Design Notes - Heft: swingweight and MOI p3

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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, gram-inches. One swingweight point is 50 gram-inches 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 mass-times-length-squared. For instance, the usual units for a US clubmaker would result in a MOI measure of gram-inches-squared. Tom Wishon's frequency meter (which we will discuss later) measures in MOI in kg-cm-squared. If you work out the units, you'll find that

1 kg-cm-squared = 155 gram-inches-squared

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 heft-sensitivity 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 moment-of-inertia difference of about 3000 gram-inches-squared. (3140 at the length of a driver, and 2940 for a wedge.)
Or, for Wishon's preferred units, a swingweight point corresponds to a moment-of-inertia difference of about 20 kg-cm-squared.

What this tells me is that a set that is matched to within 1 swingweight point (or 3000 gram-inches-squared, or 20 kg-cm-squared) 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 4-Iron 9-Iron

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 first-cut 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 swingweight-match, a gram of head weight is worth 5 grams of shaft weight.
If you're going to MOI-match, 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 4-iron,
                       to 2.3g for a 9-iron.
Thus, to go up by TWO SW points,
    add 4.2g to a 2-iron (a little under 2*2.1),
    add 4.6g to a 9-iron (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 C-8 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 super-stiff super-light 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 mid-bend point and a stiff flex.

Remember the "standard D-O" data point:

200 gram head

128 gram (standard-weight steel) shaft

43" (standard) length

Let's use it as a starting point, and count swingweight points different from it.

C-8 Standard is D-0, 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.

Aldila HM-30	$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.

Estimating moment of inertia

Here is the same table of sensitivities we had for swingweight, but this time for moment of inertia.

	CLUB

	Driver	4-Iron	9-Iron
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 g-in²	1.6 g	2.1 g	2.4 g
Grams of shaft wt. per 3000 g-in²	4.9 g	6.2 g	7.1 g
Inch of length per 3000 g-in²	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 half-century 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	200-300g
Shaft weight	90g	50-130g
Grip weight	50g	30-70g

The vertical axis is in swingweight points, with zero at D-0. 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, easily-measurable 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