Analytical Approach to Ballistic Dispersion of Projectile Weapons Based on Variant Launch Velocity

Abstract

This study quantifies the contribution of variant projectile velocity at a gun muzzle to its dispersion at an aim point from an analytical approach. The dispersion was formulated on the basis of stochastic physical conditions including potential crosswind effect. As a result, the statistical quantities of projectile impact distribution could be obtained from the stochastic formulation. In addition, this research proposes correction factors that may be needed when comparing dispersion in angular mil at multiple downrange distances. The significance of the correction factors was demonstrated through a few applicationBallistic dispersion is one of the important metrics that has been used to assess the performance of a weapon system. Over the past two decades, much research has been conducted to characterize target impact dispersion. In general, a wide range of ammunitions, including large-, medium-, and small-caliber projectiles, along with a few different weapon systems, including air guns and electromagnetic guns, has been covered for dispersion study [1][2][3][4]. Most investigations focused on dispersion analysis of experimental data for a particular weapon system. Some published research discussed ballistic dispersion with the consideration of a predefined physical condition from external environment, and others addressed the phenomenon with the demonstration of computer modeling and simulations [5,6].Conventionally, the absolute value of dispersion was initially computed based on a number of rounds at a certain range. Then, the dispersion quantity was divided by tbe corresponding downrange distance to obtain the dispersion in angular mil. This dimensionless unit enables us to compare dispersions at two or more different downrange distances. This comparison of dispersion at multiple distances is valid under the assumption that the projectile flies in a vacuum space. In other words, no external factor is considered in the calculation. Thus, one of the objectives of this study is to formulate the random nature of round-to-round errors in consideration of several varying environmental factors and evaluate if the underlying assumption for the conventional dispersion calculation is appropriate when some external forces are taken into account during flight. This analytical approach links dispersion results to projectile initial velocity conditions or vice versa from a theoretical point of view. When one of these two measurements is available, the other quantity could be derived accordingly. The proposed formulas in this study may be utilized to facilitate performance assessments of weapon systems.This investigation begins with the introduction of the most simplistic case, one where no external force is applied on a projectile during flight. That is, the initial conditions of the projectile at the muzzle remain the same throughout the entire flight period. It has been observed from many experiments that the target impact points (TIPs) were randomly distributed even when the same ammunition and weapon types were fired....

Using a 3D Model to Asses Projectile’s Impact Points Deviation Due to Manufacturing Errors

“…Also, by analyzing data from the test firing, it is possible to identify almost all disturbances leading to the final dispersionfor example, parameters related to aging barrel, inconsistent propellant or variable atmospheric conditions. But even when such an extensive analysis is completed, a certain part of dispersion remains unexplained [6]. This part of dispersion can be largely attributed to manufacturing errors, as the following analysis will show.…”

Effects of Projectile and Gun Parameters on the Dispersion

“…An analytical method has been applied to determine the effect of muzzle velocity variations on the dispersion taking into account the air drag, gravity drop and crosswind 26 . It was found that the muzzle velocity variation, in combination with gravity effect, becomes a significant parameter in determining dispersion in the elevation direction.…”

Effect of surface roughness on crosswind deflection and hit probability for large caliber direct-fire ballistics

“…The first analytical solution to point-mass differential equations was obtained by Johann Bernoulli in 1711 [18]. The Tank Accuracy Model (TAM) is one such point mass direct fire model that represents the theory of tank gun accuracy and was based on the AMSAA PH1 program [16], [19], [20]. It can simulate firing situations for an M1 tank by reading ballistic, fire control, and atmospheric data as well as various error inputs.…”