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Ballistics external and internal: concept, definition, basics of study, goals, objectives and the need for study. Information on ballistics: internal and external ballistics. wound ballistics Low ballistics

KRASNODAR UNIVERSITY

fire training

Specialty: 031001.65 Law enforcement,

specialization: operational-search activity

(activities of the operative criminal investigation department)

LECTURE

Topic number 5: "Fundamentals of ballistics"

Time: 2 hours.

Location: shooting range of the university

Methodology: story, show.

The main content of the topic: Information about explosives, their classification. Information about internal and external ballistics. Factors affecting the accuracy and accuracy of shooting. The average point of impact and how to determine it.

Material support.

1. Stands, posters.

Purpose of the lesson:

1. Familiarize students with explosives used in the manufacture of ammunition, their classification.

2. Introduce cadets to the basics of internal and external ballistics.

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

4. Develop discipline and diligence among cadets.

Practice Plan

Introduction - 5 min.

Check the availability of cadets, readiness for classes;

Announce the topic, goals, training questions.

Main part – 80 min.

Conclusion - 5 min.

Summarize the lesson;

Remind the topic, objectives of the lesson and how they are achieved;

Remind learning questions;

Answer the questions that have arisen;

Give assignments for self-study.

Main literature:

1. Manual on shooting. - M .: Military publishing house, 1987.

Additional literature:

1. Fire training: textbook / under the general editorship. - 3rd ed., Rev. and additional - Volgograd: VA Ministry of Internal Affairs of Russia, 2009.

2., Menshikov training in the internal affairs bodies: Textbook. - St. Petersburg, 1998.

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

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

Internal ballistics, which studies the processes that occur when a shot is fired inside the bore of a firearm;

Intermediate ballistics, which studies the flight of a bullet at some distance from the muzzle of the barrel, when the powder gases are still continuing their effect on the bullet;

External ballistics, which studies the processes occurring with a bullet in the air, after the cessation of exposure to powder gases;

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

Explosives

explosives (explosives) called such chemical compounds and mixtures that are capable, under the influence of external influences, of very rapid chemical transformations, accompanied by

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

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

An explosion can be caused by: mechanical impact - impact, prick, friction, thermal, electrical impact - heating, spark, flame beam, Explosion energy of another explosive that is sensitive to thermal or mechanical impact (explosion of a detonator cap).

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

According to the nature of the action and practical application, explosives are divided into initiating, crushing (blasting), propelling and pyrotechnic compositions.

Explosion- this is the process of explosive transformation, proceeding at a speed of several hundred (thousand) meters per second and accompanied by a sharp increase in gas pressure, which produces a strong destructive effect on nearby objects. The greater the rate of transformation of the explosive, the greater the force of its destruction. When the explosion proceeds at the maximum possible speed under the given conditions, then such an explosion is called detonation. The detonation velocity of the TNT charge reaches 6990 m/s. The transfer of detonation over a distance is associated with the propagation in the medium, the explosive surrounding the charge, of a sharp increase in pressure - a shock wave. Therefore, the excitation of an explosion in this way is almost no different from the 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 explosives are called those that have high sensitivity, explode from a slight thermal or mechanical effect 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(brisant) explosives are called, which explode, as a rule, under the action of detonation of initiating explosives and during the explosion, crushing of surrounding objects occurs. Crushing explosives include: TNT, melinite, tetryl, hexogen, PETN, ammonites, etc. Pyroxelin and nitroglycerin are used as a starting material for the manufacture of smokeless powders. Crushing explosives are used as explosive charges for mines, grenades, shells, and are also used in blasting.

Throwable explosives are called those 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. Throwing explosives include various types of gunpowder (smoky and smokeless). Black powder is a mechanical mixture of saltpeter, sulfur and charcoal. It is used to equip fuses for hand grenades, remote tubes, fuses, prepare a igniter cord, etc. Smokeless powders are divided into pyroxelin and nitroglycerin powder. They are used as combat (powder) charges for firearms; pyroxelin powders - for powder charges of small arms cartridges; nitroglycerin, as more powerful, - for combat charges of grenades, mines, shells.

Pyrotechnic the compositions are mixtures of combustible substances (magnesium, phosphorus, aluminum, etc.), oxidizing agents (chlorates, nitrates, etc.) and cementing agents (natural and artificial resins, etc.). In addition, they contain special impurities; substances that color the flame; 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, signal cartridges, tracer and incendiary compositions of bullets, grenades, shells.

Brief information about internal ballistics

Shot and its periods.

A shot is the ejection of a bullet from the bore by the energy of gases formed during the combustion of a powder charge. When fired from small arms, the following phenomena occur. From the impact of the striker on the primer of live cartridge 2, the percussion composition of the primer explodes and a flame is formed, which through the seed holes in the bottom of the cartridge case penetrates to the powder charge and ignites it. When the charge is burned, a large amount of highly heated powder gases are formed, which create high pressure in the barrel bore on the bottom of the bullet, the bottom and walls of the sleeve, and also on the walls of the barrel and the bolt. As a result of the pressure of 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 the speed is thrown outward in the direction of the axis of the bore. The pressure of gases on the bottom of the sleeve causes the weapon to move backward - recoil. From the pressure of gases on the walls of the sleeve and the barrel, they are stretched (elastic deformation), and the sleeve, tightly pressed against the chamber, prevents the breakthrough of powder gases towards the bolt. When fired, an oscillatory movement (vibration) of the barrel also occurs and it heats up. Hot gases and particles of unburned gunpowder flowing after the bullet, when they meet with air, generate a flame and a shock wave; the latter is the source of sound when fired.

Approximately 25-35% of the energy of powder gases is spent on communicating n-25% on secondary work, about 40% of the energy is not used and is lost after the bullet has left.

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

When fired, four consecutive periods are distinguished:

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

The first or main, which lasts from the moment the bullet cuts into the rifling until the moment the powder charge is completely burned;

The second, which lasts from the moment of complete combustion of the charge until the moment the bullet leaves the barrel,

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

Short-barreled weapons may not have a second period.

muzzle velocity

For the initial speed, the conditional speed of the bullet is taken, which is less than the maximum, but more than the muzzle. The initial speed is determined by calculations. The initial speed is the most important characteristic of the weapon. The higher the initial speed, the greater its kinetic energy and, consequently, the greater the flight range, the range of a direct shot, the penetrating effect of a bullet. The influence of external conditions on the flight of a bullet is less pronounced with increasing speed.

The value 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 grains of the powder and the loading density. Loading density is the ratio of the weight of the charge to the volume of the cartridge case with the bullet inserted. With a very deep landing of the bullet, the initial speed increases, but due to the large pressure surge when the bullet takes off, the gases can break the barrel.

The recoil of the weapon and the angle of departure.

Recoil is the movement of the weapon (barrel) back during the shot. The recoil speed of the weapon is as many times less than the bullet is lighter than the weapon. The pressure force of powder gases (recoil force) and the force of resistance to recoil (butt stop, handles, 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 upwards. the magnitude of this deviation is the greater, the greater the leverage of application of forces. 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 causes cause the bore axis to deviate from its original position at the moment of firing. The amount of deflection of the axis of the bore at the moment the bullet takes off from its original position is called the angle of departure. The departure angle increases with improper application, use of a stop, contamination of the weapon.

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

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

Causes 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 bore.

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

Causes of a thermal nature are caused by periodic local strong heating of the walls of the bore. Together with periodic stretching, they lead to the appearance of a grid of fire, the setting of 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 care of the weapon, 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 has ceased.

Having flown out of the bore under the action of powder gases, the bullet (grenade) moves by inertia. A grenade with a jet engine moves by inertia after the expiration of gases from the jet engine. The force of gravity causes the bullet (grenade) to gradually decrease, and the force of air resistance continuously slows down the movement of the bullet and tends to overturn it. To overcome the force of air resistance, part of the energy of the bullet is expended.

Trajectory and its elements

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

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

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

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

The layer of air adjacent to the surface of the bullet (grenade), in which the movement of particles changes from the speed of the bullet (grenade) to zero, is called the boundary layer. This layer of air, flowing around the bullet, breaks away from its surface and does not have time to immediately close behind the bottom. A rarefied space is formed behind the bottom of the bullet, as a result of which a pressure difference appears on the head and bottom parts. This difference creates a force directed in the direction opposite to the movement of the bullet, and reduces the speed of its flight. Air particles, trying to fill the rarefaction formed behind the bullet, create a vortex.

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

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

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

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

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

During the flight of a rapidly rotating bullet in the air, the following phenomena occur. The force of air resistance tends to turn the bullet head up and back. But the head of the bullet, as a result of rapid rotation, according to the property of the gyroscope, tends to maintain the given position and deviates not upwards, but very slightly in the direction of its rotation at right angles to the direction of the air resistance force, i.e. to the right. As soon as the head of the bullet deviates to the right, the direction of the air resistance force will change - it tends to turn the head of the bullet to the right and back, but the head of the bullet will not turn to the right, but down, etc. Since the action of the air resistance force is continuous, and its direction relative to the bullet changes with each deviation of the bullet axis, then the head of the bullet describes a circle, and its axis is a cone with a vertex at the center of gravity. There is a so-called slow conical, or precessional, movement, and the bullet flies with its head part forward, that is, it seems to follow 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 the slow conical movement deviates in the direction of rotation (to the right when the barrel is right-handed). The deviation of the bullet from the plane of fire in the direction of its rotation is called derivation.

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

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

The stability of the grenade in flight is ensured by the presence of a stabilizer, which allows you to move the center of air resistance back, behind the center of gravity of the grenade. 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. To improve accuracy, some grenades are given slow rotation due to the outflow of gases. Due to the rotation of the grenade, the moments of forces that deviate the axis of the grenade act sequentially in different directions, so the accuracy of fire improves.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

The highest point of the trajectory is called 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 point of fall is called descending branch of the trajectory.

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

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

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

The angle enclosed between the line of sight and the horizon of the weapon is called target elevation angle. The target's elevation angle is considered positive (+) when the target is above the weapon's horizon, and negative (-) when the target is below the weapon's horizon.

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

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

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

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

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

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

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

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

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

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

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

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

The trajectory of a grenade in the air can be divided into two sections: active - the flight of a grenade under the action of a reactive force (from the point of departure to the point where the action of the reactive force stops) and passive - the flight of a grenade by inertia. The shape of the trajectory of a grenade is about 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 the production of shots, each bullet (grenade), due to a number of random reasons, describes its own trajectory and has its own point of impact (meeting point) that does not coincide with the others, as a result of which the bullets scatter ( Garnet). The phenomenon of scattering of bullets (grenades) when firing from the same weapon in almost identical conditions is called natural dispersion of bullets (grenades) or dispersion 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 bundle of trajectories is called the middle trajectory. Tabular and calculated data refer to the average trajectory,

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

The area on which the meeting points (holes) of bullets (grenades) obtained by crossing a sheaf of trajectories with any plane are located is called the scattering area. The scattering area is usually elliptical in shape. When shooting from small arms at close range, the scattering area in the vertical plane may be in the form of a circle. Mutually perpendicular lines drawn through the center of dispersion (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.

Causes of dispersion

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

The reasons causing a variety of initial speeds;

Causes causing a variety of throwing angles and shooting directions;

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

The reasons for the variety of initial speeds are:

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

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

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

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

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

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

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

Angular vibrations of the barrel when firing automatic fire, arising from the movement and impact of moving parts and the recoil of the weapon. These reasons lead to the dispersion of bullets (grenades) in the lateral direction and range (height), have the greatest impact on the magnitude of the dispersion area and mainly depend on the skill of the shooter.

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

Variation in atmospheric conditions, especially in wind direction and speed between shots (bursts);

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

With each shot, all three groups of causes act in different combinations. This leads to the fact that the flight of each bullet (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, it is impossible to eliminate the dispersion itself. However, knowing the reasons on which the dispersion depends, it is possible to reduce the influence of each of them and thereby reduce the dispersion, or, as they say, increase the accuracy of fire.

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

Scattering law

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

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

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

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

Determination of the midpoint of impact (STP)

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

A hole is considered to be clearly torn off if it is removed from the intended STP by more than three diameters of the size of the accuracy of fire.

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

Aiming (pointing)

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 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 firing is called aiming or pointing.

Giving the axis of the bore the required position in the horizontal plane is called horizontal pickup. Giving the axis of the bore the required position in the vertical plane is called vertical guidance.

Aiming is carried out with the help of aiming devices and aiming mechanisms and is carried out in two stages.

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

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

When firing from small arms and grenade launchers, direct aiming is used, performed using one aiming line.

The straight line that connects the middle of the sight slot to the top of the front sight is called the aiming line.

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

In weapons with a permanent rear sight (for example, a Makarov pistol), the required position of the axis of the bore in the vertical plane is given by choosing the aiming point corresponding to the distance to the target, and directing the aiming line to this point. In weapons that have a sight slot that is stationary in the lateral direction (for example, a Kalashnikov assault rifle), the required position of the bore axis in the horizontal plane is given by selecting the aiming point corresponding to the lateral correction and directing the aiming line into 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 with the help of an optical sight, it is necessary first, using the mechanisms of the sight, to give the aiming line (carriage with the sight reticle) such a position in which an angle equal to the aiming angle is formed between this line and the axis of the bore in the vertical plane, and in the horizontal plane - the angle , equal to the lateral correction. Then, by changing the position of the weapon, you need to combine the sighting line with the target. while the axis of the bore is given the desired position in space.

direct shot

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

straight shot.

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

The range of a direct shot depends on the height of the target and the flatness of the trajectory. The higher the target and the flatter the trajectory, the greater the range of a direct shot and the greater the extent of the terrain, the target can be hit with one sight setting. Each shooter must know the value of the point-blank range at various targets from his weapon and skillfully determine the range of a point-blank shot when shooting. The range of a direct shot can be determined from the tables by comparing the height of the target with the values \u200b\u200bof the greatest excess above the line of sight or the height of the trajectory. The flight of a bullet in the air is influenced by meteorological, ballistic and topographical conditions. When using the tables, it must be remembered that the given trajectories in them correspond to normal shooting conditions.

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

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

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

There is no wind (the atmosphere is still).

b) Ballistic conditions:

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

Charge temperature +15°С;

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

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

c) Topographic conditions:

The target is on the weapon's horizon;

There is no lateral tilt of the weapon.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

The wind blowing at an acute angle to the firing plane has both an effect on the change in the range of the bullet and on its lateral deflection.

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

When firing with one sight setting (with one aiming angle), but at different target elevation angles, as a result of a number of reasons, including changes in air density at different heights, and, consequently, the air resistance force, the value of the slant (sighting) flight range changes bullets (grenades). When firing at small target elevation angles (up to ± 15 °), this bullet (grenade) flight range changes very slightly, therefore, equality of the inclined and full horizontal bullet flight ranges is allowed, i.e., the shape (rigidity) of the trajectory remains unchanged.

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

Conclusion

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

In which there is no thrust or control force and moment, is called a ballistic trajectory. If the mechanism that drives the object remains operational throughout the entire time of movement, it belongs to a number of aviation or dynamic ones. The trajectory of an aircraft during flight with the engines turned off at high altitude can also be called ballistic.

An object that moves along given coordinates is affected only by the mechanism that sets the body in motion, the forces of resistance and gravity. A set of such factors excludes the possibility of rectilinear motion. This rule works even in space.

The body describes a trajectory that is similar to an ellipse, hyperbola, parabola or circle. The last two options are achieved at the second and first cosmic velocities. Calculations for movement along a parabola or a circle are carried out to determine the trajectory of a ballistic missile.

Taking into account all the parameters during launch and flight (mass, speed, temperature, etc.), the following features of the trajectory are distinguished:

In order to launch the rocket as far as possible, you need to choose the right angle. The best is sharp, around 45º.
The object has the same initial and final speeds.
The body lands at the same angle as it is launched.
The time of movement of the object from the start to the middle, as well as from the middle to the finish point, is the same.

Trajectory properties and practical implications

The movement of the body after the influence of the driving force on it ceases to be studied by external ballistics. This science provides calculations, tables, scales, sights and develops the best options for shooting. The ballistic trajectory of a bullet is a curved line that describes the center of gravity of an object in flight.

Since the body is affected by gravity and resistance, the path that the bullet (projectile) describes forms the shape of a curved line. Under the action of the reduced forces, the speed and height of the object gradually decreases. There are several trajectories: flat, hinged and conjugated.

The first is achieved by using an elevation angle that is smaller than the greatest range angle. If for different trajectories the flight range remains the same, such a trajectory can be called conjugate. In the case when the elevation angle is greater than the angle of the greatest range, the path becomes called hinged.

The trajectory of the ballistic movement of an object (bullet, projectile) consists of points and sections:

departure(for example, the muzzle of the barrel) - this point is the beginning of the path, and, accordingly, the reference.
Horizon Arms- this section passes through the departure point. The trajectory crosses it twice: during release and fall.
Elevation site- this is a line that is a continuation of the horizon forms a vertical plane. This area is called the shooting plane.
Path vertices- this is the point that is in the middle between the start and end points (shot and fall), has the highest angle throughout the entire path.
Leads- the target or place of the sight and the beginning of the movement of the object form the aiming line. An aiming angle is formed between the horizon of the weapon and the final target.

Rockets: features of launch and movement

There are guided and unguided ballistic missiles. The formation of the trajectory is also influenced by external and external factors (resistance forces, friction, weight, temperature, required flight range, etc.).

The general path of the launched body can be described by the following steps:

Launch. In this case, the rocket enters the first stage and begins its movement. From this moment, the measurement of the height of the flight path of a ballistic missile begins.
Approximately one minute later, the second engine starts.
60 seconds after the second stage, the third engine starts.
Then the body enters the atmosphere.
The last thing is the explosion of warheads.

Rocket launch and movement curve formation

The rocket travel curve consists of three parts: the launch period, free flight, and re-entry into the earth's atmosphere.

Live projectiles are launched from a fixed point of portable installations, as well as vehicles (ships, submarines). Bringing into flight lasts from ten thousandths of a second to several minutes. Free fall makes up the largest part of the flight path of a ballistic missile.

The advantages of running such a device are:

Long free flight time. Thanks to this property, fuel consumption is significantly reduced in comparison with other rockets. For the flight of prototypes (cruise missiles), more economical engines (for example, jet engines) are used.
At the speed at which the intercontinental gun is moving (about 5 thousand m / s), interception is given with great difficulty.
A ballistic missile is able to hit a target at a distance of up to 10,000 km.

In theory, the path of movement of a projectile is a phenomenon from the general theory of physics, a section of the dynamics of rigid bodies in motion. With respect to these objects, the movement of the center of mass and the movement around it are considered. The first relates to the characteristics of the object making the flight, the second - to stability and control.

Since the body has programmed trajectories for flight, the calculation of the ballistic trajectory of the rocket is determined by physical and dynamic calculations.

Modern developments in ballistics

Since combat missiles of any kind are life-threatening, the main task of defense is to improve points for launching damaging systems. The latter must ensure the complete neutralization of intercontinental and ballistic weapons at any point in the movement. A multi-tiered system is proposed for consideration:

This invention consists of separate tiers, each of which has its own purpose: the first two will be equipped with laser-type weapons (homing missiles, electromagnetic guns).
The next two sections are equipped with the same weapons, but designed to destroy the warheads of enemy weapons.

Developments in defense rocketry do not stand still. Scientists are engaged in the modernization of a quasi-ballistic missile. The latter is presented as an object that has a low path in the atmosphere, but at the same time abruptly changes direction and range.

The ballistic trajectory of such a rocket does not affect the speed: even at extremely low altitude, the object moves faster than a normal one. For example, the development of the Russian Federation "Iskander" flies at supersonic speed - from 2100 to 2600 m / s with a mass of 4 kg 615 g, missile cruises move a warhead weighing up to 800 kg. When flying, it maneuvers and evades missile defenses.

Intercontinental weapons: control theory and components

Multistage ballistic missiles are called intercontinental. This name appeared for a reason: because of the long flight range, it becomes possible to transfer cargo to the other end of the Earth. The main combat substance (charge), basically, is an atomic or thermonuclear substance. The latter is placed in front of the projectile.

Further, the control system, engines and fuel tanks are installed in the design. Dimensions and weight depend on the required flight range: the greater the distance, the higher the starting weight and dimensions of the structure.

The ballistic flight path of an ICBM is distinguished from the trajectory of other missiles by altitude. A multi-stage rocket goes through the launch process, then moves upward at a right angle for several seconds. The control system ensures the direction of the gun towards the target. The first stage of the rocket drive after complete burnout is independently separated, at the same moment the next one is launched. Upon reaching a predetermined speed and flight altitude, the rocket begins to rapidly move down towards the target. The flight speed to the destination object reaches 25 thousand km/h.

World developments of special-purpose missiles

About 20 years ago, during the modernization of one of the medium-range missile systems, a project for anti-ship ballistic missiles was adopted. This design is placed on an autonomous launch platform. The weight of the projectile is 15 tons, and the launch range is almost 1.5 km.

The trajectory of a ballistic missile to destroy ships is not amenable to quick calculations, so it is impossible to predict the actions of the enemy and eliminate this weapon.

This development has the following advantages:

Launch range. This value is 2-3 times greater than that of the prototypes.
The speed and altitude of the flight make military weapons invulnerable to missile defense.

World experts are confident that weapons of mass destruction can still be detected and neutralized. For such purposes, special reconnaissance out-of-orbit stations, aviation, submarines, ships, etc. are used. The most important "opposition" is space reconnaissance, which is presented in the form of radar stations.

The ballistic trajectory is determined by the intelligence system. The received data is transmitted to the destination. The main problem is the rapid obsolescence of information - in a short period of time, the data loses its relevance and can diverge from the real location of the weapon at a distance of up to 50 km.

Characteristics of combat complexes of the domestic defense industry

The most powerful weapon of the present time is considered to be an intercontinental ballistic missile, which is placed permanently. The domestic R-36M2 missile system is one of the best. It houses the 15A18M heavy-duty combat weapon, which is capable of carrying up to 36 individual precision-guided nuclear projectiles.

The ballistic trajectory of such weapons is almost impossible to predict, respectively, the neutralization of the missile also presents difficulties. The combat power of the projectile is 20 Mt. If this munition explodes at a low altitude, the communication, control, and anti-missile defense systems will fail.

Modifications of the given rocket launcher can also be used for peaceful purposes.

Among solid-propellant missiles, the RT-23 UTTKh is considered especially powerful. Such a device is based autonomously (mobile). In the stationary prototype station ("15ZH60"), the starting thrust is 0.3 higher compared to the mobile version.

Missile launches that are carried out directly from the stations are difficult to neutralize, because the number of shells can reach 92 units.

Missile systems and installations of the foreign defense industry

The height of the ballistic trajectory of the rocket of the American Minuteman-3 complex does not differ much from the flight characteristics of domestic inventions.

The complex, which was developed in the United States, is the only "defender" of North America among weapons of this type to this day. Despite the age of the invention, the stability indicators of the guns are not bad even at the present time, because the missiles of the complex could withstand anti-missile defense, as well as hit a target with a high level of protection. The active phase of the flight is short, and is 160 s.

Another American invention is the Peekeper. He could also provide an accurate hit on the target due to the most advantageous ballistic trajectory. Experts say that the combat capabilities of the given complex are almost 8 times higher than those of the Minuteman. Combat duty "Peskyper" was 30 seconds.

Projectile flight and movement in the atmosphere

From the section of dynamics, the influence of air density on the speed of movement of any body in various layers of the atmosphere is known. The function of the last parameter takes into account the dependence of the density directly on the flight altitude and is expressed as:

H (y) \u003d 20000-y / 20000 + y;

where y is the flight height of the projectile (m).

The calculation of the parameters, as well as the trajectory of an intercontinental ballistic missile, can be performed using special computer programs. The latter will provide statements, as well as data on flight altitude, speed and acceleration, and the duration of each stage.

The experimental part confirms the calculated characteristics, and proves that the speed is affected by the shape of the projectile (the better the streamlining, the higher the speed).

Guided weapons of mass destruction of the last century

All weapons of the given type can be divided into two groups: ground and aviation. Ground devices are devices that are launched from stationary stations (for example, mines). Aviation, respectively, is launched from the carrier ship (aircraft).

The ground-based group includes ballistic, cruise and anti-aircraft missiles. For aviation - projectiles, ABR and guided air combat projectiles.

The main characteristic of the calculation of the ballistic trajectory is the height (several thousand kilometers above the atmosphere). At a given level above ground level, projectiles reach high speeds and create enormous difficulties for their detection and neutralization of missile defense systems.

Well-known ballistic missiles, which are designed for an average flight range, are: Titan, Thor, Jupiter, Atlas, etc.

The ballistic trajectory of a missile, which is launched from a point and hits the given coordinates, has the shape of an ellipse. The size and length of the arc depends on the initial parameters: speed, launch angle, mass. If the speed of the projectile is equal to the first space speed (8 km/s), the combat weapon, which is launched parallel to the horizon, will turn into a satellite of the planet with a circular orbit.

Despite constant improvement in the field of defense, the flight path of a live projectile remains virtually unchanged. At the moment, technology is not able to violate the laws of physics that all bodies obey. A small exception are homing missiles - they can change direction depending on the movement of the target.

Inventors of anti-missile systems are also modernizing and developing weapons for the destruction of new generation weapons of mass destruction.

external ballistics. Trajectory and its elements. Exceeding the trajectory of the bullet above the point of aim. 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 has ceased.

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

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.

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

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

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

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

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

The effect of the force of air resistance on the flight of a bullet (grenade) is very large; it causes a decrease in the speed and range of the bullet (grenade). For example, a bullet mod. 1930 at an angle of throw of 15 ° and an initial speed of 800 m / s in airless space would have flown at 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, the shape and caliber of the bullet (grenade), as well as on its surface and air density.

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

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

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

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

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

In order to prevent the bullet from tipping over under the action of air resistance, it is given a rapid rotational movement with the help of rifling in the bore.

For example, when fired from a Kalashnikov assault rifle, the speed of rotation of the bullet at the moment of departure from the bore is about 3000 revolutions per second.

During the flight of a rapidly rotating bullet in the air, the following phenomena occur. The force of air resistance tends to turn the bullet head up and back. But the head of the bullet, as a result of rapid rotation, according to the property of the gyroscope, tends to maintain the given position and deviates not upwards, but very slightly in the direction of its rotation at right angles to the direction of the air resistance force, i.e., to the right. As soon as the head of the bullet deviates to the right, the direction of the air resistance force will change - it tends to turn the head of the bullet to the right and back, but the head of the bullet will not turn 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 axis, then the head of the bullet describes a circle, and its axis is a cone with a vertex at the center of gravity. There is a so-called slow conical, or precessional, movement, and the bullet flies with its head part forward, that is, it seems to follow the change in the curvature of the trajectory.

Slow conical movement of the bullet

Derivation (Trajectory top view)

The effect of air resistance on the flight of a grenade

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

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.

To improve accuracy, some grenades are given slow rotation due to the outflow of gases. Due to the rotation of the grenade, the moments of forces that deviate the axis of the grenade act sequentially in different directions, so the 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 departure point. The departure point is the start of the trajectory.

Trajectory elements

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

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

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

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

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

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

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

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

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

The speed of a 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 vertex of the trajectory.

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

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 point of fall is called the descending branch of the trajectory.

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

The straight line that runs 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 enclosed between the line of elevation and the line of sight is called the angle of aim.

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

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 of the trajectory to the line of sight is called the excess of the trajectory over the line of sight.

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

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

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

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

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

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

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

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

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

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

Grenade trajectory (side view)

Trajectory shape

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

Angle of greatest range, flat, overhead and conjugate trajectories

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

Trajectories obtained at elevation angles smaller than the angle of greatest range are called flat. Trajectories obtained at elevation angles greater than the angle of greatest 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 extent of the terrain, the target can be hit with one sight setting (the less impact on the results of shooting is caused by errors in determining the sight setting); this is the practical significance of the flat trajectory.

Exceeding the trajectory of a bullet above the aiming point

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

From muzzle to target: basic concepts every shooter should know.

You don't need a university degree in math or physics to understand how a rifle bullet flies. In this exaggerated illustration, it can be seen that the bullet, always deviating only downward from the direction of the shot, crosses the line of sight at two points. The second of these points is exactly at the distance at which the rifle is sighted.

One of the most successful recent projects in book publishing is a series of books called "...for dummies." Whatever knowledge or skill you want to master, there is always a proper "dummies" book for you, including such subjects as raising smart children for dummies (honestly!) and aromatherapy for dummies. It is interesting, however, that these books are not written for fools at all and do not treat the subject at a simplistic level. In fact, one of the best wine books I read was called Wine for Dummies.

So probably no one will be surprised if I say that there should be “Ballistics for Dummies”. I hope that you will agree to take this title with the same sense of humor with which I offer it to you.

What do you need to know about ballistics - if anything at all - in order to become a better marksman and a more prolific hunter? Ballistics is divided into three sections: internal, external and terminal.

Internal ballistics considers what happens inside the rifle from the moment of ignition to the exit of the bullet through the muzzle. In truth, internal ballistics only concerns reloaders, it is they who assemble the cartridge and thereby determine its internal ballistics. You have to be a real teapot to start collecting cartridges without having previously received elementary ideas about internal ballistics, if only because your safety depends on it. If, on the shooting range and hunting, you shoot only factory cartridges, then you really don’t need to know anything about what is happening in the bore: you still cannot influence these processes in any way. Don't get me wrong, I'm not advising anyone to go deeper into internal ballistics. It just doesn't really matter in that context.

As for terminal ballistics, yes, we have some freedom here, but no more than in choosing a bullet loaded in a homemade or factory cartridge. Terminal ballistics begins the moment the bullet hits the target. This is a science as much qualitative as it is quantitative, because there are a great many factors that determine lethality, and not all of them can be accurately modeled in the laboratory.

What remains is external ballistics. It's just a fancy term for what happens to a bullet from muzzle to target. We will consider this subject at an elementary level, I myself do not know the subtleties. I must confess to you that I passed mathematics in college on the third run, and flunked physics in general, so believe me, what I will talk about is not difficult.

These 154-grain (10g) 7mm bullets have the same TD at 0.273, but the left flat-faced bullet has a BC of 0.433 while the SST on the right has a BC of 0.530.

To understand what happens with a bullet from muzzle to target, at least as much as we hunters need, we need to learn some definitions and basic concepts, just to put everything in its place.

Definitions

Line of sight (LL)- a straight arrow from the eye through the aiming mark (or through the rear sight and front sight) to infinity.

Throwing line (LB)- another straight line, the direction of the axis of the bore at the time of the shot.

Trajectory- the line along which the bullet moves.

The fall- decrease in the trajectory of the bullet relative to the line of throw.

We've all heard someone say that a certain rifle shoots so flat that the bullet just doesn't drop in the first hundred yards. Nonsense. Even with the flattest supermagnums, from the very moment of departure, the bullet begins to fall and deviate from the throwing line. A common misunderstanding stems from the use of the word "rise" in ballistic tables. The bullet always falls, but it also rises relative to the line of sight. This seeming awkwardness comes from the fact that the sight is positioned above the barrel, and therefore the only way to cross the line of sight with the bullet's trajectory is to tilt the sight down. In other words, if the line of throw and the line of sight were parallel, the bullet would fly out of the muzzle one and a half inches (38mm) below the line of sight and begin to fall lower and lower.

Adding to the confusion is the fact that when the sight is set so that the line of sight intersects with the trajectory at some reasonable distance - at 100, 200 or 300 yards (91.5, 183, 274m), the bullet will cross the line of sight even before that. Whether we are shooting a 45-70 zeroed at 100 yards, or a 7mm Ultra Mag zeroed at 300, the first intersection of trajectory and line of sight will occur between 20 and 40 yards from the muzzle.

Both of these 375 caliber 300-grain bullets have the same cross-sectional density of 0.305, but the left-hand one, with a sharp nose and "boat stern", has a BC of 0.493, while the round one has only 0.250.

In the case of 45-70 we will see that in order to hit the target at 100 (91.4m) yards, our bullet will cross the line of sight about 20 yards (18.3m) from the muzzle. Further, the bullet will rise above the line of sight to the highest point in the region of 55 yards (50.3m) - about two and a half inches (64mm). At this point, the bullet begins to descend relative to the line of sight, so that the two lines will again intersect at the desired distance of 100 yards.

For a 7mm Ultra Mag shot at 300 yards (274m), the first intersection will be around 40 yards (37m). Between this point and the 300 yard mark, our trajectory will reach a maximum height of three and a half inches (89mm) above the line of sight. Thus, the trajectory crosses the line of sight at two points, the second of which is the sighting distance.

Trajectory at half way

And now I will touch on a concept that is little used today, although in those years when I began to master rifle shooting as a young fool, the trajectory at halfway was the criterion by which ballistic tables compared the effectiveness of cartridges. Half-way trajectory (TPP) is the maximum height of the bullet above the line of sight, provided that the weapon is sighted to zero at a given distance. Usually ballistic tables gave this value for 100-, 200-, and 300-yard ranges. For example, the TPP for a 150 grain (9.7g) bullet in the 7mm Remington Mag cartridge according to the 1964 Remington catalog was half an inch (13mm) at 100 yards (91.5m), 1.8 inches (46mm) at 200 yards (183m) and 4.7 inches (120mm) at 300 yards (274m). This meant that if we zeroed our 7 Mag at 100 yards, the trajectory at 50 yards would rise above the line of sight by half an inch. When zeroing in at 200 yards at 100 yards, it will rise 1.8 inches, and when zeroing in at 300 yards, it will rise 4.7 inches at 150 yards. In fact, the maximum ordinate is reached a little further than the middle of the sighting distance - about 55, 110 and 165 yards, respectively - but in practice the difference is not significant.

Although the CCI was useful information and a good way to compare different cartridges and loads, the modern reference system for the same distance zeroing height or bullet drop at different points in the trajectory is more meaningful.

Cross density, ballistic coefficient

After leaving the barrel, the trajectory of the bullet is determined by its speed, shape and weight. This brings us to two sonorous terms: transverse density and ballistic coefficient. Cross-sectional density is the weight of the bullet in pounds divided by the square of its diameter in inches. But forget it, it's just a way to relate the weight of a bullet to its caliber. Take, for example, a 100 grain (6.5g) bullet: in 7mm (.284) it's a fairly light bullet, but in 6mm (.243) it's quite heavy. And in terms of cross-sectional density, it looks like this: a 100-grain seven-millimeter caliber bullet has a cross-sectional density of 0.177, and a six-millimeter bullet of the same weight will have a cross-sectional density of 0.242.

This quartet of 7mm bullets show consistent degrees of streamlining. The round nose bullet on the left has a ballistic coefficient of 0.273, the bullet on the right, the Hornady A-Max, has a ballistic coefficient of 0.623, i.e. more than twice as many.

Perhaps the best understanding of what is considered light and what is heavy can be gained from comparing bullets of the same caliber. While the lightest 7mm bullet has a transverse density of 0.177, the heaviest 175 grain (11.3g) bullet has a transverse density of 0.310. And the lightest, 55-grain (3.6g), six-millimeter bullet has a transverse density of 0.133.

Since lateral density is related only to weight and not to bullet shape, it turns out that the most blunt bullets have the same lateral density as the most streamlined bullets of the same weight and caliber. Ballistic coefficient is another matter entirely, it is a measure of how streamlined a bullet is, that is, how effectively it overcomes resistance in flight. The calculation of the ballistic coefficient is not well defined, there are several methods that often give inconsistent results. Adds uncertainty and the fact that BC depends on speed and height above sea level.

Unless you're a math freak obsessed with calculations for the sake of calculations, then I suggest you just do it like everyone else: use the value provided by the bullet manufacturer. All do-it-yourself bullet manufacturers publish cross-sectional density and ballistic coefficient values for each bullet. But for bullets used in factory cartridges, only Remington and Hornady do this. Meanwhile, this is useful information, and I think that all cartridge manufacturers should report it both in ballistic tables and directly on the boxes. Why? Because if you have ballistic programs on your computer, then all you need to do is enter muzzle velocity, bullet weight and ballistic coefficient, and you can draw a trajectory for any sighting distance.

An experienced reloader can estimate the ballistic coefficient of any rifle bullet with decent accuracy by eye. For example, no round nose bullet, from 6mm to .458 (11.6mm), has a ballistic coefficient greater than 0.300. From 0.300 to 0.400 - these are light (with a low transverse density) hunting bullets, pointed or with a recess in the nose. Over .400 are moderately heavy bullets for this caliber with an extremely streamlined nose.

If a hunting bullet has a BC close to 0.500, it means that this bullet has combined near-optimal lateral density and a streamlined shape, such as Hornady's 7mm 162-grain (10.5g) SST with a BC of 0.550 or 180-grain ( 11.7d) Barnes XBT in 30 gauge with a BC of 0.552. This extremely high MC is typical of bullets with a round tail ("boat stern") and a polycarbonate nose, like the SST. Barnes, however, achieves the same result with a very streamlined ogive and an extremely small nose front.

By the way, the ogival part is the part of the bullet in front of the leading cylindrical surface, simply what forms the nose of zeros. When viewed from the side of the bullet, the ogive is formed by arcs or curved lines, but Hornady uses an ogive of converging straight lines, i.e. a cone.

If you put flat-nosed, round-nosed and sharp-nosed bullets side by side, then common sense will tell you that the pointed-nose is more streamlined than the round-nosed, and the round-nose, in turn, is more streamlined than the flat-nosed. It follows from this that, other things being equal, at a given distance, the sharp-nosed one will decrease less than the round-nosed one, and the round-nosed one will decrease less than the flat-nosed one. Add a "boat stern" and the bullet becomes even more aerodynamic.

From an aerodynamic point of view, the shape may be good, like a 120 grain (7.8g) 7mm bullet on the left, but due to the low lateral density (i.e. weight for this caliber), it will lose speed much faster. If the 175-grain (11.3g) bullet (right) is fired at 500 fps (152m/s) slower, it will overtake the 120-grain at 500 yards (457m).

Take Barnes' 180-grain (11.7g) X-Bullet 30-gauge, available in both flat-end and boat-tail designs, as an example. The nose profile of these bullets is the same, so the difference in ballistic coefficients is due solely to the shape of the butt. A flat-ended bullet would have a BC of 0.511, while a boat stern would give a BC of 0.552. In percentage terms, you might think that this difference is significant, but in fact, at five hundred yards (457m), a boat-stern bullet will drop only 0.9 inches (23 mm) less than a flat-pointed bullet, all other things being equal .

direct shot distance

Another way to evaluate trajectories is to determine the direct shot distance (DPV). Just like halfway trajectory, point-blank range has no effect on the actual trajectory of the bullet, it's just another criterion for zeroing in on a rifle based on its trajectory. For deer-sized game, point-blank range is based on the requirement that the bullet hit a 10-inch (25.4 cm) diameter kill zone when aiming at its center without drop compensation.

Basically, it's like taking a perfectly straight 10" imaginary pipe and laying it on a given path. With a muzzle in the center of the pipe at one end of it, the direct shot distance is the maximum length at which the bullet will fly inside this imaginary pipe. Naturally, in the initial section, the trajectory should be directed slightly upwards, so that at the point of the highest ascent, the bullet only touches the upper part of the pipe. With this aiming, the DPV is the distance at which the bullet will pass through the bottom of the pipe.

Consider a 30 caliber bullet fired from a 300 magnum at 3100 fps. According to the Sierra manual, zeroing the rifle at 315 yards (288m) gives us a point-blank range of 375 yards (343m). With the same bullet fired from a .30-06 rifle at 2800 fps, when zeroed in at 285 yards (261m), we get a DPV of 340 yards (311m) - not as much of a difference as it might seem, right?

Most ballistics programs calculate point-blank range, you just need to enter the bullet weight, ac, speed and kill zone. Naturally, you can enter a four-inch (10cm) kill zone if you are hunting marmots, and an eighteen-inch (46cm) if you are hunting moose. But personally, I have never used DPV, I consider it to be a slipshod shooting. Especially now that we have laser rangefinders, it makes no sense to recommend such an approach.

Introduction 2.

Objects, tasks and subject of judicial

ballistic examination 3.

The concept of firearms 5.

Device and purpose of the main

parts and mechanisms of firearms

weapons 7.

Classification of cartridges for

hand firearms 12.

Device unitary cartridges

and their main parts 14.

Drafting an expert opinion and

Photo tables 21.

List of used literature 23.

Introduction.

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

At a specific historical stage in the development of mankind, such a technical tool as firearms was created. Over time, it began to be used not only for military purposes or for hunting, but also for illegal purposes - as a weapon of crime. As a result of its use, it was necessary to fight crimes involving the use of firearms. Historical periods provide for legal, 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 forensic system as an element of its section - forensic technology.

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

Judicial ballistics - a branch of krimtechnics that studies the methods of natural sciences with the help of specially developed methods and techniques of firearms, phenomena and traces accompanying its action, ammunition and their components in order to investigate crimes committed with the use of firearms.

Modern forensic ballistics was formed as a result of the analysis of the accumulated empirical material, active theoretical research, generalization of facts related to firearms, ammunition for it, and the patterns of formation of traces of their action. Some provisions of ballistics proper, that is, the science of the movement of a projectile, a 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, OBJECTIVES AND SUBJECT OF FORENSIC BALLISTIC EXAMINATION

Forensic ballistics - this is a special study carried out in the procedural form established by law with the preparation of an appropriate conclusion in order to obtain scientifically based factual data on firearms, ammunition for it and the circumstances of their use, which are relevant to the investigation and trial.

object any expert research are material carriers of information that can be used to solve the corresponding expert tasks.

The objects of forensic ballistic examination in most cases are associated with a shot or its possibility. The range of these objects is very diverse. It includes:

Firearms, their parts, accessories and blanks;

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

Ammunition and cartridges for firearms and other shooting devices, separate elements of cartridges;

Samples for a comparative study 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 cartridge cases, traces of the use of firearms on various objects;

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

Material conditions of the scene.

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

Despite all the diversity and diversity of the 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 membership of an object) and individual identification (establishing the identity of an object).

Group identification includes setting:

Items belonging to the category of firearms and ammunition;

Type, model and type of firearms and cartridges presented;

Type, model of weapons on traces on spent cartridges, fired shells and traces on an obstacle (in the absence of firearms);

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

To individual identification relate:

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

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

Identification of the equipment and devices used to equip ammunition, manufacture its components or weapons;

Establishing that the bullet and cartridge case belong to the same cartridge.

Non-identification tasks can be divided into three types:

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

Situational, aimed at establishing the circumstances of the firing;

Reconstruction related to the reconstruction of the original appearance of objects.

Diagnostic tasks:

Establishment of the technical condition and suitability for the production of shots of firearms and cartridges for it;

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

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

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

Situational tasks:

Establishing the distance, direction and place of the shot;

Determining the relative position of the shooter and the victim at the time 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 subject of forensic ballistic examination.

The word "subject" has two main meanings: an object as a thing and an object as the content of the phenomenon under study. Speaking about the subject of forensic ballistic examination, we mean the second meaning of this word.

The subject of forensic examination is understood as circumstances, facts established through expert research, which are important for the decision of the court and the production of 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 to be solved.

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

On the state of firearms;

About the presence or absence of the identity of firearms;

About the circumstances of the shot;

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

THE CONCEPT OF FIREARMS

The Criminal Code, providing for liability for the illegal carrying, storage, acquisition, manufacture and sale of firearms, their theft, careless storage, does not clearly define what is considered a firearm. At the same time, the explanations of the Supreme Court explicitly state that when special knowledge is required to decide whether the item that the perpetrator stole, illegally carried, stored, acquired, manufactured or sold is a weapon, the courts need to appoint an expert examination. Therefore, experts must operate with a clear and complete definition that reflects the main features of firearms.