Damaging Effects of Weapons and Ammunition. Igor A. Balagansky

value of the full target area (S_t) divided by the average number of hits required (ω) is called the vulnerable area of the target S_v . Typically, during calculations, we consider the projection of the full or vulnerable target area to the direction of the projectile's approach. Then, depending on the prevailing direction of target firing, the full or vulnerable area of the target is referred to as the average full or vulnerable area of the target. The probability of damaging the target, in this case, can be calculated as the probability of hitting the vulnerable target area S_v .

      I.2.5 Generalized Characteristics of the Damaging Effect of Remote Ammunition

      Remote ammunition not only affects targets with a direct hit but also when it explodes at some distance from the target. The target is damaged either by the products of the explosion and shock wave (high‐explosive ammunition) or by high‐velocity fragments (fragmentation ammunition).

      The main characteristic that determines the effectiveness of such ammunition is the coordinate law of damage G(x, y, z). The coordinate law of damage is a functional relationship between the probability of the target damage and coordinates of the explosion point of the ammunition relative to the target [2].

The simplest type of coordinate law is for high‐explosive ammunition, the effect of which is estimated by the target destruction radius R_d . Hence, for high‐explosive ammunition, the coordinate law is expressed as a simple stepwise dependence on the distance to the target R. If the projectile exploded at a distance R ≤ R_d from the target, then G(R) = 1, and at R > R_d , G(R) = 0. The area of space around the target, inside which G(R) = 1, is called the area of unconditional target damage. The boundaries of this area are lines or surfaces equidistant to the target contours (Figure I.2).

      It is more difficult to calculate the coordinate law of damage G(x, y, z) for fragmentation ammunition since the fact of damaging the target is accidental. After all, the number of fragments hitting the target is random at the given breakpoint position, and there is a certain probability that none of the fragments will hit the target or, if hit, will be unable to damage its vital components.

Figure I.2 Zone of unconditional target damage by the blast action.

      Source: From Wentzel [2].

Let's consider a component, the failure of which leads to the destruction of the whole target. Obviously, at some given mutual position of the target and the projectile to calculate the probability of damaging the component g, you need to know the number of fragments n that hit it and the probability of its destruction when hitting one fragment p₁ . If the number of hitting fragments were known precisely, the probability of damaging the component g could be determined by the formula

      (I.4)

      In reality, a different number of fragments may hit a component of the target. Therefore, to calculate the probability of damage of a given component, you need to know the law of distribution of hits, i.e. the probability that a certain number of fragments will hit a given area.

      Experimental data in full compliance with probability theory suggest that the law of distribution of the number of fragments hitting the components, whose angular sizes are small compared with the width of the sector of the fragment field, is close to the Poisson's law [2]. In this case, the Poisson's law formula is as follows

      (I.5)

      where p_n is the probability that exactly n fragments will hit the component; n is a random number of hitting fragments; <n> is an expected value of the number of fragments that fit into the component area.

      Having carried out the corresponding transformations and typed the designation <m > = < n > p₁, we will get the expression for the coordinate law of the damage of the component area

      (I.6)

      The coordinate law of damage the complete target will be written in the same way:

      (I.7)

      where <m> is the expected value of the number of fragments damaging the target.

      In case of a flat scattering of burst points (firing at surface targets), the coordinate law will be determined by two coordinates of the burst point on the plane:

      (I.8)

Studies have shown that coordinate laws of damage vary depending on the nature of the target, ammunition capacity, and other conditions. When considering these laws, three different areas can be identified around the center of the target (Figure I.3). One of these areas (γ_d) is characterized by the fact that a round of ammunition bursting at any point within it always leads to the destruction of the target. This area is called a reliable damage area. This is followed by an area (γ_i) where it does not necessarily result in the target being damaged. This is referred to as the area of unreliable damage. Then there is an area (γ_s) where ammunition does not damage the target at all; this area is called the safe area.

Figure I.3 Areas surrounding the center of the target.

      Source: From Fendrikov and Yakovlev [3].

      I.2.6 Specified Zone of Target Damage

      The form of the coordinate law can be simplified by artificially expanding the area of reliable damage at the expense of the area of unreliable damage and completely eliminating the area of unreliable damage from consideration. The obtained extended reliable damage area is referred to as the specified damage zone of the target, which is characterized by the area S_sp, and its sizes – by the specified target sizes [3]. For all points of the specified zone according to its definition G(x, y) = 1, and outside this zone G(x, y) = 0, in other words, in this case, the coordinate law has a stepwise graph.

      By definition, the area of a specified damage zone can be determined as follows:

      (I.9)