Читать книгу Damaging Effects of Weapons and Ammunition - Igor A. Balagansky - Страница 22

There is always dispersion in any type of firing, both with unguided and guided missiles. The main reasons for the dispersion of projectiles during firing are an inaccurate determination of target coordinates; aiming error; the influence of meteorological factors (wind, change of atmospheric pressure, humidity); fluctuations of the launcher; production tolerances during ammunition manufacturing.

All errors affecting the deviation of the projectile from the target can be divided into systematic and random errors. Systematic errors from shot to shot do not change, they can be measured and taken into account later (e.g. the deviation of the aim point from the center of the projectile dispersion) and the effect of low atmospheric pressure when firing at altitudes other than sea level. Random errors cannot be measured, as they vary from shot to shot. As a result of the combined effect of all firing errors, the actual trajectory of the projectile never coincides with the calculated trajectory, and the point of hit (or blast) of the projectile inevitably deviates from the calculated point to which the projectile was directed. This phenomenon is called “dispersion.”

The law of distribution of random values characterizing the point of hit (or blast) of ammunition is called the law of dispersion. For contact ammunition or remote one with flat dispersion, this law is presented as the law of distribution of the two coordinates (x, y) of points of hitting. Usually, the distribution is given as the value of the probability density φ(x, y). The value φ(x, y)·dx·dy is the probability of hitting an area with dimensions dx·dy adjacent to the point with coordinates (x, y) (Figure I.4).

Similarly, for projectiles with volumetric dispersion, the dispersion law is the distribution of the three coordinates of the blast point (x, y, z) and is characterized by the probability density φ(x, y, z), with the value of φ(x, y, z)·dx·dy·dz being the probability of the projectile blast in the elementary volume dx·dy·dz adjacent to the point (x, y, z).

Let's consider the case of flat dispersion as a simpler one. Imagine shooting a contact projectile or a remote one with flat dispersion. First of all, we must choose a flat surface on which we will study the dispersion of hit points. This surface is commonly referred to as a picture plane or a dispersion plane. When shooting at land or sea targets with remote ammunition, this is usually the surface of the ground or sea. When a land or sea target is shot contact projectiles, it is usually considered to be on a vertical dispersion plane. In the case of air targets, the picture plane is most often drawn through the point of hit perpendicular to the vector of the relative velocity at which the projectile meets the target.

Figure I.4 Area with dimensions of dx·dy, adjacent to a point at the coordinates (x, y).

Source: From Wentzel [2].

When the picture plane Q is fixed, the rectangular X0Y coordinate system is selected. Figure I.5 shows the picture plane and the coordinate system for the case of shooting an air target.

Usually, when a remote projectile is fired at sea or ground targets, the X‐axis is at least close to the direction of firing and the dispersion along the X‐axis characterizes the deviation along the firing line, the Y‐axis thus characterizes the deviation across the firing line.

Figure I.5 Setting up the coordinate system on the picture plane.

Source: From Wentzel [2].

As a law of dispersion, all types of firing and bombing are generally subject to normal law. This is due to the fact that the firing error on each of the axes can be represented as the sum of a large number of elementary errors resulting from various factors. If one of the coordinate axes (usually 0X) is at least close to the direction of firing, such axes are called the principal axes. In this case, the dispersion law will take the simplest form:

(I.10)

where are the coordinates of the dispersion center. They characterize a systematic firing errors. If there is no systematic error, these values are equal to zero; σ_x, σ_y – standard deviations in the 0X, 0Y axes, respectively.

In the practice, it is not the values of σ_x, σ_y that are usually used, but the so‐called probable (median) deviations of 0X, 0Y axes, which are denoted by E_x and E_y , respectively:

(I.11)

Median deviations are convenient because they correspond to the principal half‐axis of the dispersion ellipse, within which exactly half of all hits lie. The law of dispersion, in this case, takes the following form:

It is usually assumed that errors along the firing line (E_x) do not depend on errors across the firing line (E_y). Therefore, these values can be considered independently of each other.