Fundamentals of ballistics. What is the ballistic trajectory of a rocket, a bullet? Ak 74 internal and external ballistics

ballistics

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

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

ballistics

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

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, th, th. Ballistic missile (passing part of the way as a freely thrown body).

New explanatory and derivational 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 rockets, etc.

   An academic subject containing the theoretical foundations of a given scientific discipline.

   unfold A textbook that sets out the content of a given academic subject.

Encyclopedic Dictionary, 1998

ballistics

BALLISTICS (German Ballistik, from Greek ballo - I throw) the science of the movement of artillery shells, unguided rockets, mines, bombs, bullets during firing (launch). Internal ballistics studies the movement of a projectile in the bore (or in other conditions restricting movement) under the action of powder gases, external ballistics - after it has left the bore.

Ballistics

(German Ballistik, from Greek ballo ≈ I throw), the science of the movement of artillery shells, bullets, mines, air bombs, active and rocket projectiles, harpoons, etc. B. is a military-technical science based on a complex of physical and mathematical disciplines. Distinguish between internal and external ballistics.

Internal bombardment 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 action of powder gases, as well as the regularities of other processes that occur when a shot is fired in the bore or chamber of a powder rocket. Considering a shot as a complex process of rapidly converting the chemical energy of gunpowder into heat, and then into the mechanical work of moving the projectile, charge, and recoil parts of the gun, internal fire 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 combustion of gunpowder; 2nd period ≈ from the end of the combustion of gunpowder to the moment the projectile leaves the barrel (the period of adiabatic expansion of gases) and the period of aftereffect of powder gases on the projectile and barrel. The patterns of processes associated with the last period are considered in a special section of ballistics - intermediate ballistics. The end of the period of aftereffect on a projectile separates the field of phenomena studied by internal and external fireworks. The main sections of internal fireworks are pyrostatics, pyrodynamics, and ballistic design of guns. Pyrostatics studies the laws of gunpowder combustion 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 that occur in the bore during firing and establishes relationships between the design characteristics of the bore, loading conditions, and various physicochemical and mechanical processes occurring during firing. 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 process of firing, including the basic equation of internal fire, which relates the value of the burnt part of the charge, the pressure of powder gases in the bore, the velocity of the projectile, and the length the path they have travelled. The solution of this system and finding the dependence of the change in the pressure of powder gases P, projectile velocity v and other parameters on the path of the projectile 1 ( rice. one) and from the time of its movement along the bore is the first main (direct) task of internal B. To solve this problem, the following are used: the 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 shooting process and the insufficient knowledge of individual factors, some assumptions are made. Of great practical importance are the correction formulas for internal bullets, which make it possible to determine the change in the muzzle velocity of the projectile and the maximum pressure in the bore when various loading conditions change.

The ballistic design of guns is the second main (inverse) task of the internal ballistic missile. It determines the design data of the bore and the loading conditions under which a projectile of a given caliber and mass will receive a given (muzzle) velocity upon departure. For the barrel variant chosen during the design, curves of changes in gas pressure in the barrel bore and projectile velocity along the length of the barrel and over time are calculated. These curves are the initial data for the design of the artillery system as a whole and its ammunition. Internal fire 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 guns, mortars). An important section is also the internal bombardment of powder rockets, which has developed into a special science. The main sections of the internal fire of powder rockets are: pyrostatics of a semi-closed volume, which considers the laws of combustion of gunpowder at a relatively low constant pressure; solution of the main tasks int. B. powder rocket, which consists in determining (under given loading conditions) the law of change in the 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 in 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 action for a given weight of the rocket warhead.

External bombardment studies the movement of unguided projectiles (mines, bullets, etc.) after they leave the bore (launching device), as well as the factors that influence this movement. Its main content is the study of all elements of the movement of the 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 bombardment), 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 evaluating the influence of factors that determine 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 variant when designing artillery systems. The theoretical solution of problems on the motion of a projectile and problems of the theory of corrections is reduced to the formulation of equations of motion of the projectile, the simplification of these equations, and the search for methods for their solution; the latter was greatly facilitated and accelerated with the advent of the computer. To determine the initial conditions (initial velocity and angle of throw, the shape and mass of the projectile) necessary to obtain a given trajectory, special tables are used in the outer bullet. The development of a methodology for compiling firing tables consists in determining the optimal combination of theoretical and experimental studies that make it possible to obtain firing tables of the required accuracy with minimal time. External B. methods are also used in the study of 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 an important role in the formation and development of the theory of flight, becoming a special case of the latter.

B.'s emergence as a science dates back to the 16th century. The first works on ballistics are 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, and by the Italian E. Torricelli and the Frenchman M. Mersenne, who proposed that the science of projectile motion be called ballistics (1644). I. Newton carried out the first studies on the motion of a projectile, taking into account air resistance - "The 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, and the Russian scientist L. Euler, and others. 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 Le Havre law, the law of A. F. Siacci). At the beginning of the 20th century the exact solution of the main problem of internal combustion was given ≈ the work of N. F. Drozdov (1903, 1910); Zabudsky (1904, 1914), as well as the Frenchman P. Charbonnier and the Italian D. Bianchi. In the USSR, a great contribution to the further development of artillery was made by scientists from the Commission for Special Artillery Experiments (KOSLRTOP) in 1918–26. During this period, V. M. Trofimov, A. N. Krylov, D. A. Venttsel, V. V. Mechnikov, G. V. Oppokov, B. N. Okunev and others performed a number of works to improve the methods for calculating the trajectory, development of the theory of corrections and the study of the rotational motion of the projectile. The studies of 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 motion of an artillery shell.

Trofimov, Drozdov, and I. P. Grave played an important role in solving problems of internal ballistics. were introduced by M. E. Serebryakov, V. E. Slukhotsky, B. N. Okunev, and from foreign authors P. Charbonnier, J. Syugo, and others.

During the Great Patriotic War of 1941–45, under the direction of S. A. Khristianovich, theoretical and experimental work was carried out to increase the accuracy of rocket projectiles. In the post-war period, these works continued; the issues of increasing the initial velocities of projectiles, establishing new laws of air resistance, increasing the survivability of the barrel, and developing methods of ballistic design were also studied. Significant progress has been made in studies of the aftereffect period (V. E. Slukhotskii and others) and in the development of B. methods for solving special problems (smooth-bore systems, active rocket projectiles, etc.), problems of external and internal B. in relation to rocket projectiles, further improving the methods of ballistic research related to the use of computers.

Lit .: Grave I.P., Internal ballistics. Pyrodynamics, c. 1≈4, L., 1933≈37; Serebryakov M. E., Internal ballistics of barrel systems and powder rockets, M., 1962 (bibl.); Corner 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. It focuses mainly on the study of the movement of bullets and projectiles fired from firearms, rocket projectiles 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 in the muzzle area. It is important for specialists in shooting accuracy, in the development of silencers, flame arresters and muzzle brakes;
• external ballistics, which studies the movement of a projectile in the atmosphere or in a void under the influence of external forces. It is used when calculating corrections for elevation, wind and derivation;
• barrier or terminal ballistics, which explores the last stage - the movement of a bullet in an obstacle. Terminal ballistics is handled by gunsmiths-specialists in projectiles and bullets, durability and other specialists in armor and protection, as well as forensic specialists.

Examples of the use of the word ballistics in the literature.

When the excitement subsided, Barbicane spoke in an even more solemn tone: ballistics recent years, and to what a high degree of perfection firearms might have reached if the war were still going on!

Of course, there can be no question of ballistics does not progress, 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 disturb the balance of the Earth, an attempt based on exact and indisputable calculations, an attempt which development ballistics and the mechanics made it quite feasible.

On September 14, a telegram was sent to the Washington Observatory, asking them to investigate the consequences, given the laws ballistics and all geographical data.

Barbicane, as I asked myself the question: could we not, without going beyond our specialty, venture on some outstanding undertaking worthy of the nineteenth century, and would high achievements not allow ballistics implement it successfully?

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

And now, as far as I understand, we are not in a position to do anything until the police receive a report from the department ballistics regarding the bullets removed from the body of Mrs. Ellis.

If 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 in a motel, then your client does not have a 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 lay on the floor next to the woman.

I ask the department ballistics carry out the necessary experiments and compare bullets before the start of tomorrow's meeting, - said Judge Keyser.

I request that it be recorded on the record that, during the adjournment of the hearing, the expert ballistics Alexander Redfield fired several practice shots with all three revolvers owned by George Anklitas.

Freeing one hand for a short time, he ran the back of his hand over his forehead, as if to drive the ghost of the Roman ballistics once and forever.

Experiments have shown that the pressure is indeed greatly reduced, but later experts ballistics I was told that the same effect could be obtained by making a projectile with a long pointed end.

The second salvo of the Russian mortar battery, in strict accordance with the laws ballistics, covered the panicked soldiers.

And in artillery science - in ballistics- The Americans, to the marvel of everyone, even surpassed the Europeans.

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

External ballistics

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

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

Bullet trajectory (side view)

Formation of air resistance force

Trajectory and its elements

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

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

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

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

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

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

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

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

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

The effect of the force of air resistance on the flight of a bullet (grenade) is very large; it causes a decrease in the speed and range of the bullet (grenade). For example, a bullet mod. 1930 at an angle of throw of 15 ° and an initial speed of 800 m / s in airless space would have flown at a distance of 32,620 m; the flight range of this bullet under the same conditions, but in the presence of air resistance, is only 3900 m.

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

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

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

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

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

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

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

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

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

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

Slow conical movement of the bullet

Derivation (Trajectory top view)

The effect of air resistance on the flight of a grenade

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

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

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

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

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

To improve accuracy, some grenades are given slow rotation due to the outflow of gases. Due to the rotation of the grenade, the moments of forces that deviate the axis of the grenade act sequentially in different directions, so the shooting improves.

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

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

Trajectory elements

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

The shortest distance from any point of the trajectory to the line of sight is called the excess of the trajectory over the line of sight.

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

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

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

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

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

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

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

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

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

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

Grenade trajectory (side view)

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

Trajectory shape

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

Angle of greatest range, flat, overhead and conjugate trajectories

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

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

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

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

Exceeding the trajectory of a bullet above the aiming point

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

The basic concepts are presented: periods of a shot, elements of the trajectory of a bullet, a direct shot, etc.

In order to master the technique of shooting from any weapon, it is necessary to know a number of theoretical provisions, without which not a single shooter will be able to show high results and his training will be ineffective.
Ballistics is the science of the movement of projectiles. In turn, ballistics is divided into two parts: internal and external.

Internal ballistics

Internal ballistics studies the phenomena that occur in the bore during a shot, the movement of a projectile along the bore, the nature of the thermo- and aerodynamic dependences accompanying this phenomenon, both in the bore and outside it during the aftereffect of powder gases.
Internal ballistics solves the issues of the most rational use of the energy of a powder charge during a shot in order to give a projectile of a given weight and caliber a certain initial velocity (V0) while maintaining the strength of the barrel. This provides input for external ballistics and weapon design.

Shot is called the ejection of a bullet (grenade) from the bore of a weapon by the energy of gases formed during the combustion of a powder charge.
From the impact of the striker on the primer of a live cartridge sent into the chamber, the percussion composition of the primer explodes and a flame forms, which through the seed holes in the bottom of the cartridge case penetrates to the powder charge and ignites it. During the combustion of a powder (combat) charge, a large amount of highly heated gases are formed, which create high pressure in the bore on the bottom of the bullet, the bottom and walls of the sleeve, as well as on the walls of the barrel and the bolt.
As a result of the pressure of gases on the bottom of the bullet, it moves from its place and crashes into the rifling; rotating along them, it moves along the bore with a continuously increasing speed and is thrown outward in the direction of the axis of the bore. The pressure of gases on the bottom of the sleeve causes the movement of the weapon (barrel) back.
When fired from an automatic weapon, the device of which is based on the principle of using the energy of powder gases discharged through a hole in the barrel wall - a Dragunov sniper rifle, part of the powder gases, in addition, after passing through it into the gas chamber, hits the piston and discards the pusher with the shutter back.
During the combustion of a powder charge, approximately 25-35% of the energy released is spent on communicating the progressive motion of the pool (the main work); 15-25% of energy - for secondary work (cutting and overcoming the friction of a bullet when moving along the bore; heating the walls of the barrel, cartridge case and bullet; moving the moving part of the weapon, the gaseous and unburned part of the gunpowder); about 40% of the energy is not used and is lost after the bullet leaves the bore.

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

• preliminary
• first or main
• second
• the third, or period of the last gases

Preliminary period lasts from the beginning of the burning of the powder charge to the complete cutting of the shell of the bullet into the rifling of the barrel. During this period, the gas pressure is created in the barrel bore, which is necessary in order to move the bullet from its place and overcome the resistance of its shell to cutting into the rifling of the barrel. This pressure is called boost pressure; it reaches 250 - 500 kg / cm2, depending on the rifling device, the weight of the bullet and the hardness of its shell. It is assumed that the combustion of the powder charge in this period occurs in a constant volume, the shell cuts into the rifling instantly, and the movement of the bullet begins immediately when the forcing pressure is reached in the bore.

First or main period lasts from the beginning of the movement of the bullet until the moment of complete combustion of the powder charge. During this period, the combustion of the powder charge occurs in a rapidly changing volume. At the beginning of the period, when the speed of the bullet along the bore is still low, the amount of gases grows faster than the volume of the bullet space (the space between the bottom of the bullet and the bottom of the cartridge case), the gas pressure quickly rises and reaches its highest value - a rifle cartridge of 2900 kg / cm2. This pressure is called maximum pressure. It is created in small arms when a bullet travels 4 - 6 cm of the path. Then, due to the rapid speed of the movement of the bullet, the volume of the bullet space increases faster than the influx of new gases, and the pressure begins to fall, by the end of the period it is equal to approximately 2/3 of the maximum pressure. The speed of the bullet is constantly increasing and by the end of the period reaches approximately 3/4 of the initial speed. The powder charge completely burns out shortly before the bullet leaves the bore.

Second period lasts until the moment of complete combustion of the powder charge until the moment the bullet leaves the bore. With the beginning of this period, the influx of powder gases stops, however, highly compressed and heated gases expand and, putting pressure on the bullet, increase its speed. The decrease in pressure in the second period occurs quite quickly and at the muzzle, the muzzle pressure is 300 - 900 kg / cm2 for various types of weapons. The speed of the bullet at the time of its departure from the bore (muzzle velocity) is somewhat less than the initial velocity.

The third period, or the period after the action of gases lasts from the moment the bullet leaves the bore until the moment the powder gases act on the bullet. During this period, powder gases flowing out of the bore at a speed of 1200 - 2000 m / s continue to act on the bullet and give it additional speed. The bullet reaches its greatest (maximum) speed at the end of the third period at a distance of several tens of centimeters from the muzzle of the barrel. This period ends at the moment when the pressure of the powder gases at the bottom of the bullet is balanced by air resistance.

The muzzle velocity of a bullet and its practical significance

initial speed called the speed of the bullet at the muzzle of the barrel. For the initial speed, the conditional speed is taken, which is slightly more than the muzzle and less than the maximum. It is determined empirically with subsequent calculations. The value of the initial velocity of the bullet is indicated in the firing tables and in the combat characteristics of the weapon.
The initial speed is one of the most important characteristics of the combat properties of weapons. With an increase in the initial speed, the range of the bullet, the range of a direct shot, the lethal and penetrating effect of the bullet increases, and the influence of external conditions on its flight also decreases. The muzzle velocity of a bullet depends on:

• barrel length
• bullet weight
• weight, temperature and humidity of the powder charge
• shape and size of powder grains
• loading density

The longer the trunk the longer the powder gases act on the bullet and the greater the initial velocity. With a constant barrel length and a constant weight of the powder charge, the initial velocity is greater, the lower the weight of the bullet.
Powder charge weight change leads to a change in the amount of powder gases, and consequently, to a change in the maximum pressure in the bore and the initial velocity of the bullet. The greater the weight of the powder charge, the greater the maximum pressure and muzzle velocity of the bullet.
With an increase in the temperature of the powder charge the burning rate of gunpowder increases, and therefore the maximum pressure and initial speed increase. When the charge temperature drops initial speed is reduced. An increase (decrease) in initial velocity causes an increase (decrease) in the range of the bullet. In this regard, it is necessary to take into account range corrections for air and charge temperature (charge temperature is approximately equal to air temperature).
With increasing moisture content of the powder charge the speed of its burning and the initial speed of the bullet are reduced.
Shapes and sizes of gunpowder have a significant effect on the burning rate of the powder charge, and consequently, on the initial velocity of the bullet. They are selected accordingly when designing weapons.
Loading density is the ratio of the weight of the charge to the volume of the sleeve with the inserted pool (charge combustion chamber). With a deep landing of a bullet, the loading density increases significantly, which can lead to a sharp pressure jump when fired and, as a result, to a rupture of the barrel, so such cartridges cannot be used for shooting. With a decrease (increase) in the loading density, the initial velocity of the bullet increases (decreases).
recoil is called the movement of the weapon back during the shot. Recoil is felt in the form of a push to the shoulder, arm or ground. The recoil action of the weapon is about as many times less than the initial velocity of the bullet, how many times the bullet is lighter than the weapon. The recoil energy of hand-held small arms usually does not exceed 2 kg / m and is perceived by the shooter painlessly.

The recoil force and the recoil resistance force (butt stop) are not located on the same straight line and are directed in opposite directions. They form a pair of forces, under the influence of which the muzzle of the weapon barrel deviates upward. The magnitude of the deviation of the muzzle of the barrel of a given weapon is the greater, the greater the shoulder of this pair of forces. In addition, when fired, the barrel of the weapon makes oscillatory movements - it vibrates. As a result of vibration, the muzzle of the barrel at the moment the bullet takes off can also deviate from its original position in any direction (up, down, right, left).
The magnitude of this deviation increases with improper use of the firing stop, contamination of the weapon, etc.
The combination of the influence of barrel vibration, weapon recoil and other causes leads to the formation of an angle between the direction of the axis of the bore before the shot and its direction at the moment the bullet leaves the bore. This angle is called the departure angle.
The departure angle is considered positive when the axis of the bore at the time of the bullet's departure is higher than its position before the shot, negative - when it is lower. The influence of the departure angle on shooting is eliminated when it is brought to normal combat. However, in case of violation of the rules for laying weapons, using the stop, as well as the rules for caring for weapons and saving them, the value of the departure angle and the weapon’s combat change. In order to reduce the harmful effect of recoil on the results of shooting, compensators are used.
So, the phenomena of a shot, the initial velocity of a bullet, the recoil of a weapon are of great importance when shooting and affect the flight of a bullet.

External ballistics

This is a science that studies the movement of a bullet after the action of powder gases on it has ceased. The main task of external ballistics is the study of the properties of the trajectory and the laws of bullet flight. External ballistics provides data for compiling shooting tables, calculating weapon sight scales, and developing shooting rules. Conclusions from external ballistics are widely used in combat when choosing a sight and aiming point depending on the firing range, wind direction and speed, air temperature and other firing conditions.

Bullet trajectory and its elements. Trajectory properties. Types of trajectory and their practical significance

trajectory called the curved line described by the center of gravity of the bullet in flight.
A bullet flying through the air is subjected to two forces: gravity and air resistance. The force of gravity causes the bullet to gradually descend, and the force of air resistance continuously slows down the movement of the bullet and tends to topple it. As a result of the action of these forces, the bullet's flight speed gradually decreases, and its trajectory is an unevenly curved curved line in shape. Air resistance to the flight of a bullet is caused by the fact that air is an elastic medium and therefore part of the energy of the bullet is expended on movement in this medium.

The force of air resistance is caused by three main causes: air friction, the formation of vortices and the formation of a ballistic wave.
The shape of the trajectory depends on the magnitude of the elevation angle. As the elevation angle increases, the height of the trajectory and the total horizontal range of the bullet increase, but this occurs up to a certain limit. Beyond this limit, the trajectory height continues to increase and the total horizontal range begins to decrease.

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

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

When shooting from small arms, only flat trajectories are used. The flatter the trajectory, the greater the extent of the terrain, the target can be hit with one sight setting (the less impact on the shooting results is the error in determining the sight setting): this is the practical significance of the trajectory.
The flatness of the trajectory is characterized by its greatest excess over the aiming line. At a given range, the trajectory is all the more flat, the less it rises above the aiming line. In addition, the flatness of the trajectory can be judged by the magnitude of the angle of incidence: the trajectory is the more flat, the smaller the angle of incidence. The flatness of the trajectory affects the value of the range of a direct shot, struck, covered and dead space.

Trajectory elements

Departure point- the center of the muzzle of the barrel. The departure point is the start of the trajectory.
Weapon Horizon is the horizontal plane passing through the departure point.
elevation line- a straight line, which is a continuation of the axis of the bore of the aimed weapon.
Shooting plane- a vertical plane passing through the line of elevation.
Elevation angle- the angle enclosed between the line of elevation and the horizon of the weapon. If this angle is negative, then it is called the angle of declination (decrease).
Throw line- a straight line, which is a continuation of the axis of the bore at the time of the bullet's departure.
Throwing angle
Departure angle- the angle enclosed between the line of elevation and the line of throwing.
drop point- the point of intersection of the trajectory with the horizon of the weapon.
Angle of incidence- the angle enclosed between the tangent to the trajectory at the point of impact and the horizon of the weapon.
Total horizontal range- the distance from the point of departure to the point of fall.
final speed- the speed of the bullet (grenade) at the point of impact.
Total flight time- the time of movement of a bullet (grenade) from the point of departure to the point of impact.
Top of the path- the highest point of the trajectory above the horizon of the weapon.
Trajectory height- the shortest distance from the top of the trajectory to the horizon of the weapon.
Ascending branch of the trajectory- part of the trajectory from the departure point to the top, and from the top to the drop point - the descending branch of the trajectory.
Aiming point (aiming)- the point on the target (outside it) at which the weapon is aimed.
line of sight- a straight line passing from the shooter's eye through the middle of the sight slot (at the level with its edges) and the top of the front sight to the aiming point.
aiming angle- the angle enclosed between the line of elevation and the line of sight.
Target elevation angle- the angle enclosed between the aiming line and the horizon of the weapon. This angle is considered positive (+) when the target is higher and negative (-) when the target is below the weapon's horizon.
Sighting range- distance from the departure point to the intersection of the trajectory with the line of sight. The excess of the trajectory over the line of sight is the shortest distance from any point of the trajectory to the line of sight.
target line- a straight line connecting the departure point with the target.
Slant Range- distance from the departure point to the target along the target line.
meeting point- point of intersection of the trajectory with the surface of the target (ground, obstacles).
Meeting angle- the angle enclosed between the tangent to the trajectory and the tangent to the target surface (ground, obstacles) at the meeting point. The meeting angle is taken as the smaller of the adjacent angles, measured from 0 to 90 degrees.

A direct shot, hit and dead space are most closely related to issues of shooting practice. The main task of studying these issues is to obtain a solid knowledge in the use of a direct shot and the space to be struck to perform fire missions in combat.

Direct shot its definition and practical use in a combat situation

A shot in which the trajectory does not rise above the aiming line above the target for its entire length is called direct shot. Within the range of a direct shot in tense moments of the battle, shooting can be carried out without rearranging the sight, while the aiming point in height, as a rule, is chosen at the lower edge of the target.

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

Direct sniper shot in urban environments
The installation height of optical sights above the bore of the weapon is on average 7 cm. At a distance of 200 meters and the sight "2", the greatest excesses of the trajectory, 5 cm at a distance of 100 meters and 4 cm - at 150 meters, practically coincide with the aiming line - the optical axis of the optical sight. The height of the line of sight at the middle of the distance of 200 meters is 3.5 cm. There is a practical coincidence of the trajectory of the bullet and the line of sight. A difference of 1.5 cm can be neglected. At a distance of 150 meters, the height of the trajectory is 4 cm, and the height of the optical axis of the sight above the horizon of the weapon is 17-18 mm; the difference in height is 3 cm, which also does not play a practical role.

At a distance of 80 meters from the shooter, the height of the trajectory of the bullet will be 3 cm, and the height of the sighting line will be 5 cm, the same difference of 2 cm is not decisive. The bullet will fall only 2 cm below the aiming point. The vertical spread of bullets of 2 cm is so small that it is of no fundamental importance. Therefore, when shooting with division "2" of the optical sight, starting from 80 meters of distance and up to 200 meters, aim at the bridge of the nose of the enemy - you will get there and get ± 2/3 cm higher lower throughout this distance. At 200 meters, the bullet will hit exactly the aiming point. And even further, at a distance of up to 250 meters, aim with the same sight "2" at the enemy's "top", at the upper cut of the cap - the bullet drops sharply after 200 meters of distance. At 250 meters, aiming in this way, you will fall 11 cm lower - in the forehead or bridge of the nose.
The above method can be useful in street battles, when the distances in the city are about 150-250 meters and everything is done quickly, on the run.

Affected space, its definition and practical use in a combat situation

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

The distance on the ground during which the descending branch of the trajectory does not exceed the height of the target, called the affected space(the depth of the affected space).
The depth of the affected space depends on the height of the target (it will be the greater, the higher the target), on the flatness of the trajectory (it will be the greater, the flatter the trajectory) and on the angle of the terrain (on the front slope it decreases, on the reverse slope it increases).
The depth of the affected space can be determined from the tables of the excess of the trajectory above the aiming line by comparing the excess of the descending branch of the trajectory by the corresponding firing range with the height of the target, and if the target height is less than 1/3 of the trajectory height, then in the form of a thousandth.
To increase the depth of the space to be struck on sloping terrain, the firing position must be chosen so that the terrain in the enemy's disposition coincides, if possible, with the aiming line. Covered space, its definition and practical use in a combat situation.

Covered space, its definition and practical use in a combat situation

The space behind a cover that is not penetrated by a bullet, from its crest to the meeting point is called covered space.
The covered space will be the greater, the greater the height of the shelter and the flatter the trajectory. The depth of the covered space can be determined from the tables of excess trajectory over the line of sight. By selection, an excess is found that corresponds to the height of the shelter and the distance to it. After finding the excess, the corresponding setting of the sight and the firing range are determined. The difference between a certain range of fire and the range to cover is the depth of the covered space.

Dead space of its definition and practical use in a combat situation

The part of the covered space in which the target cannot be hit with a given trajectory is called dead (not affected) space.
Dead space will be the greater, the greater the height of the shelter, the lower the height of the target and the flatter the trajectory. The other part of the covered space in which the target can be hit is the hit space. The depth of the dead space is equal to the difference between the covered and affected space.

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

The phenomenon of derivation

Due to the simultaneous impact on the bullet of a rotational movement, which gives it a stable position in flight, and air resistance, which tends to tip the bullet head back, the axis of the bullet deviates from the direction of flight in the direction of rotation. As a result, the bullet encounters air resistance on more than one of its sides and therefore deviates from the firing plane more and more in the direction of rotation. Such a deviation of a rotating bullet away from the plane of fire is called derivation. This is a rather complex physical process. The derivation increases disproportionately to the flight distance of the bullet, as a result of which the latter takes more and more to the side and its trajectory in plan is a curved line. With the right cut of the barrel, the derivation takes the bullet to the right side, with the left - to the left.

At firing distances up to 300 meters inclusive, derivation has no practical significance. This is especially true for the SVD rifle, in which the PSO-1 optical sight is specially shifted to the left by 1.5 cm. The barrel is slightly turned to the left and the bullets go slightly (1 cm) to the left. It is of no fundamental importance. At a distance of 300 meters, the derivation force of the bullet returns to the aiming point, that is, in the center. And already at a distance of 400 meters, the bullets begin to thoroughly divert to the right, therefore, in order not to turn the horizontal flywheel, aim at the enemy’s left (away from you) eye. By derivation, the bullet will be taken 3-4 cm to the right, and it will hit the enemy in the bridge of the nose. At a distance of 500 meters, aim at the left (from you) side of the enemy's head between the eye and ear - this will be approximately 6-7 cm. At a distance of 600 meters - at the left (from you) edge of the enemy's head. Derivation will take the bullet to the right by 11-12 cm. At a distance of 700 meters, take a visible gap between the aiming point and the left edge of the head, somewhere above the center of the epaulette on the shoulder of the enemy. At 800 meters - give an amendment with the flywheel of horizontal corrections by 0.3 thousandth (set the grid to the right, move the middle point of impact to the left), at 900 meters - 0.5 thousandth, at 1000 meters - 0.6 thousandth.

Internal ballistics, shot and its periods

Internal ballistics- This is a science that studies the processes that occur when fired, and especially when a bullet (grenade) moves along the bore.

Shot and its periods

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

When fired from small arms, the following phenomena occur. From the impact of the striker on the primer of a live cartridge sent into the chamber, the percussion composition of the primer explodes and a flame forms, which through the seed holes in the bottom of the cartridge case penetrates to the powder charge and ignites it. During the combustion of a powder (combat) charge, a large amount of highly heated gases are formed, which create high pressure in the bore on the bottom of the bullet, the bottom and walls of the sleeve, as well as on the walls of the barrel and the bolt.

As a result of the pressure of gases on the bottom of the bullet, it moves from its place and crashes into the rifling; rotating along them, it moves along the bore with a continuously increasing speed and is thrown outward in the direction of the axis of the bore. The pressure of gases on the bottom of the sleeve causes the movement of the weapon (barrel) back. From the pressure of gases on the walls of the sleeve and the barrel, they are stretched (elastic deformation), and the sleeve, tightly pressed against the chamber, prevents the breakthrough of powder gases towards the bolt. At the same time, when fired, an oscillatory movement (vibration) of the barrel occurs and it heats up. Hot gases and particles of unburned powder, flowing from the bore after the bullet, when they meet with air, generate a flame and a shock wave; the latter is the source of sound when fired.

When fired from automatic weapons, the device of which is based on the principle of using the energy of powder gases vented through a hole in the barrel wall (for example, Kalashnikov assault rifle and machine guns, Dragunov sniper rifle, Goryunov easel machine gun), part of the powder gases, in addition, after the bullet passes through the gas outlet holes rushes through it into the gas chamber, hits the piston and throws the piston with the bolt carrier (pusher with the bolt) back.

Until the bolt frame (bolt stem) passes a certain distance, which ensures the bullet exits from the bore, the bolt continues to lock the bore. After the bullet leaves the barrel, it is unlocked; the bolt frame and the bolt, moving backward, compress the return (back-action) spring; the shutter at the same time removes the sleeve from the chamber. When moving forward under the action of a compressed spring, the bolt sends the next cartridge into the chamber and again locks the bore.

When fired from an automatic weapon, the device of which is based on the principle of using recoil energy (for example, Makarov pistol, Stechkin automatic pistol, automatic model 1941), gas pressure is transmitted through the bottom of the sleeve to the bolt and causes the bolt with the sleeve to move back. This movement begins at the moment when the pressure of the powder gases on the bottom of the sleeve overcomes the inertia of the shutter and the force of the reciprocating mainspring. The bullet by this time is already flying out of the bore.

Moving back, the bolt compresses the reciprocating mainspring, then, under the action of the energy of the compressed spring, the bolt moves forward and sends the next cartridge into the chamber.

In some types of weapons (for example, the Vladimirov heavy machine gun, easel machine gun model 1910), under the action of the pressure of powder gases on the bottom of the sleeve, the barrel first moves back together with the bolt (lock) coupled to it. After passing a certain distance, ensuring the departure of the bullet from the bore, the barrel and bolt disengage, after which the bolt moves to its rearmost position by inertia and compresses (stretches) the return spring, and the barrel returns to the front position under the action of the spring.

Sometimes, after the striker hits the primer, the shot will not follow, or it will happen with some delay. In the first case, there is a misfire, and in the second, a protracted shot. The cause of a misfire is most often dampness of the percussion composition of the primer or powder charge, as well as a weak impact of the striker on the primer. Therefore, it is necessary to protect the ammunition from moisture and keep the weapon in good condition.

A protracted shot is a consequence of the slow development of the process of ignition or ignition of a powder charge. Therefore, after a misfire, you should not immediately open the shutter, as a protracted shot is possible. If a misfire occurs when firing from an easel grenade launcher, then it is necessary to wait at least one minute before unloading it.

During the combustion of a powder charge, approximately 25-35% of the energy released is spent on communicating the progressive motion of the pool (the main work); 15-25% of energy - for secondary work (cutting and overcoming the friction of a bullet when moving along the bore; heating the walls of the barrel, cartridge case and bullet; moving the moving parts of the weapon, gaseous and unburned parts of gunpowder); about 40% of the energy is not used and is lost after the bullet leaves the bore.

The shot occurs in a very short period of time (0.001-0.06 sec). When fired, four consecutive periods are distinguished: preliminary; first, or main; second; the third, or aftereffect period of gases (Fig. 1).

Shot periods: Ro - forcing pressure; Pm - the highest (maximum) pressure: Pk and Vk pressure, gases and bullet speed at the moment of the end of the burning of gunpowder; Rd and Vd gas pressure and bullet speed at the time of its departure from the bore; Vm - the highest (maximum) bullet speed; Ratm - pressure equal to atmospheric

Preliminary period lasts from the beginning of the burning of the powder charge to the complete cutting of the shell of the bullet into the rifling of the barrel. During this period, the gas pressure is created in the barrel bore, which is necessary in order to move the bullet from its place and overcome the resistance of its shell to cutting into the rifling of the barrel. This pressure is called boost pressure; it reaches 250 - 500 kg / cm2, depending on the rifling device, the weight of the bullet and the hardness of its shell (for example, for small arms chambered in 1943, the forcing pressure is about 300 kg / cm2). It is assumed that the combustion of the powder charge in this period occurs in a constant volume, the shell cuts into the rifling instantly, and the movement of the bullet begins immediately when the forcing pressure is reached in the bore.

First or main, the period lasts from the beginning of the movement of the bullet until the moment of complete combustion of the powder charge. During this period, the burning of the powder charge occurs in a rapidly changing volume. At the beginning of the period, when the speed of the bullet along the bore is still low, the amount of gases grows faster than the volume of the bullet space (the space between the bottom of the bullet and the bottom of the cartridge case), the gas pressure quickly rises and reaches its maximum value (for example, in small arms chambered for mod. 1943 - 2800 kg / cm2, and for a rifle cartridge - 2900 kg / cm2). This pressure is called maximum pressure. It is created in small arms when a bullet travels 4-6 cm of the path. Then, due to the rapid increase in the speed of the bullet, the volume of the bullet space increases faster than the influx of new gases, and the pressure begins to fall, by the end of the period it is equal to about 2/3 of the maximum pressure. The speed of the bullet is constantly increasing and by the end of the period reaches approximately 3/4 of the initial speed. The powder charge completely burns out shortly before the bullet leaves the bore.

Second period e lasts from the moment of complete combustion of the powder charge until the moment the bullet leaves the bore. With the beginning of this period, the influx of powder gases stops, however, highly compressed and heated gases expand and, putting pressure on the bullet, increase its speed. The pressure drop in the second period occurs quite quickly and at the muzzle - the muzzle pressure - is 300-900 kg / cm2 for various types of weapons (for example, for the Simonov self-loading carbine - 390 kg / cm2, for the Goryunov easel machine gun - 570 kg / cm2) . The speed of the bullet at the time of its departure from the bore (muzzle velocity) is somewhat less than the initial velocity.

For some types of small arms, especially short-barreled ones (for example, the Makarov pistol), there is no second period, since the complete combustion of the powder charge does not actually occur by the time the bullet leaves the barrel.

The third period, or the period of aftereffect of gases, lasts from the moment the bullet leaves the bore until the moment the powder gases act on the bullet. During this period, the powder gases flowing out of the bore at a speed of 1200-2000 m/s continue to act on the bullet and impart additional speed to it.

The bullet reaches its greatest (maximum) speed at the end of the third period at a distance of several tens of centimeters from the muzzle of the barrel. This period ends at the moment when the pressure of the powder gases at the bottom of the bullet is balanced by air resistance.

Ballistics is the science of motion, flight, and the 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 refers to the impact of projectiles, a separate category covers the degree of damage to the target. What does internal and external ballistics study?

Guns and missiles

Cannon and rocket engines are types of heat propulsion, partly with the conversion of chemical energy into apropellant (the kinetic energy of a projectile). Propellants differ from conventional fuels in that their combustion does not require atmospheric oxygen. To a limited extent, the production of hot gases with combustible fuel causes an increase in pressure. The pressure propels the projectile and increases the burning rate. Hot gases tend to erode the barrel of a gun or the throat of a rocket. Small arms internal and external ballistics studies the movement, flight, and impact that the projectile has.

When the propellant charge in the gun chamber is ignited, the combustion gases are held back by the shot, so the pressure builds up. 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. Fast combustible rocket fuel is soon exhausted, and over time, the shot is ejected from the muzzle: a shot speed of up to 15 kilometers per second has been achieved. Folding cannons release gas through the back of the chamber to counteract recoil forces.

A ballistic missile is a missile 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 aerodynamically guided in flight with the engine running.

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 of motion are used to analyze the projectile's trajectory. Examples of projectiles include balls, arrows, bullets, artillery shells, rockets, and so on.

A throw is the launching of a projectile by hand. Humans are unusually good at throwing due to their high agility, this is a highly developed trait. Evidence of human throwing dates back 2 million years. The throwing speed of 145 km per hour found in many athletes far exceeds 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 remain elastic until needed to propel an object.

Internal and external ballistics: briefly about the types of weapons

Some of the most ancient launchers were ordinary slingshots, bows and arrows, and a catapult. Over time, guns, pistols, rockets appeared. Information from internal and external ballistics includes information about various types of weapons.

• Spling is a weapon commonly used to eject blunt projectiles such as rock, clay, or a 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 the target.
• Bow and arrows. A bow is a flexible piece of material that fires aerodynamic projectiles. The string connects the two ends, and when it is pulled back, the ends of the stick are bent. 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 archery.
• A catapult is a device used to launch a projectile at a great 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 proved to be one of the most efficient mechanisms during war. The word "catapult" comes from the Latin, which, in turn, comes from the Greek καταπέλτης, which means "throw, hurl". Catapults were invented by the ancient Greeks.
• A pistol is a conventional tubular weapon or other device designed to release projectiles or other material. The projectile may be solid, liquid, gaseous, or energetic, and may be loose, as with bullets and artillery shells, or with clamps, as with probes and whaling harpoons. The projection means varies according to the design, but is usually carried out by the action of gas pressure generated by the rapid combustion of the propellant, or compressed and stored by mechanical means operating inside a piston-like tube with an open end. The condensed gas accelerates the moving projectile along the length of the tube, imparting sufficient velocity to keep the projectile moving when the gas stops at the end of the tube. Alternatively, acceleration by electromagnetic field generation can be used, in which case the tube can be discarded and the guide replaced.
• A rocket is a missile, spacecraft, aircraft, or other vehicle that is hit by a rocket engine. The exhaust of a rocket engine is completely formed from the propellants carried in the rocket before use. Rocket engines work by action and reaction. Rocket engines push rockets forward by simply throwing their exhausts back very quickly. Although they are comparatively inefficient for low speed use, rockets are relatively light and powerful, capable of generating high 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 when the propellant is burned. 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 a shot taken with an ultra-high speed air gap flash helps to view the bullet without blurring the image. Ballistics is often broken down into the following four categories:

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

Internal ballistics is the study of movement in the form of a projectile. In guns, it covers the time from propellant ignition 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. Information from internal ballistics 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 balanced, so it falls between the concept of internal and external ballistics.

External ballistics studies the atmospheric pressure dynamics around a bullet and is the 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 idle free-flight phase of the bullet after it leaves the barrel of the gun and before it hits the target, so it sits between transition ballistics and terminal ballistics. However, external ballistics also concerns 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 hits its target. This category has value for both small caliber projectiles and large caliber projectiles (artillery shooting). The study of extremely high velocity effects is still very new and is currently applied mainly to spacecraft design.

Forensic ballistics

Forensic ballistics involves the analysis of bullets and bullet impacts to determine usage information in a court of law or other part of the legal system. Separate from ballistics information, the Firearms and Tool Mark (“Ballistic Fingerprint”) exams involve reviewing evidence of firearms, ammunition, and tools to determine if 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 the practical problems of propulsion of rockets and other spacecraft. The motion of these objects is usually calculated from Newton's laws of motion and the law of universal gravitation. It is the core discipline in space mission design and control.

Travel of a projectile in flight

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

Higher pressures require a larger gun with more recoil, which loads more slowly and generates more heat, resulting in more metal wear. In practice, it is difficult to measure the forces inside the 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). This is where the bullet base (equivalent to barrel diameter) is located and is constant. Therefore, the energy transferred to the bullet (with a given mass) will depend on the mass time times the time interval over which the force is applied.

The last of these factors is a function of barrel length. Bullet movement through a machine gun is characterized by an increase in acceleration as expanding gases press against it, but a reduction in barrel pressure as the gas expands. Up to the point of decreasing pressure, the longer the barrel, the greater the acceleration of the bullet. As the bullet travels down the barrel of a gun, there is a slight deformation. 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 for avoiding such situations. The effect on the subsequent trajectory of the bullet is usually negligible.

From gun to target

External ballistics can be briefly called the journey from gun to target. Bullets usually do not travel in a straight line to the target. There are rotational forces that keep the bullet from a 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 motion at the tip of a bullet. Acceleration and precession decrease as the bullet's distance from the barrel increases.

One of the tasks of external ballistics is the creation of an ideal bullet. To reduce air resistance, the ideal bullet would be a long, heavy needle, but such a projectile would go straight through the target without dissipating most of its energy. The spheres will lag behind 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 branching shape.

The best bullet composition is lead, which has a high density and is cheap to produce. Its disadvantages are that it tends to soften at >1000 fps, causing it to lubricate the barrel and reduce accuracy, and lead tends to melt completely. Alloying the lead (Pb) with a small amount of antimony (Sb) helps, but the real answer is to bond 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 (target hitting)

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

1. Destruction and crushing. Tissue crush injury diameter is the diameter of the bullet or fragment, up to the length of the axis.
2. Cavitation - A "permanent" cavity is caused by the trajectory (track) of the bullet itself with tissue crushing, whereas a "temporary" cavity is formed by radial stretching around the bullet track from the continuous acceleration of the medium (air or tissue) resulting from 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. The shock waves compress the medium and move ahead of the bullet as well as to the sides, but these waves last only a few microseconds and do not cause deep damage at low speed. At high speed, 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 person to concussion, which causes acute neurological symptoms.

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

bullet design

Bullet design is important in injury 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 jacket around the 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 bullets must be copper-jacketed as lead begins to melt due to the heat generated at >2000 fps per give me a sec.

The external and internal ballistics of the PM (Makarov pistol) differ from the ballistics of the so-called "destructible" bullets, designed to break when hitting a hard surface. Such bullets are usually made from a metal other than lead, such as copper powder, compacted into a bullet. Target distance from the muzzle plays a large role in wounding ability, as 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 the PM and military and hunting rifles designed to deliver bullets with a large number of EC over a longer distance will differ.

Designing a bullet to transfer energy efficiently to a specific target is not easy because the targets are different. The concept of internal and external ballistics also includes projectile design. To penetrate the elephant's thick hide and tough bone, the bullet must be small in diameter and strong enough to resist disintegration. However, such a bullet penetrates most tissues like a spear, dealing slightly more damage than a knife wound. A bullet designed to damage human tissue will require certain "brakes" in order for the entire CE to be transmitted to the target.

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

The design of the hollow point bullet makes it easier to turn the bullet "inside out" and flatten the front, referred to as "expansion". Expansion only reliably occurs at speeds in excess of 1200 fps, so it is only suitable for guns with maximum speed. A frangible powder bullet designed to disintegrate on impact, delivering all of the CE but without significant penetration, the size of the fragments must decrease as the impact velocity increases.

Injury potential

The type of tissue influences the injury 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 more elasticity, the less damage. Thus, light tissue with low density and high elasticity is damaged less muscle with higher density, but with some elasticity.

The liver, spleen and brain do not have elasticity and are easily injured, as is adipose tissue. Fluid-filled organs (bladder, heart, large vessels, intestines) can burst due to the pressure waves created. A bullet hitting bone can result in bone fragmentation and/or multiple secondary missiles, each causing an additional wound.

Pistol ballistics

This weapon is easy to hide, but difficult to aim accurately, especially at crime scenes. Most small-arms fires occur at less than 7 yards, but even so, most bullets miss their intended target (only 11% of attackers' rounds and 25% of police-fired bullets hit their intended target in one study). Usually low caliber guns are used in crime 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 the bullet diameter and the volume of powder in the cartridge case. Older design cartridges were limited by the pressures they could handle, but advances in metallurgy allowed the maximum pressure to be doubled and tripled so that more kinetic energy could be generated.