Читать книгу Damaging Effects of Weapons and Ammunition - Igor A. Balagansky - Страница 37

The creation of zones is shown in Figure I.19. The epicenter hitting in the zone (p_m) – the inner part of ABCD rectangle – corresponds to covering the whole target (u = 1). Hitting in the zone (p₀) (outer part of ABCD rectangle) means no target coverage (u = 0). We find the probability of hitting in the zones (p₀) and (p_m)_, as well as the outer parts of the dotted rectangles corresponding to u = u_max/3 and u = 2u_max/3

The graph of the function F(u), drawn on four points, is shown in Figure I.20.

Knowing the distribution function F(u) of value U for one shot, it is easy to find its average value (expected value) M = M[U]. For random variables of mixed type, the expected value consists of two parts: sum and integral. The sum is applied to those values that have nonzero probabilities (i.e. where the distribution function makes a jump) and the integral to the area where the distribution function is continuous.

Figure I.19 Illustration to the example: the creation of the law of distribution of the fraction of damaged area.

Source: From Wentzel [2].

Figure I.20 Illustration to the example: function of distribution of the damaged area.

Source: From Wentzel [2].

In our case, there are two jumps in the F(u) distribution function: at 0 and u_max . Hence,

(I.35)

Knowing the function of F(u) distribution of U value for one shot, it is easy to find the probability R_u that for one shot, the damaged fraction U will be not less than the set value u: