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

Design and purpose of the main

parts and mechanisms of firearms

weapons 7.

Classification of cartridges

hand-held firearms 12.

Device of unitary cartridges

and their main parts 14.

Drawing up an expert opinion and

Photo tables 21.

List of used literature 23.

Introduction.

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

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

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

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

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

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

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

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

OBJECTS, TASKS AND SUBJECT OF FORENSIC BALLISTIC EXAMINATION

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

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

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

Firearms, their parts, accessories and blanks;

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

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

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

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

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

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

Material conditions of the scene of the incident.

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

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

Rice. 1.1. Classification of tasks of forensic ballistic examination

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

Group identification includes establishing:

Belonging of objects to the category of firearms and ammunition;

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

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

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

TO individual identification relate:

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

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

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

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

Non-identification tasks can be divided into three types:

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

Situational, aimed at establishing the circumstances of the shooting;

Reconstruction, associated with recreating the original appearance of objects.

Diagnostic tasks:

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

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

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

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

Situational tasks:

Establishing the distance, direction and location of the shot;

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

Determining the sequence and number of shots.

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

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

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

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

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

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

About the condition of firearms;

About the presence or absence of firearm identity;

About the circumstances of the shot;

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

CONCEPT OF FIREARMS

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

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 travels. This exaggerated illustration shows that the bullet, always deviating only downwards from the direction of the shot, crosses the aiming line at two points. The second of these points is located exactly at the distance at which the rifle was zeroed.

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 corresponding “dummies” book for you, including such subjects as raising smart children for dummies (honestly!) and aromatherapy for them. It is interesting, however, that these books are not written for fools and do not treat the subject at a simplistic level. In fact, one of the best books I ever read about wine 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 accept this title with the same sense of humor with which I offer it to you.

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

Internal ballistics looks at what happens inside the rifle from the moment of ignition until the bullet exits the muzzle. In truth, internal ballistics only concerns the reloaders; they are the ones who assemble the cartridge and thereby determine its internal ballistics. You have to be a real nerd to start collecting cartridges without first receiving a basic understanding of internal ballistics, if only because your safety depends on it. If, both at the shooting range and on the hunt, you shoot only factory cartridges, then you really don’t need to know anything about what’s happening in the barrel: anyway, you can’t influence these processes in any way. Don't get me wrong, I'm not discouraging anyone from taking an in-depth study of internal ballistics. It's just that in this context it has no practical meaning.

As for terminal ballistics, yes, here we have some freedom, but no more than in the choice of a bullet loaded in a homemade or factory cartridge. Terminal ballistics begins the moment the bullet penetrates the target. This is a science that is as qualitative as it is quantitative, because there are 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 don’t know the subtleties. I must admit to you that I passed mathematics in college on the third try, and completely failed physics, so believe me, what I am going to talk about is not difficult.

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

To understand what happens to a bullet from muzzle to target, at least as much as we hunters need to, we need to understand some definitions and basic concepts just to put everything into perspective.

Definitions

Line of sight (LO)– straight from the arrow’s 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 barrel bore at the moment of the shot.

Trajectory- the line along which the bullet moves.

A fall– reduction of the bullet’s trajectory relative to the throwing line.

We've all heard someone say that a certain rifle shoots so flat that the bullet simply doesn't drop within the first hundred yards. Nonsense. Even with the most flat 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 “lift” in ballistics tables. The bullet always falls, but it also rises relative to the aiming line. This apparent awkwardness occurs because the scope 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 scope down. In other words, if the throwing line and the aiming line were parallel, the bullet would leave the muzzle one and a half inches (38mm) below the aiming line and begin to fall lower and lower.

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

Both of these 300-grain .375 bullets have the same .305 BC, but the left-hand, pointy-nose, boat-stern bullet has a BC of .493, while the round-nose only has a .250.

In the case of the 45-70, we will see that to hit the target at 100 (91.4m) yards, our bullet will cross the aiming line approximately 20 yards (18.3m) from the muzzle. The bullet will then rise above the line of sight to its highest point at about 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 intersect again at the desired distance of 100 yards.

For a 7mm Ultra Mag zeroed at 300 yards (274m), the first crossover 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 intersects the aiming line at two points, the second of which is the shooting distance.

Trajectory half way

And now I will touch on one concept that is rarely used these days, although in those years when I began to master rifle shooting as a young scoundrel, the halfway trajectory was the criterion by which ballistic tables compared the effectiveness of cartridges. Half-way trajectory (TMT) is the maximum height of the bullet above the aiming line, provided that the weapon is zeroed at a given distance. Typically, ballistic tables gave this value for 100-, 200-, and 300-yard ranges. For example, the TPP for a 150-grain (9.7 g) bullet in the 7mm Remington Mag cartridge according to the 1964 Remington catalog was half an inch (13 mm) at 100 yards (91.5 m), 1.8 inches (46 mm) at 200 yards (183 m) 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 zeroed at 200 yards it will rise 1.8 inches at the 100 yard mark, and when zeroed at 300 yards we get 4.7 inches of lift at 150 yards. In fact, the maximum ordinate is reached slightly further than the middle of the zeroing distance - about 55, 110 and 165 yards respectively - but in practice the difference is insignificant.

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

Lateral density, ballistic coefficient

After leaving the barrel, the bullet's flight path is determined by its speed, shape and weight. This brings us to two buzzwords: lateral density and ballistic coefficient. Lateral density is the weight of the bullet in pounds divided by the square of its diameter in inches. But forget about 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 a seven-millimeter caliber (.284) it is a fairly light bullet, but in a six-millimeter (.243) it is quite heavy. And in terms of cross-sectional density it looks like this: a 100-grain seven-millimeter bullet will have 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 exhibit successive degrees of streamlining. The round nose bullet on the left has a ballistic coefficient of 0.273, the bullet on the right, Hornady A-Max, has a ballistic coefficient of 0.623, i.e. more than twice as much.

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

Since cross-sectional density is related only to the weight and not the shape of the bullet, it turns out that the most blunt-nosed bullets have the same cross-sectional density as the most streamlined bullets of the same weight and caliber. Ballistic coefficient is a completely different matter; it is a measure of how streamlined a bullet is, that is, how effectively it overcomes drag in flight. The calculation of the ballistic coefficient is not well defined; there are several methods that often give inconsistent results. Adding to the uncertainty is the fact that the BC depends on the speed and altitude above sea level.

Unless you're a math geek obsessed with calculations for the sake of calculations, then I suggest just doing what everyone else does: using the value provided by the bullet manufacturer. All manufacturers of self-loading bullets publish lateral density and ballistic coefficient values ​​for each bullet. But for bullets used in factory cartridges, only Remington and Hornady do this. In the meantime, this is useful information, and I think all ammo manufacturers should provide it both in ballistic tables and directly on the boxes. Why? Because if you have ballistics programs on your computer, then all you need to do is enter the muzzle velocity, the weight of the bullet and its ballistic coefficient, and you can draw a trajectory for any shooting distance.

An experienced reloder 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 (low cross-sectional density) hunting bullets, pointed or with a recess in the nose. Over .400 is a moderately heavy bullet for the caliber with an extremely streamlined nose shape.

If the BC of a hunting bullet is close to .500, it means that the bullet combines near-optimal cross-sectional density and a streamlined shape, such as Hornady's 7mm 162-grain (10.5-grain) SST with a .550-grain or 180-grain BC. 11.7 g) XBT from Barnes in thirty gauge with BC 0.552. This extremely high BC is typical of round tail (“boat stern”) bullets with 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 ogive is the part of the bullet in front of the leading cylindrical surface, simply what forms the nose zeros. If you look at the bullet from the side, the ogive is formed by arcs or curved lines, but Hornady uses an ogive made of converging straight lines, that is, conical.

If you put flat-nose, round-nose and pointed-nose bullets side by side, then common sense will tell you that the pointed-nose is more streamlined than the round-nose, and the round-nose, in turn, is more streamlined than the flat-nose. It follows 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 - less than the flat-nosed one. Add a boat stern and the bullet becomes even more aerodynamic.

Aerodynamically, the shape may be good, like the 120-grain (7.8g) seven-millimeter bullet on the left, but due to its low cross-sectional density (i.e., weight for that caliber), it will lose velocity much more quickly. If the 175-grain bullet (right) is fired at 500 fps slower, it will catch up with the 120-grain bullet at 500 yards.

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

Direct shot distance

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

Essentially, it's as if we took a perfectly straight imaginary pipe with a diameter of 10 inches and superimposed it on a given path. With the muzzle cut in the center of the pipe at one end, the direct shot distance is the maximum distance over which the bullet will fly inside this imaginary pipe. Naturally, in the initial section the trajectory should be directed slightly upward, so that at the point of the highest rise the bullet only touches the top of the pipe. With this type of 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 3,100 feet per second (945 m/s). According to the Sierra manual, zeroing the rifle at 315 yards (288m), we get a direct shot distance of 375 yards (343m). The same bullet fired from a .30-06 rifle at 2800 fps, zeroed at 285 yards, would give us a DPV of 340 yards—not as big a difference as you might think, right?

Most ballistics programs will calculate point-blank range, you just need to enter the bullet's weight, BC, velocity and kill zone size. Naturally, you can enter a four-inch (10cm) killing zone if you hunt marmots, and an eighteen-inch (46cm) kill zone if you hunt elk. But personally, I have never used DPV; I consider it careless shooting. Moreover, 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 theoretical and experimental study of the movement and final impact of thrown solid bodies - bullets, artillery shells, missiles, aircraft bombs and spacecraft. Ballistics is divided into: 1) internal ballistics, which studies methods for setting a projectile in motion; 2) external ballistics, which studies the movement of a projectile along a trajectory; 3) ballistics at the end point, the subject of study of which is the patterns of the impact of projectiles on the targets they hit. The development and design of types and systems of ballistic weapons are based on the application of mathematics, physics, chemistry and design achievements to solve numerous and complex ballistics problems. I. Newton (1643–1727) is considered to be the founder of modern ballistics. Formulating the laws of motion and calculating the trajectory of a material point in space, he relied on the mathematical theory of rigid body dynamics, which was developed by I. Muller (Germany) and the Italians N. Fontana and G. Galileo in the 15th and 16th centuries.

The classic problem of internal ballistics, which consists of calculating the initial velocity of a projectile, the maximum pressure in the barrel and the dependence of pressure on time, has been theoretically solved quite completely for small arms and cannons. As for modern artillery and missile systems - recoilless rifles, gas guns, artillery rockets and rocket systems - there is a need for further clarification of ballistic theory. Typical ballistics problems involving aerodynamic, inertial and gravitational forces acting on a projectile or missile in flight have become more complex in recent years. Hypersonic and cosmic speeds, the entry of the nose cone into the dense layers of the atmosphere, the enormous 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. Its very first manifestation was, undoubtedly, the throwing of stones by prehistoric man. Precursors to modern weapons such as the bow, catapult, and ballista may typify the earliest applications of ballistics. Advances in weapons design have meant that today artillery cannons fire 90-kilogram shells over distances of more than 40 km, anti-tank shells can penetrate 50 cm of steel armor, and guided missiles can deliver tons of payload anywhere in the world. .

Over the years, various methods have been used to accelerate projectiles. The bow accelerated the arrow using the energy stored in the bent piece of wood; The springs of the ballista were the twisted tendons of animals. Electromagnetic force, steam force, and compressed air were tested. However, none of the methods was as successful as burning flammable substances.

INTERNAL BALLISTICS

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

Barrel acceleration systems.

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

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

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

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

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

Gas gun.

The gas gun consists of three main parts, shown in Fig. 3: compression section, restriction section and launch barrel. A conventional powder charge is ignited in the chamber, which causes the piston to move down the barrel compression section and compress the helium gas filling the bore. When the helium pressure increases to a certain level, the diaphragm ruptures. A sudden burst of high-pressure gas pushes the projectile out of the launch barrel, and the restrictive section stops the piston. The speed of a projectile fired by a gas gun can reach 5 km/s, while for a conventional gun this is a maximum of 2000 m/s. The higher efficiency of the gas gun is explained by 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 essentially the same functions as artillery guns. This installation plays the role of a fixed support and usually sets the initial direction of flight of the missile. When launching a guided missile, which, as a rule, has an on-board guidance system, the precise aiming required when firing a gun is not required. In the case of unguided missiles, the launcher guides must place the missile on a trajectory leading to the target.

EXTERNAL BALLISTICS

External ballistics deals with the movement of projectiles in the space between the launcher and the target. When a projectile is set in motion, its center of mass traces a curve in space called a trajectory. The main task 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 takes into account the forces and moments of force acting on the projectile.

Vacuum trajectories.

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

Trajectories of a material point.

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

D = rSv 2 C D (M),

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

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

Rigid body trajectories.

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

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

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

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

Application.

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

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

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

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

Trajectories of guided projectiles.

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

BALLISTICS AT THE END POINT

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

Explosion.

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

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

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

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

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

Fragments and penetration ability.

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

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

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

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

Wound ballistics.

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

Armor.

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

Combustion.

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

Internal ballistics, shot and its periods

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

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

As a result of the gas pressure on the bottom of the bullet, it moves from its place and crashes into the rifling; rotating along them, moves along the barrel bore with a continuously increasing speed and is thrown out in the direction of the axis of the barrel bore. The gas pressure on the bottom of the cartridge case causes the weapon (barrel) to move backward. The pressure of the gases on the walls of the cartridge case and barrel causes them to stretch (elastic deformation), and the cartridge case, pressing tightly against the chamber, prevents the breakthrough of powder gases towards the bolt. At the same time, when firing, an oscillatory movement (vibration) of the barrel occurs and it heats up. Hot gases and particles of unburnt gunpowder flowing out of the barrel after a bullet, when meeting air, generate a flame and a shock wave; the latter is the source of sound when fired.

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

Until the bolt frame (bolt stem) travels a certain distance allowing the bullet to leave the barrel, the bolt continues to lock the barrel. After the bullet leaves the barrel, it is unlocked; the bolt frame and bolt, moving backward, compress the return (recoil) spring; the bolt removes the cartridge case 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 barrel.

When firing from an automatic weapon, the design of which is based on the principle of using recoil energy (for example, a Makarov pistol, a Stechkin automatic pistol, an assault rifle model 1941), the gas pressure through the bottom of the cartridge case is transmitted to the bolt and causes the bolt with the cartridge case to move backward. This movement begins at the moment when the pressure of the powder gases on the bottom of the cartridge case overcomes the inertia of the bolt and the force of the return spring. By this time the bullet is already flying out of the barrel.

Moving back, the bolt compresses the recoil spring, then, under the influence 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, a large-caliber Vladimirov machine gun, a heavy machine gun model 1910), under the influence of the pressure of powder gases on the bottom of the cartridge case, the barrel first moves backward along with the bolt (lock) linked to it. Having passed a certain distance, ensuring that the bullet leaves the barrel, the barrel and the bolt are disengaged, after which the bolt, by inertia, moves to the rearmost position and compresses (stretches) the return spring, and the barrel, under the action of the spring, returns to the forward position.

Sometimes, after the firing pin hits the primer, there will be no shot or it will happen with some delay. In the first case, there is a misfire, and in the second, a prolonged 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 firing pin on the primer. Therefore, it is necessary to protect ammunition from moisture and keep the weapon in good condition.

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

When a powder charge is burned, approximately 25-35% of the released energy is spent on imparting forward motion to the bullet (the main work); 15-25% of energy - for performing secondary work (plunging in and overcoming the friction of a bullet when moving along the bore; heating the walls of the barrel, cartridge case and bullet; moving moving parts of the weapon, gaseous and unburnt parts of gunpowder); about 40% of the energy is not used and is lost after the bullet leaves the barrel.

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

Shot periods: Po - boost pressure; Рм - highest (maximum) pressure: Рк and Vк pressure, gases and bullet speed at the moment of the end of gunpowder burning; Pd and Vd gas pressure and bullet speed at the moment it leaves the barrel; Vm - highest (maximum) bullet speed; Ratm - pressure equal to atmospheric

Preliminary period lasts from the beginning of the combustion of the powder charge until the bullet casing completely cuts into the rifling of the barrel. During this period, gas pressure is created in the barrel bore, which is necessary to move the bullet from its place and overcome the resistance of its shell to cut into the rifling of the barrel. This pressure is called boost pressure; it reaches 250 - 500 kg/cm2 depending on the rifling design, the weight of the bullet and the hardness of its shell (for example, for small arms chambered for the Model 1943 cartridge, the boost 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 boost pressure is reached in the barrel bore.

First or main, the period lasts from the beginning of the bullet’s movement until the complete combustion of the powder charge. During this period, combustion of the powder charge occurs in a rapidly changing volume. At the beginning of the period, when the speed of the bullet moving 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 increases and reaches its greatest value (for example, in small arms chambered for 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. Then, due to the rapid increase in the speed of the bullet, the volume of the behind-the-bullet space increases faster than the influx of new gases, and the pressure begins to fall, by the end of the period it is equal to approximately 2/3 of the maximum pressure. The speed of the bullet constantly increases and by the end of the period reaches approximately 3/4 of the initial speed. The powder charge is completely burned shortly before the bullet leaves the barrel.

Second period d lasts from the moment the powder charge is completely burned until the bullet leaves the barrel. With the beginning of this period, the influx of powder gases stops, 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 a Simonov self-loading carbine - 390 kg/cm2, for a Goryunov heavy machine gun - 570 kg/cm2) . The speed of the bullet at the moment it leaves the barrel (muzzle speed) is slightly less than the initial speed.

For some types of small arms, especially short-barreled ones (for example, a Makarov pistol), there is no second period, since 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 barrel until the action of the powder gases on the bullet ceases. During this period, powder gases flowing from the barrel at a speed of 1200-2000 m/sec continue to affect the bullet and impart additional speed to it.

The bullet reaches its highest (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 the movement, flight and effects of projectiles. It is divided into several disciplines. Internal and external ballistics deal with the movement and flight of projectiles. The transition between these two modes is called intermediate ballistics. Terminal ballistics deals with the impact of projectiles, with a separate category covering the extent of target damage. What does internal and external ballistics study?

Guns and rockets

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

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

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

Shot trajectory

Projectiles and launchers

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

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

Internal and external ballistics: briefly about types of weapons

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

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

Fundamentals of external and internal ballistics: main categories

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

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

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

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

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

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

Forensic ballistics

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

Astrodynamics: orbital mechanics

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

Travel of a projectile in flight

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

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

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

From gun to target

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

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

The best bullet composition is lead, which has a high density and is cheap to produce. Its disadvantages are its tendency to soften at >1000 fps, causing it to lubricate the barrel and reduce accuracy, and the lead tends to melt completely. Alloying 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 (hit the target)

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

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

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

Bullet design

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

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

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

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

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

Injury Potential

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

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

Pistol ballistics

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

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