Читать книгу Damaging Effects of Weapons and Ammunition - Igor A. Balagansky - Страница 25

Let us first consider damaging the target with a single shot. The single‐shot probability of damaging the target W₁ is defined as the probability of a complex event, which consists of hitting the target and damaging it if the target is hit:

(I.17)

where p₁ is the probability of hitting the target with one shot; G(1) is the probability of damaging the target with one shot (the value of the conditional damage law G(m) at m = 1).

With a known average required number of hits ω for a target that has no damage accumulation,

(I.18)

The probability of hitting the target with one shot p₁ can be calculated as follows. If the target is projected on the dispersion plane by lines parallel to the direction of firing, then p₁ is the probability that the point of a hit on the picture plane will be within some region of the target's projection (Figure I.7). This probability is expressed with the formula

Figure I.7 Projecting of a target on a picture plane.

Source: From Wentzel [2].

(I.19)

where φ(x, y) is the law of dispersion (I.11).

In some cases, the integral (I.19) is expressed through known functions. Let us give the corresponding calculation formulas.

1 The target is a rectangle with sides parallel to the principle dispersion axes (Figure I.8).(I.20) where α, β, γ, δ – coordinates of target's boundaries on 0x and 0y axes; is the normalized function of Laplace:(I.21) (the values of this function for different values of the argument are given in the Appendix, Table A.2).Figure I.8 Coordinates of target boundaries.Source: From Wentzel [2].

2 Target – circle, dispersion – circular (Ex = Ey = E). If the dispersion center coincides with the target center (there is no systematic error), the probability of hitting within the circle of radius rt is expressed by the formula(I.22) If the value and configuration of the vulnerable target area Sv are known, the probability of damaging the target can be calculated simply as the probability of hitting the vulnerable target area.Let us now consider what will change if the target is damaged by remote warheads. The probability of damaging the target, in this case, will be determined by the following formula:(I.23) where G(x, y) – coordinate law of damage.If the area of the specified damage zone Ssp and its specified sizes 2lx and 2ly are known, the probability of damaging can be defined simply as a probability of hitting the specified target area Ssp, for example, by the formula (I.20).Thus, whether by contact or remote ammunition, the probability of damaging a single target can always be calculated as the probability of hitting either a vulnerable area of the target Sv or the specified damage zone of the target Ssp .