Moment of Inertia – (The not too technical version)          
   
   
 

One of the new buzzwords in golf is the term Moment of Inertia or MOI for short. MOI can be very confusing subject to discuss, let alone when we are talking about something with a complicated shape as a golf club. But let’s break MOI down to laymen’s terms in order to make it just a little easier to understand.

Moment of inertia is a measurement of the clubheads ability to resist twisting about a known

     
           
 

axis. A higher MOI is supposed to be a strong indicator as to the forgiveness of a clubhead. At impact, the golf ball is not always struck in line with the center of gravity, resulting in the head twisting and consequently consuming energy that could be imparted to the ball. A club with a higher MOI will resist the twisting more so than a lower MOI value.

Drivers went from being solid and made out of persimmon or laminated maple to metal in the early 1980's. Even though the size of the heads is approximately the same, the metal woods increased their MOI over their wooden predecessor by about 25%. This is because the metal heads were not solid, but a hollow shell with a very lightweight density foam injected to dampen sound. All the weight that would have been in the center of the head was distributed to the perimeter, thus the term "perimeter weighting". Since the advent of the petite size metal drivers of the early 1980’s, the MOI has increased nearly three-fold in modern drivers.

In an attempt to cap technology to not diminish the skills of the golfer, the USGA and R&A of St. Andrews put a limit on the moment of inertia of a golf club at 5900g-cm² or 32.259 oz-in². To obtain this type of measurement, precision instruments are available to accurately measure the MOI of a clubhead, usually taking 6 or 9 measurements about different coordinates. Moment of inertia can be measured in several planes. Illustrating this, we will show an example of a cuboid or rectangular sphere as it is the closest shape to the boundaries of a golf clubhead.

 
 


If the face of the clubhead is represented by XY plane, we can see how the object can be rotated around its center of gravity in the Y-axis (or XY plane). In this case, the moment of inertia of the rectangular sphere can be measured using the following formulas.


If you refer to the article Volume- Part II, you will see that golf clubs (drivers in particular) have limits on size as well. If we want to have as broad and long of a cuboid as possible, then the maximum the dimensions would be a 5" (12.7cm) by 5" (12.7cm) base. If we wanted to achieve a 460cc volume (28.05 in³), then the maximum height could only be 1.12" (2.85cm) tall. Since most drivers are roughly 200g, we can input the variable into the equation and the
moment of inertia about the Z-axis would be 5376g-cm² or approaching to what the USGA limits are.
 
The weight of the golf club has tremendous effect on the moment of inertia. Heads that are heavier would have an increased MOI. So why not simply add more weight? To reach the limit of 5900g-cm² then all you would have to do is increase the weight to approximately 219g using the dimensions above. The problem is that is about the same weight as a #5 wood, thus would be proportionate in length unless the person wanted to wield a club that was very head heavy at today's driver lengths.

The shape of our example was used because it was a simple shape and one that it easy to measure the MOI. Obviously, clubheads are much more rounded and asymmetrical and would not apply exactly to the formula. But if one could use it as a reference, then all we need to do is think inside the box. Examine this diagram(mouse over) of the cross section of a clubhead and see that the volume of the club takes up a percentage of the overall rectangle. The hosel was omitted from two of the diagrams as it not considered part of the volume of the head, but is important to the moment of inertia calculation.

The modern driver, fairway wood and hybrid is basically a hollow shell of minimum wall thickness made of either all titanium or stainless steel, plus may have added elements such as carbon crowns, weighted screws or other non-visual weights within the head. To start, let’s say the clubhead is made of a single material of similarly uniform wall thickness.

Because of the "Plain in Shape" rule by the USGA, most drivers take on a similar shape, just the proportions in height, length and width are different. So it is possible to predict within an acceptable tolerance what the MOI may be by measuring several heads and applying a best-fit formula to results based upon the dimensions. Remember, if we want to measure it precisely, then you will need a measurement devise that runs several thousand dollars.

Here is a formula for MOI in the face plane that one could use on basic shaped drivers, fairways, and hybrids made of a single material and did not have internal weighting within the head. It is important to measure the clubhead the same way we do.

 

To give you an example, let’s use the Synchron Medic and the Acer XP905 drivers. Both of these heads are 460cc, but their shapes are slightly different with the Acer XP905 being more "pear-shaped", while the Synchron Medic is more full-bodied. We also used an intentionally light, unfinished Synchron Medic head to demonstrate effects on MOI.
Model
Weight
X Dimension
Y Dimension
Calculated
Actual
Acer XP905
199g
12.55cm
10.4cm
4185g-cm²
4174g-cm²
Synchron Medic
185g
12.33cm
10.6cm
3873g-cm²
3889g-cm²


As we have limits to clubhead size, we still need to maintain a normal weight of a clubhead and to make the wall thickness great enough to withstand the collision of a golf ball at high speeds. In turn, MOI will have limits as well. But there are a couple of other things that can be done to increase the MOI. One is to better utilize the shape, like in the direction of the new "square-shaped" drivers.

In the illustration above, you can see that the driver on the right has more material toward the corners of the box effectively moving weight further from the center of gravity of the head and to help increase the moment of inertia and make the club more stable on off-center shots.

The other method of increasing the MOI of a clubhead is reducing the weight as much as possible by making the walls as thin as possible without risk of breaking under normal conditions. The modern 460cc titanium driver already has paper-thin walls in the non-stress areas of the head; therefore a foreign material lighter than titanium may be incorporated into the head. The most common example of this is carbon graphite, usually in the crown of the club. The weight savings is called “discretionary weight”, as the designer can now re-positioned it in strategic locations within the head, most often lower and rearward in the modern clubhead, but more importantly away from the center of gravity.

In our example above with the underweight Synchron Medic driver, we drilled and tapped two holes through the rear of the club to accept weighted screws as we wanted to see the effect by adding additional weight. Once the initial moment of inertia has been determined, then it becomes easier to determine what the MOI will be when something is added to it as long as one knows the exact weight and the distance that weight is from the center of gravity. You can see how the MOI adds up quickly with the addition of weight far from the center of the head in the chart below.

Model

Initial
Weight

Weight
Added
Distance
From CG
MOI
Addition
Final
MOI
Synchron Medic
185g
10g
5.88cm
346g-cm²
4235g-cm²
195g
10g
5.55cm
308g-cm²
4543g-cm²


To increase to moment of inertia any higher on a driver will become more and more complicated to produce. More importantly, it will come at a high cost with the addition of lighter, foreign or multi-material adjuncts fastened within the head. Regardless, new designs are all about helping you find more fairways off the tee, more greens in regulations and less putts to lower your score and make the game a more enjoyable experience.

by Jeff Summitt
Hireko Technical Director
jsummitt@hirekogolf.com