Bat Swing Weights - Moment of Inertia by Michael Ciocco, Ph.D.

The calculation of the Moment of Inertia (MOI) of a bat is detailed in the ASTM proposed test method for measuring softball bat performance factor. The Moment of Inertia is the measure of difficulty to rotate an object about a pivot point. For a bat, MOI is analogous to the bats swing weight.

For a bat the equation to calculate MOI is:

MOI (in²oz.) = (AP)²(9.779(W)[(BP)-(PP)]

Where: W = Bat weight, oz. AP = Average Period, sec. BP = Balance Point, in. (Distance from the end of the knob.) PP = Pivot Point, in. (Distance from the end of the knob.)

The average period is the time it takes the bat to cycle once about it's PP in simple pendulum oscillation. The 9.779 number is a constant with the units (in/sec.²).

The MOI of a series of bats were tested and the results summarized in Table 1. Two different PPs were used, a PP = 6" for a standard grip and a PP = 3.25" for an over-lap grip. As shown in Table 1. using an over-lap grip results in a much greater MOI and therefore greater swing weight. For instance the MOI for the TPS Outlaw with the over-lap grip is 10780 (in²oz.) compared to 8450 (in²oz.) with a standard grip. Also the MOI for the 32 oz. DSW with the standard grip is 10220 (in²oz.) which is less than the 28 oz. TPS Outlaw with the over-lap grip, 10780 (in²oz.). That is, the 28 oz. TPS Outlaw with the over-lap grip is actually harder to swing than the 32 oz. DSW with the standard grip.

It is important to remember these are the MOIs about the rotation of the bat in a players hands. That is, this is a relative measure of how hard it is to "snap" the bat around using just wrists and hands. This measurement illustrates the differences between endloaded and balanced bats.

Another consideration for swinging a bat is how hard it is to rotate the whole bat around the batter's body. Or what is the MOI if the batter, holding a bat as if hitting, locks their arms straight and spins in place. This calculation is fairly simple and involves the weight of the bat and the distance that the BP of the bat is from the center of rotation (the batter). Since every batter is different (arm length) calculating MOIs here is not relevant. However a relative comparison of the MOIs can be made by comparing the weights of the bats. Simply, a heavier bat would almost always be harder to rotate around a batters body than a lighter bat.

When swinging a bat I have found that the MOI about the PP is more important than the weight of the bat. For instance I have an easier time swinging the Thunderstick (MOI = 11370 (in²oz.), Wght = 39.2 oz) than the MVP (MOI = 13200 (in²oz.), Wght = 28.9 oz.) even though the Thunderstick weighs over 10 oz. more than the MVP.

Another important thing to remember is that these are measurements from single bats and slight variations may occur from bat to bat of the same type and weight. Hopefully in the future some duplicates will be measured in order to quantify these variations.

Also in the future additional bats will be measured and added to this list