Sunday, December 30, 2012

Measuring Effectiveness of Cartridges: Optimum Game Weight Formula

We've studied several empirical formulae in the last few pages: The Taylor KO Factor, the Thorniley Stopping Power Formula and the Hatcher Formula. In todays article, we will study another formula called the Optimum Game Weight formula.

This formula was devised by Edward A. Matunas and was first published in the April 1992 issue of Guns magazine. The author claimed that this formula was devised based on studying the effects of kinetic energy, momentum, bullet sectional density, diameter, bullet nose shape and other criteria. However, the author did not elaborate on how he managed to derive his formula.

The Optimum Game Weight formula is defined as:

OGW = V3 * W2 * 1.5 * 10-12

OGW = Optimum Game Weight in lbs.
V = velocity of bullet in feet per second
W = weight of bullet in grains

For hunting bullets, the constant used in the equation is 1.5 * 10-12. For varmint bullets, it is recommended to use 5.0 * 10-13 instead. What the OGW value tells us is the approximate maximum weight in lbs. of an animal that can be reliably killed by a particular cartridge. It is assumed that the hunter has selected an appropriate bullet type for the job.

For an example, let us consider the same rifle and cartridge that we studied with the Thorniley Stopping Power formula, two posts earlier. This is a .30-06 rifle that fires a bullet of .308 inch diameter, weighing 180 grains at approximately 2900 feet/sec. Plugging the numbers into the formula above, we get:
OGW = 29003 * 1802 * 1.5 * 10-12 = 1185.31 lbs.

This means that this formula indicates that the rifle and cartridge combination can be used to kill animals weighing up to 1185 lbs or so. Remember though that this formula is empirical and the values obtained are approximate. Also, bear in mind that we computed the velocity of 2900 feet/sec at the muzzle of the weapon and if we measured the velocity of the bullet at some distance from the rifle, it may have decreased to something like 2500 or 2600 feet/sec. Therefore the OGW value will decrease over distance.

The author included a table listing the OGW values for various common cartridges. While these numbers seem to agree with many hunters experiences, there are also some issues with this formula. Even though the author claims to have considered bullet section density, bullet diameter, bullet nose shape and bullet construction in his study, none of these appear in the formula. Therefore, according to this formula, a 150 grain bullet moving at 2800 feet/sec will behave the same, whether it is a .270 Winchester or a .30-06 bullet, whereas the performance of these two bullets are very different in real life. Also note that this formula does not care if the bullet type is a jacketed bullet, lead bullet, hollow-point, round nose etc.

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