KRASNODAR UNIVERSITY

Fire training

Specialties: 031001.65 Law enforcement activities,

specialization: operational and investigative activities

(activities of a criminal investigation officer)

LECTURE

Topic No. 5: “Basics of ballistics”

Time: 2 hours.

Venue: university shooting range

Methodology: story, show

Main content of the topic: Information about explosives, their classification. Information about internal and external ballistics. Factors influencing the accuracy and accuracy of shooting. The average point of impact and methods for determining it.

Material support.

1. Stands, posters.

Purpose of the lesson:

1. Familiarize cadets with explosives used in the manufacture of ammunition and their classification.

2. To familiarize cadets with the basics of internal and external ballistics.

3. Teach cadets to determine the midpoint of impact and how to determine it.

4. To develop discipline and diligence among cadets.

Practical lesson plan

Introduction – 5 min.

Check the availability of cadets and readiness for classes;

Announce the topic, goals, educational issues.

Main part – 80 min.

Conclusion – 5 min.

Summarize the lesson briefly;

Remind the topic, goals of the lesson and how they were achieved;

Remind study questions;

Answer any questions that arise;

Give assignments for independent preparation.

Basic literature:

1. Manual on shooting. – M.: Military Publishing House, 1987.

Further reading:

1. Fire training: textbook / edited by general editors. – 3rd ed., rev. and additional – Volgograd: VA Ministry of Internal Affairs of Russia, 2009.

2. Menshikov’s training in the internal affairs bodies: Tutorial. – St. Petersburg, 1998.

During the lesson, educational issues are considered sequentially. For this purpose, the training group is located in the fire training class.

Ballistics is the science that studies the flight of a bullet (shell, grenade). There are four areas of research in ballistics:

Internal ballistics, which studies the processes occurring during a shot inside the bore of a firearm;

Intermediate ballistics, which studies the flight of a bullet at a certain distance from the muzzle of the barrel, when the powder gases still continue to affect the bullet;

External ballistics, which studies the processes occurring with a bullet in the air after the influence of powder gases on it ceases;

Target ballistics, which studies the processes occurring with a bullet in a dense environment.

Explosives

Explosives These are chemical compounds and mixtures that, under the influence of external influences to very rapid chemical transformations accompanied by

the release of heat and the formation of a large amount of highly heated gases capable of producing throwing or destruction work.

The powder charge of a rifle cartridge weighing 3.25 g burns out in approximately 0.0012 seconds when fired. When a charge burns, about 3 calories of heat are released and about 3 liters of gases are formed, the temperature of which reaches up to degrees at the moment of firing. The gases, being highly heated, exert strong pressure (up to 2900 kg per sq. cm) and eject the bullet from the barrel at a speed of over 800 m/s.

An explosion can be caused by: mechanical impact - impact, puncture, friction, thermal, electrical impact - heating, spark, flame ray, explosion energy of another explosive sensitive to thermal or mechanical impact (explosion of a detonator capsule).

Combustion- the process of explosive transformation, occurring at a speed of several meters per second and accompanied by a rapid increase in gas pressure, resulting in the throwing or scattering of surrounding bodies. An example of explosive combustion is the combustion of gunpowder when fired. The burning rate of gunpowder is directly proportional to pressure. In the open air, the burning speed of smokeless powder is about 1 mm/s, and in the barrel bore, when fired, due to increased pressure, the burning speed of the gunpowder increases and reaches several meters per second.

Based on the nature of their action and practical application, explosives are divided into initiating, crushing (high explosive), propellant and pyrotechnic compositions.

Explosion is a process of explosive transformation that occurs at a speed of several hundred (thousands) meters per second and is accompanied by a sharp increase in gas pressure, which produces a strong destructive effect on nearby objects. The higher the rate of explosive transformation, the more power its destruction. When an explosion proceeds at the maximum speed possible under given conditions, then such a case of explosion is called detonation. The detonation speed of a TNT charge reaches 6990 m/s. The transmission of detonation over a distance is associated with the propagation in the environment surrounding the explosive charge of a sharp increase in pressure - a shock wave. Therefore, excitation of an explosion in this way is almost no different from excitation of an explosion by means of a mechanical shock. Depending on the chemical composition of the explosive and the conditions of the explosion, explosive transformations can occur in the form of combustion.

Initiators These are explosives that are highly sensitive, explode from minor thermal or mechanical effects and, by their detonation, cause an explosion of other explosives. Initiating explosives include mercury fulminate, lead azide, lead styphnate, and tetrazene. Initiating explosives are used to equip igniter caps and detonator caps.

Crushing(high explosives) are called explosives that explode, as a rule, under the influence of detonation of the initiating explosives and during the explosion, surrounding objects are crushed. Crushing explosives include: TNT, melinite, tetryl, hexogen, PETN, ammonites, etc. Pyroxelin and nitroglycerin are used as starting materials for the manufacture of smokeless gunpowder. Crushing explosives are used as explosive charges for mines, grenades, shells, and are also used in blasting operations.

Throwing These are called explosives that have an explosive transformation in the form of combustion with a relatively slow increase in pressure, which allows them to be used for throwing bullets, mines, grenades, and shells. Propellant explosives include various types of gunpowder (smoky and smokeless). Black powder is a mechanical mixture of saltpeter, sulfur and charcoal. It is used for loading fuses for hand grenades, remote tubes, fuses, preparing fire cords, etc. Smokeless powders are divided into pyroxelin and nitroglycerin powder. They are used as combat (powder) charges for firearms; pyroxelin powder - for powder charges of small arms cartridges; nitroglycerin, as more powerful, - for combat charges of grenades, mines, shells.

Pyrotechnic the compositions are mixtures of flammable substances (magnesium, phosphorus, aluminum, etc.), oxidizing agents (chlorates, nitrates, etc.) and cementing agents (natural and artificial resins, etc.) In addition, they contain special-purpose impurities; substances that color flames; substances that reduce the sensitivity of the composition, etc. The predominant form of transformation of pyrotechnic compositions under normal conditions of their use is combustion. When burned, they give the corresponding pyrotechnic (fire) effect (lighting, incendiary, etc.)

Pyrotechnic compositions are used to equip lighting and signal cartridges, tracer and incendiary compositions of bullets, grenades, and shells.

Brief Introduction to Internal Ballistics

Shot and its periods.

A shot is the ejection of a bullet from the barrel by the energy of gases formed during the combustion of a powder charge. When fired from small arms the following phenomena occur. The impact of the firing pin on the primer of the combat cartridge 2 explodes the percussion composition of the primer and a flame is formed, which penetrates through the seed holes in the bottom of the cartridge case to the powder charge and ignites it. When a charge burns, it forms large number highly heated powder gases, creating high pressure in the barrel bore on the bottom of the bullet, the bottom and walls of the cartridge case, and also on the walls of the barrel and the bolt. As a result of the pressure of the powder gases on the bottom of the bullet, it moves from its place and crashes into the rifling. Moving along the rifling, the bullet acquires a rotational motion and, gradually increasing speed, is thrown outward along the axis of the barrel bore. The pressure of the gases on the bottom of the cartridge case causes the weapon to move backward - recoil. The pressure of the gases on the walls of the cartridge case and barrel causes them to stretch (elastic deformation), and the cartridge case, pressing tightly against the chamber, prevents the breakthrough of powder gases towards the bolt. When fired, it also happens oscillatory motion(vibration) of the barrel and it heats up. Hot gases and particles of unburned gunpowder, flowing out after the bullet, when meeting air, generate a flame and shock wave; the latter is the source of sound when fired.

Approximately 25-35% of the energy of powder gases is spent on communication; 25% is spent on secondary work; about 40% of the energy is not used and is lost after the bullet leaves.

The shot occurs in a very short period of time, 0.001-0.06 seconds.

When firing, there are four consecutive periods:

Preliminary, which lasts from the moment the gunpowder ignites until the bullet completely penetrates the rifling of the barrel;

The first or main one, which lasts from the moment the bullet hits the rifling until the complete combustion of the powder charge;

The second, which lasts from the moment the charge is completely burned until the bullet leaves the barrel,

The third or gas aftereffect period lasts from the moment the bullet leaves the barrel until the gas pressure ceases to act on it.

For short-barreled weapons, the second period may be absent.

Initial bullet speed

The initial velocity is taken to be the conditional speed of the bullet, which is less than the maximum, but greater than the muzzle. The initial speed is determined using calculations. Initial speed is the most important characteristic of a weapon. The higher the initial speed, the greater its kinetic energy and, therefore, the greater the flight range, direct shot range, and penetrating effect of the bullet. The influence of external conditions on the flight of a bullet has less effect with increasing speed.

The magnitude of the initial velocity depends on the length of the barrel, the weight of the bullet, the weight, temperature and humidity of the powder charge, the shape and size of the powder grains and the loading density. Loading density is the ratio of the weight of the charge to the volume of the cartridge case when the bullet is inserted. When the bullet is planted very deeply, the initial velocity increases, but due to a large pressure surge when the bullet leaves, the gases can rupture the barrel.

Weapon recoil and launch angle.

Recoil is the backward movement of the weapon (barrel) during a shot. The recoil speed of a weapon is as many times less as the bullet is lighter than the weapon. The pressure force of the powder gases (recoil force) and the recoil resistance force (butt stop, handle, center of gravity of the weapon) are not located on the same straight line and are directed in opposite directions. They form a pair of forces that deflect the muzzle of the weapon upward. The larger the leverage of application of forces, the greater the magnitude of this deviation. The vibration of the barrel also deflects the muzzle, and the deflection can be directed in any direction. The combination of recoil, vibration and other reasons lead to the fact that at the moment of firing the axis of the barrel bore deviates from its original position. The amount of deviation of the barrel bore axis at the moment of bullet departure from its initial position is called the departure angle. The take-off angle increases with incorrect application, use of a stop, or contamination of the weapon.

The effect of powder gases on the barrel and measures to preserve it.

During the shooting process, the barrel is subject to wear. The reasons causing barrel wear can be divided into three groups: mechanical; chemical; thermal.

Reasons of a mechanical nature - impacts and friction of the bullet on the rifling, improper cleaning of the barrel without an inserted nozzle cause mechanical damage to the surface of the barrel bore.

Reasons of a chemical nature are caused by chemically aggressive powder soot, which remains after firing on the walls of the barrel bore. Immediately after shooting, it is necessary to thoroughly clean the bore and lubricate it with a thin layer of gun lubricant. If this is not done immediately, carbon deposits penetrating into microscopic cracks in the chrome coating cause accelerated corrosion of the metal. By cleaning the barrel and removing carbon deposits some time later, we will not be able to remove traces of corrosion. After the next shooting, the corrosion will penetrate deeper. later chrome chips and deep cavities will appear. Between the walls of the barrel bore and the walls of the bullet, the gap will increase into which gases will break through. The bullet will be given a lower flight speed. The destruction of the chrome coating of the barrel walls is irreversible.

Thermal reasons are caused by periodic local strong heating of the walls of the bore. Together with periodic stretching, they lead to the appearance of a network of cracks, setting the metal in the depths of the cracks. This again leads to chipping of chrome from the walls of the bore. On average, with proper weapon care, the survivability of a chrome-plated barrel is 20-30 thousand shots.

Brief information about external ballistics

External ballistics is the science that studies the movement of a bullet after the action of powder gases on it ceases.

Having flown out of the barrel under the influence of powder gases, the bullet (grenade) moves by inertia. Grenade having jet engine, moves by inertia after the exhaust of gases from the jet engine. The force of gravity causes the bullet (grenade) to gradually decline, and the force of air resistance continuously slows down the movement of the bullet and tends to knock it over. Part of the bullet's energy is spent on overcoming the force of air resistance.

Trajectory and its elements

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

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 reasons: air friction, vortex formation and ballistic wave formation.

Air particles in contact with a moving bullet (grenade), due to internal cohesion (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 varies 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, resulting in a pressure difference between the head and bottom parts. This difference creates a force directed in the direction opposite to the movement of the bullet, and reduces its flight speed. Air particles, trying to fill the vacuum formed behind the bullet, create a vortex.

When flying, a bullet (grenade) collides with air particles and causes them to vibrate. As a result, the air density in front of the bullet (grenade) increases and sound waves are formed. Therefore, the flight of a bullet (grenade) is accompanied by a characteristic sound. When the speed of a bullet (grenade) 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 speed of the bullet (grenade). When the bullet's flight speed is greater than the speed of sound, the sound waves collide with each other to create a wave of highly compressed air - a ballistic wave that slows down the bullet's flight speed, since the bullet spends part of its energy creating this wave.

The resultant (total) of all forces generated as a result of the influence of air on the flight of a bullet (grenade) is the force of air resistance. The point of application of the resistance force is called the center of resistance. The effect of air resistance on the flight of a bullet (grenade) is very great; it causes a decrease in the speed and range of a bullet (grenade). For example, a bullet arr. 1930, with a throwing angle of 15° and an initial speed of 800 m/s in airless space, it would fly to a distance of 32620 m; the flight range of this bullet under the same conditions, but in the presence of air resistance, is only 3900 m.

The magnitude of the air resistance force depends on the flight speed, shape and caliber of the bullet (grenade), as well as on its surface and air density. The force of air resistance increases with increasing bullet speed, caliber and air density. At supersonic bullet flight speeds, when the main cause of air resistance is the formation of air compaction in front of the warhead (ballistic wave), bullets with an elongated pointed head are advantageous. At subsonic flight speeds of a grenade, when the main cause of air resistance is the formation of rarefied space and turbulence, grenades with an elongated and narrowed tail section are advantageous.

The smoother the surface of the bullet, the less frictional force and air resistance. The variety of shapes of modern bullets (grenades) is largely determined by the need to reduce the force of air resistance.

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

To prevent the bullet from tipping over under the influence of air resistance, it is given a rapid rotational movement using rifling in the barrel bore. For example, when fired from a Kalashnikov assault rifle, the rotation speed of the bullet at the moment it leaves the barrel is about 3000 rpm.

When a rapidly rotating bullet flies through the air, the following phenomena occur. The force of air resistance tends to turn the bullet head up and back. But the head of the bullet, as a result of rapid rotation, according to the property of the gyroscope, tends to maintain its given position and will not deviate upward, but very slightly in the direction of its rotation at a right angle to the direction of the air resistance force, i.e. to the right. As soon as the head of the bullet deviates to the right, the direction of action of the air resistance force will change - it tends to turn the head of the bullet to the right and back, but the rotation of the head of the bullet will not occur to the right, but down, etc. Since the action of the air resistance force is continuous, and its direction relative to the bullet changes with each deviation of the bullet axis, then the head of the bullet describes a circle, and its axis is a cone with its apex at the center of gravity. The so-called slow conical, or precessional, movement occurs, and the bullet flies with its head forward, i.e., as if following the change in the curvature of the trajectory.

The axis of slow conical motion lags somewhat behind the tangent to the trajectory (located above the latter). Consequently, the bullet collides with the air flow more with its lower part and the axis of slow conical movement deviates in the direction of rotation (to the right with a right-hand rifling of the barrel). The deviation of a bullet from the firing plane in the direction of its rotation is called derivation.

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

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

The stability of the grenade in flight is ensured by the presence of a stabilizer, which allows the center of air resistance to be moved back, beyond the center of gravity of the grenade. As a result, the force of air resistance turns the axis of the grenade to a tangent to the trajectory, forcing the grenade to move forward with its head. To improve accuracy, some grenades are given a slow rotation due to the outflow of gases. Due to the rotation of the grenade, the moments of force deflecting the axis of the grenade act sequentially in different directions, so the accuracy of fire improves.

To study the trajectory of a bullet (grenade), the following definitions are accepted:

The center of the muzzle of the barrel is called the take-off point. The departure point is the beginning of the trajectory.

The horizontal plane passing through the point of departure is called the horizon of the weapon. In drawings showing the weapon and 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 that is a continuation of the axis of the barrel of an aimed weapon is called elevation line.

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

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

The straight line, which is a continuation of the axis of the barrel bore at the moment the bullet leaves, is called throwing line.

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

The angle between the elevation line and the throwing line is called departure angle .

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

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

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

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

The time it takes a bullet (grenade) to travel from the point of departure to the point of impact is called total flight time.

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

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

The part of the trajectory from the departure point to the top is called the ascending branch; the part of the trajectory from the top to the falling point is called downward branch of the trajectory.

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

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 aiming line.

The angle between the elevation line and the aiming line is called aiming angle.

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

The shortest distance from any point on the trajectory to the aiming line is called exceeding the trajectory above the aiming line.

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

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

The angle between the tangent to the trajectory and the tangent to the surface of the target (ground, obstacle) at the meeting point is called meeting angle. The meeting angle is taken to be the smaller of the adjacent angles, measured from 0 to 90°.

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

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

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

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

The lowest flight speed of a bullet when shooting at large throwing angles is on the downward branch of the trajectory, and when shooting at small throwing angles - at the point of impact;

The time it takes a bullet to move along the ascending branch of the trajectory is less than along the descending branch;

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

The trajectory of a grenade in the air can be divided into two sections: active - the flight of the grenade under the influence of reactive force (from the point of departure to the point where the action of the reactive force ceases) and passive - the flight of the grenade by inertia. The shape of a grenade's trajectory is approximately the same as that of a bullet.

Scattering phenomenon

When firing from the same weapon, with the most careful observance of the accuracy and uniformity of firing, each bullet (grenade), due to a number of random reasons, describes its trajectory and has its own point of impact (meeting point), which does not coincide with the others, as a result of which bullets are scattered ( pomegranate). The phenomenon of scattering of bullets (grenades) when firing from the same weapon under almost identical conditions is called natural scattering of bullets (grenades) or scattering of trajectories.

The set of trajectories of bullets (grenades), obtained as a result of their natural dispersion, is called a sheaf of trajectories (Fig. 1). The trajectory passing in the middle of the sheaf of trajectories is called the middle trajectory. Tabular and calculated data refer to the average trajectory,

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

The area on which the meeting points (holes) of bullets (grenades) obtained when a sheaf of trajectories intersect with any plane are located is called the dispersion area. The dispersion area usually has the shape of an ellipse. When shooting from small arms at close ranges, the dispersion area in the vertical plane may have the shape of a circle. Mutually perpendicular lines drawn through the center of dispersion (the middle point of impact) so that one of them coincides with the direction of fire are called dispersion axes. The shortest distances from the meeting points (holes) to the dispersion axes are called deviations.

Reasons for dispersion

The reasons causing the dispersion of bullets (grenades) can be summarized into three groups:

The reasons causing the variety of initial speeds;

Reasons for the variety of throwing angles and shooting directions;

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

The reasons causing the variety of initial speeds are:

Variety in the weight of powder charges and bullets (grenades), in the shape and size of bullets (grenades) and cartridges, 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 residence time of the cartridge (grenade) in the barrel heated during firing;

Variety in degree of heating and good quality condition trunk

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

The reasons causing the variety of throwing angles and firing directions are:

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

A variety of departure angles and lateral displacements of weapons, resulting from non-uniform preparation for shooting, unstable and non-uniform holding of automatic weapons, especially during burst fire, improper use of stops and non-smooth trigger release;

Angular vibrations of the barrel when firing automatic fire, resulting from the movement and impacts 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 size of the dispersion area and mainly depend on the training of the shooter.

The reasons causing the variety of bullet (grenade) flight conditions are:

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

Diversity in weight, shape and size of bullets (grenades), leading to a change in the magnitude of the air resistance force. These reasons lead to an increase in dispersion in the lateral direction and along the range (height) and mainly depend on the external shooting conditions and on the ammunition.

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

It is impossible to completely eliminate the causes that cause dispersion, and, consequently, to eliminate dispersion itself. However, knowing the reasons on which dispersion depends, you can reduce the influence of each of them and thereby reduce 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 shooting rules, correct preparation for shooting, uniform buttstock, accurate aiming (aiming), smooth trigger release, stable and uniform holding of the weapon when shooting, as well as proper care of weapons and ammunition.

Law of dispersion

At large number shots (more than 20), a certain pattern is observed in the location of meeting points on the dispersion area. The dispersion 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 located unevenly - more densely towards the center of dispersion and less often towards the edges of the dispersion area.

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

3. The meeting points (holes) in each particular case occupy not an infinite, but limited area. Thus, the law of dispersion in general can be formulated as follows: with a sufficiently large number of shots fired under almost identical conditions, the dispersion of bullets (grenades) is uneven, symmetrical and not infinite.

Determination of the average point of impact (MIP)

When determining the STP, it is necessary to identify clearly detached holes.

A hole is considered to be clearly torn off if it is more than three diameters of the firing accuracy gauge away from the intended STP.

With a small number of holes (up to 5), the position of the STP is determined by the method of sequential or proportional division of the segments.

The method of sequential division of segments is as follows:

connect two holes (meeting points) with a straight line and divide the distance between them in half, connect the resulting point with the third hole (meeting point) and divide the distance between them into three equal parts; since the holes (meeting points) are located more densely towards the center of dispersion, the division closest to the first two holes (meeting points) is taken as the average hit point of the three holes (meeting points), connect the found average hit point for the three holes (meeting points) with the fourth hole (meeting point) and divide the distance between them into four equal parts; the division closest to the first three holes is taken as the midpoint of impact of the four holes.

The proportional division method is as follows:

Connect four adjacent holes (meeting points) in pairs, connect the midpoints of both straight lines again and divide the resulting line in half; the division point will be the midpoint of the hit.

Aiming (aiming)

In order for a bullet (grenade) to reach the target and hit it or the desired point on it, it is necessary to give the axis of the barrel bore a certain position in space (in the horizontal and vertical planes) before firing.

Giving the axis of the bore of a weapon the position in space necessary for shooting is called aiming or aiming.

Giving the axis of the barrel bore the required position in the horizontal plane is called horizontal aiming. Giving the axis of the barrel bore the required position in the vertical plane is called vertical aiming.

Aiming is carried out using sights and aiming mechanisms and is carried out in two stages.

First, a diagram of angles is constructed on the weapon using sighting devices, corresponding to the distance to the target and corrections for various shooting conditions (the first stage of aiming). Then, using guidance mechanisms, the angle pattern built on the weapon is combined with the pattern determined on the ground (the second stage of guidance).

If horizontal and vertical aiming is carried out directly at the target or at an auxiliary point near the target, then such aiming is called direct.

When firing from small arms and grenade launchers, direct fire is used, carried out using a single aiming line.

The straight line connecting the middle of the sight slot to the top of the front sight is called the sighting line.

To carry out aiming using an open sight, it is necessary first by moving the rear sight (sight slot) to give the aiming line such a position that an aiming angle corresponding to the distance to the target is formed between this line and the axis of the bore in the vertical plane, and an angle in the horizontal plane, equal to the lateral correction, depending on the speed of the crosswind, derivation or speed of lateral movement of the target. Then, by directing the aiming line at the target (changing the position of the barrel using aiming mechanisms or moving the weapon itself, if there are no aiming mechanisms), give the axis of the barrel bore the required position in space.

In weapons that have a permanent rear sight installation (for example, a Makarov pistol), the required position of the bore axis in the vertical plane is achieved by selecting an aiming point corresponding to the distance to the target and directing the aiming line to this point. In a weapon that has a sight slot that is fixed in the lateral direction (for example, a Kalashnikov assault rifle), the required position of the barrel bore axis in the horizontal plane is given by selecting an aiming point corresponding to the lateral correction and directing the aiming line towards it.

The aiming line in an optical sight is a straight line passing through the top of the aiming stump and the center of the lens.

To carry out aiming using an optical sight, it is necessary first, using the sight mechanisms, to give the aiming line (carriage with the sight reticle) a position in which an angle equal to the aiming angle is formed between this line and the axis of the barrel bore in the vertical plane, and an angle in the horizontal plane , equal to the lateral correction. Then, by changing the position of the weapon, you need to align the aiming line with the target. in this case, the axis of the barrel bore is given the required position in space.

Direct shot

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

direct shot.

Within the range of a direct shot, during tense moments of battle, shooting can be carried out without rearranging the sight, while the vertical aiming point is usually selected at the lower edge of the target.

The range of a direct shot depends on the height of the target and the flatness of the trajectory. The higher the target and the flatter the trajectory, the greater the range of a direct shot and the greater the area over which the target can be hit with one sight setting. Each shooter must know the range of a direct shot at various targets from his weapon and skillfully determine the range of a direct shot when shooting. The direct shot range can be determined from tables by comparing the target height with the values ​​of the greatest elevation above the aiming line or trajectory height. The flight of a bullet in the air is influenced by meteorological, ballistic and topographic conditions. When using tables, you must remember that the trajectory data in them corresponds to normal shooting conditions.

Barometer" href="/text/category/barometr/" rel="bookmark">barometric) pressure on the weapon horizon 750 mm Hg;

The air temperature on the horizon of the weapon is +15C;

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

There is no wind (the atmosphere is still).

b) Ballistic conditions:

The weight of the bullet (grenade), initial speed and angle of departure are equal to the values ​​​​indicated in the shooting tables;

Charge temperature +15°C;

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

The height of the front sight is set based on the data of bringing the weapon to normal combat; The heights (divisions) of the sight correspond to the table aiming angles.

c) Topographic conditions:

The target is on the weapon's horizon;

There is no lateral tilt of the weapon.

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

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

With every 100 m increase in terrain, atmospheric pressure decreases by an average of 9 mm.

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

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

As the temperature of the powder charge increases, the burning rate of the powder, the initial speed and the flight range of the bullet (grenade) increase.

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

With a tailwind, the speed of a 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 speed of the bullet relative to the air will be equal to 790 m/s (800-10).

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

In a headwind, the speed of the bullet relative to the air will be greater than in a calm environment, therefore, the force of air resistance will increase and the bullet's flight range will decrease.

Longitudinal (tailwind, headwind) wind has an insignificant effect on the flight of a bullet, and in the practice of shooting from small arms, corrections for such wind are not introduced. When firing grenade launchers, corrections for strong longitudinal winds should be taken into account.

Side wind puts pressure on lateral surface the bullet and deflects it away from the firing plane depending on its direction: the wind from the right deflects the bullet to the left, the wind from the left to the right.

During the active phase of the flight (when the jet engine is running), the grenade is deflected in the direction from which the wind is blowing: with a wind from the right - to the right, with a wind from the left - to the left. This phenomenon is explained by the fact that the side wind turns the tail part 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 is blowing. During the passive part of the trajectory, the grenade deviates in the direction the wind is blowing.

Cross wind has a significant impact, especially on grenade flight, and must be taken into account when firing grenade launchers and small arms.

The wind blowing at an acute angle to the shooting plane simultaneously influences both the change in the flight range of the bullet and its lateral deflection.

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

When shooting with the same sight setting (with the same 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 force of air resistance, the value of the inclined (sighting) range of the bullet (grenade) changes. When shooting at small elevation angles of the target (up to ±15°), this flight range of the bullet (grenade) changes very slightly, therefore, equality of the inclined and full horizontal flight ranges of the bullet is allowed, i.e., the shape (rigidity) of the trajectory remains unchanged.

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

Conclusion

Today we got acquainted with the factors influencing the flight of a bullet (grenade) in the air and the law of dispersion. All shooting rules for various types weapons are designed for the median trajectory of a bullet. When aiming a weapon at a target, when choosing initial data for shooting, it is necessary to take into account ballistic conditions.

Outside the gun barrel. There is also a concept terminal(finite) ballistics, having to do with the interaction of the projectile and the body it hits, and the movement of the projectile after impact. Terminal ballistics is carried out by gunsmiths who are specialists in projectiles and bullets, strength specialists and other armor and protection specialists, as well as forensic scientists. Also in practical physics, the law of leverage is used in this direction.

The main task of scientific biology is the mathematical solution of the problem of the dependence of the curved flight (trajectory) of thrown and fired bodies on its factors (powder force, gravity, air resistance, friction). For this purpose, knowledge of higher mathematics is necessary, and the results obtained in this way are of value only for people of science and weapons designers. But it is clear that for a practical soldier, shooting is a matter of simple skill.

Story

The first studies regarding the shape of the flight curve of a projectile (from a firearm) were made in 1546 by Tartaglia. Galileo established his parabolic theory through the laws of gravity, in which the influence of air resistance on projectiles was not taken into account. This theory can be applied without much error to the study of the flight of nuclei only with little air resistance. We owe the study of the laws of air resistance to Newton, who proved in 1687 that the flight curve cannot be a parabola. Robins (in 1742) began to determine the initial velocity of the nucleus and invented the ballistic pendulum, which is still in use today. The first real solution to the basic problems of ballistics was given by the famous mathematician Euler. The further movement of B. was given by Gutton, Lombard (1797) and Obenheim (1814). From 1820 onwards, the influence of friction began to be studied more and more, and the physicist Magnus, the French scientists Poisson and Didion and the Prussian Colonel Otto worked a lot in this regard. A new impetus for the development of gunfire was the introduction into general use of rifled firearms and oblong projectiles. B. questions began to be diligently developed by artillerymen and physicists of all countries; to confirm theoretical conclusions, experiments began to be carried out, on the one hand, in artillery academies and schools, on the other hand, in weapons manufacturing factories; for example, very complete experiments to determine air resistance were carried out in St. Petersburg. in 1868 and 1869, according to resolution. gen.-ad. Barantsev, Honored Professor of the Mikhailovsky Artillery Academy, N.V. Maievsky, who provided great services to B., and in England Bashfort. IN lately On the experimental field of the Krupp cannon factory, the speed of projectiles from guns of different calibers at various points of the trajectory was determined, and very important results were achieved. In addition to N.V. Maievsky, whose merits are properly appreciated by all foreigners, among many scientists, in modern times those who worked on B. are especially noteworthy: prof. Alzh. Lycée Gautier, French artillerymen - gr. Saint Robert, c. Magnus de Sparr, Major Musot, Capt. Jouffre; Italian art. capit. Siacci, who outlined the solution to the problems of aimed shooting in 1880; Noble, Neumann, Pren, Able, Rezal, Sarro and Piobert, who laid the foundation for internal shooting; inventors of ballistic devices - Wheatstone, Konstantinov, Navet, Marcel, Depres, Leboulanger, etc.

Ballistic examination

Study of small arms on a stand during ballistic examination.

A type of forensic examination, the task of which is to give the investigation answers to technical issues arising during the investigation of cases of use of firearms. In particular, establishing a correspondence between the fired bullet (as well as the cartridge case and the nature of the destruction caused by the bullet) and the weapon from which the shot was fired.

See also

Notes

Literature

According to external ballistics

• N.V. Mayevsky “External course. B." (SPb., 1870);
• N. V. Mayevsky “On solving problems of aimed and mounted shooting” (No. 9 and 11 “Art. Journal”, 1882)
• N. V. Mayevsky “Exposition of the method least squares and its application primarily to the study of shooting results" (St. Petersburg, 1881);
• X. G., “On the integration of the equations of rotational motion of an oblong projectile” (No. 1, Art. Journal, 1887);
• N. V. Mayevsky “Trait é de Baiist, exter.” (Paris, 1872);
• Didion, "Trait é de Balist." (Par., 1860);
• Robins, "Nouv. principes d'artil. com. par Euler et trad. par Lombard" (1783);
• Legendre, “Dissertation sur la question de ballst.” (1782);
• Paul de Saint-Robert, "Mè moires scientit." (Vol. I, "Balist", Typ., 1872);
• Otto, "Tables balist, g énèrales pour le tir élevè" (Par., 1844);
• Neumann, “Theorie des Schiessens und Werfens” (“Archiv f. d. Off. d. preus. Art. und. Ing. Corps” 1838 et seq.);
• Poisson, “Recherches sur le mouvement des project” (1839);
• Gels (H élie), “Traité de Baiist, experim.” (Par., 1865);
• Siacci, “Corso di Balistica” (Typ., 1870);
• Magnus de Sparre, “Mouvement des projects oblongs dans le cas du tir du plein fouet” (Par., 1875);
• Muzeau, “Sur le mouv. des project. oblongs dans Pair" (Par., 1878);
• Bashforth, “A mathematical treatise on thy motion of projectiles” (Lond., 1873);
• Tilly, "Balist." (Bruss., 1875);
• Astier, "Balist ext." (Fontainebleau, 1877);
• Rezal (R èsal), “Traité de mec. gener.” t. i, "Mouv. des proj. obl. d. l'air" (Par., 1873);
• Mathieu, "Dynamique analyt";
• Siacci, “Nuovo metodo per rivolvere and problemi del tiro” (Giorno di Art. e Gen. 1880, part. II punt 4);
• Otto, “Erörterung über die Mittel für Beurtheilung der Wahrscheinlichkeit des Treffens” (Berl., 1856);
• Didion, “Calcul des probabilit è s applique au tir des project.” (Par., 1858);
• Liagre, “Calcul des probabilit è s”;
• Siacci, “Sur le calcul des tables de tir” (“Giorn. d’Art, et Gen.”, parte II, 1875) Jouffret,
• Siacci, “Sur r è tablisse meut et l’usage des tables de tir” (Paris, 1874);
• Siacci, “Sur la probabilit è du tir des bouches a feu et la methode des moindre carr è s” (Paris, 1875);
• Haupt, “Mathematische Theorie aer Flugbahn der gezog. Geschosse" (Berlin, 1876);
• Gentsch, Ballistik der Handfeuerwaffen (Berlin, 1876).

According to internal ballistics

• Noble and Able, “Investigation of Explosive Compositions; ignition action gunpowder" (translated by V. A. Pashkevich, 1878);
• Piobert, “Propri étè s et effets de la poudre”;
• Piobert, "Mouvement des gazs de la poudre" (1860);
• Paul de St. Robert, “Principes de thermodynamique” (1870);
• Rezal (R èsal), “Recherches sur le mouvement des project. dans des arme s a'feu" (1864);
• A. Rutzki, “Die Theorie der Schiesspr ä parate” (Vienna, 1870);
• M. E. Sarrau “Recherches theorethiqnes sur les effets de la poudre et des substances explosives” (1875);
• M. E. Sarrau “Nouvelles recherches sur les effets de la poudre dans les armes” (1876) and
• M. E. Sarrau “Formules pratiques des vitesse et des pressions dans les armes” (1877).

Links

• Dependence of the trajectory shape on the throwing angle. Path elements
• Korobeinikov A.V., Mityukov N.V. Ballistics of arrows according to archaeological data: an introduction to the problem area. Monograph addressed to students and historical reenactors. Methods for reconstructing arrows from their tips, methods of ballistic examination of ancient settlements to assess their level of protection, models of armor penetration of arrows, etc. are described.

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Synonyms:

• Unemployment
• Old Town (Vilnius)

See what “Ballistics” is in other dictionaries:

BALLISTICS- (from the Greek ballein to throw). The science of the movement of heavy bodies thrown into space, mainly artillery shells. Dictionary of foreign words included in the Russian language. Chudinov A.N., 1910. BALLISTICS [Dictionary of foreign words of the Russian language

BALLISTICS- (Ballistics) the science of the movement of a heavy body thrown into space. It is applied primarily to the study of the movement of shells, bullets, and also aerial bombs. Internal B. studies the movement of a projectile inside the gun channel, external B. by the departure of the projectile.... ... Naval Dictionary

BALLISTICS- (German Ballistik, from Greek ballo I throw), 1) the science of the movement of artillery shells, unguided rockets, mines, bombs, bullets when firing (launching). Internal ballistics studies the movement of a projectile in the barrel, external ballistics after its departure. 2) ... Modern encyclopedia

BALLISTICS- BALLISTICS, the science of the movement of projectiles, including bullets, artillery shells, bombs, missiles and GUIDED PROJECTILES. Internal ballistics studies the movement of projectiles in the bore of a gun. External ballistics studies the trajectory of projectiles.… … Scientific and technical encyclopedic dictionary

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

Internal ballistics

Internal ballistics depend on the type of propellant used and the type of barrel.

Conventionally, trunks can be divided into long and short.

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

Short trunks do not give the bullet the same speed and flatness than long ones. The bullet has greater dispersion. But a short-barreled weapon is convenient to carry, especially concealed, which is most suitable for self-defense weapons and police weapons. On the other hand, trunks can be divided into rifled and smooth.

Rifled barrels give the bullet greater speed and stability along the trajectory. Such barrels are widely used for bullet shooting. For shooting hunting bullet cartridges from smoothbore weapons, various rifled attachments are often used.

Smooth trunks. Such barrels help to increase the dispersion of damaging elements when firing. Traditionally used for shooting with shot (buckshot), as well as for shooting with special hunting cartridges at short distances.

There are four firing periods (Fig. 13).

Preliminary period (P) lasts from the beginning of the combustion of the powder charge until the bullet completely penetrates the rifling. During this period, gas pressure is created in the barrel bore, which is necessary to move the bullet from its place and overcome the resistance of its shell to cut into the rifling of the barrel. This pressure is called boost pressure and reaches 250-500 kg/cm2. 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 bullet’s movement until the complete combustion of the powder charge. At the beginning of the period, when the speed of the bullet along the barrel is still low, the volume of gases grows faster than the behind-the-bullet space. The 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 slightly and by the end of the first period it is approximately 2/3 of the maximum pressure. The speed of movement is constantly growing and by the end of this period reaches approximately 3/4 of the initial speed.
Second period (2) lasts from the moment the powder charge is completely burned until the bullet leaves 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, since 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 action of the powder gases on it ceases. During this period, powder gases flowing from the barrel at a speed of 1200-2000 m/s continue to affect the bullet, giving it additional speed. The bullet reaches its highest speed at the end of the third period at a distance of several tens of centimeters from the muzzle of the barrel (for example, when shooting from a pistol, a distance of about 3 m). This period ends at the moment when the pressure of the powder gases at the bottom of the bullet is balanced by air resistance. Then the bullet flies by inertia. This relates to the question of why a bullet fired from a TT pistol does not penetrate class 2 armor when shot at point-blank range and pierces it at a distance of 3-5 m.

As already mentioned, black and smokeless powder are used to load cartridges. Each of them has its own characteristics:

Black powder. This type of gunpowder burns very quickly. Its combustion is like an explosion. It is used for an instant surge in pressure in the barrel bore. This type of gunpowder is usually used for smooth barrels, since the friction of the projectile against the barrel walls in a smooth barrel is not so great (compared to a rifled barrel) and the residence time of the bullet in the bore is less. Therefore, at the moment the bullet leaves the barrel, greater pressure is achieved. When using black powder in a rifled barrel, the first period of the shot is quite short, 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. The gas pressure curve has a very sharp peak of maximum pressure and a fairly sharp drop in pressure in the first period.

Smokeless powder. This type of powder burns more slowly than black powder and is therefore used to gradually increase the pressure in the bore. In view of this, for rifled weapons Smokeless powder is used as standard. Due to screwing into the rifling, the time it takes for the bullet to fly down the barrel increases and by the time the bullet leaves, the powder charge is completely burned out. Due to this, the bullet is exposed to the full amount of gases, while the second period is selected to be quite small. On the gas pressure curve, the peak of maximum pressure is somewhat smoothed out, with a gentle decrease in pressure in the first period. In addition, it is useful to pay attention to some numerical methods for estimating intra-ballistic solutions.

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

KM = E0/d 3, where E0 is muzzle energy, J, d is bullets, mm. For comparison: the power coefficient 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 shot energy per gram of weapon. Used to compare bullets from cartridges of the same type or to compare the relative shot energy of different cartridges. It is measured in Joules per gram. Often, the metal utilization rate is taken as a simplified version of calculating 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, respectively, is 0.37, 0.66 and 0.76 J/g.

External ballistics

First you need to imagine the full trajectory of the bullet (Fig. 14).
In explanation of the figure, it should be noted that the line of departure of the bullet (throwing line) will be different than the direction of the barrel (elevation line). This occurs due to the occurrence of barrel vibrations when fired, 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 finishing of the barrel and the calculation of the internal ballistic characteristics of the weapon, the smaller the departure angle will be. Approximately the first two-thirds of the upward trajectory line can be considered straight. In view of this, three firing distances are distinguished (Fig. 15). Thus, the influence of third-party conditions on the trajectory is described by a simple quadratic equation, and in graphics it is a parabola. In addition to third-party conditions, the deviation of a bullet from its trajectory is also influenced by some design features of the bullet and cartridge. Below we will consider a complex of events; deflecting the bullet from its original trajectory. The ballistic tables of this topic contain data on the ballistics of the 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 once again that thanks 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 increases slightly 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 slightly shifted from the central axis of the bullet, so in the cross section you get a circle of bullet expansion - the average deviation of the bullet from the original trajectory. Taking into account this behavior of the bullet, its possible trajectory can be represented as a single-plane hyperboloid (Fig. 17). The displacement of a bullet from the main directrix due to a displacement of its axis of rotation is called dispersion. The bullet with full probability ends up in the circle of dispersion, diameter (by
peppercorn) 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 dispersion radii for shooting at various distances.

Table 3

Diffusion

Fire range (m)	Dispersion Diameter(cm)

• Considering the size of the standard head target is 50x30 cm, and the chest target is 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 slightly from the firing plane. Moreover, in the case of right-hand rifling (the bullet rotates clockwise when viewed from behind), the bullet deflects to the right, in the case of left-hand rifling - to the left.
  In table Figure 4 shows the magnitude of derivational deviations when firing at various ranges.
• Table 4
• Derivation

• Fire range (m)	Derivation (cm)
  1000
  1200

  • It is easier to take into account 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 slightly by the amount of the derivational displacement of the bullet.

  • Bullet displacement by wind

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

  • Fire range (m)	Offset (cm)

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

    • Bullet flight time

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

    Time of flight of a bullet to the target

    • • Fire range (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 (dispersion, bullet flight time) on the firing range. Such a graph will allow you to easily calculate intermediate values ​​(for example, at 350 m), and will also allow you to assume table values ​​of the function.
        In Fig. Figure 18 shows the simplest ballistic problem.
      • Shooting is carried out at a distance of 600 m, the wind blows from behind to the left at an angle of 45° to the trajectory.

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

      • Solution: The diameter of the scattering circle 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). The bullet's flight time is 1.07 s (flight time + 5% due to the direction of the wind in the direction of the bullet's flight) (see Table 6).
      • Answer; the bullet will fly 600 m in 1.07 s, the diameter of the dispersion circle 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 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 conveniently determined by some mathematical formulas.
      1. Penetration of barriers (P). Penetration determines how likely it is to break through a particular barrier. In this case, the total probability is taken as
      1. Usually used to determine the probability of penetration on various discs
    • dances of different classes of passive armor protection.
      Penetration is a dimensionless quantity.
    • P = En / Epr,
    • where En is the energy of the bullet at a given point of the trajectory, in J; Epr is the energy required to break through an obstacle, in J.
    • Taking into account the standard EPR for body armor (BZh) (500 J for protection against pistol cartridges, 1000 J - from intermediate and 3000 J - from rifle cartridges) and sufficient energy to defeat a person (max 50 J), it is easy to calculate the probability of hitting the corresponding BZh with a bullet from one or another another cartridge. Thus, the probability of penetrating a standard pistol BZ with a bullet from a 9x18 PM cartridge will be equal to 0.56, and by a bullet from a 7.62x25 TT cartridge - 1.01. The probability of penetrating a standard assault rifle bullet with a 7.62x39 AKM cartridge will be 1.32, and with a 5.45x39 AK-74 cartridge bullet will be 0.87. The given numerical data are calculated for a distance of 10 m for pistol cartridges and 25 m for intermediate cartridges. 2. Impact coefficient (ky). Impact coefficient shows the energy of a bullet per square millimeter of its maximum cross-section. Impact factor 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 9x18 PM, 7.62x25 TT and .40 Auto cartridges 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 from 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? Clarification of this issue is the most important characteristic for choosing 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 most reliably when the bullet hits a certain place on the human body (head, spine, kidneys), but some types of ammunition have a large 0B even when hitting secondary targets. In general, 0B is directly proportional to the caliber of the bullet, its mass and speed at the moment it hits the target. Also, 0V increases when using lead and expansion bullets. It must be remembered that an increase in 0B shortens the length of the wound channel (but increases its diameter) and reduces the effect of the bullet on a target protected by armor. One of the options for mathematical calculation of OM was proposed in 1935 by the American Yu. 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 the target, m/s; S - transverse area of ​​the bullet, cm 2; k is the bullet shape coefficient (from 0.9 for full-shell bullets to 1.25 for hollow-point bullets). According to these calculations, at a distance of 15 m, bullets of 7.62x25 TT, 9x18 PM and .45 cartridges have a MR of 171, 250 in 640, respectively. For comparison: RP of a bullet of a 7.62x39 cartridge (AKM) = 470, and bullets of 7.62x54 ( OVD) = 650. Penetrating impact (PE). PT can be defined as the ability of a bullet to penetrate a target to its maximum depth. Penetration ability is higher (with other equal conditions) for bullets of small caliber and slightly deformable in the body (steel, full-shell). High penetration improves the bullet's effect on targets protected by armor. In Fig. Figure 19 shows the effect of a standard PM jacketed bullet with a steel core. When a bullet hits the body, a wound channel and a wound cavity are formed. A wound channel is a channel pierced directly by a bullet. Wound cavity is a cavity of damage to fibers and vessels caused by tension and rupture of them by a bullet. Gunshot wounds are divided into through, blind, and secant.
      
      

      Penetrating wounds

      A perforation 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, smaller than the caliber of a bullet. With a direct hit, the edges of the wound are smooth, and with a hit through thick clothing at an angle, there will be a slight tear. Often the inlet closes up quite quickly. There are no traces of bleeding (except for damage to large vessels or when the wound is positioned below). The exit hole is large and can exceed the caliber of the bullet by orders of magnitude. The edges of the wound are torn, uneven, and spread to the sides. A rapidly developing tumor is observed. There is often severe bleeding. In non-fatal wounds, suppuration develops quickly. With fatal wounds, the skin around the wound quickly turns blue. Penetrating wounds are typical for bullets with a high penetrating effect (mainly for machine guns and rifles). When a bullet passes through soft tissue, the internal wound is axial, with minor damage to neighboring organs. When wounded by a bullet from a 5.45x39 (AK-74) cartridge, the steel core of the bullet in the body may come out of the shell. As a result, two wound channels appear and, accordingly, two exit holes (from the shell and the core). Such injuries are more oftenthey occur when ingested through thick clothing (peacoat). Often the wound channel from a bullet is blind. When a bullet hits a skeleton, a blind wound usually occurs, but with a high power of ammunition, a through wound is likely. In this case, large internal damage from fragments and parts of the skeleton is observed with an increase in the wound channel towards the exit hole. In this case, the wound channel can “break” due to the ricochet of the bullet from the skeleton. Perforating head wounds are characterized by cracking or fracture of the skull bones, often in a non-axial wound channel. The skull cracks even when hit by lead non-jacketed bullets of 5.6 mm caliber, not to mention more powerful ammunition. In most cases, such injuries are fatal. With through wounds to the head, severe bleeding is often observed (prolonged flow of blood from the corpse), of course, when the wound is positioned on the side or below. The inlet is fairly smooth, but the outlet is uneven, with a lot of cracking. A fatal wound quickly turns blue and swells. In case of cracking, damage may occur skin heads. The skull is easily crushed to the touch, and fragments can be felt. In case of wounds with sufficiently strong ammunition (bullets of 7.62x39, 7.62x54 cartridges) and wounds with expansive bullets, a very wide exit hole is possible with a long leakage of blood and brain matter.

      Blind wounds

      Such wounds occur when hit by bullets from less powerful (pistol) ammunition, using hollow-point bullets, passing a bullet through the skeleton, or being wounded by a bullet at the end of its life. With such wounds, the entrance hole is also quite small and smooth. 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 not axial. This is observed when weaker ammunition hits the skeleton - the bullet moves away from the entrance hole plus damage from fragments of the skeleton and shell. When such bullets hit the skull, it becomes severely cracked. A large entrance hole is formed in the bone, and the intracranial organs are severely affected.

      Cutting wounds

      Cutting wounds are observed when a bullet hits the body at an acute angle, damaging only the skin and external parts of the muscles. Most of the injuries are not dangerous. Characterized by skin rupture; the edges of the wound are uneven, torn, and often diverge greatly. Sometimes quite severe bleeding is observed, especially when large subcutaneous vessels rupture.

Introduction 2.

Objects, tasks and subject of judicial

ballistic examination 3.

The concept of firearms 5.

Design and purpose of the main

parts and mechanisms of firearms

weapons 7.

Classification of cartridges

hand-held firearms 12.

Device of unitary cartridges

and their main parts 14.

Drawing up an expert opinion and

Photo tables 21.

List of used literature 23.

Introduction.

The term " ballistics" comes from the Greek word "ballo" - throw, sword. Historically, ballistics arose as a military science that determines theoretical foundations and the practical application of the laws of projectile flight in the air and the processes that impart the necessary kinetic energy to the projectile. Its origin is associated with the great scientist of antiquity - Archimedes, who designed throwing machines (ballistas) and calculated the flight path of thrown projectiles.

At a specific historical stage in the development of mankind, such a technical means as firearms was created. Over time, it began to be used not only for military purposes or hunting, but also for illegal purposes - as a weapon of crime. As a result of its use, it became necessary to combat crimes involving the use of firearms. Historical periods provide for legal and technical measures aimed at their prevention and disclosure.

Forensic ballistics owes its emergence as a branch of forensic technology to the need to investigate, first of all, gunshot injuries, bullets, shot, buckshot and weapons.

- This is one of the types of traditional forensic examinations. The scientific and theoretical basis of forensic ballistic examination is the science called “Forensic Ballistics”, which is included in the system of forensic science as an element of its section - forensic technology.

The first specialists involved by the courts as “shooting experts” were gunsmiths, who, due to their work, knew and could assemble and disassemble weapons, had more or less accurate knowledge about shooting, and the conclusions that were required of them concerned most of the issues about whether a weapon was fired, from what distance this or that weapon hits the target.

Judicial ballistics - a branch of crime technology that studies firearms, phenomena and traces accompanying their action, ammunition and their components using the methods of natural sciences and specially developed methods and techniques for the purpose of investigating crimes committed with the use of firearms.

Modern forensic ballistics was formed as a result of the analysis of accumulated empirical material, active theoretical research, generalization of facts related to firearms, ammunition for it, patterns of formation of traces of their action. Some provisions of ballistics proper, that is, the science of the movement of a projectile or bullet, are also included in forensic ballistics and are used in solving problems related to establishing the circumstances of the use of firearms.

One of the forms of practical application of forensic ballistics is the production of forensic ballistic examinations.

OBJECTS, TASKS AND SUBJECT OF FORENSIC BALLISTIC EXAMINATION

Forensic ballistic examination - this is a special study conducted in the procedural form established by law with the drawing up of an appropriate conclusion in order to obtain scientifically based factual data about firearms, ammunition and the circumstances of their use that are relevant for the investigation and trial.

Object of any expert research are material media that can be used to solve relevant expert problems.

Objects of forensic ballistics examination in most cases are related to a shot or its possibility. The range of these objects is very diverse. This includes:

Firearms, their parts, accessories and blanks;

Shooting devices (construction and installation pistols, starting pistols), as well as pneumatic and gas weapons;

Ammunition and cartridges for firearms and other firing devices, individual elements of cartridges;

Samples for comparative research obtained as a result of an expert experiment;

Materials, tools and mechanisms used for the manufacture of weapons, ammunition and their components, as well as ammunition equipment;

Fired bullets and spent cartridges, traces of the use of firearms at various objects;

Procedural documents contained in the materials of the criminal case (protocols for examining the scene of the incident, photographs, drawings and diagrams);

Material conditions of the scene of the incident.

It should be emphasized that, as a rule, only small firearms are the objects of forensic ballistic examination. Although there are known examples of examinations of cartridges from artillery shot.

Despite all the diversity and diversity of objects of forensic ballistic examination, the tasks facing it can be divided into two large groups: tasks of an identification nature and tasks of a non-identification nature (Fig. 1.1).

Rice. 1.1. Classification of tasks of forensic ballistic examination

Identification tasks include: group identification (establishing the group affiliation of an object) and individual identification (establishing the identity of an object).

Group identification includes establishing:

Belonging of objects to the category of firearms and ammunition;

The type, model and type of firearms and ammunition presented;

Type, model of weapon based on marks on spent cartridges, fired shells and marks on an obstacle (in the absence of a firearm);

The nature of the gunshot damage and the type (caliber) of the projectile that caused it.

TO individual identification include:

Identification of the weapon used by traces of the bore on the shells;

Identification of the weapon used by traces of its parts on spent cartridges;

Identification of equipment and instruments used for loading ammunition, manufacturing their components or weapons;

Determining whether a bullet and a cartridge belong to the same cartridge.

Non-identification tasks can be divided into three types:

Diagnostic, related to recognizing the properties of the objects under study;

Situational, aimed at establishing the circumstances of the shooting;

Reconstruction, associated with recreating the original appearance of objects.

Diagnostic tasks:

Establishing the technical condition and suitability for firing firearms and ammunition for them;

Establishing the possibility of firing a weapon without pressing the trigger under certain conditions;

Establishing the possibility of firing a shot from a given weapon with certain cartridges;

Establishing the fact that a weapon fired after the last cleaning of its bore.

Situational tasks:

Establishing the distance, direction and location of the shot;

Determining the relative position of the shooter and the victim at the moment of the shot;

Determining the sequence and number of shots.

Reconstruction tasks- This is mainly the identification of destroyed numbers on firearms.

Let us now discuss the issue of the subject of forensic ballistic examination.

The word “subject” has two main meanings: subject as a thing and subject as the content of the phenomenon being studied. Speaking about the subject of forensic ballistic examination, we mean the second meaning of this word.

Under the item forensics understand the circumstances, facts established through expert research, which are important for court decisions and investigative actions.

Since forensic ballistic examination is one of the types of forensic examination, this definition also applies to it, but its subject can be specified based on the content of the tasks being solved.

The subject of forensic ballistic examination as a type of practical activity is all the facts and circumstances of the case that can be established by means of this examination, on the basis of special knowledge in the field of forensic ballistics, forensics and military technology. Namely, the data:

About the condition of firearms;

About the presence or absence of firearm identity;

About the circumstances of the shot;

On the classification of items into the category of firearms and ammunition. The subject of a specific examination is determined by the questions posed to the expert.

CONCEPT OF FIREARMS

The Criminal Code, while providing for liability for the illegal carrying, storage, acquisition, manufacture and sale of firearms, its theft, careless storage, does not clearly define what is considered a firearm. At the same time, the clarifications of the Supreme Court directly indicate that when deciding whether an item that the offender stole, illegally carried, stored, acquired, manufactured or sold is a weapon, it is required special knowledge, courts need to order an examination. Consequently, experts must operate with a clear and complete definition that reflects the main features of a firearm.

External ballistics. Trajectory and its elements. Excess of the bullet's flight path above the aiming point. Trajectory shape

External ballistics

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

Having flown out of the barrel under the influence of powder gases, the bullet (grenade) moves by inertia. A grenade with a jet engine moves by inertia after the gases flow out of the jet engine.

Bullet trajectory (side view)

Formation of air resistance force

Trajectory and its elements

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

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

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 reasons: 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 cohesion (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 varies 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, resulting in a pressure difference between the head and bottom parts. This difference creates a force directed in the direction opposite to the movement of the bullet, and reduces its flight speed. Air particles, trying to fill the vacuum formed behind the bullet, create a vortex.

When flying, a bullet (grenade) collides with air particles and causes them to vibrate. As a result, the air density in front of the bullet (grenade) increases and sound waves are formed. Therefore, the flight of a bullet (grenade) is accompanied by a characteristic sound. When the speed of a bullet (grenade) 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 speed of the bullet (grenade). When the bullet's flight speed is greater than the speed of sound, the sound waves collide with each other to create a wave of highly compressed air - a ballistic wave that slows down the bullet's flight speed, since the bullet spends part of its energy creating this wave.

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

The effect of air resistance on the flight of a bullet (grenade) is very great; it causes a decrease in the speed and range of a bullet (grenade). For example, a bullet arr. 1930, with a throwing angle of 15° and an initial speed of 800 m/sec in airless space, it would fly to a distance of 32,620 m; the flight range of this bullet under the same conditions, but in the presence of air resistance, is only 3900 m.

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

The force of air resistance increases with increasing bullet speed, caliber and air density.

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

The effect of air resistance on the flight of a bullet: CG - center of gravity; CS - center of air resistance

The smoother the surface of the bullet, the less frictional force. air resistance force.

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

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

To prevent the bullet from tipping over under the influence of air resistance, it is given a rapid rotational movement using rifling in the barrel bore.

For example, when fired from a Kalashnikov assault rifle, the rotation speed of the bullet at the moment it leaves the barrel is about 3000 rpm.

When a rapidly rotating bullet flies through the air, the following phenomena occur. The force of air resistance tends to turn the bullet head up and back. But the head of the bullet, as a result of rapid rotation, according to the property of the gyroscope, tends to maintain its given position and will not deviate upward, but very slightly in the direction of its rotation at a right angle to the direction of the air resistance force, i.e. to the right. As soon as the head of the bullet deviates to the right, the direction of action of the air resistance force will change - it tends to turn the head of the bullet to the right and back, but the rotation of the head of the bullet will not occur to the right, but down, etc. Since the action of the air resistance force is continuous, but its direction relative to the bullet changes with each deviation of the bullet’s axis, then the head of the bullet describes a circle, and its axis is a cone with its apex at the center of gravity. The so-called slow conical, or precessional, movement occurs, and the bullet flies with its head forward, i.e., as if following the change in the curvature of the trajectory.

Slow conical bullet motion

Derivation (top view of trajectory)

The effect of air resistance on the flight of a grenade

The axis of slow conical motion lags somewhat behind the tangent to the trajectory (located above the latter). Consequently, the bullet collides with the air flow more with its lower part and the axis of slow conical movement deviates in the direction of rotation (to the right with a right-hand rifling of the barrel). The deviation of a bullet from the firing plane in the direction of its rotation is called derivation.

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

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

The stability of the grenade in flight is ensured by the presence of a stabilizer, which allows the center of air resistance to be moved back, beyond the center of gravity of the grenade.

As a result, the force of air resistance turns the axis of the grenade to a tangent to the trajectory, forcing the grenade to move forward with its head.

To improve accuracy, some grenades are given a slow rotation due to the outflow of gases. Due to the rotation of the grenade, the moments of force deflecting the axis of the grenade act consistently in different directions, so shooting improves.

To study the trajectory of a bullet (grenade), the following definitions are adopted.

The center of the muzzle of the barrel is called the take-off point. The departure point is the beginning of the trajectory.

Path elements

The horizontal plane passing through the point of departure is called the horizon of the weapon. In drawings showing the weapon and 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.

The straight line, which is a continuation of the axis of the barrel of the aimed weapon, is called the elevation line.

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

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

The straight line, which is a continuation of the axis of the barrel bore at the moment the bullet leaves, is called the throwing line.

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

The angle between the elevation line and the throwing line is called the launch angle.

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

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

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

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

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

The highest point of the trajectory is called the trajectory vertex.

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

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

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

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

The angle between the elevation line and the aiming line is called the aiming angle.

The angle between the aiming line and the horizon of the weapon is called the 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 thousandths formula.

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

The shortest distance from any point on the trajectory to the aiming line is called the excess of the trajectory above the aiming line.

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

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

The angle between the tangent to the trajectory and the tangent to the surface of the target (ground, obstacle) at the meeting point is called the meeting angle. The meeting angle is taken to be the smaller of the adjacent angles, measured from 0 to 90°.

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

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

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

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

The lowest flight speed of a bullet when shooting at large throwing angles is on the downward branch of the trajectory, and when shooting at small throwing angles - at the point of impact;

The time it takes a bullet to move along the ascending branch of the trajectory is less than along the descending branch;

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

Grenade trajectory (side view)

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

Path shape

The shape of the trajectory depends on the elevation angle. With increasing elevation angle, the height of the trajectory and the full horizontal flight range of the bullet (grenade) increase, but this happens before known limit. Beyond this limit, the trajectory altitude continues to increase, and the total horizontal range begins to decrease.

Corner longest range, flat, mounted and conjugate trajectories

The elevation angle at which the total horizontal flight range of a bullet (grenade) becomes greatest is called the angle of greatest range. The value of the angle of greatest range for bullets various types weapons is about 35°.

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

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

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

Excess of the bullet's flight path above the aiming point

The flatness of the trajectory is characterized by its greatest elevation above the line of sight. At a given range, the trajectory is flatter the less it rises above the aiming line. In addition, the flatness of the trajectory can be judged by the angle of incidence: the smaller the angle of incidence, the more flat the trajectory.