S
ome of the statistical techniques used by armaments engineers and scientists to evaluate the accuracy and precision of weapons and
munitions can result in increased risk to the warfighter. It is the responsibility of the armaments community to fully understand the statistical implications of choosing a specific dispersion metric to assess performance.
TARGET IMPACT DISPERSION MODEL The bivariate normal impact distribution approach is used to model the dispersion of shot groups on a target, whether for small- caliber ammunition being fired at paper targets on a shooting range, artillery rounds impacting a target area on the ground, or darts being thrown at a dartboard.
When, for example, 10 rounds are fired at a target on a rifle range in what is typi- cally referred to as a “shot group,” each of their impact locations is a point (xi
, yi )
on the two-dimensional surface. Most of the rounds will tend to cluster around the center of impact (CoI), which is the aver- age of all points in the x and y direction (x,y), and is the best estimator of the true mean (µx
, µy ). If the weapon’s aiming sys-
tem is in zero with the ammunition, this means that the mean (µx
, µy with the point of aim such that (µx
) is aligned , µy
) =
(0, 0). Therefore we can disregard aiming error, and for the purpose of this discus- sion concern ourselves only with the weapon system’s precision.
Weapon system precision is defined by the expected error of an individual round, or “sigma” (σ).
As the distance from the CoI increases radi- ally (where distance = (xi
-µx)2 + yi-µy)2 )
on the target, the frequency of shot impacts should decrease in a manner directly related to the magnitude of σx
A S C . A RMY.MI L 69 RESEARCH AND DEVELOPMENT
Soldiers from the 82nd Airborne Division visit the Aviation and Missile Research, Development and Engineering Center’s Small Unmanned Aerial Vehicle Laboratory. (U.S. Army photo by Merv Brokke.)
and σy
, as defined by the Bivariate Nor-
mal Impact Distribution. This is similar to the way in which the distance in ‘k’ σ’s from the mean of the normal dis- tribution (with which many of us are already familiar) affects the frequency of data. That is, 95 percent fall within the range described by -1.96σ < µ < 1.96σ. This relationship affords the analyst the ability to calculate the hit probability, or P[Hit], given a specified target size and shape in relation to (σx
, σy ), by calcu-
lating the area under the distribution’s surface in the x and y direction spanned by the target.
MEASURES OF DISPERSION AND MINUTE OF ANGLE An often-heard expression in long-distance shooting circles is “minute-of-angle,” or MOA. A “1 MOA weapon system” refers to the ability of the weapon and ammu- nitions to consistently shoot three- to
five-round groups that measure approxi- mately 1 inch at 100 yards, approximately 5 inches at 500 yards, approximately 10 inches at 1,000 yards, etc. But without details about the method used to measure the shot group, we are lacking important contextual information.
Dispersion metrics commonly used to measure weapon or munition shot group precision include mean radius (MR), radial standard deviation (RSD), circular probable error (CPE), extreme horizon- tal and vertical spread (EHS/EVS), mean horizontal and vertical deviation (MHD/ MVD), extreme spread (ES), etc.
In fact, each of these measures is directly related to σ, which we previously defined as the expected error of an individual round. For any group of shots on a target, we can calculate all of these mea- sures simultaneously.
SCIENCE & TECHNOLOGY
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