Ballistic bullet trajectory. internal ballistics. Barrier and wound ballistics

The basic concepts are presented: periods of a shot, elements of the trajectory of a bullet, a direct shot, etc.

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

Internal ballistics

Internal ballistics studies the phenomena occurring in the bore during the shot, the movement of the projectile along the bore, the nature of the thermo- and aerodynamic dependences accompanying this phenomenon, both in the bore and outside it during the aftereffect of powder gases.
Internal ballistics solves the most rational use the energy of the powder charge during the shot so that the projectile given weight and caliber to report a certain initial speed (V0) while respecting the strength of the barrel. This gives the input for external ballistics and weapon design.

Shot is called the ejection of a bullet (grenade) from the bore of a weapon by the energy of gases formed during the combustion of a powder charge.
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 is formed, which through the seed holes in the bottom of the cartridge case penetrates to the powder charge and ignites it. When a powder (combat) charge is burned, a 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 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.
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 - sniper rifle Dragunov, part of the powder gases, in addition, after passing through it into the gas chamber, hits the piston and throws the pusher with the shutter back.
During the combustion of a powder charge, approximately 25-35% of the energy released is spent on communicating the bullet forward movement(main job); 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 part of the weapon, the gaseous and unburned part of the gunpowder); about 40% of the energy is not used and is lost after the bullet leaves the bore.

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

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

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

First or main period lasts from the beginning of the movement of the bullet to the moment complete combustion powder charge. During this period, the combustion of the powder charge occurs in a rapidly changing volume. At the beginning of the period, when the speed of the bullet along the bore is still low, the amount of gases grows faster than the volume of the bullet space (the space between the bottom of the bullet and the bottom of the case), the gas pressure rises rapidly and reaches largest- rifle cartridge 2900 kg / cm2. This pressure is called maximum pressure. It is created by small arms when the bullet passes 4 - 6 cm of the path. Then due to fast speed movement 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 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 until the moment of complete combustion of the powder charge until the moment the bullet leaves the bore. With the beginning of this period, the influx of powder gases stops, however, highly compressed and heated gases expand and, putting pressure on the bullet, increase its speed. The decrease in pressure in the second period occurs quite quickly and at the muzzle, the muzzle pressure is 300 - 900 kg / cm2 for various types of weapons. The speed of the bullet at the time of its departure from the bore (muzzle velocity) is somewhat less than the initial velocity.

The third period, or the period after the action 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.

The muzzle velocity of a bullet and its practical significance

initial speed 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 combat properties of weapons. With an increase in the initial speed, the range of the bullet increases, the range direct shot, lethal and penetrating action of a bullet, and also the influence of external conditions for her flight. The muzzle velocity of a bullet depends on:

barrel length
bullet weight
weight, temperature and humidity of the powder charge
shape and size of powder grains
loading density

The longer the trunk topics more time powder gases act on the bullet and the greater the initial velocity. With a constant barrel length and constant weight powder charge, the initial velocity is greater, the lower the weight of the bullet.
Powder charge weight change 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. How more weight powder charge, the greater the maximum pressure and muzzle velocity of the bullet.
With an increase in the temperature of the powder charge the burning rate of gunpowder increases, and therefore the maximum pressure and initial speed increase. When the charge temperature drops initial speed is reduced. 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 increasing moisture content of the powder charge the speed of its burning and the initial speed of the bullet are reduced.
Shapes and sizes of gunpowder have a significant effect on the burning rate of the powder charge, and consequently, on the initial velocity of the bullet. They are selected accordingly when designing weapons.
Loading density is the ratio of the weight of the charge to the volume of the sleeve with the inserted pool (charge combustion chamber). With a deep landing of a bullet, the loading 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 loading density, the initial velocity of the bullet increases (decreases).
recoil is called the movement of the weapon back during the shot. Recoil is felt in the form of a push to the shoulder, arm or ground. The recoil action of the weapon is about as many times less than the initial velocity 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.

The recoil force and the recoil resistance force (butt stop) 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. The amount of deflection of the muzzle of the barrel this weapon the more than more shoulder 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 magnitude of this deviation increases with improper use of the firing stop, contamination of the weapon, etc.
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.
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 influence of the departure angle on shooting is eliminated when it is brought to normal combat. However, in case of violation of the rules for laying weapons, using the stop, as well as the rules for caring for weapons and saving them, the value of the departure angle and the weapon’s combat change. In order to reduce the harmful effect of recoil on the results of shooting, compensators are used.
So, the phenomena of a shot, the initial velocity of a bullet, the recoil of a weapon have great importance when shooting and affect the flight of the bullet.

External ballistics

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

Bullet trajectory and its elements. Trajectory properties. Types of trajectory and their practical significance

trajectory called the curved line described by the center of gravity of the bullet in flight.
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. With an increase in the elevation angle, the height of the trajectory and the total horizontal range bullets increase, but this happens 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 greatest is called the angle longest range. The value of the angle of greatest range for bullets various kinds weapons is about 35 °.

Trajectories obtained at elevation angles, smaller angle longest 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 and swarms of different elevation angles are called conjugated.

When shooting from small arms, only flat trajectories are used. How flatter 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 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 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.
Full time flight- the time of movement of a bullet (grenade) from the point of departure to the point of impact.
Top of the path - highest point trajectories over 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.

Direct shot, hit and dead space most closely related to issues of shooting practice. The main task of studying these issues is to obtain a solid knowledge in the use of a direct shot and the space to be struck to perform fire missions in combat.

Direct shot its definition and practical use in a combat situation

A shot in which the trajectory does not rise above the aiming line above the target for its entire length is called direct shot. 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, 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 tables by comparing the height of the target with the values of the greatest excess of the trajectory above the line of sight or with the height of the trajectory.

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

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

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

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.

The distance on the ground during which the descending branch of the trajectory does not exceed the height of the target, called the affected space(the depth of the affected space).
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).
The depth of the affected space can be determined from the tables of the excess of the trajectory above 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 if the target height is less than 1/3 of the trajectory height, then in the form of a thousandth.
To increase the depth of the space to be struck on sloping terrain, the firing position must be chosen so that the terrain in the enemy's disposition coincides, if possible, with the aiming line. Covered space its definition and practical use in a combat situation.

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

The space behind a cover that is not penetrated by a bullet, from its crest to the meeting point is called covered space.
The covered space will be the greater, the greater the height of the shelter and the flatter the trajectory. The depth of the covered space can be determined from the tables of excess trajectory 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.

Dead space of its definition and practical use in a combat situation

The part of the covered space in which the target cannot be hit with a given trajectory is called dead (not affected) space.
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. The depth of the dead space is equal to the difference between the covered and affected space.

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

The phenomenon of derivation

Due to the simultaneous impact on the bullet rotary motion, giving it a stable position in flight, and air resistance, tending to tip the bullet head back, the axis of the bullet deviates from the direction of flight in the direction of rotation. As a result, the bullet encounters air resistance on more than one of its sides and therefore deviates from the firing plane more and more in the direction of rotation. Such a deviation of a rotating bullet away from the plane of fire is called derivation. This is a rather complex physical process. The derivation increases disproportionately to the flight distance of the bullet, as a result of which the latter takes more and more to the side and its trajectory in plan is a curved line. With the right cut of the barrel, the derivation takes the bullet to the right side, with the left - to the left.

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

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

1.1.1. Shot. Shot periods and their characteristics.

Shot is called 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 phenomenon occurs. 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 sleeve penetrates to the powder charge and ignites it. When the charge is burned, a large amount of highly heated gases are formed, which create 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 bottom of the bullet, it moves from its place and crashes into the rifling - rotating along them, it moves along the bore at a continuously increasing speed and is thrown out.

During the combustion of a powder charge, approximately 25-35% of the energy released is spent on communicating the progressive motion to the pool (the main work); 15-25% of energy - to perform 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(fig.116):

Preliminary;

First or main;

The 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 barrel. During this period, gas pressure is created in the barrel bore, which is necessary in order to move the bullet from its place and overcome the resistance of its shell to cutting into the rifling of the barrel. This pressure is called boost pressure. It reaches 250-500 kg/cm, depending on the rifling device, the weight of the bullet and the hardness of its shell. It is assumed that the combustion of the powder charge in this period occurs in a constant volume, the shell cuts into the rifling instantly, and the movement of the bullet begins immediately when the forcing pressure is reached in the bore.

At the beginning of the period, when the speed of the bullet along the bore is still low, the number of cores grows faster than the volume of the bullet space (the space between the bottom of the bullet and the bottom of the case), the gas pressure rises rapidly and reaches its maximum value. This pressure is called maximum pressure. It is created in small arms when a bullet passes 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 approximately 2/3 of the maximum pressure. The speed of the bullet is constantly increasing and by the end of the period reaches approximately 3/4 of the initial speed. The powder charge completely burns out shortly before the bullet leaves the bore.

The second period lasts from the moment of complete combustion of the powder charge until the moment the bullet leaves the bore. With the beginning of this period, the influx of powder gases stops, however, highly compressed and heated gases expand and, putting pressure on the bullet, increase its speed. The pressure drop in the second period occurs quite quickly and at the muzzle - the muzzle pressure - for various types of weapons is 300-900 kg/cm. 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.

Rice. 116 - Shot periods

The third period, or the period of aftereffect of gases, lasts from the moment the bullet leaves the bore until the moment the action of powder gases on the bullet ceases. During this period, the powder gases flowing out of the bore at a speed of 1200-2000 m/s continue to act on the bullet and impart additional speed to it. The bullet reaches its maximum (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.

1.1.2. Initial and maximum speed.

muzzle velocity(v o) - the speed of the bullet at the muzzle of the barrel.

For initial speed the conditional speed is accepted, 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 muzzle velocity of a bullet depends on:

1) Barrel length.

2) Bullet weight.

3) Weight, temperature and humidity of the powder charge, the shape and size of the powder grains and loading density.

1) The longer the barrel, the longer the powder gases act on the bullet and the greater the muzzle velocity of the bullet.

2) 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.

3) 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 increases when designing weapons to the most rational sizes.

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. When the temperature of the charge decreases, the initial velocity decreases. An increase (decrease) in the 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 hence on the muzzle velocity of the bullet. They are selected accordingly when designing weapons.

Loading density is the ratio of the weight of the charge to the volume of the sleeve with the inserted pool (charge combustion chamber). With a deep landing of a bullet, the loading 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 when firing. With a decrease (increase) in the loading density, the initial velocity of the bullet increases (decreases).

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.

1.1.3 Weapon recoil and takeoff angle (Fig. 117).

Recoil is 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 kgm 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. Recoil energy is generated when firing from such 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.

The magnitude of the deviation 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.

In an automatic weapon 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, when fired, deviates somewhat 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.

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 influence of the departure angle on firing for each weapon is eliminated when it is set to normal combat.

In order to reduce the harmful effect of recoil on the results of shooting, some types of small arms (for example, the Kalashnikov assault rifle) use special devices - 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.

1.2. Basic terms and concepts of the theory of external ballistics

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

1.2.1 Bullet flight path and its elements

trajectory called a curved line, described by the center of gravity of a bullet (grenade) in flight (Fig. 118) .

A bullet (grenade) when flying in the air is subjected to two forces :

gravity

Forces of resistance.

The force of gravity causes the bullet (grenade) to gradually drop, 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 line in shape.

Air resistance to the flight of a bullet (grenade) is caused by the fact that air is an elastic medium and therefore part of the energy of the bullet is expended on movement in this medium.

The force of air resistance is caused by three main reasons (Fig. 119):

1) Air friction.

2) The formation of swirls.

3) The formation of a ballistic wave.

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

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

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 to the side 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 on creating this wave.

The resultant (total) of all forces, formed due to the influence of air on the flight of a bullet (grenade), is the force of air resistance. The point of application of the resistance force is called the center of resistance. The effect of the resistance force on the flight of a bullet (grenade) is very large. It causes a decrease in the speed and range of a bullet (grenade).

To study the trajectory of a bullet (grenade), the following definitions were adopted (Fig. 120)

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

2) The horizontal plane passing through the departure point, called the weapon horizon. 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.

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

4) The vertical plane passing through the line of elevation, called the shooting plane.

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

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

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

8) The angle enclosed between the line of elevation and the line of throwing , is called the departure angle.

9) Point of intersection of the trajectory with the horizon of the weapon called the drop point.

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

11) Distance from departure point to drop point is called the total horizontal range.

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

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

14) The highest point of the trajectory called the vertex of the trajectory.

15) The part of the trajectory from the departure point to the top is called the ascending branch; part of the trajectory from the top to the point of impact is called the outgoing branch of the trajectory.

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

17) 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, called the line of sight.

18) The angle enclosed between the line of elevation and the line of sight, called the aiming angle.

19) The angle enclosed between the aiming line and the horizon of the weapon, called the elevation angle of the target.

20) Distance from the point of departure to the intersection of the trajectory with the line of sight called the target range.

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

23) Distance from the departure point to the target along the target line called slant range.

24) Point of intersection of the trajectory with the surface of the target (land, obstacles) called the meeting point.

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

The trajectory of a bullet in the air has the following properties:

The descending branch is shorter and steeper than the ascending one;

The angle of incidence is greater than the angle of throw;

The final speed of the bullet is less than the initial one;

The lowest speed of a bullet when firing at high angles of throw - at

descending branch of the trajectory, and when firing at small throwing angles - at the point

The time of movement of the bullet on the ascending branch of the trajectory is less than on the descending one.

1.2.2. The shape of the trajectory and its practical significance(Fig. 121)

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.

Elevation angle, at which the full horizontal range of the bullet (grenade) becomes the greatest, called the angle of greatest range. The value of the angle of greatest range for bullets of various types of weapons is about 35 degrees.

Rice. 121 Trajectory shapes

Trajectories obtained with elevation angles less than the angle of greatest range, called flat.

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

When firing from the same weapon (at the same initial speeds), you can get two trajectories with the same horizontal range: flat and mounted

Trajectories having the same horizontal range at different elevation angles, are called conjugate.

When firing from small arms and grenade launchers, only flat trajectories are used .

The flatter the trajectory, the greater the extent of the terrain, the target can be hit with one sight setting (the less impact on the result of shooting is caused by errors in determining the sight setting).

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 flat trajectory affects the value of the range of a direct shot, the affected, covered and dead space.

1.2.3. Direct shot (Fig. 122).

direct shot- a shot in which the trajectory does not rise above the aiming line above the target throughout its entire length.

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:

target heights;

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.

1.2.4. Affected space (depth of the affected space) (Fig. 123).

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 is at

some area will not be affected with the same installation of the sight. 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.

Affected space (depth of the affected space) - the distance on the ground during which the descending branch of the trajectory does not exceed the height of the target.

The depth of the affected space depends on:

From the height of the target (it will be the higher, the higher the target);

From the flatness of the trajectory (it will be the greater, the flatter

trajectory);

From the angle of inclination of the terrain (on the front slope it decreases, on the reverse slope

increases).

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 reverse slope - the difference of these angles;

In this case, the value of the meeting angle also depends on the elevation angle of the target:

With a negative elevation angle of the target, the meeting angle increases by the magnitude of the 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.

1.2.5. Covered space (Fig. 123).

covered space- the space behind the shelter, not penetrated by a bullet, from its crest to the meeting point.

The covered space will be the greater, the greater the height of the shelter and the flatter the trajectory.

Dead (unaffected) space- part of the covered space in which the target cannot be hit with a given trajectory.

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.

The depth of the covered space (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 firing range is determined. The difference between a certain range of fire and the range to cover is the depth of the covered space.

The depth of the dead space is equal to the difference between the covered and affected space.

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

Rice. 123 - Covered, dead and affected space

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

The following are accepted as normal (table) conditions:

A) Meteorological conditions:

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

The air temperature on the horizon of the weapon is + 15 degrees. WITH. ;

Relative Humidity air 50% (relative humidity

is the ratio of the amount of water vapor in the air to

the largest amount of 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 deg. S.;t

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; - the height (divisions) of the sight correspond to the tabular aiming angles.

C) Topographic conditions:

The target is on the weapon's horizon;

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.

Influence of atmospheric pressure

1) With magnification atmospheric pressure the air density increases, and as a result, the air resistance force increases and the range of the bullet (grenade) decreases.

2) With a decrease in atmospheric pressure, the density and force of air resistance decrease, and the range of the bullet increases.

Temperature effect

1) As the temperature rises, the air density decreases, and as a result, the air resistance force decreases and the range of the bullet increases.

2) 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.

Wind influence

1) With a tailwind, the speed of a bullet (grenade) relative to the air decreases. With a decrease in the speed of the bullet relative to the air, the air resistance force decreases. Therefore, with a tailwind, the bullet will fly further than with no wind.

2) 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 a grenade launcher, corrections for a strong longitudinal wind should be taken into account.

3) Crosswind exerts pressure on side surface bullets and deflects it away from the firing plane depending on its direction. Crosswind has a significant effect, especially on the flight of a grenade, and must be taken into account when firing grenade launchers and small arms.

4) The wind blowing at an acute angle to the plane of fire, simultaneously affects both the change in the range of the bullet and its lateral deviation.

Influence of air humidity

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.

Influence of sight installation

When firing with one sight setting (with one aiming angle), but at different target elevation angles, as a result of a number of reasons, incl. Changes in air density at different heights, and, consequently, the air resistance force, change the value of the oblique (sighting range of a bullet (grenade).

When firing at small target elevation angles (up to +_ 15 degrees), this bullet (grenade) flight range changes very slightly, therefore, equality of the inclined and full horizontal bullet flight range is allowed, i.e. the invariance of the shape (rigidity) of the trajectory (Fig. 124).

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

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

The inertia of a bullet is formed while it is in the bore. Under the action of the energy of powder gases, the bullet is given the speed and direction of translational motion. And if external forces did not act on it, then according to the first law of Galileo - Newton, it would rectilinear motion in a given direction at a constant speed to infinity. In this case, in every second it would pass a distance equal to the initial speed of the bullet (see Fig. 8).

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

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

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

and air resistance)

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

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

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

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

under the influence of gravity

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

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

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

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

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

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

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

Rice. 11. Causes of air resistance

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

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

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

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

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

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

Rotation of a bullet around its axis

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

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

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

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

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

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

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

Bullet rotation speed can be calculated by the formula:

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

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

Rice. 14. Conical rotation of the bullet head

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

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

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

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

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

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

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

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

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

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

Bullet trajectory characteristics

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

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

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

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

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

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

Rice. 17. Bullet trajectory indicators

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

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

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

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

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

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

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

Full horizontal range is the distance from the point of departure to the point of impact.

The vertex of the trajectory is its highest point.

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

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

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

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

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

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

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

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

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

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

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

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

Table 1

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

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

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

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

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

Aiming (weapon aiming)

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

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

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

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

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

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

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

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

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

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

Bullet trajectory shape and its practical significance

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

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

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

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

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

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

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

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

The flight paths of a bullet that occur at angles of throw smaller than the angle of greatest range are called flat.

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

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

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

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

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

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

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

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

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

Rice. 20. Features of the use of hinged trajectories

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

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

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

Rice. 21. Direct shot

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

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

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

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

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

height equal to segment AB

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

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

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

Thus, the depth of the dead space is the difference between the covered and affected space.

Rice. 23. Covered, dead and affected space

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Shot periodization

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

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

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

First or main period lasts from the beginning of the movement of the bullet 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 under 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 speed of the movement of the bullet, the volume of the bullet space increases faster than the influx of new gases, and the pressure begins to fall, by the end of the period it is equal to approximately 2/3 of the maximum pressure. The speed of the bullet is constantly increasing and by the end of the period reaches approximately 3/4 of the initial speed. The powder charge completely burns out shortly before the bullet leaves the bore.

Second period lasts until the moment of complete combustion of the powder charge until the moment the bullet leaves the bore. With the beginning of this period, the influx of powder gases stops, however, highly compressed and heated gases expand and, putting pressure on the bullet, increase its speed. The pressure drop in the second period occurs quite quickly and at the muzzle, the muzzle pressure is 300 - 900 kg / cm 2 for various types of weapons (for example, for the Simonov self-loading carbine - 390 kg / cm 2, for the Goryunov easel machine gun - 570 kg / cm 2 ). The speed of the bullet at the time of its departure from the bore (muzzle velocity) is somewhat less than the initial velocity.

The basic concepts are presented: periods of a shot, elements of the trajectory of a bullet, a direct shot, etc.

Internal ballistics

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

Shot is called the ejection of a bullet (grenade) from the bore of a weapon by the energy of gases formed during the combustion of a powder charge.
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 is formed, 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 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.
When fired from an automatic weapon, the device of which is based on the principle of using the energy of powder gases discharged through a hole in the barrel wall - a Dragunov sniper rifle, part of the powder gases, in addition, after passing through it into the gas chamber, hits the piston and discards the pusher with the shutter back.
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 part of the weapon, the gaseous and unburned part of the gunpowder); about 40% of the energy is not used and is lost after the bullet leaves the bore.

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

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

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 quickly rises and reaches its highest value - a rifle cartridge of 2900 kg / cm2. 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 speed of the movement of the bullet, the volume of the bullet space increases faster than the influx of new gases, and the pressure begins to fall, by the end of the period it is equal to approximately 2/3 of the maximum pressure. The speed of the bullet is constantly increasing and by the end of the period reaches approximately 3/4 of the initial speed. The powder charge completely burns out shortly before the bullet leaves the bore.

The muzzle velocity of a bullet and its practical significance

initial speed 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 muzzle velocity of a bullet depends on:

barrel length
bullet weight
weight, temperature and humidity of the powder charge
shape and size of powder grains
loading density

The longer the trunk 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.
Powder charge weight change 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.
With an increase in the temperature of the powder charge the burning rate of gunpowder increases, and therefore the maximum pressure and initial speed increase. When the charge temperature drops initial speed is reduced. 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 increasing moisture content of the powder charge the speed of its burning and the initial speed of the bullet are reduced.
Shapes and sizes of gunpowder have a significant effect on the burning rate of the powder charge, and consequently, on the initial velocity of the bullet. They are selected accordingly when designing weapons.
Loading density is the ratio of the weight of the charge to the volume of the sleeve with the inserted pool (charge combustion chamber). With a deep landing of a bullet, the loading 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 loading density, the initial velocity of the bullet increases (decreases).
recoil is called the movement of the weapon back during the shot. Recoil is felt in the form of a push to the shoulder, arm or ground. The recoil action of the weapon is about as many times less than the initial velocity 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.

The recoil force and the recoil resistance force (butt stop) 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. The magnitude of the deviation 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 magnitude of this deviation increases with improper use of the firing stop, contamination of the weapon, etc.
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.
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 influence of the departure angle on shooting is eliminated when it is brought to normal combat. However, in case of violation of the rules for laying weapons, using the stop, as well as the rules for caring for weapons and saving them, the value of the departure angle and the weapon’s combat change. In order to reduce the harmful effect of recoil on the results of shooting, compensators are used.
So, the phenomena of a shot, the initial velocity of a bullet, the recoil of a weapon are of great importance when shooting and affect the flight of a bullet.

External ballistics

Bullet trajectory and its elements. Trajectory properties. Types of trajectory and their practical significance

trajectory called the curved line described by the center of gravity of the bullet in flight.
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 an 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 of greatest angle of greatest range are called mounted. When firing from the same weapon (at the same initial speeds), you can get two trajectories with the same horizontal range: flat and mounted. Trajectories having the same horizontal range and swarms of different elevation angles are called conjugated.

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

A direct shot, hit and dead space are most closely related to issues of shooting practice. The main task of studying these issues is to obtain a solid knowledge in the use of a direct shot and the space to be struck to perform fire missions in combat.

Direct shot its definition and practical use in a combat situation

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

The distance on the ground during which the descending branch of the trajectory does not exceed the height of the target, called the affected space(the depth of the affected space).
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).
The depth of the affected space can be determined from the tables of the excess of the trajectory above 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 if the target height is less than 1/3 of the trajectory height, then in the form of a thousandth.
To increase the depth of the space to be struck on sloping terrain, the firing position must be chosen so that the terrain in the enemy's disposition coincides, if possible, with the aiming line. Covered space, its definition and practical use in a combat situation.

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

Dead space of its definition and practical use in a combat situation

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

The phenomenon of derivation

Due to the simultaneous impact on the bullet of a rotational movement, which gives it a stable position in flight, and air resistance, which tends to tip the bullet head back, the axis of the bullet deviates from the direction of flight in the direction of rotation. As a result, the bullet encounters air resistance on more than one of its sides and therefore deviates from the firing plane more and more in the direction of rotation. Such a deviation of a rotating bullet away from the plane of fire is called derivation. This is a rather complex physical process. The derivation increases disproportionately to the flight distance of the bullet, as a result of which the latter takes more and more to the side and its trajectory in plan is a curved line. With the right cut of the barrel, the derivation takes the bullet to the right side, with the left - to the left.

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

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