Damaging Effects of Weapons and Ammunition. Igor A. Balagansky

and so on. These vastly different parameters do not allow for sufficient characterization of the damaging effect and, thus, to compare various ammunition types with each other. This makes the task of selecting and justifying the design parameters of the newly developed munitions even more challenging.

      To solve these problems, the so‐called generalized characteristics of the damaging effect are used, which contain information about the design parameters of the ammunition, the particular indicators of their damaging effect, the vulnerability of the target, the conditions for the use of ammunition, and the degree of damage to the target.

      I.2.1 Degrees of Damage

      In the case of land‐based targets, the minimum time during which an affected object cannot function as a combat unit is used as a numerical value of the damage degree. Three main degrees of damage are used, depending on the time the object remains nonfunctioning:

       A – time sufficient to solve the operation's objectives;

       B – time sufficient to address the daily objectives;

       C – when the object is suppressed for the duration of a battle.

      Note that for different targets and different combat missions, the times corresponding to different degrees of damage may vary significantly and, in some cases, additional degrees of damage are introduced (e.g. for armored vehicles, an additional D degree may be used). Sometimes the A degree is associated with the total destruction of the target, B with its partial failure, and C with temporary suppression.

The degree of damage is established in the statement of design and is determined for military equipment by the duration of disruption of the combat function and by the minimum required hospitalization and treatment time for the personnel (Table I.1).

Table I.1 Degrees of damage of targets.

      Source: From Balagansky et al. [1].

Target	Military equipment	Personnel
Degree of damage	А	B	C	D	A	B	C
Duration of disruption	7 days	12–24 hours	3 hours	30 minutes	2–3 months	1 month	7 days

      I.2.2 Contact and Remote Ammunition

      All ammunition can be divided into ammunition with an impact or contact effect that can only damage a target after a direct hit (shaped charges, armor‐piercing, concrete‐piercing) and those with a remote effect that can damage a target when exploded at some distance from it (fragmentation, high‐explosive ammunition).

      I.2.3 Generalized Characteristics of Contact Ammunition

For contact ammunition, the exhaustive characteristic that defines their destructive effect on single small‐size targets is the conditional damage law G(m), which is understood to be the probability of damaging a target that is hit by m projectiles [2]. The conditional damage law simultaneously determines both the destructive power and the degree of vulnerability of the target to the projectile attack. The G(m) function only makes sense for integer m, but for clarity, all points in the smooth curve are usually connected, as shown in Figure I.1.

      A convenient numerical characteristic of the conditional damage law is the average number of hits required for destroying a target:

      (I.1)

Figure I.1 Type of conditional damage low.

      Source: From Wentzel [2].

The higher the ordinates of the damage law values are, the lower the value of ω. The value of ω, being an integral characteristic of the conditional damage law, fully determines the destructive effect of the projectile and the vulnerability of the target. The more powerful the projectile and the more vulnerable the target is, the lower the average number of hits is required.

      I.2.4 The Accumulation of Damage

      The conditional damage law is particularly simple if there is no accumulation of damage. Accumulation of damage is the phenomenon where the projectiles “help each other” to damage the target, i.e. when the target can be damaged by the combined action of two or more projectiles (or other hitting elements), neither of which, used separately, would damage the target. For example, if an airplane target has fuel tanks with an inert filler, it often requires at least two projectiles to destroy such tanks, the first of which penetrates the tank and the second ignites the fuel spill. Strictly speaking, the accumulation of damage always takes place. However, in most cases, it is negligible and can be ignored.

      Suppose there is no accumulation of damage and the projectiles damage the target independently of each other. Let's denote r the probability of damaging the target if one projectile hits it. Then the law of damage G(m) – the probability of damaging the target when m projectiles hit it – is equal to the probability that at least one of the projectiles will damage the target:

      (I.2)

      Such a law of damage is called a degree law. So, if there is no accumulation of damage for some target, its law of damage is a degree law, where r is the probability of damaging the target in one hit.

      The value of r can be interpreted as the relative area of vulnerable target components. Indeed, let the target consist of only two types of components: certainly vulnerable and absolutely non‐vulnerable. Then the probability of damage is equal to the probability that a projectile hitting the target will hit its vulnerable components. If we consider the distribution of projectiles hitting the target to be approximately uniform, which is true for small targets, the r‐value will be equal to the relative area of vulnerable components.

      It can be demonstrated that for a target that has no accumulation of damage, the average number of hits required is the value inverse of the relative area of its vulnerable components:

      (I.3)

The