Bullet trajectory elements. external ballistics. Trajectory and its elements. Exceeding the trajectory of the bullet above the point of aim. Trajectory shape. Methods for determining the midpoint of impact

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

Rice. 3. Trajectory

Rice. 4. Bullet trajectory parameters

A bullet flying through the air is subjected to two forces: gravity and air resistance. The force of gravity causes the bullet to gradually descend, and the force of air resistance continuously slows down the movement of the bullet and tends to topple it.

As a result of the action of these forces, the bullet's flight speed gradually decreases, and its trajectory is an unevenly curved curved line in shape.

Parameter trajectories	Parameter characteristic	Note
Departure point	Center of muzzle	The departure point is the start of the trajectory
Weapon Horizon	Horizontal plane passing through the departure point	The horizon of the weapon 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 bore of the aimed weapon
Shooting plane	The 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	Straight line, a line that is a continuation of the axis of the bore at the time of the bullet's departure
Throwing angle	The angle enclosed between the line of throw and the horizon of the weapon
Departure angle	The angle enclosed between the line of elevation and the line of throw
drop point	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	Distance from departure point to drop point
Ultimate speed	Bullet speed at point of impact
Total flight time	The time it takes for a bullet to travel from point of departure to point of impact
Top of the path	highest point trajectories
Trajectory height	The 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 summit
descending branch	Part of the trajectory from the top to the point of impact
Aiming point (aiming)	The point on or off the target 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 (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 line of sight and the horizon of the weapon	The target's elevation angle is considered positive (+) when the target is above the weapon's horizon, and negative (-) when the target is below the weapon's horizon.
Sighting range	Distance from the point of departure to the intersection of the trajectory with the line of sight
Exceeding the trajectory above the line of sight	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	When firing direct fire, the target line practically coincides with the aiming line
Slant Range	Distance from point of origin to target along target line	When firing direct fire, the slant range practically coincides with the aiming range.
meeting point	Intersection point of the trajectory with the target surface (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 smaller of the adjacent angles, measured from 0 to 90°, is taken as the meeting angle.
Sighting line	A straight line connecting the middle of the sight slot to the top of the front sight
Aiming (pointing)	Giving the axis of the bore of the weapon the position in space necessary for firing	In order for the bullet to reach the target and hit it or the desired point on it
Horizontal aiming	Giving the axis of the bore the desired position in the horizontal plane
vertical guidance	Giving the axis of the bore the desired 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 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 the bullet along the ascending branch of the trajectory is less than along the descending one;
the trajectory of a rotating bullet due to the lowering of the bullet under the action of gravity and derivation is a line of double curvature.

Types of trajectories and their practical value.

When firing from any type of weapon with an increase in the 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 kinds weapons is about 35 °.

The angle of greatest range divides all trajectories into two types: on trajectories flooring and hinged(Fig. 6).

Rice. 5. The affected area and the greatest horizontal and aiming ranges when firing at different elevation angles.

Rice. 6. Angle of greatest range. flat, hinged and conjugate trajectories

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

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

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

When firing from small arms and grenade launchers, only flat trajectories are used. The flatter the trajectory, the greater the 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 range direct shot, affected, covered and dead space.

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trajectory called the curved line described by the center of gravity of the bullet in flight.
A bullet flying through the air is subjected to two forces: gravity and air resistance. The force of gravity causes the bullet to gradually descend, 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 bullet's flight speed gradually decreases, and its trajectory is an unevenly curved curved line in shape. Air resistance to the flight of a bullet is caused by the fact that air is elastic medium and therefore part of the energy of the bullet 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. 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 begins to decrease.

The angle of elevation at which the full horizontal range of the bullet is at its 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 largest angle longest range are called mounted. When firing from the same weapon (with the same initial speeds) you can get two trajectories with the same horizontal range: flat and hinged. Trajectories having the same horizontal range swarms of different elevation angles are called conjugated.

When shooting from small arms, only flat trajectories are used. The flatter the trajectory, the greater the 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.

Trajectory elements

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.

Rice. 1. Artillery battleship"Marat"

Ballistics(from the Greek βάλλειν - to throw) - the science of the movement of bodies thrown in space, based on mathematics and physics. It deals mainly with the study of the movement of projectiles fired from firearms, rocket projectiles and ballistic missiles.

Basic concepts

Rice. 2. Elements of firing naval artillery

The main objective of shooting is to hit the target. To do this, the tool must be given a strictly defined position in the vertical and horizontal planes. If we point the gun so that the axis of the bore is directed at the target, then we will not hit the target, since the trajectory of the projectile will always pass below the direction of the axis of the bore, the projectile will not reach the target. To formalize the terminological apparatus of the subject under consideration, we introduce the main definitions used when considering the theory of artillery firing.
Departure point called the center of the muzzle of the gun.

drop point called the point of intersection of the trajectory with the horizon of the gun.

horizon guns called the horizontal plane passing through the departure point.

Elevation line called the continuation of the axis of the bore of the pointed gun.

Throwing line OB is the continuation of the axis of the bore at the time of the shot. At the moment of the shot, the gun shudders, as a result of which the projectile is thrown not along the line of elevation of the OA, but along the line of throwing of the OV (see Fig. 2).

Goal line OC is the line connecting the gun to the target (see Fig. 2).

Line of sight (sight) called the line running from the gunner's eye through the optical axis of the sight to the aiming point. When firing direct fire, when the line of sight is directed at the target, the line of sight coincides with the line of the target.

Falling line is called the tangent to the trajectory at the point of incidence.

Rice. 3. Shooting at an overlying target

Rice. 4. Shooting at the underlying target

Elevation (greek phi) called the angle between the line of elevation and the horizon of the gun. If the bore axis is directed below the horizon, then this angle is called the angle of descent (see Fig. 2).

The firing range of the gun depends on the elevation angle and firing conditions. Therefore, in order to throw the projectile to the target, it is necessary to give the gun such an elevation angle at which the firing range will correspond to the distance to the target. The firing tables indicate which aiming angles must be given to the gun in order for the projectile to fly to the desired range.

Throwing angle (Greek theta zero) the angle between the line of throw and the horizon of the gun is called (see Fig. 2).

Departure angle (Greek gamma) called the angle between the line of throw and the line of elevation. In naval artillery, the departure angle is small and is sometimes not taken into account, assuming that the projectile is thrown at an elevation angle (see Fig. 2).

Aiming angle (Greek alpha) the angle between the line of elevation and the line of sight is called (see Fig. 2).

Target elevation angle (greek epsilon) called the angle between the line of the target and the horizon of the gun. When a ship fires at sea targets, the elevation angle of the target is equal to zero, since the target line is directed along the horizon of the gun (see Fig. 2).

Incident angle (Greek theta s Latin letter with) the angle between the target line and the fall line is called (see Fig. 2).

Meeting angle (Greek mu) is the angle between the line of incidence and the tangent to the target surface at the meeting point (see Fig. 2).
The value of the value of this angle greatly affects the resistance of the armor of the ship, which is fired at, to penetration by shells. Obviously, the closer this angle is to 90 degrees, the higher the probability of penetration, and the opposite is also true.
Shooting plane called the vertical plane passing through the line of elevation. When the ship fires at sea targets, the aiming line is directed along the horizon, in this case the elevation angle equal to the angle aiming. When a ship fires at coastal and air targets, the elevation angle is equal to the sum of the aiming angle and the elevation angle of the target (see Fig. 3). When firing a coastal battery at sea targets, the elevation angle is equal to the difference between the aiming angle and the elevation angle of the target (see Fig. 4). Thus, the magnitude of the elevation angle is equal to the algebraic sum of the aiming angle and the elevation angle of the target. If the target is above the horizon, the target elevation angle is "+", if the target is below the horizon, the target elevation angle is "-".

The influence of air resistance on the trajectory of the projectile

Rice. 5. Changing the trajectory of the projectile from air resistance

The flight path of a projectile in airless space is a symmetrical curved line, called a parabola in mathematics. The ascending branch coincides in shape with the descending branch and, therefore, the angle of incidence is equal to the angle of elevation.

When flying in the air, the projectile spends part of its speed to overcome air resistance. Thus, two forces act on the projectile in flight - the force of gravity and the force of air resistance, which reduces the speed and range of the projectile, as illustrated in Fig. 5. The magnitude of the air resistance force depends on the shape of the projectile, its size, flight speed and air density. The longer and more pointed the head of the projectile, the less air resistance. The shape of the projectile is especially affected at flight speeds exceeding 330 meters per second (that is, at supersonic speeds).

Rice. 6. Short-range and long-range projectiles

On fig. 6, on the left, is a short-range, old-style projectile and a more oblong, pointed, long-range projectile on the right. It can also be seen that a long-range projectile has a conical narrowing at the bottom. The fact is that a rarefied space and turbulence are formed behind the projectile, which significantly increase air resistance. By narrowing the bottom of the projectile, a decrease in the amount of air resistance resulting from rarefaction and turbulence behind the projectile is achieved.

The force of air resistance is proportional to the speed of its flight, but not directly proportional. Dependence is formalized more difficult. Due to the action of air resistance, the ascending branch of the projectile's flight path is longer and delayed than the descending one. The angle of incidence is greater than the angle of elevation.

In addition to reducing the range of the projectile and changing the shape of the trajectory, the force of air resistance tends to overturn the projectile, as can be seen from Fig. 7.

Rice. 7. Forces acting on a projectile in flight

Therefore, a non-rotating elongated projectile will roll over under the action of air resistance. In this case, the projectile can hit the target in any position, including sideways or bottom, as shown in Fig. eight.

Rice. 8. Rotation of a projectile in flight under the influence of air resistance

So that the projectile does not roll over in flight, it is given rotary motion using rifling in the bore.

If we consider the effect of air on a rotating projectile, we can see that this leads to a lateral deviation of the trajectory from the plane of fire, as shown in Fig. nine.

Rice. 9. Derivation

derivation called the deviation of the projectile from the plane of fire due to its rotation. If the rifling twists from left to right, then the projectile deflects to the right.

The influence of the angle of elevation and the initial velocity of the projectile on the range of its flight

The range of a projectile depends on the elevation angles at which it is thrown. An increase in the flight range with an increase in the elevation angle occurs only up to a certain limit (40-50 degrees), with a further increase in the elevation angle, the range begins to decrease.

Range limit angle called the elevation angle at which the greatest firing range is obtained for a given initial velocity and projectile. When firing in an airless space, the greatest range of the projectile is obtained at an elevation angle of 45 degrees. When firing in the air, the maximum range angle differs from this value and is not the same for different guns (usually less than 45 degrees). For ultra-long-range artillery, when the projectile flies for a significant part of the path high altitude in highly rarefied air, the maximum range angle is more than 45 degrees.

For a gun of this type and when firing a certain type of ammunition, each elevation angle corresponds to a strictly defined range of the projectile. Therefore, in order to throw the projectile at the distance we need, it is necessary to give the gun an elevation angle corresponding to this distance.

The trajectories of projectiles fired at elevation angles smaller than the maximum range angle are called flat trajectories .

The trajectories of projectiles fired at elevation angles greater than the maximum range angle are called " hinged trajectories" .

Projectile dispersion

Rice. 10. Dispersion of projectiles

If several shots are fired from the same gun, with the same ammunition, with the same direction of the gun barrel, under the same, at first glance, conditions, then the shells will not hit the same point, but will fly along different trajectories, forming a bundle of trajectories, as illustrated in fig. 10. This phenomenon is called projectile dispersion .

The reason for the dispersion of projectiles is the impossibility of achieving exactly the same conditions for each shot. The table shows the main factors that cause projectile dispersion and possible ways reduce this dispersion.

The main groups of causes of dispersion	Conditions that give rise to the causes of dispersion	Control measures to reduce dispersion
1. Variety of starting speeds	A variety of properties of gunpowder (composition, moisture and solvent content). Variety of charge weights. Variety of charge temperatures. Variety of loading density. (dimensions and location of the leading belt, sending shells). A variety of shapes and weights of projectiles.	Storage in a sealed container. Each shooting should be carried out with charges of one batch. Maintaining the proper temperature in the cellar. Load uniformity. Each shooting is carried out with shells of the same weight mark.
2. Variety of throwing angles	A variety of elevation angles (dead moves in the aiming device and in the vertical guidance mechanism). Variety of launch angles. Variety of guidance.	Careful maintenance of the material. Good gunner training.
3. A variety of conditions in the flight of a projectile	Variety of influence of the air environment (density, wind).

The area on which projectiles fired from a gun with the same direction of the barrel bore fall is called scattering area .

The middle of the scattering area is called midpoint of fall .

An imaginary trajectory passing through the point of departure and the middle point of fall is called average trajectory .

The scattering area has the shape of an ellipse, so the scattering area is called scattering ellipse .

The intensity with which projectiles hit different points of the dispersion ellipse is described by a two-dimensional Gaussian (normal) distribution law. From here, if we follow exactly the laws of probability theory, we can conclude that the scattering ellipse is an idealization. The percentage of projectiles hitting inside the ellipse is described by the three-sigma rule, namely, the probability of projectiles hitting an ellipse whose axis is equal to three times the square root of the variances of the corresponding one-dimensional Gaussian distribution laws is 0.9973.
Due to the fact that the number of shots from one gun, especially large caliber, as already mentioned above, due to wear often does not exceed one thousand, this inaccuracy can be neglected and it can be assumed that all shells fall into the dispersion ellipse. Any section of a beam of projectile flight paths is also an ellipse. The dispersion of projectiles in range is always greater than in the lateral direction and in height. The value of the median deviations can be found in the main shooting table and the size of the ellipse can be determined from it.

Rice. 11. Shooting at a target with no depth

Affected space is the space over which the trajectory passes through the target.

According to fig. 11, the affected space is equal to the distance along the horizon AC from the base of the target to the end of the trajectory passing through the top of the target. Each projectile that fell outside the affected space either passed above the target or fell before it. The affected space is limited by two trajectories - the OA trajectory passing through the base of the target, and the OS trajectory passing through the top point of the target.

Rice. 12. Shooting at a target with depth

In case the target being hit has a depth, the amount of the hit space is increased by the value of the target depth, as illustrated in Fig. 12. The depth of the target will depend on the size of the target and its position relative to the plane of fire. Consider the most likely target for naval artillery - an enemy ship. In such a case, if the target is coming from us or towards us, the depth of the target is equal to its length, when the target is perpendicular to the plane of fire, the depth is equal to the width of the target, as illustrated in the figure.

Given the fact that the scattering ellipse has great length and a small width, it can be concluded that at a shallow target depth, fewer projectiles hit the target than at a large depth. That is, than more depth target, the easier it is to hit. With an increase in the firing range, the affected target space decreases, as the angle of incidence increases.

Straight shot a shot is called, in which the entire distance from the point of departure to the point of impact is the affected space (see Fig. 13).

Rice. 13. Direct shot

This is obtained if the height of the trajectory does not exceed the height of the target. The range of a direct shot depends on the steepness of the trajectory and the height of the target.

Range of a direct shot (or range of flattening) called the distance at which the height of the trajectory does not exceed the height of the target.

The most important works on ballistics

17th century

- Tartaglia theory,
1638- labor Galileo Galilei about the parabolic motion of a body thrown at an angle.
1641- a student of Galileo - Toricelli, developing the parabolic theory, derives an expression for horizontal range, which later formed the basis of artillery firing tables.
1687- Isaac Newton proves the influence of air resistance on a thrown body, introducing the concept of the shape factor of the body, and also drawing a direct dependence of the movement resistance on the cross section (caliber) of the body (projectile).
1690— Ivan Bernoulli mathematically describes main task ballistics, solving the problem of determining the motion of a ball in a resisting medium.

18th century

1737- Bigot de Morogues (1706-1781) published a theoretical study of internal ballistics, which laid the foundation for the rational design of guns.
1740- the Englishman Robins learned to determine the initial speeds of the projectile and proved that the projectile flight parabola has a double curvature - its descending branch is shorter than the ascending one, in addition, he empirically concluded that the air resistance to the flight of projectiles at initial speeds above 330 m / s increases abruptly and should calculated using a different formula.
Second half of the 18th century
Daniel Bernoulli deals with the issue of air resistance to the movement of projectiles;
mathematician Leonhard Euler develops the work of Robins, Euler's work on internal and external ballistics forms the basis for the creation of artillery firing tables.
Mordashev Yu. N., Abramovich I. E., Mekkel M. A. Textbook of deck artillery commander. M.: Military publishing house of the Ministry armed forces Union of the SSR. 1947. 176 p.

Internal and external ballistics.

Shot and its periods. The initial speed of the bullet.

Lesson number 5.

"RULES FOR SHOOTING FROM SMALL ARMS"

1. Shot and its periods. The initial speed of the bullet.

Internal and external ballistics.

2. Shooting rules.

Ballistics is the science of the movement of bodies thrown in space. It focuses primarily on the movement of projectiles fired from firearms, rocket projectiles and ballistic missiles.

A distinction is made between internal ballistics, which studies the movement of a projectile in a gun channel, as opposed to external ballistics, which studies the movement of a projectile as it leaves the gun.

We will consider ballistics as the science of the movement of a bullet when fired.

Internal ballistics is a science that studies the processes that take place when a shot is fired and, in particular, when a bullet moves along a barrel bore.

A shot is the ejection of a bullet from the bore of a weapon by the energy of gases formed during the combustion of a powder charge.

When fired from small arms, the following phenomena occur. From the impact of the striker on the primer of a live cartridge sent into the chamber, the percussion composition of the primer explodes and a flame forms, which penetrates through the hole in the bottom of the sleeve to the powder charge and ignites it. When a powder (or so-called combat) charge is burned, a large number of highly heated gases that create in the bore high pressure on the bottom of the bullet, the bottom and walls of the sleeve, as well as on the walls of the barrel and the bolt. As a result of the pressure of gases on the bullet, it moves from its place and crashes into the rifling; rotating along them, it moves along the bore with a continuously increasing speed and is thrown outward in the direction of the axis of the bore. The pressure of gases on the bottom of the sleeve causes recoil - the movement of the weapon (barrel) back. From the pressure of gases on the walls of the sleeve and the barrel, they are stretched (elastic deformation) and the sleeves, tightly pressed against the chamber, prevent the breakthrough of powder gases towards the bolt. At the same time, when fired, an oscillatory movement (vibration) of the barrel occurs and it heats up.

During the combustion of a powder charge, approximately 25-30% of the energy released is spent on communicating the translational motion to the pool (the main work); 15-25% of energy - for secondary work (cutting and overcoming the friction of a bullet when moving along the bore, heating the walls of the barrel, cartridge case and bullet; moving the moving parts of the weapon, gaseous and unburned parts of gunpowder); about 40% of the energy is not used and is lost after the bullet leaves the bore.

The shot passes in a very short period of time: 0.001‑0.06 seconds. When fired, four periods are distinguished:

Preliminary;

First (or main);

Third (or period of aftereffect of 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 bore. 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 (depending on the rifling device, the weight of the bullet and the hardness of its shell) is called forcing pressure and reaches 250-500 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 (main) period lasts from the beginning of the movement of the bullet to the moment complete combustion powder charge. 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 cartridge case), the gas pressure rises rapidly and reaches its maximum value. 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 the rapid increase in the speed of the bullet, the volume of the bullet space increases faster than inflow 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 3/4 of the initial speed. The powder charge completely burns out shortly before the bullet leaves the bore.

Second period lasts from the moment of complete combustion of the powder charge until the moment the bullet leaves the barrel. With the beginning of this period, the influx of powder gases stops, however, highly compressed and heated gases expand and, putting pressure on the bullet, increases its speed. The speed of the bullet at the exit from the bore ( muzzle velocity) is slightly less than the initial speed.

initial speed called the speed of the bullet at the muzzle of the barrel, i.e. at the time of its departure from the bore. It is measured in meters per second (m/s). The initial speed of caliber bullets and projectiles is 700‑1000 m/s.

The value of the initial speed is one of the most important characteristics combat properties of weapons. For the same bullet an increase in the initial speed leads to an increase in the flight range, penetrating and lethal action of the bullet, as well as to reduce the influence of external conditions on its flight.

Bullet penetration is characterized by its kinetic energy: the depth of penetration of a bullet into an obstacle of a certain density.

When firing from AK74 and RPK74, a bullet with a steel core of 5.45 mm cartridge pierces:

o steel sheets with thickness:

2 mm at a distance of up to 950 m;

3 mm - up to 670 m;

5 mm - up to 350 m;

o steel helmet (helmet) - up to 800 m;

o earthen barrier 20-25 cm - up to 400 m;

o pine beams 20 cm thick - up to 650 m;

o brickwork 10-12 cm - up to 100 m.

Bullet lethality characterized by its energy (live force of impact) at the moment of meeting with the target.

Bullet energy is measured in kilogram-force-meters (1 kgf m is the energy required to do the work of lifting 1 kg to a height of 1 m). To inflict damage on a person, an energy equal to 8 kgf m is needed, to inflict the same defeat on an animal - about 20 kgf m. The bullet energy of the AK74 at 100 m is 111 kgf m, and at 1000 m it is 12 kgf m; the lethal effect of the bullet is maintained up to a range of 1350 m.

The value of the muzzle velocity of a bullet depends on the length of the barrel, the mass of the bullet and the properties of the powder. The longer the barrel, the longer the powder gases act on the bullet and the greater the initial velocity. With a constant barrel length and a constant mass of the powder charge, the initial velocity is greater, the smaller the mass of the bullet.

Some types of small arms, especially short-barreled ones (for example, the Makarov pistol), do not have a second period, because. complete combustion of the powder charge by the time the bullet leaves the bore does not occur.

The third period (the period of aftereffect of gases) lasts from the moment the bullet leaves the bore until the moment the action of the powder gases on the bullet ceases. During this period, powder gases flowing out of the bore at a speed of 1200-2000 m/s continue to act on the bullet and give it additional speed. The bullet reaches its greatest (maximum) speed at the end of the third period at a distance of several tens of centimeters from the muzzle of the barrel.

Hot powder gases escaping from the barrel after the bullet, when they meet with air, cause shock wave, which is the source of the sound of the shot. The mixing of hot powder gases (among which there are oxides of carbon and hydrogen) with atmospheric oxygen causes a flash, observed as a shot flame.

The pressure of the powder gases acting on the bullet ensures that it is given translational speed, as well as rotational speed. The pressure acting in the opposite direction (on the bottom of the sleeve) creates a recoil force. The movement of a weapon under the influence of recoil force is called bestowal. When shooting from small arms, the recoil force is felt in the form of a push to the shoulder, arm, acts on the installation or the ground. The recoil energy is greater than more powerful weapon. For hand-held small arms, the recoil usually does not exceed 2 kg / m and is perceived by the shooter painlessly.

Rice. 1. Throwing the muzzle of the weapon barrel up when fired

as a result of the action of recoil.

When firing from automatic weapons, the device of which is based on the principle of using recoil energy, part of it is spent on communicating movement to moving parts and reloading weapons. Therefore, the recoil energy when fired from such a weapon is less than when fired from non-automatic weapons or from automatic weapons, the device of which is based on the principle of using the energy of powder gases discharged through holes in the barrel wall.

The pressure force of powder gases (recoil force) and the recoil resistance force (butt stop, handles, weapon center of gravity, etc.) are not located on the same straight line and are directed in opposite directions. The resulting dynamic pair of forces leads to the angular displacement of the weapon. Deviations can also occur due to the influence of the action of small arms automation and the dynamic bending of the barrel as the bullet moves along it. These reasons lead to the formation of an angle between the direction of the axis of the bore before the shot and its direction at the moment the bullet leaves the bore - departure angle. The magnitude of the deviation of the muzzle of the barrel of a given weapon is the greater, than more shoulder this pair of forces.

In addition, when fired, the barrel of the weapon makes an oscillatory movement - it vibrates. As a result of vibration, the muzzle of the barrel at the moment the bullet takes off can also deviate from its original position in any direction (up, down, right, left). The value of this deviation increases with improper use of the firing stop, contamination of the weapon, etc. The departure angle is considered positive when the axis of the bore at the time of the bullet's departure is higher than its position before the shot, negative when it is lower. The value of the departure angle is given in the firing tables.

The influence of the departure angle on firing for each weapon is eliminated when bringing him to a normal fight (see 5.45mm Kalashnikov manual... - Chapter 7). However, in case of violation of the rules for laying the weapon, using the stop, as well as the rules for caring for the weapon and saving it, the value of the launch angle and the weapon's combat change.

In order to reduce the harmful effect of recoil on the results, in some samples of small arms (for example, the Kalashnikov assault rifle), special devices are used - compensators.

Muzzle brake-compressor is a special device on the muzzle of the barrel, acting on which, the powder gases after the bullet takes off, reduce the recoil speed of the weapon. In addition, the gases flowing out of the bore, hitting the walls of the compensator, somewhat lower the muzzle of the barrel to the left and down.

In the AK74, the muzzle brake compensator reduces recoil by 20%.

1.2. External ballistics. Bullet flight path

External ballistics is a science that studies the movement of a bullet in the air (i.e. after the cessation of the action of powder gases on it).

Having flown out of the bore under the action of powder gases, the bullet moves by inertia. In order to determine how the bullet moves, it is necessary to consider the trajectory of its movement. trajectory called the curved line described by the center of gravity of the bullet during flight.

A bullet flying through the air is subjected to two forces: gravity and air resistance. The force of gravity causes it to gradually decrease, and the force of air resistance continuously slows down the movement of the bullet and tends to overturn it. As a result of the action of these forces, the bullet's flight speed gradually decreases, and its trajectory is an unevenly curved curve in shape.

The resistance of air to the flight of a bullet is caused by the fact that air is an elastic medium, therefore, part of the energy of the bullet is expended in this medium, which is caused by three main reasons:

Air friction

The formation of swirls

formation of a ballistic wave.

The resultant of these forces is the air resistance force.

Rice. 2. Formation of air resistance force.

Rice. 3. The action of the force of air resistance on the flight of a bullet:

CG - center of gravity; CS is the center of air resistance.

Air particles in contact with a moving bullet create friction and reduce the speed of the bullet. The air layer adjacent to the surface of the bullet, in which the movement of particles changes depending on the speed, 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 discharged 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.

The bullet collides with air particles during flight and causes them to oscillate. As a result, the air density increases in front of the bullet and a sound wave is formed. Therefore, the flight of a bullet is accompanied by a characteristic sound. When the speed of the bullet is less than the speed of sound, the formation of these waves has little effect on its flight, because. The waves travel faster than the speed of the bullet. 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, because. the bullet spends some of its energy creating this wave.

The effect of the force of air resistance on the flight of a bullet is very large: it causes a decrease in speed and range. For example, a bullet at an initial speed of 800 m/s in airless space would fly to a distance of 32,620 m; the flight range of this bullet in the presence of air resistance is only 3900 m.

The magnitude of the air resistance force mainly depends on:

§ bullet speed;

§ the shape and caliber of the bullet;

§ from the surface of the bullet;

§ air density

and increases with an 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 air compaction in front of the head (ballistic wave), bullets with an elongated pointed head are advantageous.

Thus, the force of air resistance reduces the speed of the bullet and overturns it. As a result of this, the bullet begins to “tumble”, the air resistance force increases, the flight range decreases and its effect on the target decreases.

The stabilization of the bullet in flight is ensured by giving the bullet a rapid rotational movement around its axis, as well as by the tail of the grenade. Departure rotation speed rifled weapons is: bullets 3000-3500 rpm, turning feathered grenades 10-15 rpm. Due to the rotational movement of the bullet, the impact of air resistance and gravity, the bullet deviates to the right side from the vertical plane drawn through the axis of the bore, - firing plane. The deviation of a bullet from it when flying in the direction of rotation is called derivation.

Rice. 4. Derivation (view of the trajectory from above).

As a result of the action of these forces, the bullet flies in space along an unevenly curved curve called trajectory.

Let's continue consideration of elements and definitions of a trajectory of a bullet.

Rice. 5. Trajectory elements.

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

The horizontal plane passing through the departure point is called weapon 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.

pointed weapons , is called elevation line.

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

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

A straight line that is a continuation of the axis of the bore at the time of the bullet's departure , is called throw line.

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

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

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

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

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

The speed of the bullet at the point of impact is called final speed.

The time it takes for a bullet to travel from point of departure to point of impact is called full time flight.

The highest point of the trajectory is called the top of the path.

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

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

The point on the target (or outside it) at which the weapon is aimed is called aiming point (TP).

The straight line from the shooter's eye to the aiming point is called aiming line.

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

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

The angle enclosed between the line of sight and the horizon of the weapon is called target elevation angle.

The line joining the departure point with the target is called target line.

The distance from the departure point to the target along the target line is called 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 meeting point.

The angle enclosed between the tangent to the trajectory and the tangent to the surface of the target (ground, obstacles) at the meeting point is called meeting angle.

The shape of the trajectory depends on the magnitude of the elevation angle. As the elevation angle increases, the height of the trajectory and the total horizontal range of the bullet increases. But this happens to a certain 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 is greatest is called farthest angle(the value of this angle is about 35°).

There are flat and mounted trajectories:

1. flat- called the trajectory obtained at elevation angles smaller than the angle of greatest range.

2. hinged- called the trajectory obtained at elevation angles of a large angle of greatest range.

Flat and hinged trajectories obtained by firing from the same weapon at the same initial speed and having the same total horizontal range are called - conjugate.

Rice. 6. Angle of greatest range,

flat, hinged and conjugate trajectories.

The trajectory is flatter if it rises less above the line of the target, and the smaller the angle of incidence. The flatness of the trajectory affects the value of the range of a direct shot, as well as the amount of affected and dead space.

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 has an error in determining the setting of the sight): this is the practical significance of the trajectory.

Topic 3. Information from internal and external ballistics.

The essence of the phenomenon of a shot and its period

A shot is the ejection of a bullet (grenade) from the bore of a weapon by the energy of gases formed during the combustion of a powder charge.

When fired from small arms, the following phenomena occur.

From the impact of the striker on the primer of a live cartridge sent into the chamber, the percussion composition of the primer explodes and a flame forms, which through the seed holes in the bottom of the cartridge case penetrates to the powder charge and ignites it. During the combustion of a powder (combat) charge, a large amount of highly heated gases are formed, which create high pressure in the barrel bore on the bottom of the bullet, the bottom and walls of the sleeve, as well as on the walls of the barrel and the bolt.

As a result of the pressure of gases on the bottom of the bullet, it moves from its place and crashes into the rifling; rotating along them, it moves along the bore with a continuously increasing speed and is thrown outward, in the direction of the axis of the bore. The pressure of gases on the bottom of the sleeve causes the movement of the weapon (barrel) back. From the pressure of gases on the walls of the sleeve and the barrel, they are stretched (elastic deformation), and the sleeve, tightly pressed against the chamber, prevents the breakthrough of powder gases towards the bolt. At the same time, when fired, an oscillatory movement (vibration) of the barrel occurs and it heats up. Hot gases and particles of unburned powder, flowing from the bore after the bullet, when they meet with air, generate a flame and a shock wave; the latter is the source of sound when fired.

When fired from automatic weapons, the device of which is based on the principle of using the energy of powder gases discharged through a hole in the barrel wall (for example, Kalashnikov assault rifles and machine guns, sniper rifle Dragunov, Goryunov easel machine gun), part of the powder gases, in addition, after the bullet passes through the gas outlet, it rushes through it into the gas chamber, hits the piston and throws the piston with the bolt carrier (pusher with bolt) back.

Until the bolt carrier (bolt stem) travels a certain distance to allow the bullet to exit the bore, the bolt continues to lock the bore. After the bullet leaves the barrel, it is unlocked; the bolt frame and the bolt, moving backward, compress the return (back-action) spring; the shutter at the same time removes the sleeve from the chamber. When moving forward under the action of a compressed spring, the bolt sends the next cartridge into the chamber and again locks the bore.

When fired from an automatic weapon, the device of which is based on the principle of using recoil energy (for example, a Makarov pistol, an automatic pistol of Stechkin, an automatic rifle of the 1941 model), the gas pressure through the bottom of the sleeve is transmitted to the bolt and causes the bolt with the sleeve to move back. This movement begins at the moment when the pressure of the powder gases on the bottom of the sleeve overcomes the inertia of the shutter and the force of the reciprocating mainspring. The bullet by this time is already flying out of the bore. Moving back, the bolt compresses the reciprocating mainspring, then, under the action of the energy of the compressed spring, the bolt moves forward and sends the next cartridge into the chamber.

In some types of weapons (for example, the Vladimirov heavy machine gun, the easel machine gun of the 1910 model), under the action of the pressure of powder gases on the bottom of the sleeve, the barrel first moves back along with the bolt (lock) coupled to it.

After passing a certain distance, ensuring the departure of the bullet from the bore, the barrel and bolt disengage, after which the bolt moves to its rearmost position by inertia and compresses (stretches) the return spring, and the barrel returns to the front position under the action of the spring.

Sometimes, after the striker hits the primer, the shot will not follow, or it will happen with some delay. In the first case, there is a misfire, and in the second, a protracted shot. The cause of a misfire is most often dampness of the percussion composition of the primer or powder charge, as well as a weak impact of the striker on the primer. Therefore, it is necessary to protect the ammunition from moisture and keep the weapon in good condition.

A protracted shot is a consequence of the slow development of the process of ignition or ignition of a powder charge. Therefore, after a misfire, you should not immediately open the shutter, as a protracted shot is possible. If a misfire occurs when firing from mounted grenade launcher, wait at least one minute before discharging it.

During the combustion of a powder charge, approximately 25 - 35% of the energy released is spent on communicating the progressive motion of the pool (the main work);

15 - 25% of energy - for secondary work (cutting and overcoming the friction of a bullet when moving along the bore; heating the walls of the barrel, cartridge case and bullet; moving the moving parts of the weapon, gaseous and unburned parts of gunpowder); about 40% of the energy is not used and is lost after the bullet leaves the bore.

The shot occurs in a very short period of time (0.001 0.06 sec). When fired, four consecutive periods are distinguished: preliminary; first, or main; second; the third, or period of aftereffect of gases (see Fig. 30).

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 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 forcing 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 until the moment of complete combustion of the 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 cartridge case), the gas pressure rises rapidly and reaches its highest value (for example, in small arms chambered for sample 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 the rapid increase in the speed 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 about 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 from the moment of complete combustion of the powder charge until the moment the bullet leaves the barrel. With the beginning of this period, the influx of powder gases stops, however, highly compressed and heated gases expand and, putting pressure on the bullet, increase its speed. The pressure drop in the second period occurs quite quickly and at the muzzle - muzzle pressure- is 300 - 900 kg / cm 2 for various types of weapons (for example, for a Simonov self-loading carbine 390 kg / cm 2, for a 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.

For some types of small arms, especially short-barreled ones (for example, the Makarov pistol), there is no second period, since the complete combustion of the powder charge does not actually occur by the time the bullet leaves the barrel.

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

muzzle velocity

Initial speed (v0) called the speed of the bullet at the muzzle of the barrel.

For the initial speed, the conditional speed is taken, which is slightly more than the muzzle and less than the maximum. It is determined empirically with subsequent calculations. The value of the initial velocity of the bullet is indicated in the firing tables and in the combat characteristics of the weapon.

The initial speed is one of the most important characteristics of the combat properties of weapons. With an increase in the initial speed, the range of the bullet, the range of a direct shot, the lethal and penetrating effect of the bullet increases, and the influence of external conditions on its flight also decreases.

The value of the muzzle velocity depends on the length of the barrel; bullet weight; weight, temperature and humidity of the powder charge, shape and size of powder grains and charge density.

The longer the barrel, the longer the powder gases act on the bullet and the greater the initial velocity.

With a constant barrel length and a constant weight of the powder charge, the initial velocity is greater, the lower the weight of the bullet.

A change in the weight of the powder charge leads to a change in the amount of powder gases, and, consequently, to a change in the maximum pressure in the bore and the initial velocity of the bullet. The greater the weight of the powder charge, the greater the maximum pressure and muzzle velocity of the bullet.

The length of the barrel and the weight of the powder charge increase during the design of the weapon to the most rational dimensions.

With an increase in the temperature of the powder charge, the burning rate of the powder increases, and therefore the maximum pressure and initial speed increase. As the charge temperature decreases, the initial speed decreases. An increase (decrease) in initial velocity causes an increase (decrease) in the range of the bullet. In this regard, it is necessary to take into account range corrections for air and charge temperature (charge temperature is approximately equal to air temperature).

With an increase in the humidity of the powder charge, its burning rate and the initial speed of the bullet decrease. The shape and size of the powder have a significant impact on the burning rate of the powder charge, and, consequently, on the muzzle velocity of the bullet. They are selected accordingly when designing weapons.

The charge density is the ratio of the weight of the charge to the volume of the sleeve with the inserted pool (charge combustion chambers). With a deep landing of a bullet, the charge density increases significantly, which can lead to a sharp pressure jump when fired and, as a result, to a rupture of the barrel, so such cartridges cannot be used for shooting. With a decrease (increase) in the charge density, the initial velocity of the bullet increases (decreases).

Weapon recoil and launch angle

recoil called the movement of the weapon (barrel) back during the shot. Recoil is felt in the form of a push to the shoulder, arm or 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 hand-held small arms usually does not exceed 2 kg / m and is perceived by the shooter painlessly.

When firing from an automatic weapon, the device of which is based on the principle of using recoil energy, part of it is spent on communicating movement to moving parts and reloading the weapon. Therefore, the recoil energy when fired from such a weapon is less than when fired from non-automatic weapons or from automatic weapons, the device of which is based on the principle of using the energy of powder gases discharged through a hole in the barrel wall.

The pressure force of powder gases (recoil force) and the recoil resistance force (butt stop, handles, weapon center of gravity, etc.) are not located on the same straight line and are directed in opposite directions. They form a pair of forces, under the influence of which the muzzle of the weapon barrel deviates upward (see Fig. 31).

Rice. 31. Weapon recoil

Throwing the muzzle of the weapon barrel up when fired as a result of recoil.

The magnitude of the deflection of the muzzle of the barrel of a given weapon is the greater, the greater the shoulder of this pair of forces.

In addition, when fired, the barrel of the weapon makes oscillatory movements - it vibrates. As a result of vibration, the muzzle of the barrel at the moment the bullet takes off can also deviate from its original position in any direction (up, down, right, left). The value of this deviation increases with improper use of the firing stop, contamination of the weapon, etc.

For automatic weapons with a gas outlet in the barrel, as a result of gas pressure on the front wall of the gas chamber, the muzzle of the weapon barrel deviates slightly when fired in the direction opposite to the location of the gas outlet.

The combination of the influence of barrel vibration, weapon recoil and other causes leads to the formation of an angle between the direction of the axis of the bore before the shot and its direction at the moment the bullet leaves the bore; this angle is called the departure angle (y). The departure angle is considered positive when the axis of the bore at the time of the bullet's departure is higher than its position before the shot, and negative when it is lower. The value of the departure angle is given in the firing tables.

The influence of the departure angle on firing for each weapon is eliminated when it is brought to normal combat. However, in case of violation of the rules for laying the weapon, using the stop, as well as the rules for caring for the weapon and saving it, the value of the launch angle and the weapon's combat change. To ensure the uniformity of the departure angle and reduce the effect of recoil on the results of shooting, it is necessary to strictly follow the shooting techniques and the rules for caring for weapons specified in the manuals on shooting.

In order to reduce the harmful effect of recoil on the results of firing, in some samples of small arms (for example, the Kalashnikov assault rifle), special devices are used - compensators. The gases flowing out of the bore, hitting the walls of the compensator, somewhat lower the muzzle of the barrel to the left and down.

Features of a shot from hand-held anti-tank grenade launchers

Hand-held anti-tank grenade launchers are dynamo-reactive weapons. When fired from a grenade launcher, part of the powder gases is thrown back through the open breech of the barrel, the resulting reactive force balances the recoil force; the other part of the powder gases puts pressure on the grenade, as in a conventional weapon (dynamic action), and gives it the necessary initial speed.

The reactive force when fired from a grenade launcher is formed as a result of the outflow of powder gases through the breech breech. In this regard, that the area of the bottom of the grenade, which is, as it were, the front wall of the barrel, more area nozzle, blocking the path of gases back, an excess pressure force of powder gases (reactive force) appears, directed in the direction opposite to the outflow of gases. This force compensates for the recoil of the grenade launcher (it is practically absent) and gives the grenade initial speed.

When a grenade jet engine acts in flight, due to the difference in the areas of its front wall and the back wall, which has one or more nozzles, the pressure on the front wall is greater and the generating reactive force increases the speed of the grenade.

The magnitude of the reactive force is proportional to the amount of outflowing gases and the speed of their outflow. The rate of outflow of gases when fired from a grenade launcher is increased with the help of a nozzle (a narrowing and then expanding hole).

Approximately, the value of the reactive force is equal to one tenth of the amount of outflowing gases in one second, multiplied by the speed of their expiration.

The nature of the change in gas pressure in the bore of the grenade launcher is influenced by low loading densities and the outflow of powder gases, therefore, the value of the maximum gas pressure in the grenade launcher barrel is 3-5 times less than in the barrel of small arms. The powder charge of a grenade burns out by the time it leaves the barrel. The charge of the jet engine ignites and burns out when the grenade is flying in the air at some distance from the grenade launcher.

Under the action of the reactive force of the jet engine, the speed of the grenade increases all the time and reaches its maximum value on the trajectory at the end of the outflow of powder gases from the jet engine. Top speed the flight of a grenade is called the maximum speed.

bore wear

In the process of firing, the barrel is subject to wear. The causes of barrel wear can be divided into three main groups - chemical, mechanical and thermal.

As a result of chemical causes, carbon deposits form in the bore, which has big influence for bore wear.

Note. Nagar consists of soluble and insoluble substances. Soluble substances are salts formed during the explosion of the shock composition of the primer (mainly potassium chloride). Insoluble substances of soot are: ash formed during the combustion of a powder charge; tompak, plucked from the shell of a bullet; copper, brass, melted from a sleeve; lead smelted from the bottom of the bullet; iron, melted from the barrel and torn off the bullet, etc. Soluble salts, absorbing moisture from the air, form a solution that causes rust. Insoluble substances in the presence of salts increase rusting.

If, after firing, all the powder deposits are not removed, then the bore for a short time in the places where the chrome is chipped will be covered with rust, after the removal of which traces remain. With the repetition of such cases, the degree of damage to the trunk will increase and may reach the appearance of shells, i.e., significant depressions in the walls of the trunk canal. Immediate cleaning and lubrication of the bore after shooting protects it from rust damage.

The causes of a mechanical nature - impacts and friction of the bullet on the rifling, improper cleaning (cleaning the barrel without using a muzzle lining or cleaning from the breech without a sleeve inserted into the chamber with a hole drilled in its bottom), etc. - lead to erasing of the rifling fields or rounding corners of the rifling fields, especially their left side, chipping and chipping of chrome in the places of the grid of the ramp.

Causes of a thermal nature - heat powder gases, periodic expansion of the bore, and its return to its original state - lead to the formation of a run-up grid and the contents of the surfaces of the walls of the bore in places where the chrome is chipped.

Under the influence of all these reasons, the bore expands and its surface changes, as a result of which the breakthrough of powder gases between the bullet and the walls of the bore increases, the initial velocity of the bullet decreases and the dispersion of bullets increases. To increase the life of the barrel for firing, it is necessary to follow the established rules for cleaning and inspecting weapons and ammunition, to take measures to reduce the heating of the barrel during firing.

The strength of the barrel is the ability of its walls to withstand a certain pressure of powder gases in the bore. Since the pressure of the gases in the bore during the shot is not the same throughout its entire length, the walls of the barrel are made of different thicknesses - thicker in the breech and thinner towards the muzzle. At the same time, the barrels are made of such a thickness that they can withstand pressure 1.3 - 1.5 times the maximum.

Fig 32. Bloating the trunk

If the pressure of the gases for some reason exceeds the value for which the strength of the barrel is calculated, then the barrel may swell or burst.

Bloating of the trunk can occur in most cases from foreign objects (tow, rags, sand) entering the trunk (see Fig. 32). When moving along the bore, the bullet, having met a foreign object, slows down the movement and therefore the space behind the bullet increases more slowly than with a normal shot. But since the burning of the powder charge continues and the flow of gases increases intensively, increased pressure is created at the point where the bullet slows down; when the pressure exceeds the value for which the strength of the barrel is calculated, swelling and sometimes rupture of the barrel is obtained.

Measures to prevent barrel wear

In order to prevent swelling or rupture of the barrel, you should always protect the bore from foreign objects getting into it, be sure to inspect it before shooting and, if necessary, clean it.

With prolonged use of the weapon, as well as with insufficient preparation for firing, an increased gap between the bolt and the barrel may form, which allows the cartridge case to move backward when fired. But since the walls of the sleeve under the pressure of gases are tightly pressed against the chamber and the friction force prevents the movement of the sleeve, it stretches and, if the gap is large, breaks; a so-called transverse rupture of the sleeve occurs.

In order to avoid case ruptures, it is necessary to check the gap size when preparing the weapon for firing (for weapons with gap regulators), keep the chamber clean and not use contaminated cartridges for firing.

The survivability of the barrel is the ability of the barrel to withstand a certain number of shots, after which it wears out and loses its qualities (the spread of bullets increases significantly, the initial speed and stability of the flight of bullets decrease). The survivability of chrome-plated small arms barrels reaches 20 - 30 thousand shots.

The increase in barrel survivability is achieved proper care for weapons and observance of the regime of fire.

The mode of fire is the maximum number of shots that can be fired in a certain period of time without compromising the material part of the weapon, safety and without compromising shooting results. Each type of weapon has its own fire mode. In order to comply with the fire regime, it is necessary to change the barrel or cool it after a certain number of shots. Failure to comply with the fire regime leads to excessive heating of the barrel and, consequently, to its premature wear, as well as to sharp decline shooting results.

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.

Formation of the flight path of a bullet (grenade)

trajectory called a curved line, described by the center of gravity of a bullet (grenade) in flight (see Fig. 33).

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.

Rice. 33. Bullet trajectory (side view)

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.

Rice. 34. Formation of the force of resistance

The force of air resistance is caused by three main causes: air friction, the formation of vortices and the formation of a ballistic wave (see Fig. 34).

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 force of air resistance. The point of application of the resistance force is called 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 150 and an initial speed of 800 m / s. in airless space it would fly to a distance of 32620 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 smoother the surface of the bullet, the lower the friction force and the air resistance force (see Fig. 35).

Rice. 35. The effect of air resistance force on the flight of a bullet:

CG - center of gravity; CA - center 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 does not turn to the right, but down, etc.

Since the action of the air resistance force is continuous, and its direction relative to the bullet changes with each deviation of the bullet axis, the head of the 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, or precessional movement, and the bullet flies with its head part forward, that is, as if following a change in the curvature of the trajectory.

The deviation of a bullet from the plane of fire in the direction of its rotation is called derivation. The axis of slow conical motion lags somewhat behind the tangent to the trajectory (located above the latter) (see Fig. 36).

Rice. 36. Slow conical movement of a bullet

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 cut right) (see Fig. 37).

Rice. 37. Derivation (view of the trajectory from above)

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.

Rice. 38. The effect of the force of air resistance on the flight of a 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 (see Fig. 38).

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 accuracy of fire improves.

To study the trajectory of a bullet (grenade), the following definitions were adopted (see Fig. 39).

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

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.

Rice. 39. Trajectory elements

The angle enclosed between the line of throw and the horizon of the weapon is called the throw angle (6).

The angle enclosed between the line of elevation and the line of throwing is called the departure angle (y).

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 (6).

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

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

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

The highest point of the trajectory is called the top of the path. The shortest distance from the top of the trajectory to the horizon of the weapon is called trajectory height (U).

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

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

A straight line passing 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 aiming line.

The angle enclosed between the line of elevation and the line of sight is called aiming angle (a).

The angle enclosed between the line of sight and the horizon of the weapon is called target elevation angle (E). 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

where e is the elevation angle of the target in thousandths;

AT- excess of the target above the horizon of the weapon in meters; D - firing range in meters.

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

The shortest distance from any point of the trajectory to the line of sight is called exceeding the trajectory above the line of sight.

The line joining the departure point with the target is called target line.

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

The trajectory of a bullet in the air has the following properties: downward branch is shorter and steeper ascending;

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 bullet flight speed when firing at high throwing angles - on the descending branch of the trajectory, and when firing at small throwing angles - at the point of impact;

the time of movement of the bullet along the ascending branch of the trajectory is less than that along the descending one;

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

The trajectory of a grenade in the air can be divided into two sections (see Fig. 40): 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- flight grenades by inertia. The shape of the trajectory of a grenade is about the same as that of a bullet.

Rice. 40. Grenade trajectory (side view)

The shape of the trajectory and its practical significance

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 (see Figure 40).

The elevation angle at which the full horizontal range of a bullet (grenade) becomes the greatest is called farthest angle. The value of the maximum range angle for a bullet of various types of weapons is about 35 degrees.

Trajectories (see Fig. 41) 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 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 at different elevation angles are called conjugated.

Rice. 41. Angle of greatest range, flat, hinged and conjugate trajectories

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.

Example. Compare the flatness of the trajectory when firing from a Goryunov heavy machine gun and a Kalashnikov light machine gun with a 5 sight at a distance of 500 m.

Solution: From the table of excess of average trajectories over the line of sight and the main table, we find that when firing from an easel machine gun at 500 m with a sight 5, the maximum excess of the trajectory over the line of sight is 66 cm and the angle of incidence is 6.1 thousandths; when firing from a light machine gun - respectively 121 cm and 12 thousandths. Consequently, the trajectory of a bullet when firing from an easel machine gun is flatter than the trajectory of a bullet when firing from a light machine gun.

direct shot

The flatness of the trajectory affects the value of the range of a direct shot, struck, covered and dead space.

A shot in which the trajectory does not rise above the aiming line above the target throughout its entire length is called a direct shot (see Fig. 42).

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

The range of a direct shot can be determined from the tables by comparing the height of the target with the values \u200b\u200bof the greatest excess of the trajectory above the line of sight or with the height of the trajectory.

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

Rice. 42. Direct shot

Affected, covered and dead space The distance on the ground during which the descending branch of the trajectory does not exceed the height of the target is called the affected space (the depth of the affected space).

Rice. 43. Dependence of the depth of the affected space on the height of the target and flatness of the trajectory (angle of incidence)

The depth of the affected space depends on the height of the target (it will be the greater, the higher the target), on the flatness of the trajectory (it will be the greater, the flatter the trajectory) and on the angle of the terrain (on the front slope it decreases, on the reverse slope it increases) ( see Fig. 43).

Depth of affected area (Ppr) can determine from the tables the excess of trajectories over the aiming line by comparing the excess of the descending branch of the trajectory by the corresponding firing range with the height of the target, and in the event that the target height is less than 1/3 of the trajectory height - according to the thousandth formula:

where Ppr- depth of the affected space in meters;

Vts- target height in meters;

os is the angle of incidence in thousandths.

Example. Determine the depth of the affected space when firing from the Goryunov heavy machine gun at the enemy infantry (target height 0 = 1.5 m) at a distance of 1000 m.

Decision. According to the table of excesses of average trajectories above the aiming line, we find: at 1000 m, the excess of the trajectory is 0, and at 900 m - 2.5 m (more than the height of the target). Consequently, the depth of the affected space is less than 100 m. To determine the depth of the affected space, we make up the proportion: 100 m corresponds to an excess of the trajectory of 2.5 m; X m corresponds to an excess of the trajectory of 1.5 m:

Since the height of the target is less than the height of the trajectory, the depth of the affected space can also be determined using the thousandth formula. From the tables we find the angle of incidence Os \u003d 29 thousandths.

In the case when the target is located on a slope or there is an elevation angle of the target, the depth of the affected space is determined by the above methods, and the result obtained must be multiplied by the ratio of the angle of incidence to the angle of impact.

The value of the meeting angle depends on the direction of the slope: on the opposite slope, the meeting angle is equal to the sum of the angles of incidence and slope, on the opposite slope - the difference of these angles. In this case, the value of the angle of the meeting also depends on the elevation angle of the target: with a negative angle of the target elevation, the angle of encounter increases by the value of the target elevation angle, with a positive elevation angle of the target it decreases by its value.

The affected space to some extent compensates for the errors made when choosing a sight, and allows you to round the measured distance to the target up.

To increase the depth of the space to be struck on sloping terrain, the firing position must be chosen so that the terrain in the enemy's disposition, if possible, coincides with the continuation of the aiming line.

The space behind a cover that is not penetrated by a bullet, from its crest to the meeting point is called covered space(see fig. 44). The covered space will be the greater, the greater the height of the shelter and the flatter the trajectory.

The part of the covered space in which the target cannot be hit with a given trajectory is called dead (unaffected) space.

Rice. 44. Covered, dead and affected 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 other part of the covered space in which the target can be hit is the hit space.

Depth of covered area (Pp) can be determined from the tables of excess trajectories over the line of sight. By selection, an excess is found that corresponds to the height of the shelter and the distance to it. After finding the excess, the corresponding setting of the sight and the firing range are determined. The difference between a certain range of fire and the range to cover is the depth of the covered space.

Influence of firing conditions on the flight of a bullet (grenade)

The tabular trajectory data corresponds to normal firing conditions.

The following are accepted as normal (table) conditions.

a) Meteorological conditions:

atmospheric (barometric) pressure on the horizon of the weapon 750 mm Hg. Art.;

air temperature on the weapon horizon + 15 WITH;

relative air humidity 50% ( relative humidity is the ratio of the amount of water vapor in the air to most water vapor that can be contained in the air at a given temperature);

there is no wind (the atmosphere is still).

b) Ballistic conditions:

bullet (grenade) weight, muzzle velocity and departure angle are equal to the values indicated in the shooting tables;

charge temperature +15 WITH; the shape of the bullet (grenade) corresponds to the established drawing; the height of the front sight is set according to the data of bringing the weapon to normal combat;

heights (divisions) of the sight correspond to the tabular aiming angles.

c) Topographic conditions:

the target is on the horizon of the weapon;

there is no side slope of the weapon. If the firing conditions deviate from normal, it may be necessary to determine and take into account corrections for the range and direction of fire.

With the increase atmospheric pressure the air density increases, and as a result, the air resistance force increases and the range of the bullet (grenade) decreases. On the contrary, with a decrease in atmospheric pressure, the density and force of air resistance decrease, and the range of the bullet increases. For every 100 m elevation, atmospheric pressure decreases by an average of 9 mm.

When shooting from small arms on flat terrain, range corrections for changes in atmospheric pressure are insignificant and are not taken into account. In mountainous conditions, at an altitude of 2000 m above sea level, these corrections must be taken into account when shooting, guided by the rules specified in the manuals on shooting.

As the temperature rises, the air density decreases, and as a result, the air resistance force decreases and the range of the bullet (grenade) increases. On the contrary, with a decrease in temperature, the density and force of air resistance increase and the range of a bullet (grenade) decreases.

With an increase in the temperature of the powder charge, the burning rate of the powder, the initial speed and range of the bullet (grenade) increase.

When shooting in summer conditions, the corrections for changes in air temperature and powder charge are insignificant and are practically not taken into account; when shooting in winter (under conditions low temperatures) these amendments must be taken into account, guided by the rules specified in the manuals on shooting.

With a tailwind, the speed of the bullet (grenade) relative to the air decreases. For example, if the speed of the bullet relative to the ground is 800 m/s, and the speed of the tailwind is 10 m/s, then the velocity of the bullet relative to the air will be 790 m/s (800-10).

As the speed of the bullet relative to the air decreases, the force of air resistance decreases. Therefore, with a fair wind, the bullet will fly further than with no wind.

With a headwind, the speed of the bullet relative to the air will be greater than with no wind, therefore, the air resistance force will increase and the range of the bullet will decrease.

The longitudinal (tail, head) wind has little effect on the flight of a bullet, and in the practice of shooting from small arms, corrections for such a wind are not introduced. When firing from grenade launchers, corrections for strong longitudinal wind should be taken into account.

Side wind exerts pressure on side surface bullet and deflects it away from the plane of fire depending on its direction: the wind from the right deflects the bullet into left side, wind from left to right.

The grenade on the active part of the flight (when the jet engine is running) deviates to the side where the wind is blowing from: with the wind from the right - to the right, with the wind from the left - to the left. This phenomenon is explained by the fact that the side wind turns the tail of the grenade in the direction of the wind, and the head part against the wind and under the action of a reactive force directed along the axis, the grenade deviates from the firing plane in the direction from which the wind blows. On the passive part of the trajectory, the grenade deviates to the side where the wind blows.

Crosswind has a significant effect, especially on the flight of a grenade (see Fig. 45), and must be taken into account when firing grenade launchers and small arms.

The wind blowing at an acute angle to the firing plane has both an effect on the change in the range of the bullet and on its lateral deflection. Changes in air humidity have little effect on air density and, consequently, on the range of a bullet (grenade), so it is not taken into account when shooting.

When firing with one sight setting (with one aiming angle), but at different target elevation angles, as a result of a number of reasons, including changes in air density at different heights, and therefore the air resistance force / the value of the slant (sighting) flight range changes bullets (grenades).

When firing at large target elevation angles, the slant range of the bullet changes significantly (increases), therefore, when shooting in the mountains and at air targets, it is necessary to take into account the correction for the target elevation angle, guided by the rules specified in the shooting manuals.

scattering phenomenon

When firing from the same weapon, with the most careful observance of the accuracy and uniformity of the shot, each bullet (grenade) due to a number random reasons describes its trajectory and has its own point of fall (meeting point), which does not coincide with others, as a result of which bullets (grenades) are scattered.

The phenomenon of scattering of bullets (grenades) when firing from the same weapon in almost identical conditions is called natural dispersion of bullets (grenades) and also dispersion of trajectories.

The set of trajectories of bullets (grenades obtained as a result of their natural dispersion) is called a sheaf of trajectories (see Fig. 47). The trajectory passing in the middle of the bundle of trajectories is called the middle trajectory. Tabular and calculated data refer to the average trajectory.

The point of intersection of the average trajectory with the surface of the target (obstacle) is called the middle point of impact or the center of dispersion.

The area on which the meeting points (holes) of bullets (grenades) are located, obtained by crossing a sheaf of trajectories with any plane, is called the dispersion area.

The scattering area is usually elliptical in shape. When shooting from small arms at close range, the scattering area in the vertical plane may be in the form of a circle.

Mutually perpendicular lines drawn through the center of dispersion (middle point of impact) so that one of them coincides with the direction of fire are called axes scattering.

The shortest distances from meeting points (holes) to dispersion axes are called deviations

Causes scattering

The causes causing dispersion of bullets (grenades) can be summarized in three groups:

the reasons causing a variety of initial speeds;

reasons causing a variety of throwing angles and shooting directions;

reasons causing a variety of conditions for the flight of a bullet (grenade). The reasons for the variety of initial speeds are:

diversity in the weight of powder charges and bullets (grenades), in the shape and size of bullets (grenades) and shells, in the quality of gunpowder, in the charge density, etc., as a result of inaccuracies (tolerances) in their manufacture; a variety of temperatures, charges, depending on the air temperature and the unequal time spent by the cartridge (grenade) in the barrel heated during firing;

variety in the degree of heating and in the quality condition of the trunk. These reasons lead to fluctuations in the initial speeds, and therefore in the ranges of the bullets (grenades), i.e., they lead to the dispersion of bullets (grenades) in range (height) and depend mainly on ammunition and weapons.

The reasons for the variety of throwing angles and shooting directions are:

variety in horizontal and vertical aiming of weapons (mistakes in aiming);

a variety of launch angles and lateral displacements of the weapon, resulting from a non-uniform preparation for firing, unstable and non-uniform retention of automatic weapons, especially during burst firing, improper use of stops and unsmooth trigger release;

angular vibrations of the barrel when firing automatic fire, arising from the movement and impact of moving parts and the recoil of the weapon.

These reasons lead to the dispersion of bullets (grenades) in the lateral direction and range (height), have the greatest impact on the magnitude of the dispersion area and mainly depend on the skill of the shooter.

The reasons causing a variety of conditions for the flight of a bullet (grenade) are:

variety in atmospheric conditions, especially in the direction and speed of the wind between shots (bursts);

variety in the weight, shape and size of bullets (grenades), leading to a change in the magnitude of the air resistance force.

These reasons lead to an increase in dispersion in the lateral direction and in range (altitude) and mainly depend on the external conditions of firing and ammunition.

With each shot, all three groups of causes act in different combinations. This leads to the fact that the flight of each bullet (grenades) occurs along a trajectory different from the trajectories of other bullets (grenades).

It is impossible to completely eliminate the causes that cause dispersion, therefore, it is impossible to eliminate the dispersion itself. However, knowing the reasons on which the dispersion depends, it is possible to reduce the influence of each of them and thereby reduce the dispersion, or, as they say, increase the accuracy of fire.

Reducing the dispersion of bullets (grenades) is achieved by excellent training of the shooter, careful preparation weapons and ammunition for shooting, skillful application of the rules of shooting, correct preparation for shooting, uniform application, accurate aiming (aiming), smooth trigger release, steady and uniform holding of the weapon when shooting, as well as proper care of weapons and ammunition.

Scattering law

At large numbers shots (more than 20) in the location of the meeting points on the dispersion area, a certain pattern is observed. The scattering of bullets (grenades) obeys the normal law of random errors, which in relation to the dispersion of bullets (grenades) is called the law of dispersion. This law is characterized by the following three provisions (see Fig. 48):

1) Meeting points (holes) on the scattering area are unevenly denser towards the center of dispersion and less often towards the edges of the dispersion area.

2) On the scattering area, you can determine the point that is the center of dispersion (middle point of impact). Relative to which the distribution of meeting points (holes) symmetrical: the number of meeting points on both sides of the scattering axes, consisting in equal absolute value limits (bands), the same, and each deviation from the scattering axis in one direction corresponds to the same deviation in the opposite direction.

3) The meeting points (holes) in each particular case do not occupy an unlimited, but a limited area.

Thus, the scattering law in general form can be formulated as follows: with a sufficiently large number of shots fired under practically identical conditions, the dispersion of bullets (grenades) is uneven, symmetrical and not limitless.

Rice. 48. Scattering pattern

Definition middle point hits

With a small number of holes (up to 5), the position of the midpoint of the hit is determined by the method of successive division of the segments (see Fig. 49). For this you need:

Rice. 49. Determination of the position of the midpoint of the hit by the method of successive division of segments: a) By 4 holes, b) By 5 holes.

connect two holes (meeting points) with a straight line and divide the distance between them in half;

connect the resulting point with the third hole (meeting point) and divide the distance between them into three equal parts;

since the holes (meeting points) are located more densely towards the dispersion center, the division closest to the first two holes (meeting points) is taken as the middle point of hit of the three holes (meeting points); the found middle point of impact for three holes (meeting points) is connected with the fourth hole (meeting point) and the distance between them is divided into four equal parts;

the division closest to the first three holes (meeting points) is taken as the midpoint of the four holes (meeting points).

For four holes (meeting points), the middle point of impact can also be determined as follows: connect the adjacent holes (meeting points) in pairs, connect the midpoints of both lines again and divide the resulting line in half; the division point will be the mid-point of impact. If there are five holes (meeting points), the average point of impact for them is determined in a similar way.

Rice. 50. Determining the position of the midpoint of the hit by drawing dispersion axes. BBi- axis of scattering in height; BBi- dispersion axis in the lateral direction

With a large number of holes (meeting points), based on the symmetry of dispersion, the average point of impact is determined by the method of drawing the axes of dispersion (see Fig. 50). For this you need:

count the right or left half of the breakdowns and (meeting points) in the same order and separate it with the dispersion axis in the lateral direction; the intersection of the dispersion axes is the midpoint of impact. The mid-point of impact can also be determined by the method of calculation (calculation). for this you need:

draw a vertical line through the left (right) hole (meeting point), measure the shortest distance from each hole (meeting point) to this line, add up all the distances from the vertical line and divide the sum by the number of holes (meeting points);

draw a horizontal line through the lower (upper) hole (meeting point), measure the shortest distance from each hole (meeting point) to this line, add up all the distances from the horizontal line and divide the sum by the number of holes (meeting points).

The resulting numbers determine the distance of the midpoint of impact from the specified lines.

The probability of hitting and hitting the target. The concept of the reality of shooting. The reality of the shooting

In the conditions of a fleeting tank firefight, as already mentioned, it is very important to inflict the greatest losses on the enemy in the shortest time and with minimal ammunition consumption.

There is a concept shooting reality, characterizing the results of firing and their compliance with the assigned fire task. In combat conditions, a sign of the high reality of shooting is either the visible defeat of the target, or the weakening of the enemy’s fire, or its violation. order of battle, or the departure of manpower to the shelter. However, the expected reality of the shooting can be assessed even before the opening of fire. To do this, the probability of hitting the target, the expected consumption of ammunition to obtain the required number of hits, and the time required to solve the fire mission are determined.

Hit Probability- this is a value that characterizes the possibility of hitting a target under certain firing conditions and depends on the size of the target, the size of the dispersion ellipse, the position of the average trajectory relative to the target, and, finally, the direction of fire relative to the front of the target. It is expressed either as a fractional number or as a percentage.

The imperfection of human vision and sighting devices does not allow, after each shot, the barrel of the weapon to be ideally accurately restored to its previous position. Dead moves and backlash in the guidance mechanisms also cause the displacement of the barrel of the weapon at the time of the shot in the vertical and horizontal planes.

As a result of the difference in the ballistic shape of the projectiles and the state of its surface, as well as the change in the atmosphere during the time from shot to shot, the projectile can change the direction of flight. And this leads to dispersion both in range and in direction.

With the same dispersion, the probability of hitting, if the center of the target coincides with the center of dispersion, the greater, the more larger size goals. If, however, shooting is carried out at targets of the same size and the average trajectory passes through the target, the probability of hitting is greater, the smaller the dispersion area. The probability of hitting the higher, the closer the center of dispersion is located to the center of the target. When firing at targets that have a large extent, the probability of hitting is higher if the longitudinal axis of the dispersion ellipse coincides with the line of the greatest extent of the target.

In quantitative terms, the probability of hitting can be calculated different ways, including the dispersion core, if the target area does not go beyond its limits. As already noted, the dispersion core contains the best (in terms of accuracy) half of all holes. Obviously, the probability of hitting the target will be less than 50 percent. as many times as the area of the target is less than the area of the core.

The area of the dispersion core is easy to determine from the special shooting tables available for each type of weapon.

The number of hits required to reliably hit a particular target is usually a known value. So, one direct hit is enough to destroy an armored personnel carrier, two or three hits are enough to destroy a machine-gun trench, etc.

Knowing the probability of hitting a particular target and the required number of hits, it is possible to calculate the expected consumption of projectiles to hit the target. So, if the probability of hitting is 25 percent, or 0.25, and three direct hits are needed to reliably hit the target, then to find out the consumption of shells, the second value is divided by the first.

The balance of time during which the firing task is performed includes the time for preparing the firing and the time for the firing itself. The time for preparing the shooting is determined practically and depends not only on design features weapons, but also the training of the shooter or crew members. To determine the time to fire, the amount of expected ammunition consumption is divided by the rate of fire, i.e., by the number of bullets, shells fired per unit of time. To the figure thus obtained, add the time to prepare for shooting.