Internal ballistics. Shot and its periods. Initial bullet speed and its practical value Ballistics calculations

The content of the article

BALLISTICS, a complex of physical and technical disciplines covering theoretical and experimental study of the movement and final impact of thrown solid bodies - bullets, artillery shells, missiles, aircraft bombs and spacecraft. Ballistics is divided into: 1) internal ballistics, which studies methods for setting a projectile in motion; 2) external ballistics, which studies the movement of a projectile along a trajectory; 3) ballistics at the end point, the subject of study of which is the patterns of the impact of projectiles on the targets they hit. Development and design of types and systems ballistic weapons are based on the application of mathematics, physics, chemistry and design achievements to solve numerous and complex ballistics problems. I. Newton (1643–1727) is considered to be the founder of modern ballistics. Formulating the laws of motion and calculating the trajectory of a material point in space, he relied on the mathematical theory of dynamics solid, which was developed by I. Muller (Germany) and the Italians N. Fontana and G. Galileo in the 15th and 16th centuries.

The classic problem of internal ballistics, which consists of calculating the initial velocity of a projectile, the maximum pressure in the barrel and the dependence of pressure on time, has been theoretically solved quite completely for small arms and cannons. As for modern artillery and missile systems - recoilless rifles, gas guns, artillery rockets and systems with jet thrust, – then here there is a need for additional clarification of the ballistic theory. Typical ballistics problems involving aerodynamic, inertial and gravitational forces acting on a projectile or missile in flight have become more complex in recent years. Hypersonic and cosmic speeds, entry of the nose cone into dense layers of the atmosphere, huge trajectory lengths, flight outside the atmosphere and interplanetary space flights– all this requires updating the laws and theories of ballistics.

The origins of ballistics are lost in antiquity. Its very first manifestation was, undoubtedly, the throwing of stones by prehistoric man. Precursors to modern weapons such as the bow, catapult, and ballista may typify the earliest applications of ballistics. Progress in weapon design has led to the fact that today artillery pieces fire 90-kilogram shells at distances of more than 40 km, anti-tank shells capable of penetrating steel armor 50 cm thick, and guided missiles can deliver tons of combat load to any point on the globe.

Have been used for many years different ways acceleration of projectiles. The bow accelerated the arrow using the energy stored in the bent piece of wood; The springs of the ballista were the twisted tendons of animals. Electromagnetic force, steam force, and compressed air were tested. However, none of the methods was as successful as burning flammable substances.

INTERNAL BALLISTICS

Internal ballistics is a branch of ballistics that studies the processes of bringing a projectile into forward movement. Such processes require: 1) energy; 2) the presence of a working substance; 3) the presence of a device that controls the supply of energy and accelerates the projectile. The device for accelerating the projectile can be a gun system or a jet engine.

Barrel acceleration systems.

The general classical problem of internal ballistics, as applied to barreled systems of initial acceleration of a projectile, is to find the limiting relationships between the loading characteristics and the ballistic elements of the shot, which together completely determine the firing process. Loading characteristics are the dimensions of the powder chamber and bore, the design and shape of the rifling, as well as the mass of the powder charge, projectile and gun. Ballistic elements are gas pressure, temperature of gunpowder and powder gases, speed of gases and projectile, distance traveled by the projectile, and the amount of gases currently active. The gun is essentially a single-stroke internal combustion engine in which the projectile moves like a free piston under the pressure of a rapidly expanding gas.

The pressure resulting from the transformation of a solid combustible substance (gunpowder) into gas rises very quickly to a maximum value of 70 to 500 MPa. As the projectile moves down the barrel, the pressure drops quite quickly. The duration of high pressure is on the order of several milliseconds for a rifle and several tenths of a second for large-caliber weapons (Fig. 1).

The characteristics of the internal ballistics of the barrel acceleration system depend on chemical composition propellant, its burning rate, the shape and size of the powder charge, and the loading density (the mass of the powder charge per unit volume of the gun chamber). In addition, the characteristics of the system can be affected by the length of the gun barrel, the volume of the powder chamber, the mass and “lateral density” of the projectile (the mass of the projectile divided by the square of its diameter). From an internal ballistics point of view, low density is desirable because it allows the projectile to achieve greater velocity.

To keep a recoil gun in balance during a shot, a significant external force is required (Fig. 2). External force is typically provided by a recoil mechanism consisting of mechanical springs, hydraulic devices and gas shock absorbers designed to dampen the rearward impulse of the gun's barrel and breech. (Momentum, or momentum, is defined as the product of mass and velocity; by Newton's third law, the momentum imparted to the gun is equal to the momentum imparted to the projectile.)

In a recoilless rifle, no external force is required to maintain the equilibrium of the system, since here the total change in impulse imparted to all elements of the system (gases, projectile, barrel and breech) for a given time is zero. To prevent a weapon from recoil, the momentum of the gases and projectile moving forward must be equal and opposite to the momentum of the gases moving backward and exiting through the breech.

Gas gun.

The gas gun consists of three main parts, shown in Fig. 3: compression section, restriction section and launch barrel. A conventional powder charge is ignited in the chamber, which causes the piston to move down the barrel compression section and compress the helium gas filling the bore. When the helium pressure increases to a certain level, the diaphragm ruptures. A sudden burst of high-pressure gas pushes the projectile out of the launch barrel, and the restrictive section stops the piston. The speed of a projectile fired by a gas gun can reach 5 km/s, while for a conventional gun this is a maximum of 2000 m/s. More high efficiency gas gun is explained by the low molecular weight of the working substance (helium) and, accordingly, high speed sound in helium acting on the bottom of the projectile.

Reactive systems.

Rocket launchers perform essentially the same functions as artillery guns. This installation plays the role of a fixed support and usually sets the initial direction of flight of the missile. When launching a guided missile, which, as a rule, has an on-board guidance system, the precise aiming required when firing a gun is not required. In the case of unguided missiles, the launcher guides must place the missile on a trajectory leading to the target.

EXTERNAL BALLISTICS

External ballistics deals with the movement of projectiles in the space between the launcher and the target. When a projectile is set in motion, its center of mass traces a curve in space called a trajectory. The main task external ballistics is to describe this trajectory by determining the position of the center of mass and the spatial position of the projectile as a function of flight time (time after launch). To do this, you need to solve a system of equations that takes into account the forces and moments of force acting on the projectile.

Vacuum trajectories.

The simplest of the special cases of projectile motion is the motion of a projectile in a vacuum above a flat, stationary earth's surface. In this case, it is assumed that the projectile is not affected by any other forces other than gravity. The equations of motion corresponding to this assumption are easily solved and give a parabolic trajectory.

Trajectories of a material point.

Another special case is the movement of a material point; here the projectile is considered as a material point, and its drag (the force of air resistance acting in the opposite direction tangential to the trajectory and slowing down the movement of the projectile), gravity, the speed of rotation of the Earth and the curvature of the earth's surface are taken into account. (The rotation of the Earth and the curvature of the earth's surface can be ignored if the flight time along the trajectory is not very long.) A few words should be said about drag. Drag force D, exerted on the motion of the projectile, is given by the expression

D = rSv 2 C D (M),

Where r– air density, S– cross-sectional area of ​​the projectile, v– speed of movement, and C D (M) is a dimensionless function of the Mach number (equal to the ratio of the projectile speed to the speed of sound in the medium in which the projectile moves), called the drag coefficient. Generally speaking, the drag coefficient of a projectile can be determined experimentally in a wind tunnel or at a test site equipped with precision measuring equipment. The task is made easier by the fact that for projectiles of different diameters the drag coefficient is the same if they have the same shape.

The theory of the motion of a material point (although it does not take into account many forces acting on a real projectile) describes with a very good approximation the trajectory of missiles after the engine stops operating (in the passive part of the trajectory), as well as the trajectory of conventional artillery shells. Therefore, it is widely used to calculate data used in the targeting systems of weapons of this kind.

Rigid body trajectories.

In many cases, the theory of motion of a material point does not adequately describe the trajectory of a projectile, and then it is necessary to consider it as a rigid body, i.e. take into account that it will not only move translationally, but also rotate, and take into account all aerodynamic forces, and not just drag. This approach is required, for example, to calculate the movement of a rocket with a running engine (in the active part of the trajectory) and projectiles of any type fired perpendicular to the flight path of a high-speed aircraft. In some cases it is generally impossible to do without the idea of ​​a solid body. So, for example, to hit the target, it is necessary that the projectile be stable (move with its head forward) along the trajectory. Both in the case of missiles and in the case of conventional artillery shells, this is achieved in two ways - with the help of tail stabilizers or by rapidly rotating the projectile around the longitudinal axis. Further, speaking about flight stabilization, we note some considerations that are not taken into account by the theory of a material point.

Tail stabilization is a very simple and obvious idea; It is not for nothing that one of the most ancient projectiles - an arrow - was stabilized in flight in precisely this way. When a finned projectile moves with an angle of attack or yaw (the angle between the tangent to the trajectory and the longitudinal axis of the projectile) other than zero, the area behind the center of mass that is affected by air resistance is greater than the area in front of the center of mass. The difference in unbalanced forces causes the projectile to rotate around the center of mass so that this angle becomes zero. Here we can note one important circumstance that is not taken into account by the theory of a material point. If a projectile moves with a non-zero angle of attack, then it is acted upon by lifting forces caused by the occurrence of a pressure difference on both sides of the projectile. (This is what an airplane's ability to fly is based on.)

The idea of ​​rotational stabilization is not so obvious, but it can be explained by comparison. It is well known that if a wheel rotates quickly, it resists attempts to turn its axis of rotation. (An ordinary top is an example, and this phenomenon is used in control, navigation and guidance systems devices - gyroscopes.) The most common way to set a projectile in rotation is to cut spiral grooves in the barrel bore, into which the metal belt of the projectile would crash as the projectile accelerates along the barrel , which would make it rotate. In spin-stabilized rockets, this is achieved by using multiple inclined nozzles. Here, too, we can note some features that are not taken into account by the theory of a material point. If you shoot vertically upward, the stabilizing effect of rotation will force the projectile to fall downwards with its bottom part after reaching the top point of flight. This, of course, is undesirable, and therefore guns are not fired at an angle of more than 65–70° to the horizontal. Second interesting phenomenon due to the fact that, as can be shown on the basis of the equations of motion, a projectile stabilized by rotation must fly with a non-zero nutation angle, called “natural”. Therefore, such a projectile is subject to forces that cause derivation - a lateral deviation of the trajectory from the firing plane. One of these powers is the power of Magnus; It is precisely this that causes the curvature of the trajectory of a “spin” ball in tennis.

Everything that has been said about flight stability, while not fully covering the phenomena that determine the flight of a projectile, nevertheless illustrates the complexity of the problem. Let us only note that in the equations of motion it is necessary to take into account many different phenomena; these equations include a number of variable aerodynamic coefficients (such as the drag coefficient) that must be known. Solving these equations is a very time-consuming task.

Application.

The use of ballistics in combat involves the location of the weapon system in a location that would allow it to quickly and effectively hit the intended target with minimal risk to operating personnel. Delivery of a missile or projectile to a target is usually divided into two stages. At the first, tactical stage, it is selected fighting position cannon weapons and ground-based missiles or the position of the carrier of air-launched missiles. The target must be within the warhead delivery radius. At the shooting stage, aiming is carried out and shooting is carried out. To do this, it is necessary to determine the exact coordinates of the target relative to the weapon - azimuth, elevation and range, and in the case of a moving target - its future coordinates, taking into account the time of flight of the projectile.

Before firing, corrections must be made for changes in initial velocity associated with bore wear, powder temperature, deviations in projectile mass and ballistic coefficients, as well as corrections for constantly changing weather and associated changes in atmospheric density, wind speed and direction. In addition, corrections must be made for projectile derivation and (at long ranges) for the rotation of the Earth.

With the increasing complexity and expansion of the range of problems of modern ballistics, new technical means have appeared, without which the possibilities for solving current and future ballistic problems would be greatly limited.

Calculations of near-Earth and interplanetary orbits and trajectories, taking into account the simultaneous movement of the Earth, the target planet and the spacecraft, as well as the influence of various celestial bodies, would be extremely difficult without computers. The approach speeds of hyper-speed targets and projectiles are so high that solving shooting problems on the basis of conventional tables and manually setting shooting parameters is completely excluded. Currently, firing data from most weapon systems is stored in electronic data banks and quickly processed by computers. The computer's output commands automatically position the weapon at the azimuth and elevation required to deliver the warhead to the target.

Trajectories of guided projectiles.

In the case of guided projectiles, the already complex task of describing the trajectory is complicated by the fact that a system of equations called guidance equations is added to the equations of motion of a rigid body, which relates the deviations of the projectile from a given trajectory with corrective actions. The essence of projectile flight control is this. If in one way or another, using the equations of motion, a deviation from a given trajectory is determined, then, based on the guidance equations, a corrective action is calculated for this deviation, for example, turning the air or gas rudder, changing thrust. This corrective action, changing certain terms of the equations of motion, leads to a change in the trajectory and a decrease in its deviation from the given one. This process is repeated until the deviation is reduced to an acceptable level.

BALLISTICS AT THE END POINT

Endpoint ballistics examines the physics of the destructive effect of weapons on the targets they hit. Its data is used to improve most weapons systems - from rifles and hand grenades to nuclear warheads delivered to the target by intercontinental ballistic missiles, as well as protective equipment - soldiers' body armor, tank armor, underground shelters, etc. Both experimental and theoretical studies are carried out on the phenomena of explosion (chemical explosives or nuclear charges), detonation, penetration of bullets and fragments into different environments, shock waves in water and soil, combustion and nuclear radiation.

Explosion.

Experiments in the field of explosion are carried out both with chemical explosives in quantities measured in grams and with nuclear charges with a yield of up to several megatons. Explosions can occur in a variety of environments, such as earth and rock, underwater, near the surface of the earth in normal atmospheric conditions, or in thin air at high altitudes. The main result of the explosion is the formation of a shock wave in the environment. The shock wave propagates from the explosion site at first at a speed exceeding the speed of sound in the medium; then, as the intensity of the shock wave decreases, its speed approaches the speed of sound. Shock waves (in the air, water, ground) can hit enemy personnel, destroy underground fortifications, sea vessels, buildings, ground vehicles, aircraft, missiles and satellites.

To simulate intense shock waves that occur in the atmosphere and near the surface of the earth during nuclear explosions, special devices called shock tubes are used. The shock tube is typically a long tube made up of two sections. At one end there is a compression chamber, which is filled with air or other gas compressed to a relatively high pressure. Its other end is an expansion chamber open to the atmosphere. When the thin diaphragm separating two sections of the pipe instantly ruptures, a shock wave appears in the expansion chamber, traveling along its axis. In Fig. Figure 4 shows shock wave pressure curves in three cross sections of the pipe. In cross section 3 it takes the classic form of a shock wave that occurs during detonation. Miniature models can be placed inside the shock tubes, which will undergo shock loads, similar to action nuclear explosion. Tests are often carried out in which larger models and sometimes full-scale objects are exposed to explosions.

Experimental studies are complemented by theoretical ones, and semi-empirical rules are developed that make it possible to predict the destructive effect of an explosion. The results of such research are used in the design of warheads for intercontinental ballistic missiles and anti-missile systems. Data of this kind are also necessary when designing missile silos and underground shelters to protect the population from the explosive effects of nuclear weapons.

To solve specific problems characteristic of the upper layers of the atmosphere, there are special chambers in which high-altitude conditions are simulated. One of these tasks is assessing the reduction in explosion force at high altitudes.

Research is also being conducted to measure the intensity and duration of the shock wave in the ground that occurs during underground explosions. The propagation of such shock waves is influenced by the type of soil and the degree of its layering. Laboratory experiments are carried out with chemical explosives in quantities of less than 0.5 kg, while in full-scale experiments the charges can be measured in hundreds of tons. Such experiments are complemented by theoretical studies. The research results are used not only to improve the design of weapons and shelters, but also to detect unauthorized underground nuclear explosions. Detonation research requires fundamental research in solid state physics, chemical physics, gas dynamics and metal physics.

Fragments and penetration ability.

Fragmentation warheads and projectiles have a metal outer shell, which, upon detonation of the chemical high explosive charge enclosed in it, breaks into numerous pieces (fragments) that fly apart at high speed. During World War II, projectiles and warheads with shaped charges were developed. Such a charge is usually a cylinder of explosive, at the front end of which there is a conical recess with a conical metal liner, usually copper, placed in it. When an explosion begins at the other end of the explosive charge and the liner is compressed under the influence of very high detonation pressures, a thin cumulative jet of liner material is formed, flying towards the target at a speed of more than 7 km/s. Such a jet is capable of penetrating steel armor tens of centimeters thick. The process of formation of a jet in ammunition with a charge of cumulative action is shown in Fig. 5.

If the metal is in direct contact with the explosive, shock wave pressures measured in tens of thousands of MPa can be transferred to it. With a typical explosive charge size of about 10 cm, the duration of the pressure pulse is a fraction of a millisecond. Such enormous pressures acting for a short time cause unusual destruction processes. An example of such phenomena is “chipping”. The detonation of a thin layer of explosives placed on an armor plate creates a very strong short-duration pressure pulse (impact) running through the thickness of the plate. Having reached the opposite side of the slab, the shock wave is reflected as a wave of tensile stresses. If the intensity of the stress wave exceeds the tensile strength of the armor material, tensile failure occurs near the surface at a depth depending on the initial thickness of the explosive charge and the speed of propagation of the shock wave in the plate. As a result of an internal rupture of the armor plate, a metal “shard” is formed, flying off the surface at high speed. Such a flying fragment can cause great destruction.

To clarify the mechanism of fracture phenomena, additional experiments are carried out in the field of metal physics of high-speed deformation. Such experiments are carried out both with polycrystalline metal materials and with single crystals of various metals. They made it possible to draw an interesting conclusion regarding the initiation of cracks and the beginning of destruction: in cases where there are inclusions (impurities) in the metal, cracks always begin at the inclusions. Experimental studies are being carried out on the penetrating ability of shells, fragments and bullets in different environments. Impact velocities range from several hundred meters per second for low-velocity bullets to cosmic velocities on the order of 3–30 km/s, consistent with fragments and micrometeors encountered by interplanetary vehicles.

Based on such studies, it is concluded empirical formulas regarding penetration ability. Thus, it has been established that the depth of penetration into a dense medium is directly proportional to the amount of movement of the projectile and inversely proportional to its cross-sectional area. The phenomena observed during an impact at hypersonic speed are shown in Fig. 6. Here a steel pellet hits a lead plate at a speed of 3000 m/s. At different times, measured in microseconds from the start of the collision, a sequence of X-ray images was taken. A crater forms on the surface of the plate, and as the images show, plate material is ejected from it. The results of the study of impacts at hypersonic speed make it more clear the formation of craters on celestial bodies, for example on the Moon, in places where meteorites fall.

Wound ballistics.

To simulate the effect of shrapnel and bullets hitting a person, shots are fired at massive gelatin targets. Such experiments belong to the so-called. wound ballistics. Their results allow us to judge the nature of the wounds that a person may receive. The information provided by wound ballistics studies makes it possible to optimize effectiveness different types weapons intended to destroy enemy personnel.

Armor.

Using Van de Graaff accelerators and other sources of penetrating radiation, the degree of radiation protection of people in tanks and armored vehicles provided by special armor materials is being studied. In experiments, the coefficient of transmission of neutrons through plates of different layers of materials having typical tank configurations is determined. The energy of neutrons can range from fractions to tens of MeV.

Combustion.

Research in the field of ignition and combustion is carried out for a twofold purpose. The first is to obtain the data necessary to increase the ability of bullets, shrapnel and incendiary shells to cause fires in the fuel systems of aircraft, missiles, tanks, etc. The second is to increase the protection of vehicles and stationary objects from the incendiary effects of enemy ammunition. Research is being conducted to determine the flammability of various fuels under the influence of various means of ignition - electrical sparks, pyrophoric (self-igniting) materials, high-velocity fragments and chemical igniters.

ballistics

and. Greek the science of the movement of thrown (thrown) bodies; now especially cannon shells; ballistic, related to this science; ballista w. and ballista m. projectile, a tool for marking weights, especially an ancient military machine, for marking stones.

Explanatory dictionary of the Russian language. D.N. Ushakov

ballistics

(ali), ballistics, pl. no, w. (from Greek ballo - sword) (military). The science of the flight of gun shells.

Explanatory dictionary of the Russian language. S.I.Ozhegov, N.Yu.Shvedova.

ballistics

And, well. The science of the laws of flight of shells, mines, bombs, bullets.

adj. ballistic, -aya, -oh. Ballistic missile(traversing part of the path as a freely thrown body).

New explanatory dictionary of the Russian language, T. F. Efremova.

ballistics

A branch of theoretical mechanics that studies the laws of motion of a body thrown at an angle to the horizon.

1. A scientific discipline that studies the laws of motion of projectiles, mines, bullets, unguided missiles, etc.

   A subject containing theoretical basis of this scientific discipline.

   decomposition A textbook setting out the content of a given academic subject.

Encyclopedic Dictionary, 1998

ballistics

BALLISTICS (German Ballistik, from Greek ballo - throw) the science of the movement of artillery shells, unguided rockets, mines, bombs, bullets when firing (launching). Internal ballistics studies the movement of a projectile in the barrel bore (or in other conditions limiting movement) under the influence of powder gases, external ballistics - after it leaves the barrel bore.

Ballistics

(German Ballistik, from Greek ballo ≈ throwing), the science of the movement of artillery shells, bullets, mines, aerial bombs, active and reactive rockets, harpoons, etc. Biology is a military-technical science based on a complex of physical and mathematical disciplines. There are internal and external ballistics.

Internal biology studies the movement of a projectile (or other bodies whose mechanical freedom is limited by certain conditions) in the bore of a gun under the influence of powder gases, as well as the patterns of other processes that occur during a shot in the bore or chamber of a powder rocket. Considering a shot as a complex process of rapid transformation of the chemical energy of gunpowder into thermal, and then into mechanical work of moving the projectile, charge, and recoil parts of the gun, internal biology distinguishes in the phenomenon of a shot: a preliminary period ≈ from the beginning of the burning of gunpowder to the beginning of the movement of the projectile; 1st (main) period ≈ from the beginning of the movement of the projectile to the end of the burning of gunpowder; 2nd period ≈ from the end of the combustion of gunpowder until the moment the projectile leaves the barrel (the period of adiabatic expansion of gases) and the period of the aftereffect of powder gases on the projectile and barrel. The patterns of processes associated with the last period are considered by a special section of ballistics - intermediate ballistics. The end of the period of aftereffect on a projectile separates the area of ​​phenomena studied by internal and external ballistics. The main sections of internal ballistics are pyrostatics, pyrodynamics, and ballistic design of guns. Pyrostatics studies the laws of combustion of gunpowder and gas formation during the combustion of gunpowder in a constant volume and establishes the influence of the chemical nature of gunpowder, its shape and size on the laws of combustion and gas formation. Pyrodynamics studies the processes and phenomena occurring in the barrel bore during a shot, and establishes connections between the design characteristics of the barrel bore, loading conditions and various physical, chemical and mechanical processes occurring during a shot. Based on the consideration of these processes, as well as the forces acting on the projectile and barrel, a system of equations is established that describes the firing process, including the basic equation of internal combustion, which relates the size of the burned part of the charge, the pressure of the powder gases in the barrel, the velocity of the projectile and the length the path he has traveled. Solving this system and finding the dependence of the change in pressure of powder gases P, projectile speed v and other parameters on the path of the projectile 1 ( rice. 1) and from the time of its movement along the bore is the first main (direct) task of the internal B. To solve this problem, the following are used: analytical method, numerical integration methods [including those based on electronic computers (computers)] and tabular methods . In all these methods, due to the complexity of the firing process and insufficient knowledge of individual factors, certain assumptions are made. Of great practical importance are the correction formulas of internal ammunition, which make it possible to determine the change in the muzzle velocity of a projectile and the maximum pressure in the barrel bore when different loading conditions change.

══Ballistic design of guns is the second main (inverse) task of internal ballistics. It determines the design data of the barrel bore and loading conditions under which a projectile of a given caliber and weight will receive a given (muzzle) velocity upon departure. For the barrel option selected during design, curves of changes in gas pressure in the barrel bore and projectile velocity along the barrel length and over time are calculated. These curves are the initial data for designing the artillery system as a whole and its ammunition. Internal warfare also studies the process of firing with special and combined charges, in small arms, systems with conical barrels, and systems with the outflow of gases during the combustion of gunpowder (gas-dynamic and recoilless rifles, mortars). An important section is also the internal biology of powder rockets, which has developed into a special science. The main sections of the internal biology of gunpowder rockets are: pyrostatics of a semi-closed volume, which examines the laws of combustion of gunpowder at a relatively low constant pressure; solving the main internal problems. B. powder rocket, which consists in determining (under given loading conditions) the law of change in pressure of powder gases in the chamber depending on time, as well as the law of change in thrust force to ensure the required rocket speed; ballistic design of a powder rocket, which consists of determining the energy characteristics of the powder, the weight and shape of the charge, as well as the design parameters of the nozzle, which provide the necessary thrust force during its operation for a given weight of the rocket warhead.

External biology studies the movement of unguided projectiles (mines, bullets, etc.) after they leave the barrel (launching device), as well as the factors influencing this movement. Its main content is the study of all elements of the movement of a projectile and the forces acting on it in flight (air resistance force, gravity, reactive force, force arising during the aftereffect period, etc.); movement of the center of mass of the projectile in order to calculate its trajectory ( rice. 2) under given initial and external conditions (the main task of external ballistics), as well as determining the stability of flight and dispersion of projectiles. Important sections of external ballistics are the theory of corrections, which develops methods for assessing the influence of factors determining the flight of a projectile on the nature of its trajectory, as well as methods for compiling firing tables and methods for finding the optimal external ballistic option when designing artillery systems. The theoretical solution of problems on projectile motion and problems of the theory of corrections comes down to drawing up equations of projectile motion, simplifying these equations and finding methods for solving them; the latter was greatly facilitated and accelerated with the advent of computers. To determine the initial conditions (initial velocity and throwing angle, shape and mass of the projectile) necessary to obtain a given trajectory, special tables are used in external ballistics. The development of a methodology for compiling shooting tables consists of determining the optimal combination of theoretical and experimental studies that make it possible to obtain shooting tables of the required accuracy with minimal time. External motion methods are also used to study the laws of motion of spacecraft (when they move without the influence of control forces and moments). With the advent of guided projectiles, external flight played a major role in the formation and development of the theory of flight, becoming a special case of the latter.

The emergence of biology as a science dates back to the 16th century. The first works on artillery were the books of the Italian N. Tartaglia, “New Science” (1537) and “Questions and Discoveries Relating to Artillery Shooting” (1546). In the 17th century The fundamental principles of external ballistics were established by G. Galileo, who developed the parabolic theory of projectile motion, the Italian E. Torricelli, and the Frenchman M. Mersenne, who proposed calling the science of projectile motion ballistics (1644). I. Newton conducted the first studies on the movement of a projectile taking into account air resistance ≈ “Mathematical principles of natural philosophy” (1687). In the 17th-18th centuries. The movement of projectiles was studied by the Dutchman H. Huygens, the Frenchman P. Varignon, the Swiss D. Bernoulli, the Englishman B. Robins, the Russian scientist L. Euler, and others. The experimental and theoretical foundations of internal ballistics were laid in the 18th century. in the works of Robins, C. Hetton, Bernoulli and others. In the 19th century. the laws of air resistance were established (the laws of N.V. Maievsky, N.A. Zabudsky, the Havre law, the law of A.F. Siacci). At the beginning of the 20th century. an exact solution to the main problem of internal combustion was given - the work of N. F. Drozdov (1903, 1910), the issues of combustion of gunpowder in a constant volume were studied - the work of I. P. Grave (1904) and the pressure of powder gases in the barrel bore - the work of N. A Zabudsky (1904, 1914), as well as the Frenchman P. Charbonnier and the Italian D. Bianchi. IN THE USSR huge contribution The further development of artillery was introduced by scientists of the Commission for Special Artillery Experiments (KOSLRTOP) in 1918–26. During this period, V. M. Trofimov, A. N. Krylov, D. A. Ventzel, V. V. Mechnikov, G. V. Oppokov, B. N. Okunev and others carried out a number of works to improve methods for calculating the trajectory, development of the theory of corrections and the study of the rotational motion of the projectile. Research by N. E. Zhukovsky and S. A. Chaplygin on the aerodynamics of artillery shells formed the basis for the work of E. A. Berkalov and others on improving the shape of shells and increasing their flight range. V. S. Pugachev was the first to solve the general problem of the movement of an artillery shell.

An important role in solving the problems of internal ballistics was played by the research of Trofimov, Drozdov, and I. P. Grave, who wrote the most complete course of theoretical internal ballistics in 1932–38. He made a significant contribution to the development of methods for assessing and ballistic research of artillery systems and to solving special problems of internal ballistics contributed by M. E. Serebryakov, V. E. Slukhotsky, B. N. Okunev, and from foreign authors ≈ P. Charbonnier, J. Sugo and others.

During the Great Patriotic War of 1941–45, under the leadership of S. A. Khristianovich, theoretical and experimental work was carried out to increase the accuracy of rockets. In the post-war period, these works continued; The issues of increasing the initial velocities of projectiles, establishing new laws of air resistance, increasing barrel survivability, and developing ballistic design methods were also studied. Work on the study of the aftereffect period (V. E. Slukhotsky and others) and the development of firefighting methods for solving special problems (smooth-bore systems, active rocket projectiles, etc.), problems of external and internal firefighting in relation to rockets, further improving the methodology of ballistic research associated with the use of computers.

Lit.: Grave I.P., Internal ballistics. Pyrodynamics, in. 1≈4, L., 1933≈37; Serebryakov M.E., Internal ballistics of barrel systems and powder rockets, M., 1962 (bib.); Korner D., Internal ballistics of guns, trans. from English, M., 1953; Shapiro Ya. M., External ballistics, M., 1946.

Yu. V. Chuev, K. A. Nikolaev.

Wikipedia

Ballistics

Ballistics- the science of the movement of bodies thrown in space, based on mathematics and physics. She is mainly concerned with the study of the movement of bullets and projectiles fired from firearms, missiles and ballistic missiles.

Depending on the stage of movement of the projectile, there are:

• internal ballistics, which studies the movement of a projectile in a gun barrel;
• intermediate ballistics, which studies the passage of a projectile through the muzzle and behavior at the muzzle. It is important for specialists in shooting accuracy, when developing silencers, flash suppressors and muzzle brakes;
• external ballistics, which studies the movement of a projectile in the atmosphere or void under the influence of external forces. It is used when calculating corrections for elevation, wind and derivation;
• barrier or terminal ballistics, which studies the last stage - the movement of a bullet in a barrier. Terminal ballistics is carried out by gunsmiths who are specialists in projectiles and bullets, strength and other armor and protection specialists, as well as forensic scientists.

Examples of the use of the word ballistics in literature.

When the excitement subsided, Barbicane spoke in an even more solemn tone: “You know what progress has been made ballistics in recent years, and to what a high degree of perfection firearms might have reached if the war had still continued!

Of course, there can be no question that ballistics is not progressing, but let it be known to you that in the Middle Ages they achieved results, I dare say, even more amazing than ours.

Now it was a question of an attempt to upset the balance of the Earth - an attempt based on accurate and indisputable calculations, an attempt that development ballistics and the mechanics made it quite feasible.

On the fourteenth of September a telegram was forwarded to the Washington Observatory, asking them to investigate the consequences, taking into account the laws ballistics and all geographical data.

Barbicane, - as I asked myself the question: could we, without going beyond the limits of our specialty, venture on some outstanding enterprise worthy of the nineteenth century, and whether high achievements would allow ballistics implement it successfully?

We have to solve one of the main problems ballistics, this science of sciences that treats the movement of projectiles, that is, bodies that, having received a certain push, rush into space and then fly due to inertia.

And now, as far as I understand, we are unable to do anything until the police receive a report from the department ballistics regarding the bullets recovered from Mrs. Ellis's body.

If in the Department ballistics found out that Nadine Ellis was killed by a bullet fired from a revolver that the police found among Helen Robb's belongings at the motel, then your client doesn't have one chance in a hundred.

As far as I know, she was transferred to the Department ballistics and the experts came to the conclusion that it was fired from the revolver that was lying on the floor next to the woman.

I ask the department ballistics conduct the necessary experiments and compare the bullets before the start of tomorrow's hearing,” Judge Keyser said.

I request that it be recorded that during a break in the hearing, the expert on the issues ballistics Alexander Redfield fired several test shots from all three revolvers owned by George Anklitas.

Freeing one hand for a short time, he ran the back of his hand across his forehead, as if wanting to exorcise the ghost of the Roman ballistics Once and for all.

Experiments have shown that the pressure really decreases greatly, but later experts ballistics they told me that the same effect could be achieved by making a projectile with a long sharp end.

The second salvo of a Russian mortar battery, in strict accordance with the laws ballistics, covered the soldiers running away in panic.

And in artillery science - in ballistics- Americans, to everyone’s surprise, even surpassed the Europeans.

Ministry of Internal Affairs for the Udmurt Republic

Center vocational training

TUTORIAL

FIRE PREPARATION

Izhevsk

Compiled by:

Teacher of the cycle of combat and physical training at the Professional Training Center of the Ministry of Internal Affairs of the Udmurt Republic, police lieutenant colonel Gilmanov D.S.

This manual “Fire training” was compiled on the basis of Order of the Ministry of Internal Affairs of the Russian Federation dated November 13, 2012 No. 1030dsp “On approval of the Manual on the organization of fire training in the internal affairs bodies of the Russian Federation”, “Manuals on shooting “9 mm Makarov pistol””, “Manuals” 5.45 mm Kalashnikov assault rifle" in accordance with the training program for police officers.

The textbook “Fire Training” is intended for use by students of the Professional Training Center of the Ministry of Internal Affairs of the Udmurt Republic in classes and self-study.

Instill the skills of independent work with methodological material;

Improve the “quality” of knowledge on the design of small arms.

The textbook is recommended for students undergoing training at the Professional Training Center of the Ministry of Internal Affairs of the Udmurt Republic when studying the subject “Fire Training,” as well as for police officers for professional service training.

The manual was reviewed at a meeting of the combat and physical training cycle of the Ministry of Internal Affairs Center for SD

Protocol No. 12 dated November 24, 2014.

Reviewers:

Colonel of the Internal Service V.M. Personnel – Head of the service and combat training department of the Ministry of Internal Affairs for the Udmurt Republic.

Section 1. Basic information from internal and external ballistics…………………..………….…………....... 4

Section 2. Shooting accuracy. Ways to increase it……………………………………………………….………………………...5

Section 3. Stopping and penetrating effect of a bullet………………………………………………………........6

Section 4. Purpose and design of parts and mechanisms of the Makarov pistol………………...................................6

Section 5. Purpose and design of parts and mechanisms of the pistol, cartridges and accessories…………...7

Section 6. Operation of parts and mechanisms of the pistol……………………………………………..………………..9

Section 7. Procedure for partial disassembly of the PM…………………………………………………………………………………....……............12

Section 8. Procedure for assembling the PM after partial disassembly……………………………………………………….…....12

Section 9. Operation of the PM fuse…….……………………………...……………………………………..…..…..12

Section 10. Delays when firing a pistol and ways to eliminate them……...………………………..…..…..13

Section 11. Inspection of the assembled pistol………………………………………………………………………………........….13

Section 12.Checking the engagement and bringing the pistol to normal engagement………….…………………….....…….....14

Section 13. Pistol shooting techniques…………………………………………………………………………………..……..….15

Section 14. Purpose and combat properties of the Kalashnikov AK-74 assault rifle ………………………………………21

Section 15. Design of the machine and operation of its parts……………………………………..……………..……22

Section 16. Disassembly and assembly of the machine…………………………………………………………………………………….…...23

Section 17. The principle of operation of the Kalashnikov assault rifle…………………………………………………………..23

Section 18. Safety measures during shooting…………………………………………………………...24

Section 19. Safety measures when handling weapons in daily work activities............25

Section 20. Cleaning and lubrication of the gun…………………………………….……………………………………………………………25

Section 21. Standards for fire training………..………………...................…..………………………… ....26

Applications………..……………………………………………………………………………………………………………..30

References………….…………………………..……………………………………………………...……..34

Basic information from internal and external ballistics

Firearms is a weapon in which a bullet (grenade, projectile) is ejected from the bore of a weapon using the energy of gases formed during the combustion of a powder charge.

Small arms called a weapon that fires a bullet.

Ballistics- a science that studies the flight of a bullet (shell, mine, grenade) after a shot.

Internal ballistics- a science that studies the processes that occur during a shot, during the movement of a bullet (grenade, projectile) along the barrel.

With a shot is called the ejection of a bullet (grenade, mine, shell) from the bore of a weapon by the energy of gases formed during the combustion of a powder charge.

When a small weapon is fired, the following phenomenon occurs. When the firing pin strikes the primer of a live cartridge sent into the chamber, the percussion composition of the primer explodes and a flame is formed, which penetrates through the seed holes in the bottom of the cartridge case to the powder charge and ignites it. When a powder (combat) charge burns, a large amount of highly heated gases are formed, creating high pressure in the barrel bore for:

· bottom of the bullet;

· bottom and walls of the sleeve;

· trunk walls;

· shutter

As a result of the gas pressure on the bottom of the bullet, it moves from its place and crashes into the rifling; rotating along them, moves along the barrel bore with a continuously increasing speed and is thrown out in the direction of the axis of the barrel bore.

The gas pressure on the bottom of the cartridge case causes the weapon (barrel) to move backward. The pressure of the gases on the walls of the cartridge case and barrel causes them to stretch (elastic deformation), and the cartridge case, pressing tightly against the chamber, prevents the breakthrough of powder gases towards the bolt. At the same time, when firing, an oscillatory movement (vibration) of the barrel occurs and it heats up. Hot gases and particles of unburnt gunpowder flowing out of the barrel after a bullet when meeting air generate a flame and a shock wave. The shock wave is the source of sound when fired.

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

Preliminary;

First (main);

Third (period of gas effects).

Preliminary the period lasts from the beginning of the combustion of the powder charge until the bullet casing completely cuts into the rifling of the barrel.

First (basic)the period lasts from the beginning of the bullet’s movement until the complete combustion of the powder charge.

At the beginning of the period, when the speed of movement along the bore of the bullet is still low, the amount of gases grows faster than the volume of the bullet space, and the gas pressure reaches its maximum value (Pm = 2,800 kg/cm² of the 1943 model cartridge); This pressure called maximum.

The maximum pressure in small arms is created when the bullet travels 4-6 cm. Then, due to the rapid increase in the speed of the bullet, the volume of the behind-the-bullet space increases faster than the influx of new gases, and the pressure begins to fall. By the end of the period, it is about 2/3 of the maximum, and the bullet speed increases and is 3/4 of the initial speed. The powder charge is completely burned shortly before the bullet leaves the barrel.

Second the period lasts from the moment the powder charge is completely burned until the bullet leaves the barrel.

From the beginning of this period, the influx of powder gases stops, however, highly compressed and heated gases expand and, putting pressure on the bullet, increase its speed.

Third period (period of gas effects ) lasts from the moment the bullet leaves the barrel until the action of the powder gases on the bullet ceases.

During this period, powder gases flowing from the barrel at a speed of 1200-2000 m/s continue to affect the bullet and impart additional speed to it. The bullet reaches its maximum speed at the end of the third period at a distance of several tens of centimeters from the muzzle of the barrel. This period ends at the moment when the pressure of the powder gases at the bottom of the bullet is balanced by air resistance.

starting speed - the speed of the bullet at the muzzle of the barrel. The initial speed is taken to be a conditional speed, which is slightly greater than the muzzle speed, but less than the maximum.

As the initial velocity of the bullet increases, the following happens::

· the bullet's flight range increases;

· the direct shot range increases;

· the lethal and penetrating effect of the bullet increases;

· the influence of external conditions on its flight is reduced.

The magnitude of the initial velocity of the bullet depends on:

- trunk length;

- bullet weight;

- powder charge temperature;

- humidity of the powder charge;

- shape and size of gunpowder grains;

- powder loading density.

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

Trajectory – the curved line that the bullet's center of gravity describes during flight.

The forces of gravity cause the bullet to gradually decrease, and the force of air resistance gradually slows down the movement of the bullet and tends to overturn it. As a result, the speed of the bullet decreases, and its trajectory is shaped like an unevenly curved curved line. To increase the stability of the bullet in flight, it is given a rotational movement due to the rifling of the barrel bore.

When a bullet flies in the air, it is affected by various atmospheric conditions:

· Atmosphere pressure;

· air temperature;

· movement of air (wind) in different directions.

With increase atmospheric pressure The air density increases, as a result of which the force of air resistance increases, the flight range of the bullet decreases. And, conversely, with a decrease in atmospheric pressure, the density and force of air resistance decreases, and the range of the bullet increases. Corrections for atmospheric pressure when shooting are taken into account in mountain conditions at an altitude of more than 2000 m.

The temperature of the powder charge, and therefore the burning rate of the gunpowder, depends on the ambient air temperature. The lower the temperature, the slower the gunpowder burns, the slower the pressure rises, and the slower the bullet speed.

As the air temperature increases, its density and, consequently, the resistance force decrease, and the bullet's flight range increases. On the contrary, as the temperature decreases, the density and force of air resistance increase, and the bullet's flight range decreases.

Exceeding line of sight - the shortest distance from any point of the trajectory to the aiming line

The excess can be positive, zero, negative. The excess depends on design features weapons and ammunition used.

Sighting range – this is the distance from the departure point to the intersection of the trajectory with the aiming line

Direct shot - a shot in which the trajectory height does not exceed the target height throughout the entire flight of the bullet.

Ballistics is the science of the movement, flight and effects of projectiles. It is divided into several disciplines. Internal and external ballistics deal with the movement and flight of projectiles. The transition between these two modes is called intermediate ballistics. Terminal ballistics concerns the effects of projectiles separate category covers the degree of target destruction. What does internal and external ballistics study?

Guns and rockets

Gun and rocket engines are types of heat engine, partially converting chemical energy into propellant (kinetic energy of the projectile). Propellant differs from conventional fuels in that their combustion does not require atmospheric oxygen. In limited quantities, the production of hot gases by combustible fuel causes an increase in pressure. Pressure propels the projectile and increases the burning rate. Hot gases tend to erode a gun barrel or rocket throat. Internal and external small arms ballistics studies the movement, flight, and impact a projectile has.

When the propellant charge in the gun's chamber ignites, the combustion gases are contained by the shot, so the pressure increases. The projectile begins to move when the pressure on it overcomes its resistance to movement. The pressure continues to rise for a while and then drops as the shot accelerates to high speed. The fast-burning rocket fuel is soon exhausted, and over time the shot is ejected from the muzzle: shot speeds of up to 15 kilometers per second are achieved. The flip-up cannons release gas through the rear of the chamber to counter recoil forces.

A ballistic missile is one that is guided during a relatively short initial active phase of flight, whose trajectory is subsequently governed by the laws of classical mechanics, unlike, for example, cruise missiles, which are guided aerodynamically during powered flight.

Shot trajectory

Projectiles and launchers

A projectile is any object projected into space (empty or not) when a force is applied. Although any object in motion through space (such as a thrown ball) is a projectile, the term most often refers to a ranged weapon. Mathematical equations movements are used to analyze the trajectory of the projectile. Examples of projectiles include balls, arrows, bullets, artillery shells, rockets, and so on.

Throwing is the act of launching a projectile manually. Humans are extraordinarily good at throwing due to their high agility, an evolved trait. Evidence of human throwing dates back 2 million years. The throwing speed of 145 km per hour found in many athletes is much higher than the speed at which chimpanzees can throw objects, which is about 32 km per hour. This ability reflects the ability of human shoulder muscles and tendons to maintain elasticity until needed to propel an object.

Internal and external ballistics: briefly about types of weapons

One of the most ancient starting devices there were ordinary slingshots, bows and arrows, and a catapult. Over time, guns, pistols, and missiles appeared. Information from internal and external ballistics includes information about various types of weapons.

• A spling is a weapon typically used to eject blunt projectiles such as rock, clay, or lead "bullet". The sling has a small cradle (bag) in the middle of the connected two lengths of cord. The stone is placed in a bag. The middle finger or thumb is placed through the loop at the end of one cord, and the tab at the end of the other cord is placed between the thumb and forefinger. The sling swings in an arc and the tab is released at a certain moment. This frees the projectile to fly towards its target.
• Bow and arrows. A bow is a flexible piece of material that fires aerodynamic projectiles. A string connects the two ends, and when it is pulled back, the ends of the stick bend. When the string is released, the potential energy of the bent stick is converted into the speed of the arrow. Archery is the art or sport of shooting with bows.
• A catapult is a device used to launch a projectile over a long distance without the aid of explosive devices - especially various types of ancient and medieval siege engines. The catapult has been used since ancient times as it has proven to be one of the most effective mechanisms during war. The word "catapult" comes from the Latin, which in turn comes from the Greek καταπέλτης, meaning "throw, hurl." Catapults were invented by the ancient Greeks.
• A pistol is a conventional tubular weapon or other device designed to fire projectiles or other material. The projectile can be solid, liquid, gaseous or energetic and can be loose, as with bullets and artillery shells, or with clamps, as with probes and whaling harpoons. The means of projection varies according to design, but is usually effected by gas pressure generated by rapid combustion of propellant, or compressed and stored by mechanical means operating within an open-ended tube in the form of a piston. The condensed gas accelerates the moving projectile along the length of the tube, imparting sufficient velocity to keep the projectile moving when the action of the gas ceases at the end of the tube. As an alternative, acceleration by generating an electromagnetic field can be used, in which case the tube can be dispensed with and the guide replaced.
• A rocket is a missile, spaceship, aircraft, or other vehicle that receives an impact from a rocket engine. A rocket engine's exhaust is formed entirely from propellants carried in the rocket before use. Rocket engines work by action and reaction. Rocket engines propel rockets forward by simply throwing their exhausts back very quickly. Although they are relatively ineffective for low speed use, the rockets are relatively light and powerful, capable of generating large accelerations and reaching extremely high speeds with reasonable efficiency. Rockets are independent of the atmosphere and work great in space. Chemical rockets are the most common type of high-performance rocket, and they typically create their exhaust gases by burning rocket fuel. Chemical rockets store large amounts of energy in an easily released form and can be very dangerous. However, careful design, testing, construction and use will minimize risks.

Fundamentals of external and internal ballistics: main categories

Ballistics can be studied using high-speed photography or high-speed cameras. A photograph of the shot taken with ultra-high speed air gap flash helps to see the bullet without blurring the image. Ballistics are often broken down into the following four categories:

• Internal ballistics - study of the processes that initially accelerate projectiles.
• Transient ballistics - studying projectiles during the transition to cashless flight.
• External ballistics - study of the passage of a projectile (trajectory) in flight.
• Terminal ballistics - studying the projectile and its consequences as it is completed

Internal ballistics is the study of projectile motion. In guns, it covers the time from ignition of the rocket fuel until the projectile exits the gun barrel. This is what internal ballistics studies. This is important for designers and users of firearms of all types, from rifles and pistols to high-tech artillery. Internal ballistics information for rocket projectiles covers the period during which the rocket engine provides thrust.

Transient ballistics, also known as intermediate ballistics, is the study of the behavior of a projectile from the moment it leaves the muzzle until the pressure behind the projectile is equalized, so it falls between the concepts of internal and external ballistics.

External ballistics studies the dynamics of atmospheric pressure around a bullet and is a part of the science of ballistics that deals with the behavior of an unpowered projectile in flight. This category is often associated with firearms and is associated with the unoccupied free-flight phase of a bullet after it exits the gun barrel and before it hits the target, so it falls between transient ballistics and terminal ballistics. However, external ballistics also deals with the free flight of missiles and other projectiles such as balls, arrows, and so on.

Terminal ballistics is the study of the behavior and effects of a projectile as it reaches its target. This category has value for both small-caliber shells and large-caliber shells (artillery fire). The study of extremely high velocity impacts is still very new and is currently applied primarily to spacecraft design.

Forensic ballistics

Forensic ballistics involves the analysis of bullets and bullet effects to determine information about use in a court or other part of the legal system. Separate from ballistics information, firearms and tool mark ("ballistic fingerprint") exams involve the analysis of evidence from firearms, ammunition, and tools to determine whether any firearm or tool was used in the commission of a crime.

Astrodynamics: orbital mechanics

Astrodynamics is the application of weapon ballistics, external and internal, and orbital mechanics to practical problems of rocket and other spacecraft propulsion. The motion of these objects is usually calculated from Newton's laws of motion and universal gravity. It is a core discipline in space mission design and control.

Travel of a projectile in flight

The fundamentals of external and internal ballistics concern the travel of a projectile in flight. The bullet's flight path includes: down the barrel, through the air, and through the target. The basics of internal ballistics (or raw, inside the gun) vary according to the type of weapon. Bullets fired from a rifle will have more energy than similar bullets fired from a pistol. Even more powder can also be used in gun cartridges because the bullet chambers can be designed to withstand greater pressure.

Higher pressures require a larger gun with more recoil, which is slower to load and generates more heat, causing more wear on the metal. In practice, it is difficult to measure forces inside a gun barrel, but one easily measured parameter is the speed at which the bullet exits the barrel (muzzle velocity). The controlled expansion of gases from burning gunpowder creates pressure (force/area). Here is the base of the bullet (equivalent to the diameter of the barrel) and is constant. Therefore, the energy transferred to a bullet (of a given mass) will depend on the mass time multiplied by the time interval over which the force is applied.

The last of these factors is a function of barrel length. Bullet motion through a machine gun device is characterized by an increase in acceleration as the expanding gases push against it, but a decrease in barrel pressure as the gas expands. Up to the point of pressure reduction, the longer the barrel, the greater the acceleration of the bullet. When a bullet travels down the barrel of a gun, a slight deformation occurs. This is due to minor (rarely major) imperfections or variations in the rifling or marks in the barrel. The main task of internal ballistics is to create favorable conditions to avoid such situations. The effect on the subsequent trajectory of the bullet is usually negligible.

From gun to target

External ballistics can be briefly described as the journey from the gun to the target. Bullets usually do not travel in a straight line to the target. There are rotational forces that keep the bullet off the straight axis of flight. The basics of external ballistics include the concept of precession, which refers to the rotation of a bullet around its center of mass. Nutation is a small circular movement at the tip of the bullet. Acceleration and precession decrease as the bullet's distance from the barrel increases.

One of the tasks of external ballistics is to create the ideal bullet. To reduce air resistance, the ideal bullet would be a long, heavy needle, but such a projectile would pass straight through the target without dissipating much of its energy. The spheres will lag and release more energy, but may not even hit the target. A good aerodynamic compromise bullet shape is a parabolic curve with a low frontal area and a branching shape.

The best bullet composition is lead, which has a high density and is cheap to produce. Its disadvantages are its tendency to soften at >1000 fps, causing it to lubricate the barrel and reduce accuracy, and the lead tends to melt completely. Alloying of lead (Pb) with non big amount Antimony (Sb) helps, but the real answer is to bind the lead bullet to a hard steel barrel through another metal soft enough to seal the bullet in the barrel, but with a high melting point. Copper (Cu) is best suited for this material as a "jacket" for lead.

Terminal ballistics (hit the target)

The short, high-velocity bullet begins to growl, turn, and even spin as it enters the tissue. This causes more tissue to move, increasing drag and imparting more of the kinetic energy to the target. A longer, heavier bullet may have more energy over a wider range when it hits the target, but it may penetrate so well that it leaves the target with for the most part your energy. Even a bullet with low kinetics can cause significant tissue damage. Bullets cause tissue damage in three ways:

1. Destruction and crushing. The diameter of a tissue crush injury is the diameter of the bullet or fragment, down to the length of the axle.
2. Cavitation - a "permanent" cavity is caused by the trajectory (track) of the bullet itself, crushing tissue, while a "temporary" cavity is formed by radial stretching around the bullet track from the continuous acceleration of the medium (air or tissue) as a result of the bullet, causing the wound cavity to stretch outward. For projectiles moving at low speed, the permanent and temporary cavities are almost the same, but at high speed and with bullet yaw, the temporary cavity becomes larger.
3. Shock waves. Shock waves compress the medium and move in front of the bullet, as well as to the sides, but these waves last only a few microseconds and do not cause deep destruction at low speeds. At high speeds, the generated shock waves can reach up to 200 atmospheres of pressure. However, bone fracture due to cavitation is an extremely rare event. The ballistic pressure wave from a long-range bullet impact can cause a concussion in a person, causing acute neurological symptoms.

Experimental methods to demonstrate tissue damage have used materials with characteristics similar to soft tissue and human skin.

Bullet design

Bullet design matters in wounding potential. The 1899 Hague Convention (and subsequently the Geneva Convention) prohibited the use of expanding, deformable bullets in wartime. This is why military bullets have a metal coating around a lead core. Of course, the treaty had less to do with compliance than the fact that modern military assault rifles fire projectiles at high velocities and the bullets must be copper jacketed as lead begins to melt due to the heat generated at >2000 fps give me a sec.

The external and internal ballistics of the PM (Makarov pistol) differs from the ballistics of the so-called “breakable” bullets, designed to break upon impact on a hard surface. Such bullets are usually made from a metal other than lead, such as copper powder compacted into a bullet shape. The distance of the target from the muzzle plays a large role in wounding ability, since most bullets fired from handguns have lost significant kinetic energy (KE) at 100 yards, while high-velocity military guns still have significant KE even at 500 yards. Thus, the external and internal ballistics of PMs and military and hunting rifles designed to deliver bullets with a large number of EC over a greater distance will differ.

Designing a bullet to efficiently transfer energy to a specific target is not simple because targets differ. The concept of internal and external ballistics also includes projectile design. To penetrate the thick hide and tough bone of an elephant, the bullet must be small in diameter and strong enough to resist disintegration. However, such a bullet penetrates most tissue like a spear, causing slightly more damage than a knife wound. A bullet intended to damage human tissue will require certain “brakes” so that all the CE is transferred to the target.

It is easier to design features that help slow a large, slow-moving bullet through tissue than a small, high-velocity bullet. These measures include shape modifications such as round, flattened or domed. Round nose bullets provide the least amount of drag, are usually jacketed, and are useful primarily in low-velocity pistols. The flattened design provides the most drag from the shape alone, is not jacketed, and is used in low velocity pistols (often for target practice). The dome design is intermediate between round and cutting tool and is useful at medium speeds.

The hollow point design of the bullet makes it easier to turn the bullet "inside out" and align the front, called "flare". Expansion only occurs reliably at speeds greater than 1200 fps, so is only suitable for maximum speed pistols. A fracturing bullet consisting of powder is designed to disintegrate on impact, delivering all the CE but without significant penetration, the fragment size should decrease as impact velocity increases.

Injury Potential

The type of tissue affects the wounding potential as well as the depth of penetration. Specific gravity (density) and elasticity are the main tissue factors. The higher the specific gravity, the greater the damage. The greater the elasticity, the less damage. Thus, lightweight tissue with low density and high elasticity is damaged less than muscle with higher density but with some elasticity.

The liver, spleen and brain have no elasticity and are easily injured, like adipose tissue. Fluid-filled organs ( bladder, heart, large vessels, intestines) can burst due to the pressure waves created. A bullet striking bone may result in bone fragmentation and/or the formation of numerous secondary missiles, each causing additional injury.

Pistol ballistics

These weapons are easy to conceal but difficult to aim accurately, especially in crime scenes. Most small arms shootings occur at a distance of less than 7 yards, but even then, most bullets miss their intended target (only 11% of assailant rounds and 25% of police bullets hit their intended target in one study). Typically, low caliber guns are used in crimes because they are cheaper and easier to carry and easier to control while shooting.

Tissue destruction can be increased by any caliber using an expanding hollow point bullet. The two main variables in handgun ballistics are bullet diameter and the volume of powder in the cartridge body. Older cartridge designs were limited by the pressures they could withstand, but advances in metallurgy allowed the maximum pressure to be doubled and tripled so that more kinetic energy could be generated.

KRASNODAR UNIVERSITY

Fire training

Specialties: 031001.65 Law enforcement activities,

specialization: operational and investigative activities

(activities of a criminal investigation officer)

LECTURE

Topic No. 5: “Basics of ballistics”

Time: 2 hours.

Location: university shooting range

Methodology: story, show

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

Material support.

1. Stands, posters.

Purpose of the lesson:

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

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

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

4. To develop discipline and diligence among cadets.

Practical lesson plan

Introduction – 5 min.

Check the availability of cadets and readiness for classes;

Announce the topic, goals, educational questions.

Main part – 80 min.

Conclusion – 5 min.

Summarize the lesson briefly;

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

Remind study questions;

Answer any questions that arise;

Give assignments for independent preparation.

Main literature:

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

Additional literature:

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

2., Menshikov training in internal affairs bodies: Training manual. – St. Petersburg, 1998.

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

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

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

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

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

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

Explosives

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

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

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

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

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

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

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

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

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

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

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

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

Brief Introduction to Internal Ballistics

Shot and its periods.

A shot is the ejection of a bullet from the barrel by the energy of gases formed during the combustion of a powder charge. When a small weapon is fired, the following phenomena occur. The impact of the firing pin on the primer of the combat cartridge 2 explodes the percussion composition of the primer and a flame is formed, which penetrates through the seed holes in the bottom of the cartridge case to the powder charge and ignites it. When a charge burns, a large amount of highly heated powder gases is formed, creating high pressure in the barrel bore on the bottom of the bullet, the bottom and walls of the cartridge case, and also on the walls of the barrel and the bolt. As a result of the pressure of the powder gases on the bottom of the bullet, it moves from its place and crashes into the rifling. Moving along the rifling, the bullet acquires a rotational motion and, gradually increasing speed, is thrown outward along the axis of the barrel bore. The pressure of the gases on the bottom of the cartridge case causes the weapon to move backward - recoil. The pressure of the gases on the walls of the cartridge case and barrel causes them to stretch (elastic deformation), and the cartridge case, pressing tightly against the chamber, prevents the breakthrough of powder gases towards the bolt. When fired, the barrel also vibrates (vibrates) and heats up. Hot gases and particles of unburnt gunpowder, flowing out after a bullet, when meeting 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 communication; 25% is spent on secondary work; about 40% of the energy is not used and is lost after the bullet leaves.

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

When firing, there are four consecutive periods:

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

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

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

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

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

Initial bullet speed

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

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

Weapon recoil and launch angle.

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

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

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

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

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

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

Brief information about external ballistics

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

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

Trajectory and its elements

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

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

The force of air resistance is caused by three main reasons: air friction, vortex formation and ballistic wave formation.

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

The layer of air adjacent to the surface of the bullet (grenade), in which the movement of particles varies from the speed of the bullet (grenade) to zero, is called the boundary layer. This layer of air, flowing around the bullet, breaks away from its surface and does not have time to immediately close behind the bottom part. A rarefied space is formed behind the bottom of the bullet, resulting in a pressure difference between the head and bottom parts. This difference creates a force directed towards reverse movement bullets, and reducing the speed of its flight. Air particles, trying to fill the vacuum formed behind the bullet, create a vortex.

When flying, a bullet (grenade) collides with air particles and causes them to vibrate. As a result, the air density in front of the bullet (grenade) increases and sound waves are formed. Therefore, the flight of a bullet (grenade) is accompanied by a characteristic sound. When the speed of a bullet (grenade) is less than the speed of sound, the formation of these waves has no effect significant influence on its flight, as the waves spread faster speed flight of a bullet (grenade). When the bullet's flight speed is greater than the speed of sound, the sound waves collide with each other to create a wave of highly compressed air - a ballistic wave that slows down the bullet's flight speed, since the bullet spends part of its energy creating this wave.

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

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

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

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

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

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

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

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

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

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

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

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

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

A straight line that is a continuation of the axis of the barrel of an aimed weapon is called elevation line.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Scattering phenomenon

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

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

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

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

Reasons for dispersion

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

The reasons causing the variety of initial speeds;

Reasons for the variety of throwing angles and shooting directions;

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

The reasons causing the variety of initial speeds are:

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Law of dispersion

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

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

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

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

Determination of the average point of impact (MIP)

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

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

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

The method of sequential division of segments is as follows:

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

The proportional division method is as follows:

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

Aiming (aiming)

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

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

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

Guidance is carried out using sighting devices and aiming mechanisms and is performed in two stages.

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

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

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

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

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

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

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

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

Direct shot

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

direct shot.

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

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

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

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

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

There is no wind (the atmosphere is still).

b) Ballistic conditions:

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

Charge temperature +15°C;

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

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

c) Topographic conditions:

The target is on the weapon's horizon;

There is no lateral tilt of the weapon.

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

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

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

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

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

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

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

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

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

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

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

The side wind puts 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, the wind from the left to the right.

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

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

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

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

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

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

Conclusion

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