Formation of the trajectory of the bullet. Sniper training. Internal and external ballistics The value of which angle is greater than the fall or throw

Ballistics studies the throwing of a projectile (bullet) from a barreled 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.

Basics 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 parts of the weapon between themselves and the body of the shooter, gas and bullets, bullets with the walls of the bore, bullets with the 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 large and extreme shooting distances (which is typical for hunting), knowledge of the laws of ballistics is absolutely necessary.

Note that air guns usually give a light bullet a low or medium speed (from 100 to 380 m / s), so the curvature of the trajectory of the bullet from different influences greater than for firearms.

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

To increase the stability of the bullet in flight on the surface of the bore rifled weapons there are spiral grooves (rifling) that give the bullet rotary 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 more air resistance on one of the sides and in flight deviates more and more from the plane of fire in the direction of its rotation. This phenomenon is called derivation. The action of derivation is uneven and intensifies towards the end of the trajectory.

Powerful air rifles can give the bullet an initial velocity higher than the sound one (up to 360-380 m/s). The speed of sound in air is not constant (depends on atmospheric conditions, height above sea level, etc.), but it can be taken equal to 330-335 m/s. Light bullets for pneumatics with small transverse load experience strong perturbations and deviate from their trajectory, overcoming sound barrier. Therefore, it is advisable to shoot heavier bullets with an initial 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 its 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 airgun. The impact of a 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 a handkerchief by two corners, then with a light wind it will sway slightly, with a moderate one it will deviate by 45 °, and with a strong one it will develop horizontally to the surface of the earth.

Normal weather conditions are: 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. High humidity leads to a decrease in the trajectory, and low humidity leads to an increase in the trajectory. Recall that Atmosphere pressure varies not only with the weather, but also with altitude - the higher the pressure, the lower the trajectory.

Each "long-range" weapon and ammunition has its own correction tables, which allow taking into account the influence of weather conditions, derivation, relative position of the shooter and target in height, bullet speed and other factors on the bullet's flight path. Unfortunately, such tables are not published for pneumatic weapons, therefore, lovers of shooting 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 evaluating the results of firing, it must be remembered that from the moment of firing until the end of its flight, some random (not taken into account) factors act on the bullet, which leads to small deviations in the trajectory of the bullet from shot to shot. Therefore, even under "ideal" conditions (for example, when the weapon is rigidly fixed in the machine, constancy external conditions etc.) bullet hits on the target look like an oval, thickening towards the center. Such random deviations are called deviation. The formula for its calculation is given below in this section.

And now consider the trajectory of the bullet and its elements (see Figure 1).

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

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

The start of the trajectory is the departure point. The horizontal plane passing through the departure point is called the weapon's horizon. The vertical plane passing through the point of departure along the line of throw is called the shooting plane.

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

The point of intersection of the trajectory with the horizon of the weapon is called the (table) point of incidence. The horizontal distance from the departure point to the (table) drop 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 (table) angle of incidence.

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

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

Shooter and target are on the same level.
- the shooter is located below the target (shoots up at an angle).
- the shooter is located above the target (shoots down at an angle).

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

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

The straight line connecting the middle of the slot in the rear sight with the top of the front sight is called the aiming line.

tip small arms using sighting devices not from the horizon of the weapon, but relative to the location of the target. In this regard, the elements of pickup and trajectory 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 slot of the sight (or front sight) in height corresponding to the firing range.

The point of intersection of the descending branch of the trajectory with the line of sight 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 incidence and the line of sight is called the angle of incidence.

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

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

At its end, the trajectory of the bullet 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 ricochet 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 rendezvous point is called the actual range. A shot in which the trajectory does not rise above the line of sight above the target throughout effective range, is called a direct shot.

From the foregoing, it is clear that before practical shooting the weapon must be shot (otherwise it must be brought to a normal battle). Zeroing should be carried out with the same ammunition and under the same conditions that will be typical for subsequent firing. Be sure to take into account the size of the target, the shooting position (lying, kneeling, standing, from unstable positions), even the thickness of clothing (when zeroing in a rifle).

The line of sight, 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's flight is an unevenly curved downward line. The line of sight is located 2-3 cm above the barrel in the case of an open sight and much higher in the case of an optical one.

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

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

For practical shooting (for example, hunting), the firing range is usually much longer and the curvature of the trajectory has to be taken into account. But here the arrow plays into the hands of the fact that the size of the target (slaughter place) in height in this case can reach 5-10 cm or more. If we choose such a horizontal range of sighting of 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 aiming at the edge of the target, we will be able to hit it throughout the firing distance.

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

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

Target size is smaller than usual.
the shooting distance is greater than the sighting distance of the weapon.
the shooting distance is closer than the first point of intersection of the trajectory with the line of sight (typical for shooting with a telescopic sight).

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

The trajectory of a bullet is understood as a line drawn in space by its center of gravity.

This trajectory is formed under the influence of the inertia of the bullet, the forces of gravity and air resistance acting on it.

The inertia of a bullet is formed while it is in the bore. Under the influence of the energy of powder gases, the speed and direction are set to the bullet forward movement. And if external forces did not act on it, then according to the first law of Galileo - Newton, it would move in a straight line in a given direction at a constant speed to infinity. At the same time, in every second it would cover a distance equal to initial speed bullets (see fig. 8).

However, due to the fact that the forces of gravity and air resistance act on the bullet in flight, they together, in accordance with the fourth law of Galileo - Newton, impart to it an acceleration equal to the vector sum of the accelerations arising from the actions of each of these forces separately.

Therefore, in order to understand the features of the formation of the flight path of a bullet in the air, it is necessary to consider how the force of gravity and the force of air resistance act separately on the bullet.

Rice. 8. The movement of a bullet by inertia (in the absence of the influence of gravity

and air resistance)

The force of gravity acting on the bullet gives it an acceleration equal to the acceleration of free fall. This force is directed vertically downward. In this regard, the bullet under the action of gravity will constantly fall to the ground, and the speed and height of its fall will be determined, respectively, by formulas 6 and 7:

where: v - bullet fall speed, H - bullet fall height, g - free fall acceleration (9.8 m/s2), t - bullet fall time in seconds.

If the bullet flew out of the bore without having the kinetic energy given by the pressure of the powder gases, then, in accordance with the above formula, it would fall vertically down: in one second by 4.9 m; two seconds later at 19.6 m; after three seconds at 44.1 m; four seconds later at 78.4 m; after five seconds at 122.5 m, etc. (see fig. 9).

Rice. 9. The fall of a bullet without kinetic energy in a vacuum

under the influence of gravity

When a bullet with a given kinetic energy moves by inertia, under the action of gravity, it will move a given distance down relative to the line that is a continuation of the axis of the bore. By constructing parallelograms, the lines of which will be the values of the distances covered by the bullet by inertia and under the action of gravity in

corresponding time intervals, we can determine the points that the bullet will pass in these time intervals. Connecting them with a line, we get the trajectory of the bullet in airless space (see Fig. 10).

Rice. 10. The trajectory of a bullet in a vacuum

This trajectory is a symmetrical parabola, the most highest point which is called the vertex of the trajectory; its part, located from the point of departure of the bullet to the top, is called the ascending branch of the trajectory; and the part located after the top is descending. In vacuum, these parts will be the same.

In this case, the height of the top of the trajectory and, accordingly, its figure will depend only on the initial velocity of the bullet and the angle of its departure.

If the force of gravity acting on the bullet is directed vertically downward, then the force of air resistance is directed in the direction opposite to the movement of the bullet. It continuously slows down the movement of the bullet and tends to overturn it. To overcome the force of air resistance, part of the kinetic energy of the bullet is expended.

The main causes of air resistance are: its friction against the surface of the bullet, the formation of a vortex, the formation of a ballistic wave (see Fig. 11).

Rice. 11. Causes of air resistance

The bullet in flight collides with air particles and causes them to oscillate, as a result of which the density of the air in front of the bullet increases, and sound waves are formed that cause a characteristic sound and a ballistic wave. In this case, the layer of air flowing around the bullet does not have time to close behind its bottom part, as a result of which a rarefied space is created there. The difference in air pressure exerted on the head and bottom parts of the bullet forms a force directed to the side opposite to the direction of its flight and reduces its speed. In this case, air particles, trying to fill the rarefied space formed behind the bottom of the bullet, create a vortex.

The air resistance force is the sum of all the forces generated due to the influence of air on the flight of a bullet.

The center of drag is the point at which the force of air resistance is applied to the bullet.

The force of air resistance depends on the shape of the bullet, its diameter, flight speed, air density. With an increase in the speed of the bullet, its caliber and air density, it increases.

Under the influence of air resistance, the flight path of the bullet loses its symmetrical shape. The speed of a bullet in the air decreases all the time as it moves away from the point of departure, therefore average speed there are more bullets on the ascending branch of the trajectory than on the descending one. In this regard, the ascending branch of the flight path of a bullet in the air is always longer and flatter than the descending one; when shooting at medium distances, the ratio of the length of the ascending branch of the trajectories to the length of the descending one is conditionally taken as 3: 2 (see Fig. 12).

Rice. 12. The trajectory of a bullet in the air

Rotation of a bullet around its axis

When a bullet is flying in the air, the force of its resistance constantly strives to overturn it. It manifests itself in the following way. The bullet, moving by inertia, constantly strives to maintain the position of its axis, given direction barrel of the weapon. At the same time, under the influence of gravity, the direction of the bullet's flight constantly deviates from its axis, which is characterized by an increase in the angle between the axis of the bullet and the tangent to its flight path (see Fig. 13).

Rice. 13. The effect of the force of air resistance on the flight of a bullet: CG - center of gravity, CA - center of air resistance

The action of the air resistance force is directed opposite to the direction of the bullet and parallel to its tangent trajectory, i.e. from below at an angle to the axis of the bullet.

Based on the shape of the bullet, air particles hit the surface of its head at an angle close to a straight line, and into the surface of the tail at a fairly sharp angle (see Fig. 13). In this regard, at the head of the bullet there is a compacted air, and at the tail - a rarefied space. Therefore, the air resistance in the head of the bullet significantly exceeds its resistance in the tail. As a result, the speed of the head section decreases faster than the speed of the tail section, which causes the head of the bullet to tip back (bullet rollover).

Rolling the bullet backwards causes it to rotate erratically in flight, with a significant decrease in its flight range and accuracy of hitting the target.

In order to prevent the bullet from tipping over in flight under the action of air resistance, it is given a rapid rotational movement around the longitudinal axis. This rotation is formed due to the helical cutting in the bore of the weapon.

The bullet, passing through the bore, under the pressure of powder gases, enters the rifling and fills them with its body. In the future, like a bolt in a nut, it simultaneously moves forward and rotates around its axis. At the exit from the bore, the bullet retains both translational and rotational motion by inertia. At the same time, the rotation speed of the bullet reaches very high values, for the Kalashnikov 3000 assault rifle, and for sniper rifle Dragunov - about 2600 rpm.

Bullet rotation speed can be calculated by the formula:

where Vvr - rotation speed (rpm), Vo - muzzle velocity (mm/s), Lnar - rifling stroke length (mm).

During the flight of a bullet, the force of air resistance tends to tip the bullet head up and back. But the head of the bullet, rotating rapidly, according to the property of the gyroscope, tends to maintain its position and deviate not upwards, but slightly in the direction of its rotation - to the right, at right angles to the direction of the air resistance force. When the head part is deflected to the right, the direction of the air resistance force changes, which now tends to turn the head part of the bullet to the right and back. But as a result of rotation, the head of the bullet does not turn to the right, but down and further to its description full circle(see fig. 14).

Rice. 14. Conical rotation of the bullet head

Thus, the head of a flying and rapidly rotating bullet describes a circle, and its axis is a cone with a vertex at the center of gravity. There is a so-called slow conical movement, in which the bullet flies head first in accordance with the change in the curvature of the trajectory (see Fig. 15).

Rice. 15. Flight of a spinning bullet in the air

The axis of slow conical rotation is located above the tangent to the flight path of the bullet, so the lower part of the bullet is in more subject to the pressure of the oncoming air flow than the top. In this regard, the axis of slow conical rotation deviates in the direction of rotation, i.e. to the right. This phenomenon is called derivation (see Fig. 16).

Derivation is the deviation of the bullet from the plane of fire in the direction of its rotation.

The plane of fire is understood as a vertical plane in which lies the axis of the bore of the weapon.

The reasons for the derivation are: the rotational movement of the bullet, air resistance and the constant decrease under the action of gravity of the tangent to the bullet's flight path.

In the absence of at least one of these reasons, there will be no derivation. For example, when shooting vertically up and vertically down, there will be no derivation, since the air resistance force in this case is directed along the bullet axis. There will be no derivation when firing in a vacuum due to the lack of air resistance and when firing from smoothbore weapons due to the lack of rotation of the bullet.

Rice. 16. The phenomenon of derivation (view of the trajectory from above)

During the flight, the bullet deviates more and more to the side, while the degree of increase in derivational deviations significantly exceeds the degree of increase in the distance traveled by the bullet.

Derivation is not of great practical importance for the shooter when shooting at close and medium distances, it must be taken into account only for particularly accurate shooting at long distances, making certain adjustments to the installation of the sight in accordance with the table of derivational deviations for the corresponding firing range.

Bullet trajectory characteristics

To study and describe the flight path of a bullet, the following indicators characterizing it are used (see Fig. 17).

The departure point is located in the center of the muzzle of the barrel, is the beginning of the bullet's flight path.

The weapon's horizon is the horizontal plane passing through the departure point.

The line of elevation is a straight line that is a continuation of the axis of the bore of the weapon aimed at the target.

The elevation angle is the angle enclosed between the elevation line and the horizon of the weapon. If this angle is negative, for example, when

shooting down from a significant hill, it is called the angle of declination (or descent).

Rice. 17. Bullet trajectory indicators

The line of throw is a straight line, which is a continuation of the axis of the bore at the time of the bullet's departure.

The throw angle is the angle between the throw line and the weapon's horizon.

The departure angle is the angle enclosed between the line of elevation and the line of throw. Represents the difference between the values of the angles of throw and elevation.

Point of impact - is the point of intersection of the trajectory with the horizon of the weapon.

The angle of incidence is the angle at the point of impact between the tangent to the bullet's flight path and the weapon's horizon.

The final velocity of the bullet is the velocity of the bullet at the point of impact.

The total flight time is the time it takes the bullet to travel from the point of departure to the point of impact.

Complete horizontal range is the distance from the point of departure to the point of fall.

The vertex of the trajectory is its highest point.

The height of the trajectory is the shortest distance from its top to the horizon of the weapon.

The ascending branch of the trajectory is the part of the trajectory from the departure point to its top.

The descending branch of the trajectory is the part of the trajectory from its top to the point of fall.

The meeting point is a point lying at the intersection of the bullet's flight path with the target surface (ground, obstacles).

The meeting angle is the angle between the tangent to the bullet's flight path and the tangent to the target surface at the meeting point.

The point of aim (aiming) is the point on or off the target at which the weapon is aimed.

The line of sight is a straight line from the shooter's eye through the middle of the sight slit and the top of the front sight to the point of aim.

The angle of aim is the angle between the line of sight and the line of elevation.

Target elevation angle is the angle between the line of sight and the horizon of the weapon.

Sighting range is the distance from the point of departure to the intersection of the trajectory with the line of sight.

The excess of the trajectory over the line of sight is the shortest distance from any point of the trajectory to the line of sight.

When shooting at close range, the values of the excess of the trajectory over the aiming line will be quite low. But when firing at long distances, they reach significant values (see Table 1).

Table 1

Exceeding the trajectory above the aiming line when firing from a Kalashnikov assault rifle (AKM) and a Dragunov sniper rifle (SVD) at distances of 600 m or more

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For 7.62mm AKM
Range, m		100		200		300		400		500		600		700		800		900		1000
Aim		meters
6		0,98		1,8		2,2		2,1		1,4		0		-2,7		-6,4		-		-
7		1,3		2,5		3,3		3,6		3,3		2,1		-3,5		-8,4		-
8		1,8		3,4		4,6		5,4		5,5		4,7		3,0		0		-4,5		-10,5
For SVD using an optical sight
Range,	100		200	300	400		500		600	700	800		900		1000	1100	1200		1300		1400
Aim	meters
6	0,53		0,95	1,2	1,1		0,74		0	-1,3	-		-		-	-	-		-		-
7	0,71		1,3	1,7	1,9		1,6		1,0	0	-1,7		-		-	-	-		-		-
8	0,94		1,8	2,4	2,7		2,8		2,4	1,5	0		-2,2		-	-	-		-		-
9	1,2		2,2	3,1	3,7		4,0		3,9	2,3	2,0		0		-2,9	-	-		-		-
10	1,5		2,8	4,0	4,9		5,4		5,7	5,3	4,3		2,6		0	-3,7	-		-		-
11	1,8		3,5	5,0	6,2		7,1		7,6	7,7	7,1		5,7		3,4	0	-4,6		-		-
12	2,2		4,3	6,2	7,8		9,1		10,0	10,5	10,0		9,2		7,3	4,3	0		-5,5		-
13	2,6		5,1	7,4	9,5		11		12,5	13,5	13,5		13,0		11,5	8,9	5,1		0		-6,6

Note: The number of units in the scope value corresponds to the number of hundreds of meters of shooting distance for which the scope is designed.

(6 - 600 m, 7 - 700 m, etc.).

From Table. 1 shows that the excess of the trajectory above the aiming line when firing from the AKM at a distance of 800 m (sight 8) exceeds 5 meters, and when firing from the SVD at a distance of 1300 m (sight 13) - the bullet trajectory rises above the aiming line by more than 13 meters.

Aiming (weapon aiming)

In order for the bullet to hit the target as a result of the shot, it is first necessary to give the axis of the barrel bore an appropriate position in space.

Giving the axis of the bore of a weapon the position necessary to hit a given target is called aiming or aiming.

This position must be given both in the horizontal plane and in the vertical. Giving the axis of the bore the required position in the vertical plane is a vertical pickup, giving it the desired position in the horizontal plane is a horizontal pickup.

If the aiming reference is a point on or near the target, such aiming is called direct. When shooting from small arms, direct aiming is used, performed using a single sighting line.

The sight line is a straight line connecting the middle of the sight slot to the top of the front sight.

To carry out aiming, it is necessary first, by moving the rear sight (slot of the sight), to give the aiming line such a position in which between it and the axis of the bore, an aiming angle is formed in the vertical plane corresponding to the distance to the target, and in the horizontal plane - an angle equal to the lateral correction, taking into account crosswind speed, derivation and lateral movement speed of the target (see Fig. 18).

After that, directing the sighting line to the area, which is the aiming reference point, by changing the position of the barrel of the weapon, the axis of the bore is given the desired position in space.

At the same time, in weapons with a permanent rear sight, as, for example, in most pistols, in order to give the necessary position of the bore in the vertical plane, the aiming point is selected corresponding to the distance to the target, and the aiming line is directed to given point. In weapons with a sight slot fixed in the side position, as in a Kalashnikov assault rifle, to give the necessary position of the bore in the horizontal plane, the aiming point is selected corresponding to the side correction, and the aiming line is directed to this point.

Rice. 18. Aiming (weapon aiming): O - front sight; a - rear sight; aO - aiming line; сС - the axis of the bore; oO - a line parallel to the axis of the bore;

H - sight height; M - the amount of movement of the rear sight; a - aiming angle; Ub - angle of lateral correction

Bullet trajectory shape and its practical significance

The shape of the trajectory of a bullet in the air depends on the angle at which it is fired in relation to the horizon of the weapon, its muzzle velocity, kinetic energy and shape.

To produce a targeted shot, the weapon is aimed at the target, while the aiming line is directed to the aiming point, and the axis of the bore in the vertical plane is brought to a position corresponding to the required elevation line. Between the axis of the bore and the horizon of the weapon, the required elevation angle is formed.

When fired, under the action of the recoil force, the axis of the barrel bore is shifted by the value of the departure angle, while it goes into a position corresponding to the throw line and forms a throw angle with the horizon of the weapon. At this angle, the bullet flies out of the bore of the weapon.

Due to the insignificant difference between the angle of elevation and the angle of throwing, they are often identified, while, however, it is more correct in this case talk about the dependence of the trajectory of a bullet on the angle of throw.

With an increase in the angle of throw, the height of the trajectory of the flight of the bullet and the total horizontal range increase to a certain value given angle, after which the trajectory height continues to increase, and the total horizontal range decreases.

The angle of throw at which the full horizontal range of the bullet is greatest is called the angle longest range.

In accordance with the laws of mechanics in an airless space, the angle of greatest range will be 45 °.

When a bullet is flying in air, the relationship between the angle of throw and the shape of the bullet's flight path is similar to the dependence of these characteristics observed when a bullet is flying in airless space, but due to the influence of air resistance, the maximum range angle does not reach 45 °. Depending on the shape and mass of the bullet, its value varies between 30 - 35 °. For calculations, the angle of the greatest firing range in the air is assumed to be 35°.

Bullet trajectories arising at angles of impact smaller angle the greatest range are called flat.

The flight paths of a bullet that occur at angles of throw of a large angle of greatest range are called hinged (see Fig. 19).

Rice. 19. Angle of greatest range, flat and overhead trajectories

Flat trajectories are used when firing direct fire at fairly short distances. When firing from small arms, only this type of trajectory is used. The flatness of the trajectory is characterized by its maximum excess over the aiming line. The less the trajectory rises above the aiming line at a given firing range, the more flat it is. Also, the flatness of the trajectory is estimated by the angle of incidence: the smaller it is, the flatter the trajectory.

The flatter the trajectory used when shooting, the greater the distance the target can be hit with one set of

intact, i.e. errors in the installation of the sight have a lesser effect on the effectiveness of shooting.

Mounted trajectories are not used when firing from small arms, in turn, they have widespread in firing shells and mines over long distances out of line of sight of the target, which in this case is set by coordinates. Mounted trajectories are used when firing from howitzers, mortars and other types of artillery weapons.

Due to the peculiarities of this type of trajectory, these types of weapons can hit targets located in cover, as well as behind natural and artificial barriers (see Fig. 20).

Trajectories that have the same horizontal range at different throw angles are called conjugate. One of these trajectories will be flat, the second hinged.

Conjugated trajectories can be obtained when firing from one weapon, using throwing angles greater and less than the angle of greatest range.

Rice. 20. Features of the use of hinged trajectories

A shot in which the excess of the trajectory over the line of sight throughout its entire length does not reach values greater than the height of the target is considered a direct shot (see Fig. 21).

Practical value direct shot lies in the fact that within its range in tense moments of the battle, it is allowed to fire without rearranging the sight, while the aiming point in height, as a rule, is chosen at the lower edge of the target.

The range of a direct shot depends, firstly, on the height of the target and, secondly, on the flatness of the trajectory. The higher the goal and the flatter trajectory, the greater the range of a direct shot and the longer the target can be hit with one sight setting.

Rice. 21. Direct shot

The range of a direct shot can be determined from the tables, comparing the height of the target with the values of the greatest excess of the trajectory above the line of sight or with the height of the trajectory.

When shooting at a target that is at a distance greater than the range of a direct shot, the trajectory near the top rises above the target, and the target in a certain area will not be hit with this setting of the sight. In this case, there will be a space near the target, on which the descending branch of the trajectory will lie within its height.

The distance at which the descending branch of the trajectory is within the height of the target is called the affected space (see Fig. 22).

The depth (length) of the affected space directly depends on the height of the target and the flatness of the trajectory. It also depends on the angle of inclination of the terrain: when the terrain rises up, it decreases, when it slopes down, it increases.

Rice. 22. Affected space with a depth equal to the segment AC, for the target

height equal to segment AB

If the target is behind cover, impenetrable by a bullet, then the possibility of hitting it depends on where it is located.

The space behind the shelter from its crest to the meeting point is called the covered space (see Fig. 23). The covered space will be the greater, the greater the height of the shelter and the flatter the trajectory of the bullet.

The part of the covered space in which the target cannot be hit with a given trajectory is called dead (non-hit) space. Dead space will be the greater, the greater the height of the shelter, the lower the height of the target and the flatter the trajectory. The part of the covered space in which the target can be hit is the hit space.

So the depth dead space represents the difference between the covered and affected space.

Rice. 23. Covered, dead and affected space

The shape of the trajectory also depends on the muzzle velocity of the bullet, its kinetic energy and shape. Consider how these indicators affect the formation of the trajectory.

The further speed of its flight directly depends on the initial speed of the bullet, the value of its kinetic energy, with equal shapes and sizes, provides a smaller degree of speed reduction under the action of air resistance.

Thus, a bullet fired at the same elevation (throw) angle, but with a higher initial velocity or with higher kinetic energy, will have a higher speed during further flight.

If we imagine a certain horizontal plane at some distance from the departure point, then at the same value elevation angle-

When thrown (thrown), a bullet with a higher speed will reach it faster than a bullet with a lower speed. Accordingly, a slower bullet, having reached this plane and spending more time on it, will have time to go down more under the action of gravity (see Fig. 24).

Rice. 24. The dependence of the trajectory of the flight of a bullet on its speed

In the future, the trajectory of a bullet with lower speed characteristics will also be located below the trajectory of a faster bullet, and under the influence of gravity, it will drop faster in time and closer in distance from the point of departure to the level of the weapon’s horizon.

Thus, the muzzle velocity and kinetic energy of the bullet directly affect the height of the trajectory and the full horizontal range of its flight.

external ballistics. Trajectory and its elements. Exceeding the trajectory of the bullet above the point of aim. Trajectory shape

External ballistics

External ballistics is a science that studies the movement of a bullet (grenade) after the action of powder gases on it has ceased.

Having flown out of the bore under the action of powder gases, the bullet (grenade) moves by inertia. A grenade with a jet engine moves by inertia after the expiration of gases from the jet engine.

Bullet trajectory (side view)

Formation of air resistance force

Trajectory and its elements

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

A bullet (grenade) when flying in the air is subject to the action of 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 an unevenly curved curved line in shape.

Air resistance to the flight of a bullet (grenade) is caused by the fact that air is 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 causes: air friction, the formation of vortices and the formation of a ballistic wave.

Air particles in contact with a moving bullet (grenade), due to internal adhesion (viscosity) and adhesion to its surface, create friction and reduce the speed of the bullet (grenade).

The layer of air adjacent to the surface of the bullet (grenade), in which the movement of particles changes from the speed of the bullet (grenade) to zero, is called the boundary layer. This layer of air, flowing around the bullet, breaks away from its surface and does not have time to immediately close behind the bottom.

A rarefied space is formed behind the bottom of the bullet, as a result of which a pressure difference appears on the head and bottom parts. This difference creates a force directed in the direction opposite to the movement of the bullet, and reduces the speed of its flight. Air particles, trying to fill the rarefaction formed behind the bullet, create a vortex.

A bullet (grenade) in flight collides with air particles and causes them to oscillate. As a result, air density increases in front of the bullet (grenade) and sound waves are formed. Therefore, the flight of a bullet (grenade) is accompanied by a characteristic sound. At a bullet (grenade) flight speed that is less than the speed of sound, the formation of these waves has little effect on its flight, since the waves propagate faster than the bullet (grenade) flight speed. When the speed of the bullet is higher than the speed of sound, a wave of highly compacted air is created from the incursion of sound waves against each other - a ballistic wave that slows down the speed of the bullet, since the bullet spends part of its energy to create this wave.

The resultant (total) of all forces resulting from the influence of air on the flight of a bullet (grenade) is the force of air resistance. The point of application of the resistance force is called the center of resistance.

The effect of the force of air resistance on the flight of a bullet (grenade) is very large; it causes a decrease in the speed and range of the bullet (grenade). For example, a bullet mod. 1930 at an angle of throw of 15 ° and an initial speed of 800 m / s in airless space would have flown at a distance of 32,620 m; the flight range of this bullet under the same conditions, but in the presence of air resistance, is only 3900 m.

The magnitude of the air resistance force depends on the flight speed, the shape and caliber of the bullet (grenade), as well as on its surface and air density.

The force of air resistance increases with the increase in the speed of the bullet, its caliber and air density.

At supersonic bullet speeds, when the main cause of air resistance is the formation of an air seal in front of the head (ballistic wave), bullets with an elongated pointed head are advantageous. At subsonic grenade flight speeds, when the main cause of air resistance is the formation of rarefied space and turbulence, grenades with an elongated and narrowed tail section are beneficial.

The effect of the force of air resistance on the flight of a bullet: CG - center of gravity; CA - center of air resistance

The smoother the surface of the bullet, the lower the friction force and. force of air resistance.

The variety of shapes of modern bullets (grenades) is largely determined by the need to reduce the force of air resistance.

Under the influence of initial perturbations (shocks) at the moment the bullet leaves the bore, an angle (b) is formed between the bullet axis and the tangent to the trajectory, and the air resistance force acts not along the bullet axis, but at an angle to it, trying not only to slow down the movement of the bullet, but and knock her over.

In order to prevent the bullet from tipping over under the action of air resistance, it is given a rapid rotational movement with the help of rifling in the bore.

For example, when fired from a Kalashnikov assault rifle, the speed of rotation of the bullet at the moment of departure from the bore is about 3000 revolutions per second.

During the flight of a rapidly rotating bullet in the air, the following phenomena occur. The force of air resistance tends to turn the bullet head up and back. But the head of the bullet, as a result of rapid rotation, according to the property of the gyroscope, tends to maintain the given position and deviates not upwards, but very slightly in the direction of its rotation at right angles to the direction of the air resistance force, i.e., to the right. As soon as the head of the bullet deviates to the right, the direction of the air resistance force will change - it tends to turn the head of the bullet to the right and back, but the head of the bullet will not turn to the right, but down, etc. Since the action of the air resistance force is continuous, but its direction relative to the bullet changes with each deviation of the bullet axis, then the head of the bullet describes a circle, and its axis is a cone with a vertex at the center of gravity. The so-called slow conical, or precessional, movement occurs, and the bullet flies with its head part forward, i.e., as it were, follows the change in the curvature of the trajectory.

Slow conical movement of the bullet

Derivation (Trajectory top view)

The effect of air resistance on the flight of a grenade

The axis of slow conical motion lags somewhat behind the tangent to the trajectory (located above the latter). Consequently, the bullet collides with the air flow more with its lower part and the axis of the slow conical movement deviates in the direction of rotation (to the right when the barrel is right-handed). The deviation of the bullet from the plane of fire in the direction of its rotation is called derivation.

Thus, the causes of derivation are: the rotational movement of the bullet, air resistance and the decrease under the action of gravity of the tangent to the trajectory. In the absence of at least one of these reasons, there will be no derivation.

In shooting charts, derivation is given as heading correction in thousandths. However, when shooting from small arms, the magnitude of the derivation is insignificant (for example, at a distance of 500 m it does not exceed 0.1 thousandth) and its effect on the results of shooting is practically not taken into account.

The stability of the grenade in flight is ensured by the presence of a stabilizer, which allows you to move the center of air resistance back, behind the center of gravity of the grenade.

As a result, the force of air resistance turns the axis of the grenade to a tangent to the trajectory, forcing the grenade to move forward.

To improve accuracy, some grenades are given slow rotation due to the outflow of gases. Due to the rotation of the grenade, the moments of forces that deviate the axis of the grenade act sequentially in different directions, so the shooting improves.

To study the trajectory of a bullet (grenade), the following definitions are adopted.

The center of the muzzle of the barrel is called the departure point. The departure point is the start of the trajectory.

Trajectory elements

The horizontal plane passing through the departure point is called the weapon's horizon. In the drawings depicting the weapon and the trajectory from the side, the horizon of the weapon appears as a horizontal line. The trajectory crosses the horizon of the weapon twice: at the point of departure and at the point of impact.

A straight line, which is a continuation of the axis of the bore of the aimed weapon, is called the line of elevation.

The vertical plane passing through the line of elevation is called the shooting plane.

The angle enclosed between the line of elevation and the horizon of the weapon is called the angle of elevation. If this angle is negative, then it is called the angle of declination (decrease).

The straight line, which is a continuation of the axis of the bore at the moment the bullet takes off, is called the line of throw.

The angle enclosed between the line of throw and the horizon of the weapon is called the angle of throw.

The angle enclosed between the line of elevation and the line of throw is called the departure angle.

The point of intersection of the trajectory with the horizon of the weapon is called the point of impact.

The angle enclosed between the tangent to the trajectory at the point of impact and the horizon of the weapon is called the angle of incidence.

The distance from the point of departure to the point of impact is called the full horizontal range.

The speed of a bullet (grenade) at the point of impact is called the final speed.

The time of movement of a bullet (grenade) from the point of departure to the point of impact is called full time flight.

The highest point of the trajectory is called the vertex of the trajectory.

The shortest distance from the top of the trajectory to the horizon of the weapon is called the height of the trajectory.

The part of the trajectory from the departure point to the top is called the ascending branch; the part of the trajectory from the top to the point of fall is called the descending branch of the trajectory.

The point on or off the target at which the weapon is aimed is called the point of aim.

The straight line that runs 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 is called the aiming line.

The angle enclosed between the line of elevation and the line of sight is called the angle of aim.

The angle enclosed between the line of sight and the horizon of the weapon is called the elevation angle of the target. 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. The elevation angle of the target can be determined using instruments or using the thousandth formula.

The distance from the departure point to the intersection of the trajectory with the aiming line is called the aiming range.

The shortest distance from any point of the trajectory to the line of sight is called the excess of the trajectory over the line of sight.

The straight line connecting the departure point with the target is called the target line. The distance from the departure point to the target along the target line is called the slant range. When firing direct fire, the target line practically coincides with the aiming line, and the slant range with the aiming range.

The point of intersection of the trajectory with the surface of the target (ground, obstacles) is called the meeting point.

The angle enclosed between the tangent to the trajectory and the tangent to the target surface (ground, obstacles) at the meeting point is called the meeting angle. The smaller of the adjacent angles, measured from 0 to 90°, is taken as the meeting angle.

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 one;

The lowest speed of the bullet when firing at high angles of throw - on the descending branch of the trajectory, and when firing at small angles of throw - 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 one;

The trajectory of a rotating bullet due to the drop of the bullet under the action of gravity and derivation is a line of double curvature.

Grenade trajectory (side view)

The trajectory of a grenade in the air can be divided into two sections: active - the flight of a grenade under the action of a reactive force (from the point of departure to the point where the action of the reactive force stops) and passive - the flight of a grenade by inertia. The shape of the trajectory of a grenade is about the same as that of a bullet.

Trajectory shape

The shape of the trajectory depends on the magnitude of the elevation angle. With an increase in the elevation angle, the height of the trajectory and the full horizontal range of the bullet (grenade) increase, but this occurs up to a known limit. Beyond this limit, the trajectory height continues to increase and the total horizontal range begins to decrease.

Angle of greatest range, flat, overhead and conjugate trajectories

The angle of elevation at which the full horizontal range of the bullet (grenade) becomes the greatest is called the angle of greatest range. The value of the angle of greatest range for bullets various kinds weapons is about 35 °.

Trajectories obtained at elevation angles smaller than the angle of greatest range are called flat. Trajectories obtained at elevation angles greater than the angle of greatest range are called hinged.

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 at different elevation angles are called conjugate.

When firing from small arms and grenade launchers, only flat trajectories are used. The flatter the trajectory, the greater the extent of the terrain, the target can be hit with one sight setting (the less impact on the results of shooting is caused by errors in determining the sight setting); this is the practical significance of the flat trajectory.

Exceeding the trajectory of a bullet above the aiming point

The flatness of the trajectory is characterized by its greatest exceeding the line of sight. At a given range, the trajectory is all the more flat, 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 trajectory is the more flat, the smaller the angle of incidence.

trajectory called a curved line, described by the center of gravity of a bullet (grenade) in flight. A bullet (grenade) when flying in the air is subject to the action of 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 an unevenly curved curved line in shape. 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 causes: air friction, the formation of vortices and the formation of a ballistic wave. The shape of the trajectory depends on the magnitude of the elevation angle. With an increase in the elevation angle, the height of the trajectory and the full horizontal range of the bullet (grenade) increase, but this occurs up to a known limit. Beyond this limit, the trajectory height continues to increase and the total horizontal range begins to decrease. The angle of elevation at which the full horizontal range of the bullet (grenade) becomes the greatest is called the angle of greatest range. The value of the angle of greatest range for bullets of various types of weapons is about 35 °.
Trajectories obtained at elevation angles smaller than the angle of greatest range are called flat. Trajectories obtained at elevation angles greater than the angle of greatest angle of greatest range are called hinged. 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 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 extent of the terrain, the target can be hit with one sight setting (the less impact on the shooting results is the error in determining the sight setting): this is the practical significance of the trajectory. The flatness of the trajectory is characterized by its greatest excess over the aiming line. At a given range, the trajectory is all the more flat, 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 trajectory is the more flat, the smaller the angle of incidence. The flatness of the trajectory affects the value of the range of a direct shot, struck, covered and dead space.

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

Departure point- the center of the muzzle of the barrel. The departure point is the start of the trajectory. Weapon Horizon is the horizontal plane passing through the departure point. elevation line- a straight line, which is a continuation of the axis of the bore of the aimed weapon. Shooting plane- a vertical plane passing through the line of elevation. Elevation angle- the angle enclosed between the line of elevation and the horizon of the weapon. If this angle is negative, then it is called the angle of declination (decrease). Throw line- a straight line, which is a continuation of the axis of the bore at the time of the bullet's departure. Throwing angle Departure angle- the angle enclosed between the line of elevation and the line of throwing. drop point- the point of intersection of the trajectory with the horizon of the weapon. Angle of incidence- the angle enclosed between the tangent to the trajectory at the point of impact and the horizon of the weapon. Total horizontal range- the distance from the point of departure to the point of fall. final speed- the speed of the bullet (grenade) at the point of impact. Total flight time- the time of movement of a bullet (grenade) from the point of departure to the point of impact. Top of the path- the highest point of the trajectory above the horizon of the weapon. Trajectory 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 departure point to the top, and from the top to the drop point - the descending branch of the trajectory. Aiming point (aiming)- the point on the target (outside it) at which the weapon is aimed. line of sight- a straight line passing 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 enclosed between the line of elevation and the line of sight. Target elevation angle- the angle enclosed between the aiming line and the horizon of the weapon. This angle is considered positive (+) when the target is higher 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 line of sight. The excess of the trajectory over the line of sight is the shortest distance from any point of the trajectory to the line of sight. target line- a straight line connecting the departure point with the target. Slant Range- distance from the departure point to the target along the target line. meeting point- point of intersection of the trajectory with the surface of the target (ground, obstacles). Meeting angle- the angle enclosed between the tangent to the trajectory and the tangent to the target surface (ground, obstacles) at the meeting point. The meeting angle is taken as 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 in tense moments of the battle, shooting can be carried out without rearranging the sight, while the aiming point in height, as a rule, is chosen at the lower edge of the target.

The order of incomplete disassembly of the AK-74:

We disconnect the magazine, remove it from the fuse and distort the bolt carrier, make a control descent, 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 shim.

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 area in which the target can be hit is called affected space

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

3.1 What charters 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

Military charter of the armed forces of the Russian Federation

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

2. Military discipline is based on the awareness of each serviceman 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 servicemen.

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

3. Military discipline obliges each soldier:

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 their military duty skillfully and courageously, conscientiously study military affairs, protect state and military property;

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

be vigilant, strictly keep state secrets;

to maintain the rules of relations between servicemen determined by general military regulations, to strengthen the military camaraderie;

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

behave with dignity in public places, prevent oneself and keep others from unworthy acts, contribute to the protection of 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 moral-psychological, combat qualities and conscious obedience to commanders (chiefs) among military personnel;

knowledge and observance by military personnel of 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 duties of military service;

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

a clear organization of combat training and its full coverage of personnel;

everyday exactingness of commanders (chiefs) to subordinates and control over their diligence, respect for the personal dignity of military personnel and constant concern for them, skillful combination and correct application of measures of persuasion, coercion and social influence of the team;

the creation in the military unit (subdivision) 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 (subunit), who must constantly maintain military discipline, require subordinates to observe it, encourage the worthy, strictly but fairly exact from the negligent.

Military discipline must be observed in the unit, it is a necessary condition for the life 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 evaluating the daily activities of commanders.

28% of the dead comes in number suicidal.

Consistency, and the habit of strict order.

Discipline is a Teaching, a science.

The characteristic features of military discipline are:

unity of command

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

Obligation and unconditional performance

Clear subordination

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

To form 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, build reasoning correctly, reason, 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 causes of violation of military disciplines

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

The internal order is the strict observance of the rules of accommodation, daily activities, life of military personnel in a military unit (subdivision) and serving in a daily outfit determined by military regulations.

Internal order is achieved:

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

purposeful educational work, a combination of the high demands of commanders (chiefs) with constant concern for subordinates and maintaining their health;

clear organization of combat training;

exemplary bearing combat duty and daily service;

exact implementation of the daily routine and regulations of working hours;

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

compliance with the requirements fire safety, as well as the adoption of measures to protect the environment in the area of activity of the military unit.

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 the current rules 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. Similarly, passageways within a unit and subdivision must be uncluttered.

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

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

An order is a form of bringing tasks by the head of the task to subordinates on private issues. It is given in writing or orally. It is issued in writing by the chief of staff, is an administrative document and is given on the estate of the unit commander

When giving an order, someone should not abuse official powers. Do not give an order that is not related to the conduct of military service.

The order is formulated clearly and concisely. They are given in order of subordination.

Completed without question and on time.

The soldier answers "yes".

unity of command

It consists in vesting the commander (chief) with full administrative power in relation to subordinates and placing on him personal responsibility for all aspects of the life and activities of a 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 the troops. It should be noted that it best ensures the unity of will and actions of all personnel, strict centralization, maximum flexibility and efficiency in command and control of troops. Unity of command allows the commander to act boldly, decisively, to 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 commanding qualities in officers. It creates conditions for high organization, strict military discipline and firm order.

Shot is a complex set of physical and chemical phenomena. The firing event can be conditionally divided into two stages - the movement of the projectile in the gun barrel and the complex of phenomena that occur after the projectile leaves the barrel.

Shot is called the ejection of a bullet from the bore under the action of powder gases formed during the combustion of a powder charge. From the impact of the striker on the primer of the cartridge, a flame arises that ignites the powder charge. This creates a large number of highly heated gases that create high pressure acting in all directions with the same force. At a gas pressure of 250-500 kg / cm 2, the bullet moves from its place and crashes into the rifling of the bore, receiving rotational motion. Gunpowder continues to burn, therefore, the amount of gases increases. Then, due to the rapid increase in the speed of the bullet, the volume of the bullet space increases faster than inflow new gases, and the pressure starts to drop. However, the speed of the bullet in the bore continues to increase, as the gases, although to a lesser extent, still put pressure on it. The bullet moves along the bore at a continuously increasing speed and is ejected outward in the direction of the axis of the bore. The entire firing process takes place in a very short period of time (0.001–0.06 s). Further, the flight of the bullet in the air continues by inertia and largely depends on its initial velocity.

muzzle velocity is the speed at which the bullet leaves the bore. The value of the muzzle velocity of a bullet depends on the length of the barrel, the mass of the bullet, the mass of the powder charge, and other factors. An increase in the initial speed increases the range of the bullet, its penetrating and lethal action, reduces the influence of external conditions on its flight. The movement of the weapon backwards while firing is called recoil. The pressure of powder gases in the bore acts in all directions with the same force. The pressure of the gases on the bottom of the bullet makes it move forward, and the pressure on the bottom of the cartridge case is transmitted to the bolt and causes the weapon to move backward. When recoil, a pair of forces is formed, under the influence of which the muzzle of the weapon deviates upward. The recoil force acts along the axis of the bore, and the butt rest against the shoulder and the center of gravity of the weapon are located below the direction of this force, therefore, when firing, the muzzle of the weapon deviates upward.

recoil small arms is felt in the form of a push in the shoulder, arm or into the ground. The recoil action of a weapon is characterized by the amount of speed and energy that it has when moving backward. The recoil speed of the weapon is about as many times less than the initial speed of the bullet, how many times the bullet is lighter than the weapon. The recoil energy of the Kalashnikov assault rifle is small and is perceived painlessly by the shooter. Correct and uniform holding of the weapon reduces the impact of recoil and increases the effectiveness of shooting. The presence of muzzle brakes-compensators or compensators for weapons improves the results of firing bursts and reduces recoil.

At the time of the shot, the barrel of the weapon, depending on the elevation angle, occupies a certain position. The flight of a bullet in the air begins in a straight line, representing the continuation of the axis of the bore at the time of the bullet's departure. This line is called throw line. When flying in the air, two forces act on a bullet: gravity and air resistance. Gravity pushes the bullet further and further away from the line of throw, while air resistance slows the bullet down. Under the influence of these two forces, the bullet continues to fly along a curve located below the line of throw. Trajectory shape depends on the magnitude of the elevation angle and the initial speed of the bullet, it affects the value of the range of a direct shot, covered, affected and dead space. As the elevation angle increases, the height of the trajectory and the total horizontal range of the bullet increase, but this occurs up to a certain limit. Beyond this limit, the trajectory height continues to increase and the total horizontal range decreases.

The angle of elevation at which the full horizontal range of the bullet is greatest is called farthest angle. The value of the angle of greatest range for bullets of various types of weapons is about 35 °. Trajectories obtained at elevation angles smaller than the angle of greatest range are called flat.

Straight shot called a shot in which the trajectory of the bullet does not rise above the line of sight above the target throughout its entire length.

Direct shot range depends on the height of the target and flatness of the trajectory. The higher the target and the flatter the trajectory, the greater the range of a direct shot and, therefore, the distance at which the target can be hit with one sight setting. The practical significance of a direct shot lies in the fact that in tense moments of the battle, shooting can be carried out without rearranging the sight, while the aiming point in height will be selected along the lower edge of the target.

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

The covered space is the greater, the higher the shelter and the flatter the trajectory. The part of the covered space on which the target cannot be hit with a given trajectory is called dead (non-hit) space. It is the greater, the greater the height of the shelter, the lower the height of the target and the flatter the trajectory. The other part of the covered space in which the target can be hit is the hit space.

Shot periodization

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

preliminary;
first, or main;
second;
the third, or period of the last gases.

Preliminary period lasts from the beginning of the burning of the powder charge to the complete cutting of the shell of the bullet into the rifling of the barrel. During this period, the gas pressure is created in the barrel bore, which is necessary in order to move the bullet from its place and overcome the resistance of its shell to cutting into the rifling of the barrel. This pressure is called boost pressure; it reaches 250 - 500 kg / cm 2, depending on the rifling device, the weight of the bullet and the hardness of its shell (for example, for small arms chambered for the 1943 sample, the forcing pressure is about 300 kg / cm 2). 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 forcing pressure is reached in the bore.

First or main period lasts from the beginning of the movement of the bullet to the moment complete combustion powder charge. During this period, the combustion of the powder charge occurs in a rapidly changing volume. At the beginning of the period, when the speed of the bullet 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 case), the gas pressure rises rapidly and reaches largest(for example, for small arms chambered for a sample of 1943 - 2800 kg / cm 2, and for a rifle cartridge 2900 kg / cm 2). This pressure is called maximum pressure. It is created in small arms when a bullet travels 4 - 6 cm of the path. Then due to fast speed movement of the bullet, the volume of the bullet space increases faster than the influx of new gases, and the pressure begins to fall, by the end of the period it is equal to approximately 2/3 of the maximum pressure. The speed of the bullet is constantly increasing and by the end of the period reaches approximately 3/4 of the initial speed. The powder charge completely burns out shortly before the bullet leaves the bore.

Second period lasts until the moment of complete combustion of the powder charge until the moment the bullet leaves the bore. 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 / cm 2 for various types of weapons (for example, for the Simonov self-loading carbine - 390 kg / cm 2, for the Goryunov easel machine gun - 570 kg / cm 2 ). The speed of the bullet at the time of its departure from the bore (muzzle velocity) is somewhat less than the initial velocity.