Application of ballistics. What is the ballistic trajectory of a missile or bullet? Ministry of Internal Affairs for the Udmurt Republic

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 fired from small arms 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, it forms a large number of highly heated gases that create 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 following a bullet, when meeting 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 discharged through a hole in the barrel wall (for example, Kalashnikov assault rifle and machine guns, sniper rifle Dragunov, 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 decline in the second period occurs quite quickly and at the muzzle end - the muzzle pressure - is 300-900 kg/cm2 for various types of weapons (for example, self-loading carbine Simonov - 390 kg/cm2, for the 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.

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 rocket in flight, for last years have become more complex. 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. Progress in weapon design has led to the fact that today artillery pieces fire 90-kilogram shells over distances of more than 40 km, anti-tank shells can penetrate 50 cm thick steel armor, and guided missiles can deliver tons of payload to any point on the globe.

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 covered by the projectile, and the number of acting in this moment gases The gun is essentially a single-stroke internal combustion engine in which the projectile moves like a free piston under the pressure of a rapidly expanding gas.

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

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

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

Not required in a recoilless rifle external force 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 a piston to move down the barrel of the 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 curvature are taken into account earth's surface. (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, without which the ability to solve 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 weapon 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 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 be carried out in different environments, such as earth and rocks, under water, near the surface of the earth in normal atmospheric conditions, or in thin air in high altitudes. The main result of the explosion is the formation of a shock wave in 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 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 opposite side plates, the shock wave is reflected as a tensile stress wave. 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. Conducted experimental studies 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. IN different time, measured in microseconds from the beginning of the collision, a sequence of X-ray images was taken. A crater forms on the surface of the plate, and as the images show, plate material is ejected from it. The results of the study of impacts at hypersonic speed make it more clear the formation of craters on celestial bodies, for example on the Moon, in places where meteorites fall.

Wound ballistics.

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

Armor.

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

Combustion.

Research in the field of ignition and combustion is carried out for a twofold purpose. The first is to obtain the data necessary to increase the ability of bullets, shrapnel and incendiary shells to cause fires in the fuel systems of aircraft, missiles, tanks, etc. The second is to increase security Vehicle 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 ignition - electrical sparks, pyrophoric (self-igniting) materials, high-velocity fragments and chemical igniters.

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

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

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

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

• In order to launch the rocket as far as possible, you need to choose the right angle. The best is sharp, about 45º.
• The object has the same initial and final speed.
• The body lands at the same angle as it launches.
• The time it takes for an object to move from the start to the middle, as well as from the middle to the finishing point, is the same.

Trajectory properties and practical implications

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

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

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

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

• Departure(for example, the muzzle of a barrel) - this point is the beginning of the path, and, accordingly, the reference.
• Weapons horizon- this section passes through the departure point. The trajectory crosses it twice: during release and during fall.
• Elevation area- this is a line that is a continuation of the horizon and forms a vertical plane. This area is called the firing plane.
• Trajectory vertices- this is the point that is located in the middle between the starting and ending points (shot and fall), has the highest angle along the entire path.
• Tips- the target or sighting location and the beginning of the object’s movement form the aiming line. An aiming angle is formed between the horizon of the weapon and the final target.

Rockets: features of launch and movement

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

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

• Launch. In this case, the rocket enters the first stage and begins its movement. From this moment, the measurement of the height of the ballistic missile’s flight path begins.
• After about a minute, the second engine starts.
• 60 seconds after the second stage, the third engine starts.
• Then the body enters the atmosphere.
• Lastly, the warheads explode.

Launching a rocket and forming a movement curve

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

Combat projectiles are launched from a fixed point on portable installations, as well as vehicles (ships, submarines). The flight initiation lasts from tenths of a thousandths of a second to several minutes. Free fall constitutes the largest portion of a ballistic missile's flight path.

The advantages of running such a device are:

• Long free flight time. Thanks to this property, fuel consumption is significantly reduced in comparison with other rockets. To fly prototypes (cruise missiles), more economical engines (for example, jets) are used.
• At the speed at which the intercontinental weapon moves (approximately 5 thousand m/s), interception is very difficult.
• The ballistic missile is capable of hitting a target at a distance of up to 10 thousand km.

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

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

Modern developments in ballistics

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

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

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

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

Intercontinental weapons: control theory and components

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

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

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

World developments of special-purpose missiles

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

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

This development has the following advantages:

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

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

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

Characteristics of combat systems of the domestic defense industry

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

The ballistic flight path of such a weapon is almost impossible to predict; accordingly, neutralizing a missile also poses difficulties. The combat power of the projectile is 20 Mt. If this ammunition explodes at a low altitude, the communication, control, and missile defense systems will fail.

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

Among solid fuel missiles, the RT-23 UTTH is considered especially powerful. Such a device is based autonomously (mobile). In the stationary prototype station (“15Zh60”), the starting thrust is 0.3 higher compared to the mobile version.

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

Missile systems and installations of the foreign defense industry

The height of the ballistic trajectory of the American Minuteman-3 missile is not very different from the flight characteristics of domestic inventions.

The complex, which was developed in the USA, is the only “defender” of North America among weapons of this type to this day. Despite the age of the invention, the gun’s stability indicators are quite good even today, because the complex’s missiles could withstand missile defense and also hit a target with high level protection. The active part of the flight is short and lasts 160 seconds.

Another American invention is the Peakkeeper. It could also ensure an accurate hit on the target thanks to the most favorable trajectory of ballistic movement. Experts say that the combat capabilities of the above complex are almost 8 times higher than those of the Minuteman. The Peacekeeper's combat duty was 30 seconds.

Projectile flight and movement in the atmosphere

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

N (y) = 20000-y/20000+y;

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

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

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

Guided weapons of mass destruction of the last century

All weapons of this type can be divided into two groups: ground and airborne. Ground-based devices are those that are launched from stationary stations (for example, mines). Aviation, accordingly, is launched from a carrier ship (aircraft).

The ground group includes ballistic, winged and anti-aircraft missiles. Aviation - projectile aircraft, ADB and guided air combat missiles.

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

Well-known ballistic missiles that are designed for average range flights are: “Titan”, “Thor”, “Jupiter”, “Atlas”, etc.

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

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

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

Outside the gun barrel. There is also a concept terminal(finite) ballistics, having to do with the interaction of the projectile and the body it hits, and the movement of the projectile after impact. Terminal ballistics is carried out by gunsmiths who are specialists in projectiles and bullets, strength specialists and other armor and protection specialists, as well as forensic scientists. Also in practical physics, the law of leverage is used in this direction.

The main task of scientific biology is the mathematical solution of the problem of the dependence of the curved flight (trajectory) of thrown and fired bodies on its factors (powder force, gravity, air resistance, friction). For this purpose, knowledge of higher mathematics is necessary, and the results obtained in this way are of value only for people of science and weapons designers. But it is clear that for a practical soldier, shooting is a matter of simple skill.

Story

The first studies regarding the shape of the projectile flight curve (from firearms) made in 1546 by Tartaglia. Galileo established his parabolic theory through the laws of gravity, in which the influence of air resistance on projectiles was not taken into account. This theory can be applied without much error to the study of the flight of nuclei only with little air resistance. We owe the study of the laws of air resistance to Newton, who proved in 1687 that the flight curve cannot be a parabola. Robins (in 1742) began to determine the initial velocity of the nucleus and invented the ballistic pendulum, which is still in use today. The first real solution to the basic problems of ballistics was given by the famous mathematician Euler. The further movement of B. was given by Gutton, Lombard (1797) and Obenheim (1814). From 1820 onwards, the influence of friction began to be studied more and more, and the physicist Magnus, the French scientists Poisson and Didion and the Prussian Colonel Otto worked a lot in this regard. A new impetus for the development of gunfire was the introduction into general use of rifled firearms and oblong projectiles. B. questions began to be diligently developed by artillerymen and physicists of all countries; to confirm theoretical conclusions, experiments began to be carried out, on the one hand, in artillery academies and schools, on the other hand, in factories producing weapons; for example, very complete experiments to determine air resistance were carried out in St. Petersburg. in 1868 and 1869, according to resolution. gen.-ad. Barantsev, Honored Professor of the Mikhailovsky Artillery Academy, N.V. Maievsky, who provided great services to B., and in England Bashfort. IN Lately On the experimental field of the Krupp cannon factory, the speed of projectiles from guns of different calibers at various points of the trajectory was determined, and very important results were achieved. In addition to N.V. Maievsky, whose merits are properly appreciated by all foreigners, among many scientists, in modern times those who worked on B. are especially noteworthy: prof. Alzh. Lycée Gautier, French artillerymen - gr. Saint Robert, c. Magnus de Sparr, Major Musot, Capt. Jouffre; Italian art. capit. Siacci, who outlined the solution to the problems of aimed shooting in 1880; Noble, Neumann, Pren, Able, Rezal, Sarro and Piobert, who laid the foundation for internal shooting; inventors of ballistic devices - Wheatstone, Konstantinov, Navet, Marcel, Depres, Leboulanger, etc.

Ballistic examination

Examination of small arms on a stand during a ballistic examination.

A type of forensic examination, the task of which is to give investigators answers to technical questions that arise during the investigation of cases of use of firearms. In particular, establishing a correspondence between the fired bullet (as well as the cartridge case and the nature of the destruction caused by the bullet) and the weapon from which the shot was fired.

see also

Notes

Literature

According to external ballistics

• N.V. Mayevsky “External course. B." (SPb., 1870);
• N. V. Mayevsky “On solving problems of aimed and mounted shooting” (No. 9 and 11 “Art. Journal”, 1882)
• N. V. Mayevsky “Exposition of the method of least squares and its application primarily to the study of shooting results” (St. Petersburg, 1881);
• X. G., “On the integration of the equations of rotational motion of an oblong projectile” (No. 1, Art. Journal, 1887);
• N. V. Mayevsky “Trait é de Baiist, exter.” (Paris, 1872);
• Didion, "Trait é de Balist." (Par., 1860);
• Robins, "Nouv. principes d'artil. com. par Euler et trad. par Lombard" (1783);
• Legendre, “Dissertation sur la question de ballst.” (1782);
• Paul de Saint-Robert, "Mè moires scientit." (Vol. I, "Balist", Typ., 1872);
• Otto, "Tables balist, g énèrales pour le tir élevè" (Par., 1844);
• Neumann, “Theorie des Schiessens und Werfens” (“Archiv f. d. Off. d. preus. Art. und. Ing. Corps” 1838 et seq.);
• Poisson, “Recherches sur le mouvement des project” (1839);
• Gels (H élie), “Traité de Baiist, experim.” (Par., 1865);
• Siacci, “Corso di Balistica” (Typ., 1870);
• Magnus de Sparre, “Mouvement des projects oblongs dans le cas du tir du plein fouet” (Par., 1875);
• Muzeau, “Sur le mouv. des project. oblongs dans Pair" (Par., 1878);
• Bashforth, “A mathematical treatise on thy motion of projectiles” (Lond., 1873);
• Tilly, "Balist." (Bruss., 1875);
• Astier, "Balist ext." (Fontainebleau, 1877);
• Rezal (R èsal), “Traité de mec. gener." t. i, "Mouv. des proj. obl. d. l'air" (Par., 1873);
• Mathieu, "Dynamique analyt";
• Siacci, “Nuovo metodo per rivolvere and problemi del tiro” (Giorno di Art. e Gen. 1880, part. II punt 4);
• Otto, “Erörterung über die Mittel für Beurtheilung der Wahrscheinlichkeit des Treffens” (Berl., 1856);
• Didion, “Calcul des probabilit è s applique au tir des project.” (Par., 1858);
• Liagre, “Calcul des probabilit è s”;
• Siacci, “Sur le calcul des tables de tir” (“Giorn. d’Art, et Gen.”, parte II, 1875) Jouffret,
• Siacci, “Sur r è tablisse meut et l’usage des tables de tir” (Paris, 1874);
• Siacci, “Sur la probabilit è du tir des bouches a feu et la methode des moindre carr è s” (Paris, 1875);
• Haupt, “Mathematische Theorie aer Flugbahn der gezog. Geschosse" (Berlin, 1876);
• Gentsch, Ballistik der Handfeuerwaffen (Berlin, 1876).

According to internal ballistics

• Noble and Able, “Investigation of Explosive Compositions; ignition action gunpowder" (translated by V. A. Pashkevich, 1878);
• Piobert, “Propri étè s et effets de la poudre”;
• Piobert, "Mouvement des gazs de la poudre" (1860);
• Paul de St. Robert, “Principes de thermodynamique” (1870);
• Rezal (R èsal), “Recherches sur le mouvement des project. dans des arme s a'feu" (1864);
• A. Rutzki, “Die Theorie der Schiesspr ä parate” (Vienna, 1870);
• M. E. Sarrau “Recherches theorethiqnes sur les effets de la poudre et des substances explosives” (1875);
• M. E. Sarrau “Nouvelles recherches sur les effets de la poudre dans les armes” (1876) and
• M. E. Sarrau “Formules pratiques des vitesse et des pressions dans les armes” (1877).

Links

• Dependence of the trajectory shape on the throwing angle. Path elements
• Korobeinikov A.V., Mityukov N.V. Ballistics of arrows according to archaeological data: an introduction to the problem area. Monograph addressed to students and historical reenactors. Methods for reconstructing arrows from their tips, methods of ballistic examination of ancient settlements to assess their level of protection, models of armor penetration of arrows, etc. are described.

Wikimedia Foundation. 2010.

• Unemployment
• Old Town (Vilnius)

See what “Ballistics” is in other dictionaries:

BALLISTICS- (from the Greek ballein to throw). The science of the movement of heavy bodies thrown into space, mainly artillery shells. Dictionary of foreign words included in the Russian language. Chudinov A.N., 1910. BALLISTICS [Dictionary of foreign words of the Russian language

BALLISTICS- (Ballistics) the science of the movement of a heavy body thrown into space. It is applied primarily to the study of the movement of shells, bullets, and also aerial bombs. Internal B. studies the movement of a projectile inside the gun channel, external B. by the departure of the projectile.... ... Naval Dictionary

BALLISTICS- (German Ballistik, from Greek ballo I throw), 1) the science of the movement of artillery shells, unguided rockets, mines, bombs, bullets when firing (launching). Internal ballistics studies the movement of a projectile in the barrel, external ballistics after its departure. 2) ... Modern encyclopedia

BALLISTICS- BALLISTICS, the science of the movement of projectiles, including bullets, artillery shells, bombs, missiles and GUIDED PROJECTILES. Internal ballistics studies the movement of projectiles in the bore of a gun. External ballistics studies the trajectory of projectiles.… … Scientific and technical encyclopedic dictionary

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 projects the latest in book publishing is a series of books with the titles “... 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'd have to be a real idiot to start collecting ammo without first receiving elementary ideas about 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-handed, pointy-nose, boat-stern bullet has a BC of .493, while the round-nose only has a BC of .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. Next, the bullet will rise above the aiming line until highest point around 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. Halfway Trajectory (HAT) is maximum height raising 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 CCI was useful information and in a good way compare different cartridges and charges, modern system reduction for the same distance, zeroing in height or lowering the bullet in different points trajectories are 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 bookmaker hunting bullet is close to .500, which means that this bullet combines near-optimal cross-sectional density and a streamlined shape, such as Hornady's 7mm 162gr (10.5g) SST with a BC of 0.550 or 180gr (11.7g) XBT from Barnes in thirty gauge with a BC of 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 extremely small frontal surface spout

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 next to each other, then common sense will tell you that the pointed-nosed one is more streamlined than the round-nosed one, and the round-nosed one, in turn, is more streamlined than the flat-nosed one. 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 (261m) would give us a DPV of 340 yards (311m) - not that a big difference, as it might seem, 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.