Damaging Effects of Weapons and Ammunition. Igor A. Balagansky

Damaging Effects of Weapons and Ammunition - Igor A. Balagansky


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target T so that the random point O1 (the epicenter of the explosion) is dispersed around the origin of coordinates O according to normal law. The probable deviations, chosen as units, are equal to one. It is necessary to find the average damaged fraction U.

      (I.33)upper U equals StartFraction upper S Subscript d Baseline Over upper S Subscript t Baseline EndFraction period

Schematic illustration of mutual position and sizes of the target and the damage zone.

      Source: From Wentzel [2].

Schematic illustration of random area overlapping the damage zone with the target.

      Source: From Wentzel [2].

u Subscript max Baseline equals StartFraction upper S Subscript upper L Baseline Over upper S Subscript t Baseline EndFraction equals StartFraction upper L Subscript x Baseline upper L Subscript y Baseline Over upper T Subscript x Baseline upper T Subscript y Baseline EndFraction period Schematic illustration of complete coverage of the target area by a damage zone.

      Source: From Wentzel [2].

u Subscript max Baseline equals 1 period

      One or another, at any ratio of damage zone and target size, there is some maximal value of umax of damaged fraction U.

      A random value U is a so‐called mixed type value that has separate values with finite probabilities other than zero and intervals where the distribution function is continuous and only a certain probability density corresponds to each individual value. The distribution function (integral distribution law) for such random variables has breaks (jumps) in several points, and in the intervals between them grow continuously [4].

      Remember that the integral law of distribution of the portion of the damaged area at one shot determines the probability of the occurrence that the portion of the damaged area U will be less than that specified by argument u.

upper F left-parenthesis u right-parenthesis equals upper P left-parenthesis upper U less-than u right-parenthesis p 0 equals upper P left-parenthesis upper U equals 0 right-parenthesis comma p Subscript m Baseline equals upper P left-parenthesis upper U equals u Subscript max Baseline right-parenthesis period

      For intermediate values 0 < u < umax, the distribution function is continuous and the probability of each individual value is zero.

      At a single shot, it is not difficult to build an exact law of U value distribution.

Schematic illustration of the function of the damaged fraction distribution with one shot.

      Source: From Wentzel [2].

Schematic illustration of creating a distribution law of a portion of the damaged area.

      Source: From Wentzel [2].

Schematic illustration of creating a distribution law of portion of the damaged area.

      Source:


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