I
Introduction

I.1 Ammunition Types and Characteristics of Their Damaging Effect

I.1.1 Basic Concepts and Definitions

The term "weapons and ammunition" includes a wide range of different elements: from small arms ammunition and hand grenades to artillery and mortar projectiles, aircraft bombs and depth charges, missile and torpedo warheads, as well as engineering and sea mines designed to destroy enemy personnel and equipment, destroy structures and fortifications, and perform special tasks.

Damaging effect is defined as the ability of ammunition to damage a target provided that it is already close to it and all its elements have operated without failure. The effectiveness of the damaging effect of ammunition on the target and its combat effectiveness should not, therefore, be confused. Obviously, the combat effectiveness depends not only on the effectiveness of the ammunition near a target but also on the accuracy of ammunition delivery, the reliability of all its elements (the fuse in particular), the ability to withstand the enemy's defensive actions, and many other factors.

As an example, you might recall the history of thermonuclear weapons. The first thermonuclear device was exploded in the United States, yet the first thermonuclear bomb was created in the USSR. The device created in the United States had such a weight (62?tons) that it was meaningless to think about delivering it to a real target. It had a damaging effect, but its combat effectiveness was completely absent.

I.1.2 Types of Ammunition and Their Damaging Effects

In order to ensure a damaging effect on targets, it is necessary to exert any action on them. It is customary to highlight:

• action of fragment flow;
• penetrating action;
• shaped charge action;
• action of a shock wave and explosion products;
• incendiary action;
• action of penetrating and electromagnetic radiation of a nuclear explosion.

All ammunition is divided into the following types, depending on its main effects:

• fragmentation (with natural, controlled fragmentation, and preformed fragments; rod warheads; gunpowder and explosive shrapnel; case-shot);
• penetrating (small arms ammunition, armor-piercing, and concrete-piercing);
• shaped charges (with single or tandem shaped charges; explosion-formed projectiles);
• high explosive (blast) ammunition, including volumetric explosion ammunition;
• incendiary;
• nuclear (based on fission or fusion);
• unified by type of action.

Ammunition that does not damage targets but serves as a countermeasure to protect or reduce the damage from the enemy's ammunition can be identified as a separate group. For the same purpose, active protection of armored vehicles is developed to destroy enemy ammunitions as it approaches the target.

There are also many auxiliary and special-purpose munitions: lighting, smoke, and others that will not be considered here.

As we can see, there are just a few ways for ammunition to act on targets, despite the huge variety of weapon and ammunition designs. For the most part, all of them are determined either by the kinetic energy of the munition itself or by the chemical energy of the explosive that the munition is equipped with. In both cases, the equations that describe the behavior of materials during impulse loading determine the parameters of the field of damage and the processes of damage itself.

In this textbook, we will examine in some detail the effects of fragmentation, high explosive, penetrating ammunition, and ammunition with shaped charges.

I.2 Generalized Characteristics of the Damaging Effect

The damaging effects of weapons and ammunition can be described by different parameters. For example, for fragmentation ammunition, such characteristics are sometimes used as the number of effective fragments, the distance at which a fragment is able to pierce a barrier of a given thickness. The effect of ammunition with shaped charges is assessed by the thickness of the pierced armor. To assess the effect of high-explosive ammunition, the value of overpressure at the front of the shock wave is used, 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].

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:

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 ?. The value of ?, 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...