Design Notes - Heft: swingweight and MOI p4

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Reference

Measuring Swingweight

Measuring swingweight is more accurate than estimating it from tables or equations. So why did I wait so long to touch on it? Well, so far I've been dealing with the early design process, the part where you're selecting the components to order from a catalog. Once you have the components in hand, actual measurement is superior to (or at least a valued adjunct to) calculation or estimation.

There are two common ways to measure swingweight:

With a swingweight scale. We covered this early in the chapter on heft.
With a gram scale and other general-purpose shop tools.

Of course the swingweight scale is the fastest and easiest way to measure swingweight. A typical swingweight scale costs about $100, but they are available for as little $50 for an economy model (similar to the Ping scale I've used for years), and as much as $300 for a deluxe digital version. Every professional clubmaker has a swingweight scale, but most beginners and even some serious amateurs can't justify the purchase. For them, here is a way to measure swingweight with more general-purpose tools. It is less convenient, and requires computation, but uses tools you should have anyway if you're going to build clubs.

You will need a good postal scale that measures in grams or small fractions of ounces, and a ruler that measures to over 40 inches. You have to take pains to be precise. Remember:

A 0.1 ounce (3 gram) error in weight will result in more than one swingweight point of error in the result.
A 1/4" error in position of the CG will result in more than one swingweight point of error in the result.

This should give you some idea of just how good your scale has to be.

Having covered that caveat, here's the method. (My thanks to Rich G. Ciccotti for pointing out this method from Ralph Maltby's book.)

Measure the distance of the balance point of the club from the end of the grip (in inches).
Subtract 14" from the result, and multiply it by the club's total weight in ounces or grams.
The result is the torque (in inch-grams or inch-ounces) about an axis 14" from the butt, the base definition of swingweight.
Use the following table to convert to the swingweight point scale:

Swingweight	Inch-ounces	Inch-grams
C-0	196.00	5550
C-1	197.75	5600
C-2	199.50	5650
C-3	201.25	5700
C-4	203.00	5750
-
C-5	204.75	5800
C-6	206.50	5850
C-7	208.25	5900
C-8	210.00	5950
C-9	211.75	6000
-
D-0	213.50	6050
D-1	215.25	6100
D-2	217.00	6150
D-3	218.75	6200
D-4	220.50	6250
-
D-5	222.25	6300
D-6	224.00	6350
D-7	225.75	6400
D-8	227.50	6450
D-9	229.25	6500
E-0	231.00	6550

Measuring Moment of Inertia

Like swingweight, measuring moment of inertia is more accurate than computing it from the component specifications. And it can be done. The instrumentation to directly measure MOI is considerably more expensive and complex than swingweight, because MOI is a dynamic quantity while swingweight can be measured statically.

...With a Pendulum

The simplest way to measure the moment of inertia of a golf club is to mount the club the club by the butt in a frictionless bearing, and let it swing like a pendulum. The period of the pendulum's swing is partially determined by the moment of inertia of the club. We can find the equation for the period (T, a time in seconds) in most college physics textbooks:

T = 2πsqrt( I
mgL )

Where:

T =
The period of a full cycle of the pendulum, in seconds.

I =
Moment of inertia. (Scientists use "I", not "MOI")

mg =
Total weight of the club (mass times the acceleration of gravity)

L =
The distance from the axis to the balance point of the club.

Note that everything here except the moment of inertia can be measured with tools on hand:

Period of the pendulum with a stopwatch.
Weight with a scale.
Position of the balance point with a ruler.

That means that you can measure everything else and solve the equation for I, the moment of inertia of the club. The solution turns out to be:

I = const * T² m L

where the constant depends on the units you're using for mass (grams, Kg, or ounces), length (inches or cm), and moment of inertia.

If you are so inclined, you can do it all yourself.

You measure length and weight all the time. This part is not a problem.
The computation is easy, just multiplication on a calculator.
Measuring the period accurately enough is harder, but you can do it. You can probably click your stopwatch accurately to within a fifth of a second (0.2 sec). The period for most clubs is in the vicinity of 2 seconds. So you are only measuring to an accuracy of 10%, not nearly good enough. You will have to let the pendulum swing for a counted number of cycles (somewhere in the 20 cycle range will be OK), and divide the total time by the number of cycles.

If you do this all the time, it might be worth the money to get one of the moment of inertia meters on the market. Tom Wishon's was probably the first, and seems to by typical of the breed. It consists of:

A pivot that grips the club at the butt and allows it to swing like a pendulum.
An electronic timer that measures the period of a pendulum swing. The technology is much like that of an optically-sensed frequency meter.
A computer program that prompts you for measured period, m, and L -- you still have to measure mass and balance point -- and gives you back a moment of inertia.

There are convenience features and new variations, but basically that is how they work. And you can use them like a swingweight scale to match a set of clubs. But you're now matching them according to MOI rather than swingweight.

As of 2008, there is another, better MOI meter on the market. GolfMechanix makes a device they call the Speed Match. Think of it as a horizontal pendulum, so gravity does not play a part. Instead, the club vibrates back and forth against a spring. So the moment of inertia is a function of only the spring constant (which is built into the instrument) and the period (which is measured by the instrument). This gives a more precise MOI measurement than the pendulum (no errors due to weight or length measurements), and possibly more accurate as well (this depends on how carefully the spring is calibrated).

...With a Swingweight Scale

But wait! Usually you are matching a set to a club that you have determined is the right heft for the golfer. It isn't important to know the numerical value of the MOI, just that all the clubs have the same MOI. If that is the problem you are trying to solve, you can do it with your swingweight scale.

Let me start with the rules of thumb for matching MOI with a swingweight scale, and how to use them to MOI-match a set of clubs. Then we'll discuss why the procedure works, with lots of numerical examples.

First, the simplest possible guideline:

The swingweight should go down by one point for every inch the club's overall length increases. That's a simple slope of one point per inch.

Now, here's a somewhat more precise and general guideline:

The swingweight should go down by 1.3-1.4 points for every inch the club's overall length increases. That's about one and a third points per inch. This is a little more precise about the slope.
If, at some point in the set being matched, you change shaft models so that one is substantially lighter than the other, then add one swingweight point to the target swingweight for each 20 grams the raw, uncut shaft gets lighter.

So what does this say about how to build an MOI-matched set using your swingweight scale? A lot of the process is the same as swingweight-matching a set, using adjustments controlled by what you see on the swingweight scale. Here are the differences:

You are not trying to match all the clubs to the same swingweight. Measure the swingweight of the club whose heft you're trying to duplicate -- that's the same as swingweight matching -- but then make a list of target swingweights for each of the clubs. You will use the guidelines above to come up with the target swingweights.
Make sure you are measuring swingweight with the same grips on all the clubs. Better yet, match them before you put the grips on. That's because we know that, while grips will affect the reading on the swingweight scale, they have very little effect on MOI. So, if you're matching MOI using a swingweight scale, you have to take the grip weight out of the picture. (Actually, that's also a great idea with swingweight matching as well -- but the logic for it isn't as obvious as for MOI matching.)
You can adjust the swingweight to get the target weight using either clubhead weight or the length interval between the clubs. Again, you can do this when adjusting swingweight as well. But you're more likely to need length interval adjustment when trying to MOI-match a set. That's because the clubheads you buy as components have a weight interval built in that assumes swingweight matching. You're going to need heavier short iron heads. Even more of a problem, you may need lighter heads for your longer clubs. While you can generally add weight, it's very hard to remove it from a clubhead.
Tom Wishon, who has more experience with MOI-matched clubs than almost anybody, says that you should not use the same MOI for the woods that you do for the irons. He's probably right; it's a good idea to fit woods and irons separately, for reasons I laid out at the beginning of this chapter.

Pretty simple, huh? Well, if you don't think so, then use a pendulum and measure the MOI itself.

The rest of this page is a bunch of numerical examples intended to convince you that MOI-matching with a swingweight scale works. I used an Excel spreadsheet to design a number of MOI-matched sets, and looked at the swingweights that resulted -- again using the spreadsheet. Carey Winquist built the spreadsheet using the formulas from earlier in this chapter.

Remember that I cautioned about putting to much faith in the accuracy of those equations. So why should I believe them now? For one thing, Carey was very careful to use as much information about the components as possible -- much more than my simplest equation, and closer to the exact equation. But there is a more important reason. The sort of thing that fools the equation for swingweight also fools the equation for MOI -- and by a similar amount in the same direction. For instance, a shaft with a high balance point will reduce the swingweight; but it will also similarly reduce the MOI. This sort of thing is true for all the clubhead and shaft properties that might fool the equation. So, if you build to a measured swingweight and not just the length and weight on the spreadsheet, it is very likely that you will get the expected MOI.

That means you need to be working with a real swingweight scale to get the MOI match, not just using the trim and weight from the spreadsheet. Any errors the components induce in the equations will affect the swingweight and MOI similarly, so a sloped swingweight according to the guidelines will give a pretty darn good MOI match. You may have noticed that I never mentioned an 8-gram head weight interval nor a 0.4-inch length interval, as I did in my earlier recommendations. You will get a much more accurate MOI match if you work from swingweight rather than computed dimensions.

Anyway, here is the raw data pasted from the spreadsheet, so you can see for yourself what is happening...

First I did a simple match, MOI-matching across a whole set with graphite shafts. I started with pre-determined lengths, and chose the head weights to give an MOI match. The graph is a plot of swingweight vs club length, for the MOI-matched clubs. It is very close to a straight line, with a slope of 1.35 points per inch. That means that for this combination of shaft weight and starting head weight, you can MOI-match a set of clubs by building them so the swingweight decreases 1.35 points for each inch longer the club is.

Club	Length (inches)	Head Weight (grams)	Swingweight (points above/below D-0)	MOI (1000s gram- inches²)	Slope = 1.35 points per inch
D	44	197.5	-4.3	420
3W	43	208.5	-2.7	420
5W	42	220	-1.3	420
7W	41	232	0.0	420
2I	39.5	246	1.9	420
3I	39.0	253	2.5	420
4I	38.5	260.5	3.2	420
5I	38.0	268.5	4.0	420
6I	37.5	276.5	4.6	420
7I	37.0	285	5.3	420
8I	36.5	293.5	5.9	420
9I	36.0	302.5	6.5	420
Note: All the runs have in common: 52-gram grips on all clubs. Graphite shafts weigh 75 grams raw uncut. Steel shafts weigh 118 grams raw uncut.

But is the straight line and 1.35 slope a general property of swingweight-matched clubs? Or is it just a property of the particular set I matched? I designed a few more sets with different constraints to find out.

First I repeated the exercise for a set of steel-shafted clubs, built to the same lengths and MOI as the graphite-shafted set above. Again, the swingweight is a nearly straight line, this time with a slope of 1.3 points per inch. So far at least, we have a consistent slope.

But the swingweight plot is at a considerably lower swingweight for each club. On average, the steel clubs have 2.2 points less swingweight than the graphite clubs, for the same MOI. That means that shaft weight matters. When we divide the 43 grams difference in shaft weight by the 2.2 points of swingweight, we get 20 grams per point. That means that, for every 20 grams of shaft weight increase, we have to decrease the target swingweight by a point.

Club	Length (inches)	Head Weight (grams)	Swingweight (points above/below D-0)	MOI (1000s gram- inches²)	Slope = 1.3 points per inch Swingweight about 2.2 points less than graphite ( 20 grams per point )
D	44	181	-5.9	420
3W	43	192	-4.6	420
5W	42	204	-3.1	420
7W	41	216.5	-1.8	420
2I	39.5	232.5	-0.5	420
3I	39.0	239.5	-0.1	420
4I	38.5	247.5	0.8	420
5I	38.0	255.5	1.4	420
6I	37.5	264	2.2	420
7I	37.0	272.5	2.8	420
8I	36.5	281.5	3.5	420
9I	36.0	290.5	4.0	420

For my next trick, I matched a set where the irons had steel shafts and the woods graphite. If the rules of thumb are valid, we would expect a pair of straight lines, each with a slope of 1.3 to 1.4, and offset from each other by several swingweight points. With a 43-gram difference between the raw shafts, the offset should be 43/20 = 2.2 swingweight points.

And that is pretty much what the data shows. The two segments have slightly different slopes of 1.3 and 1.4, but both well within the guidelines. The offset between the two segments is about 2.5 points -- close enough to the 2.2 points from the guidelines.

Club	Length (inches)	Head Weight (grams)	Swingweight (points above/below D-0)	MOI (1000s gram- inches²)	Slope (irons) = 1.3 Slope (woods) = 1.4 Swingweight about 2.5 points less in steel ( 17 grams per point )
D	44	197.5	-4.3	420
3W	43	208.5	-2.7	420
5W	42	220	-1.3	420
7W	41	232	0.0	420
2I	39.5	232.5	-0.5	420
3I	39.0	239.5	-0.1	420
4I	38.5	247.5	0.8	420
5I	38.0	255.5	1.4	420
6I	37.5	264	2.2	420
7I	37.0	272.5	2.8	420
8I	36.5	281.5	3.5	420
9I	36.0	290.5	4.0	420

So far, we have achieved the swingweight match by adding or subtracting weight to the clubheads. But we know (from the graphs on the previous page) that swingweight and MOI don't track exactly the same way if you vary head weight or vary length. So suppose we just took a standard set of clubheads, and achieved the MOI match by messing with the length interval between the clubs instead of the clubhead weights. Would we see the same result?

I did it. Here is the result. The range of club lengths over the set is a little compressed, as we would expect. But the compression is not all that much: 7.4" instead of 8.0" with the usual increments.

And the guidelines are still pretty good. Again, the two segments (graphite woods and steel irons) have slightly different slopes: 1.2 and 1.4. But those are still pretty consistent with the guidelines. And the offset is again about 2.5 swingweight points between graphite and steel, giving a shaft weight allowance of 17 grams per swingweight point.

Club	Length (inches)	Head Weight (grams)	Swingweight (points above/below D-0)	MOI (1000s gram- inches²)	Slope (irons) = 1.2 Slope (woods) = 1.4 Swingweight about 2.5 points less in steel ( 17 grams per point )
D	43.80	200	-3.8	421
3W	42.90	210	-2.3	421
5W	42.05	220	-1.0	421
7W	41.20	230	0.0	421
2I	39.35	235	-0.2	421
3I	38.90	242	0.6	421
4I	38.45	249	1.2	421
5I	38.00	256	1.7	421
6I	37.60	263	2.4	421
7I	37.20	270	3.0	421
8I	36.80	277	3.5	421
9I	36.40	284	3.9	421

Another confirmation of this approach is anecdotal and purely empirical. In September of 2009, I got a call from Charles Homes, a professional auto mechanic and serious amateur golfer and clubmaker. Without having ever heard of MOI matching, he spent months tinkering with the swingweight of his irons until they all felt alike when he swung them. The result was the best set of irons he had ever used. He had run across my web site, and wanted to ask me what I made of his experience. He gave me the measurements of his irons, 6-iron through gap wedge. Here is how they plot, swingweight vs length.

The yellow dotted line is the best-fit linear regression line, the best straight-line fit to the data. Things to note:

The fit is really good, both by eye and according to the .94 correlation measure R-squared. So the best fit for Charles probably is indeed a straight line for swingweight vs length.
The slope of the yellow line is 1.28 points per inch. That is almost incredibly close the the 1.3 slope proposed above.

This admittedly limited and anecdotal evidence implies that matching clubs on a 1.3 swingweight slope is a very good way to make them play the same.

My conclusion is that you can MOI-match a set of clubs quite well using a swingweight scale and some fairly simple guidelines. I have built sets of irons like this and corresponded with others who have, and the results are uniformly good. The clubs are playable and the subjective reaction of golfers who try them is that they feel very similar.

My older guidelines were based on matching sets of irons only. But these new rules of thumb, based on a per-length slope rather than a per-club slope, seem to work well for woods as well.

Last modified Oct 16, 2009