Читать книгу Damaging Effects of Weapons and Ammunition - Igor A. Balagansky - Страница 34

As an indicator of the effectiveness of firing at an area target, an expected value of the fraction of the damaged area is often used.

(I.31)

where U = S_d/S_t is the ratio of the damaged area to the full target area.

In general, if no assumptions are made about the target, damage area, and firing conditions, the task of evaluating the effectiveness of firing at an area target becomes quite difficult. However, taking into account the overall low accuracy of the information we have about the area target, we can make a number of assumptions and significantly simplify the problem. In particular, it makes no sense to enter into the calculation of the exact configuration of the target and the damage area, and it is possible to replace both areas with rectangles.

Let's accept the following assumptions:

 the target is a rectangle with dimensions Tx, Ty, with sides parallel to the principal axes of dispersion;

 the damage zone is also a rectangle with the dimensions of Lx, Ly, with the sides parallel to the principal dispersion axes.

Let's imagine the process of firing at an area target as if each time when the target T is shot, the damage area of L is reset onto the target. The position of zone L with respect to the target T is characterized by one random point O₁, the epicenter of the explosion, which may take one or another position with respect to the origin of coordinates – the aiming point O. If the origin of coordinates O coincides with the center of the target, it is said about aiming at the center of the target; if it does not coincide, it is said about a takeaway aiming point from the center of the target.

Depending on which position the O₁ point will take as a result of the shooting, the damage zone L will cover one or another part of the target area (Figure I.10). For several shots, the damaged target area depends on the concrete location of the centers of all damage zones. The total damaged area S_d does not equal the sum of the areas damaged by the individual shots, as the damage zones may overlap. Where there are overlaps, the increase in the destructive effect is usually neglected in target zones that are covered twice, three times, or more, and the damaged area S_d is taken to be the area covered by at least one damage zone. By dividing the damaged area of S_d by the target area of S_t, we obtain a portion of the damaged area.

This random value characterizes the success of firing at an area target.

Figure I.10 The mutual position of the target area and its damaged zone.

Source: From Wentzel [2].

Thus, we are interested in the average fraction (expected value) of the damaged area M = M[U]. The methods of calculating of this value are different depending on whether one or more shots are fired at the target.