external ballistics. Trajectory and its elements. Exceeding the trajectory of the bullet above the point of aim. Trajectory shape. internal ballistics. Shot and its periods Ballistics Department

Introduction 2.

Objects, tasks and subject of judicial

ballistic examination 3.

The concept of firearms 5.

Device and purpose of the main

parts and mechanisms of firearms

weapons 7.

Classification of cartridges for

hand firearms 12.

Device unitary cartridges

and their main parts 14.

Drafting an expert opinion and

Photo tables 21.

List of used literature 23.

Introduction.

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

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

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

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

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

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

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

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

OBJECTS, OBJECTIVES AND SUBJECT OF FORENSIC BALLISTIC EXAMINATION

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

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

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

Firearms, their parts, accessories and blanks;

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

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

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

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

Fired bullets and spent cartridge cases, traces of the use of firearms on various objects;

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

Material conditions of the scene.

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

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

Rice. 1.1. Classification of tasks of forensic ballistic examination

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

Group identification includes setting:

Items belonging to the category of firearms and ammunition;

Type, model and type of firearms and cartridges presented;

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

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

To individual identification relate:

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

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

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

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

Non-identification tasks can be divided into three types:

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

Situational, aimed at establishing the circumstances of the firing;

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

Diagnostic tasks:

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

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

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

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

Situational tasks:

Establishing the distance, direction and place of the shot;

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

Determining the sequence and number of shots.

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

Let us now discuss the subject of forensic ballistic examination.

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

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

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

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

On the state of firearms;

About the presence or absence of the identity of firearms;

About the circumstances of the shot;

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

THE CONCEPT OF FIREARMS

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

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

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

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

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

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

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

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

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

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

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

Definitions

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

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

Trajectory- the line along which the bullet moves.

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

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

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

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

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

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

Trajectory at half way

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

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

Cross density, ballistic coefficient

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

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

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

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

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

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

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

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

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

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

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

direct shot distance

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

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

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

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

The content of the article

BALLISTICS, a complex of physical and technical disciplines covering the theoretical and experimental study of the motion and final impact of projectile solids - bullets, artillery shells, rockets, air 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 which is the regularities of the impact of projectiles on the targets being hit. The development and design of types and systems of ballistic weapons is based on the application of mathematics, physics, chemistry and design achievements to solve the many and complex problems of ballistics. 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 rigid body dynamics, which was developed by I. Müller (Germany) and the Italians N. Fontana and G. Galilei in the 15th and 16th centuries.

The classical problem of internal ballistics, which consists in calculating the initial velocity of the projectile, the maximum pressure in the barrel and the dependence of pressure on time, for small arms and cannons has been solved theoretically quite completely. With regard to modern artillery and rocket systems - recoilless rifles, gas guns, artillery rockets and jet propulsion systems - there is a need for further refinement of the ballistic theory. Typical ballistics problems with the presence of aerodynamic, inertial and gravitational forces acting on a projectile or missile in flight have become more complex in recent years. Hypersonic and space velocities, the entry of the nose cone into the dense layers of the atmosphere, the huge length of the trajectory, 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. The very first manifestation of it was undoubtedly the throwing of stones by prehistoric man. The forerunners of modern weapons such as the bow, catapult, and ballista may typify the earliest applications of ballistics. Advances in weapon design have led to the fact that today artillery guns can fire 90-kilogram projectiles at distances of more than 40 km, anti-tank projectiles can penetrate 50 cm thick steel armor, and guided missiles can deliver a combat load calculated in tons anywhere on the globe. .

Over the years, various methods have been used to accelerate projectiles. The bow accelerated the arrow due to the energy stored in the bent piece of wood; the springs of the ballista were twisted tendons of animals. Were tested electromagnetic force, the power of steam, compressed air. However, none of the methods has been as successful as burning combustible substances.

INTERIOR BALLISTICS

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

Barrel acceleration systems.

The general classical task of internal ballistics as applied to barrel systems of the initial acceleration of the projectile is to find the limiting relationships between the loading characteristics and the ballistic elements of the shot, which together completely determine the shot 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. The ballistic elements are the gas pressure, the temperature of the powder and powder gases, the speed of the gases and the projectile, the distance traveled by the projectile, and the amount of gases currently acting. The gun, in essence, is 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 a gas rises very quickly to a maximum value of 70 to 500 MPa. As the projectile moves through the bore, the pressure drops rather quickly. The duration of the high pressure is on the order of a few milliseconds for a rifle and a few tenths of a second for a large caliber weapon (Fig. 1).

The characteristics of the internal ballistics of the barrel acceleration system depend on the chemical composition of the propellant, its burning rate, the shape and size of the powder charge, and on the loading density (mass of the powder charge per unit volume of the gun chamber). In addition, the length of the gun barrel, the volume of the powder chamber, the mass and "transverse density" of the projectile (the mass of the projectile divided by the square of its diameter) can affect the characteristics of the system. From the point of view of internal ballistics, low density is desirable, since in this case the projectile reaches a higher speed.

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

In a recoilless gun, no external force is required to maintain the equilibrium of the system, since here the total change in the momentum imparted to all elements of the system (gases, projectile, barrel and breech) for a given time is zero. In order for the weapon to not recoil, the momentum of the forward-moving gases and the projectile must be equal and opposite to the momentum of the gases moving backward and out through the breech.

Gas gun.

The gas gun consists of three main parts, shown in fig. 3: compression section, restrictive section and starting barrel. A conventional propellant charge is ignited in the chamber, which causes the piston to move along the barrel of the compression section and compress the helium gas that fills the bore. When the helium pressure rises to a certain level, the diaphragm ruptures. A sudden burst of high-pressure gas pushes the projectile out of the firing barrel, and the restrictor section stops the piston. Projectile speeds fired by a gas cannon can reach 5 km/s, while for a conventional gun this is a maximum of 2000 m/s. The higher efficiency of the gas gun is due to the low molecular weight of the working substance (helium) and, accordingly, the high speed of sound in helium acting on the bottom of the projectile.

reactive systems.

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

EXTERIOR 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 draws a curve in space called a trajectory. The main task of 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 would take into account the forces and moments of forces acting on the projectile.

Vacuum trajectories.

The simplest of the special cases of projectile motion is the motion of a projectile in a vacuum over a flat motionless earth's surface. In this case, it is assumed that no other forces act on the projectile, except for terrestrial 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 frontal resistance (the force of air resistance acting in the opposite direction tangentially 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, rendered to the movement of the projectile, is given by the expression

D = rsv 2 C D (M),

where r- air density, S is the cross-sectional area of ​​the projectile, v is the 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 on a testing ground equipped with precise measuring equipment. The task is facilitated 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 movement of a material point (although it does not take into account many forces acting on a real projectile) with a very good approximation describes the trajectory of rockets after the engine has stopped working (in the passive part of the trajectory), just like the trajectory of conventional artillery shells. Therefore, it is widely used to calculate data used in systems for aiming weapons of this kind.

Trajectories of a rigid body.

In many cases, the theory of motion of a material point does not adequately describe the trajectory of the projectile, and then it is necessary to consider it as a rigid body, i.e. take into account that it will not only move forward, but also rotate, and take into account all aerodynamic forces, and not just drag. Such an approach is required, for example, to calculate the motion of a rocket with a running engine (on 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 (moving head part forward) on the trajectory. Both in the case of rockets and in the case of conventional artillery shells, this is achieved in two ways - with the help of tail stabilizers or due to the rapid rotation of the projectile around the longitudinal axis. Further, speaking of 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; not without reason one of the most ancient projectiles - an arrow - was stabilized in flight in this way. When a feathered projectile moves at 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 ahead of the center of mass. The difference of unbalanced forces causes the projectile to rotate around the center of mass so that this angle becomes equal to zero. Here we can note one important circumstance that is not taken into account by the theory of a material point. If the projectile moves with a non-zero angle of attack, then it is affected by lifting forces due to the occurrence of a pressure difference on both sides of the projectile. (The aircraft's ability to fly is based on this.)

The idea of ​​stabilization by rotation is not so obvious, but it can be explained by comparison. It is well known that if a wheel is spinning rapidly, it resists attempts to turn its axis of rotation. (An ordinary spinning top is an example, and this phenomenon is used in control, navigation and guidance systems devices - gyroscopes.) The most common way to spin a projectile is to cut spiral grooves in the barrel bore, into which the metal belt of the projectile would crash when the projectile accelerates along the barrel. , which would cause it to rotate. In spin-stabilized rockets, this is achieved by using several inclined nozzles. Here, too, one can note some features that are not taken into account by the theory of a material point. If fired vertically upwards, the stabilizing effect of rotation will cause the projectile to bottom down after reaching the top of its flight. This, of course, is undesirable, and therefore guns are not fired at an angle of more than 65–70° to the horizon. The second interesting phenomenon is related to the fact that, as can be shown on the basis of the equations of motion, a spin-stabilized projectile 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 plane of fire. One of these powers is the power of Magnus; it is she who causes the curvature of the trajectory of the "twisted" ball in tennis.

All that has been said about the stability of flight, while not fully covering the phenomena that determine the flight of a projectile, nevertheless illustrates the complexity of the problem. We only note that many different phenomena must be taken into account in the equations of motion; these equations involve a number of variable aerodynamic coefficients (such as the drag coefficient) that must be known. Solving these equations is a very laborious task.

Application.

The use of ballistics in combat operations provides for the location of the weapon system in a place that would allow it to quickly and effectively hit the intended target with minimal risk to service personnel. The delivery of a missile or projectile to a target is usually divided into two stages. At the first, tactical stage, the combat position of the barreled weapon and ground-based missiles or the position of the carrier of air-based missiles is selected. The target must be within the delivery radius of the warhead. At the stage of shooting, 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 - and its future coordinates, taking into account the flight time of the projectile.

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

With the increase in complexity and the expansion of the range of problems of modern ballistics, new technical means have appeared, without which the possibilities of solving current and future ballistic problems would be severely 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 speeds of approach of hypervelocity targets and projectiles are so high that it completely excludes the solution of firing problems based on conventional tables and manual setting of firing parameters. Currently, data for firing from most weapon systems is stored in electronic data banks and processed quickly by computers. The computer's output commands automatically position the weapon in the azimuth and elevation required to deliver the warhead to the target.

Trajectories of guided projectiles.

In the case of guided projectiles, the already difficult 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 as follows. If in one way or another, using the equations of motion, a deviation from a given trajectory is determined, then on the basis of the guidance equations for this deviation, a corrective action is calculated, for example, turning an air or gas steering wheel, changing thrust. This corrective action, which changes 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

End point ballistics considers the physics of the destructive effect of weapons on targets. 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 - soldier's body armor, tank armor, underground shelters, etc. Both experimental and theoretical studies of explosion phenomena (chemical explosives or nuclear charges), detonation, penetration of bullets and fragments into various media, shock waves in water and soil, combustion and nuclear radiation are being conducted.

Explosion.

Experiments in the field of explosion are carried out both with chemical explosives in quantities measured in grams, and with nuclear charges up to several megatons. Explosions can be carried out in different environments, such as the earth and rocks, under water, at the surface of the earth in normal atmospheric conditions, or in rarefied 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 with a speed exceeding the speed of sound in the medium; then, as the intensity of the shock wave decreases, its velocity approaches the speed of sound. Shock waves (in air, water, soil) can hit enemy manpower, destroy underground fortifications, ships, buildings, ground vehicles, aircraft, missiles and satellites.

To simulate intense shock waves that occur in the atmosphere and at the earth's surface during nuclear explosions, special devices called shock tubes are used. A shock tube is typically a long tube made up of two sections. At one end 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. With an instantaneous rupture of a thin diaphragm separating two sections of the pipe, a shock wave arises in the expansion chamber, running along its axis. On fig. 4 shows the pressure curves of the shock wave in three cross sections of the pipe. in section 3 it takes the classical 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 the action of a nuclear explosion. Tests are often carried out in which larger models, and sometimes full-scale objects, are subjected to the action of the explosion.

Experimental studies are supplemented 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 studies are used in the design of warheads for intercontinental ballistic missiles and anti-missile systems. Data of this kind are also needed in the design of missile silos and underground shelters to protect the population from the explosive action of nuclear weapons.

To solve specific problems characteristic of the upper layers of the atmosphere, there are special chambers in which altitude conditions are simulated. One such task is to estimate the reduction in the force of an explosion at high altitudes.

Studies are also being carried out that measure the intensity and duration of the passage of a 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, charges can be measured in hundreds of tons. Such experiments are complemented by theoretical studies. 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.

Shards and penetration.

Fragmentation warheads and projectiles have a metal outer shell, which, upon detonation of a high-explosive chemical explosive charge enclosed in it, breaks into numerous pieces (shards) that fly apart at high speed. During World War II, shaped charge projectiles and warheads were developed. Such a charge is usually an explosive cylinder, at the front end of which there is a conical recess with a conical metal insert placed in it, usually copper. When an explosion starts at the other end of the explosive charge and the liner is compressed under the action of very high detonation pressures, a thin cumulative jet of the liner material is formed, flying out in the direction of 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 jet formation in a cumulative charge munition is shown in Fig. 5.

If the metal is in direct contact with the explosive, shock wave pressures measured in the tens of thousands of MPa can be transmitted to it. For conventional explosive charge sizes of the order of 10 cm, the duration of the pressure pulse is fractions of a millisecond. Such huge 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 the armor plate creates a very strong pressure pulse of short duration (impact) that runs through the thickness of the plate. Having reached the opposite side of the plate, the shock wave is reflected as a wave of tensile stresses. If the intensity of the stress wave exceeds the ultimate tensile strength of the armor material, tensile failure occurs near the surface at a depth that depends on the initial thickness of the explosive charge and the speed of propagation of the shock wave in the plate. As a result of the internal rupture of the armor plate, a metal “splinter” is formed, which flies off the surface at high speed. Such a flying fragment can cause great destruction.

To elucidate 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 metallic materials and with single crystals of various metals. They allowed us to draw an interesting conclusion regarding the initiation of cracks and the onset of fracture: in those cases where there are inclusions (impurities) in the metal, cracks always begin on the inclusions. Experimental studies of the penetrating ability of shells, fragments and bullets in different environments are being carried out. Impact velocities range from a few hundred meters per second for low-velocity bullets to cosmic velocities of the order of 3-30 km/s, which corresponds to fragments and micrometeors encountered by interplanetary aircraft.

On the basis of such studies, empirical formulas are derived for penetration. Thus, it has been established that the depth of penetration into a dense medium is directly proportional to the momentum of the projectile and inversely proportional to its cross-sectional area. The phenomena observed during an impact with 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 is formed on the surface of the plate, and, as the pictures show, the material of the plate is ejected from it. The results of the study of impact at hypersonic speeds make more understandable the formation of craters on celestial bodies, for example, on the Moon, in places where meteorites fall.

Wound ballistics.

To imitate the action of fragments and bullets that hit a person, shots are fired at massive targets made of gelatin. Similar experiments belong to the so-called. wound ballistics. Their results make it possible to judge the nature of the wounds that a person can receive. The information provided by research on wound ballistics makes it possible to optimize the effectiveness of various types of weapons intended for the destruction of enemy manpower.

Armor.

With the use of 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 materials for armor, is investigated. In experiments, the coefficient of neutron transmission through plates of different layers of materials, having typical tank configurations, is determined. The neutron energy can range from fractions to tens of MeV.

Combustion.

Research in the field of ignition and combustion is carried out with a dual purpose. The first is to obtain the data necessary to increase the ability of bullets, shrapnel and incendiary projectiles to set fire to the fuel systems of aircraft, missiles, tanks, etc. The second is to increase the protection of vehicles and stationary objects from the incendiary action of enemy ammunition. Research is being carried out to determine the flammability of various fuels under the action of various means of ignition - electric sparks, pyrophoric (self-igniting) materials, high-speed fragments and chemical igniters.

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 sleeve 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 rocket fuel 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 device is characterized by an increase in acceleration as expanding gases press against it, but a decrease 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 CE over a longer distance will differ.

Designing a bullet to transfer energy efficiently to a particular 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 fragmentation of the bone 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.