Yuriev A.A. "Bullet sports shooting". The trajectory of the flight of a bullet in the air and its shape; the influence of gravity and air resistance on the flight of a bullet; trajectory properties The shape of the trajectory of a bullet in the air

Topic 3. Information from internal and external ballistics.

The essence of the phenomenon of a shot and its period

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

When fired from small arms, the following phenomena occur.

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

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

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

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

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

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

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

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

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

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

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

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

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

First, or main period lasts from the beginning of the movement of the bullet to the moment complete combustion powder charge. During this period, the combustion of the powder charge occurs in a rapidly changing volume. At the beginning of the period, when the speed of the bullet along the bore is still low, the amount of gases grows faster than the volume of the bullet space (the space between the bottom of the bullet and the bottom of the cartridge case), the gas pressure rises rapidly and reaches its maximum value (for example, in small arms chambered for the sample 1943 - 2800 kg / cm 2, and for a rifle cartridge - 2900 kg / cm 2). This pressure is called maximum pressure. It is created in small arms when a bullet travels 4-6 cm of the path. Then, due to the rapid increase in the speed of the bullet, the volume of the bullet space increases faster than 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 from the moment of complete combustion of the powder charge until the moment the bullet leaves the barrel. With the beginning of this period, the influx of powder gases stops, however, highly compressed and heated gases expand and, putting pressure on the bullet, increase its speed. The pressure drop in the second period occurs quite quickly and at the muzzle - muzzle pressure- is 300 - 900 kg / cm 2 for various types of weapons (for example, for Simonov's self-loading carbine 390 kg / cm 2, for easel machine gun Goryunov - 570 kg / cm 2). The speed of the bullet at the time of its departure from the bore (muzzle velocity) is somewhat less than the initial velocity.

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

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

muzzle velocity

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

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

The initial speed is one of the most important characteristics 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 the bullet, and also the influence of external conditions on its flight is reduced.

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

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

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

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

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

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

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

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

Weapon recoil and launch angle

recoil called the movement of the weapon (barrel) back during the shot. Recoil is felt in the form of a push to the shoulder, arm or ground.

The recoil action of a weapon is characterized by the amount of speed and energy that it has when moving backward. The recoil speed of the weapon is about as many times less than the initial speed of the bullet, how many times the bullet is lighter than the weapon. The recoil energy of hand-held small arms usually does not exceed 2 kg / m and is perceived by the shooter painlessly.

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

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

Rice. 31. Weapon recoil

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

The 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 value of this deviation increases with improper use of the firing stop, contamination of the weapon, etc.

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

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

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

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

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

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

The reactive force when fired from a grenade launcher is formed as a result of the outflow of powder gases through the breech breech. In connection with this, that the area of the bottom of the grenade, which is, as it were, the front wall of the barrel, is larger than the area of \u200b\u200bthe nozzle that blocks the path of gases back, an excess pressure force of powder gases (reactive force) appears, directed in the direction opposite to the outflow of gases. This force compensates for the recoil of the grenade launcher (it is practically absent) and gives the grenade initial speed.

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

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

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

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

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

bore wear

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

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

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

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

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

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

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

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

Fig 32. Bloating the trunk

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

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

Measures to prevent barrel wear

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

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

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

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

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

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

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

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

Formation of the flight path of a bullet (grenade)

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

A bullet (grenade) when flying in the air is subjected to two forces: gravity and air resistance. The force of gravity causes the bullet (grenade) to gradually lower, and the force of air resistance continuously slows down the movement of the bullet (grenade) and tends to overturn it. As a result of the action of these forces, the speed of the bullet (grenade) gradually decreases, and its trajectory is an unevenly curved curved line in shape.

Rice. 33. Bullet trajectory (side view)

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

Rice. 34. Formation of the force of resistance

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

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

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

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

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

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

The effect of the force of air resistance on the flight of a bullet (grenade) is very large; it causes a decrease in the speed and range of the bullet (grenade). For example, a bullet mod. 1930 at an angle of throw of 150 and an initial speed of 800 m / s. in airless space it would fly to a distance of 32620 m; the flight range of this bullet under the same conditions, but in the presence of air resistance, is only 3900 m.

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

At supersonic bullet speeds, when the main cause of air resistance is the formation of an air seal in front of the head (ballistic wave), bullets with an elongated pointed head are advantageous.

At subsonic grenade flight speeds, when the main cause of air resistance is the formation of rarefied space and turbulence, grenades with an elongated and narrowed tail section are beneficial.

The smoother the surface of the bullet, the lower the friction force and the air resistance force (see Fig. 35).

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

CG - center of gravity; CA - center of air resistance

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

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

In order to prevent the bullet from tipping over under the action of air resistance, it is given a rapid rotational movement with the help of rifling in the bore. For example, when fired from a Kalashnikov assault rifle, the speed of rotation of the bullet at the moment of departure from the bore is about 3000 revolutions per second.

During the flight of a rapidly rotating bullet in the air, the following phenomena occur. The force of air resistance tends to turn the bullet head up and back. But the head of the bullet, as a result of rapid rotation, according to the property of the gyroscope, tends to maintain the given position and deviates not upwards, but very slightly in the direction of its rotation at right angles to the direction of the air resistance force, i.e. to the right.

As soon as the head of the bullet deviates to the right, the direction of the air resistance force will change - it tends to turn the head of the bullet to the right and back, but the head of the bullet does not turn to the right, but down, etc.

Since the action of the air resistance force is continuous, and its direction relative to the bullet changes with each deviation of the bullet axis, the head of the bullet describes a circle, and its axis is a cone with a vertex at the center of gravity.

There is a so-called slow conical, or precessional movement, and the bullet flies with its head part forward, that is, as if following a change in the curvature of the trajectory.

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

Rice. 36. Slow conical movement of a bullet

Consequently, the bullet collides with the air flow more with its lower part, and the axis of the slow conical movement deviates in the direction of rotation (to the right when the barrel is cut right) (see Fig. 37).

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

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

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

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

Rice. 38. The effect of the force of air resistance on the flight of a grenade

As a result, the force of air resistance turns the axis of the grenade to a tangent to the trajectory, forcing the grenade to move forward (see Fig. 38).

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

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

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

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

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

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

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

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

Rice. 39. Trajectory elements

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

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

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

The angle enclosed between the tangent to the trajectory at the point of impact and the horizon of the weapon is called the angle of incidence (6).

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

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

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

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

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

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

A straight line passing from the shooter's eye through the middle of the sight slot (level with its edges) and the top of the front sight to the aiming point is called aiming line.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

The trajectory of a grenade in the air can be divided into two sections (see Fig. 40): active- the flight of a grenade under the action of a reactive force (from the point of departure to the point where the action of the reactive force stops) and passive- flight grenades by inertia. The shape of the trajectory of a grenade is about the same as that of a bullet.

Rice. 40. Grenade trajectory (side view)

The shape of the trajectory and its practical value

The shape of the trajectory depends on the magnitude of the elevation angle. With an increase in the elevation angle, the height of the trajectory and the full horizontal range of the bullet (grenade) increase, but this occurs up to a known limit. Beyond this limit, the trajectory height continues to increase and the total horizontal range begins to decrease (see Figure 40).

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

Trajectories (see Fig. 41) obtained at elevation angles smaller than the angle of greatest range are called flat. Trajectories obtained at elevation angles greater than the angle of greatest range are called mounted.

When firing from the same weapon (at the same initial speeds), you can get two trajectories with the same horizontal range: flat and mounted. Trajectories having the same horizontal range at different elevation angles are called conjugated.

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

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

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.

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

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

direct shot

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

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

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

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

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

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

Rice. 42. Direct shot

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

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

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

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

where Ppr- depth of the affected space in meters;

Vts- target height in meters;

os is the angle of incidence in thousandths.

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

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

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

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

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

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

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

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

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

Rice. 44. Covered, dead and affected space

Dead space will be the greater, the greater the height of the shelter, the lower the height of the target and the flatter the trajectory. The other part of the covered space in which the target can be hit is the hit space.

Depth of covered 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.

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

The tabular trajectory data corresponds to normal firing conditions.

The following are accepted as normal (table) conditions.

a) Meteorological conditions:

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

air temperature on the weapon horizon + 15 WITH;

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

there is no wind (the atmosphere is still).

b) Ballistic conditions:

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

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

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

c) Topographic conditions:

the target is on the horizon of the weapon;

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

scattering phenomenon

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

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

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

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

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

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

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

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

Causes scattering

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

the reasons causing a variety of initial speeds;

reasons causing a variety of throwing angles and shooting directions;

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

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

variety in the degree of heating and in the quality condition of the trunk. These reasons lead to fluctuations in the initial speeds, and therefore in the 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 unsmooth trigger release;

angular oscillations of the barrel when firing with 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 conditions for the flight of a bullet (grenade) are:

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

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

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

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

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

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

Scattering law

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

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

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

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

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

Rice. 48. Scattering pattern

Determination of 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 (see Fig. 49). For this you need:

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

1.1.1. Shot. Shot periods and their characteristics.

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

When fired from small arms, the following phenomenon occurs. From the impact of the striker on the primer of a live cartridge sent into the chamber, the percussion composition of the primer explodes and a flame forms, which through the seed holes in the bottom of the cartridge case penetrates to the powder charge and ignites it. When the charge is burned, a large amount of highly heated gases are formed, which create high pressure on the bottom of the bullet, the bottom and walls of the sleeve, as well as on the walls of the barrel and the bolt. As a result of the pressure of gases on the bottom of the bullet, it moves from its place and crashes into the rifling - rotating along them, it moves along the bore at a continuously increasing speed and is thrown out.

During the combustion of a powder charge, approximately 25-35% of the released energy is spent on communicating the translational motion to the pool (the main work); 15-25% of energy - to perform secondary work (cutting and overcoming the friction of a bullet when moving along the bore; heating the walls of the barrel, cartridge case and bullet; moving the moving parts of the weapon, gaseous and unburned parts of gunpowder); about 40% of the energy is not used and is lost after the bullet leaves the bore.

The shot occurs in a very short period of time (0.001 - 0.06 sec).

When fired, four consecutive periods are distinguished(fig.116):

Preliminary;

First or main;

The third or period of aftereffect of gases.

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

At the beginning of the period, when the speed of the bullet along the bore is still low, the number of cores grows faster than the volume of the bullet space (the space between the bottom of the bullet and the bottom of the case), the gas pressure rises rapidly and reaches its maximum value. This pressure is called maximum pressure. It is created in small arms when a bullet passes 4-6 cm. of the path. Then, due to the rapid increase in the speed of the bullet, the volume of the bullet space increases faster than the influx of new gases, and the pressure begins to fall. By the end of the period, it is approximately 2/3 of the maximum pressure. The speed of the bullet is constantly increasing and by the end of the period reaches approximately 3/4 of the initial speed. The powder charge completely burns out shortly before the bullet leaves the bore.

The second period lasts from the moment of complete combustion of the powder charge until the moment the bullet leaves the bore. With the beginning of this period, the influx of powder gases stops, however, highly compressed and heated gases expand and, putting pressure on the bullet, increase its speed. The pressure drop in the second period occurs quite quickly and at the muzzle - the muzzle pressure - is 300-900 kg / cm 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. For some types of small arms, especially short-barreled ones (for example, the Makarov pistol), there is no second period, since the complete combustion of the powder charge does not actually occur by the time the bullet leaves the barrel.

Rice. 116 - Shot periods

The third period, or the period of aftereffect of gases, lasts from the moment the bullet leaves the bore until the moment the action of powder gases on the bullet ceases. During this period, 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.

1.1.2. Initial and maximum speed.

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

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

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

The muzzle velocity of a bullet depends on:

1) Barrel length.

2) Bullet weight.

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

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

2) With a constant barrel length and a constant weight of the powder charge, the initial velocity is greater, the lower the weight of the bullet. A change in the weight of the powder charge leads to a change in the amount of powder gases, and, consequently, to a change in the maximum pressure in the bore and the initial velocity of the bullet.

3) The greater the weight of the powder charge, the greater the maximum pressure and muzzle velocity of the bullet. The length of the barrel and the weight of the powder charge increases when designing weapons to the most rational sizes.

With an increase in the temperature of the powder charge, the burning rate of the powder increases, and therefore the maximum pressure and initial speed increase. When the temperature of the charge decreases, the initial velocity decreases. An increase (decrease) in the initial velocity causes an increase (decrease) in the range of the bullet.

In this regard, it is necessary to take into account range corrections for air and charge temperature (charge temperature is approximately equal to air temperature).

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

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

The bullet reaches its greatest (maximum) speed at the end of the third period at a distance of several tens of centimeters from the muzzle of the barrel.

1.1.3 The recoil of the weapon and the angle of departure (Fig. 117).

Recoil is the movement of the weapon (barrel) back during the shot.. Recoil is felt in the form of a push to the shoulder, arm or ground. The recoil action of a weapon is characterized by the amount of speed and energy that it has when moving backward.

The recoil speed of the weapon is about as many times less than the initial speed of the bullet, how many times the bullet is lighter than the weapon. The recoil energy of hand-held small arms usually does not exceed 2 kgm and is perceived by the shooter painlessly.

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

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

In addition, when fired, the barrel of the weapon makes oscillatory movements - it vibrates.

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

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

The departure angle is considered positive when the axis of the bore at the time of the bullet's departure is higher than its position before the shot, and negative when it is lower.

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

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

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

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

1.2.1 Bullet flight path and its elements

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

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

gravity

Forces of resistance.

The force of gravity causes the bullet (grenade) to gradually drop, and the force of air resistance continuously slows down the movement of the bullet (grenade) and tends to overturn it.

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

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

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

1) Air friction.

2) The formation of swirls.

3) The formation of a ballistic wave.

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

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

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

When the speed of the bullet is higher than the speed of sound, a wave of highly compacted air is created from the incursion of sound waves against each other - a ballistic wave that slows down the speed of the bullet, since the bullet spends part of its energy on creating this wave.

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

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

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

2) The horizontal plane passing through the departure point, called the weapon horizon. The horizon of the weapon looks like a horizontal line. The trajectory crosses the horizon of the weapon twice: at the point of departure and at the point of impact.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

17) A straight line passing from the shooter's eye through the middle of the sight slot (level with its edges) and the top of the front sight to the aiming point, called the line of sight.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Rice. 121 Trajectory shapes

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

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

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

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

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

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

The flatness of the trajectory is characterized by its greatest excess over the aiming line. At a given range, the trajectory is all the more flat, the less it rises above the aiming line. In addition, the flatness of the trajectory can be judged by the magnitude of the angle of incidence - the trajectory is the more flat, the smaller the angle of incidence.

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

1.2.3. Direct shot (Fig. 122).

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

The range of a direct shot depends on:

target heights;

Flatness of the trajectory;

The higher the target and the flatter the trajectory, the greater the range of a direct shot and the greater the extent of the terrain, the target can be hit with one sight setting. The range of a direct shot can be determined from the tables by comparing the height of the target with the values \u200b\u200bof the greatest excess of the trajectory above the line of sight or with the height of the trajectory.

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

When firing at targets located at a distance greater than the range of a direct shot, the trajectory near its top rises above the target and the target is at

some area will not be affected with the same installation of the sight. However, there will be such a space (distance) near the target in which the trajectory does not rise above the target and the target will be hit by it.

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

The depth of the affected space depends on:

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

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

trajectory);

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

increases).

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

On the opposite slope, the meeting angle is equal to the sum of the angles of incidence and slope;

On the reverse slope - the difference of these angles;

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

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

With a positive elevation angle of the target, it decreases by its value.

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

1.2.5. Covered space (Fig. 123).

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

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

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

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

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

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

Rice. 123 - Covered, dead and affected space

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

The following are accepted as normal (table) conditions:

A) Meteorological conditions:

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

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

Relative Humidity air 50% (relative humidity

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

the largest amount of water vapor that can be contained in the air

at a given temperature);

There is no wind (the atmosphere is still);

B) Ballistic conditions:

Bullet (grenade) weight, muzzle velocity and departure angle are equal to the values

indicated in the shooting tables;

Charge temperature + 15 deg. S.;t

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

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

C) Topographic conditions:

The target is on the weapon's horizon;

There is no side slope of the weapon;

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

Influence of atmospheric pressure

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

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

Temperature effect

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

2) With a decrease in temperature, the density and force of air resistance increase and the range of a bullet (grenade) decreases.

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

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

Wind influence

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

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

The longitudinal (tail, head) wind has little effect on the flight of a bullet, and in the practice of shooting from small arms, corrections for such a wind are not introduced.

When firing from a grenade launcher, corrections for a strong longitudinal wind should be taken into account.

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

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

Influence of air humidity

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

Influence of sight installation

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

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

2.3.4 Dependence of the shape of the trajectory on the angle of throw. Trajectory elements

The angle formed by the horizon of the weapon and the continuation of the axis of the bore before the shot is called elevation angle.

However, it is more correct to speak about the dependence of the horizontal firing range, and, consequently, the shape of the trajectory on throw angle, which is the algebraic sum of the elevation angle and the departure angle (Fig. 48).

Rice. 48 - Elevation and throw angle

So, there is a certain relationship between the range of a bullet and the angle of throw.

According to the laws of mechanics, the greatest horizontal flight range in airless space is achieved when the throw angle is 45°. With an increase in the angle from 0 to 45 °, the range of the bullet increases, and from 45 to 90 ° it decreases. The angle of throw at which the horizontal range of the bullet is greatest is called farthest angle.

When flying a bullet in the air, the maximum range angle does not reach 45 °. Its value for modern small arms ranges from 30-35 °, depending on the weight and shape of the bullet.

Trajectories formed at throw angles less than the angle of greatest range (0-35 °) are called flat. Trajectories formed at throwing angles greater than the angle of greatest range (35-90 °) are called hinged(Fig. 49).

Rice. 49 - Flat and mounted trajectories

When studying the movement of a bullet in the air, the designations of the elements of the trajectory are used, indicated in Fig. fifty.

Rice. 50 - Trajectory and its elements:
departure point- the center of the muzzle of the barrel; it is the beginning of the trajectory;
weapon horizon is the horizontal plane passing through the departure point. In the drawings and figures depicting the trajectory from the side, the horizon has the form of a horizontal line;
elevation line- a straight line, which is a continuation of the axis of the bore of the aimed weapon;
throw line- a straight line, which is a continuation of the axis of the bore at the time of the shot. Tangent to the trajectory at the departure point;
firing plane- vertical plane passing through the line of elevation;
elevation angle- the angle formed by the line of elevation and the horizon of the weapon;
throw angle- the angle formed by the line of throw and the horizon of the weapon;
departure angle- the angle formed by 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 formed by the tangent to the trajectory at the point of impact and the horizon of the weapon;
horizontal range- distance from the point of departure to the point of fall;
vertex of the trajectory - highest point trajectories over the horizon of the weapon. The vertex divides the trajectory into two parts - the branches of the trajectory;
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;
trajectory height- distance from the top of the trajectory to the horizon of the weapon.

Since the distances for each type of weapon remain basically the same in sports shooting, many shooters do not even think at what angle of elevation or throw they need to shoot. In practice, it turned out to be much more convenient to replace the throwing angle with another, very similar to it, - aiming angle(Fig. 51). Therefore, somewhat deviating from the presentation of issues of external ballistics, we give the elements of aiming weapons (Fig. 52).

Rice. 51 - Line of sight and angle of aim

Rice. 52 - Elements of aiming weapons at the target:
line of sight- a straight line passing from the eye of the shooter through the slots of the sight and the top of the front sight to the aiming point;
aiming point- the point of intersection of the aiming line with the target or the plane of the target (when taking out the aiming point);
aiming angle- the angle formed by the aiming line and the elevation line;
target elevation angle- the angle formed by the aiming line and the horizon of the weapon;
elevation angle is the algebraic sum of the aiming angles and the elevation angle of the target.

The shooter does not interfere with knowing the degree of sloping trajectories of bullets used in sports shooting. Therefore, we present graphs characterizing the excess of the trajectory when firing from various rifles, pistols and revolvers (Fig. 53-57).

Rice. 53 - Exceeding the trajectory above the line of sight when firing a 7.6 mm heavy bullet from a service rifle

Rice. 54 - Exceeding the trajectory of a bullet above the line of sight when firing from a small-caliber rifle (at V 0 =300 m/s)

Rice. 55 - Exceeding the trajectory of a bullet above the aiming line when firing from a small-caliber pistol (at V 0 = 210 m/s)

Rice. 56 - Exceeding the trajectory of a bullet over the line of sight when firing:
a- from a revolver (at V 0 =260 m/s); b- from the PM gun (at V 0 =315 m/s).

Rice. 57 - Exceeding the trajectory of a bullet above the line of sight when firing from a rifle with a 5.6 mm sports and hunting cartridge (at V 0 = 880 m / s)

2.3.5 The dependence of the shape of the trajectory on the value of the muzzle velocity of the bullet, its shape and transverse load

While retaining their basic properties and elements, the trajectories of bullets can differ sharply from one another in their shape: be longer and shorter, have different slopes and curvature. These various changes depend on a number of factors.

Influence of initial speed. If two identical bullets are fired at the same throwing angle with different initial velocities, then the trajectory of the bullet with a higher initial velocity will be higher than the trajectory of the bullet with a lower initial velocity (Fig. 58).

Rice. 58 - Dependence of the height of the trajectory and the range of the bullet from the initial speed

A bullet flying at a lower initial speed will take longer to reach the target, so under the influence of gravity it will have time to go down much more. It is also obvious that with an increase in speed, the range of its flight will also increase.

Influence of bullet shape. The desire to increase the range and accuracy of fire required to give the bullet a shape that would allow it to maintain speed and stability in flight as long as possible.

The condensation of air particles in front of the bullet head and the rarefied space zone behind it are the main factors in the air resistance force. The head wave, which sharply increases the deceleration of the bullet, occurs when its speed is equal to the speed of sound or exceeds it (over 340 m / s).

If the speed of the bullet is less than the speed of sound, then it flies at the very crest of the sound wave, without experiencing excessively high air resistance. If it is greater than the speed of sound, the bullet overtakes all sound waves formed in front of its head. In this case, a head ballistic wave occurs, which slows down the flight of the bullet much more, which is why it quickly loses speed.

If you look at the outlines of the bow wave and the air turbulence that arise when bullets of various shapes move (Fig. 59), it can be seen that the pressure on the head of the bullet is the less, the sharper its shape. The area of rarefied space behind the bullet is the smaller, the more its tail is bevelled; in this case, there will also be less turbulence behind the flying bullet.

Rice. 59 - The nature of the outlines of the bow wave that occurs when moving bullets of various shapes

Both theory and practice have confirmed that the most streamlined is the shape of the bullet, which is outlined by the so-called curve of least resistance - cigar-shaped. Experiments show that the coefficient of air resistance, depending only on the shape of the head of the bullet, can vary by one and a half to two times.

Different flight speeds correspond to their own, most advantageous, bullet shape.

When firing at short distances with bullets having a low initial velocity, their shape slightly affects the shape of the trajectory. Therefore, revolver, pistol and small-caliber cartridges they are equipped with blunt bullets: this is more convenient for reloading weapons, and also helps to preserve it from damage (especially shellless ones - to small-caliber weapons).

Given the dependence of shooting accuracy on the shape of the bullet, the shooter must protect the bullet from deformation, make sure that scratches, nicks, dents, etc. do not appear on its surface.

Influence transverse load . The heavier the bullet, the more kinetic energy it has, therefore, the less the force of air resistance affects its flight. However, the ability of a bullet to maintain its speed depends not just on its weight, but on the ratio of weight to the area that meets air resistance. The ratio of the bullet's weight to its largest cross-sectional area is called transverse load(Fig. 60).

Rice. 60 - Cross-sectional area of bullets:
a- to a 7.62 mm rifle; b- to a 6.5 mm rifle; in- to a 9 mm pistol; G- to a 5.6-mm rifle for shooting at a target "Running Deer"; d- to 5.6 mm side-firing rifle (long cartridge).

The transverse load is greater, the greater the weight of the bullet and the smaller the caliber. Therefore, with the same caliber, the lateral load is greater for a longer bullet. A bullet with a larger transverse load has both a greater flight range and a more gentle trajectory (Fig. 61).

Rice. 61 - Influence of the transverse load of a bullet on the range of its flight

However, there is a certain limit to the increase in this load. First of all, with an increase in it (with the same caliber), the total weight of the bullet increases, and hence the recoil of the weapon. In addition, an increase in the transverse load due to excessive elongation of the bullet will cause a significant overturning action of its head part back by the force of air resistance. From this they proceed, setting the most favorable dimensions of modern bullets. So, the transverse load of a heavy bullet (weight 11.75 g) for a service rifle is 26 g / cm 2, a small-caliber bullet (weight 2.6 g) - 10.4 g / cm 2.

How great is the influence of the lateral load of a bullet on its flight, can be seen from the following data: a heavy bullet with an initial velocity of about 770 m/s has the greatest flight range of 5100 m, a light bullet with an initial velocity of 865 m/s has only 3400 m.

2.3.6 Dependence of the trajectory on meteorological conditions

Continuously changing while shooting weather conditions can have a significant effect on bullet flight. However, certain knowledge and practical experience help to significantly reduce their harmful effect on shooting accuracy.

Since sport shooting distances are relatively short and the bullet travels them in a very short time, some atmospheric factors, such as air density, will not significantly affect its flight. Therefore, in sports shooting, it is necessary to take into account mainly the influence of wind and, to a certain extent, air temperature.

Wind influence. Headwinds and tailwinds have little effect on shooting accuracy, so shooters usually neglect their effect. So, when shooting at a distance of 600 m, a strong (10 m/sec) head or tail wind changes the STP in height by only 4 cm.

The side wind significantly deflects the bullet to the side, even when shooting at close range.

Wind is characterized by strength (speed) and direction.

The strength of the wind is measured by its speed in meters per second. In shooting practice, wind is distinguished: weak - 2 m / s, moderate - 4-5 m / s and strong - 8-10 m / s.

The strength and direction of the wind arrows are practically determined by various local features: with the help of a flag, by the movement of smoke, by the swaying of grass, bushes and trees, etc. (Fig. 62).

Rice. 62 - Determination of wind strength by flag and smoke

Depending on the strength and direction of the wind, one should either make a lateral correction of the sight, or make a point, aiming in the direction opposite to its direction (taking into account the deflection of bullets under the action of the wind - mainly when shooting at curly targets). In table. Figures 8 and 9 show the bullet deflections under the influence of crosswind.

Bullet deflection under the influence of crosswind when firing from rifles of caliber 7.62 mm

Table 8

Firing range, m	Heavy bullet deflection (11.8 g), cm
Firing range, m	light wind (2 m/s)	moderate wind (4 m/s)	strong wind (8 m/s)
100	1	2	4
200	4	8	18
300	10	20	41
400	20	40	84
500	34	68	140
600	48	100	200
700	70	140	280
800	96	180	360
900	120	230	480
1000	150	300	590

Deflection of bullets under the influence of crosswind when firing from a small-caliber rifle

As can be seen from these tables, when shooting at short distances, the deflection of bullets is almost proportional to the strength (speed) of the wind. From Table. 8 also shows that when firing from service and free rifles at 300 m, a side wind with a speed of 1 m / s blows the bullet to the side by one dimension of the target No. 3 (5 cm). These simplified data should be used in practice when determining the value of wind corrections.

An oblique wind (at an angle to the firing plane of 45, 135, 225 and 315 °) deflects a bullet half as much as a side wind.

However, during firing, it is, of course, impossible to make a correction for the wind, so to speak, "formally" guided solely by the data of the tables. This data should only serve as source material and help the shooter navigate in difficult shooting conditions in the wind.

It rarely happens that in such a relatively small area of \u200b\u200bthe area as a shooting range, the wind always had the same direction, and even more so the same strength. It usually blows in gusts. Therefore, the shooter needs the ability to time the shot to the moment when the strength and direction of the wind become approximately the same as with previous shots.

Flags are usually posted at the shooting range so that the athlete can determine the strength and direction of the wind. You need to learn how to correctly follow the indications of the flags. Flags should not be relied entirely on when they are high above the target line and the line of fire. It is also impossible to navigate by the flags set at the edge of the forest, steep cliffs, ravines and hollows, since the wind speed in different layers atmosphere, as well as uneven terrain, obstacles is different. As an example, in fig. 63 gives approximate data on wind speed in summer on a plain at various heights from the ground. It is clear that the readings of flags mounted on a high bullet-receiving shaft or on a high mast will not correspond to the true force of the wind, which acts directly on the bullet. It is necessary to be guided by the indications of flags, paper ribbons, etc., set at the same level at which the weapon is located at the time of firing.

Rice. 63 - Approximate data on wind speed in summer at different heights on the plain

It must also be borne in mind that the wind, bending around uneven terrain, obstacles, can create turbulence. If flags are placed along the entire shooting distance, they often show a completely different, even opposite wind direction. Therefore, one should try to determine the main direction and strength of the wind along the entire shooting path, carefully observing individual local landmarks in the area between the shooter and the target.

Naturally, in order to make accurate corrections for the wind, some experience is needed. And experience does not come by itself. The shooter must constantly carefully observe and carefully study the effect of wind in general and on a given shooting range in particular, systematically record the conditions under which shooting is carried out. Over time, he develops a subconscious feeling, gains experience that allows him to quickly navigate in the meteorological situation and make the necessary corrections to ensure accurate shooting in difficult conditions.

Influence of air temperature. The lower the air temperature, the greater its density. A bullet flying in denser air encounters a large number of its particles on its way, and therefore loses its initial velocity faster. Therefore, in cold weather, at low temperatures, the firing range decreases and the STP decreases (Table 10).

Moving the midpoint of impact when firing from a rifle of caliber 7.62 mm under the influence of changes in air temperature and powder attire for every 10 °

Table 10

Firing range, m	Movement of the STP in height, cm
Firing range, m	light bullet (9.6 g)	heavy bullet (11.8 g)
100	-	-
200	1	1
300	2	2
400	4	4
500	7	7
600	12	12
700	21	19
800	35	28
900	54	41
1000	80	59

The temperature also affects the process of burning the powder charge in the barrel of a weapon. As is known, with an increase in temperature, the burning rate of the powder charge increases, since the heat consumption required to heat and ignite the powder grains decreases. Therefore, the lower the air temperature, the slower there is a process increase in gas pressure. As a result, the initial velocity of the bullet also decreases.

It has been established that a change in air temperature by 1° changes the initial velocity by 1 m/sec. Significant temperature fluctuations between summer and winter lead to changes in the initial speed in the range of 50-60 m/s.

Given this, for zeroing weapons, compiling relevant tables, etc. take a certain "normal" temperature - + 15 °.

Considering the relationship between the temperature of the powder charge and the initial velocity of the bullet, the following must be borne in mind.

During long-term shooting in large series, when the rifle barrel is very hot, one should not allow the next cartridge to be in the chamber for a long time: the relatively high temperature of the heated barrel, transmitted through the cartridge case to the powder charge, will cause the powder to ignite faster, which ultimately can lead to to a change in the STP and "separations" upwards (depending on the length of stay of the cartridge in the chamber).

Therefore, if the shooter is tired and he needs some rest before the next shot, then during such a break in shooting, the cartridge should not be in the chamber; it should be removed or even replaced with another cartridge from the pack, that is, unheated.

2.3.7 Scattering bullets

Even under the most favorable shooting conditions, each of the fired bullets describes its own trajectory, somewhat different from the trajectories of other bullets. This phenomenon is called natural dispersion.

With a significant number of shots, the trajectories in their totality form sheaf, which, when meeting with the target, gives a series of holes, more or less distant from each other. The area they occupy is called scattering area(fig.64).

Rice. 64 - Sheaf of trajectories, average trajectory, scattering area

All holes are located on the dispersion area around a certain point, called scattering center or mid point of impact (STP). The trajectory located in the middle of the sheaf and passing through the middle point of impact is called average trajectory . When making adjustments to the installation of the sight during the shooting process, it is always this average trajectory that is implied.

For different types of weapons and cartridges, there are certain bullet dispersion standards, as well as bullet dispersion standards according to factory specifications and tolerances for the production of certain types of weapons and batches of cartridges.

With a large number of shots, the dispersion of bullets obeys a certain dispersion law, the essence of which is as follows:

- holes are located unevenly on the dispersion area, most densely grouped around the STP;

- holes are located symmetrically relative to the STP, since the probability of a bullet deflecting in any direction from the STP is the same;

- the scattering area is always limited by a certain limit and has the shape of an ellipse (oval), elongated on a vertical plane in height.

By virtue of this law, as a whole, holes are located on the dispersion area in a regular way, and therefore in symmetrical strips of equal width, equally distant from the dispersion axes, the same and a certain number of holes are located, although the dispersion areas may have different sizes (depending on the type of weapon and cartridges). The dispersion measure is: the median deviation, the core band and the radius of the circle containing the best half of the holes (P 50) or all hits (P 100). It should be emphasized that the law of dispersion fully manifests itself with a large number of shots. In sports shooting in relatively small series, the dispersion area approaches the shape of a circle, therefore, the radius of the circle containing 100% of holes (P 100) or the best half of the holes (P 50) (Fig. 65) serves as a measure of dispersion. The radius of the circle that contains all the holes is about 2.5 times the radius of the circle that contains the best half of them. During factory tests of cartridges, when shooting is carried out in small series (usually 20) shots, a circle that includes all holes - P 100 (diameter that includes all holes, see Fig. 16) also serves as a measure of dispersion.

Rice. 65 - Large and small radii of circles containing 100 and 50% hits

So, the natural dispersion of bullets is an objective process that operates independently of the will and desire of the shooter. This is partly true, and it makes no sense to demand from weapons and cartridges that all bullets hit the same point.

At the same time, the shooter must remember that the natural dispersion of bullets is by no means an inevitable norm, once and for all established for a given type of weapon and certain shooting conditions. The art of marksmanship is to know the causes of the natural dispersion of bullets and to reduce their influence. Practice has convincingly proved how important the correct debugging of weapons and the selection of cartridges, the technical preparedness of the shooter and the experience of shooting in adverse meteorological conditions are to reduce dispersion.

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 effect of a bullet on the client's body) will be considered. The section of forensic ballistics that also exists is considered in the course of forensic science 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 firing 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

To get started, you need to submit complete trajectory bullet flight (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 of the bullet 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 shifts somewhat 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 guaranteed hit distance 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. 5.
- Table 5
- Bullet displacement by wind
- Range of fire (m)
  
  Displacement (cm)
  - To find out bullet displacement strong wind(12-16 m/s) it is necessary to double the table values, for light 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
  - - 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 the maximum depth into 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 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. During the combustion of a powder (combat) charge, a large amount of highly heated gases are formed, which create high pressure in the bore on the bottom of the bullet, the bottom and walls of the sleeve, as well as on the walls of the barrel and the bolt.
As a result of the pressure of gases on the bottom of the bullet, it moves from its place and crashes into the rifling; rotating along them, it moves along the bore with a continuously increasing speed and is thrown outward in the direction of the axis of the bore. The pressure of gases on the bottom of the sleeve causes the movement of the weapon (barrel) back.
When fired from an automatic weapon, the device of which is based on the principle of using the energy of powder gases discharged through a hole in the barrel wall - a Dragunov sniper rifle, part of the powder gases, in addition, after passing through it into the gas chamber, hits the piston and discards the pusher with the shutter back.
During the combustion of a powder charge, approximately 25-35% of the energy released is spent on communicating the progressive motion of the pool (the main work); 15-25% of energy - for secondary work (cutting and overcoming the friction of a bullet when moving along the bore; heating the walls of the barrel, cartridge case and bullet; moving the moving part of the weapon, the gaseous and unburned part of the gunpowder); about 40% of the energy is not used and is lost after the bullet leaves the bore.

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

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

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 until the moment of complete combustion of the powder charge. During this period, the combustion of the powder charge occurs in a rapidly changing volume. At the beginning of the period, when the speed of the bullet along the bore is still low, the amount of gases grows faster than the volume of the bullet space (the space between the bottom of the bullet and the bottom of the cartridge case), the gas pressure quickly rises and reaches its highest value - a rifle cartridge of 2900 kg / cm2. This pressure is called maximum pressure. It is created in small arms when a bullet travels 4 - 6 cm of the path. Then due to fast speed movement of the bullet, the volume of the bullet space increases faster than the influx of new gases, and the pressure begins to fall, by the end of the period it is equal to approximately 2/3 of the maximum pressure. The speed of the bullet is constantly increasing and by the end of the period reaches approximately 3/4 of the initial speed. The powder charge completely burns out shortly before the bullet leaves the bore.

Second period lasts until the moment of complete combustion of the powder charge until the moment the bullet leaves the bore. With the beginning of this period, the influx of powder gases stops, however, highly compressed and heated gases expand and, putting pressure on the bullet, increase its speed. The pressure drop in the second period occurs quite quickly and at the muzzle, the muzzle pressure is 300 - 900 kg/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, the 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, the range of a direct shot, the lethal and penetrating effect of the bullet increases, and the influence of external conditions on its flight also decreases. The muzzle velocity of a bullet depends on:

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

The longer the trunk the longer the powder gases act on the bullet and the greater the initial velocity. With a constant barrel length and a constant weight of the powder charge, the initial velocity is greater, the lower the weight of the bullet.
Powder charge weight change leads to a change in the amount of powder gases, and consequently, to a change in the maximum pressure in the bore and the initial velocity of the bullet. The greater the weight of the powder charge, the greater the maximum pressure and muzzle velocity of the bullet.
With an increase in the temperature of the powder charge the burning rate of gunpowder increases, and therefore the maximum pressure and initial speed increase. When the charge temperature drops initial speed is reduced. An increase (decrease) in initial velocity causes an increase (decrease) in the range of the bullet. In this regard, it is necessary to take into account range corrections for air and charge temperature (charge temperature is approximately equal to air temperature).
With increasing moisture content of the powder charge the speed of its burning and the initial speed of the bullet are reduced.
Shapes and sizes of gunpowder have a significant effect on the burning rate of the powder charge, and consequently, on the initial velocity of the bullet. They are selected accordingly when designing weapons.
Loading density is the ratio of the weight of the charge to the volume of the sleeve with the inserted pool (charge combustion chamber). With a deep landing of a bullet, the loading density increases significantly, which can lead to a sharp pressure jump when fired and, as a result, to a rupture of the barrel, so such cartridges cannot be used for shooting. With a decrease (increase) in the loading density, the initial velocity of the bullet increases (decreases).
recoil is called the movement of the weapon back during the shot. Recoil is felt in the form of a push to the shoulder, arm or ground. The recoil action of the weapon is about as many times less than the initial velocity of the bullet, how many times the bullet is lighter than the weapon. The recoil energy of hand-held small arms usually does not exceed 2 kg / m and is perceived by the shooter painlessly.

The recoil force and the recoil resistance force (butt stop) are not located on the same straight line and are directed in opposite directions. They form a pair of forces, under the influence of which the muzzle of the weapon barrel deviates upward. The magnitude of the deflection of the muzzle of the barrel of a given weapon is the greater, the greater the shoulder of this pair of forces. In addition, when fired, the barrel of the weapon makes oscillatory movements - it vibrates. As a result of vibration, the muzzle of the barrel at the moment the bullet takes off can also deviate from its original position in any direction (up, down, right, left).
The magnitude of this deviation increases with improper use of the firing stop, contamination of the weapon, etc.
The combination of the influence of barrel vibration, weapon recoil and other causes leads to the formation of an angle between the direction of the axis of the bore before the shot and its direction at the moment the bullet leaves the bore. This angle is called the departure angle.
The departure angle is considered positive when the axis of the bore at the time of the bullet's departure is higher than its position before the shot, negative - when it is lower. The influence of the departure angle on shooting is eliminated when it is brought to normal combat. However, in case of violation of the rules for laying weapons, using the stop, as well as the rules for caring for weapons and saving them, the value of the departure angle and the weapon’s combat change. In order to reduce the harmful effect of recoil on the results of shooting, compensators are used.
So, the phenomena of a shot, the initial velocity of a bullet, the recoil of a weapon have great importance when shooting and affect the flight of the bullet.

External ballistics

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

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

trajectory called the curved line described by the center of gravity of the bullet in flight.
A bullet flying through the air is subjected to two forces: gravity and air resistance. The force of gravity causes the bullet to gradually descend, and the force of air resistance continuously slows down the movement of the bullet and tends to topple it. As a result of the action of these forces, the bullet's flight speed gradually decreases, and its trajectory is an unevenly curved curved line in shape. Air resistance to the flight of a bullet is caused by the fact that air is an elastic medium and therefore part of the energy of the bullet is expended on movement in this medium.

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

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

Trajectories obtained at elevation angles smaller than the angle of greatest range are called flat. Trajectories obtained at elevation angles greater than the angle largest angle longest range are called mounted. When firing from the same weapon (at the same initial speeds), you can get two trajectories with the same horizontal range: flat and mounted. Trajectories having the same horizontal range and swarms of different elevation angles are called conjugated.

When shooting from small arms, only flat trajectories are used. The flatter the trajectory, the greater the extent of the terrain, the target can be hit with one sight setting (the less impact on the shooting results is the error in determining the sight setting): this is the practical significance of the trajectory.
The flatness of the trajectory is characterized by its greatest excess over the aiming line. At a given range, the trajectory is all the more flat, the less it rises above the aiming line. In addition, the flatness of the trajectory can be judged by the magnitude of the angle of incidence: the trajectory is the more flat, the smaller the angle of incidence. The flatness of the trajectory affects the value of the range of a direct shot, struck, covered and dead space.

Trajectory elements

Departure point- the center of the muzzle of the barrel. The departure point is the start of the trajectory.
Weapon horizon is the horizontal plane passing through the departure point.
elevation line- a straight line, which is a continuation of the axis of the bore of the aimed weapon.
Shooting plane- a vertical plane passing through the line of elevation.
Elevation angle- the angle enclosed between the line of elevation and the horizon of the weapon. If this angle is negative, then it is called the angle of declination (decrease).
Throw line- a straight line, which is a continuation of the axis of the bore at the time of the bullet's departure.
Throwing angle
Departure angle- the angle enclosed between the line of elevation and the line of throwing.
drop point- the point of intersection of the trajectory with the horizon of the weapon.
Angle of incidence- the angle enclosed between the tangent to the trajectory at the point of impact and the horizon of the weapon.
Total horizontal range- the distance from the point of departure to the point of fall.
final speed- the speed of the bullet (grenade) at the point of impact.
Full time flight- the time of movement of a bullet (grenade) from the point of departure to the point of impact.
Top of the path- the highest point of the trajectory above the horizon of the weapon.
Trajectory height- the shortest distance from the top of the trajectory to the horizon of the weapon.
Ascending branch of the trajectory- part of the trajectory from the departure point to the top, and from the top to the drop point - the descending branch of the trajectory.
Aiming point (aiming)- the point on the target (outside it) at which the weapon is aimed.
line of sight- a straight line passing from the shooter's eye through the middle of the sight slot (at the level with its edges) and the top of the front sight to the aiming point.
aiming angle- the angle enclosed between the line of elevation and the line of sight.
Target elevation angle- the angle enclosed between the aiming line and the horizon of the weapon. This angle is considered positive (+) when the target is higher and negative (-) when the target is below the weapon's horizon.
Sighting range- distance from the departure point to the intersection of the trajectory with the line of sight. The excess of the trajectory over the line of sight is the shortest distance from any point of the trajectory to the line of sight.
target line- a straight line connecting the departure point with the target.
Slant Range- distance from the departure point to the target along the target line.
meeting point- point of intersection of the trajectory with the surface of the target (ground, obstacles).
Meeting angle- the angle enclosed between the tangent to the trajectory and the tangent to the target surface (ground, obstacles) at the meeting point. The meeting angle is taken as the smaller of the adjacent angles, measured from 0 to 90 degrees.

A direct shot, hit and dead space are most closely related to issues of shooting practice. The main task of studying these issues is to 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

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 choosing the right firing positions and firing at targets from weapons with a more hinged trajectory.

The phenomenon of derivation

Due to the simultaneous impact on the bullet 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 shoulder strap on the enemy’s shoulder. At 800 meters - give an amendment with the flywheel of horizontal corrections by 0.3 thousandth (set the grid to the right, move the middle point of impact to the left), at 900 meters - 0.5 thousandth, at 1000 meters - 0.6 thousandth.

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

Yuriev A.A. "Bullet sports shooting". The trajectory of the flight of a bullet in the air and its shape; the influence of gravity and air resistance on the flight of a bullet; trajectory properties The shape of the trajectory of a bullet in the air

1.1.1. Shot. Shot periods and their characteristics.

1.1.2. Initial and maximum speed.

1.1.3 The recoil of the weapon and the angle of departure (Fig. 117).

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

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

1.2.1 Bullet flight path and its elements

1.2.3. Direct shot (Fig. 122).

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

1.2.5. Covered space (Fig. 123).

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

Influence of atmospheric pressure

Temperature effect

Wind influence

Influence of air humidity

Influence of sight installation

2.3.4 Dependence of the shape of the trajectory on the angle of throw. Trajectory elements

2.3.5 The dependence of the shape of the trajectory on the value of the muzzle velocity of the bullet, its shape and transverse load

2.3.6 Dependence of the trajectory on meteorological conditions

2.3.7 Scattering bullets

Internal ballistics

External ballistics

Diffusion

Derivation

Bullet displacement by wind

bullet flight time

Solution of ballistic problems

Barrier and wound ballistics

Barrier ballistics

Wound ballistics

through wounds

Blind wounds

Cutting wounds

Internal ballistics

The muzzle velocity of a bullet and its practical significance

External ballistics

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

Trajectory elements

Direct shot its definition and practical use in a combat situation

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

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

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

The phenomenon of derivation