Читать книгу Damaging Effects of Weapons and Ammunition - Igor A. Balagansky - Страница 17

The conditional damage law is particularly simple if there is no accumulation of damage. Accumulation of damage is the phenomenon where the projectiles “help each other” to damage the target, i.e. when the target can be damaged by the combined action of two or more projectiles (or other hitting elements), neither of which, used separately, would damage the target. For example, if an airplane target has fuel tanks with an inert filler, it often requires at least two projectiles to destroy such tanks, the first of which penetrates the tank and the second ignites the fuel spill. Strictly speaking, the accumulation of damage always takes place. However, in most cases, it is negligible and can be ignored.

Suppose there is no accumulation of damage and the projectiles damage the target independently of each other. Let's denote r the probability of damaging the target if one projectile hits it. Then the law of damage G(m) – the probability of damaging the target when m projectiles hit it – is equal to the probability that at least one of the projectiles will damage the target:

(I.2)

Such a law of damage is called a degree law. So, if there is no accumulation of damage for some target, its law of damage is a degree law, where r is the probability of damaging the target in one hit.

The value of r can be interpreted as the relative area of vulnerable target components. Indeed, let the target consist of only two types of components: certainly vulnerable and absolutely non‐vulnerable. Then the probability of damage is equal to the probability that a projectile hitting the target will hit its vulnerable components. If we consider the distribution of projectiles hitting the target to be approximately uniform, which is true for small targets, the r‐value will be equal to the relative area of vulnerable components.

It can be demonstrated that for a target that has no accumulation of damage, the average number of hits required is the value inverse of the relative area of its vulnerable components:

(I.3)

The 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 .