Estimating Heft
This is an important page. There are numbers, graphs, and tables
that may be a little scary at first. But this is where you find out the
answers to some important questions about heft:
 How big is big? What is the significance of a swingweight point, or a unit of MOI, to the way the club feels and performs?
 What is the relationship between swingweight and moment of inertia? If we know about one, what can we tell about the other?
How big is big?
The unit of swingweight is a "point". We've already seen
the definition, but let's review it anyway. Swingweight is a torque, so
it would normally be measured in units of torque  for instance,
graminches. One swingweight point is 50 graminches of torque. How big is this, in terms that matter to a golfer.

Very few golfers, maybe none, can feel a difference of one swingweight
point. (That's at the same length. A driver that's one point heavier than
a wedge will feel quite different. But that's because the length is very different, as is the total weight.)
 Some golfers can feel a difference of two points, but the
difference in
feel is small and subtle. However, there can be performance effects
even
if there isn't a tangible difference in feel. I have observed in
several golfers (including myself) the tendency to hit thin and sometimes
pull shots with a club as little as two swingweight points too light.
And that makes some sense. After all, a heft that is too small will
result in a release that's too early  hence a pull or a thin since
the club is past full release when it impacts the ball.

Three points of difference is quite distinct. Most golfers can feel it, and many will note performance differences.
Moment of inertia is measured in units of
masstimeslengthsquared. For instance, the usual units for a US clubmaker would result in a MOI measure of
graminchessquared. Tom Wishon's frequency meter (which we will
discuss later) measures in MOI in kgcmsquared. If you work out the
units, you'll find that
1 kgcmsquared = 155 graminchessquared
So unit conversion is pretty easy.
But what about relating swingweight to moment of inertia?
That's harder, because they are different quantities and measured in
different units. But we can get a pretty good idea of the
heftsensitivity of swingweight vs MOI if we vary the length or head
weight of a club to change its swingweight by one point, and evaluate
the MOI before and after. Doing that, we find:

A swingweight point corresponds to a momentofinertia
difference of about 3000 graminchessquared. (3140 at the length of a driver,
and 2940 for a wedge.)
 Or, for Wishon's preferred units, a swingweight point corresponds to a momentofinertia difference of about 20 kgcmsquared.
What this tells me is that a set that is matched to within 1 swingweight
point (or 3000 graminchessquared, or 20 kgcmsquared) is as good as it
needs to be for any golfer.
Estimating swingweight
OK, suppose I've figured out the swingweight I'll need to build a particular
club for a particular golfer. But how do I estimate in advance the swingweight
of a club for which I haven't even bought the components yet?
For instance, suppose I want to try a "lighter and longer" driver
(originally the Yonex principle). How much lighter gives how much longer, with the
same swingweight? Questions like this come up all the time in clubmaking.
You could use the equations to
estimate the swingweight. But, in my experience, the equations are
frequently off by as much as 2 points, and occasionally by more than
that. But there is an approach that seems to work.
The start of my answer came in the form of a data point and some "sensitivities"
in the Golfsmith Clubmaker, March/April 1992.
DATA POINT: 
Driver with 
200 
gram head 


128 
gram (standard) shaft 


43" 
(standard) length 
Swingweight 
= 
D0 
SENSITIVITY: 

One inch of length is worth 6 swingweight points. 

Four extra grams of weight in the butt of the club REDUCES
the swingweight by one point. 
I found a few more sensitivities in other books and catalogs. Then I dusted
off the Physics and Calc 101 books, and came up with a set of conversion
and sensitivity tables, based on the approximate formula for swingweight.
The sensitivity tables are, IMHO, more useful than the
formula for absolute swingweight. They are also probably more accurate.
But I present both as potentially useful to someone trying to estimate
the swingweight of a club being designed. The tables are more useful in
knowing how much to "tweak" a design to achieve a swingweight that you
know (from experience) feels good to the golfer who will play with the
club.
Now the tables.
The first set of numbers reflects the sensitivity of swingweight to
(1) head weight, (2) shaft weight, and (3) length. Using these numbers,
I've computed the tradeoff factors among (1), (2), and (3).

CLUB 



Driver

4Iron

9Iron

Head weight 
200 g 
250 g 
285 g 
Shaft weight 
128 g 
128 g 
128 g 
Total Length 
43 " 
38 " 
35.5 " 




Grams of head wt. per SW point 
1.7 g 
2.1 g 
2.3 g 
Grams of shaft wt. per SW point 
7 g 
10 g 
13 g 
Inch of length per SW point 
1/5 " 
1/6 " 
1/7 " 

Head wt vs. Shaft wt. (constant SW) 
4.1 
4.8 
5.6 
Head wt vs. Length (constant SW) 
9 g/in 
13 g/in 
16 g/in 
Shaft wt vs. Length (constant SW) 
36 g/in 
60 g/in 
91 g/in 


Two other sensitivities that don't need a table:

4 grams of weight at the butt REDUCES swingweight 1 point.
 5 grams of weight in the grip REDUCES swingweight 1 point. (Note that the
vast majority of grips are within a few grams of 50 gm.)
This is probably more information than you need for your firstcut design
or component shopping. I've memorized the much simpler approximate table:

2 grams of head weight per swingweight point.

6 swingweight points per inch of length.

If you're going to swingweightmatch, a gram of head weight is worth 5
grams of shaft weight.

If you're going to MOImatch, a gram of head weight is worth 3 grams of
shaft weight.

This is plenty good enough for most practical purposes.
You might have noticed that my rules of thumb do not
include any rules for grip weight. That's because I think such rules
are counterproductive, for reasons we'll see later on this page.
Design Examples
What do these tables mean? Here are a few examples (the first being my
original question: lighter and longer):

I'm going to get a head that's 4 grams lighter than "average" and a shaft
that's 24 grams lighter than "average". How much longer can I make the
club, and keep the same swingweight as an "average" driver?
Head wt vs. length = 9 g/in. Thus 4g off the head gives us an extra 1/2". Shaft wt vs. length = 36 g/in. Thus 24g off the shaft gives us an extra 2/3". Net is almost an inch and a quarter extra.
My clubs are the right length, but they feel too light. I'd like to get
an extra 2 swingweight points on my irons. How much weight should I add
to the head? Head wt per SW point = 2.1g for a 4iron, to 2.3g for a 9iron. Thus, to go up by TWO SW points, add 4.2g to a 2iron (a little under 2*2.1), add 4.6g to a 9iron (2*2.3), and scale the weight added to the clubs between. Realistically, this means "add 4 grams to each club".
I know from experience that I can swing a C8 driver consistently, but
I get a little wild with a lighter swingweight. I've decided to make a
new driver from a head I like that weighs 205 grams. I'd like as long a
shaft as possible, but no shorter than the standard 43"; I'd also like
NOT to spend a bundle on the shaft, so a superstiff superlight shaft
is out of the question. Just for laughs, let's say the shaft has to cost
under $35 and torque under 4 degrees. It should have a midbend point and
a stiff flex.
Remember the "standard DO" data point: 

200 gram head 

128 gram (standardweight steel) shaft 

43" (standard) length 
Let's use it as a starting point, and count swingweight points different
from it.

C8 
Standard is D0, we need to lose 
2 pts. 

205 gm. 
Standard is 200, we need to lose 
3 pts. 

43" 
Let's start with this, and add length only if we find we
can. 

So we need to save 5 swingweight points, and our first tool is to lighten
the shaft.

From the tables, we need 7*5 = 35 grams.

Thus the shaft has to be under 128  35 = 93 grams.
This is easy; a few namebrand shafts in the vicinity are:

Aldila HM30 
$25 
85 gm. 
3.6 deg 

Grafalloy ASW 
$35 
85 gm. 
3.0 deg 

Grafalloy Sen.Pro 
$29 
90 gm. 
3.5 deg 

Kunnan K2 
$28 
100 gm. 
3.6 deg 

TrueTemper Gold+ 
$10 
104 gm. 
2.5 deg 

This shaft data is from the first issue
of these notes, in 1993. The shafts that meet the spec today are more
plentiful
and less expensive. But the principle is the same, so you should have
no trouble going through the example yourself with a current catalog in
your hands. 
How much additional length can we get from one of the lighter shafts on
this list? With the HM30, we have 93  85 = 8 grams to play with. From
the table, we can get another 8/36 inch (which we'll round to 1/4").
Estimating moment of inertia
Here is the same table of sensitivities we had for swingweight, but this time for moment of inertia.

CLUB 



Driver

4Iron

9Iron

Head weight 
200 g 
250 g 
285 g 
Shaft weight 
128 g 
128 g 
128 g 
Total Length 
43 " 
38 " 
35.5 " 




Grams of head wt. per 3000 ginē

1.6 g 
2.1 g 
2.4 g 
Grams of shaft wt. per 3000 ginē 
4.9 g 
6.2 g 
7.1 g 
Inch of length per 3000 ginē 
1/7 " 
1/7 " 
1/8 " 

Head wt vs. Shaft wt. (constant MOI) 
3 
3 
3 
Head wt vs. Length (constant MOI) 
11 g/in 
15 g/in 
18 g/in 
Shaft wt vs. Length (constant MOI) 
34 g/in 
46 g/in 
55 g/in 


You can use it in the same way, if you're trying to design or build a club to a moment of inertia.
Graphs of Moment of Inertia and Swingweight
I keep coming back to these fundamental points:
 Moment of inertia is a basic physical quantity that governs a golf club's behavior.
 Swingweight is an arbitrary measure, adopted because it can be
measured inexpensively, that worked pretty well to match the clubs of a
halfcentury ago.
Given these facts of life, it really behooves us to better understand
the relation between MOI and swingweight  unless you plan to spend a
few hundred dollars on an MOI meter and throw away your swingweight
scale. So let's take another look. And  since I always understand
something better when I can see it visually rather than just words or
numbers  I'm going to look at some graphs.
The first step in understanding the relationship between moment of
inertia and swingweight is to see how each one varies as the
characteristics of the club vary. Our simple equations
for swingweight and MOI are in four variables: club length, head
weight, shaft weight, and grip weight. So let us plot a graph of how both measures
of heft  MOI and swingweight  vary with each of the variables.
In the graphs below, we plot swingweight (the dark blue line) and
moment of inertia (the yellow line) as we vary one of the critical
parameters and hold the others steady at some nominal value. Here are
the values and the ranges:

Nominal
Value

Range of
Values

Club length

40"

34"46"

Head weight

250g

200300g

Shaft weight

90g

50130g

Grip weight

50g

3070g

The vertical axis is in swingweight points, with zero at D0. The moment of inertia has been
scaled and offset so it lies in the same range as the swingweight on
the graph. That way, we can compare by eye how well they track together.
The point of this exercise is to see where swingweight and MOI track
well and where they don't. If they track well, then maybe we can continue to use
swingweight as surrogate for MOI, at least for club matching purposes.
Club Length:
We can see from this graph that swingweight tracks MOI very closely for
club length. With the scaling chosen, the two graphs cross one another
twice. That is because MOI is proportional to the square of length, so
its value is curved instead of a straight line. But the tracking is
very good over the entire range of interest.

Head Weight:
Swingweight still tracks quite well as we vary clubhead weight, though
not as well as for length. The errors are about 5 swingweight points at
the ends, in an overall variation of 50 points. That's about a 10%
error.

Shaft Weight:
Swingweight also tracks MOI quite well as we vary shaft weight. The
errors, as a percent of the total variation, are about 10%, very
similar to the head weight errors.

Grip Weight: Whoops! We have a problem. Not only does swingweight not track
MOI as we vary grip weight; it actually moves in the opposite
direction. While swingweight drops as grip weight increases, MOI is
affected almost not at all  and that effect is to rise slightly.
Now it's time to remember physics and history. The fundamental physical
quantity representing heft is MOI. Swingweight was a convenient,
easilymeasurable quantity that seemed to match clubs about as well as
MOI. But it looks like swingweight does a lousy job of reflecting how
grip weight affects heft.
Why did swingweight last so long as a heft measure with this
discrepancy? Because, until about 1990, nobody played with
grip weight as a heft parameter. All grips were pretty much the same
weight, so you could ignore it in matching clubs. But today there's a
wider range of grip weights available, and people are trying to use it
to trim swingweight to the desired value. But, as this graph shows,
while it may trim the measured swingweight to some target number, that
does not mean the heft of the club will be what you want.
We'll talk a little more about this later in the chapter, when we
discuss backweighting. For now, let's just say that swingweight
adjustment using grip weight changes is phony, false, and bogus.

Here are the things we should learn from these graphs:
 As long as we are adjusting heft with club length, head weight,
and shaft weight, we should be able to use swingweight as a good
estimator for MOI.
 But there is a significant, measurable difference between swingweight and MOI. We can't say that a swingweight match is
an MOI match; we'll have to look for a way to vary swingweight to give
us an MOI match. Looking ahead to the next page, we will look for a sloped swingweight to give a constant MOI.
 If we are going to use swingweight as a way to match MOI, we
should do it either without grips on the clubs or with identical grips
on the clubs. Variations in grip weight will produce variations in
swingweight that are not reflected in the MOI.
Last modified Nov 4, 2006
