Elements of the flight path of a bullet definition. Yuriev A.A. "Bullet sports shooting". The dependence of the shape of the trajectory on the angle of throw. Trajectory elements

1.1.1. Shot. Shot periods and their characteristics.

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

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

During the combustion of a powder charge, approximately 25-35% of the energy released is spent on communicating the bullet forward movement(main job); 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, the gas pressure is created in the barrel bore, which is necessary in order to move the bullet from its place and overcome the resistance of its shell to cutting into the rifling of the barrel. This pressure is called boost pressure. It reaches 250-500 kg/cm, depending on the rifling device, the weight of the bullet and the hardness of its shell. It is assumed that the combustion of the powder charge in this period occurs in a constant volume, the shell cuts into the rifling instantly, and the movement of the bullet begins immediately when the forcing pressure is reached in the bore.

First or main period lasts from the beginning of the movement of the bullet to the moment complete combustion powder charge. During this period, the combustion of the powder charge occurs in a rapidly changing volume.

At the beginning of the period, when the speed of the bullet along the bore is still low, the 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 quickly rises and reaches largest. 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 inflow new gases, and the pressure starts to drop. 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 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, the powder gases flowing out of the bore at a speed of 1200-2000 m/s continue to act on the bullet and impart additional speed to it. The bullet reaches its 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 combat properties of weapons. With an increase in the initial speed, the range of the bullet increases, the range direct shot, lethal and penetrating action of a bullet, and also the influence of external conditions for her flight.

The muzzle velocity of a bullet depends on:

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 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.

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

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

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

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

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

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

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

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

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

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

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

The amount of deflection of the muzzle of the barrel this weapon the more than more shoulder this pair of forces.

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

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

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

The combination of the influence of barrel vibration, weapon recoil and other causes leads to the formation of an angle between the direction of the axis of the bore before the shot and its direction at the moment the bullet leaves the bore - this angle is called the departure angle.

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

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

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

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

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

1.2.1 Bullet flight path and its elements

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

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

gravity

Forces of resistance.

The force of gravity causes the bullet (grenade) to gradually fall, 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 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 full time flight.

14) highest point 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 in 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 is 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 value (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 an angle longest range. The value of the angle of greatest range for bullets various kinds arms is about 35 degrees.

Rice. 121 Trajectory shapes

Trajectories obtained with elevation angles, smaller angle longest 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 .

How flatter trajectory, the greater the extent of the terrain, the target can be hit with one sight setting (the less impact on the shooting result 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, struck, covered and dead space.

1.2.3. Direct shot (Fig. 122).

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

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

The range of a direct shot depends on:

target heights;

Flatness of the trajectory;

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

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

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

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

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

The depth of the affected space depends on:

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

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

trajectory);

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

increases).

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

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

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

On the reverse slope - the difference of these angles;

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

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

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

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

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

1.2.5. Covered space (Fig. 123).

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

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

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

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

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

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

Knowing the size of the covered and dead space allows you to correctly use shelters to protect against enemy fire, as well as take measures to reduce dead spaces 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 50% (relative humidity

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

most water vapor that may be present in the air

at a given temperature);

There is no wind (the atmosphere is still);

B) Ballistic conditions:

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

indicated in the shooting tables;

Charge temperature + 15 deg. S.;t

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

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

C) Topographic conditions:

The target is on the weapon's horizon;

There is no side slope of the weapon;

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

Influence of atmospheric pressure

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

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

Temperature effect

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

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

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

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

Wind influence

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

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

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

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

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

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

Influence of air humidity

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

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 range bullet flight, i.e. the invariance of the shape (rigidity) of the trajectory (Fig. 124).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

D - firing range in meters.

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

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

A shot in which the trajectory does not rise above the aiming line above the target along its entire length is called straight shot.

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

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

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

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

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

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

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

Vts- target height in meters;

θс is the angle of incidence in thousandths.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

The reasons causing a variety of initial speeds;

Causes causing a variety of throwing angles and shooting directions;

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

The reasons for the variety of initial speeds are:

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Scattering law

At large numbers shots (more than 20), a certain regularity is observed in the location of the meeting points on the dispersion area. 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:

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

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

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

Thus, the scattering law in general view can be formulated as follows: with a sufficiently large number of shots fired under practically identical conditions, the dispersion of bullets (grenades) is uneven, symmetrical and non-limiting.

Methods for determining the midpoint of impact

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

For this you need:

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

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

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

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

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

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

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

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

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

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

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

Normal (table) firing conditions; influence of firing conditions on the flight of a bullet (grenade).

The following are accepted as normal (table) conditions.

a) Meteorological conditions:

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

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

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

There is no wind (the atmosphere is still).

b) Ballistic conditions:

Bullet (grenade) mass, muzzle velocity and departure angle are equal to the values indicated in the firing tables;

Charge temperature +15° С;

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

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

c) Topographic conditions:

The target is on the weapon's horizon;

There is no lateral tilt of the weapon.

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

With 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 (at low temperatures), these amendments must be taken into account, guided by the rules specified in the instructions for shooting.

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

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

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

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

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 - the tear - to the left. This phenomenon is explained by the fact that the side wind turns the tail of the grenade in the direction of the wind, and the head part against the wind and under the action of a reactive force directed along the axis, the grenade deviates from the firing plane in the direction from which the wind blows. On the passive part of the trajectory, the grenade deviates to the side where the wind blows.

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

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

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

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

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

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.

Flight of a bullet in the air

Having flown out of the bore, the bullet moves by inertia and is subjected to the action of two forces of gravity and air resistance

The force of gravity causes the bullet to gradually descend, and the force of air resistance continuously slows down the movement of the bullet and tends to knock it over. To overcome the force of air resistance, part of the energy of the bullet is expended

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

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

Rice. 4. Formation of air resistance force

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

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

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

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

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

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

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

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

· throw angle - the angle enclosed between the line of throw and the horizon of the weapon;

· departure angle - the angle enclosed between the line of elevation and the line of throwing;

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

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

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

· top of the trajectory the highest point of the trajectory;

· trajectory height - the shortest distance from the top of the trajectory to the horizon of the weapon,

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

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

· meeting point - intersection of the trajectory with the surface of the target (ground, obstacles),

· meeting angle - the angle enclosed between the tangent to the trajectory and the tangent to the target surface at the meeting point;

· aiming point - the point on or off the target at which the weapon is aimed,

· line of sight - a straight line from the shooter's eye through the middle of the sight slot and the top of the front sight to the aiming point,

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

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

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

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

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

Rice. 5. Bullet trajectory elements

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

The descending branch is steeper than the ascending one;

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

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

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

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

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

descending;

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

The shape of the trajectory depends on the magnitude of the elevation angle (Fig. 6). As the elevation angle increases, the height of the trajectory and the total horizontal range of the bullet increase, but this occurs up to a certain limit. Beyond this limit, the trajectory height continues to increase and the total horizontal range begins to decrease.

Rice. 6. Angle of greatest reach, flat,

hinged and conjugate trajectories

The angle of elevation at which the full horizontal range of the bullet is at its greatest is called the angle of greatest range. The value of the angle of greatest range for small arms is 30-35 degrees, and for the range artillery systems 45-56 degrees.

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

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

Flat trajectories allow:

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

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

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

Mounted trajectories allow:

1. Hit targets behind cover and in deep terrain.

2. Destroy the ceilings of structures.

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

Aiming (aiming) weapons at the target.

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

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

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

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

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

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

a - aiming angle; Ub - angle of lateral correction

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

Internal and external ballistics.

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

Lesson number 5.

"RULES FOR SHOOTING FROM SMALL ARMS"

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

Internal and external ballistics.

2. Shooting rules.

Ballistics is the science of the movement of bodies thrown in space. It deals mainly with the study of the movement of projectiles fired from firearms, rocket projectiles and ballistic missiles.

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

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

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

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

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

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

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

Preliminary;

First (or main);

Third (or period of aftereffect of gases).

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

First (main) period lasts from the beginning of the movement of the bullet until the moment of 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 amount of gases grows faster than the volume of the bullet space (the space between the bottom of the bullet and the bottom of the case), the gas pressure rises rapidly and reaches its maximum value. This pressure is called maximum pressure. It is created in small arms when a bullet travels 4-6 cm of the path. Then, due to the rapid increase in the speed of the bullet, the volume of the bullet space increases faster than 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 3/4 of the initial speed. The powder charge completely burns out shortly before the bullet leaves the bore.

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

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

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

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

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

o steel sheets with thickness:

2 mm at a distance of up to 950 m;

3 mm - up to 670 m;

5 mm - up to 350 m;

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

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

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

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

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

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

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

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

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

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

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

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

as a result of the action of recoil.

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.

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 holes in the barrel wall.

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

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

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

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

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

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

1.2. external ballistics. Bullet flight path

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

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

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

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

Air friction

The formation of swirls

formation of a ballistic wave.

The resultant of these forces is the air resistance force.

Rice. 2. Formation of air resistance force.

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

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

Air particles in contact with a moving bullet create friction and reduce the speed of the bullet. The air layer adjacent to the surface of the bullet, in which the movement of particles changes depending on the speed, is called the boundary layer. This layer of air, flowing around the bullet, breaks away from its surface and does not have time to immediately close behind the bottom.

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

The bullet collides with air particles during flight and causes them to oscillate. As a result, the air density increases in front of the bullet and a sound wave is formed. Therefore, the flight of a bullet is accompanied by a characteristic sound. When the speed of the bullet is less than the speed of sound, the formation of these waves has little effect on its flight, because. The waves travel faster than the speed of the bullet. When the speed of the bullet is higher than the speed of sound, a wave of highly compacted air is created from the incursion of sound waves against each other - a ballistic wave that slows down the speed of the bullet, because. the bullet spends some of its energy creating this wave.

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

The magnitude of the air resistance force mainly depends on:

§ bullet speed;

§ the shape and caliber of the bullet;

§ from the surface of the bullet;

§ air density

and increases with an increase in the speed of the bullet, its caliber and air density.

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

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

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

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

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

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

Rice. 5. Trajectory elements.

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

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

pointed weapons , is called elevation line.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

The point of intersection of the trajectory with the surface of the target (ground, obstacles) is called meeting point.

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

The shape of the trajectory depends on the magnitude of the elevation angle. As the elevation angle increases, the height of the trajectory and the total horizontal range of the bullet increases. But this happens to a certain limit. Beyond this limit, the trajectory height continues to increase and the total horizontal range begins to decrease.

The angle of elevation at which the full horizontal range of the bullet is greatest is called farthest angle(the value of this angle is about 35°).

There are flat and mounted trajectories:

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

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

Floor and hinged trajectory, obtained by firing from the same weapon at the same muzzle velocity and having the same total horizontal range, are called - conjugate.

Rice. 6. Angle of greatest range,

flat, hinged and conjugate trajectories.

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

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

Bullet flight trajectory, its elements, properties. Types of trajectories and their practical significance

A trajectory is a curved line, described by the center of gravity of a bullet in flight.

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

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

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

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

Types of trajectories and their practical significance

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

The angle of elevation at which the greatest range is obtained 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°.

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

Flat trajectories are called trajectories obtained at elevation angles smaller than the angle of greatest range (see Fig. trajectories 1 and 2).

Overhead trajectories are called trajectories obtained at elevation angles greater than the angle of greatest range (see Fig. trajectories 3 and 4).

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

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

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