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value of the full target area (St) divided by the average number of hits required (ω) is called the vulnerable area of the target Sv . 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 Sv .

      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].

      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.

      Source: From Wentzel [2].

      (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 pn 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)

      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 Ssp, 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) Скачать книгу