Elements of the flight path of a bullet definition. Bullet trajectory shape and its meaning. The most important works on 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 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 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 - 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 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

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 the rapid speed of the 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 pressure drop 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 of the 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 gunpowder gases act on the bullet and the more starting speed. 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, the larger 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 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. 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 of various types of 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 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 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 - 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 (level with its edges) and the top of the front sight in 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 gain solid knowledge in the use of a direct shot and the affected space 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 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 enemy’s left (from you) side of the 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 epaulette on the shoulder of the enemy. 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.

Flight of a bullet in the air

Having flown out of the bore, the bullet moves by inertia and is subjected to the action of two forces of 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. To overcome the force of air resistance, part of the energy of the bullet is expended

The force of air resistance is caused by three main reasons: air friction, the formation of eddies, and the formation of a ballistic wave (Fig. 4)

The bullet collides with air particles during flight and causes them to oscillate. As a result, the air density in front of the bullet increases and sound waves are formed, a ballistic wave is formed. The force of air resistance depends on the shape of the bullet, flight speed, caliber, air density

Rice. 4. Formation of air resistance force

In order to prevent the bullet from tipping over under the action of air resistance, it is given a rapid rotational movement with the help of rifling in the bore. Thus, as a result of the action of gravity and air resistance on the bullet, it will not move uniformly and rectilinearly, but will describe a curved line - a trajectory.

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

To study the trajectory, the following definitions are adopted (Fig. 5):

· departure point - the center of the muzzle of the barrel, in which the center of gravity of the bullet is located at the time of departure. The moment of departure is the passage of the bottom of the bullet through the muzzle of the barrel;

· weapon horizon - a horizontal plane passing through the departure point;

· elevation line - a straight line, which is a continuation of the axis of the bore at the moment of departure;

· shooting plane - a vertical plane passing through the line of elevation;

· throw line - a straight line, which is a continuation of the axis of the bore at the time of the bullet's departure;

· throw 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 throwing;

· drop point - the point of intersection of the trajectory with the horizon of the weapon,

· injection fall – the angle at the point of impact between the tangent to the trajectory and the horizon of the weapon,

· full horizontal range - distance from point of departure to point of fall,

· top of the trajectory 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 of the trajectory - part of the trajectory from the departure point to its top;

· descending branch of the trajectory - part of the trajectory from the top to the point of fall,

· meeting point - 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 at the meeting point;

· aiming point - 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 and the top of the front sight to the aiming point,

· aiming angle - the angle enclosed between the aiming line and the elevation line;

· target elevation angle the angle enclosed between the aiming line and the horizon of the weapon;

· aiming range - distance from the point of departure to the intersection of the trajectory with the line of sight;

· excess of the trajectory over the aiming line - the shortest distance from any point of the trajectory to the line of sight;

· elevation angle - the angle enclosed between the line of elevation and the horizon of the weapon. The shape of the trajectory depends on the elevation angle

Rice. five. Bullet trajectory elements

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

The descending branch is steeper than the ascending one;

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

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

The lowest speed of a bullet when shooting at high angles of throw

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

the time of movement of the bullet along the ascending branch of the trajectory is less than

descending;

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

The shape of the trajectory depends on the magnitude of the elevation angle (Fig. 6). 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.

Rice. 6. Angle of greatest reach, flat,

hinged and conjugate trajectories

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 small arms is 30-35 degrees, and for the range of artillery systems 45-56 degrees.

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

Trajectories obtained at elevation angles greater than the angle of greatest range are called mounted. When firing from the same weapon, you can get two trajectories with the same horizontal range - flat and mounted. Trajectories having the same horizontal range at different elevation angles are called conjugated.

Flat trajectories allow:

1. It is good to hit openly located and fast moving targets.

2. Successfully fire from guns at a long-term firing structure (DOS), a long-term firing point (DOT), from stone buildings at tanks.

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

Mounted trajectories allow:

1. Hit targets behind cover and in deep terrain.

2. Destroy the ceilings of structures.

These various tactical properties of flat and hinged trajectories can be taken into account when organizing a fire system. The flatness of the trajectory affects the range of a direct shot, the affected and covered space.

Aiming (aiming) weapons at the target.

The objective of any shooting is to hit the target in the shortest possible time and with the least expenditure of ammunition. This problem can be solved only in close proximity to the target and if the target is motionless. In most cases, hitting a target is associated with certain difficulties arising from the properties of the trajectory, meteorological and ballistic conditions shooting and the nature of the target.

Let the target be at point A - at some distance from the firing position. In order for the bullet to reach this point, the barrel of the weapon must be given a certain angle in the vertical plane (Fig. 7).

But from the wind, lateral deflections of the bullet can occur. Therefore, when aiming, it is necessary to take a lateral correction for the wind. Thus, in order for the bullet to reach the target and hit it or the desired point on it, it is necessary to give the axis of the bore a certain position in space (in the horizontal and vertical plane) before firing.

Giving the axis of the bore of a weapon the position in space necessary for firing is called aiming or pointing. Giving the axis of the bore of the weapon the required position in the horizontal plane is called horizontal pickup, and in the vertical plane - vertical pickup.

Rice. 7. Aiming (aiming) with open sight:

O - front sight, a - rear sight, aO - aiming line; сС - the axis of the bore, оО - a line parallel to the axis of the bore: H - the height of the sight, M - the amount of displacement of the rear sight;

a - aiming angle; Ub - angle of lateral correction

Accurate solution of aiming problems of any type sights depends on the correct alignment of them on the weapon. Alignment of sights of small arms for shooting at ground targets carried out in the process of checking the combat of the weapon and bringing it to normal combat.

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.

In addition, 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 velocity while respecting the strength of the weapon barrel: this provides initial data for both 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 sleeve and cuts 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 slightly 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, 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 speed 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 if the firing stop is used incorrectly, the weapon is contaminated, or non-standard cartridges are used.

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 it 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 the results of shooting, 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 on it stops. 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 a 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 "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 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 so that the terrain in the enemy's disposition coincides, if possible, 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 space 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 barrel of the weapon: 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

Ballistics is divided into internal (the behavior of the projectile inside the weapon), external (the behavior of the projectile on the trajectory) and barrier (the action of the projectile on the target). This topic will cover the basics of internal and external ballistics. From barrier ballistics wound ballistics (the action of a bullet on the client's body) will be considered. Existing also section forensic ballistics considered in the course of criminology and will not be covered in this manual.

Internal ballistics

Internal ballistics depends on the type of powder used and the type of barrel.

Conditionally trunks can be divided into long and short.

Long barrels (length over 250 mm) serve to increase the initial speed of the bullet and its flatness on the trajectory. Increases (compared to short barrels) accuracy. On the other hand, a long barrel is always more cumbersome than a short barrel.

Short barrels do not give the bullet that speed and flatness than long ones. The bullet has more dispersion. But short-barreled weapons are comfortable to wear, especially hidden, which is most appropriate for self-defense weapons and police weapons. On the other hand, trunks can be conditionally divided into rifled and smooth.

rifled barrels give the bullet greater speed and stability on the trajectory. Such trunks are widely used for bullet shooting. For firing bullet hunting cartridges from smoothbore weapons often used various threaded nozzles.

smooth trunks. Such barrels contribute to an increase in the dispersion of striking elements during firing. Traditionally used for shooting with shot (buckshot), as well as for shooting with special hunting cartridges at short distances.

There are four periods of the shot (Fig. 13).

Preliminary period (P) lasts from the beginning of the burning of the powder charge to the full penetration of the bullet into the rifling. 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 forcing pressure and reaches 250-500 kg/cm 2 . It is assumed that the combustion of the powder charge at this stage occurs in a constant volume.

First period (1) lasts from the beginning of the movement of the bullet until the complete combustion of the powder charge. At the beginning of the period, when the speed of the bullet along the bore is still low, the volume of gases grows faster than the bullet space. Gas pressure reaches its peak (2000-3000 kg/cm2). This pressure is called maximum pressure. Then, due to a rapid increase in the speed of the bullet and a sharp increase in the bullet space, the pressure drops somewhat and by the end of the first period it is approximately 2/3 of the maximum pressure. The speed of movement is constantly growing and reaches by the end of this period approximately 3/4 of the initial speed.
Second period (2) lasts from the moment of complete combustion of the powder charge to the departure of the bullet from the barrel. With the beginning of this period, the influx of powder gases stops, but highly compressed and heated gases expand and, putting pressure on the bottom of the bullet, increase its speed. The pressure drop in this period occurs quite quickly and at the muzzle - muzzle pressure - is 300-1000 kg/cm 2 . Some types of weapons (for example, Makarov, and most types of short-barreled weapons) do not have a second period, because by the time the bullet leaves the barrel, the powder charge does not completely burn out.

Third period (3) lasts from the moment the bullet leaves the barrel until the powder gases stop acting on it. During this period, powder gases flowing out of the bore at a speed of 1200-2000 m/s continue to act on the bullet, giving it additional speed. fastest speed the bullet reaches at the end of the third period at a distance of several tens of centimeters from the muzzle of the barrel (for example, when shooting from a pistol, a distance of about 3 m). This period ends at the moment when the pressure of the powder gases at the bottom of the bullet is balanced by air resistance. Further, the bullet flies already by inertia. This is to the question of why a bullet fired from a TT pistol does not pierce armor of the 2nd class when fired at close range and pierces it at a distance of 3-5 m.

As already mentioned, smoky and smokeless powders are used to equip cartridges. Each of them has its own characteristics:

black powder. This type of powder burns very quickly. Its burning is like an explosion. It is used to instantly release pressure in the bore. Such gunpowder is usually used for smooth barrels, since the friction of the projectile against the walls of the barrel in a smooth barrel is not so great (compared to a rifled barrel) and the time the bullet stays in the bore is less. Therefore, at the moment the bullet leaves the barrel, more pressure is reached. When using black powder in a rifled barrel, the first period of the shot is short enough, due to which the pressure on the bottom of the bullet decreases quite significantly. It should also be noted that the gas pressure of burnt black powder is approximately 3-5 times less than that of smokeless powder. On the gas pressure curve there is a very sharp peak of maximum pressure and a rather sharp drop in pressure in the first period.

Smokeless powder. Such powder burns more slowly than smoky powder, and is therefore used to gradually increase the pressure in the bore. In view of this, for rifled weapons smokeless powder is used as standard. Due to screwing into the rifling, the time for the bullet to fly along the barrel increases and by the time the bullet takes off, the powder charge completely burns out. Due to this, the full amount of gases acts on the bullet, while the second period is chosen to be sufficiently small. On the gas pressure curve, the maximum pressure peak is somewhat smoothed, with a gentle pressure drop in the first period. In addition, it is useful to pay attention to some numerical methods for estimating intraballistic solutions.

1. Power factor(kM). Shows the energy that falls on one conventional cubic mm of a bullet. Used to compare bullets of the same type of cartridges (for example, pistol). It is measured in joules per millimeter cubed.

KM \u003d E0 / d 3, where E0 - muzzle energy, J, d - bullets, mm. For comparison: the power factor for the 9x18 PM cartridge is 0.35 J/mm 3 ; for cartridge 7.62x25 TT - 1.04 J / mm 3; for cartridge.45ACP - 0.31 J / mm 3. 2. Metal utilization factor (kme). Shows the energy of the shot, which falls on one gram of the weapon. Used to compare bullets of cartridges for one sample or to compare the relative energy of a shot for different cartridges. Measured in Joules per gram. Often, the metal utilization coefficient is taken as a simplified version of the calculation of the recoil of a weapon. kme=E0/m, where E0 is the muzzle energy, J, m is the mass of the weapon, g. For comparison: the metal utilization coefficient for the PM pistol, machine gun and rifle is 0.37, 0.66 and 0.76 J/g, respectively.

External ballistics

First you need to imagine the full trajectory of the bullet (Fig. 14).
In explanation to the figure, it should be noted that the line of departure of the bullet (line of throwing) will be different than the direction of the barrel (line of elevation). This is due to the occurrence of barrel vibrations during the shot, which affect the trajectory of the bullet, as well as due to the recoil of the weapon when fired. Naturally, the departure angle (12) will be extremely small; moreover, the better the manufacture of the barrel and the calculation of the intra-ballistic characteristics of the weapon, the smaller the departure angle will be. Approximately the first two thirds of the ascending line of the trajectory can be considered a straight line. In view of this, three firing distances are distinguished (Fig. 15). Thus, the influence of external conditions on the trajectory is described by a simple quadratic equation, and in the graph is a parabola. In addition to third-party conditions, the deviation of the bullet from the trajectory is also affected by some design features bullets and cartridge. The complex of events will be considered below; deflecting the bullet from its original trajectory. The ballistic tables of this topic contain data on the ballistics of a 7.62x54R 7H1 cartridge bullet when fired from an SVD rifle. In general, the influence of external conditions on the flight of a bullet can be shown by the following diagram (Fig. 16).

Diffusion

It should be noted again that due to the rifled barrel, the bullet acquires rotation around its longitudinal axis, which gives greater flatness (straightness) to the flight of the bullet. Therefore, the distance of dagger fire is somewhat increased compared to a bullet fired from a smooth barrel. But gradually towards the distance of the mounted fire, due to the already mentioned third-party conditions, the axis of rotation is somewhat shifted from the central axis of the bullet, therefore, in the cross section, a circle of expansion of the bullet is obtained - the average deviation of the bullet from the original trajectory. Given this behavior of the bullet, its possible trajectory can be represented as a one-plane hyperboloid (Fig. 17). The displacement of a bullet from the main directrix due to the displacement of its axis of rotation is called dispersion. The bullet with full probability is in the circle of dispersion, the diameter (according to
list) which is determined for each specific distance. But the specific point of impact of the bullet inside this circle is unknown.

In table. 3 shows the dispersion radii for firing at various distances.

Table 3

Diffusion

Range of fire (m)	Diffusion Diameter (cm)

• Given the size of a standard head target 50x30 cm, and a chest target 50x50 cm, it can be noted that the maximum distance of a guaranteed hit is 600 m. At a greater distance, dispersion does not guarantee the accuracy of the shot.

• Derivation

• Due to complex physical processes, a rotating bullet in flight deviates somewhat from the plane of fire. Moreover, in the case of right-handed rifling (the bullet rotates clockwise when viewed from behind), the bullet deviates to the right, in the case of left-handed rifling - to the left.
  In table. 4 shows the values ​​of derivational deviations when firing at different ranges.
• Table 4
• Derivation

• Range of fire (m)	Derivation (cm)
  1000
  1200

  • It is easier to take into account the derivational deviation when shooting than dispersion. But, taking into account both of these values, it should be noted that the center of dispersion will shift somewhat by the value of the derivational displacement of the bullet.

  • Bullet displacement by wind

  • Among all the external conditions affecting the flight of a bullet (humidity, pressure, etc.), it is necessary to single out the most serious factor - the influence of wind. The wind blows the bullet quite seriously, especially at the end of the ascending branch of the trajectory and beyond.
    The displacement of the bullet by a side wind (at an angle of 90 0 to the trajectory) of medium force (6-8 m / s) is shown in Table. five.
  • Table 5
  • Bullet displacement by wind

  • Range of fire (m)	Displacement (cm)

    • To determine the displacement of the bullet by a strong wind (12-16 m/s), it is necessary to double the values ​​of the table, for a weak wind (3-4 m/s), the table values ​​are divided in half. For wind blowing at an angle of 45° to the path, the table values ​​are also divided in half.

    • bullet flight time

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

    Bullet time to target

    • • Range of fire (m)	Flight time (s)
        	0,15
        	0,28
        	0,42
        	0,60
        	0,80
        	1,02
        	1,26

        Solution of ballistic problems

      • To do this, it is useful to make a graph of the dependence of the displacement (scattering, bullet flight time) on the firing range. Such a graph will allow you to easily calculate intermediate values ​​(for example, at 350 m), and also allow you to assume out-of-table values ​​of the function.
        On fig. 18 shows the simplest ballistic problem.
      • Shooting is carried out at a distance of 600 m, the wind at an angle of 45 ° to the trajectory blows from behind-left.

        Question: the diameter of the circle of dispersion and the offset of its center from the target; flight time to the target.

      • Solution: The diameter of the circle of dispersion is 48 cm (see Table 3). The derivational shift of the center is 12 cm to the right (see Table 4). The displacement of the bullet by the wind is 115 cm (110 * 2/2 + 5% (due to the direction of the wind in the direction of the derivational displacement)) (see Table 5). Bullet flight time - 1.07 s (flight time + 5% due to wind direction in the direction of bullet flight) (see table 6).
      • Answer; the bullet will fly 600 m in 1.07 s, the diameter of the circle of dispersion will be 48 cm, and its center will shift to the right by 127 cm. Naturally, the answer data is quite approximate, but their discrepancy with the real data is no more than 10%.

      • Barrier and wound ballistics

      • Barrier ballistics

      • The impact of a bullet on obstacles (as, indeed, everything else) is quite convenient to determine by some mathematical formulas.
      1. Penetration of barriers (P). Penetration determines how likely it is to break through one or another obstacle. In this case, the total probability is taken as
      1. It is usually used to determine the probability of penetration on various dis
    • stations of different classes of passive armor protection.
      Penetration is a dimensionless quantity.
    • P \u003d En / Epr,
    • where En is the energy of the bullet at a given point in the trajectory, in J; Epr is the energy required to break through the barrier, in J.
    • Taking into account the standard Epr for body armor (BZ) (500 J for protection against pistol cartridges, 1000 J - from intermediate and 3000 J - from rifle cartridges) and sufficient energy to hit a person (max 50 J), it is easy to calculate the probability of hitting the corresponding BZ with a bullet of one or more another patron. So, the probability of penetrating a standard pistol BZ with a 9x18 PM cartridge bullet will be 0.56, and with a 7.62x25 TT cartridge bullet - 1.01. The probability of penetrating a standard machine-gun BZ with a 7.62x39 AKM cartridge bullet will be 1.32, and with a 5.45x39 AK-74 cartridge bullet - 0.87. The given numerical data are calculated for a distance of 10 m for pistol cartridges and 25 m for intermediate ones. 2. Coefficient, impact (ky). The impact coefficient shows the energy of the bullet, which falls on the square millimeter of its maximum section. Impact ratio is used to compare cartridges of the same or different classes. It is measured in J per square millimeter. ky=En/Sp, where En is the energy of the bullet at a given point of the trajectory, in J, Sn is the area of ​​the maximum cross-section of the bullet, in mm 2. Thus, the impact coefficients for bullets of cartridges 9x18 PM, 7.62x25 TT and .40 Auto at a distance of 25 m will be equal to 1.2, respectively; 4.3 and 3.18 J / mm 2. For comparison: at the same distance, the impact coefficient of bullets of 7.62x39 AKM and 7.62x54R SVD cartridges are respectively 21.8 and 36.2 J/mm 2 .

      Wound ballistics

      How does a bullet behave when it hits a body? The clarification of this issue is the most important characteristic for the choice of weapons and ammunition for a particular operation. There are two types of impact of a bullet on a target: stopping and penetrating, in principle, these two concepts have an inverse relationship. Stopping effect (0V). Naturally, the enemy stops as reliably as possible when the bullet hits a certain place on the human body (head, spine, kidneys), but some types of ammunition have a large 0V when it hits secondary targets. In the general case, 0V is directly proportional to the caliber of the bullet, its mass and speed at the moment of impact with the target. Also, 0V increases when using lead and expansive bullets. It must be remembered that an increase in 0V reduces the length of the wound channel (but increases its diameter) and reduces the effect of a bullet on a target protected by armored clothing. One of the variants of the mathematical calculation of OM was proposed in 1935 by the American J. Hatcher: 0V = 0.178*m*V*S*k, where m is the mass of the bullet, g; V is the speed of the bullet at the moment of meeting with the target, m/s; S is the transverse area of ​​the bullet, cm 2; k is the bullet shape factor (from 0.9 for full-shell to 1.25 for expansion bullets). According to such calculations, at a distance of 15 m, bullets of cartridges 7.62x25 TT, 9x18 PM and .45 have OB, respectively, 171, 250 in 640. For comparison: OB bullets of the cartridge 7.62x39 (AKM) \u003d 470, and bullets 7.62x54 ( ATS) = 650. Penetrating effect (PV). PV can be defined as the ability of a bullet to penetrate maximum depth to the target. Penetration is higher (ceteris paribus) for bullets of small caliber and weakly deformed in the body (steel, full-shell). The high penetrating effect improves the action of the bullet against armored targets. On fig. 19 shows the action of a standard PM jacketed bullet with a steel core. When a bullet enters the body, a wound channel and a wound cavity are formed. Wound channel - a channel pierced directly by a bullet. Wound cavity - a cavity of damage to fibers and blood vessels caused by tension and rupture of their bullet. Gunshot wounds are divided into through, blind, secant.
      
      

      through wounds

      A penetrating wound occurs when a bullet passes through the body. In this case, the presence of inlet and outlet holes is observed. The entrance hole is small, less than the caliber of the bullet. With a direct hit, the edges of the wound are even, and with a hit through tight clothing at an angle - with a slight tear. Often the inlet is quickly tightened. There are no traces of bleeding (except for the defeat of large vessels or when the wound is at the bottom). The exit hole is large, it can exceed the caliber of the bullet by orders of magnitude. The edges of the wound are torn, uneven, diverging to the sides. A rapidly developing tumor is observed. There is often heavy bleeding. With non-fatal wounds, suppuration quickly develops. With fatal wounds, the skin around the wound quickly turns blue. Through wounds are typical for bullets with a high penetrating effect (mainly for submachine guns and rifles). When a bullet passed through soft tissues, the internal wound was axial, with slight damage to neighboring organs. When wounded by a bullet cartridge 5.45x39 (AK-74), the steel core of the bullet in the body can come out of the shell. As a result, there are two wound channels and, accordingly, two outlets (from the shell and the core). Such injuries are most oftenth occur when it enters through dense clothing (pea jacket). Often the wound channel from the bullet is blind. When a bullet hits a skeleton, a blind wound usually occurs, but with a high power of the ammunition, a through wound is also likely. In this case, there are large internal injuries from fragments and parts of the skeleton with an increase in the wound channel to the outlet. In this case, the wound channel can "break" due to the ricochet of the bullet from the skeleton. Penetrating wounds to the head are characterized by cracking or fracture of the bones of the skull, often with a non-axial wound channel. The skull cracks even when hit by 5.6 mm lead-free jacketed bullets, not to mention more powerful ammunition. In most cases, these wounds are fatal. With penetrating wounds to the head, severe bleeding is often observed (prolonged leakage of blood from the corpse), of course, when the wound is located on the side or below. The inlet is quite even, but the outlet is uneven, with many cracks. A mortal wound quickly turns blue and swells. In case of cracking, violations of the skin of the head are possible. To the touch, the skull easily misses, fragments are felt. In case of wounds with sufficiently strong ammunition (bullets of cartridges 7.62x39, 7.62x54) and wounds with expansive bullets, a very wide exit hole with a long outflow of blood and brain matter is possible.

      Blind wounds

      Such wounds occur when bullets from less powerful (pistol) ammunition hit, using expansive bullets, passing a bullet through the skeleton, and being wounded by a bullet at the end. With such wounds, the inlet is also quite small and even. Blind wounds are usually characterized by multiple internal injuries. When wounded by expansive bullets, the wound channel is very wide, with a large wound cavity. Blind wounds are often non-axial. This is observed when weaker ammunition hits the skeleton - the bullet goes away from the inlet, plus damage from fragments of the skeleton, the shell. When such bullets hit the skull, the latter cracks heavily. A large inlet is formed in the bone, and the intracranial organs are severely affected.

      Cutting wounds

      Cutting wounds are observed when a bullet enters the body at an acute angle with a violation of only the skin and external parts of the muscles. Most of the injuries are harmless. Characterized by rupture of the skin; the edges of the wound are uneven, torn, often strongly divergent. Quite severe bleeding is sometimes observed, especially when large subcutaneous vessels rupture.

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

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

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

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

The layer of air adjacent to the surface of the bullet (grenade), in which the movement of particles changes from the speed of the bullet (grenade) to zero, is called the boundary layer. This layer of air, flowing around the bullet, breaks away from its surface and does not have time to immediately close behind the bottom 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 in the direction opposite to the movement of the bullet, and reduces the speed of its flight. Air particles, trying to fill the rarefaction formed behind the bullet, create a vortex.

A bullet (grenade) in flight collides with air particles and causes them to oscillate. As a result, air density increases in front of the bullet (grenade) and sound waves are formed. Therefore, the flight of a bullet (grenade) is accompanied by a characteristic sound. At a bullet (grenade) flight speed that is less than the speed of sound, the formation of these waves has little effect on its flight, since the waves propagate faster speed flight of a bullet (grenade). 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 resulting from the influence of air on the flight of a bullet (grenade) is the force of air resistance. The point of application of the resistance force is called the center of resistance.

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

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

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

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

The variety of forms of modern zero (grenades) "is largely determined by the need to reduce the force of air resistance.

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

1) the descending branch is shorter and steeper than the ascending one;

2) the angle of incidence is greater than the angle of throw;

3) the final speed of the bullet is less than the initial one;

4) 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;

5) the time of movement of the bullet along the ascending branch of the trajectory is less than but downward;

6) 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.

Trajectory elements: departure point, weapon horizon, line of elevation, elevation (declination), plane of fire, point of impact, full horizontal range.

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

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

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

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

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

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

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

Trajectory elements: aiming point, aiming line, aiming angle, target elevation angle, effective range.

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

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 is called line of sight.

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

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

The target's elevation angle is considered positive (+) when the target is above the weapon's horizon, and negative (-) when the target is below the weapon's horizon. The elevation angle of the target can be determined using instruments or using the thousandth formula:

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

B - the excess of the target above the horizon of the weapon in meters;

D - firing range in meters.

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

Direct shot, covered, hit and dead spaces and their practical significance

A shot in which the trajectory does not rise above the aiming line above the target along its entire length is called straight 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 and the flatness of the trajectory. The higher the target and the closer the trajectory, the greater the range of a direct shot and the greater the extent of the terrain, the target can be hit with one sight setting.

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

When 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.

The distance on the ground during which the descending branch of the trajectory does not exceed the height of the target is called 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 than the flat 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 (Ppr) can be determined from the tables of excess of the trajectory over the aiming line by comparing the excess of the descending branch of the trajectory by the corresponding firing range with the height of the target, and in the event that the target height is less than 1/3 of the trajectory height, according to the thousandth formula:

where PPR- the depth of the affected space in meters;

Vts- target height in meters;

θс is the angle of incidence in thousandths.

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

The value of the meeting angle depends on the direction of the slope:

On the opposite slope, the meeting angle is equal to the sum of the angles of incidence and slope, on the reverse slope - the difference of these angles.

In this case, the value of the meeting angle also depends on the target elevation angle: with a negative target elevation angle, the meeting angle increases by the value of the target elevation angle, with a positive target elevation angle, it decreases by its value.

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

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

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

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

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

The depth of dead space (Mpr) is different from the difference between the covered and affected space.

From machine guns on machine tools, the depth of the covered space can be determined by the aiming angles.

To do this, you need to install a sight corresponding to the distance to the shelter, and aim the machine gun at the crest of the shelter. After that, without knocking down the machine gun, mark yourself with a sight under the base of the shelter. The difference between these sights, expressed in meters, is the depth of the covered space. It is assumed that the terrain behind the shelter is a continuation of the aiming line directed under the base of the shelter.

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.

The phenomenon and causes of dispersion of projectiles (bullets) during firing; dispersion law and its main provisions

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

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

The causes causing zero (garnet) scattering can be summarized in three groups:

The reasons causing a variety of initial speeds;

Causes causing a variety of throwing angles and shooting directions;

Reasons causing a variety of conditions for the flight of a bullet (grenade).

The reasons for the variety of initial speeds are:

Variety in the mass of powder charges and bullets (grenades), in the shape and size of bullets (grenades) and shells, in the quality of gunpowder, in loading density, etc. as a result of inaccuracies (tolerances) in their manufacture;

A variety of charge temperatures, depending on the air temperature and the unequal time spent by the cartridge (grenade) in the barrel heated during firing;

Variety in the degree of heating and in the quality of the barrel.

These reasons lead to fluctuations in the initial speeds, and consequently, in the flight ranges of bullets (grenades), i.e., they lead to dispersion of bullets (grenades) in range (altitude) and depend mainly on ammunition and weapons.

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

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

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

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

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

The reasons causing a variety of flight conditions for zeros (grenades) are:

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

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

These reasons lead to an increase in dispersion in the lateral direction, but the range (altitude) and in iiobhom depends on the external shooting conditions and on the ammunition.

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

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

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

Scattering law

At large numbers shots (more than 20), a certain regularity is observed in the location of the meeting points on the dispersion area. The scattering of bullets (grenades) obeys the normal law of random errors, which in relation to the dispersion of bullets (grenades) is called the law of dispersion.

This law is characterized by the following three provisions:

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

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

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

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

Methods for determining the midpoint of impact

With a small number of holes (up to 5), the position of the midpoint of the hit is determined by the method of successive division of the segments.

For this you need:

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

Connect the resulting point to the third hole (meeting point) and divide the distance between them into three equal parts; since the holes (meeting points) are located more densely towards the dispersion center, the division closest to the first two holes (meeting points) is taken as the middle point of hit of the three holes (meeting points);

The found middle point of impact for three holes (meeting points) is connected with the fourth hole (meeting point) and the distance between them is divided into four equal parts; the division closest to the first three holes (meeting points) is taken as the midpoint of the four holes (meeting points).

For four holes (meeting points), the middle point of impact can also be determined as follows: connect the adjacent holes (meeting points) in pairs, connect the midpoints of both lines again and divide the resulting line in half; the division point will be the mid-point of impact.

If there are five holes (meeting points), the average point of impact for them is determined in a similar way.

With a large number of holes (meeting points), based on the symmetry of dispersion, the average point of impact is determined by the method of drawing the dispersion axes.

The intersection of the dispersion axes is the midpoint of impact.

The mid-point of impact can also be determined by the method of calculation (calculation). For this you need:

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

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

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

Normal (table) firing conditions; 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. Art.;

The air temperature at the weapon horizon is 4-15°С;

Relative humidity 50% (relative humidity is the ratio of the amount of water vapor contained 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) mass, muzzle velocity and departure angle are equal to the values ​​indicated in the firing tables;

Charge temperature +15° С;

The shape of the bullet (grenade) corresponds to the established drawing;

The height of the front sight is set according to the data of bringing the weapon to normal combat; heights (divisions) of the aisle correspond to the tabular aiming angles.

c) Topographic conditions:

The target is on the weapon's horizon;

There is no lateral tilt of the weapon.

If the firing conditions deviate from normal, it may be necessary to determine and take into account corrections for the range and direction of fire.

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

For every 100 m elevation, atmospheric pressure decreases by an average of 9 mm.

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

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

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

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

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

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

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

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

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

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

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

The wind blowing at an acute angle to the plane of fire simultaneously affects the change in the range of the bullet and its lateral deflection.

Changes in air humidity have little effect on air density and, consequently, on the range of a bullet (grenade), so it is not taken into account when shooting.

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

When firing at small target elevation angles (up to ± 15 °), this bullet (grenade) flight range changes very slightly, therefore, equality of the inclined and full horizontal ranges the flight of a bullet, i.e., the invariance of the shape (rigidity) of the trajectory.

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