A straight line that is a continuation of the axis of the bore. Sniper training. Internal and external ballistics. Dead space of its definition and practical use in a combat situation

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 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 forms, 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 - the Dragunov sniper rifle, part of the powder gases, in addition, after passing through it into the gas chamber, hits the piston and throws the pusher with the bolt 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 topple it. As a result of the action of these forces, the bullet's flight speed gradually decreases, and its trajectory is an unevenly curved curved line in shape. Air resistance to the flight of a bullet is caused by the fact that air is elastic medium and therefore part of the energy of the bullet is expended on movement in this medium.

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

The angle of elevation at which the full horizontal range of the bullet is 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 setting of the sight): this is practical value trajectories.
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.

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

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 "crown", 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 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 through right choice firing positions and shelling targets from weapons with a more hinged 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 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 - 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.

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 due to 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 flight path of a bullet in the air is always longer and flatter than the descending one; when shooting at medium distances, the ratio of the length of the ascending branch of the trajectories to the length of the descending one is conditionally taken as 3: 2 (see Fig. 12).

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

Rotation of a bullet around its axis

When a bullet is flying in the air, the force of its resistance constantly strives to overturn it. It manifests itself in the following way. The bullet, moving by inertia, constantly strives to maintain the position of its axis, given direction barrel of the weapon. At the same time, under the influence of gravity, the direction of the bullet's flight constantly deviates from its axis, which is characterized by an increase in the angle between the axis of the bullet and the tangent to 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 sniper rifle Dragunov - about 2600 rpm.

Bullet rotation speed can be calculated by the formula:

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

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

Rice. 14. Conical rotation of the bullet head

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

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

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

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

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

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

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

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

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

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

Bullet trajectory characteristics

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

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

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

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

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

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

Rice. 17. Bullet trajectory indicators

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

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

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

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

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

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

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

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

colspan=2bgcolor=white>0

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 barrel bore, an aiming angle corresponding to the distance to the target is formed in the vertical plane, 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 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 trajectory of a bullet with lower speed characteristics will also be located below the trajectory of a faster bullet, and under the influence of gravity, it will drop faster in time and closer in distance from the point of departure to the level of the weapon’s horizon.

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

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

To successfully master the technique of shooting from any small arms, it is necessary to master the knowledge of the laws of ballistics and a number of basic concepts related to it. Not a single sniper could and does not do without this, and without studying this discipline, a sniping training course is of little use.

Ballistics is the science of the movement of bullets and projectiles fired from small arms when fired. Ballistics is subdivided into external And internal.

Internal ballistics

Internal ballistics studies the processes occurring in the bore of a weapon during a shot, the movement of a bullet along the bore and the aero- and thermodynamic dependences accompanying this phenomenon both in the bore and outside it until the end of the aftereffect of powder gases.

Besides, internal ballistics studies the issues of the most rational use of the energy of a powder charge during a shot in order to give a bullet of a given caliber and weight an optimal initial speed while respecting the strength of the weapon barrel: this provides initial data both for external ballistics and for weapon design.

Shot

Shot- this is the ejection of a bullet from the bore of a weapon under the influence of the energy of gases formed during the combustion of the powder charge of the cartridge.

Shot dynamics. When the striker hits the primer of a live cartridge sent into the chamber, the percussion composition of the primer explodes, and a flame is formed, which is transmitted through the seed holes in the bottom of the sleeve to the powder charge and ignites it. With the simultaneous combustion of a combat (powder) charge, a large amount of heated powder 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 bore and the bolt.

Under strong pressure of powder gases on the bottom of the bullet, it is separated from the cartridge case and crashes into the channels (rifling) of the weapon barrel and, rotating along them at a constantly increasing speed, is thrown outward in the direction of the axis of the barrel bore.

In turn, the pressure of gases on the bottom of the sleeve causes the movement of the weapon (the barrel of the weapon) back: this phenomenon is called bestowal. How more caliber weapons and, accordingly, ammunition (cartridge) under it - the greater the recoil force (see below).

When fired from an automatic weapon, the principle of operation of which is based on the use of powder gases energy removed through a hole in the barrel wall, such as in SVD, part of the powder gases, after passing into the gas chamber, hits the piston and throws the pusher with the bolt back.

The shot occurs in an ultra-short period of time: from 0.001 to 0.06 seconds and is divided into four consecutive periods:

preliminary
first (main)
second
third (aftereffect period of powder gases)

Pre-shot period. It lasts from the moment the powder charge of the cartridge ignites until the moment the bullet completely cuts into the rifling of the barrel bore. During this period, sufficient gas pressure is created in the bore to move the bullet from its place and overcome the resistance of its shell to cutting into the rifling of the bore. This type of pressure is called boost pressure, which reaches a value of 250 - 600 kg / cm², depending on the weight of the bullet, the hardness of its shell, caliber, barrel type, number and type of rifling.

First (main) shot period. It lasts from the moment the bullet begins to move along the bore of the weapon until the moment of complete combustion of the powder charge of the cartridge. During this period, the combustion of the powder charge occurs in rapidly changing volumes: at the beginning of the period, when the speed of the bullet along the bore is still relatively 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 rapidly rises and reaches its maximum value - 2900 kg / cm² for a 7.62 mm rifle cartridge: 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 a very rapid increase in the speed of the bullet, the volume of the bullet space increases faster than the influx of new gases, as a result of which 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 shot period. It lasts from the moment of complete combustion of the powder charge until the moment the bullet leaves the barrel. With the beginning of this period, the influx of powder gases stops, but highly heated, compressed gases expand and, putting pressure on the bullet, significantly increase its speed. The pressure drop in the second period occurs quite quickly and the muzzle pressure at the muzzle of the weapon barrel is 300 - 1000 kg / cm² for various types of weapons. muzzle velocity, that is, the speed of the bullet at the time of its departure from the bore is somewhat less than the initial speed.

The third period of the shot (the period of aftereffect of powder gases). It lasts from the moment the bullet leaves the bore of the weapon until the moment the action of the 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. Max Speed the bullet reaches at the end of the third period at a distance of several tens of centimeters from the muzzle of the weapon barrel. This period ends at the moment when the pressure of the powder gases at the bottom of the bullet is fully balanced by the air resistance.

muzzle velocity

muzzle velocity- this is the speed of the bullet at the muzzle of the barrel of the weapon. For the value of the initial speed of the bullet, the conditional speed is taken, which is less than the maximum, but more than the muzzle, which is determined empirically and by the corresponding calculations.

This parameter is one of the most important characteristics of the combat properties of weapons. The value of the initial velocity of the bullet is indicated in the firing tables and in the combat characteristics of the weapon. 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:

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

Bullet weight. The smaller it is, the greater its initial speed.

Barrel length. The larger it is, the longer the period of time the powder gases act on the bullet, respectively, the greater its initial speed.

Powder charge temperature. With a decrease in temperature, the initial velocity of the bullet decreases, with an increase, it increases due to an increase in the burning rate of the gunpowder and the pressure value. Under normal weather conditions, the temperature of the powder charge is approximately equal to the air temperature.

Powder charge weight. The greater the weight of the powder charge of the cartridge, the greater the amount of powder gases acting on the bullet, the greater the pressure in the bore and, accordingly, the speed of the bullet.

Powder charge moisture content. With its increase, the burning rate of gunpowder decreases, respectively, the speed of the bullet decreases.

The size and shape of the grains of gunpowder. Gunpowder grains of various sizes and shapes have different speed combustion, and this has a significant impact on the initial velocity of the bullet. The best option is selected at the stage of weapon development and during its subsequent tests.

Loading density. This is the ratio of the weight of the powder charge to the volume of the cartridge case with the bullet inserted: this space is called charge combustion chamber. If the bullet is too deep into the cartridge case, the loading density increases significantly: when fired, this can lead to a rupture of the weapon barrel due to a sharp pressure surge inside it, therefore such cartridges cannot be used for shooting. The greater the loading density, the lower the muzzle velocity, the lower the loading density, the greater the muzzle velocity.

recoil

recoil- This is the movement of the weapon back at the time of the shot. It is felt as a push in the shoulder, arm, ground, or a combination of these sensations. 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: they are directed in opposite directions and 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 vibrates, that is, it makes oscillatory movements. 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, left, right).

It should always be remembered that the value of this deviation increases with improper use of the firing stop, contamination of the weapon, and the use of non-standard cartridges.

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 departure angle.

Departure angle is considered positive if 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. But in case of violation of the rules for caring for a weapon and its conservation, the rules for applying a weapon, using an emphasis, the value of the angle of departure and the battle of the weapon change. In order to reduce the harmful effect of recoil on shooting results, recoil compensators are used, located on the muzzle of the weapon barrel or removable, attached to it.

External ballistics

External ballistics studies the processes and phenomena accompanying the movement of a bullet that occur after the effect of powder gases ceases on it. The main task of this sub-discipline is to study the patterns of bullet flight and the study of the properties of the trajectory of its flight.

Also, this discipline provides data for developing shooting rules, compiling shooting tables and calculating weapon sight scales. Conclusions from external ballistics have long been widely used in combat when choosing a sight and aiming point depending on the firing range, wind speed and direction, air temperature and other firing conditions.

This is the curved line described by the bullet's center of gravity during flight.

Bullet flight path, bullet flight in space

When flying in space, two forces act on a bullet: the force of gravity And air resistance force.

The force of gravity causes the bullet to gradually descend horizontally towards the plane of the ground, and the force of air resistance permanently (continuously) slows down the flight of the bullet and tends to overturn it: as a result, the speed of the bullet 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 some part of the bullet's energy is expended on movement in this medium.

Force of air resistance caused by three main factors:

air friction
swirls
ballistic wave

Shape, properties and types of toolpath

Trajectory shape depends on the elevation angle. As the elevation angle increases, the trajectory height and total horizontal range of the bullet increase, but this happens up to a certain limit, after which the trajectory height continues to increase, and the total horizontal range begins to decrease.

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

Hinged trajectory is the trajectory obtained at elevation angles greater than the angle of greatest range.

Flat trajectory- trajectory obtained at elevation angles smaller than the angle of greatest range.

Conjugate trajectory- a trajectory having the same horizontal range at different elevation angles.

When firing from weapons of the same model (with the same initial bullet speeds), you can get two flight paths with the same horizontal range: mounted and flat.

When shooting from small arms, only flat trajectories. The flatter the trajectory, the greater the distance the target can be hit with one sight setting, and 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 angle of incidence: the trajectory is 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.

Departure point- the center of the muzzle of the barrel of the weapon. 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 that 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 angle of declination (descent).

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 b is the speed of the bullet at the point of impact.

Total flight time- the time of movement of the bullet 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.

Descending branch of the trajectory- part of the trajectory from the top to the point of fall.

Aiming point (sighting point)- 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 smaller of the adjacent angles, measured from 0 to 90°, is taken as the meeting angle.

Direct shot, covered area, hit area, dead space

This is a shot in which the trajectory does not rise above the line of sight above the target for its entire length.

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

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

Within the range of a direct shot, in tense moments of the battle, shooting can be carried out without rearranging the sight values, while the aiming point in height, as a rule, is selected at the lower edge of the target.

Practical use

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 line of sight - optical axis of the optical sight. Line of sight height 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 bullet trajectory height will be 3 cm, and aiming line height- 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 a distance of 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 "crown", 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 of firing can be useful in street battles, when relatively open distances in the city are about 150-250 meters.

Affected space

Affected space is the distance on the ground during which the descending branch of the trajectory does not exceed the height of the target.

When shooting 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.

Depth of affected space depends on:

target height (the higher the height, the greater the value)
flatness of the trajectory (the flatter the trajectory, the greater the value)
the angle of inclination of the terrain (on the front slope it decreases, on the reverse slope it increases)

Depth of affected area 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 affected space on sloping terrain the firing position must be chosen in such a way that the terrain in the enemy's disposition, if possible, coincides with the aiming line.

Covered, affected and dead space

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

The greater the height of the shelter and the flatter the trajectory, the greater the covered space. Depth of covered area can be determined from the tables of the excess of the trajectory above the aiming line: by selection, an excess is found that corresponds to the height of the shelter and the distance to it. After finding the excess, the corresponding 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- this is the part of the covered space in which the target cannot be hit with a given trajectory.

The greater the height of the shelter, the lower the height of the target and the flatter the trajectory - the greater the dead space.

Pimaginable space- this is the part of the covered area in which the target can be hit. 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 choosing the right firing positions and firing at targets from weapons with a more hinged trajectory.

This is a rather complicated process. Due to the simultaneous impact on the bullet of rotational motion, 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 of this, the bullet encounters more air resistance on 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.

It increases disproportionately to the flight distance of the bullet, as a result of which the latter deviates more and more to the side of the intended target and its trajectory is a curved line. The direction of the bullet deflection depends on the direction of the rifling of the weapon's barrel: with left-sided rifling of the barrel, the derivation takes the bullet into left side, with right-handed - to the right.

At firing distances up to 300 meters inclusive, derivation has no practical significance.

Distance, m	Derivation, cm	Thousandths (horizontal adjustment of the sight)	Aiming point without corrections (SVD rifle)
100	0	0	sight center
200	1	0	Same
300	2	0,1	Same
400	4	0,1	left (from the shooter) eye of the enemy
500	7	0,1	on the left side of the head between the eye and ear
600	12	0,2	left side of the enemy's head
700	19	0,2	over the center of the epaulette on the opponent's shoulder
800	29	0,3	without corrections, accurate shooting is not performed
900	43	0,5	Same
1000	62	0,6	Same

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

Rice. 3. Trajectory

Rice. 4. Bullet trajectory parameters

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

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

Parameter trajectories	Parameter characteristic	Note
Departure point	Center of muzzle	The departure point is the start of the trajectory
Weapon horizon	Horizontal plane passing through the departure point	The horizon of the weapon looks like a horizontal line. The trajectory crosses the horizon of the weapon twice: at the point of departure and at the point of impact
elevation line	A straight line that is a continuation of the axis of the bore of the aimed weapon
Shooting plane	The vertical plane passing through the line of elevation
Elevation angle	The angle enclosed between the line of elevation and the horizon of the weapon	If this angle is negative, then it is called the angle of declination (decrease)
Throw line	Straight line, a line that is a continuation of the axis of the bore at the time of the bullet's departure
Throwing angle	The angle enclosed between the line of throw and the horizon of the weapon
Departure angle	The angle enclosed between the line of elevation and the line of throw
drop point	Point of intersection of the trajectory with the horizon of the weapon
Angle of incidence	The angle enclosed between the tangent to the trajectory at the point of impact and the horizon of the weapon
Total horizontal range	Distance from departure point to drop point
Ultimate speed	Bullet speed at point of impact
Total flight time	The time it takes for a bullet to travel from point of departure to point of impact
Top of the path	The highest point of the trajectory
Trajectory height	The shortest distance from the top of the trajectory to the horizon of the weapon
Ascending branch	Part of the trajectory from the departure point to the summit
descending branch	Part of the trajectory from the top to the point of impact
Aiming point (aiming)	The point on or off the target at which the weapon is aimed
line of sight	A straight line from the shooter's eye through the middle of the sight slot (level with its edges) and the top of the front sight to the aiming point
aiming angle	The angle enclosed between the line of elevation and the line of sight
Target elevation angle	The angle enclosed between the line of sight and the horizon of the weapon	The target's elevation angle is considered positive (+) when the target is above the weapon's horizon, and negative (-) when the target is below the weapon's horizon.
Sighting range	Distance from the point of departure to the intersection of the trajectory with the line of sight
Exceeding the trajectory above the line of sight	The shortest distance from any point of the trajectory to the line of sight
target line	A straight line connecting the departure point with the target	When firing direct fire, the target line practically coincides with the aiming line
Slant Range	Distance from point of origin to target along target line	When firing direct fire, the slant range practically coincides with the aiming range.
meeting point	Intersection point of the trajectory with the target surface (ground, obstacles)
Meeting angle	The angle enclosed between the tangent to the trajectory and the tangent to the target surface (ground, obstacles) at the meeting point	The smaller of the adjacent angles, measured from 0 to 90°, is taken as the meeting angle.
Sighting line	A straight line connecting the middle of the sight slot to the top of the front sight
Aiming (pointing)	Giving the axis of the bore of the weapon the position in space necessary for firing	In order for the bullet to reach the target and hit it or the desired point on it
Horizontal aiming	Giving the axis of the bore the desired position in the horizontal plane
vertical guidance	Giving the axis of the bore the desired position in the vertical plane

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

the descending branch is shorter and steeper than the ascending one;
the angle of incidence is greater than the angle of throw;
the final speed of the bullet is less than the initial one;
the lowest speed of the bullet when firing at high angles of throw - on the descending branch of the trajectory, and when firing at small angles of throw - at the point of impact;
the time of movement of the bullet along the ascending branch of the trajectory is less than along the descending one;
the trajectory of a rotating bullet due to the lowering of the bullet under the action of gravity and derivation is a line of double curvature.

Types of trajectories and their practical significance.

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

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

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

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

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

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

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

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

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

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

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