Success 

Ballistics of naval artillery. Yuriev A.A. "Bullet sport shooting" External ballistics of weapons

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 will be considered wound ballistics(the effect of a bullet on the client’s body). There is also a section forensic ballistics is considered in a criminology course 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 full trajectory bullet flight (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 bullets 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

        • To solve the simplest ballistic tasks It is necessary to note the dependence of the bullet’s flight time on the firing range. Without taking this factor into account, it will be quite problematic to hit even a slowly moving target.
        The bullet's flight time to the target is presented in table. 6.
        Table 6

        Time of flight of a bullet to the target

          • 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
      • dancing different classes 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? Clarifying this issue is the most important characteristic to select weapons and ammunition for a specific 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 (0B). 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 maximum depth on target. 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.

Trajectory called the curved line described by the center of gravity of the bullet in flight.

Rice. 3. Trajectory


Rice. 4. Bullet flight path parameters

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
Full time flight 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 Yu 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 one;
  • 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 the bullet travels 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 elevation angle at which the greatest range is obtained is called angle longest range . The value of the angle of greatest range for bullets various types weapons is about 35°.

The angle of greatest range divides all trajectories into two types: on the trajectory flooring And mounted(Fig. 6).


Rice. 5. The affected area and the largest horizontal and sighting ranges when firing at different elevation angles. Rice. 6. Angle of greatest range. flat, mounted and conjugate trajectories

Flat trajectories are called trajectories obtained at elevation angles, smaller angle longest range (see figure, trajectories 1 and 2).

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

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

When shooting from small arms and grenade launchers, only flat trajectories are used. How flatter 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 direct shot, affected, covered and dead space.

Read full summary

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 elastic medium and therefore part of the bullet’s energy is expended on movement in this environment.

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 maximum range angle for bullets of various types of weapons is about 35°.

Trajectories obtained at elevation angles less than the angle of greatest range are called flat. Trajectories obtained at elevation angles greater than the angle largest angle longest range are called mounted. When firing from the same weapon (at the same initial speeds), you can get two trajectories with the same horizontal range: flat and mounted. Trajectories having the same horizontal range swarms at 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 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.

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.
Total flight time- 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.

Trajectory called a curved line described by the center of gravity of a bullet (grenade) in flight. When flying in the air, a bullet (grenade) is subject to two forces: gravity and air resistance. The force of gravity causes the bullet (grenade) to gradually lower, and the force of air resistance continuously slows down the movement of the bullet (grenade) and tends to overturn it. As a result of the action of these forces, the speed of the bullet (grenade) gradually decreases, and its trajectory is shaped like an unevenly curved curved line. Air resistance to the flight of a bullet (grenade) is caused by the fact that air is an elastic medium and therefore part of the energy of the bullet (grenade) 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 flight range of the bullet (grenade) 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 elevation angle at which the total horizontal flight range of a bullet (grenade) becomes greatest is called the angle of greatest range. The maximum range angle for bullets of various types of weapons is about 35°.
Trajectories obtained at elevation angles less than the angle of greatest range are called flat. Trajectories obtained at elevation angles greater than the greatest angle of greatest range are called mounted. When firing from the same weapon (at 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 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.

To study the trajectory of a bullet, the following definitions are accepted:

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. Total flight time- 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.

2.6 Direct shot - a shot in which the top of the bullet’s flight path does not exceed the height of the target.

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 procedure for partial disassembly of the AK-74:

We disconnect the magazine, remove the safety and jerk the bolt carrier, perform a control release, right hand press the spring stop and remove the box cover, disconnect the frame with the piston, remove the bolt from the bolt frame, disconnect the gas tube, disconnect the muzzle brake-compensator, remove the ram.

2.7 The space behind cover that is not penetrated by a bullet, from its crest to the meeting point is called covered space

The part of the covered space in which the target cannot be hit with a given trajectory is called dead space (the more, the higher the height of the shelter)

The part of the covered space in which the target can be hit is called affected area

Derivation(from lat. derivatio- abduction, deflection) in military affairs - deviation of the flight path of a bullet or artillery shell (this applies only to rifled weapons or special ammunition for smooth-bore weapons) under the influence of rotation imparted by the rifling of the barrel, inclined nozzles or inclined stabilizers of the ammunition itself, that is, due to the gyroscopic effect and effect Magnus. The phenomenon of derivation during the movement of elongated projectiles was first described in the works of the Russian military engineer General N.V. Maievsky.

3.1 What statutes are included in the ovu of the Armed Forces of the Russian Federation,

Charter of the internal service of the armed forces of the Russian Federation

Disciplinary Charter of the Armed Forces of the Russian Federation

Charter of the garrison, commandant and guard services of the Armed Forces of the Russian Federation

Drill regulations of the Armed Forces of the Russian Federation

3.2 Military discipline is strict and precise observance by all military personnel of the order and rules established by law Russian Federation, general military regulations of the Armed Forces of the Russian Federation (hereinafter referred to as general military regulations) and orders of commanders (chiefs).

2. Military discipline is based on each serviceman’s awareness of military duty and personal responsibility for the defense of the Russian Federation. It is built on legal basis, respect for the honor and dignity of military personnel.

The main method of instilling discipline in military personnel is persuasion. However, this does not exclude the possibility of using coercive measures against those who are dishonest in fulfilling their military duty.

3. Military discipline obliges every serviceman:

be faithful to the Military Oath (obligation), strictly observe the Constitution of the Russian Federation, the laws of the Russian Federation and the requirements of general military regulations;

perform your military duty skillfully and courageously, conscientiously study military affairs, take care of state and military property;

to unquestioningly carry out assigned tasks in any conditions, including at the risk of life, to steadfastly endure the difficulties of military service;

be vigilant, strictly keep state secrets;

support the rules of relationships between military personnel determined by general military regulations, strengthen military camaraderie;

show respect to commanders (superiors) and each other, observe the rules of military greeting and military courtesy;

behave with dignity in public places, prevent yourself and restrain others from unworthy actions, help protect the honor and dignity of citizens;

comply with the norms of international humanitarian law in accordance with the Constitution of the Russian Federation.

4. Military discipline is achieved:

instilling in military personnel moral, psychological, combat qualities and conscious obedience to commanders (superiors);

knowledge and compliance by military personnel with the laws of the Russian Federation, other regulatory legal acts of the Russian Federation, the requirements of general military regulations and the norms of international humanitarian law;

the personal responsibility of each serviceman for the performance of military service duties;

maintaining internal order in a military unit (unit) by all military personnel;

clear organization of combat training and full coverage of personnel;

the daily demands of commanders (chiefs) on subordinates and control over their performance, respect for the personal dignity of military personnel and constant care for them, the skillful combination and correct use of measures of persuasion, coercion and social influence of the team;

creation in the military unit (unit) of the necessary conditions for military service, life and a system of measures to limit the dangerous factors of military service.

5. The commander and deputy commander for educational work are responsible for the state of military discipline in a military unit (unit), who must constantly maintain military discipline, demand that subordinates observe it, encourage the worthy, and strictly but fairly punish the negligent.

Military discipline must be observed in the unit; it is a necessary condition for the functioning of the army.

The effectiveness of work to strengthen military discipline in the armed forces largely depends on the activities of the officer in charge, and the state of law and order and discipline among subordinates is the main criterion for assessing the daily activities of commanders.

28% of the death toll, goes by number suicide

Consistency and the habit of strict order.

Discipline is Teaching, science.

The characteristic features of military discipline are:

    Unity of command

    Strict regulation of all aspects of the life and activities of military personnel

    Commitment and unconditional performance

    Clear chain of command

    The inevitability and severity of coercive measures against violators of military discipline.

For the formation of a team, the essential factors are:

    High performance

    Healthy public opinion (take into account the opinion of the team)

    Sense of responsibility

    General optimistic mood of the team

    Willingness to overcome difficulties

Analysis of the state of military discipline:

    Requirements for an officer: must think logically, formulate arguments correctly, reason, and draw conclusions.

    Master the rules of formal logic

Stages of analytical work on studying the state of military discipline:

    Planning

    Collection of information

    Data processing

    Identification of the reasons for violation of military disciplines

3.3 Internal order and how it is achieved. Fire safety measures in V.Ch. and divisions

Internal order is strict adherence to the rules of accommodation, daily activities, and life of military personnel in a military unit (unit) determined by military regulations and the performance of daily duty.

Internal order is achieved:

    deep understanding, conscious and accurate fulfillment by all military personnel of the duties defined by laws and military regulations;

    targeted educational work, a combination of the high demands of commanders (superiors) with constant care for subordinates and the preservation of their health;

    clear organization of combat training;

    exemplary performance combat duty and daily duty services;

    accurate implementation of the daily routine and work time regulations;

    compliance with the rules of operation (use) of weapons, military equipment and other material resources; creating conditions in the locations of military personnel for their daily activities, life and everyday life that meet the requirements of military regulations;

    compliance with requirements fire safety, as well as taking measures to protect the environment in the area where the military unit operates.

Fire safety measures:

    The territory of the military unit must be constantly cleared of debris and dry grass.

    military property must be equipped with lightning protection devices and other engineering systems that ensure its fire and explosion safety in accordance with the requirements of current standards and regulations.

    Entrances to sources of fire water supply, to buildings and all passages through the territory must always be free for the movement of fire engines. Also, passages within the unit and subdivision must be unobstructed.

It is forbidden to light a fire and keep an open fire closer than 50m from the military unit. Use faulty equipment and use flammable materials. Telephone sets must have inscriptions indicating the telephone number of the nearest fire brigade, and on the territory of a military unit there must be sound alarms to sound a fire alarm. These and other fire safety standards must be checked daily by the duty officer.

An order is an order from a commander-in-chief addressed to subordinates and requiring the mandatory performance of certain actions, compliance with rules or establishing any order of its issuance. In writing or by technical communication to one or a group of military personnel. Discussion of an order is not permissible. Failure to comply with an order given in the prescribed manner is a crime against military service.

An order is a form of communication by the commander of tasks to subordinates on private issues. Issued in writing or orally. Issued in writing by the chief of staff, is an administrative document and is issued from the estate of the unit commander

When giving orders, the commander must not abuse his official powers. Do not give orders that are not related to the conduct of military service.

The order is formulated clearly and concisely. Issued in order of subordination.

Completed unquestioningly accurately and on time.

The serviceman answers “yes.”

Unity of command

It consists of vesting the commander (chief) with full administrative power in relation to his subordinates and assigning personal responsibility to him for all aspects of the life and activities of the military unit, unit and each serviceman.

determines the construction of the army as a centralized military organism, the unity of training and education of personnel, organization and discipline and, ultimately, the high combat readiness of troops. It should be noted that it best ensures the unity of will and actions of all personnel, strict centralization, maximum flexibility and efficiency of troop leadership. Unity of command allows the commander to act boldly, decisively, and show broad initiative, placing on the commander personal responsibility for all aspects of the life of the troops, and contributes to the development of the necessary leadership qualities in officers. It creates conditions for high organization, strict military discipline and firm order.

The bullet, having received a certain initial speed, strive by inertia to maintain the magnitude and direction of this speed.

If the flight of a bullet took place in airless space, and it was not affected by gravity, the bullet would move straight, uniformly and endlessly. However, a bullet flying in the air is subject to forces that change its flight speed and direction of movement. These forces are gravity and air resistance (Fig. 4).

Rice. 4. Forces acting on a bullet during its flight

Due to the combined action of these forces, the bullet loses speed and changes the direction of its movement, moving in the air along a curved line passing below the direction of the axis of the barrel bore.

The line that a moving bullet describes in space (its center of gravity) is called trajectory.

Typically, ballistics considers the trajectory over weapon horizon- an imaginary infinite horizontal plane passing through the departure point (Fig. 5).

Rice. 5. Weapon Horizon

The movement of the bullet, and therefore the shape of the trajectory, depends on many conditions. Therefore, in order to understand how the trajectory of a bullet is formed in space, it is necessary to consider first of all how the force of gravity and the force of air resistance act on the bullet separately.

The action of gravity. Let's imagine that no force acts on the bullet after it leaves the barrel. In this case, as mentioned above, the bullet would move by inertia endlessly, uniformly and rectilinearly along the axis of the barrel bore; for every second it would fly the same distances with a constant speed equal to the initial one. In this case, if the barrel of the weapon were aimed directly at the target, the bullet, following in the direction of the axis of the barrel bore, would hit it (Fig. 6).

Rice. 6. The movement of a bullet by inertia (if there were no gravity and air resistance)

Let us now assume that only one force of gravity acts on the bullet. Then the bullet will begin to fall vertically down, like any freely falling body.

If we assume that the force of gravity acts on the bullet as it flies by inertia in airless space, then under the influence of this force the bullet will drop lower from the extension of the axis of the barrel bore - in the first second - by 4.9 m, in the second - by 19.6 m etc. In this case, if you point the barrel of a weapon at a target, the bullet will never hit it, since, being exposed to gravity, it will fly under the target (Fig. 7).

Rice. 7. The movement of the bullet (if gravity acted on it,

but air resistance did not work)

It is quite obvious that in order for a bullet to fly a certain distance and hit the target, it is necessary to point the barrel of the weapon somewhere above the target. To do this, it is necessary that the axis of the barrel bore and the horizon plane of the weapon make a certain angle, which is called elevation angle(Fig. 8).

As can be seen from Fig. 8, the trajectory of a bullet in airless space, which is affected by gravity, is a regular curve, which is called parabola. The most high point the trajectory above the horizon of the weapon is called its top. The part of the curve from the departure point to the apex is called ascending branch. This bullet trajectory is characterized by the fact that the ascending and descending branches are exactly the same, and the throwing and falling angles are equal to each other.

Rice. 8. Elevation angle (bullet trajectory in airless space)

Action of air resistance force. At first glance, it seems unlikely that air, which has such a low density, could provide significant resistance to the movement of a bullet and thereby significantly reduce its speed.

However, experiments have established that the force of air resistance acting on a bullet fired from a rifle of the 1891/30 model is large - 3.5 kg.

Considering that the bullet weighs only a few grams, the large braking effect that air has on a flying bullet becomes quite obvious.

During flight, a bullet expends a significant portion of its energy to push apart air particles that interfere with its flight.

As a photograph of a bullet flying at supersonic speed (over 340 m/s) shows, an air compaction forms in front of its head (Fig. 9). From this compaction the head ballistic wave diverges in all directions. Air particles, sliding along the surface of the bullet and falling off its side walls, form a zone of rarefied space behind the bullet. In an effort to fill the void behind the bullet, air particles create turbulence, resulting in a tail wave trailing behind the bottom of the bullet.

The compaction of air in front of the bullet's head slows down its flight; the discharged zone behind the bullet sucks it in and thereby further enhances the braking; the walls of the bullet experience friction against air particles, which also slows down its flight. The resultant of these three forces is the air resistance force.

Rice. 9. Photograph of a bullet flying at supersonic speed

(over 340 m/sec.)

The enormous influence that air resistance has on the flight of a bullet can also be seen from the following example. A bullet fired from a Mosin rifle model 1891/30. or from sniper rifle Dragunov (SVD). Under normal conditions (with air resistance), it has the greatest horizontal flight range of 3400 m, and when firing in airless space it could fly 76 km.

Consequently, under the influence of air resistance, the trajectory of the bullet loses the shape of a regular parabola, taking on the shape of an asymmetrical curved line; the apex divides it into two unequal parts, of which the ascending branch is always longer and shallower than the descending one. When shooting at medium distances, you can conditionally take the ratio of the length of the ascending branch of the trajectory to the descending branch as 3:2.

Rotation of a bullet around its axis. It is known that a body acquires significant stability if it is given a rapid rotational movement around its axis. An example of the stability of a rotating body is the “top” toy. A non-rotating “top” will not stand on its pointed leg, but if the “top” is given a rapid rotational movement around its axis, it will stand stably on it (Fig. 10).

In order for the bullet to acquire the ability to combat the overturning effect of air resistance and maintain stability during flight, it is given a rapid rotational movement around its longitudinal axis. The bullet acquires this rapid rotational movement thanks to helical rifling in the bore of the weapon (Fig. 11). Under the influence of the pressure of the powder gases, the bullet moves forward along the barrel bore, simultaneously rotating around its longitudinal axis. Upon departure from the barrel, the bullet, by inertia, retains the resulting complex motion - translational and rotational.

Without going into detail the explanation physical phenomena associated with the action of forces on a body experiencing complex motion, it is still necessary to say that the bullet makes regular oscillations during flight and its head describes a circle around the trajectory (Fig. 12). In this case, the longitudinal axis of the bullet seems to “follow” the trajectory, describing a conical surface around it (Fig. 13).

Rice. 12. Conical rotation of the bullet head

Rice. 13. Flight of a spinning bullet in the air

If we apply the laws of mechanics to a flying bullet, it will become obvious that the greater the speed of its movement and the longer the bullet, the more strongly the air tends to knock it over. Therefore, the bullets of cartridges different types it is necessary to give different rotation speeds. Thus, a light bullet fired from a rifle has a rotation speed of 3604 rpm.

However, the rotational motion of the bullet, which is so necessary to give it stability during flight, also has its negative sides.

A rapidly rotating bullet, as already mentioned, is subject to a continuous tipping effect by the force of air resistance, due to which the head of the bullet describes a circle around the trajectory. As a result of adding these two rotational movements a new movement arises, deflecting its head part away from the firing plane1 (Fig. 14). In this case, one side surface of the bullet is subjected to more particle pressure than the other. Such unequal air pressure on side surfaces bullet and deflects it away from the firing plane. The lateral deviation of a rotating bullet from the firing plane in the direction of its rotation is called derivation(Fig. 15).

Rice. 14. As a result of two rotational movements, the bullet gradually turns the head to the right (in the direction of rotation)

Rice. 15. The phenomenon of derivation

As the bullet moves away from the muzzle of the weapon, the magnitude of its derivational deviation quickly and progressively increases.

When shooting at short and medium distances, derivation does not have a large practical significance for the shooter. So, at a firing range of 300 m, the derivation deviation is 2 cm, and at 600 m - 12 cm. Derivation has to be taken into account only when shooting with precision at long distances, making appropriate adjustments to the installation of the sight, in accordance with the table of derivational deviations of the bullet for a certain range shooting.