Damaging Effects of Weapons and Ammunition. Igor A. Balagansky
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Название: Damaging Effects of Weapons and Ammunition

Автор: Igor A. Balagansky

Издательство: John Wiley & Sons Limited

Жанр: Химия

Серия:

isbn: 9781119779551

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СКАЧАТЬ degree of dependence between the shots can be characterized by the correlation ratio of the hit points coordinates. In the scheme of two error groups, the correlation ratio for each pair of shots is equal to the ratio of the square of the group error probable deviation to the square of the total error probable deviation:

      (I.14)normal mu Superscript left-parenthesis x right-parenthesis Baseline equals StartFraction upper E Subscript x Baseline 0 Superscript 2 Baseline Over upper E Subscript x Baseline 0 Superscript 2 Baseline plus upper B Subscript d Superscript 2 Baseline EndFraction comma

      (I.15)normal mu Superscript left-parenthesis y right-parenthesis Baseline equals StartFraction upper E Subscript y Baseline 0 Superscript 2 Baseline Over upper E Subscript y Baseline 0 Superscript 2 Baseline plus upper B Subscript s Superscript 2 Baseline EndFraction period

Schematic illustration of effect of the group and individual shooting errors.

      Source: From Wentzel [2].

      Theoretically, there can be two extreme cases of dependence between shot errors: the first case is when there is no common error source, i.e. no repeating component (μ = 0); the second case is when all error sources are common, i.e. all components are repeated as many times as the shot is fired (μ = 1). In the first case, the shots will be independent, and in the second case, the shots will be functionally dependent. With concentrated firing and independent shots, the ammunition hits into different points randomly spread around the center of aim, and with functionally dependent shots, all ammunition hits into the same point at a random distance from the center of aim.

      I.3.5 Probability of Damaging a Single Target

      The probability of damaging a single target W is one of the key indicators of combat effectiveness in the theory of firing, which underlies the calculation of many other indicators. A single target is damaged by one or more shots. Most methods of estimating the effectiveness of multiple shots are based on a preliminary determination of the probability of a single shot damaging the target, so the methods of calculating this probability greatly contribute to the simplicity and accuracy of estimating the effectiveness of the shooting in more complex cases.

      I.3.5.1 Damaging the Target with a Single Shot

      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)upper W 1 equals p 1 upper G left-parenthesis 1 right-parenthesis comma

      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)upper W 1 equals StartFraction p 1 Over normal omega EndFraction period

Schematic illustration of projecting of a target on a picture plane.

      Source: From Wentzel [2].

      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 .

      I.3.5.2 Damaging the Target with Multiple Shots

      When shooting with multiple shots, the probability of damaging the target is affected by the dependence of the shots due to repeated errors.