The movement of a bullet in the air. Sniper training. Internal and external ballistics. c) Topographic conditions
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 elastic medium, therefore, 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 section are beneficial.
The smoother the surface of the bullet, the lower the friction force and air resistance force.
The variety of forms of modern zero (grenades) "is largely determined by the need to reduce the force of air resistance.
The trajectory of a bullet in the air has the following properties:
1) the descending branch is shorter and steeper than the ascending one;
2) the angle of incidence is greater than the angle of throw;
3) the final speed of the bullet is less than the initial one;
4) the lowest speed of the bullet when firing at high angles of throw - on the descending branch of the trajectory, and when firing at small angles of throw - at the point of impact;
5) the time of movement of the bullet along the ascending branch of the trajectory is less than but downward;
6) the trajectory of a rotating bullet due to the lowering of the bullet under the action of gravity and derivation is a line of double curvature.
Trajectory elements: departure point, weapon horizon, line of elevation, elevation (declination), plane of fire, point of impact, full horizontal range.
The center of the muzzle of a barrel is called departure point. The departure point is the start of the trajectory.
The horizontal plane passing through the departure point is called arms horizon. In the drawings depicting the weapon and the trajectory from the side, the horizon of the weapon appears as a horizontal line. The trajectory crosses the horizon of the weapon twice: at the point of departure and at the point of impact.
A straight line, which is a continuation of the axis of the bore of a pointed weapon, is called elevation line.
The angle enclosed between the line of elevation and the horizon of the weapon is called elevation angle. If this angle is negative, then it is called the angle of declination (decrease).
The vertical plane passing through the line of elevation is called firing plane.
The point of intersection of the trajectory with the horizon of the weapon is called drop point.
The distance from the point of departure to the point of impact is called full horizontal range.
Trajectory elements: aiming point, aiming line, aiming angle, target elevation angle, effective range.
The point on or off the target at which the weapon is aimed is called aiming point(finds).
A straight line passing from the shooter's eye through the middle of the sight slot (at the level with its edges) and the top of the front sight to the aiming point is called line of sight.
The angle enclosed between the line of elevation and the line of sight is called aiming angle.
The angle enclosed between the line of sight and the horizon of the weapon is called target elevation angle.
The target's elevation angle is considered positive (+) when the target is above the weapon's horizon, and negative (-) when the target is below the weapon's horizon. The elevation angle of the target can be determined using instruments or using the thousandth formula:
where ε is the elevation angle of the target in thousandths;
B - the excess of the target above the horizon of the weapon in meters;
D - firing range in meters.
The distance from the departure point to the intersection of the trajectory with the aiming line is called effective range.
Direct shot, covered, hit and dead spaces and their practical significance
A shot in which the trajectory does not rise above the aiming line above the target along its entire length is called straight shot.
Within range direct shot in tense moments of the battle, shooting can be carried out without rearranging the sight, while the aiming point in height, as a rule, is chosen at the lower edge of the target.
The range of a direct shot depends on the height of the target and the flatness of the trajectory. The higher the target and the closer the trajectory, the greater the range of a direct shot and the greater the extent of the terrain, the target can be hit with one sight setting.
The range of a direct shot can be determined from the tables by comparing the height of the target with the values \u200b\u200bof the greatest excess of the trajectory above the line of sight or with the height of the trajectory.
When shooting at targets located at a distance greater than the range of a direct shot, the trajectory near its top rises above the target and the target in some area will not be hit with the same sight setting. However, there will be such a space (distance) near the target in which the trajectory does not rise above the target and the target will be hit by it.
The distance on the ground during which the descending branch of the trajectory does not exceed the height of the target is called affected space(the depth of the affected space).
The depth of the affected space depends on the height of the target (it will be the greater, the higher the target), on the flatness of the trajectory (it will be the greater than the flat trajectory) and on the angle of the terrain (on the front slope it decreases, on the reverse slope it increases).
The depth of the affected space (Ppr) can be determined from the tables of excess of the trajectory over the aiming line by comparing the excess of the descending branch of the trajectory by the corresponding firing range with the height of the target, and in the event that the target height is less than 1/3 of the trajectory height, according to the thousandth formula:
where Ppr- the depth of the affected space in meters;
Vts- target height in meters;
θс is the angle of incidence in thousandths.
In the case when the target is located on a slope or there is an elevation angle of the target, the depth of the affected space is determined by the above methods, and the result obtained must be multiplied by the ratio of the angle of incidence to the angle of impact.
The value of the meeting angle depends on the direction of the slope:
On the opposite slope, the meeting angle is equal to the sum of the angles of incidence and slope, on the reverse slope - the difference of these angles.
In this case, the value of the meeting angle also depends on the target elevation angle: with a negative target elevation angle, the meeting angle increases by the value of the target elevation angle, with a positive target elevation angle, it decreases by its value.
The affected space to some extent compensates for the errors made when choosing a sight, and allows you to round the measured distance to the target up.
To increase the depth of the space to be struck on sloping terrain, the firing position must be chosen so that the terrain in the enemy's disposition, if possible, coincides with the continuation of the aiming line.
The space behind a cover that is not penetrated by a bullet, from its crest to the meeting point is called covered space.
The covered space will be the greater, the greater the height of the shelter and the flatter the trajectory.
The part of the covered space in which the target cannot be hit with a given trajectory is called dead(unbeatable) space.
Dead space will be the greater, the greater the height of the shelter, the lower the height of the target and the flatter the trajectory. The other part of the covered space in which the target can be hit is the hit space.
The depth of the covered space (Pp) can be determined from the tables of excess trajectories over the line of sight. By selection, an excess is found that corresponds to the height of the shelter and the distance to it. After finding the excess, the corresponding setting of the sight and the firing range are determined. The difference between a certain range of fire and the range to cover is the depth of the covered space.
The depth of dead space (Mpr) is different from the difference between the covered and affected space.
From machine guns on machine tools, the depth of the covered space can be determined by the aiming angles.
To do this, you need to install a sight corresponding to the distance to the shelter, and aim the machine gun at the crest of the shelter. After that, without knocking down the machine gun, mark yourself with a sight under the base of the shelter. The difference between these sights, expressed in meters, is the depth of the covered space. It is assumed that the area behind the shelter is a continuation of the line of sight 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 automatic weapons, especially during burst firing, improper use of stops and clumsy 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 the greatest impact on the magnitude 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:
Variation in atmospheric conditions, especially in wind direction and speed 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 the dispersion in the lateral direction and but the range (altitude) and in oc iiobhom depend on external conditions 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 that is different from the trajectory of other bullets (grenades).
It is impossible to completely eliminate the causes that cause dispersion, and therefore, it is impossible to eliminate the dispersion itself. However, knowing the reasons on which the dispersion depends, it is possible to reduce the influence of each of them and thereby reduce the dispersion or, as they say, increase the accuracy of fire.
Reducing the dispersion of bullets (grenades) is achieved by excellent training of the shooter, careful preparation weapons and ammunition for shooting, skillful application of the rules of shooting, correct preparation for shooting, uniform application, accurate aiming (aiming), smooth trigger release, steady and uniform holding of the weapon when shooting, as well as proper care of weapons and ammunition.
Scattering law
At large numbers shots (more than 20), a certain regularity is observed in the location of the meeting points on the dispersion area. The scattering of bullets (grenades) obeys the normal law of random errors, which in relation to the dispersion of bullets (grenades) is called the law of dispersion.
This law is characterized by the following three provisions:
1) Meeting points (holes) on the dispersion 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 scattering axes, which are equal in absolute value to the limits (bands), is the same , and each deviation from the scattering axis in one direction corresponds to the same deviation in the opposite direction.
3) The meeting points (holes) in each particular case do not occupy an unlimited, but a limited area.
Thus, the scattering law in general view can be formulated as follows: with a sufficiently large number of shots fired under practically the same conditions, the dispersion of bullets (grenades) is uneven, symmetrical and not limitless.
Methods for determining the midpoint of impact
With a small number of holes (up to 5), the position of the midpoint of the hit is determined by the method of successive division of the segments.
For this you need:
Connect two holes (meeting points) with a straight line and divide the distance between them in half;
Connect the resulting point to the third hole (meeting point) and divide the distance between them into three equal parts; since the holes (meeting points) are located more densely towards the dispersion center, the division closest to the first two holes (meeting points) is taken as the middle point of hit of the three holes (meeting points);
The found middle point of impact for three holes (meeting points) is connected with the fourth hole (meeting point) and the distance between them is divided into four equal parts; the division closest to the first three holes (meeting points) is taken as the midpoint of the four holes (meeting points).
For four holes (meeting points), the middle point of impact can also be determined as follows: connect the nearby 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 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) 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.
The target is on the weapon's horizon;
There is no lateral tilt of the weapon.
If the firing conditions deviate from normal, it may be necessary to determine and take into account corrections for the range and direction of fire.
With the increase atmospheric pressure the air density increases, and as a result, the air resistance force increases, the range of the bullet (grenade) decreases. On the contrary, with a decrease in atmospheric pressure, the density and force of air resistance decrease, and the range of the bullet increases.
For every 100 m elevation, atmospheric pressure decreases by an average of 9 mm.
When firing from small arms on flat terrain, range corrections for changes in atmospheric pressure are insignificant and are not taken into account. In mountainous conditions, at an altitude of 2000 m above sea level, these corrections must be taken into account when shooting, guided by the rules specified in the manuals on shooting.
As the temperature rises, the air density decreases, and as a result, the air resistance force decreases, and the range of the bullet (grenade) increases. On the contrary, with a decrease in temperature, the density and force of air resistance increase, and the range of a bullet (grenade) decreases.
With an increase in the temperature of the powder charge, the burning rate of the powder, the initial speed and range of the bullet (grenade) increase.
When shooting in summer conditions, the corrections for changes in air temperature and powder charge are insignificant and are practically not taken into account; when shooting in winter (under conditions low temperatures) these amendments must be taken into account, guided by the rules specified in the manuals on shooting.
With a tailwind, the speed of the bullet (grenade) relative to the air decreases. For example, if the speed of the bullet relative to the ground is 800 m/s, and the speed of the tailwind is 10 m/s, then the velocity of the bullet relative to the air will be 790 m/s (800 - 10).
As the flight speed decreases, zeros relative to the air, the air resistance force decreases. Therefore, with a fair wind, the bullet will fly further than with no wind.
With a headwind, the speed of the bullet relative to the air will be greater than with no wind, therefore, the air resistance force will increase, and the range of the bullet will decrease.
The longitudinal (tail, head) wind has little effect on the flight of a bullet, and in the practice of shooting from small arms, corrections for such a wind are not introduced. When firing from grenade launchers, corrections for strong longitudinal wind should be taken into account.
Side wind exerts pressure on side surface bullet and deflects it away from the plane of fire depending on its direction: the wind from the right deflects the bullet into left side, wind from left to right.
The grenade in the active part of the flight (when the jet engine is running) deviates to the side where the wind is blowing from: with the wind from the right - to the right, with the wind - the tear - to the left. This phenomenon is explained by the fact that the side wind turns the tail of the grenade in the direction of the wind, and the head part against the wind and under the action of a reactive force directed along the axis, the grenade deviates from the firing plane in the direction from which the wind blows. On the passive part of the trajectory, the grenade deviates to the side where the wind blows.
Crosswind has a significant effect, especially on the flight of a grenade, and must be taken into account when firing grenade launchers and small arms.
The wind blowing at an acute angle to the plane of fire simultaneously affects the change in the range of the bullet and its lateral deflection.
Changes in air humidity have little effect on air density and, consequently, on the range of a bullet (grenade), so it is not taken into account when shooting.
When firing with one sight setting (with one aiming angle), but at different target elevation angles, as a result of a number of reasons, including changes in air density at different heights, and, consequently, the air resistance force, the value of the slant (sighting) flight range changes bullets (grenades).
When firing at small target elevation angles (up to ± 15 °), this bullet (grenade) flight range changes very slightly, therefore, equality of the inclined and full horizontal 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.
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 issues of the most rational use of the energy of a powder charge during a 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 in the bore high pressure on the bottom of the bullet, the bottom and walls of the sleeve, as well as on the walls of the barrel and the bolt.
As a result of the pressure of gases on the bottom of the bullet, it moves from its place and crashes into the rifling; rotating along them, it moves along the bore with a continuously increasing speed and is thrown outward in the direction of the axis of the bore. The pressure of gases on the bottom of the sleeve causes the movement of the weapon (barrel) back.
When fired from 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 bullet forward movement(main job); 15-25% of energy - for secondary work (cutting and overcoming the friction of a bullet when moving along the bore; heating the walls of the barrel, cartridge case and bullet; moving the moving part of the weapon, the gaseous and unburned part of the gunpowder); about 40% of the energy is not used and is lost after the bullet leaves the bore.
The shot occurs in a very short period of time (0.001-0.06 s.). When fired, four consecutive periods are distinguished:
- preliminary
- first or main
- second
- the third, or period of the last gases
Preliminary period lasts from the beginning of the burning of the powder charge to the complete cutting of the shell of the bullet into the rifling of the barrel. During this period, the gas pressure is created in the barrel bore, which is necessary in order to move the bullet from its place and overcome the resistance of its shell to cutting into the rifling of the barrel. This pressure is called boost pressure; it reaches 250 - 500 kg / cm2, depending on the rifling device, the weight of the bullet and the hardness of its shell. It is assumed that the combustion of the powder charge in this period occurs in a constant volume, the shell cuts into the rifling instantly, and the movement of the bullet begins immediately when the forcing pressure is reached in the bore.
First or main period lasts from the beginning of the movement of the bullet 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 case), the gas pressure rises rapidly and reaches largest- rifle cartridge 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 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 initial speed. The powder charge completely burns out shortly before the bullet leaves the bore.
Second period lasts until the moment of complete combustion of the powder charge until the moment the bullet leaves the bore. With the beginning of this period, the influx of powder gases stops, however, highly compressed and heated gases expand and, putting pressure on the bullet, increase its speed. The pressure drop in the second period occurs quite quickly and at the muzzle, the muzzle pressure is 300 - 900 kg/cm2 for various types of weapons. The speed of the bullet at the time of its departure from the bore (muzzle velocity) is somewhat less than the initial velocity.
The third period, or the period after the action of gases lasts from the moment the bullet leaves the bore until the moment the powder gases act on the bullet. During this period, powder gases flowing out of the bore at a speed of 1200 - 2000 m / s continue to act on the bullet and give it additional speed. The bullet reaches its greatest (maximum) speed at the end of the third period at a distance of several tens of centimeters from the muzzle of the barrel. This period ends at the moment when the pressure of the powder gases at the bottom of the bullet is balanced by air resistance.
The muzzle velocity of a bullet and its practical significance
initial speed called the speed of the bullet at the muzzle of the barrel. For the initial speed, the conditional speed is taken, which is slightly more than the muzzle and less than the maximum. It is determined empirically with subsequent calculations. The value of the initial velocity of the bullet is indicated in the firing tables and in the combat characteristics of the weapon.
The initial speed is one of the most important characteristics of the combat properties of weapons. With an increase in the initial speed, the range of the bullet, 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 topics more time powder gases act on the bullet and the greater the initial velocity. With a constant barrel length and constant weight powder charge, the initial velocity is greater, the lower the weight of the bullet.
Powder charge weight change leads to a change in the amount of powder gases, and consequently, to a change in the maximum pressure in the bore and the initial velocity of the bullet. The greater the weight of the powder charge, the greater the maximum pressure and muzzle velocity of the bullet.
With an increase in the temperature of the powder charge the burning rate of gunpowder increases, and therefore the maximum pressure and initial speed increase. When the charge temperature drops initial speed is reduced. An increase (decrease) in initial velocity causes an increase (decrease) in the range of the bullet. In this regard, it is necessary to take into account range corrections for air and charge temperature (charge temperature is approximately equal to air temperature).
With increasing moisture content of the powder charge the speed of its burning and the initial speed of the bullet are reduced.
Shapes and sizes of gunpowder have a significant effect on the burning rate of the powder charge, and consequently, on the initial velocity of the bullet. They are selected accordingly when designing weapons.
Loading density is the ratio of the weight of the charge to the volume of the sleeve with the inserted pool (charge combustion chamber). With a deep landing of a bullet, the loading density increases significantly, which can lead to a sharp pressure jump when fired and, as a result, to a rupture of the barrel, so such cartridges cannot be used for shooting. With a decrease (increase) in the loading density, the initial velocity of the bullet increases (decreases).
recoil is called the movement of the weapon back during the shot. Recoil is felt in the form of a push to the shoulder, arm or ground. The recoil action of the weapon is about as many times less than the initial velocity of the bullet, how many times the bullet is lighter than the weapon. The recoil energy of hand-held small arms usually does not exceed 2 kg / m and is perceived by the shooter painlessly.
The recoil force and the recoil resistance force (butt stop) are not located on the same straight line and are directed in opposite directions. They form a pair of forces, under the influence of which the muzzle of the weapon barrel deviates upward. The magnitude of the deviation of the muzzle of the barrel of a given weapon is the greater, the greater the shoulder of this pair of forces. In addition, when fired, the barrel of the weapon makes oscillatory movements - it vibrates. As a result of vibration, the muzzle of the barrel at the moment the bullet takes off can also deviate from its original position in any direction (up, down, right, left).
The magnitude of this deviation increases with improper use of the firing stop, contamination of the weapon, etc.
The combination of the influence of barrel vibration, weapon recoil and other causes leads to the formation of an angle between the direction of the axis of the bore before the shot and its direction at the moment the bullet leaves the bore. This angle is called the departure angle.
The departure angle is considered positive when the axis of the bore at the time of the bullet's departure is higher than its position before the shot, negative - when it is lower. The influence of the departure angle on shooting is eliminated when it is brought to normal combat. However, in case of violation of the rules for laying weapons, using the stop, as well as the rules for caring for weapons and saving them, the value of the departure angle and the weapon’s combat change. In order to reduce the harmful effect of recoil on the results of shooting, compensators are used.
So, the phenomena of a shot, the initial velocity of a bullet, the recoil of a weapon 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 greatest is called the angle longest range. The value of the angle of greatest range for bullets various kinds weapons is about 35 °.
Trajectories obtained at elevation angles, smaller angle longest range are called flat. Trajectories obtained at elevation angles greater than the angle largest angle longest range are called mounted. When firing from the same weapon (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- nai highest point trajectories over the horizon of the weapon.
Trajectory height- the shortest distance from the top of the trajectory to the horizon of the weapon.
Ascending branch of the trajectory- part of the trajectory from the departure point to the top, and from the top to the drop point - the descending branch of the trajectory.
Aiming point (aiming)- the point on the target (outside it) at which the weapon is aimed.
line of sight- a straight line passing from the shooter's eye through the middle of the sight slot (at the level with its edges) and the top of the front sight to the aiming point.
aiming angle- the angle enclosed between the line of elevation and the line of sight.
Target elevation angle- the angle enclosed between the aiming line and the horizon of the weapon. This angle is considered positive (+) when the target is higher and negative (-) when the target is below the weapon's horizon.
Sighting range- distance from the departure point to the intersection of the trajectory with the line of sight. The excess of the trajectory over the line of sight is the shortest distance from any point of the trajectory to the line of sight.
target line- a straight line connecting the departure point with the target.
Slant Range- distance from the departure point to the target along the target line.
meeting point- point of intersection of the trajectory with the surface of the target (ground, obstacles).
Meeting angle- the angle enclosed between the tangent to the trajectory and the tangent to the target surface (ground, obstacles) at the meeting point. The meeting angle is taken as the smaller of the adjacent angles, measured from 0 to 90 degrees.
A direct shot, hit and dead space are most closely related to issues of shooting practice. The main task of studying these issues is to gain solid knowledge in the use of a direct shot and the affected space to perform fire missions in combat.
Direct shot its definition and practical use in a combat situation
A shot in which the trajectory does not rise above the aiming line above the target for its entire length is called direct shot. Within the range of a direct shot in tense moments of the battle, shooting can be carried out without rearranging the sight, while the aiming point in height, as a rule, is chosen at the lower edge of the target.
The range of a direct shot depends on the height of the target, the flatness of the trajectory. The higher the target and the flatter the trajectory, the greater the range of a direct shot and the greater the extent of the terrain, the target can be hit with one sight setting.
The range of a direct shot can be determined from tables by comparing the height of the target with the values of the greatest excess of the trajectory above the line of sight or with the height of the trajectory.
Direct sniper shot in urban environments
The installation height of optical sights above the bore of the weapon is on average 7 cm. At a distance of 200 meters and the sight "2", the greatest excesses of the trajectory, 5 cm at a distance of 100 meters and 4 cm - at 150 meters, practically coincide with the aiming line - the optical axis of the optical sight. The height of the line of sight at the middle of the distance of 200 meters is 3.5 cm. There is a practical coincidence of the trajectory of the bullet and the line of sight. A difference of 1.5 cm can be neglected. At a distance of 150 meters, the height of the trajectory is 4 cm, and the height of the optical axis of the sight above the horizon of the weapon is 17-18 mm; the difference in height is 3 cm, which also does not play a practical role.
At a distance of 80 meters from the shooter, the height of the trajectory of the bullet will be 3 cm, and the height of the sighting line will be 5 cm, the same difference of 2 cm is not decisive. The bullet will fall only 2 cm below the aiming point. The vertical spread of bullets of 2 cm is so small that it is of no fundamental importance. Therefore, when shooting with division "2" of the optical sight, starting from 80 meters of distance and up to 200 meters, aim at the bridge of the nose of the enemy - you will get there and get ± 2/3 cm higher lower throughout this distance. At 200 meters, the bullet will hit exactly the aiming point. And even further, at a distance of up to 250 meters, aim with the same sight "2" at the enemy's "top", at the upper cut of the cap - the bullet drops sharply after 200 meters of distance. At 250 meters, aiming in this way, you will fall 11 cm lower - in the forehead or bridge of the nose.
The above method can be useful in street battles, when the distances in the city are about 150-250 meters and everything is done quickly, on the run.
Affected space, its definition and practical use in a combat situation
When firing at targets located at a distance greater than the range of a direct shot, the trajectory near its top rises above the target and the target in some area will not be hit with the same sight setting. However, there will be such a space (distance) near the target in which the trajectory does not rise above the target and the target will be hit by it.
The distance on the ground during which the descending branch of the trajectory does not exceed the height of the target, called the affected space(the depth of the affected space).
The depth of the affected space depends on the height of the target (it will be the greater, the higher the target), on the flatness of the trajectory (it will be the greater, the flatter the trajectory) and on the angle of the terrain (on the front slope it decreases, on the reverse slope it increases).
The depth of the affected space can be determined from the tables of the excess of the trajectory above the aiming line by comparing the excess of the descending branch of the trajectory by the corresponding firing range with the height of the target, and if the target height is less than 1/3 of the trajectory height, then in the form of a thousandth.
To increase the depth of the space to be struck on sloping terrain, the firing position must be chosen so that the terrain in the enemy's disposition coincides, if possible, with the aiming line. Covered space its definition and practical use in a combat situation.
Covered space, its definition and practical use in a combat situation
The space behind a cover that is not penetrated by a bullet, from its crest to the meeting point is called covered space.
The covered space will be the greater, the greater the height of the shelter and the flatter the trajectory. The depth of the covered space can be determined from the tables of excess trajectory over the line of sight. By selection, an excess is found that corresponds to the height of the shelter and the distance to it. After finding the excess, the corresponding setting of the sight and the firing range are determined. The difference between a certain range of fire and the range to cover is the depth of the covered space.
Dead space of its definition and practical use in a combat situation
The part of the covered space in which the target cannot be hit with a given trajectory is called dead (not affected) space.
Dead space will be the greater, the greater the height of the shelter, the lower the height of the target and the flatter the trajectory. The other part of the covered space in which the target can be hit is the hit space. The depth of the dead space is equal to the difference between the covered and affected space.
Knowing the size of the affected space, covered space, dead space allows you to correctly use shelters to protect against enemy fire, as well as take measures to reduce dead spaces by choosing the right firing positions and firing at targets from weapons with a more hinged trajectory.
The phenomenon of derivation
Due to the simultaneous impact on the bullet of a rotational movement, which gives it a stable position in flight, and air resistance, which tends to tip the bullet head back, the axis of the bullet deviates from the direction of flight in the direction of rotation. As a result, the bullet encounters air resistance on more than one of its sides and therefore deviates from the firing plane more and more in the direction of rotation. Such a deviation of a rotating bullet away from the plane of fire is called derivation. This is a rather complex physical process. The derivation increases disproportionately to the flight distance of the bullet, as a result of which the latter takes more and more to the side and its trajectory in plan is a curved line. With the right cut of the barrel, the derivation takes the bullet to the right side, with the left - to the left.
| Distance, m | Derivation, cm | thousandths |
| 100 | 0 | 0 |
| 200 | 1 | 0 |
| 300 | 2 | 0,1 |
| 400 | 4 | 0,1 |
| 500 | 7 | 0,1 |
| 600 | 12 | 0,2 |
| 700 | 19 | 0,2 |
| 800 | 29 | 0,3 |
| 900 | 43 | 0,5 |
| 1000 | 62 | 0,6 |
At firing distances up to 300 meters inclusive, derivation has no practical value. This is especially true for the SVD rifle, in which the PSO-1 optical sight is specially shifted to the left by 1.5 cm. The barrel is slightly turned to the left and the bullets go slightly (1 cm) to the left. It is of no fundamental importance. At a distance of 300 meters, the derivation force of the bullet returns to the aiming point, that is, in the center. And already at a distance of 400 meters, the bullets begin to thoroughly divert to the right, therefore, in order not to turn the horizontal flywheel, aim at the enemy’s left (away from you) eye. By derivation, the bullet will be taken 3-4 cm to the right, and it will hit the enemy in the bridge of the nose. At a distance of 500 meters, aim at the 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.
The trajectory of a bullet is understood as a line drawn in space by its center of gravity.
This trajectory is formed under the influence of the inertia of the bullet, the forces of gravity and air resistance acting on it.
The inertia of a bullet is formed while it is in the bore. Under the action of the energy of powder gases, the bullet is given the speed and direction of translational motion. And if external forces did not act on it, then according to the first law of Galileo - Newton, it would rectilinear motion in a given direction at a constant speed to infinity. In this case, in every second it would pass a distance equal to the initial speed of the bullet (see Fig. 8).
However, due to the fact that the forces of gravity and air resistance act on the bullet in flight, they together, in accordance with the fourth law of Galileo - Newton, impart to it an acceleration equal to the vector sum of the accelerations arising from the actions of each of these forces separately.
Therefore, in order to understand the features of the formation of the flight path of a bullet in the air, it is necessary to consider how the force of gravity and the force of air resistance act separately on the bullet.
Rice. 8. The movement of a bullet by inertia (in the absence of the influence of gravity
and air resistance)
The force of gravity acting on the bullet gives it an acceleration equal to the acceleration of free fall. This force is directed vertically downward. In this regard, the bullet under the action of gravity will constantly fall to the ground, and the speed and height of its fall will be determined, respectively, by formulas 6 and 7:
where: v - bullet fall speed, H - bullet fall height, g - free fall acceleration (9.8 m/s2), t - bullet fall time in seconds.
If the bullet flew out of the bore without having the kinetic energy given by the pressure of the powder gases, then, in accordance with the above formula, it would fall vertically down: in one second by 4.9 m; two seconds later at 19.6 m; after three seconds at 44.1 m; four seconds later at 78.4 m; after five seconds at 122.5 m, etc. (see fig. 9).
Rice. 9. The fall of a bullet without kinetic energy in a vacuum
under the influence of gravity
When a bullet with a given kinetic energy moves by inertia, under the action of gravity, it will move a given distance down relative to the line that is a continuation of the axis of the bore. By constructing parallelograms, the lines of which will be the values of the distances covered by the bullet by inertia and under the action of gravity in
corresponding time intervals, we can determine the points that the bullet will pass in these time intervals. Connecting them with a line, we get the trajectory of the bullet in airless space (see Fig. 10).
Rice. 10. The trajectory of a bullet in a vacuum
This trajectory is a symmetrical parabola, the highest point of which is called the vertex of the trajectory; its part, located from the point of departure of the bullet to the top, is called the ascending branch of the trajectory; and the part located after the top is descending. In vacuum, these parts will be the same.
In this case, the height of the top of the trajectory and, accordingly, its figure will depend only on the initial velocity of the bullet and the angle of its departure.
If the force of gravity acting on the bullet is directed vertically downward, then the force of air resistance is directed in the direction opposite to the movement of the bullet. It continuously slows down the movement of the bullet and tends to overturn it. To overcome the force of air resistance, part of the kinetic energy of the bullet is expended.
The main causes of air resistance are: its friction against the surface of the bullet, the formation of a vortex, the formation of a ballistic wave (see Fig. 11).
Rice. 11. Causes of air resistance
The bullet in flight collides with air particles and causes them to oscillate, as a result of which the density of the air in front of the bullet increases, and sound waves are formed that cause a characteristic sound and a ballistic wave. In this case, the layer of air flowing around the bullet does not have time to close behind its bottom part, as a result of which a rarefied space is created there. The difference in air pressure exerted on the head and bottom parts of the bullet forms a force directed to the side opposite to the direction of its flight and reduces its speed. In this case, air particles, trying to fill the rarefied space formed behind the bottom of the bullet, create a vortex.
The air resistance force is the sum of all the forces generated due to the influence of air on the flight of a bullet.
The center of drag is the point at which the force of air resistance is applied to the bullet.
The force of air resistance depends on the shape of the bullet, its diameter, flight speed, air density. With an increase in the speed of the bullet, its caliber and air density, it increases.
Under the influence of air resistance, the flight path of the bullet loses its symmetrical shape. The speed of a bullet in the air decreases all the time as it moves away from the point of departure, so the average speed of a bullet on the ascending branch of the trajectory is greater than on the descending one. In this regard, the ascending branch of the flight path of a bullet in the air is always longer and flatter than the descending one; when shooting at medium distances, the ratio of the length of the ascending branch of the trajectories to the length of the descending one is conditionally taken as 3: 2 (see Fig. 12).
Rice. 12. The trajectory of a bullet in the air
Rotation of a bullet around its axis
When a bullet is flying in the air, the force of its resistance constantly strives to overturn it. It manifests itself in the following way. The bullet, moving by inertia, constantly strives to maintain the position of its axis, given direction barrel of the weapon. At the same time, under the influence of gravity, the direction of the bullet's flight constantly deviates from its axis, which is characterized by an increase in the angle between the axis of the bullet and the tangent to the trajectory of its flight (see Fig. 13).
Rice. 13. The effect of air resistance force on the flight of a bullet: CG - center of gravity, CA - center of air resistance
The action of the air resistance force is directed opposite to the direction of the bullet and parallel to its tangent trajectory, i.e. from below at an angle to the axis of the bullet.
Based on the features of the shape of the bullet, air particles hit the surface of its head at an angle close to a straight line, and into the surface of the tail at a fairly sharp angle (see Fig. 13). In this regard, at the head of the bullet there is a compacted air, and at the tail - a rarefied space. Therefore, the air resistance in the head of the bullet significantly exceeds its resistance in the tail. As a result, the speed of the head section decreases faster than the speed of the tail section, which causes the head of the bullet to tip back (bullet rollover).
Rolling the bullet backwards causes it to rotate erratically in flight, with a significant decrease in its flight range and accuracy of hitting the target.
In order for the bullet not to tip over in flight under the action of air resistance, it is given a quick rotary motion around the longitudinal axis. This rotation is formed due to the helical cutting in the bore of the weapon.
The bullet, passing through the bore, under the pressure of powder gases, enters the rifling and fills them with its body. In the future, like a bolt in a nut, it simultaneously moves forward and rotates around its axis. At the exit from the bore, the bullet retains both translational and rotational motion by inertia. At the same time, the rotation speed of the bullet reaches very high values, for the Kalashnikov 3000 assault rifle, and for sniper rifle Dragunov - about 2600 rpm.
Bullet rotation speed can be calculated by the formula:
where Vvr - rotation speed (rpm), Vo - muzzle velocity (mm/s), Lnar - rifling stroke length (mm).
During the flight of a bullet, the force of air resistance tends to tip the bullet head up and back. But the head of the bullet, rotating rapidly, according to the property of the gyroscope, tends to maintain its position and deviate not upwards, but slightly in the direction of its rotation - to the right, at right angles to the direction of the air resistance force. When the head part is deflected to the right, the direction of the air resistance force changes, which now tends to turn the head part of the bullet to the right and back. But as a result of rotation, the head of the bullet does not turn to the right, but down and further until it describes a full circle (see Fig. 14).
Rice. 14. Conical rotation of the bullet head
Thus, the head of a flying and rapidly rotating bullet describes a circle, and its axis is a cone with a vertex at the center of gravity. There is a so-called slow conical movement, in which the bullet flies head first in accordance with the change in the curvature of the trajectory (see Fig. 15).
Rice. 15. Flight of a spinning bullet in the air
The axis of slow conical rotation is located above the tangent to the flight path of the bullet, so the lower part of the bullet is in more subject to the pressure of the oncoming air flow than the top. In this regard, the axis of slow conical rotation deviates in the direction of rotation, i.e. to the right. This phenomenon is called derivation (see Fig. 16).
Derivation is the deviation of the bullet from the plane of fire in the direction of its rotation.
The plane of fire is understood as a vertical plane in which lies the axis of the bore of the weapon.
The reasons for the derivation are: the rotational movement of the bullet, air resistance and the constant decrease under the action of gravity of the tangent to the flight path of the bullet.
In the absence of at least one of these reasons, there will be no derivation. For example, when shooting vertically up and vertically down, there will be no derivation, since the air resistance force in this case is directed along the axis of the bullet. There will be no derivation when firing in a vacuum due to the lack of air resistance and when firing from smoothbore weapons due to the lack of rotation of the bullet.
Rice. 16. The phenomenon of derivation (view of the trajectory from above)
During the flight, the bullet deviates more and more to the side, while the degree of increase in derivational deviations significantly exceeds the degree of increase in the distance traveled by the bullet.
Derivation is not of great practical importance for the shooter when shooting at close and medium distances, it must be taken into account only for particularly accurate shooting at long distances, making certain adjustments to the installation of the sight in accordance with the table of derivational deviations for the corresponding firing range.
Bullet trajectory characteristics
To study and describe the flight path of a bullet, the following indicators characterizing it are used (see Fig. 17).
The departure point is located in the center of the muzzle of the barrel, is the beginning of the bullet's flight path.
The weapon's horizon is the horizontal plane passing through the departure point.
The line of elevation is a straight line that is a continuation of the axis of the bore of the weapon aimed at the target.
The elevation angle is the angle enclosed between the elevation line and the horizon of the weapon. If this angle is negative, for example, when
shooting down from a significant hill, it is called the angle of declination (or descent).
Rice. 17. Bullet trajectory indicators
The line of throw is a straight line, which is a continuation of the axis of the bore at the time of the bullet's departure.
The throw angle is the angle between the throw line and the weapon's horizon.
The departure angle is the angle enclosed between the line of elevation and the line of throw. Represents the difference between the values of the angles of throw and elevation.
Point of impact - is the point of intersection of the trajectory with the horizon of the weapon.
The angle of incidence is the angle at the point of impact between the tangent to the bullet's flight path and the weapon's horizon.
The final velocity of the bullet is the velocity of the bullet at the point of impact.
The total flight time is the time it takes the bullet to travel from the point of departure to the point of impact.
Full horizontal range is the distance from the point of departure to the point of impact.
The vertex of the trajectory is its highest point.
The height of the trajectory is the shortest distance from its top to the horizon of the weapon.
The ascending branch of the trajectory is the part of the trajectory from the departure point to its top.
The descending branch of the trajectory is the part of the trajectory from its top to the point of fall.
The meeting point is a point lying at the intersection of the bullet's flight path with the target surface (ground, obstacles).
The meeting angle is the angle between the tangent to the bullet's flight path and the tangent to the target surface at the meeting point.
The point of aim (aiming) is the point on or off the target at which the weapon is aimed.
The line of sight is a straight line from the shooter's eye through the middle of the sight slit and the top of the front sight to the point of aim.
The angle of aim is the angle between the line of sight and the line of elevation.
Target elevation angle is the angle between the line of sight and the horizon of the weapon.
Sighting range is the distance from the point of departure to the intersection of the trajectory with the line of sight.
The excess of the trajectory over the line of sight is the shortest distance from any point of the trajectory to the line of sight.
When shooting at close range, the values of the excess of the trajectory over the aiming line will be quite low. But when firing at long distances, they reach significant values (see Table 1).
Table 1
Exceeding the trajectory above the aiming line when firing from a Kalashnikov assault rifle (AKM) and a Dragunov sniper rifle (SVD) at distances of 600 m or more
| For 7.62mm AKM | |||||||||||||||||||||
| Range, m | 100 | 200 | 300 | 400 | 500 | 600 | 700 | 800 | 900 | 1000 | |||||||||||
| Aim | meters | ||||||||||||||||||||
| 6 | 0,98 | 1,8 | 2,2 | 2,1 | 1,4 | 0 | -2,7 | -6,4 | - | - | |||||||||||
| 7 | 1,3 | 2,5 | 3,3 | 3,6 | 3,3 | 2,1 | colspan=2bgcolor=white>0-3,5 | -8,4 | - | ||||||||||||
| 8 | 1,8 | 3,4 | 4,6 | 5,4 | 5,5 | 4,7 | 3,0 | 0 | -4,5 | -10,5 | |||||||||||
| For SVD using an optical sight | |||||||||||||||||||||
| Range, | 100 | 200 | 300 | 400 | 500 | 600 | 700 | 800 | 900 | 1000 | 1100 | 1200 | 1300 | 1400 | |||||||
| Aim | meters | ||||||||||||||||||||
| 6 | 0,53 | 0,95 | 1,2 | 1,1 | 0,74 | 0 | -1,3 | - | - | - | - | - | - | - | |||||||
| 7 | 0,71 | 1,3 | 1,7 | 1,9 | 1,6 | 1,0 | 0 | -1,7 | - | - | - | - | - | - | |||||||
| 8 | 0,94 | 1,8 | 2,4 | 2,7 | 2,8 | 2,4 | 1,5 | 0 | -2,2 | - | - | - | - | - | |||||||
| 9 | 1,2 | 2,2 | 3,1 | 3,7 | 4,0 | 3,9 | 2,3 | 2,0 | 0 | -2,9 | - | - | - | - | |||||||
| 10 | 1,5 | 2,8 | 4,0 | 4,9 | 5,4 | 5,7 | 5,3 | 4,3 | 2,6 | 0 | -3,7 | - | - | - | |||||||
| 11 | 1,8 | 3,5 | 5,0 | 6,2 | 7,1 | 7,6 | 7,7 | 7,1 | 5,7 | 3,4 | 0 | -4,6 | - | - | |||||||
| 12 | 2,2 | 4,3 | 6,2 | 7,8 | 9,1 | 10,0 | 10,5 | 10,0 | 9,2 | 7,3 | 4,3 | 0 | -5,5 | - | |||||||
| 13 | 2,6 | 5,1 | 7,4 | 9,5 | 11 | 12,5 | 13,5 | 13,5 | 13,0 | 11,5 | 8,9 | 5,1 | 0 | -6,6 | |||||||
Note: The number of units in the scope value corresponds to the number of hundreds of meters of shooting distance for which the scope is designed.
(6 - 600 m, 7 - 700 m, etc.).
From Table. 1 shows that the excess of the trajectory above the aiming line when firing from the AKM at a distance of 800 m (sight 8) exceeds 5 meters, and when firing from the SVD at a distance of 1300 m (sight 13) - the bullet trajectory rises above the aiming line by more than 13 meters.
Aiming (weapon aiming)
In order for the bullet to hit the target as a result of the shot, it is first necessary to give the axis of the barrel bore an appropriate position in space.
Giving the axis of the bore of a weapon the position necessary to hit a given target is called aiming or aiming.
This position must be given both in the horizontal plane and in the vertical. Giving the axis of the bore the required position in the vertical plane is a vertical pickup, giving it the desired position in the horizontal plane is a horizontal pickup.
If the aiming reference is a point on or near the target, such aiming is called direct. When shooting from small arms, direct aiming is used, performed using a single sighting line.
The sight line is a straight line connecting the middle of the sight slot to the top of the front sight.
To carry out aiming, it is necessary first, by moving the rear sight (slot of the sight), to give the aiming line such a position in which between it and the axis of the bore, an aiming angle is formed in the vertical plane corresponding to the distance to the target, and in the horizontal plane - an angle equal to the lateral correction, taking into account crosswind speed, derivation and lateral movement speed of the target (see Fig. 18).
After that, directing the sighting line to the area, which is the aiming reference point, by changing the position of the barrel of the weapon, the axis of the bore is given the desired position in space.
In this case, in weapons with a permanent rear sight, as, for example, in most pistols, to give the necessary position of the bore in the vertical plane, an aiming point is selected corresponding to the distance to the target, and the aiming line is directed to this point. In weapons with a sight slot fixed in the side position, as in a Kalashnikov assault rifle, to give the necessary position of the bore in the horizontal plane, the aiming point is selected corresponding to the side correction, and the aiming line is directed to this point.
Rice. 18. Aiming (weapon aiming): O - front sight; a - rear sight; aO - aiming line; сС - the axis of the bore; oO - a line parallel to the axis of the bore;
H - sight height; M - the amount of movement of the rear sight; a - aiming angle; Ub - angle of lateral correction
Bullet trajectory shape and its practical significance
The shape of the trajectory of a bullet in the air depends on the angle at which it is fired in relation to the horizon of the weapon, its muzzle velocity, kinetic energy and shape.
To produce a targeted shot, the weapon is aimed at the target, while the aiming line is directed to the aiming point, and the axis of the bore in the vertical plane is brought to a position corresponding to the required elevation line. Between the axis of the bore and the horizon of the weapon, the required elevation angle is formed.
When fired, under the action of the recoil force, the axis of the barrel bore is shifted by the value of the departure angle, while it goes into a position corresponding to the throw line and forms a throw angle with the horizon of the weapon. At this angle, the bullet flies out of the bore of the weapon.
Due to the insignificant difference between the angle of elevation and the angle of throwing, they are often identified, while, however, it is more correct in this case talk about the dependence of the trajectory of a bullet on the angle of throw.
As the throw angle increases, the height of the bullet's flight path and the total horizontal range increase to a certain value of this angle, after which the height of the trajectory continues to increase, and the total horizontal range decreases.
The angle of throw at which the full horizontal range of the bullet is greatest is called the angle of greatest range.
In accordance with the laws of mechanics in an airless space, the angle of greatest range will be 45 °.
When a bullet is flying in air, the relationship between the angle of throw and the shape of the bullet's flight path is similar to the dependence of these characteristics observed when a bullet is flying in airless space, but due to the influence of air resistance, the maximum range angle does not reach 45 °. Depending on the shape and mass of the bullet, its value varies between 30 - 35 °. For calculations, the angle of the greatest firing range in the air is assumed to be 35°.
The flight paths of a bullet that occur at angles of throw smaller than the angle of greatest range are called flat.
The flight paths of a bullet that occur at angles of throw of a large angle of greatest range are called hinged (see Fig. 19).
Rice. 19. Angle of greatest range, flat and overhead trajectories
Flat trajectories are used when firing direct fire at fairly short distances. When firing from small arms, only this type of trajectory is used. The flatness of the trajectory is characterized by its maximum excess over the aiming line. The less the trajectory rises above the aiming line at a given firing range, the more flat it is. Also, the flatness of the trajectory is estimated by the angle of incidence: the smaller it is, the flatter the trajectory.
The flatter the trajectory used when shooting, the greater the distance the target can be hit with one set of
intact, i.e. errors in the installation of the sight have a lesser effect on the effectiveness of shooting.
Mounted trajectories are not used when firing from small arms, in turn, they are very common in firing shells and mines over long distances outside the line of sight of the target, which in this case is set by coordinates. Mounted trajectories are used when firing from howitzers, mortars and other types of artillery weapons.
Due to the peculiarities of this type of trajectory, these types of weapons can hit targets located in cover, as well as behind natural and artificial barriers (see Fig. 20).
Trajectories that have the same horizontal range at different throw angles are called conjugate. One of these trajectories will be flat, the second hinged.
Conjugated trajectories can be obtained when firing from one weapon, using throwing angles greater and less than the angle of greatest range.
Rice. 20. Features of the use of hinged trajectories
A shot in which the excess of the trajectory over the line of sight throughout its entire length does not reach values greater than the height of the target is considered a direct shot (see Fig. 21).
The practical significance of a direct shot lies in the fact that, within its range, in tense moments of the battle, it is allowed to fire without rearranging the sight, while the aiming point in height, as a rule, is chosen at the lower edge of the target.
The range of a direct shot depends, firstly, on the height of the target and, secondly, on the flatness of the trajectory. The higher the target and the flatter the trajectory, the greater the range of a direct shot and the greater the distance the target can be hit with one sight setting.
Rice. 21. Direct shot
The range of a direct shot can be determined from the tables, comparing the height of the target with the values of the greatest excess of the trajectory above the line of sight or with the height of the trajectory.
When shooting at a target that is at a distance greater than the range of a direct shot, the trajectory near the top rises above the target, and the target in a certain area will not be hit with this setting of the sight. In this case, there will be a space near the target, on which the descending branch of the trajectory will lie within its height.
The distance at which the descending branch of the trajectory is within the height of the target is called the affected space (see Fig. 22).
The depth (length) of the affected space directly depends on the height of the target and the flatness of the trajectory. It also depends on the angle of inclination of the terrain: when the terrain rises up, it decreases, when it slopes down, it increases.
Rice. 22. Affected space with a depth equal to the segment AC, for the target
height equal to segment AB
If the target is behind cover, impenetrable by a bullet, then the possibility of hitting it depends on where it is located.
The space behind the shelter from its crest to the meeting point is called the covered space (see Fig. 23). The covered space will be the greater, the greater the height of the shelter and the flatter the trajectory of the bullet.
The part of the covered space in which the target cannot be hit with a given trajectory is called dead (non-hit) space. Dead space will be the greater, the greater the height of the shelter, the lower the height of the target and the flatter the trajectory. The part of the covered space in which the target can be hit is the hit space.
Thus, the depth of the dead space is the difference between the covered and affected space.
Rice. 23. Covered, dead and affected space
The shape of the trajectory also depends on the muzzle velocity of the bullet, its kinetic energy and shape. Consider how these indicators affect the formation of the trajectory.
The further speed of its flight directly depends on the initial speed of the bullet, the value of its kinetic energy, with equal shapes and sizes, provides a smaller degree of speed reduction under the action of air resistance.
Thus, a bullet fired at the same elevation (throw) angle, but with a higher initial velocity or with higher kinetic energy, will have a higher speed during further flight.
If we imagine a certain horizontal plane at some distance from the departure point, then at the same value elevation angle-
When thrown (thrown), a bullet with a higher speed will reach it faster than a bullet with a lower speed. Accordingly, a slower bullet, having reached this plane and spending more time on it, will have time to go down more under the action of gravity (see Fig. 24).
Rice. 24. The dependence of the trajectory of the flight of a bullet on its speed
In the future, the trajectory of a bullet with lower speed characteristics will also be located below the trajectory of a faster bullet, and under the influence of gravity, it will drop faster in time and closer in distance from the point of departure to the level of the weapon’s horizon.
Thus, the muzzle velocity and kinetic energy of the bullet directly affect the height of the trajectory and the full horizontal range of its flight.
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. Existing also section forensic ballistics considered in the course of criminology and will not be covered in this manual.
Internal ballistics
Internal ballistics depends on the type of powder used and the type of barrel.
Conditionally trunks can be divided into long and short.
Long barrels (length over 250 mm) serve to increase the initial speed of the bullet and its flatness on the trajectory. Increases (compared to short barrels) accuracy. On the other hand, a long barrel is always more cumbersome than a short barrel.
Short barrels do not give the bullet that speed and flatness than long ones. The bullet has more dispersion. But short-barreled weapons are comfortable to wear, especially hidden, which is most appropriate for self-defense weapons and police weapons. On the other hand, trunks can be conditionally divided into rifled and smooth.
rifled barrels give the bullet greater speed and stability on the trajectory. Such barrels are widely used for bullet shooting. Various rifled nozzles are often used for firing bullet hunting cartridges from smoothbore weapons.
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 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, smokeless powder is used as standard for rifled weapons. 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 is somewhat shifted from the central axis of the bullet, therefore, in the cross section, a circle of bullet expansion 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) |
|
- Given the size of a standard head target 50x30 cm, and a chest target 50x50 cm, it can be noted that the maximum distance of a guaranteed hit is 600 m. At a greater distance, dispersion does not guarantee the accuracy of the shot.
Derivation
- Due to complex physical processes, a rotating bullet in flight deviates somewhat from the plane of fire. Moreover, in the case of right-handed rifling (the bullet rotates clockwise when viewed from behind), the bullet deviates to the right, in the case of left-handed rifling - to the left.
In table. 4 shows the values of derivational deviations when firing at different ranges. - Table 4
- Derivation
- Range of fire (m)
- Derivation (cm)
- 1000
- 1200
- It is easier to take into account the derivational deviation when shooting than dispersion. But, taking into account both of these values, it should be noted that the center of dispersion will shift somewhat by the value of the derivational displacement of the bullet.
Bullet displacement by wind
- Among all the external conditions affecting the flight of a bullet (humidity, pressure, etc.), it is necessary to single out the most serious factor - the influence of wind. The wind blows the bullet quite seriously, especially at the end of the ascending branch of the trajectory and beyond.
The displacement of the bullet by a side wind (at an angle of 90 0 to the trajectory) of medium force (6-8 m / s) is shown in Table. five. - Table 5
- Bullet displacement by wind
- Range of fire (m)
- Displacement (cm)
- To 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. It is usually used to determine the probability of penetration on various dis
- dances different classes 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 question is the most important characteristic to select weapons and ammunition for a particular operation. There are two types of impact of a bullet on a target: stopping and penetrating, in principle, these two concepts have an inverse relationship. Stopping effect (0V). Naturally, the enemy stops as reliably as possible when the bullet hits a certain place on the human body (head, spine, kidneys), but some types of ammunition have a large 0V when it hits secondary targets. In the general case, 0V is directly proportional to the caliber of the bullet, its mass and speed at the moment of impact with the target. Also, 0V increases when using lead and expansive bullets. It must be remembered that an increase in 0V reduces the length of the wound channel (but increases its diameter) and reduces the effect of a bullet on a target protected by armored clothing. One of the variants of the mathematical calculation of OM was proposed in 1935 by the American J. Hatcher: 0V = 0.178*m*V*S*k, where m is the mass of the bullet, g; V is the speed of the bullet at the moment of meeting with the target, m/s; S is the transverse area of the bullet, cm 2; k is the bullet shape factor (from 0.9 for full-shell to 1.25 for expansion bullets). According to such calculations, at a distance of 15 m, bullets of cartridges 7.62x25 TT, 9x18 PM and .45 have OB, respectively, 171, 250 in 640. For comparison: OB bullets of the cartridge 7.62x39 (AKM) \u003d 470, and bullets 7.62x54 ( ATS) = 650. Penetrating effect (PV). PV can be defined as the ability of a bullet to penetrate maximum depth to the target. Penetration is higher (ceteris paribus) for bullets of small caliber and weakly deformed in the body (steel, full-shell). The high penetrating effect improves the action of the bullet against armored targets. On fig. 19 shows the action of a standard PM jacketed bullet with a steel core. When a bullet enters the body, a wound channel and a wound cavity are formed. Wound channel - a channel pierced directly by a bullet. Wound cavity - a cavity of damage to fibers and blood vessels caused by tension and rupture of their bullet. Gunshot wounds are divided into through, blind, secant.
through wounds
A penetrating wound occurs when a bullet passes through the body. In this case, the presence of inlet and outlet holes is observed. The entrance hole is small, less than the caliber of the bullet. With a direct hit, the edges of the wound are even, and with a hit through tight clothing at an angle - with a slight tear. Often the inlet is quickly tightened. There are no traces of bleeding (except for the defeat of large vessels or when the wound is at the bottom). The exit hole is large, it can exceed the caliber of the bullet by orders of magnitude. The edges of the wound are torn, uneven, diverging to the sides. A rapidly developing tumor is observed. There is often heavy bleeding. With non-fatal wounds, suppuration quickly develops. With fatal wounds, the skin around the wound quickly turns blue. Through wounds are typical for bullets with a high penetrating effect (mainly for submachine guns and rifles). When a bullet passed through soft tissues, the internal wound was axial, with slight damage to neighboring organs. When wounded by a bullet cartridge 5.45x39 (AK-74), the steel core of the bullet in the body can come out of the shell. As a result, there are two wound channels and, accordingly, two outlets (from the shell and the core). Such injuries are most oftenth occur when it enters through dense clothing (pea jacket). Often the wound channel from the bullet is blind. When a bullet hits a skeleton, a blind wound usually occurs, but with a high power of the ammunition, a through wound is also likely. In this case, there are large internal injuries from fragments and parts of the skeleton with an increase in the wound channel to the outlet. In this case, the wound channel can "break" due to the ricochet of the bullet from the skeleton. Penetrating wounds to the head are characterized by cracking or fracture of the bones of the skull, often with a non-axial wound channel. The skull cracks even when hit by 5.6 mm lead-free jacketed bullets, not to mention more powerful ammunition. In most cases, these wounds are fatal. With penetrating wounds to the head, severe bleeding is often observed (prolonged leakage of blood from the corpse), of course, when the wound is located on the side or below. The inlet is quite even, but the outlet is uneven, with many cracks. A mortal wound quickly turns blue and swells. In case of cracking, violations of the skin of the head are possible. To the touch, the skull easily misses, fragments are felt. In case of wounds with sufficiently strong ammunition (bullets of cartridges 7.62x39, 7.62x54) and wounds with expansive bullets, a very wide exit hole with a long outflow of blood and brain matter is possible.Blind wounds
Such wounds occur when bullets from less powerful (pistol) ammunition hit, using expansive bullets, passing a bullet through the skeleton, and being wounded by a bullet at the end. With such wounds, the inlet is also quite small and even. Blind wounds are usually characterized by multiple internal injuries. When wounded by expansive bullets, the wound channel is very wide, with a large wound cavity. Blind wounds are often non-axial. This is observed when weaker ammunition hits the skeleton - the bullet goes away from the inlet, plus damage from fragments of the skeleton, the shell. When such bullets hit the skull, the latter cracks heavily. A large inlet is formed in the bone, and the intracranial organs are severely affected.Cutting wounds
Cutting wounds are observed when a bullet enters the body at an acute angle with a violation of only the skin and external parts of the muscles. Most of the injuries are harmless. Characterized by rupture of the skin; the edges of the wound are uneven, torn, often strongly divergent. Quite severe bleeding is sometimes observed, especially when large subcutaneous vessels rupture.
To solve the simplest ballistic problems, it is necessary to note the dependence of the bullet flight time on the firing range. Without taking into account this factor, it will be quite problematic to hit even a slowly moving target.
The time of flight of a bullet to the target is presented in Table. 6.
Table 6Bullet time to target
trajectory called a curved line, described by the center of gravity of a bullet (grenade) in flight. A bullet (grenade) when flying in the air is subject to the action of 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. 
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 (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. 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. The angle of elevation at which the full horizontal range of the bullet (grenade) becomes the greatest is called the angle of greatest range. The value of the angle of greatest range for bullets of various types of weapons is about 35 °. 
Trajectories obtained at elevation angles smaller than the angle of greatest range are called flat. Trajectories obtained at elevation angles greater than the angle of greatest angle of greatest range are called 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 and swarms of different elevation angles are called conjugated. 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.
To study the trajectory of a bullet, the following definitions are accepted:
Departure point- the center of the muzzle of the barrel. The departure point is the start of the trajectory. Weapon Horizon is the horizontal plane passing through the departure point. elevation line- a straight line, which is a continuation of the axis of the bore of the aimed weapon. Shooting plane- a vertical plane passing through the line of elevation. Elevation angle- the angle enclosed between the line of elevation and the horizon of the weapon. If this angle is negative, then it is called the angle of declination (decrease). Throw line- a straight line, which is a continuation of the axis of the bore at the time of the bullet's departure. Throwing angle Departure angle- the angle enclosed between the line of elevation and the line of throwing. drop point- the point of intersection of the trajectory with the horizon of the weapon. Angle of incidence- the angle enclosed between the tangent to the trajectory at the point of impact and the horizon of the weapon. Total horizontal range- the distance from the point of departure to the point of fall. final speed- the speed of the bullet (grenade) at the point of impact. Total flight time- the time of movement of a bullet (grenade) from the point of departure to the point of impact. Top of the path- the highest point of the trajectory above the horizon of the weapon. Trajectory height- the shortest distance from the top of the trajectory to the horizon of the weapon. Ascending branch of the trajectory- part of the trajectory from the departure point to the top, and from the top to the drop point - the descending branch of the trajectory. Aiming point (aiming)- the point on the target (outside it) at which the weapon is aimed. line of sight- a straight line passing from the shooter's eye through the middle of the sight slot (at the level with its edges) and the top of the front sight to the aiming point. aiming angle- the angle enclosed between the line of elevation and the line of sight. Target elevation angle- the angle enclosed between the aiming line and the horizon of the weapon. This angle is considered positive (+) when the target is higher and negative (-) when the target is below the weapon's horizon. Sighting range- distance from the departure point to the intersection of the trajectory with the line of sight. The excess of the trajectory over the line of sight is the shortest distance from any point of the trajectory to the line of sight. target line- a straight line connecting the departure point with the target. Slant Range- distance from the departure point to the target along the target line. meeting point- point of intersection of the trajectory with the surface of the target (ground, obstacles). Meeting angle- the angle enclosed between the tangent to the trajectory and the tangent to the target surface (ground, obstacles) at the meeting point. The meeting angle is taken as the smaller of the adjacent angles, measured from 0 to 90 degrees.
2.6 Direct shot - a shot in which the top of the bullet's flight path does not exceed the height of the target.
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 order of incomplete disassembly of the AK-74:
We disconnect the magazine, remove it from the fuse and distort the bolt carrier, make a control descent, right hand press the spring stop and remove the box cover, disconnect the frame with the piston, remove the bolt from the bolt frame, disconnect the gas tube, disconnect the muzzle brake-compensator, remove the shim.
2.7 The space behind cover that is not penetrated by a bullet, from its crest to the meeting point is called covered space
The part of the covered space in which the target cannot be hit with a given trajectory is called dead space (the more, the higher the height of the shelter)
The part of the covered area in which the target can be hit is called affected space
Derivation(from lat. derivatio- retraction, deviation) in military affairs - deviation of the flight path of a bullet or artillery projectile (this applies only to rifled weapons or special ammunition for smooth-bore weapons) under the influence of rotation imparted by barrel rifling, inclined nozzles or inclined stabilizers of the ammunition itself, that is, due to the gyroscopic effect and the effect Magnus. The phenomenon of derivation during the movement of oblong projectiles was first described in the works of the Russian military engineer, General N.V. Maievsky.
3.1 What charters are included in the ovu of the armed forces of the Russian Federation,
Charter of the internal service of the armed forces of the Russian Federation
Disciplinary charter of the armed forces of the Russian Federation
Charter of the garrison, commandant and guard services of the armed forces of the Russian Federation
Military charter of the armed forces of the Russian Federation
3.2 Military discipline is the strict and exact observance by all military personnel of the order and rules established by the laws of the Russian Federation, the general military regulations of the Armed Forces of the Russian Federation (hereinafter referred to as the general military regulations) and orders of commanders (chiefs).
2. Military discipline is based on the awareness of each serviceman of military duty and personal responsibility for the defense of the Russian Federation. It is built on a legal basis, respect for the honor and dignity of servicemen.
The main method of instilling discipline among servicemen is persuasion. However, this does not exclude the possibility of using coercive measures against those who are not conscientious in the performance of their military duty.
3. Military discipline obliges each soldier:
be faithful to the Military Oath (obligation), strictly observe the Constitution of the Russian Federation, the laws of the Russian Federation and the requirements of general military regulations;
perform their military duty skillfully and courageously, conscientiously study military affairs, protect state and military property;
unquestioningly carry out the assigned tasks in any conditions, including at the risk of life, endure the hardships of military service;
be vigilant, strictly keep state secrets;
to maintain the rules of relations between servicemen determined by general military regulations, to strengthen the military camaraderie;
show respect to commanders (chiefs) and each other, observe the rules of military greeting and military courtesy;
behave with dignity in public places, prevent oneself and keep others from unworthy acts, contribute to the protection of the honor and dignity of citizens;
comply with the norms of international humanitarian law in accordance with the Constitution of the Russian Federation.
4. Military discipline is achieved:
instilling moral-psychological, combat qualities and conscious obedience to commanders (chiefs) among military personnel;
knowledge and observance by military personnel of the laws of the Russian Federation, other regulatory legal acts of the Russian Federation, the requirements of general military regulations and the norms of international humanitarian law;
the personal responsibility of each serviceman for the performance of duties of military service;
maintaining internal order in the military unit (subdivision) by all military personnel;
a clear organization of combat training and its full coverage of personnel;
everyday exactingness of commanders (chiefs) to subordinates and control over their diligence, respect for the personal dignity of military personnel and constant concern for them, skillful combination and correct application of measures of persuasion, coercion and social influence of the team;
the creation in the military unit (subdivision) of the necessary conditions for military service, life and a system of measures to limit the dangerous factors of military service.
5. The commander and deputy commander for educational work are responsible for the state of military discipline in a military unit (subunit), who must constantly maintain military discipline, require subordinates to observe it, encourage the worthy, strictly but fairly exact from the negligent.
Military discipline must be observed in the unit, it is a necessary condition for the life of the army.
The effectiveness of work to strengthen military discipline in the armed forces largely depends on the activities of the officer in charge, and the state of law and order and discipline among subordinates is the main criterion for evaluating the daily activities of commanders.
28% of the dead comes in number suicidal.
Consistency, and the habit of strict order.
Discipline is a Teaching, a science.
The characteristic features of military discipline are:
unity of command
Strict regulation of all aspects of life and activities of military personnel
Obligation and unconditional performance
Clear subordination
The inevitability and severity of coercive measures against violators of military discipline.
To form a team, the essential factors are:
High performance
Healthy public opinion (take into account the opinion of the team)
sense of responsibility
General optimistic mood of the team
Willingness to overcome difficulties
Analysis of the state of military discipline:
Requirements for an officer: must think logically, build reasoning correctly, reason, draw conclusions.
Master the rules of formal logic
Stages of analytical work on studying the state of military discipline:
Planning
Collection of information
Data processing
Identification of the causes of violation of military disciplines
3.3 Internal order and how it is achieved. Fire safety measures in V.Ch. and divisions
The internal order is the strict observance of the rules of accommodation, daily activities, life of military personnel in a military unit (subdivision) and serving in a daily outfit determined by military regulations.
Internal order is achieved:
deep understanding, conscious and precise fulfillment by all military personnel of the duties determined by laws and military regulations;
purposeful educational work, a combination of the high demands of commanders (chiefs) with constant concern for subordinates and maintaining their health;
clear organization of combat training;
exemplary bearing combat duty and daily service;
exact implementation of the daily routine and regulations of working hours;
compliance with the rules for the operation (use) of weapons, military equipment and other materiel; creating conditions for their daily activities, life and life in the locations of military personnel that meet the requirements of military regulations;
compliance with the requirements fire safety, as well as the adoption of measures to protect the environment in the area of activity of the military unit.
Fire safety measures:
The territory of the military unit must be constantly cleared of debris and dry grass.
military property must be equipped with lightning protection devices and other engineering systems that ensure its fire and explosion safety in accordance with the requirements of the current rules and regulations.
Entrances to sources of fire water supply, to buildings and all passages through the territory must always be free for the movement of fire engines. Similarly, passageways within a unit and subdivision must be uncluttered.
It is forbidden to make a fire and keep an open fire closer than 50m from the top. Use defective equipment and use flammable products. Telephone sets must have inscriptions indicating the telephone number of the nearest fire brigade, and on the territory of the military unit for sounding a fire alarm there must be sound alarms. These and other fire safety standards must be checked daily by the duty officer.
An order is an order of the commander-in-chief addressed to subordinates and requiring the obligatory performance of certain actions, compliance with the rules or establishing some kind of order for its delivery. In writing or by technical communication to one or a group of military personnel. Discussion of an order is not allowed. Failure to comply with an order given in the prescribed manner is a crime against military service.
An order is a form of bringing tasks by the head of the task to subordinates on private issues. It is given in writing or orally. It is issued in writing by the chief of staff, is an administrative document and is given on the estate of the unit commander
When giving an order, someone should not abuse official powers. Do not give an order that is not related to the conduct of military service.
The order is formulated clearly and concisely. They are given in order of subordination.
Completed without question and on time.
The soldier answers "yes".
unity of command
It consists in vesting the commander (chief) with full administrative power in relation to subordinates and placing on him personal responsibility for all aspects of the life and activities of a military unit, unit and each serviceman.
determines the construction of the army as a centralized military organism, the unity of training and education of personnel, organization and discipline, and, ultimately, the high combat readiness of the troops. It should be noted that it best ensures the unity of will and actions of all personnel, strict centralization, maximum flexibility and efficiency in command and control of troops. Unity of command allows the commander to act boldly, decisively, to show broad initiative, placing on the commander personal responsibility for all aspects of the life of the troops, and contributes to the development of the necessary commanding qualities in officers. It creates conditions for high organization, strict military discipline and firm order.