort of
"pivot point" in the golfer's swing? No, it was just a number that
seemed to work; it yielded a set of clubs that Adams' clients felt were
well matched. (As we shall see later, this is not a
perfect match to moment of inertia, but it's not a bad match at
all. So Adams-matched clubs would be a little different from
MOI-matched clubs, but not hugely so.) Adams' scale was used to
match Francis Ouimet's and Bobby Jones' clubs, with obvious success.
Adams used an arbitrary letter-number scale (e.g.- "D-1") to measure
swingweight. That scale, which he called the "Lorythmic" scale,
remains the most popular swingweight measure right up to the present.
Around 1945, Kenneth Smith bought Adams' rights to the swingweight
scale, and began experimenting with it himself. He came to the conclusion
that the 14" fulcrum gave a good match for professional golfers, but a
12" fulcrum would produce a better set for the average amateur, which
he called the "Official" scale -- even though the industry has never
adopted it as official anything. He was soon producing both kinds of
So, by the mid-1900s, we have three approaches to heft-matching a set of golf clubs:
- The 12" so-called Official scale.
- The 14" Lorythmic scale (still the most popular).
- Moment of inertia (not much used by then, because it was so tedious compared with a swingweight scale).
The major difference among them is the amount by which the clubhead
gets lighter as the club gets longer. Smith believed that the average
golfer couldn't handle light long irons and woods, hence his proposed (and never really accepted)
change in fulcrum placement.
For example, consider a heft-matched set in each of the systems,
using the standard club lengths from the late 1900s (35.5" for a 9-iron and 43" for a
driver). Let's choose a common weight for the 9-iron head, and
see what the driver head would weigh in a matched set.
Thus there is some difference across the set between and 12" and a
14" scale, and a lot more difference between either and an MOI-matched
set. In particular, the 12" scale allows the longer clubs to be
heavier-headed than an MOI-matched set would. Smith felt that the
long clubs had to feel heavier-headed for the Sunday golfer to swing
them, though the lighter heads would give better performance to the
accomplished golfer. Put another way, the longer the fulcrum, the faster the clubheads get lighter as the club gets longer.
So, you ask, which one is "Right", in some absolute sense?
Obviously, "it depends". To understand how to heft-match clubs, we'll have to
look at some mechanics of how the club is released during the swing.
Heft and Release
I'd like to thank Bernie Baymiller for the
strobe pictures of Bobby Jones. Bernie's father was the director of
R&D for Spalding Golf in the 1940s, which is where and when the
pictures were taken.
is a strobe picture of Bobby Jones swinging a driver. It was taken by
Dr. Harold Edgerton of MIT, inventor of the strobe flash, and captures
Jones and his club's position at intervals of about 0.007 second. I
have taken the liberty of marking three positions of the swing with the
"double pendulum", as follows:
So "release" is the process of the loss of wrist cock angle, from fully
cocked during the downswing to almost straight at impact. And a club
that is well-fit to the golfer will release so that the two arms of the
pendulum are aligned at impact, with only a degree or two of wrist cock
- The red position, about
70 milliseconds before impact. Note that the wrist is still fully
cocked at an acute angle. This is about where Jorgensen has identified
the beginning of release, and Jones' swing corroborates that.
- The green position,
about 20 milliseconds before impact. The wrist angle is much smaller,
indicating that the wrists are well into the uncocking process.
- The blue position --
impact. The wrist is almost straight here, with just a little wrist
cock left. This is a very good impact position; the club is just about
|In order to understand how to design the club for proper release, let's review the physics
of the club's release. "Release" means rotation of the club about the
wrist hinge. According to Newtonian mechanics, such rotation can only
occur by the imposition of a torque on the club. The torque comes from
- Centrifugal force rotates the club about the wrist hinge.
- In addition, the golfer may apply some torque via through
the wrist hinge, using the muscles of the wrists, hands, and forearms.
This is a relatively small component of the release torque for most
golfers, especially good golfers.
Resisting this torque -- retarding the club from turning -- is the club's own moment of inertia
around an axis at the wrist hinge. So, if we assume that the golfer
makes the same swing -- applies all the same forces at the same times
-- regardless of which club he is swinging, then it would appear that
the way to match a set of golf clubs is to match their moment of
inertia. That way, identical swings would result in identical release.
So, if you find the correct moment of inertia for the golfer for some
favorite club, you should build every club in the set to that same MOI.
This is idealistic rather than ideal. Or, as my science teachers used
to tell me, "The difference between theory and practice is bigger in
practice than in theory." Here are some reasons that our argument for
MOI matching may be too simple:
Let's address each of these points:
The need for identical release
instruction today teaches to place the ball in the same place in the
stance, regardless of what club is being used. Usually, that
recommended ball position is just inside the heel of the front foot
(the left heel for right-handed golfers). For instance, see Butch Harmon's lesson article
endorsing constant ball position. (Note: the links here worked at the
time this was written. If it doesn't work for you, please contact me so
I can find another page.)
With the ball in a constant position with respect to the golfer's
stance, an MOI-matched set of clubs should be ideal. All other things
being equal, it will result in complete release occurring at the same
position in the swing. If you can find an MOI such that the release
position corresponds to the ball position, build all the clubs for that
golfer to that MOI.
constant ball position was not always the way golf was taught. In fact,
it's a fairly recent development. Only a few decades ago, most golfers
were taught to play the short clubs back in the middle of the stance,
and move the ball forward as the clubs get longer. How do I know? I was
taught that way in the early 1950s. And, since it works for me, I have
not bothered to change. I'm sure there are many old fogeys like me, who
still play that way. Not only that, there are a few instructors who still teach that even today.
So what does that say about heft matching. The first thing we should
notice is that we want an earlier release in the short clubs and a
later release in the long clubs. We can accomplish this by making the
MOI progress across the set, so it is lower in the short clubs and
higher in the long ones.
Another way of saying this is: the heads still get lighter as the clubs
get longer, but they don't get lighter as fast. Now look at the table
above, where we compared the three ways of measuring heft. Swingweight
has the property we just described: as the club gets longer, the heads
don't get as light for swingweight as they do for MOI. So swingweight
matching may be good for a golfer who uses a variable ball position.
Indeed, history also seems to support this. The popularity of
swingweight scales with clubfitters dates back to the middle 1900s.
And, at that time, variable ball position was the way almost all
golfers were taught. So swingweight might have been exactly the right
way to match clubs at the time. And it might still
be the right way to match clubs for dinosaurs (like me) who still play
that way. (Actually, I discovered this the hard way in my early experiments with MOI-matching in 1995. I am continuing to experiment with MOI matching and constant ball position; some day that may be my usual game.)
Different swings for different clubs
Everything up to this point is about physics, not the physiology or
psychology of the golfer. Face it, many golfers do not use the same
swing for all their
clubs. There are some good reasons for this, as well as some bad ones.
But, good or bad, we have to fit golfers who may use different swings
for different clubs.
Here are a few of the reasons, and what we can do about it:
- A lot of modern instruction says to "hit down" through the irons,
but to "sweep" the woods. This necessarily produces slightly different
swings for irons and woods. In particular, release should not be
complete for the irons; there should be more wrist cock remaining at
impact than for the woods. Remedy:
Match the irons to one MOI and the woods to another. Logic would say
that the irons' MOI should be greater than the woods' (to retard the
irons' release so there is still significant wrist cock at impact), but
you have to determine this by experiment with the individual golfer.
- Different clubs obviously have different lengths. This
necessarily results in different swing planes. This may result in
different application of the muscles to produce the forces. Remedy:
This is likely to be a smooth progression across the set, because the swing plane itself is a smooth progression. If so, some
sort of "slope" on the swingweight or MOI may solve the problem.
the clubs don't feel the same (what ever that means, for that
particular golfer), then he may change his swing a little in response.
(We'll get back to this later in the section, when we talk about
backweighting.) Remedy: The simplest way to deal with
this is to work hard at making the clubs feel the same. Experience shows that MOI matching provides the most "same
feel" across the set for most golfers. But not all; some golfers will
be problems in this regard, and will have to be fitted on a
club-by-club basis -- or perhaps a more drastic solution like a
- Golfers are inclined to think of different clubs in different
ways, and swing them differently. Many will apply a different swing to
the driver, because they are trying to kill the ball. Many will try to
lift the ball with the wedges, rather than hitting down through it. Remedy:
If you are trying to band-aid this problem by clubfitting (rather
than fixing it properly, with lessons and lots of practice), you'll
have to recognize it first, then experiment with clubs to find what
works. But let me suggest the first experiment be increasing the MOI for the trouble clubs --
for both these faults.
Centrifugal force and MOI
The analysis so far treats the torque due to centrifugal force as a
constant, independent of the design of the club. But it isn't. In fact,
most things that will increase the MOI of the club will also increase
the torque due to centrifugal force. For instance:
The torque changes in the same direction as the MOI, but not nearly as
much as the MOI. Experience has shown that MOI matching still produces
good results, both in release and feel, despite this flaw in the
analytical model. Here's a tentative conclusion I have drawn:
- Making the club longer will increase the MOI. It will also move
the balance point further from the wrist hinge, increasing the "moment
arm" of the centrifugal force -- so the torque will increase.
- Making the head heavier will increase the MOI. It will also
increase the centrifugal force, as well as move the balance point
closer to the clubhead (hence further from the wrist hinge). Both of
these effects increase the torque on the club.
In other words, a pure hitter needs to have the set matched by MOI
(either constant MOI for a constant ball position or a sloped MOI for a
variable ball position). A pure swinger probably won't be hurt by
errors in the heft match; it almost doesn't matter how you match the
clubs. A caveat for that last statement: it won't matter for release performance, but that's not all you need to worry about. He may still feel
the difference and change his swing accordingly. That is an argument
for not being careless about the match, even if you know you are
fitting a swinger.
- To the extent that the golfer "hits" (applies torque via the
hands, wrists, and forearms), using MOI to match the clubs is the right
answer for heft matching.
- To the extent that the golfer "swings" (depends on centrifugal
force to produce clubhead speed), MOI matching does not hurt -- but the
golfer is relatively immune to heft errors in the set anyway.
While we're questioning centrifugal force in the model...
page has drawn considerable criticism on the basis that centrifugal
force is phony. True, some centrifugal forces are fictitious, but not
all. The centrifugal force in this analysis is an example of the
fictitious force, so the criticism is at least partly true. So why do I
So, if I were
actually writing a program to analyze the swing, I'd use d'Alembert's
principle from classical physics (as in the link above) and never use
centrifugal force at all. (Not that CF would give a wrong answer if
programmed correctly, but it's much harder to program right.) But I
still maintain that it's easier for most people to understand using
centrifugal force -- so that's the way I'm explaining things for this tutorial.
- Just because it is fictitious does not mean it gives
wrong answers. There are plenty of fictitious constructs in physics,
that we use because they behave analytically as if they were real,
and centrifugal force is one of them.
- From a tutorial point of view, it is much easier for the non-physicist, non-engineer reader to understand. Here is a good explanation
of the more classical physics. Not many people -- actually not even a
majority of physicists and engineers -- would be able to visualize how
release works from the diagrams and equations in the reference. You
have to be able to mentally step through the Digital Differential
Analyzer and see what the output would be.
2008, André Cantin pointed out that the shafts are different lengths,
and so will have different weights. As we can imagine, this increases
the moment of inertia of the longer clubs relative to the shorter ones,
because there is additional shaft weight at the tip in the longer clubs.
I didn't think it would matter much, but did the calculations to see.
As it turns out, there is enough of a difference to measure. In fact,
it appears that the match is just about halfway between a
moment-of-inertia match and a 14" swingweight match. Basic information
for the calculations:
the information that Dave Miko shared with me was some interesting
correspondence between Kenneth Smith and Lloyd Rittenhouse, an engineer
who got sucked into a discussion of how to convert between Smith's
"Official" swingweight and the more common Lorythmic swingweight. The
discussion, which went on for a year in the 1976-77 period, centered on
Rittenhouse's unpopular assertion that there is no one-to-one
correspondence; it is a function of the swingweight and the total weight.
Eventually Smith came to see it the same way as Rittenhouse, and Lloyd
published a technical paper (I don't know where it was published --
might have been just a private correspondence) on the conversion. Here
is the bottom line, the conversion chart from Rittenhouse's paper.
- The specific gravity of hickory is about 0.7. (That's a density of 0.7 grams per cc.)
- The hickory shafts of the time had a diameter of about 0.45" near the tip. (See Wishon & Summitt.)
Last modified Oct 10, 2008