A trajectory in the air has the following property. Ballistics information: internal and external ballistics. wound ballistics. Types of trajectories and their practical significance

Ballistics is divided into internal (the behavior of the projectile inside the weapon), external (the behavior of the projectile along the trajectory) and barrier (the effect of the projectile on the target). This topic will cover the basics of internal and external ballistics. From barrier ballistics, wound ballistics (the effect of a bullet on the client’s body) will be considered. The existing section of forensic ballistics is discussed in the course of criminalistics and will not be covered in this manual.

Internal ballistics

Internal ballistics depend on the type of propellant used and the type of barrel.

Conventionally, trunks can be divided into long and short.

Long trunks (length more than 250 mm) serve to increase the initial speed of the bullet and its flatness along the trajectory. Accuracy increases (compared to short barrels). On the other hand, a long barrel is always more cumbersome than a short barrel.

Short trunks do not give the bullet the same speed and flatness than long ones. The bullet has greater dispersion. But a short-barreled weapon is convenient to carry, especially concealed, which is most suitable for self-defense weapons and police weapons. On the other hand, trunks can be divided into rifled and smooth.

Rifled barrels give the bullet greater speed and stability along the trajectory. Such trunks are widely used for bullet shooting. For shooting bullet hunting cartridges from smoothbore weapons Various threaded attachments are often used.

Smooth trunks. Such barrels help to increase the dispersion of damaging elements when firing. Traditionally used for shooting with shot (buckshot), as well as for shooting with special hunting cartridges at short distances.

There are four firing periods (Fig. 13).

Preliminary period (P) lasts from the beginning of the combustion of the powder charge until the bullet completely penetrates the rifling. During this period, gas pressure is created in the barrel bore, which is necessary to move the bullet from its place and overcome the resistance of its shell to cut into the rifling of the barrel. This pressure is called boost pressure and reaches 250-500 kg/cm2. It is assumed that the combustion of the powder charge at this stage occurs in a constant volume.

First period (1) lasts from the beginning of the bullet's movement until complete combustion powder charge. At the beginning of the period, when the speed of the bullet along the barrel is still low, the volume of gases grows faster than the behind-the-bullet space. The gas pressure reaches its peak (2000-3000 kg/cm2). This pressure is called maximum pressure. Then, due to a rapid increase in the speed of the bullet and a sharp increase in the bullet space, the pressure drops slightly and by the end of the first period it is approximately 2/3 of the maximum pressure. The speed of movement is constantly growing and by the end of this period reaches approximately 3/4 of the initial speed.
Second period (2) lasts from the moment the powder charge is completely burned until the bullet leaves the barrel. With the beginning of this period, the influx of powder gases stops, but highly compressed and heated gases expand and, putting pressure on the bottom of the bullet, increase its speed. The pressure drop in this period occurs quite quickly and at the muzzle - muzzle pressure - is 300-1000 kg/cm 2. Some types of weapons (for example, Makarov, and most types of short-barreled weapons) do not have a second period, since by the time the bullet leaves the barrel the powder charge does not completely burn out.

Third period (3) lasts from the moment the bullet leaves the barrel until the action of the powder gases on it ceases. During this period, powder gases flowing from the barrel at a speed of 1200-2000 m/s continue to affect the bullet, giving it additional speed. Highest speed the bullet reaches at the end of the third period at a distance of several tens of centimeters from the muzzle of the barrel (for example, when shooting from a pistol, a distance of about 3 m). This period ends at the moment when the pressure of the powder gases at the bottom of the bullet is balanced by air resistance. Then the bullet flies by inertia. This relates to the question of why a bullet fired from a TT pistol does not penetrate class 2 armor when shot at point-blank range and pierces it at a distance of 3-5 m.

As already mentioned, black and smokeless powder are used to load cartridges. Each of them has its own characteristics:

Black powder. This type of gunpowder burns very quickly. Its combustion is like an explosion. It is used for an instant surge in pressure in the barrel bore. This type of gunpowder is usually used for smooth barrels, since the friction of the projectile against the barrel walls in a smooth barrel is not so great (compared to a rifled barrel) and the residence time of the bullet in the barrel is less. Therefore, at the moment the bullet leaves the barrel, greater pressure is achieved. When using black powder in a rifled barrel, the first period of the shot is quite short, due to which the pressure on the bottom of the bullet decreases quite significantly. It should also be noted that the gas pressure of burnt black powder is approximately 3-5 times less than that of smokeless powder. The gas pressure curve has a very sharp peak of maximum pressure and a fairly sharp drop in pressure in the first period.

Smokeless powder. This type of powder burns more slowly than black powder and is therefore used to gradually increase the pressure in the bore. In view of this, for rifled weapons Smokeless powder is used as standard. Due to screwing into the rifling, the time it takes for the bullet to fly down the barrel increases and by the time the bullet leaves, the powder charge is completely burned out. Due to this, the bullet is exposed to the full amount of gases, while the second period is selected to be quite small. On the gas pressure curve, the peak of maximum pressure is somewhat smoothed out, with a gentle decrease in pressure in the first period. In addition, it is useful to pay attention to some numerical methods for estimating intra-ballistic solutions.

1. Power coefficient(kM). Shows the energy that falls on one conventional cubic mm of bullet. Used to compare bullets of the same type of cartridge (for example, pistol). It is measured in Joules per millimeter cubed.

KM = E0/d 3, where E0 is muzzle energy, J, d is bullets, mm. For comparison: the power coefficient for the 9x18 PM cartridge is 0.35 J/mm 3 ; for cartridge 7.62x25 TT - 1.04 J/mm 3; for cartridge.45ACP - 0.31 J/mm 3. 2. Metal utilization factor (kme). Shows the shot energy per gram of weapon. Used to compare bullets from cartridges of the same type or to compare the relative shot energy of different cartridges. It is measured in Joules per gram. Often, the metal utilization rate is taken as a simplified version of calculating the recoil of a weapon. kme=E0/m, where E0 is the muzzle energy, J, m is the mass of the weapon, g. For comparison: the metal utilization coefficient for the PM pistol, machine gun and rifle, respectively, is 0.37, 0.66 and 0.76 J/g.

External ballistics

First you need to imagine the full trajectory of the bullet (Fig. 14).
In explanation of the figure, it should be noted that the line of departure of the bullet (throwing line) will be different than the direction of the barrel (elevation line). This occurs due to the occurrence of barrel vibrations when fired, which affect the trajectory of the bullet, as well as due to the recoil of the weapon when fired. Naturally, the departure angle (12) will be extremely small; Moreover, the better the finishing of the barrel and the calculation of the internal ballistic characteristics of the weapon, the smaller the departure angle will be. Approximately the first two-thirds of the upward trajectory line can be considered straight. In view of this, three firing distances are distinguished (Fig. 15). Thus, the influence of third-party conditions on the trajectory is described by a simple quadratic equation, and in graphics it is a parabola. In addition to third-party conditions, the deviation of a bullet from its trajectory is also influenced by some design features of the bullet and cartridge. Below we will consider a complex of events; deflecting the bullet from its original trajectory. The ballistic tables of this topic contain data on the ballistics of the 7.62x54R 7H1 cartridge bullet when fired from an SVD rifle. In general, the influence of external conditions on the flight of a bullet can be shown by the following diagram (Fig. 16).

Diffusion

It should be noted once again that thanks to the rifled barrel, the bullet acquires rotation around its longitudinal axis, which gives greater flatness (straightness) to the flight of the bullet. Therefore, the distance of dagger fire increases slightly compared to a bullet fired from a smooth barrel. But gradually, towards the distance of the mounted fire, due to the already mentioned third-party conditions, the axis of rotation shifts somewhat from the central axis of the bullet, so in the cross section you get a circle of bullet expansion - the average deviation of the bullet from the original trajectory. Taking into account this behavior of the bullet, its possible trajectory can be represented as a single-plane hyperboloid (Fig. 17). The displacement of a bullet from the main directrix due to a displacement of its axis of rotation is called dispersion. The bullet with full probability ends up in the circle of dispersion, diameter (by
peppercorn) which is determined for each specific distance. But the specific point of impact of the bullet inside this circle is unknown.

In table 3 shows dispersion radii for shooting at various distances.

Table 3

Diffusion

Fire range (m)	Dispersion Diameter(cm)

Considering the size of the standard head target is 50x30 cm, and the chest target is 50x50 cm, it can be noted that the maximum distance of a guaranteed hit is 600 m. At a greater distance, dispersion does not guarantee the accuracy of the shot.
Derivation
Due to complex physical processes, a rotating bullet in flight deviates slightly from the firing plane. Moreover, in the case of right-hand rifling (the bullet rotates clockwise when viewed from behind), the bullet deflects to the right, in the case of left-hand rifling - to the left.
In table Figure 4 shows the magnitude of derivational deviations when firing at various ranges.
Table 4
Derivation
Fire range (m)
Derivation (cm)
1000
1200
- It is easier to take into account derivational deviation when shooting than dispersion. But, taking into account both of these values, it should be noted that the center of dispersion will shift slightly by the amount of the derivational displacement of the bullet.
- Bullet displacement by wind
- Among all the third-party conditions affecting the flight of a bullet (humidity, pressure, etc.), it is necessary to highlight the most serious factor - the influence of wind. The wind blows the bullet away quite seriously, especially at the end of the ascending branch of the trajectory and beyond.
  The displacement of a bullet by a side wind (at an angle of 90 0 to the trajectory) of average force (6-8 m/s) is shown in table. 5.
- Table 5
- Bullet displacement by wind
- Fire range (m)
  
  Offset (cm)
  - To find out the bullet's displacement strong wind(12-16 m/s) it is necessary to double the table values; for weak winds (3-4 m/s) the table values are divided in half. For wind blowing at an angle of 45° to the trajectory, the table values are also divided in half.
  - Bullet flight time
  - - Fire range (m)
      
      Flight time (s)
      
      0,15
      
      0,28
      
      0,42
      
      0,60
      
      0,80
      
      1,02
      
      1,26
      Solution of ballistic problems
    - To do this, it is useful to make a graph of the dependence of the displacement (dispersion, bullet flight time) on the firing range. Such a graph will allow you to easily calculate intermediate values (for example, at 350 m), and will also allow you to assume table values of the function.
      In Fig. Figure 18 shows the simplest ballistic problem.
    - Shooting is carried out at a distance of 600 m, the wind blows from behind to the left at an angle of 45° to the trajectory.
      Question: the diameter of the scattering circle and the displacement of its center from the target; flight time to target.
    - Solution: The diameter of the scattering circle is 48 cm (see Table 3). The derivational shift of the center is 12 cm to the right (see Table 4). The displacement of the bullet by the wind is 115 cm (110 * 2/2 + 5% (due to the direction of the wind in the direction of the derivational displacement)) (see Table 5). The bullet's flight time is 1.07 s (flight time + 5% due to the direction of the wind in the direction of the bullet's flight) (see Table 6).
    - Answer; the bullet will fly 600 m in 1.07 s, the diameter of the dispersion circle will be 48 cm, and its center will shift to the right by 127 cm. Naturally, the answer data is quite approximate, but their discrepancy with real data is no more than 10%.
    - Barrier and wound ballistics
    - Barrier ballistics
    - The impact of a bullet on obstacles (as, indeed, everything else) is quite conveniently determined by some mathematical formulas.
    1. Penetration of barriers (P). Penetration determines how likely it is to break through a particular barrier. In this case, the total probability is taken as
    1. Usually used to determine the probability of penetration on various disks
  - dances of different classes of passive armor protection.
    Penetration is a dimensionless quantity.
  - P = En / Epr,
  - where En is the energy of the bullet at a given point of the trajectory, in J; Epr is the energy required to break through an obstacle, in J.
  - Taking into account the standard EPR for body armor (BZh) (500 J for protection against pistol cartridges, 1000 J - from intermediate and 3000 J - from rifle cartridges) and sufficient energy to defeat a person (max 50 J), it is easy to calculate the probability of hitting the corresponding BZh with a bullet from one or another another cartridge. Thus, the probability of penetrating a standard pistol BZ with a bullet from a 9x18 PM cartridge will be equal to 0.56, and by a bullet from a 7.62x25 TT cartridge - 1.01. The probability of penetrating a standard assault rifle bullet with a 7.62x39 AKM cartridge will be 1.32, and with a 5.45x39 AK-74 cartridge bullet will be 0.87. The given numerical data are calculated for a distance of 10 m for pistol cartridges and 25 m for intermediate cartridges. 2. Impact coefficient (ky). Impact coefficient shows the energy of a bullet per square millimeter of its maximum cross-section. Impact factor is used to compare cartridges of the same or different classes. It is measured in J per square millimeter. ky=En/Sp, where En is the energy of the bullet at a given point of the trajectory, in J, Sn is the area of the maximum cross-section of the bullet, in mm 2. Thus, the impact coefficients for bullets of 9x18 PM, 7.62x25 TT and .40 Auto cartridges at a distance of 25 m will be equal to 1.2, respectively; 4.3 and 3.18 J/mm 2. For comparison: at the same distance, the impact coefficient of bullets from 7.62x39 AKM and 7.62x54R SVD cartridges are 21.8 and 36.2 J/mm 2 , respectively.
    Wound ballistics
    How does a bullet behave when it hits a body? Clarification of this issue is the most important characteristic for choosing weapons and ammunition for a particular operation. There are two types of impact of a bullet on a target: stopping and penetrating, in principle, these two concepts have an inverse relationship. Stopping effect (0V). Naturally, the enemy stops most reliably when the bullet hits a certain place on the human body (head, spine, kidneys), but some types of ammunition have a large 0B even when hitting secondary targets. In general, 0B is directly proportional to the caliber of the bullet, its mass and speed at the moment it hits the target. Also, 0B increases when using lead and expansion bullets. It must be remembered that an increase in 0B shortens the length of the wound channel (but increases its diameter) and reduces the effect of the bullet on a target protected by armor. One of the options for mathematical calculation of OM was proposed in 1935 by the American Yu. Hatcher: 0V = 0.178*m*V*S*k, where m is the mass of the bullet, g; V is the speed of the bullet at the moment of meeting the target, m/s; S - transverse area of the bullet, cm 2; k is the bullet shape coefficient (from 0.9 for full-shell bullets to 1.25 for hollow-point bullets). According to these calculations, at a distance of 15 m, bullets of 7.62x25 TT, 9x18 PM and .45 cartridges have a MR of 171, 250 in 640, respectively. For comparison: RP of a bullet of a 7.62x39 cartridge (AKM) = 470, and bullets of 7.62x54 ( OVD) = 650. Penetrating impact (PE). PT can be defined as the ability of a bullet to penetrate a target to its maximum depth. The penetrating ability is higher (all other things being equal) for bullets of small caliber and those that are slightly deformed in the body (steel, full-shell). High penetration improves the bullet's effect on targets protected by armor. In Fig. Figure 19 shows the effect of a standard PM jacketed bullet with a steel core. When a bullet hits the body, a wound channel and a wound cavity are formed. A wound channel is a channel pierced directly by a bullet. A wound cavity is a cavity of damage to fibers and blood vessels caused by tension and rupture by a bullet. Gunshot wounds are divided into through, blind, and secant.
    
    Through wounds
    A perforation wound occurs when a bullet passes through the body. In this case, the presence of inlet and outlet holes is observed. The entrance hole is small, smaller than the caliber of a bullet. With a direct hit, the edges of the wound are smooth, and with a hit through thick clothing at an angle, there will be a slight tear. Often the inlet closes up quite quickly. There are no traces of bleeding (except for damage to large vessels or when the wound is positioned below). The exit hole is large and can exceed the caliber of the bullet by orders of magnitude. The edges of the wound are torn, uneven, and spread to the sides. A rapidly developing tumor is observed. There is often severe bleeding. In non-fatal wounds, suppuration develops quickly. With fatal wounds, the skin around the wound quickly turns blue. Penetrating wounds are typical for bullets with a high penetrating effect (mainly for machine guns and rifles). When a bullet passes through soft tissue, the internal wound is axial, with minor damage to neighboring organs. When wounded by a bullet from a 5.45x39 (AK-74) cartridge, the steel core of the bullet in the body may come out of the shell. As a result, two wound channels appear and, accordingly, two exit holes (from the shell and the core). Such injuries are more oftenthey occur when ingested through thick clothing (peacoat). Often the wound channel from a bullet is blind. When a bullet hits a skeleton, a blind wound usually occurs, but with a high power of ammunition, a through wound is likely. In this case, large internal damage from fragments and parts of the skeleton is observed with an increase in the wound channel towards the exit hole. In this case, the wound channel can “break” due to the ricochet of the bullet from the skeleton. Perforating head wounds are characterized by cracking or fracture of the skull bones, often in a non-axial wound channel. The skull cracks even when hit by 5.6 mm lead non-jacketed bullets, not to mention more powerful ammunition. In most cases, such injuries are fatal. With through wounds to the head, severe bleeding is often observed (prolonged flow of blood from the corpse), of course, when the wound is positioned on the side or below. The inlet is fairly smooth, but the outlet is uneven, with a lot of cracking. A fatal wound quickly turns blue and swells. In case of cracking, damage to the scalp may occur. The skull is easily crushed to the touch, and fragments can be felt. In case of wounds with sufficiently strong ammunition (bullets of 7.62x39, 7.62x54 cartridges) and wounds with expansive bullets, a very wide exit hole is possible with a long leakage of blood and brain matter.
    Blind wounds
    Such wounds occur when hit by bullets from less powerful (pistol) ammunition, using hollow-point bullets, passing a bullet through the skeleton, or being wounded by a bullet at the end of its life. With such wounds, the entrance hole is also quite small and smooth. Blind wounds are usually characterized by multiple internal injuries. When wounded by expansive bullets, the wound channel is very wide, with a large wound cavity. Blind wounds are often not axial. This is observed when weaker ammunition hits the skeleton - the bullet moves away from the entrance hole plus damage from fragments of the skeleton and shell. When such bullets hit the skull, it becomes severely cracked. A large entrance hole is formed in the bone, and the intracranial organs are severely affected.
    Cutting wounds
    Cutting wounds are observed when a bullet hits the body at an acute angle, damaging only the skin and external parts of the muscles. Most of the injuries are not dangerous. Characterized by skin rupture; the edges of the wound are uneven, torn, and often diverge greatly. Sometimes quite severe bleeding is observed, especially when large subcutaneous vessels rupture.

Ballistics studies throwing a projectile (bullet) from a barrel weapon. Ballistics is divided into internal, which studies the phenomena occurring in the barrel at the time of the shot, and external, which explains the behavior of the bullet after leaving the barrel.

Fundamentals of External Ballistics

Knowledge of external ballistics (hereinafter referred to as ballistics) allows the shooter, even before the shot, with sufficient practical application know exactly where the bullet will hit. The accuracy of a shot is influenced by a lot of interrelated factors: the dynamic interaction of parts and pieces of the weapon between themselves and the shooter’s body, gas and bullet, bullet with the walls of the barrel bore, bullet with environment after leaving the barrel and much more.

After leaving the barrel, the bullet does not fly in a straight line, but along the so-called ballistic trajectory, close to a parabola. Sometimes at short shooting distances the deviation of the trajectory from a straight line can be neglected, but at long and extreme shooting distances (which is typical for hunting), knowledge of the laws of ballistics is absolutely necessary.

Note that pneumatic weapons usually give a light bullet a small or medium speed (from 100 to 380 m/s), so the curvature of the bullet’s flight path from different influences more significant than for firearms.

A bullet fired from a barrel at a certain speed is affected by two main forces in flight: gravity and air resistance. The force of gravity is downward, causing the bullet to continuously descend. The action of the air resistance force is directed towards the movement of the bullet, it forces the bullet to continuously reduce its flight speed. All this leads to a downward deviation of the trajectory.

To increase the stability of a bullet in flight, there are spiral grooves (rifling) on the surface of the barrel of a rifled weapon, which give the bullet a rotational motion and thereby prevent it from tumbling in flight.

Due to the rotation of the bullet in flight

Due to the rotation of the bullet in flight, the force of air resistance acts unevenly on different parts of the bullet. As a result, the bullet encounters greater air resistance on one side and, in flight, deviates more and more from the firing plane in the direction of its rotation. This phenomenon is called derivation. The effect of derivation is uneven and intensifies towards the end of the trajectory.

Powerful air rifles can give the bullet an initial speed higher than sound (up to 360-380 m/s). The speed of sound in air is not constant (depends on atmospheric conditions, altitude above sea level, etc.), but it can be taken equal to 330-335 m/s. Lightweight pneumatic bullets with low lateral load experience strong disturbances and deviate from their trajectory, overcoming sound barrier. Therefore, it is advisable to shoot heavier bullets with muzzle velocity approaching to the speed of sound.

The trajectory of a bullet is also affected by weather conditions - wind, temperature, humidity and air pressure.

The wind is considered weak at a speed of 2 m/s, medium (moderate) at 4 m/s, strong at 8 m/s. Side moderate wind, acting at an angle of 90° to the trajectory, already has a very significant effect on a light and “low-velocity” bullet fired from an air gun. The influence of wind of the same strength, but blowing at an acute angle to the trajectory - 45° or less - causes half the deflection of the bullet.

The wind blowing along the trajectory in one direction or another slows down or speeds up the speed of the bullet, which must be taken into account when shooting at a moving target. When hunting, the wind speed can be estimated with acceptable accuracy using a handkerchief: if you take the handkerchief by two corners, then in a weak wind it will sway slightly, in a moderate wind it will deviate by 45°, and in a strong wind it will develop horizontally to the surface of the earth.

Normal weather conditions are considered to be: air temperature - plus 15°C, humidity - 50%, pressure - 750 mm Hg. An excess of air temperature above normal leads to an increase in the trajectory at the same distance, and a decrease in temperature leads to a decrease in the trajectory. Increased humidity leads to a decrease in the trajectory, and decreased humidity leads to an increase in the trajectory. Let us remind you that atmospheric pressure changes not only from the weather, but also from the altitude above sea level - the higher the pressure, the lower the trajectory.

Each “long-range” weapon and ammunition has its own correction tables that allow one to take into account the influence of weather conditions, derivations, the relative position of the shooter and the target in height, bullet speed and other factors on the bullet’s flight path. Unfortunately, such tables are not published for air guns, so those who like to shoot at extreme distances or at small targets are forced to compile such tables themselves - their completeness and accuracy are the key to success in hunting or competitions.

When assessing the results of shooting, you need to remember that from the moment the shot is fired until the end of its flight, some random (not taken into account) factors act on the bullet, which leads to slight deviations in the bullet’s flight path from shot to shot. Therefore, even under “ideal” conditions (for example, when the weapon is rigidly secured in the machine, constant external conditions etc.) bullets hitting the target look like an oval, condensing towards the center. Such random deviations are called deviation. The formula for calculating it is given below in this section.

Now let’s look at the bullet’s flight path and its elements (see Figure 1).

The straight line representing the continuation of the bore axis before the shot is fired is called the shot line. The straight line, which is a continuation of the axis of the barrel when a bullet leaves it, is called the throwing line. Due to the vibrations of the barrel, its position at the moment of the shot and at the moment the bullet leaves the barrel will differ by the angle of departure.

As a result of gravity and air resistance, the bullet does not fly along the throwing line, but along an unevenly curved curve passing below the throwing line.

The beginning of the trajectory is the departure point. The horizontal plane passing through the point of departure is called the horizon of the weapon. The vertical plane passing through the point of departure along the throwing line is called the shooting plane.

To throw a bullet to any point on the horizon of the weapon, you need to direct the throwing line above the horizon. The angle made by the line of fire and the horizon of the weapon is called the elevation angle. The angle made by the throwing line and the horizon of the weapon is called the throwing angle.

The point of intersection of the trajectory with the horizon of the weapon is called the (tabular) point of impact. The horizontal distance from the departure point to the (tabular) impact point is called the horizontal range. The angle between the tangent to the trajectory at the point of impact and the horizon of the weapon is called the (tabular) angle of incidence.

The highest point of the trajectory above the weapon horizon is called the trajectory apex, and the distance from the weapon horizon to the trajectory apex is the trajectory height. The top of the trajectory divides the trajectory into two unequal parts: the ascending branch is longer and flatter, and the descending branch is shorter and steeper.

Considering the position of the target relative to the shooter, three situations can be distinguished:

The shooter and target are located on the same level.
- the shooter is positioned below the target (shoots upward at an angle).
- the shooter is positioned above the target (shoots downward at an angle).

In order to direct the bullet at the target, it is necessary to give the axis of the barrel bore a certain position in the vertical and horizontal plane. Giving the desired direction to the axis of the barrel bore in the horizontal plane is called horizontal aiming, and giving direction in the vertical plane is called vertical aiming.

Vertical and horizontal aiming is done using sighting devices. Mechanical sights rifled weapons consist of a front sight and rear sight (or diopter).

The straight line connecting the middle of the rear sight slot to the top of the front sight is called the sighting line.

Tip small arms using sighting devices is carried out not from the horizon of the weapon, but relative to the location of the target. In this regard, the guidance and trajectory elements receive the following designations (see Figure 2).

The point at which the weapon is aimed is called the aiming point. The straight line connecting the shooter's eye, the middle of the rear sight slot, the top of the front sight and the aiming point is called the aiming line.

The angle formed by the aiming line and the shooting line is called the aiming angle. This aiming angle is obtained by setting the sight slot (or front sight) at a height corresponding to the firing range.

The point of intersection of the downward branch of the trajectory with the aiming line is called the point of incidence. The distance from the point of departure to the point of impact is called the target range. The angle between the tangent to the trajectory at the point of impact and the aiming line is called the angle of incidence.

When positioning the weapon and target at the same height the aiming line coincides with the horizon of the weapon, and the aiming angle coincides with the elevation angle. When the target is located above or below the horizon weapons, the target elevation angle is formed between the aiming line and the horizon line. The target elevation angle is calculated positive, if the target is above the weapon's horizon and negative, if the target is below the weapon's horizon.

The target elevation angle and the aiming angle together make up the elevation angle. With a negative target elevation angle, the shot line may be directed below the weapon's horizon; in this case, the elevation angle becomes negative and is called the declination angle.

At its end, the bullet’s trajectory intersects either with the target (obstacle) or with the surface of the earth. The point of intersection of the trajectory with the target (obstacle) or the surface of the earth is called the meeting point. The possibility of a rebound depends on the angle at which the bullet hits the target (obstacle) or the ground, their mechanical characteristics, and the material of the bullet. The distance from the departure point to the meeting point is called the actual range. A shot in which the trajectory does not rise above the aiming line above the target throughout the entire aiming range is called a direct shot.

From all of the above, it is clear that before practical shooting the weapon must be shot (otherwise it will lead to a normal battle). Sighting should be carried out with the same ammunition and under the same conditions that will be typical for subsequent shootings. It is imperative to take into account the size of the target, the shooting position (prone, kneeling, standing, from unstable positions), even the thickness of clothing (when zeroing the rifle).

The aiming line passing from the shooter's eye through the top of the front sight, the top edge of the rear sight and the target is a straight line, while the trajectory of the bullet is an unevenly curved line downwards. The aiming line is located 2-3 cm above the barrel in the case of an open sight and much higher in the case of an optical sight.

In the simplest case, if the aiming line is horizontal, the bullet trajectory crosses the aiming line twice: on the ascending and descending parts of the trajectory. The weapon is usually zeroed (sights are adjusted) at the horizontal distance at which the downward part of the trajectory intersects the aiming line.

It may seem that there are only two distances to the target - where the trajectory intersects the line of sight - at which a hit is guaranteed. Thus, sports shooting is carried out at a fixed distance of 10 meters, at which the trajectory of the bullet can be considered linear.

For practical shooting (for example, hunting), the firing range is usually much longer and the curvature of the trajectory must be taken into account. But here the arrow plays into the hands of the fact that the dimensions of the target (killing place) in height in this case can reach 5-10 cm or more. If we choose such a horizontal shooting range for the weapon that the height of the trajectory at a distance does not exceed the height of the target (the so-called direct shot), then by aiming at the edge of the target, we will be able to hit it throughout the entire firing distance.

The direct shot range, at which the trajectory height does not rise above the aiming line above the target height, is a very important characteristic of any weapon, determining the flatness of the trajectory.
The aiming point is usually chosen to be the bottom edge of the target or its center. It is more convenient to aim under the bleed, when the entire target is visible when aiming.

When shooting, it is usually necessary to introduce vertical corrections if:

the target size is smaller than usual.
The shooting distance exceeds the zeroing distance of the weapon.
the firing distance is closer than the first point of intersection of the trajectory with the aiming line (typical for shooting with an optical sight).

Horizontal corrections usually have to be introduced during shooting in windy conditions or when shooting at a moving target. Typically, corrections for open sights are introduced by shooting with anticipation (moving the aiming point to the right or left of the target), and not by adjusting the sights.

2.3.4 Dependence of the trajectory shape on the throwing angle. Path elements

The angle formed by the horizon of the weapon and the continuation of the axis of the barrel bore before the shot is called elevation angle.

However, it is more correct to talk about dependence horizontal range firing, and therefore the shape of the trajectory from throwing angle, which is the algebraic sum of the elevation angle and the departure angle (Fig. 48).

Rice. 48 - Elevation angle and throwing angle

So, there is a certain relationship between the flight range of a bullet and the throwing angle.

According to the laws of mechanics, the greatest horizontal flight range in airless space is achieved when the throwing angle is 45°. As the angle increases from 0 to 45°, the range of the bullet increases, and from 45 to 90° it decreases. The throwing angle at which the horizontal range of the bullet is greatest is called angle of greatest range.

When a bullet flies in the air, the angle of maximum range does not reach 45°. Its value for modern small arms ranges from 30-35°, depending on the weight and shape of the bullet.

Trajectories formed at throwing angles less than the angle of greatest range (0-35°) are called flat. Trajectories formed at throwing angles greater than the angle of greatest range (35-90°) are called mounted(Fig. 49).

Rice. 49 - Floor and mounted trajectories

When studying the movement of a bullet in the air, the designations of trajectory elements shown in Fig. are used. 50.

Rice. 50 - Trajectory and its elements:
departure point- center of the muzzle of the barrel; it is the beginning of the trajectory;
weapon horizon- horizontal plane passing through the departure point. In drawings and drawings depicting a trajectory from the side, the horizon looks like a horizontal line;
elevation line- a straight line, which is a continuation of the axis of the barrel of the aimed weapon;
throwing line- a straight line, which is a continuation of the axis of the barrel bore at the moment of the shot. Tangent to the trajectory at the departure point;
firing plane- vertical plane passing through the elevation line;
elevation angle- the angle formed by the elevation line and the horizon of the weapon;
throwing angle- the angle formed by the throwing line and the horizon of the weapon;
departure angle- the angle formed by the elevation line and the throwing line;
impact point- the point of intersection of the trajectory with the horizon of the weapon;
angle of incidence- the angle formed by the tangent to the trajectory at the point of impact and the horizon of the weapon;
horizontal range- distance from the point of departure to the point of impact;
top of trajectory- the highest point of the trajectory above the horizon of the weapon. The vertex divides the trajectory into two parts - the branches of the trajectory;
ascending branch of the trajectory- part of the trajectory from the departure point to the top;
descending branch of the trajectory- part of the trajectory from the top to the point of fall;
trajectory height- the distance from the top of the trajectory to the horizon of the weapon.

Since when sports shooting The distances for each type of weapon remain largely unchanged; many shooters do not even think about what elevation or throwing angle they should shoot at. In practice, it turned out to be much more convenient to replace the throwing angle with another, very similar to it - aiming angle(Fig. 51). Therefore, slightly departing from the presentation of issues of external ballistics, we give elements of weapon aiming (Fig. 52).

Rice. 51 - Line of sight and aiming angle

Rice. 52 - Elements of aiming a weapon at a target:
aiming line- a straight arrow passing from the eye through the slots of the sight and the top of the front sight to the aiming point;
aiming point- the point of intersection of the aiming line with the target or target plane (when moving the aiming point);
aiming angle- the angle formed by the aiming line and the elevation line;
target elevation angle- the angle formed by the aiming line and the horizon of the weapon;
elevation angle- algebraic sum of aiming angles and target elevation angle.

It does not hurt the shooter to know the degree of flatness of the trajectories of bullets used in sports shooting. Therefore, we present graphs characterizing the excess of the trajectory when shooting from various rifles, pistols and revolvers (Fig. 53-57).

Rice. 53 - Exceeding the trajectory above the aiming line when firing a 7.6 mm heavy bullet from a service rifle

Rice. 54 - Excess of the bullet trajectory above the aiming line when shooting from a small-caliber rifle (at V 0 =300 m/sec)

Rice. 55 - Excess of the bullet trajectory above the aiming line when shooting from a small-caliber pistol (at V 0 =210 m/sec)

Rice. 56 - Excess of the bullet trajectory above the aiming line when shooting:
A- from a re-barreled revolver (at V 0 =260 m/sec); b- from a PM pistol (at V 0 =315 m/sec).

Rice. 57 - Excess of the bullet trajectory above the aiming line when shooting from a rifle with a 5.6 mm sporting and hunting cartridge (at V 0 = 880 m/sec)

2.3.5 Dependence of the trajectory shape on the initial velocity of the bullet, its shape and lateral load

While retaining their basic properties and elements, bullet trajectories can differ sharply from one another in their shape: be longer and shorter, have different slopes and curvatures. These varied changes depend on a number of factors.

Effect of initial speed. If two identical bullets are fired at the same throwing angle with different initial speeds, then the trajectory of the bullet with a higher initial speed will be higher than the trajectory of the bullet with a lower initial speed (Fig. 58).

Rice. 58 - Dependence of the trajectory height and flight range of a bullet on the initial speed

A bullet flying at a lower initial speed will take more time to reach the target, so under the influence of gravity it will have time to go down significantly more. It is also obvious that with an increase in speed, its flight range will also increase.

Effect of bullet shape. The desire to increase the range and accuracy of shooting required giving the bullet a shape that would allow it to maintain speed and stability in flight for as long as possible.

The condensation of air particles in front of the bullet head and the rarefied zone behind it are the main factors in the force of air resistance. The head wave, which sharply increases the deceleration of a bullet, occurs when its speed is equal to or exceeds the speed of sound (over 340 m/sec).

If the speed of a bullet is less than the speed of sound, then it flies at the very crest of the sound wave, without experiencing excessively high air resistance. If it is greater than the speed of sound, the bullet overtakes all sound waves generated in front of its head. In this case, a head ballistic wave appears, which significantly slows down the flight of the bullet, causing it to quickly lose speed.

If you look at the outlines of the head wave and air turbulence that arise when bullets of different shapes move (Fig. 59), you can see that the sharper its shape, the less pressure on the head of the bullet. The area of rarefied space behind the bullet is smaller, the more its tail is beveled; in this case, there will also be less turbulence behind the flying bullet.

Rice. 59 - The nature of the outlines of the head wave that occurs during the movement of bullets of different shapes

Both theory and practice have confirmed that the most streamlined shape of the bullet is the one outlined along the so-called curve of least resistance - cigar-shaped. Experiments show that the coefficient of air resistance, depending only on the shape of the bullet head, can change by one and a half to two times.

Different flight speeds have their own, most advantageous, bullet shape.

When shooting at short distances with bullets that have a low initial velocity, their shape has little effect on the shape of the trajectory. Therefore, revolver, pistol and small-caliber cartridges are equipped with blunt-pointed bullets: this is more convenient for reloading weapons, and also helps preserve them from damage (especially non-sheathed ones - for small-caliber weapons).

Considering the dependence of shooting accuracy on the shape of the bullet, the shooter must protect the bullet from deformation and ensure that scratches, nicks, dents, etc. do not appear on its surface.

Effect of lateral load. The heavier the bullet, the more kinetic energy it has, therefore, the less air resistance affects its flight. However, the ability of a bullet to maintain its speed depends not simply on its weight, but on the ratio of weight to area encountering air resistance. The ratio of the weight of a bullet to its largest cross-sectional area is called lateral load(Fig. 60).

Rice. 60 - Cross-sectional area of bullets:
A- to a 7.62 mm rifle; b- to a 6.5 mm rifle; V- to a 9 mm pistol; G- for a 5.6 mm rifle for target shooting “Running Deer”; d- for a 5.6 mm side-fire rifle (long cartridge).

The lateral load is greater, the more more weight bullets and smaller caliber. Consequently, with the same caliber, the lateral load is greater for a longer bullet. A bullet with a greater lateral load has both a longer flight range and a flatter trajectory (Fig. 61).

Rice. 61 - The influence of the lateral load of a bullet on its flight range

However, there is a certain limit to increasing this load. First of all, as it increases (with the same caliber), the total weight of the bullet increases, and hence the recoil of the weapon. In addition, an increase in lateral load due to excessive elongation of the bullet will cause a significant tipping effect of its head part back by air resistance. This is what we proceed from when establishing the most advantageous dimensions of modern bullets. Thus, the lateral load of a heavy bullet (weight 11.75 g) for a service rifle is 26 g/cm 2 , and a small-caliber bullet (weight 2.6 g) is 10.4 g/cm 2 .

How great the influence of the lateral load of a bullet on its flight is can be seen from the following data: a heavy bullet with an initial speed of about 770 m/sec has a maximum flight range of 5100 m, while a light bullet with an initial speed of 865 m/sec has only 3400 m.

2.3.6 Dependence of the trajectory on meteorological conditions

Continuously changing meteorological conditions during shooting can have a significant impact on the flight of the bullet. However, certain knowledge and practical experience help to significantly reduce their harmful effect on shooting accuracy.

Since sport shooting distances are relatively short and the bullet travels over them in a very short time, some atmospheric factors, such as air density, will not have a significant effect on its flight. Therefore, in sports shooting it is necessary to take into account mainly the influence of wind and, to a certain extent, air temperature.

Wind influence. Headwinds and tailwinds have little effect on shooting accuracy, so shooters usually neglect their effect. Thus, when shooting at a distance of 600 m, a strong (10 m/sec) head or tail wind changes the height of the STP by only 4 cm.

The side wind significantly deflects the bullet to the side, even when shooting at close distances.

Wind is characterized by strength (speed) and direction.

The strength of the wind is determined by its speed in meters per second. In shooting practice, winds are distinguished: weak - 2 m/sec, moderate - 4-5 m/sec and strong - 8-10 m/sec.

The strength and direction of the wind are practically determined by the arrows based on various local characteristics: using a flag, by the movement of smoke, the vibration of grass, bushes and trees, etc. (Fig. 62).

Rice. 62 - Determining wind strength by flag and smoke

Depending on the strength and direction of the wind, you should either make a lateral correction of the sight, or move the point, aiming in the direction opposite to its direction (taking into account the deflection of bullets under the influence of the wind - mainly when shooting at figured targets). In table 8 and 9 show the deflection values of bullets under the influence of side winds.

Deflection of bullets under the influence of side winds when firing from 7.62 mm rifles

Table 8

Firing range, m	Heavy bullet deflection (11.8 g), cm
Firing range, m	light wind (2 m/sec)	moderate wind (4 m/sec)	strong wind (8 m/sec)
100	1	2	4
200	4	8	18
300	10	20	41
400	20	40	84
500	34	68	140
600	48	100	200
700	70	140	280
800	96	180	360
900	120	230	480
1000	150	300	590

Deflection of bullets under the influence of side wind when shooting from a small-caliber rifle

As can be seen from these tables, when shooting at short distances, the deflection of bullets is almost proportional to the strength (speed) of the wind. From the table 8 also shows that when shooting from service and free rifles at 300 m, a side wind with a speed of 1 m/sec blows the bullet to the side by one dimension of target No. 3 (5 cm). These simplified data should be used in practice when determining the magnitude of wind corrections.

Oblique wind (at an angle to the shooting plane of 45, 135, 225 and 315°) deflects the bullet half as much as side wind.

However, during shooting, it is, of course, impossible to make corrections for the wind, so to speak, “formally,” guided solely by the data in the tables. This data should serve only as initial material and help the shooter navigate difficult shooting conditions in the wind.

It practically rarely happens that on such a relatively small area of terrain as a shooting range, the wind always has the same direction, much less the same strength. It usually blows in gusts. Therefore, the shooter needs the ability to time the shot to the moment when the strength and direction of the wind become approximately the same as during previous shots.

Flags are usually hung at the shooting range so that the athlete can determine the strength and direction of the wind. You need to learn to correctly follow the indications of the flags. Flags should not be relied upon entirely if they are mounted high above the target line and line of fire. You also cannot navigate by flags installed at the edge of the forest, steep cliffs, ravines and hollows, since the wind speed is different layers the atmosphere, as well as uneven terrain and obstacles are different. As an example in Fig. 63 provides approximate data on wind speed in summer on the plain at various heights from the ground. It is clear that the readings of flags mounted on a high bullet receiving shaft or on a high mast will not correspond to the true force of the wind, which acts directly on the bullet. You need to be guided by the readings of flags, paper ribbons, etc., installed at the same level at which the weapon is located during shooting.

Rice. 63 - Approximate data on wind speed in summer at various altitudes on the plain

It should also be borne in mind that the wind, bending around uneven terrain and obstacles, can create turbulence. If flags are installed along the entire shooting distance, they often show completely different, even opposite, wind directions. Therefore, you need to try to determine the main direction and strength of the wind along the entire shooting route, carefully observing individual local landmarks in the area of the terrain lying between the shooter and the target.

Naturally, making accurate wind corrections requires some experience. But experience does not come by itself. The shooter must constantly carefully observe and carefully study the influence of wind in general and at a given shooting range in particular, and systematically record the conditions under which shooting is carried out. Over time, he develops a subconscious feeling and experience that allows him to quickly navigate the meteorological situation and make the necessary adjustments to ensure accurate shooting in difficult conditions.

Effect of air temperature. The lower the air temperature, the greater its density. A bullet flying in denser air encounters a large number of air particles on its path, and therefore loses its initial speed faster. Therefore, in cold weather, at low temperatures, the firing range decreases and the STP decreases (Table 10).

Moving the average point of impact when shooting from a 7.62 mm rifle under the influence of changes in air temperature and powder charge every 10°

Table 10

Firing range, m	STP movement in height, cm
Firing range, m	light bullet (9.6 g)	heavy bullet (11.8 g)
100	-	-
200	1	1
300	2	2
400	4	4
500	7	7
600	12	12
700	21	19
800	35	28
900	54	41
1000	80	59

Temperature also affects the combustion process of the powder charge in the barrel of a weapon. As is known, with increasing temperature, the burning rate of a powder charge increases, since the heat consumption required to heat and ignite the powder grains decreases. Consequently, the lower the air temperature, the slower the process of increasing gas pressure. As a result, the initial speed of the bullet decreases.

It has been established that a change in air temperature by 1° changes the initial speed by 1 m/sec. Significant temperature fluctuations between summer and winter lead to changes in the initial speed within the range of 50-60 m/sec.

Taking this into account, for zeroing weapons, compiling appropriate tables, etc. take a certain “normal” temperature - +15°.

Considering the relationship between the temperature of the powder charge and the initial velocity of the bullet, the following must be kept in mind.

When firing in large batches for a long time, when the rifle barrel gets very hot, you should not allow the next cartridge to remain in the chamber for a long time: the relatively high temperature of the heated barrel, transmitted through the cartridge case to the powder charge, will lead to accelerated ignition of the gunpowder, which can ultimately lead to to a change in STP and upward “breaks” (depending on the duration of the cartridge’s stay in the chamber).

Therefore, if the shooter is tired and needs some rest before the next shot, then during such a break in shooting the cartridge should not be in the chamber; it should be removed or replaced altogether with another cartridge from the pack, that is, unheated.

2.3.7 Bullet dispersion

Even under the most favorable shooting conditions, each of the fired bullets describes its own trajectory, somewhat different from the trajectories of other bullets. This phenomenon is called natural dispersion.

With a significant number of shots, the trajectories in their totality form sheaf, which, when meeting a target, produces a number of holes, more or less distant from each other. The area they occupy is called dispersion area(Fig. 64).

Rice. 64 - Sheaf of trajectories, average trajectory, dispersion area

All holes are located on the dispersion area around a certain point called center of dispersion or midpoint of impact (STP). A trajectory located in the middle of the sheaf and passing through midpoint hits are called average trajectory . When making adjustments to the installation of the sight during the shooting process, this average trajectory is always implied.

For different types of weapons and cartridges, there are certain standards for bullet dispersion, as well as standards for bullet dispersion according to factory specifications and tolerances for the production of certain types of weapons and batches of cartridges.

With a large number of shots, the dispersion of bullets obeys a certain dispersion law, the essence of which is as follows:

— the holes are located unevenly across the dispersion area, most densely grouped around the STP;

— the holes are located symmetrically relative to the STP, since the probability of a bullet deflecting in any direction from the STP is the same;

— the dispersion area is always limited to a certain limit and has the shape of an ellipse (oval), elongated in height on a vertical plane.

By virtue of this law, in general, holes are located on the dispersion area naturally, and therefore, in symmetrical stripes of equal width, equally distant from the dispersion axes, the same and certain number of holes are contained, although the dispersion areas can have different sizes (depending on the type of weapon and cartridges). The measure of dispersion is: median deviation, core band and radius of the circle containing better half holes (P 50) or all hits (P 100). It should be emphasized that the law of dispersion fully manifests itself with a large number of shots. When shooting sports in relatively small series, the dispersion area approaches the shape of a circle, therefore the measure of dispersion is the value of the radius of the circle that contains 100% of the holes (P 100) or the better half of the holes (P 50) (Fig. 65). The radius of the circle containing all the holes is approximately 2.5 times larger than the radius of the circle containing the best half of them. During factory tests of cartridges, when shooting is carried out in small series (usually 20) of shots, a circle that includes all the holes - P 100 (the diameter that includes all the holes, see Fig. 16) also serves as a measure of dispersion.

Rice. 65 - Large and small radii of circles containing 100 and 50% hits

So, the natural dispersion of bullets is an objective process that operates independently of the will and desire of the shooter. This is partly true, and requiring weapons and cartridges to ensure that all bullets hit the same point is pointless.

At the same time, the shooter must remember that the natural dispersion of bullets is by no means an inevitable norm, once and for all established for a given type of weapon and certain shooting conditions. The art of marksmanship is to know the causes of natural bullet dispersion and reduce their influence. Practice has convincingly proven how important correct debugging of weapons and selection of cartridges, technical preparedness of the shooter and experience of shooting in adverse weather conditions are to reduce dispersion.

Basic concepts are presented: periods of a shot, elements of a bullet’s flight path, direct shot, etc.

In order to master the technique of shooting from any weapon, you need to know a number of theoretical principles, without which not a single shooter will be able to show high results and his training will be ineffective.
Ballistics is the science of projectile movement. In turn, ballistics is divided into two parts: internal and external.

Internal ballistics

Internal ballistics studies the phenomena occurring in the barrel bore during a shot, the movement of the projectile along the bore, the nature of the thermo- and aerodynamic dependencies accompanying this phenomenon, both in the bore and beyond during the aftereffect of powder gases.
Internal ballistics solves the most rational use energy of a powder charge during a shot in order to impart a certain initial velocity (V0) to a projectile of a given weight and caliber while maintaining the strength of the barrel. This provides input for external ballistics and weapon design.

With a shot is called the ejection of a bullet (grenade) from the bore of a weapon by the energy of gases formed during the combustion of a powder charge.
When the firing pin strikes the primer of a live cartridge sent into the chamber, the percussion composition of the primer explodes and a flame is formed, which penetrates through the seed holes in the bottom of the cartridge case to the powder charge and ignites it. When a powder (combat) charge burns, a large amount of highly heated gases is formed, creating high pressure on the bottom of the bullet, the bottom and walls of the cartridge case, as well as on the walls of the barrel and the bolt.
As a result of the gas pressure on the bottom of the bullet, it moves from its place and crashes into the rifling; rotating along them, moves along the barrel bore with a continuously increasing speed and is thrown out in the direction of the axis of the barrel bore. The gas pressure on the bottom of the cartridge case causes the weapon (barrel) to move backward.
When fired from an automatic weapon, the design of which is based on the principle of using the energy of powder gases discharged through a hole in the wall of the barrel - a Dragunov sniper rifle, part of the powder gases, in addition, after passing through it into the gas chamber, strikes the piston and throws away the pusher with the bolt back.
When a powder charge is burned, approximately 25-35% of the released energy is spent on communicating with the bullet forward movement(main job); 15-25% of energy - for performing secondary work (plunging in and overcoming the friction of a bullet when moving along the bore; heating the walls of the barrel, cartridge case and bullet; moving the moving part of the weapon, the gaseous and unburnt part of the gunpowder); about 40% of the energy is not used and is lost after the bullet leaves the bore.

The shot occurs in a very short period of time (0.001-0.06 s.). When firing, there are four consecutive periods:

preliminary
first or main
second
third, or period of last gases

Preliminary period lasts from the beginning of the combustion of the powder charge until the bullet casing completely cuts into the rifling of the barrel. During this period, gas pressure is created in the barrel bore, which is necessary to move the bullet from its place and overcome the resistance of its shell to cut into the rifling of the barrel. This pressure is called boost pressure; it reaches 250 - 500 kg/cm2 depending on the rifling design, the weight of the bullet and the hardness of its shell. It is assumed that the combustion of the powder charge in this period occurs in a constant volume, the shell cuts into the rifling instantly, and the movement of the bullet begins immediately when the boost pressure is reached in the barrel bore.

First or main period lasts from the beginning of the bullet’s movement until the complete combustion of the powder charge. During this period, combustion of the powder charge occurs in a rapidly changing volume. At the beginning of the period, when the speed of the bullet moving along the bore is still low, the amount of gases grows faster than the volume of the bullet space (the space between the bottom of the bullet and the bottom of the cartridge case), the gas pressure quickly increases and reaches greatest value- rifle cartridge 2900 kg/cm2. This pressure is called maximum pressure. It is created in small arms when a bullet travels 4 - 6 cm. Then due to fast speed bullet movement, the volume of the bullet space increases faster than the influx new gases, and the pressure begins to fall, by the end of the period it is approximately 2/3 of the maximum pressure. The speed of the bullet constantly increases and by the end of the period reaches approximately 3/4 of the initial speed. The powder charge is completely burned shortly before the bullet leaves the barrel.

Second period lasts until the powder charge is completely burned until the bullet leaves the barrel. With the beginning of this period, the influx of powder gases stops, however, highly compressed and heated gases expand and, putting pressure on the bullet, increase its speed. The pressure drop in the second period occurs quite quickly and at the muzzle the muzzle pressure is 300 - 900 kg/cm2 for various types of weapons. The speed of the bullet at the moment it leaves the barrel (muzzle speed) is slightly less than the initial speed.

The third period, or the period after the action of gases lasts from the moment the bullet leaves the barrel until the action of the powder gases on the bullet ceases. During this period, powder gases flowing from the barrel at a speed of 1200 - 2000 m/s continue to affect the bullet and impart additional speed to it. The bullet reaches its highest (maximum) speed at the end of the third period at a distance of several tens of centimeters from the muzzle of the barrel. This period ends at the moment when the pressure of the powder gases at the bottom of the bullet is balanced by air resistance.

Initial bullet speed and its practical significance

Initial speed called the speed of the bullet at the muzzle of the barrel. The initial speed is taken to be a conditional speed, which is slightly greater than the muzzle and less than the maximum. It is determined experimentally with subsequent calculations. The magnitude of the muzzle velocity is indicated in the shooting tables and in the combat characteristics of the weapon.
The initial speed is one of the most important characteristics combat properties of weapons. As the initial speed increases, the bullet's flight range, direct shot range, lethal and penetrating effect of the bullet increases, and the influence of external conditions on its flight decreases. The magnitude of the initial bullet speed depends on:

barrel length
bullet weight
weight, temperature and humidity of the powder charge
shapes and sizes of gunpowder grains
loading density

The longer the trunk, the longer the powder gases act on the bullet and the greater the initial speed. With a constant barrel length and constant weight of a powder charge, the lower the bullet weight, the greater the initial speed.
Changing the weight of the powder charge leads to a change in the amount of powder gases, and consequently to a change in the maximum pressure in the barrel bore and the initial velocity of the bullet. The greater the weight of the powder charge, the greater the maximum pressure and muzzle velocity.
With increasing temperature of the powder charge The burning rate of the gunpowder increases, and therefore the maximum pressure and initial speed increase. When the charge temperature decreases the initial speed decreases. An increase (decrease) in the initial speed causes an increase (decrease) in the range of the bullet. In this regard, it is necessary to take into account range corrections for air and charge temperatures (charge temperature is approximately equal to air temperature).
With increasing humidity of the powder charge its burning speed and the initial speed of the bullet decrease.
Shapes and sizes of gunpowder have a significant impact on the burning rate of the powder charge, and therefore on the initial speed of the bullet. They are selected accordingly when designing weapons.
Loading density is called the ratio of the weight of the charge to the volume of the cartridge case with the bullet inserted (charge combustion chamber). When the bullet is seated deeply, the loading density increases significantly, which can lead to a sharp surge in pressure when fired and, as a result, to rupture of the barrel, so such cartridges cannot be used for shooting. As the loading density decreases (increases), the initial bullet speed increases (decreases).
Recoil called the backward movement of the weapon during a shot. Recoil is felt in the form of a push to the shoulder, arm or ground. The recoil effect of a weapon is approximately as many times less than the initial speed of a bullet, as many times the bullet is lighter than the weapon. The recoil energy of hand-held small arms usually does not exceed 2 kg/m and is perceived painlessly by the shooter.

The recoil force and the recoil resistance force (butt support) are not located on the same straight line and are directed in opposite directions. They form a pair of forces, under the influence of which the muzzle of the weapon barrel is deflected upward. The amount of deflection of the muzzle of the barrel of this weapon the more than more shoulder this pair of forces. In addition, when fired, the barrel of the weapon makes oscillatory movements - vibrates. As a result of vibration, the muzzle of the barrel at the moment the bullet leaves can also deviate from its original position in any direction (up, down, right, left).
The magnitude of this deviation increases when the shooting rest is used incorrectly, the weapon is dirty, etc.
The combination of the influence of barrel vibration, weapon recoil and other reasons leads to the formation of an angle between the direction of the axis of the barrel bore before the shot and its direction at the moment the bullet leaves the bore. This angle is called the departure angle.
The departure angle is considered positive when the axis of the barrel bore at the moment the bullet leaves is above its position before the shot, negative when it is below. The influence of the take-off angle on shooting is eliminated when it is brought to normal combat. However, if the rules for placing a weapon are violated, the use of a stop, as well as the rules for caring for and preserving the weapon, the value of the angle of departure and the engagement of the weapon changes. In order to reduce the harmful effects of recoil on shooting results, compensators are used.
So, the phenomena of a shot, the initial speed of a bullet, and the recoil of a weapon have great importance when shooting and affect the flight of the bullet.

External ballistics

This is a science that studies the movement of a bullet after the action of powder gases on it ceases. The main task of external ballistics is the study of the properties of the trajectory and patterns of flight of a bullet. External ballistics provides data for compiling shooting tables, calculating weapon sight scales, and developing shooting rules. Conclusions from external ballistics are widely used in combat when choosing a sight and aiming point depending on the firing range, wind direction and speed, air temperature and other shooting conditions.

The trajectory of a bullet and its elements. Trajectory properties. Types of trajectory and their practical significance

Trajectory called the curved line described by the center of gravity of the bullet in flight.
When flying in the air, a bullet is subject to two forces: gravity and air resistance. The force of gravity causes the bullet to gradually lower, and the force of air resistance continuously slows down the movement of the bullet and tends to knock it over. As a result of the action of these forces, the speed of the bullet gradually decreases, and its trajectory is shaped like an unevenly curved curved line. Air resistance to the flight of a bullet is caused by the fact that air is an elastic medium and therefore part of the bullet’s energy is expended on movement in this medium.

The force of air resistance is caused by three main reasons: air friction, the formation of vortices and the formation of a ballistic wave.
The shape of the trajectory depends on the elevation angle. As the elevation angle increases, the trajectory height and the full horizontal range of the bullet increase, but this occurs to a certain limit. Beyond this limit, the trajectory altitude continues to increase, and the total horizontal range begins to decrease.

The angle of elevation at which the total horizontal range of the bullet becomes greatest is called the angle of greatest range. The value of the angle of greatest range for bullets various types weapons is about 35°.

Trajectories obtained at elevation angles smaller angles longest range are called flat. Trajectories obtained at elevation angles greater than the greatest angle of greatest range are called mounted. When shooting from the same weapon (with the same initial speeds) you can get two trajectories with the same horizontal range: flat and mounted. Trajectories that have the same horizontal range and swarms of different elevation angles are called conjugated.

When shooting from small arms, only flat trajectories are used. The flatter the trajectory, the greater the area over which the target can be hit with one sight setting (the less impact an error in determining the sight setting has on the shooting results): this is practical significance trajectories.
The flatness of the trajectory is characterized by its greatest excess above the aiming line. At a given range, the trajectory is flatter the less it rises above the aiming line. In addition, the flatness of the trajectory can be judged by the magnitude of the angle of incidence: the smaller the angle of incidence, the more flat the trajectory. The flatness of the trajectory affects the range of a direct shot, hit, covered and dead space.

Path elements

Departure point- center of the muzzle of the barrel. The departure point is the beginning of the trajectory.
Weapon Horizon- horizontal plane passing through the departure point.
Elevation line- a straight line, which is a continuation of the axis of the barrel of the aimed weapon.
Firing plane- a vertical plane passing through the elevation line.
Elevation angle- the angle between the elevation line and the horizon of the weapon. If this angle is negative, then it is called the declination (decrease) angle.
Throwing line- a straight line, which is a continuation of the axis of the barrel bore at the moment the bullet leaves.
Throwing angle
Departure angle- the angle between the elevation line and the throwing line.
Drop point- the point of intersection of the trajectory with the horizon of the weapon.
Angle of incidence- the angle between the tangent to the trajectory at the point of impact and the horizon of the weapon.
Full horizontal range- the distance from the point of departure to the point of impact.
Final speed- the speed of the bullet (grenade) at the point of impact.
Full time flight- time of movement of a bullet (grenade) from the point of departure to the point of impact.
Top of the trajectory- the highest point of the trajectory above the horizon of the weapon.
Path height- the shortest distance from the top of the trajectory to the horizon of the weapon.
Ascending branch of the trajectory- part of the trajectory from the point of departure to the top, and from the top to the point of fall - the descending branch of the trajectory.
Aiming point (aims)- a point on the target (outside it) at which the weapon is aimed.
Line of sight- a straight line running from the shooter’s eye through the middle of the sight slot (at the level with its edges) and the top of the front sight to the aiming point.
Aiming angle- the angle between the elevation line and the aiming line.
Target elevation angle- the angle between the aiming line and the horizon of the weapon. This angle is considered positive (+) when the target is above, and negative (-) when the target is below the weapon's horizon.
Sighting range - the distance from the departure point to the intersection of the trajectory with the aiming line. The excess of the trajectory above the aiming line is the shortest distance from any point on the trajectory to the aiming line.
Target line- a straight line connecting the departure point to the target.
Slant range- the distance from the departure point to the target along the target line.
Meeting point- the point of intersection of the trajectory with the target surface (ground, obstacle).
Meeting angle- the angle between the tangent to the trajectory and the tangent to the surface of the target (ground, obstacle) at the meeting point. The meeting angle is taken to be the smaller of the adjacent angles, measured from 0 to 90 degrees.

Direct shot, striking and dead space most closely related to issues of shooting practice. The main objective of studying these issues is to gain solid knowledge in the use of a direct shot and the target space to perform fire missions in combat.

Direct shot, its definition and practical use in a combat situation

A shot in which the trajectory does not rise above the aiming line above the target throughout its entire length is called direct shot. Within the range of a direct shot, during tense moments of battle, shooting can be carried out without rearranging the sight, while the vertical aiming point is usually selected at the lower edge of the target.

The range of a direct shot depends on the height of the target and the flatness of the trajectory. The higher the target and the flatter the trajectory, the greater the range of a direct shot and the greater the area over which the target can be hit with one sight setting.
The range of a direct shot can be determined from tables by comparing the height of the target with the values of the greatest elevation of the trajectory above the aiming line or with the height of the trajectory.

Direct sniper shot in an urban environment
The installation height of optical sights above the bore of a weapon is on average 7 cm. At a distance of 200 meters and sight "2", the greatest excesses of the trajectory, 5 cm at a distance of 100 meters and 4 cm at 150 meters, practically coincide with the aiming line - the optical axis of the optical sight. The height of the aiming line at the middle of a distance of 200 meters is 3.5 cm. There is a practical coincidence of the bullet trajectory and the aiming line. The difference of 1.5 cm can be neglected. At a distance of 150 meters, the height of the trajectory is 4 cm, and the height of the optical axis of the sight above the horizon of the weapon is 17-18 mm; the difference in height is 3 cm, which also does not play a practical role.

At a distance of 80 meters from the shooter, the height of the bullet trajectory will be 3 cm, and the height of the aiming line will be 5 cm, the same difference of 2 cm is not decisive. The bullet will land only 2 cm below the aiming point. The vertical dispersion of bullets of 2 cm is so small that it is of no fundamental importance. Therefore, when shooting with the “2” division of the optical sight, starting from a distance of 80 meters and up to 200 meters, aim at the bridge of the enemy’s nose - you will hit there ±2/3 cm higher and lower throughout this distance. At 200 meters the bullet will hit exactly the aiming point. And even further, at a distance of up to 250 meters, aim with the same scope “2” at the enemy’s “top”, at the upper cut of the cap - the bullet drops sharply after 200 meters of distance. At 250 meters, aiming this way, you will hit 11 cm lower - on the forehead or bridge of the nose.
The method described above can be useful in street battles, when the distances in the city are approximately 150-250 meters and everything is done quickly, on the run.

Target space, its definition and practical use in a combat situation

When shooting at targets located at a distance greater than the direct shot range, the trajectory near its top rises above the target and the target in some area will not be hit with the same sight setting. However, there will be a space (distance) near the target at which the trajectory does not rise above the target and the target will be hit by it.

The distance on the ground over which the descending branch of the trajectory does not exceed the target height, called target space(depth of affected space).
The depth of the affected space depends on the height of the target (it will be greater, the higher the target), on the flatness of the trajectory (it will be greater, the flatter the trajectory) and on the angle of inclination of the terrain (on the forward slope it decreases, on the reverse slope it increases).
The depth of the affected space can be determined from tables of trajectory elevation above the aiming line by comparing the excess of the descending branch of the trajectory at the corresponding firing range with the target height, and if the target height is less than 1/3 of the trajectory height, then in the form of a thousandth.
To increase the depth of the affected area on sloping terrain, the firing position must be chosen so that the terrain at the enemy’s location coincides, if possible, with the line of sight. Covered space its definition and practical use in a combat situation.

Covered space, its definition and practical use in a combat situation

The space behind cover that cannot be penetrated by a bullet, from its crest to the meeting point is called covered space.
The greater the height of the shelter and the flatter the trajectory, the greater the covered space. The depth of the covered space can be determined from tables of trajectory elevation above the aiming line. By selection, an excess is found that corresponds to the height of the shelter and the distance to it. After finding the excess, the corresponding sight setting and firing range are determined. The difference between a certain firing range and the distance to cover represents the depth of the covered space.

Dead space definition and practical use in a combat situation

The part of the covered space in which the target cannot be hit with a given trajectory is called dead (not affected) space.
The greater the height of the cover, the lower the height of the target and the flatter the trajectory, the greater the dead space. The other part of the covered space in which the target can be hit is the target space. The depth of the dead space is equal to the difference between the covered and affected space.

Knowing the size of the target space, covered space, and dead space allows you to correctly use shelters to protect against enemy fire, as well as take measures to reduce dead spaces by the right choice firing positions and firing at targets from weapons with a more advanced trajectory.

Derivation phenomenon

Due to the simultaneous impact on the bullet rotational movement, giving it a stable position in flight, and air resistance tending to tip the bullet head back, the axis of the bullet deviates from the direction of flight in the direction of rotation. As a result of this, the bullet encounters air resistance on more than one side and therefore deviates from the firing plane more and more in the direction of rotation. This deflection of a rotating bullet away from the firing plane is called derivation. This is a rather complex physical process. Derivation increases disproportionately to the flight distance of the bullet, as a result of which the latter takes more and more to the side and its trajectory in plan is a curved line. When the barrel is cut to the right, the derivation takes the bullet to the right, and when the barrel is cut to the left, to the left.

Distance, m	Derivation, cm	thousandths
100	0	0
200	1	0
300	2	0,1
400	4	0,1
500	7	0,1
600	12	0,2
700	19	0,2
800	29	0,3
900	43	0,5
1000	62	0,6

At firing distances up to 300 meters inclusive, derivation has no practical significance. This is especially typical for the SVD rifle, in which the PSO-1 optical sight is specially shifted to the left by 1.5 cm. At the same time, the barrel is slightly turned to the left and the bullets move slightly (1 cm) to the left. This is not of fundamental importance. At a distance of 300 meters, the force of derivation returns the bullets to the aiming point, that is, in the center. And already at a distance of 400 meters, the bullets begin to move thoroughly to the right, therefore, in order not to turn the horizontal flywheel, aim at the enemy’s left (away from you) eye. Derivation will move the bullet 3-4 cm to the right, and it will hit the enemy on the bridge of the nose. At a distance of 500 meters, aim at the left (from you) side of the enemy’s head between the eye and ear - this will be approximately 6-7 cm. At a distance of 600 meters, aim at the left (from you) side of the enemy’s head. Derivation will move the bullet to the right by 11-12 cm. At a distance of 700 meters, take the visible gap between the aiming point and the left edge of the head, somewhere above the center of the shoulder strap on the enemy’s shoulder. At 800 meters - correct the horizontal corrections with the flywheel by 0.3 thousandths (move the reticle to the right, move the middle point of impact to the left), at 900 meters - 0.5 thousandths, at 1000 meters - 0.6 thousandths.

The trajectory of a bullet, its elements, properties. Types of trajectories and their practical significance

A trajectory is a curved line described by the center of gravity of a bullet in flight.

When flying in the air, a bullet is subject to two forces: gravity and air resistance. The force of gravity causes the bullet to gradually lower, and the force of air resistance continuously slows down the movement of the bullet and tends to knock it over.

As a result of the action of these forces, the speed of the bullet gradually decreases, and its trajectory is shaped like an unevenly curved curved line.

Parameter trajectories	Parameter characteristics	Note
Departure point	Center of the muzzle of the barrel	The departure point is the beginning of the trajectory
Weapon Horizon	Horizontal plane passing through the departure point	The weapon horizon looks like a horizontal line. The trajectory crosses the horizon of the weapon twice: at the point of departure and at the point of impact
Elevation line	A straight line that is a continuation of the axis of the barrel of the aimed weapon
Firing plane	Vertical plane passing through the elevation line
Elevation angle	The angle between the elevation line and the horizon of the weapon	If this angle is negative, then it is called the declination (decrease) angle
Throwing line	Straight, a line that is a continuation of the axis of the bore at the moment the bullet leaves
Throwing angle	The angle between the throwing line and the horizon of the weapon
Departure angle	The angle between the elevation line and the throwing line
Drop point	The point of intersection of the trajectory with the horizon of the weapon
Angle of incidence	The angle between the tangent to the trajectory at the point of impact and the horizon of the weapon
Full horizontal range	Distance from departure point to impact point
Ultimate speed	Bullet speed at impact point
Total flight time	Time of movement of a bullet from the point of departure to the point of impact
Top of the trajectory	Highest point of the trajectory
Path height	Shortest distance from the top of the trajectory to the horizon of the weapon
Ascending branch	Part of the trajectory from the departure point to the top
Descending branch	Part of the trajectory from the top to the point of fall
Aiming point (aims)	The point on or off the target at which the weapon is aimed
Line of sight	A straight line running from the shooter's eye through the middle of the sight slot (level with its edges) and the top of the front sight to the aiming point
Aiming angle	The angle between the elevation line and the aiming line
Target elevation angle	The angle between the line of sight and the horizon of the weapon	The target's elevation angle is considered positive (+) when the target is above the weapon's horizon, and negative (-) when the target is below the weapon's horizon.
Sighting range	Distance from the departure point to the intersection of the trajectory with the aiming line
Exceeding the trajectory above the aiming line	The shortest distance from any point on the trajectory to the aiming line
Target line	Straight line connecting the departure point to the target	When firing direct fire, the target line practically coincides with the aiming line
Slant range	Distance from departure point to target along target line	When firing direct fire, the slant range practically coincides with the target range.
Meeting point	The point of intersection of the trajectory with the target surface (ground, obstacles)
Meeting angle	The angle between the tangent to the trajectory and the tangent to the surface of the target (ground, obstacle) at the meeting point	The meeting angle is taken to be the smaller of the adjacent angles, measured from 0 to 90°
Sighting line	A straight line connecting the middle of the sight slot to the top of the front sight
Aiming (aiming)	Giving the axis of the weapon barrel the necessary position in space for shooting	In order for the bullet to reach the target and hit it or the desired point on it
Horizontal aiming	Giving the bore axis the required position in the horizontal plane
Vertical aiming	Giving the bore axis the required position in the vertical plane

The trajectory of a bullet in the air has the following properties:
- the descending branch is shorter and steeper than the ascending branch;
- the angle of incidence is greater than the angle of throw;
- the final speed of the bullet is less than the initial speed;
- the lowest flight speed of a bullet when shooting at large throwing angles is on the downward branch of the trajectory, and when shooting at small throwing angles - at the point of impact;
- the time of movement of a bullet along the ascending branch of the trajectory is less than along the descending branch;
- the trajectory of a rotating bullet due to the lowering of the bullet under the influence of gravity and derivation is a line of double curvature.

Types of trajectories and their practical significance

When firing from any type of weapon with an increase in elevation angle from 0° to 90°, the horizontal range first increases to a certain limit and then decreases to zero (Fig. 5).

The angle of elevation at which the greatest range is obtained is called the angle of greatest range. The maximum range angle for bullets of various types of weapons is about 35°.

The angle of greatest range divides all trajectories into two types: flat and mounted trajectories (Fig. 6).

Flat trajectories are trajectories obtained at elevation angles smaller than the angle of greatest range (see Fig., trajectories 1 and 2).

Mounted trajectories are called trajectories obtained at elevation angles greater than the angle of greatest range (see Fig. trajectories 3 and 4).

Conjugate trajectories are trajectories obtained at the same horizontal distance by two trajectories, one of which is flat, the other is mounted (see Fig., trajectories 2 and 3).

When firing from small arms and grenade launchers, only flat trajectories are used. The flatter the trajectory, the greater the area over which the target can be hit with one sight setting (the less impact an error in determining the sight setting has on the shooting results): this is the practical significance of the trajectory.

The flatness of the trajectory is characterized by its greatest excess above the aiming line. At a given range, the trajectory is flatter the less it rises above the aiming line. In addition, the flatness of the trajectory can be judged by the magnitude of the angle of incidence: the smaller the angle of incidence, the more flat the trajectory. The flatness of the trajectory affects the range of the direct shot, the target, covered and dead space.

Fire range (m)	Flight time (s)
	0,15
	0,28
	0,42
	0,60
	0,80
	1,02
	1,26

A trajectory in the air has the following property. Ballistics information: internal and external ballistics. wound ballistics. Types of trajectories and their practical significance

Internal ballistics

External ballistics

Diffusion

Derivation

Bullet displacement by wind

Bullet flight time

Solution of ballistic problems

Barrier and wound ballistics

Barrier ballistics

Wound ballistics

Through wounds

Blind wounds

Cutting wounds

Due to the rotation of the bullet in flight

2.3.4 Dependence of the trajectory shape on the throwing angle. Path elements

2.3.5 Dependence of the trajectory shape on the initial velocity of the bullet, its shape and lateral load

2.3.6 Dependence of the trajectory on meteorological conditions

2.3.7 Bullet dispersion

Internal ballistics

Initial bullet speed and its practical significance

External ballistics

The trajectory of a bullet and its elements. Trajectory properties. Types of trajectory and their practical significance

Path elements

Direct shot, its definition and practical use in a combat situation

Target space, its definition and practical use in a combat situation

Covered space, its definition and practical use in a combat situation

Dead space definition and practical use in a combat situation

Derivation phenomenon