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

2.3.4 Dependence of the shape of the trajectory on the angle of throw. Trajectory elements

The angle formed by the horizon of the weapon and the continuation of the axis of the bore before the shot is called elevation angle.

However, it is more correct to speak of dependence horizontal range shooting, and consequently, the shape of the trajectory from throw angle, which is the algebraic sum of the elevation angle and the departure angle (Fig. 48).

Rice. 48 - Elevation and throw angle

So, there is a certain relationship between the range of a bullet and the angle of throw.

According to the laws of mechanics, the greatest horizontal flight range in airless space is achieved when the throw angle is 45°. With an increase in the angle from 0 to 45 °, the range of the bullet increases, and from 45 to 90 ° it decreases. The angle of throw at which the horizontal range of the bullet is greatest is called angle longest range .

When flying a bullet in the air, the maximum range angle does not reach 45 °. Its value for modern small arms ranges from 30-35 °, depending on the weight and shape of the bullet.

Trajectories formed at throw angles less than the angle of greatest range (0-35 °) are called flat. Trajectories formed at throwing angles greater than the angle of greatest range (35-90 °) are called hinged(Fig. 49).

Rice. 49 - Flat and mounted trajectories

When studying the movement of a bullet in the air, the designations of the elements of the trajectory are used, indicated in Fig. fifty.

Rice. 50 - Trajectory and its elements:
departure point- the center of the muzzle of the barrel; it is the beginning of the trajectory;
weapon horizon is the horizontal plane passing through the departure point. In the drawings and figures depicting the trajectory from the side, the horizon has the form of a horizontal line;
elevation line- a straight line, which is a continuation of the axis of the bore of the aimed weapon;
throw line- a straight line, which is a continuation of the axis of the bore at the time of the shot. Tangent to the trajectory at the departure point;
firing plane- vertical plane passing through the line of elevation;
elevation angle- the angle formed by the line of elevation and the horizon of the weapon;
throw angle- the angle formed by the line of throw and the horizon of the weapon;
departure angle- the angle formed by the line of elevation and the line of throwing;
drop point- the point of intersection of the trajectory with the horizon of the weapon;
angle of incidence- the angle formed by the tangent to the trajectory at the point of impact and the horizon of the weapon;
horizontal range- distance from the point of departure to the point of fall;
vertex of the trajectory- the highest point of the trajectory above the horizon of the weapon. The vertex divides the trajectory into two parts - the branches of the trajectory;
ascending branch of the trajectory- part of the trajectory from the departure point to the top;
descending branch of the trajectory- part of the trajectory from the top to the point of fall;
trajectory height- distance from the top of the trajectory to the horizon of the weapon.

Since the distances for each type of weapon remain basically the same in sports shooting, many shooters do not even think at what angle of elevation or throw they need to shoot. In practice, it turned out to be much more convenient to replace the throwing angle with another, very similar to it, - aiming angle(Fig. 51). Therefore, deviating somewhat from the presentation of questions external ballistics, we give the elements of aiming weapons (Fig. 52).

Rice. 51 - Line of sight and angle of aim

Rice. 52 - Elements of aiming weapons at the target:
line of sight- a straight line passing from the eye of the shooter through the slots of the sight and the top of the front sight to the aiming point;
aiming point- the point of intersection of the aiming line with the target or the plane of the target (when taking out the aiming point);
aiming angle- the angle formed by the aiming line and the elevation line;
target elevation angle- the angle formed by the aiming line and the horizon of the weapon;
elevation angle is the algebraic sum of the aiming angles and the elevation angle of the target.

The shooter does not interfere with knowing the degree of sloping trajectories of bullets used in sports shooting. Therefore, we present graphs characterizing the excess of the trajectory when firing from various rifles, pistols and revolvers (Fig. 53-57).

Rice. 53 - Exceeding the trajectory above the line of sight when firing a 7.6 mm heavy bullet from a service rifle

Rice. 54 - Exceeding the trajectory of a bullet above the line of sight when firing from a small-caliber rifle (at V 0 =300 m/s)

Rice. 55 - Exceeding the trajectory of a bullet above the aiming line when firing from a small-caliber pistol (at V 0 = 210 m/s)

Rice. 56 - Exceeding the trajectory of a bullet over the line of sight when firing:
a- from a revolver (at V 0 =260 m/s); b- from the PM gun (at V 0 =315 m/s).

Rice. 57 - Exceeding the trajectory of a bullet above the line of sight when firing from a rifle with a 5.6 mm sports and hunting cartridge (at V 0 = 880 m / s)

2.3.5 The dependence of the shape of the trajectory on the value of the muzzle velocity of the bullet, its shape and transverse load

While retaining their basic properties and elements, the trajectories of bullets can differ sharply from one another in their shape: be longer and shorter, have different slopes and curvature. These various changes depend on a number of factors.

Influence of initial speed. If two identical bullets are fired at the same throwing angle with different initial velocities, then the trajectory of the bullet with a greater initial speed, will be higher than the trajectory of the bullet, which had a lower initial speed (Fig. 58).

Rice. 58 - Dependence of the height of the trajectory and the range of the bullet from the initial speed

A bullet flying at a lower initial speed will take longer to reach the target, so under the influence of gravity it will have time to go down much more. It is also obvious that with an increase in speed, the range of its flight will also increase.

Influence of bullet shape. The desire to increase the range and accuracy of shooting required to give the bullet a shape that would allow it to maintain speed and stability in flight as long as possible.

The thickening of air particles in front of the bullet head and the rarefied space zone behind it are the main factors in the air resistance force. The head wave, which sharply increases the deceleration of the bullet, occurs when its speed is equal to the speed of sound or exceeds it (over 340 m / s).

If the speed of the bullet is less than the speed of sound, then it flies at the very crest of the sound wave, without experiencing excessively high air resistance. If it is greater than the speed of sound, the bullet overtakes all sound waves formed in front of its head. In this case, a head ballistic wave occurs, which slows down the flight of the bullet much more, which is why it quickly loses speed.

If you look at the outlines of the bow wave and the air turbulence that arise when bullets of various shapes move (Fig. 59), it can be seen that the pressure on the head of the bullet is the less, the sharper its shape. The area of rarefied space behind the bullet is the smaller, the more its tail is bevelled; in this case, there will also be less turbulence behind the flying bullet.

Rice. 59 - The nature of the outlines of the bow wave that occurs when moving bullets of various shapes

Both theory and practice have confirmed that the most streamlined is the shape of the bullet, which is outlined by the so-called curve of least resistance - cigar-shaped. Experiments show that the coefficient of air resistance, depending only on the shape of the head of the bullet, can vary by one and a half to two times.

Different flight speeds correspond to their own, most advantageous, bullet shape.

When firing at short distances with bullets having a low initial velocity, their shape slightly affects the shape of the trajectory. Therefore, revolver, pistol and small-caliber cartridges they are equipped with blunt bullets: this is more convenient for reloading weapons, and also helps to preserve it from damage (especially shellless ones - to small-caliber weapons).

Given the dependence of shooting accuracy on the shape of the bullet, the shooter must protect the bullet from deformation, make sure that scratches, nicks, dents, etc. do not appear on its surface.

Influence of shear load. The heavier the bullet, the more kinetic energy it has, therefore, the less the force of air resistance affects its flight. However, the ability of a bullet to maintain its speed depends not just on its weight, but on the ratio of weight to the area that meets air resistance. The ratio of the bullet's weight to its largest cross-sectional area is called transverse load(Fig. 60).

Rice. 60 - Cross-sectional area of bullets:
a- to a 7.62 mm rifle; b- to a 6.5 mm rifle; in- to a 9 mm pistol; G- to a 5.6-mm rifle for shooting at a target "Running Deer"; d- to 5.6 mm side-firing rifle (long cartridge).

The transverse load is greater than more weight bullets and smaller caliber. Therefore, with the same caliber, the lateral load is greater for a longer bullet. A bullet with a larger transverse load has both a greater flight range and a more gentle trajectory (Fig. 61).

Rice. 61 - Influence of the transverse load of a bullet on the range of its flight

However, there is a certain limit to the increase in this load. First of all, with an increase in it (with the same caliber) increases total weight bullets, and hence the recoil of the weapon. In addition, an increase in the transverse load due to excessive elongation of the bullet will cause a significant overturning action of its head part back by the force of air resistance. From this they proceed, setting the most favorable dimensions of modern bullets. So, the transverse load of a heavy bullet (weight 11.75 g) for a service rifle is 26 g / cm 2, a small-caliber bullet (weight 2.6 g) - 10.4 g / cm 2.

How great is the influence of the lateral load of a bullet on its flight, can be seen from the following data: a heavy bullet with an initial velocity of about 770 m/s has the greatest flight range of 5100 m, a light bullet with an initial velocity of 865 m/s has only 3400 m.

2.3.6 Dependence of the trajectory on meteorological conditions

Continuously changing while shooting weather conditions can have a significant effect on bullet flight. However, certain knowledge and practical experience help to significantly reduce their harmful effect on shooting accuracy.

Since sport shooting distances are relatively short and the bullet travels them in a very short time, some atmospheric factors, such as air density, will not significantly affect its flight. Therefore, in sports shooting, it is necessary to take into account mainly the influence of wind and, to a certain extent, air temperature.

Wind influence. Headwinds and tailwinds have little effect on shooting accuracy, so shooters usually neglect their effect. So, when shooting at a distance of 600 m, a strong (10 m/sec) head or tail wind changes the STP in height by only 4 cm.

The side wind significantly deflects the bullet to the side, even when shooting at close range.

Wind is characterized by strength (speed) and direction.

The strength of the wind is measured by its speed in meters per second. In shooting practice, wind is distinguished: weak - 2 m / s, moderate - 4-5 m / s and strong - 8-10 m / s.

The strength and direction of the wind arrows are practically determined by various local features: with the help of a flag, by the movement of smoke, by the swaying of grass, bushes and trees, etc. (Fig. 62).

Rice. 62 - Determination of wind strength by flag and smoke

Depending on the strength and direction of the wind, one should either make a lateral correction of the sight, or make a point, aiming in the direction opposite to its direction (taking into account the deflection of bullets under the action of the wind - mainly when shooting at curly targets). In table. Figures 8 and 9 give the values of bullet deflections under the influence of crosswind.

Bullet deflection under the influence of crosswind when firing from rifles of caliber 7.62 mm

Table 8

Firing range, m	Heavy bullet deflection (11.8 g), cm
Firing range, m	light wind (2 m/s)	moderate wind(4 m/s)	strong wind (8 m/s)
100	1	2	4
200	4	8	18
300	10	20	41
400	20	40	84
500	34	68	140
600	48	100	200
700	70	140	280
800	96	180	360
900	120	230	480
1000	150	300	590

Deflection of bullets under the influence of crosswind when firing from a small-caliber rifle

As can be seen from these tables, when shooting at short distances, the deflection of bullets is almost proportional to the strength (speed) of the wind. From Table. 8 also shows that when firing from service and free rifles at 300 m, a side wind with a speed of 1 m / s blows the bullet to the side by one dimension of the target No. 3 (5 cm). These simplified data should be used in practice when determining the value of wind corrections.

An oblique wind (at an angle to the firing plane of 45, 135, 225 and 315 °) deflects a bullet half as much as a side wind.

However, during firing, it is, of course, impossible to make a correction for the wind, so to speak, "formally" guided solely by the data of the tables. This data should only serve as source material and help the shooter navigate in difficult conditions shooting in the wind.

In practice, it rarely happens that in such a relatively small piece of terrain as a shooting range, the wind always had one direction, and even more so the same strength. It usually blows in gusts. Therefore, the shooter needs the ability to time the shot to the moment when the strength and direction of the wind become approximately the same as with previous shots.

Flags are usually posted at the shooting range so that the athlete can determine the strength and direction of the wind. You need to learn how to correctly follow the indications of the flags. Flags should not be relied entirely on when they are high above the target line and the line of fire. It is also impossible to navigate by the flags set at the edge of the forest, steep cliffs, ravines and hollows, since the wind speed in different layers atmosphere, as well as uneven terrain, obstacles is different. As an example, in fig. 63 gives approximate data on wind speed in summer on a plain at various heights from the ground. It is clear that the readings of flags mounted on a high bullet-receiving shaft or on a high mast will not correspond to the true force of the wind, which acts directly on the bullet. It is necessary to be guided by the indications of flags, paper ribbons, etc., set at the same level at which the weapon is located at the time of firing.

Rice. 63 - Approximate data on wind speed in summer at different heights on the plain

It must also be borne in mind that the wind, bending around uneven terrain, obstacles, can create turbulence. If the flags are placed along the entire shooting range, they often show a completely different, even opposite wind direction. Therefore, one should try to determine the main direction and strength of the wind along the entire shooting path, carefully observing individual local landmarks in the area between the shooter and the target.

Naturally, in order to make accurate corrections for the wind, some experience is required. And experience does not come by itself. The shooter must constantly carefully observe and carefully study the effect of wind in general and on a given shooting range in particular, systematically record the conditions under which the shooting is carried out. Over time, he develops a subconscious feeling, gains experience that allows him to quickly navigate in the meteorological situation and make the necessary corrections to ensure accurate shooting in difficult conditions.

Influence of air temperature. The lower the air temperature, the greater its density. A bullet flying in denser air meets a large number of of its particles, and therefore loses its initial speed faster. Therefore, in cold weather, at low temperatures, the firing range decreases and the STP decreases (Table 10).

Moving the midpoint of impact when firing from a rifle of caliber 7.62 mm under the influence of changes in air temperature and powder load for every 10 °

Table 10

Firing range, m	Movement of the STP in height, cm
Firing range, m	light bullet (9.6 g)	heavy bullet (11.8 g)
100	-	-
200	1	1
300	2	2
400	4	4
500	7	7
600	12	12
700	21	19
800	35	28
900	54	41
1000	80	59

The temperature also affects the process of burning the powder charge in the barrel of a weapon. As is known, with an increase in temperature, the burning rate of the powder charge increases, since the heat consumption required to heat and ignite the powder grains decreases. Therefore, the lower the air temperature, the slower there is a process increase in gas pressure. As a result, the initial velocity of the bullet also decreases.

It has been established that a change in air temperature by 1° changes the initial velocity by 1 m/sec. Significant temperature fluctuations between summer and winter lead to changes in the initial speed in the range of 50-60 m/s.

Given this, for zeroing weapons, compiling relevant tables, etc. take a certain "normal" temperature - + 15 °.

Considering the relationship between the temperature of the powder charge and the initial velocity of the bullet, the following must be borne in mind.

During long-term shooting in large series, when the rifle barrel is very hot, one should not allow the next cartridge to stay in the chamber for a long time: relatively heat the heated barrel, being transmitted through the cartridge case to the powder charge, will cause the ignition of the powder to accelerate, which ultimately can lead to a change in the STP and “separations” upwards (depending on the length of time the cartridge stays in the chamber).

Therefore, if the shooter is tired and he needs some rest before the next shot, then during such a break in shooting, the cartridge should not be in the chamber; it should be removed or even replaced with another cartridge from the pack, that is, unheated.

2.3.7 Scattering bullets

Even under the most favorable shooting conditions, each of the fired bullets describes its own trajectory, somewhat different from the trajectories of other bullets. This phenomenon is called natural dispersion.

With a significant number of shots, the trajectories in their totality form sheaf, which, when meeting with the target, gives a series of holes, more or less distant from each other. The area they occupy is called scattering area(fig.64).

Rice. 64 - Sheaf of trajectories, average trajectory, scattering area

All holes are located on the dispersion area around a certain point, called scattering center or mid point of impact (STP). The trajectory located in the middle of the sheaf and passing through the middle point of impact is called average trajectory . When making adjustments to the installation of the sight during the shooting process, it is always this average trajectory that is implied.

For different types of weapons and cartridges, there are certain bullet dispersion standards, as well as bullet dispersion standards according to factory specifications and tolerances for the production of certain types of weapons and batches of cartridges.

With a large number of shots, the dispersion of bullets obeys a certain dispersion law, the essence of which is as follows:

- holes are located unevenly on the dispersion area, most densely grouped around the STP;

- holes are located symmetrically relative to the STP, since the probability of a bullet deflecting in any direction from the STP is the same;

- the scattering area is always limited by a certain limit and has the shape of an ellipse (oval), elongated on a vertical plane in height.

By virtue of this law, as a whole, holes are located on the dispersion area in a regular manner, and therefore in symmetrical strips of equal width, equally distant from the dispersion axes, the same and a certain number of holes are located, although the dispersion areas may have different sizes (depending on the type of weapon and cartridges). The measure of dispersion are: the median deviation, the core band and the radius of the circle containing better half holes (P 50) or all hits (P 100). It should be emphasized that the law of dispersion fully manifests itself with a large number of shots. In sports shooting in relatively small series, the dispersion area approaches the shape of a circle, therefore, the radius of the circle containing 100% of holes (P 100) or the best half of the holes (P 50) (Fig. 65) serves as a measure of dispersion. The radius of the circle that contains all the holes is about 2.5 times the radius of the circle that contains the best half of them. During factory tests of cartridges, when shooting is carried out in small series (usually 20) shots, the circle that includes all holes - P 100 (diameter that includes all holes, see Fig. 16) also serves as a measure of dispersion.

Rice. 65 - Large and small radii of circles containing 100 and 50% hits

So, the natural dispersion of bullets is an objective process that operates independently of the will and desire of the shooter. This is partly true, and it makes no sense to demand from weapons and cartridges that all bullets hit the same point.

At the same time, the shooter must remember that the natural dispersion of bullets is by no means an inevitable norm, once and for all established for a given type of weapon and certain shooting conditions. The art of marksmanship is to know the causes of the natural dispersion of bullets and to reduce their influence. Practice has convincingly proved how important the correct debugging of weapons and the selection of cartridges, the technical readiness of the shooter and the experience of shooting in adverse meteorological conditions are to reduce dispersion.

1.1.1. Shot. Shot periods and their characteristics.

Shot is called the ejection of a bullet 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 phenomenon occurs. From the impact of the striker on the primer of a live cartridge sent into the chamber, the percussion composition of the primer explodes and a flame forms, which through the seed holes in the bottom of the sleeve penetrates to the powder charge and ignites it. When the charge is burned, a large amount of highly heated gases is formed, creating high pressure on the bottom of the bullet, the bottom and walls of the sleeve, as well as on the walls of the barrel and the bolt. As a result of the pressure of gases on the bottom of the bullet, it moves from its place and crashes into the rifling - rotating along them, it moves along the bore at a continuously increasing speed and is thrown out.

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

The shot occurs in a very short period of time (0.001 - 0.06 sec).

When fired, four consecutive periods are distinguished(fig.116):

Preliminary;

First or main;

The third or period of aftereffect of gases.

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

First or main period lasts from the beginning of the movement of the bullet to the moment complete combustion powder charge. During this period, the combustion of the powder charge occurs in a rapidly changing volume.

At the beginning of the period, when the speed of the bullet along the bore is still low, the number of bolts grows faster than the volume of the bullet space (the space between the bottom of the bullet and the bottom of the case), the gas pressure quickly rises and reaches largest. This pressure is called maximum pressure. It is created in small arms when a bullet passes 4-6 cm. of the path. Then, due to the rapid increase in the speed of the bullet, the volume of the bullet space increases faster than the influx of new gases, and the pressure begins to fall. By the end of the period, it is approximately 2/3 of the maximum pressure. The speed of the bullet is constantly increasing and by the end of the period reaches approximately 3/4 of the initial speed. The powder charge completely burns out shortly before the bullet leaves the bore.

The second period lasts from the moment of complete combustion of the powder charge until the moment the bullet leaves the bore. With the beginning of this period, the influx of powder gases stops, however, highly compressed and heated gases expand and, putting pressure on the bullet, increase its speed. The pressure drop in the second period occurs quite quickly and at the muzzle - the muzzle pressure - for various types of weapons is 300-900 kg/cm. The speed of the bullet at the time of its departure from the bore (muzzle velocity) is somewhat less than the initial velocity. For some types of small arms, especially short-barreled ones (for example, the Makarov pistol), there is no second period, since the complete combustion of the powder charge does not actually occur by the time the bullet leaves the barrel.

Rice. 116 - Shot periods

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

1.1.2. Initial and maximum speed.

muzzle velocity(v o) - the speed of the bullet at the muzzle of the barrel.

For initial speed the conditional speed is accepted, which is slightly more than the muzzle and less than the maximum. It is determined empirically with subsequent calculations. The value of the initial velocity of the bullet is indicated in the firing tables and in the combat characteristics of the weapon.

The initial speed is one of the most important characteristics of the combat properties of weapons. With an increase in the initial speed, the range of the bullet increases, the range direct shot, lethal and penetrating action of a bullet, and also the influence of external conditions for her flight.

The muzzle velocity of a bullet depends on:

1) Barrel length.

2) Bullet weight.

3) Weight, temperature and humidity of the powder charge, the shape and size of the powder grains and loading density.

1) The longer the barrel, the more time powder gases act on the bullet and the greater the initial velocity of the bullet.

2) With a constant barrel length and constant weight powder charge, the initial velocity is greater, the lower the weight of the bullet. A change in the weight of the powder charge leads to a change in the amount of powder gases, and, consequently, to a change in the maximum pressure in the bore and the initial velocity of the bullet.

3) The greater the weight of the powder charge, the greater the maximum pressure and muzzle velocity of the bullet. The length of the barrel and the weight of the powder charge increases when designing weapons to the most rational sizes.

With an increase in the temperature of the powder charge, the burning rate of the powder increases, and therefore the maximum pressure and initial speed increase. When the temperature of the charge decreases, the initial velocity decreases. An increase (decrease) in the initial velocity causes an increase (decrease) in the range of the bullet.

In this regard, it is necessary to take into account range corrections for air and charge temperature (charge temperature is approximately equal to air temperature).

With an increase in the humidity of the powder charge, its burning rate and the initial speed of the bullet decrease. The shape and size of the powder have a significant impact on the burning rate of the powder charge, and hence on the muzzle velocity of the bullet. They are selected accordingly when designing weapons.

Loading density is the ratio of the weight of the charge to the volume of the sleeve with the inserted pool (charge combustion chamber). With a deep landing of a bullet, the loading density increases significantly, which can lead to a sharp pressure jump when fired and, as a result, to a rupture of the barrel, so such cartridges cannot be used when firing. With a decrease (increase) in the loading density, the initial velocity of the bullet increases (decreases).

The bullet reaches its greatest (maximum) speed at the end of the third period at a distance of several tens of centimeters from the muzzle of the barrel.

1.1.3 Weapon recoil and takeoff angle (Fig. 117).

Recoil is the movement of the weapon (barrel) back during the shot.. Recoil is felt in the form of a push to the shoulder, arm or ground. The recoil action of a weapon is characterized by the amount of speed and energy that it has when moving backward.

The recoil speed of the weapon is about as many times less than the initial speed of the bullet, how many times the bullet is lighter than the weapon. The recoil energy of hand-held small arms usually does not exceed 2 kgm and is perceived by the shooter painlessly.

When firing from automatic weapons, the device of which is based on the principle of using recoil energy - part of it is spent on communicating movement to moving parts and reloading weapons. Recoil energy is generated when firing from such weapons or 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.

The pressure force of powder gases (recoil force) and the recoil resistance force (butt stop, handles, weapon center of gravity, etc.) are not located on the same straight line and are directed in opposite directions. They form a pair of forces, under the influence of which the muzzle of the weapon barrel deviates upward.

The amount of deflection of the muzzle of the barrel this weapon the more than more shoulder this pair of forces.

In addition, when fired, the barrel of the weapon makes oscillatory movements - it vibrates.

As a result of vibration, the muzzle of the barrel at the moment the bullet takes off can also deviate from its original position in any direction (up, down, right, left). The value of this deviation increases with improper use of the firing stop, contamination of the weapon, etc.

In an automatic weapon with a gas outlet in the barrel, as a result of gas pressure on the front wall of the gas chamber, the muzzle of the weapon barrel, when fired, deviates somewhat in the direction opposite to the location of the gas outlet.

The combination of the influence of barrel vibration, weapon recoil and other causes leads to the formation of an angle between the direction of the axis of the bore before the shot and its direction at the moment the bullet leaves the bore - this angle is called the departure angle.

The departure angle is considered positive when the axis of the bore at the time of the bullet's departure is higher than its position before the shot, and negative when it is lower.

The influence of the departure angle on firing for each weapon is eliminated when it is set to normal combat.

In order to reduce the harmful effect of recoil on the results of shooting, some types of small arms (for example, the Kalashnikov assault rifle) use special devices - compensators. The gases flowing out of the bore, hitting the walls of the compensator, somewhat lower the muzzle of the barrel to the left and down.

1.2. Basic terms and concepts of the theory of external ballistics

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

1.2.1 Bullet flight path and its elements

trajectory called a curved line, described by the center of gravity of a bullet (grenade) in flight (Fig. 118) .

A bullet (grenade) when flying in the air is subjected to two forces :

gravity

Forces of resistance.

The force of gravity causes the bullet (grenade) to gradually drop, and the force of air resistance continuously slows down the movement of the bullet (grenade) and tends to overturn it.

As a result of the action of these forces, the speed of the bullet (grenade) gradually decreases, and its trajectory is an unevenly curved line in shape.

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

The force of air resistance is caused by three main reasons (Fig. 119):

1) Air friction.

2) The formation of swirls.

3) The formation of a ballistic wave.

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

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

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

When the speed of the bullet is higher than the speed of sound, a wave of highly compacted air is created from the incursion of sound waves against each other - a ballistic wave that slows down the speed of the bullet, since the bullet spends part of its energy on creating this wave.

The resultant (total) of all forces, formed due to the influence of air on the flight of a bullet (grenade), is the force of air resistance. The point of application of the resistance force is called the center of resistance. The effect of the resistance force on the flight of a bullet (grenade) is very large. It causes a decrease in the speed and range of a bullet (grenade).

To study the trajectory of a bullet (grenade), the following definitions were adopted (Fig. 120)

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

2) The horizontal plane passing through the departure point, called the weapon horizon. The horizon of the weapon looks like a horizontal line. The trajectory crosses the horizon of the weapon twice: at the point of departure and at the point of impact.

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

4) The vertical plane passing through the line of elevation, called the shooting plane.

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

6) A straight line, which is a continuation of the axis of the bore at the time of the bullet's departure, called the throw line.

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

8) The angle enclosed between the line of elevation and the line of throwing , is called the departure angle.

9) Point of intersection of the trajectory with the horizon of the weapon called the drop point.

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

11) Distance from departure point to drop point is called the total horizontal range.

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

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

14) The highest point of the trajectory called the vertex of the trajectory.

15) The part of the trajectory from the departure point to the top is called the ascending branch; part of the trajectory from the top to the point of impact is called the outgoing branch of the trajectory.

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

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

18) The angle enclosed between the line of elevation and the line of sight, called the aiming angle.

19) The angle enclosed between the aiming line and the horizon of the weapon, called the elevation angle of the target.

20) Distance from the point of departure to the intersection of the trajectory with the line of sight called the target range.

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

23) Distance from the departure point to the target along the target line called slant range.

24) Point of intersection of the trajectory with the surface of the target (land, obstacles) called the meeting point.

25) The angle enclosed between the tangent to the trajectory and the tangent to the surface of the target (ground, obstacles) at the meeting point, called the meeting angle.

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

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

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

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

The lowest speed of a bullet when firing at high angles of throw - at

descending branch of the trajectory, and when firing at small throwing angles - at the point

The time of movement of the bullet on the ascending branch of the trajectory is less than on the descending one.

1.2.2. The shape of the trajectory and its practical value (Fig. 121)

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

Elevation angle, at which the full horizontal range of the bullet (grenade) becomes the greatest, called the angle of greatest range. The value of the angle of greatest range for bullets various kinds arms is about 35 degrees.

Rice. 121 Trajectory shapes

Trajectories obtained with elevation angles, smaller angle longest range, called flat.

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

When firing from the same weapon (at the same initial speeds), you can get two trajectories with the same horizontal range: flat and mounted

Trajectories having the same horizontal range at different elevation angles, are called conjugate.

When firing from small arms and grenade launchers, only flat trajectories are used .

How flatter trajectory, the greater the extent of the terrain, the target can be hit with one sight setting (the less impact on the shooting result is caused by errors in determining the sight setting).

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

The flat trajectory affects the value of the range of a direct shot, struck, covered and dead space.

1.2.3. Direct shot (Fig. 122).

direct shot- a shot in which the trajectory does not rise above the aiming line above the target throughout its entire length.

Within the range of a direct shot in tense moments of the battle, shooting can be carried out without rearranging the sight, while the aiming point in height, as a rule, is chosen at the lower edge of the target.

The range of a direct shot depends on:

target heights;

Flatness of the trajectory;

The higher the target and the flatter the trajectory, the greater the range of a direct shot and the greater the extent of the terrain, the target can be hit with one sight setting. The range of a direct shot can be determined from the tables by comparing the height of the target with the values \u200b\u200bof the greatest excess of the trajectory above the line of sight or with the height of the trajectory.

1.2.4. Affected space (depth of the affected space) (Fig. 123).

When firing at targets located at a distance greater than the range of a direct shot, the trajectory near its top rises above the target and the target is at

some area will not be affected with the same installation of the sight. However, there will be such a space (distance) near the target in which the trajectory does not rise above the target and the target will be hit by it.

Affected space (depth of the affected space) - the distance on the ground during which the descending branch of the trajectory does not exceed the height of the target.

The depth of the affected space depends on:

From the height of the target (it will be the higher, the higher the target);

From the flatness of the trajectory (it will be the greater, the flatter

trajectory);

From the angle of inclination of the terrain (on the front slope it decreases, on the reverse slope

increases).

In the case when the target is located on a slope or there is an elevation angle of the target, the depth of the affected space is determined by the above methods, and the result obtained must be multiplied by the ratio of the angle of incidence to the angle of impact.

The value of the meeting angle depends on the direction of the slope:

On the opposite slope, the meeting angle is equal to the sum of the angles of incidence and slope;

On the reverse slope - the difference of these angles;

In this case, the value of the meeting angle also depends on the elevation angle of the target:

With a negative elevation angle of the target, the meeting angle increases by the magnitude of the elevation angle

With a positive elevation angle of the target, it decreases by its value.

The affected space to some extent compensates for the errors made when choosing a sight, and allows you to round the measured distance to the target up.

To increase the depth of the space to be struck on sloping terrain, the firing position must be chosen so that the terrain in the enemy's disposition, if possible, coincides with the continuation of the aiming line.

1.2.5. Covered space (Fig. 123).

covered space- the space behind the shelter, not penetrated by a bullet, from its crest to the meeting point.

The covered space will be the greater, the greater the height of the shelter and the flatter the trajectory.

Dead (unaffected) space- part of the covered space in which the target cannot be hit with a given trajectory.

Dead space will be the greater, the greater the height of the shelter, the lower the height of the target and the flatter the trajectory. The other part of the covered space in which the target can be hit is the hit space.

The depth of the covered space (PP) can be determined from the tables of excess trajectories over the line of sight. By selection, an excess is found that corresponds to the height of the shelter and the distance to it. After finding the excess, the corresponding setting of the sight and firing range is determined. The difference between a certain range of fire and the range to cover is the depth of the covered space.

The depth of the dead space is equal to the difference between the covered and affected space.

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

Rice. 123 - Covered, dead and affected space

1.2.6. Influence of firing conditions on the flight of a bullet (grenade).

The following are accepted as normal (table) conditions:

A) Meteorological conditions:

Atmospheric (barometric) pressure on the horizon of the weapon 750 mm Hg. ;

The air temperature on the horizon of the weapon is + 15 degrees. WITH. ;

Relative Humidity air 50% (relative humidity

is the ratio of the amount of water vapor in the air to

the largest amount of water vapor that can be contained in the air

at a given temperature);

There is no wind (the atmosphere is still);

B) Ballistic conditions:

Bullet (grenade) weight, muzzle velocity and departure angle are equal to the values

indicated in the shooting tables;

Charge temperature + 15 deg. S.;t

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

The height of the front sight is set according to the data of bringing the weapon to normal combat; - the height (divisions) of the sight correspond to the tabular aiming angles.

C) Topographic conditions:

The target is on the weapon's horizon;

There is no side slope of the weapon;

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

Influence of atmospheric pressure

1) With an increase in atmospheric pressure, the air density increases, and as a result, the air resistance force increases and the range of a bullet (grenade) decreases.

2) With a decrease in atmospheric pressure, the density and force of air resistance decrease, and the range of the bullet increases.

Temperature effect

1) As the temperature rises, the air density decreases, and as a result, the air resistance force decreases and the range of the bullet increases.

2) With a decrease in temperature, the density and force of air resistance increase and the range of a bullet (grenade) decreases.

With an increase in the temperature of the powder charge, the burning rate of the powder, the initial speed and range of the bullet (grenade) increase.

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

Wind influence

1) With a tailwind, the speed of a bullet (grenade) relative to the air decreases. With a decrease in the speed of the bullet relative to the air, the air resistance force decreases. Therefore, with a tailwind, the bullet will fly further than with no wind.

2) With a headwind, the speed of the bullet relative to the air will be greater than with no wind, therefore, the air resistance force will increase and the range of the bullet will decrease

The longitudinal (tail, head) wind has little effect on the flight of a bullet, and in the practice of shooting from small arms, corrections for such a wind are not introduced.

When firing from a grenade launcher, corrections for a strong longitudinal wind should be taken into account.

3) Crosswind exerts pressure on side surface bullets and deflects it away from the firing plane depending on its direction. Crosswind has a significant effect, especially on the flight of a grenade, and must be taken into account when firing grenade launchers and small arms.

4) The wind blowing at an acute angle to the plane of fire, simultaneously affects both the change in the range of the bullet and its lateral deviation.

Influence of air humidity

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

Influence of sight installation

When firing with one sight setting (with one aiming angle), but at different target elevation angles, as a result of a number of reasons, incl. Changes in air density at different heights, and, consequently, the air resistance force, the magnitude of the slope changes ( effective range flight of a bullet (grenade).

When firing at small target elevation angles (up to +_ 15 degrees), this bullet (grenade) flight range changes very slightly, therefore, equality of the inclined and full horizontal bullet flight range is allowed, i.e. the invariance of the shape (rigidity) of the trajectory (Fig. 124).

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

External ballistics

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

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

Bullet trajectory (side view)

Formation of air resistance force

Trajectory and its elements

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

In order for the bullet not to tip over under the action of air resistance, it is given a quick rotary motion.

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

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

Slow conical movement of the bullet

Derivation (Trajectory top view)

The effect of air resistance on the flight of a grenade

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

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

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

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

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

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

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

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

Trajectory elements

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Grenade trajectory (side view)

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

Trajectory shape

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

Angle of greatest range, flat, overhead and conjugate trajectories

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

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

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

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

Exceeding the trajectory of a bullet above the aiming point

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

Ballistics studies the throwing of a projectile (bullet) from a barreled weapon. Ballistics is divided into internal, which studies the phenomena occurring in the barrel at the time of the shot, and external, which explains the behavior of the bullet after leaving the barrel.

Fundamentals of external ballistics

Knowledge of external ballistics (hereinafter referred to as ballistics) allows the shooter even before the shot with sufficient practical application know exactly where the bullet will hit. The accuracy of a shot is influenced by a lot of interrelated factors: the dynamic interaction of parts and parts of the weapon between themselves and the body of the shooter, gas and bullets, bullets with bore walls, bullets with environment after departure from the trunk and much more.

After leaving the barrel, the bullet does not fly in a straight line, but along the so-called ballistic trajectory, close to a parabola. Sometimes at short shooting distances, the deviation of the trajectory from a straight line can be neglected, but at large and extreme shooting distances (which is typical for hunting), knowledge of the laws of ballistics is absolutely necessary.

Note that airguns usually give a light bullet a small or average speed(from 100 to 380 m / s), therefore, the curvature of the trajectory of the flight of a bullet from various influences is more significant than for firearms.

A bullet fired from a barrel at a certain speed is subject to two main forces in flight: gravity and air resistance. The action of gravity is directed downward, it causes the bullet to descend continuously. The action of the air resistance force is directed towards the movement of the bullet, it causes the bullet to continuously reduce its flight speed. All this leads to a downward deviation of the trajectory.

To increase the stability of the bullet in flight on the surface of the bore rifled weapons there are spiral grooves (rifling) that give the bullet a rotational motion and thereby prevent it from tumbling in flight.

Due to the rotation of the bullet in flight

Due to the rotation of the bullet in flight, the force of air resistance acts unevenly on different parts of the bullet. As a result, the bullet encounters more air resistance on one of the sides and in flight deviates more and more from the plane of fire in the direction of its rotation. This phenomenon is called derivation. The action of derivation is uneven and intensifies towards the end of the trajectory.

Powerful air rifles can give the bullet an initial velocity higher than the sound one (up to 360-380 m/s). The speed of sound in air is not constant (depends on atmospheric conditions, height above sea level, etc.), but it can be taken equal to 330-335 m/s. Light bullets for pneumatics with a small transverse load experience strong perturbations and deviate from their trajectory, overcoming sound barrier. Therefore, it is advisable to shoot heavier bullets with an initial velocity approaching to the speed of sound.

The trajectory of a bullet is also affected by weather conditions - wind, temperature, humidity and air pressure.

The wind is considered weak at its speed of 2 m/s, medium (moderate) - at 4 m/s, strong - at 8 m/s. Lateral moderate wind, acting at an angle of 90° to the trajectory, already has a very significant effect on a light and "low-velocity" bullet fired from an airgun. The impact of a wind of the same strength, but blowing at an acute angle to the trajectory - 45 ° or less - causes half the deflection of the bullet.

The wind blowing along the trajectory in one direction or another slows down or speeds up the speed of the bullet, which must be taken into account when shooting at a moving target. When hunting, the wind speed can be estimated with acceptable accuracy using a handkerchief: if you take a handkerchief by two corners, then with a light wind it will sway slightly, with a moderate one it will deviate by 45 °, and with a strong one it will develop horizontally to the surface of the earth.

Normal weather conditions are: air temperature - plus 15 ° C, humidity - 50%, pressure - 750 mm Hg. An excess of air temperature above normal leads to an increase in the trajectory at the same distance, and a decrease in temperature leads to a decrease in the trajectory. High humidity leads to a decrease in the trajectory, and low humidity leads to an increase in the trajectory. Recall that Atmosphere pressure varies not only with the weather, but also with altitude - the higher the pressure, the lower the trajectory.

Each "long-range" weapon and ammunition has its own correction tables, which allow taking into account the influence of weather conditions, derivation, relative position of the shooter and target in height, bullet speed and other factors on the bullet's flight path. Unfortunately, such tables are not published for pneumatic weapons, therefore, lovers of shooting at extreme distances or at small targets are forced to compile such tables themselves - their completeness and accuracy are the key to success in hunting or competitions.

When evaluating the results of firing, it must be remembered that from the moment of firing until the end of its flight, some random (not taken into account) factors act on the bullet, which leads to small deviations in the trajectory of the bullet from shot to shot. Therefore, even under "ideal" conditions (for example, when the weapon is rigidly fixed in the machine, external conditions are constant, etc.), bullet hits on the target look like an oval, thickening towards the center. Such random deviations are called deviation. The formula for its calculation is given below in this section.

And now consider the trajectory of the bullet and its elements (see Figure 1).

The straight line representing the continuation of the axis of the bore before the shot is called the shot line. The straight line, which is a continuation of the axis of the barrel when the bullet leaves it, is called the line of throw. Due to the vibrations of the barrel, its position at the time of the shot and at the moment the bullet leaves the barrel will differ by the angle of departure.

As a result of the action of gravity and air resistance, the bullet does not fly along the line of throw, but along an unevenly curved curve passing below the line of throw.

The start of the trajectory is the departure point. The horizontal plane passing through the departure point is called the weapon's horizon. The vertical plane passing through the point of departure along the line of throw is called the shooting plane.

To throw a bullet to any point on the horizon of the weapon, it is necessary to direct the throwing line above the horizon. The angle formed by the line of fire and the horizon of the weapon is called the angle of elevation. The angle formed by the line of throw and the horizon of the weapon is called the angle of throw.

The point of intersection of the trajectory with the horizon of the weapon is called the (table) point of incidence. The horizontal distance from the departure point to the (table) drop point is called the horizontal range. The angle between the tangent to the trajectory at the point of impact and the horizon of the weapon is called the (table) angle of incidence.

The most high point of the trajectory above the weapon's horizon is called the trajectory apex, and the distance from the weapon's horizon to the trajectory's apex is called the trajectory height. The top of the trajectory divides the trajectory into two unequal parts: the ascending branch is longer and gentler and the descending branch is shorter and steeper.

Considering the position of the target relative to the shooter, three situations can be distinguished:

Shooter and target are on the same level.
- the shooter is located below the target (shoots up at an angle).
- the shooter is located above the target (shoots down at an angle).

In order to direct the bullet to the target, it is necessary to give the axis of the bore a certain position in the vertical and horizontal plane. Giving the desired direction to the axis of the bore in the horizontal plane is called horizontal pickup, and giving direction in the vertical plane is called vertical pickup.

Vertical and horizontal aiming is carried out using sighting devices. Mechanical sights rifled weapons consist of a front sight and a rear sight (or diopter).

The straight line connecting the middle of the slot in the rear sight with the top of the front sight is called the aiming line.

Aiming of small arms with the help of sighting devices is carried out not from the horizon of the weapon, but relative to the location of the target. In this regard, the elements of pickup and trajectory receive the following designations (see Figure 2).

The point at which the weapon is aimed is called the aiming point. The straight line connecting the shooter's eye, the middle of the rear sight slot, the top of the front sight and the aiming point is called the aiming line.

The angle formed by the aiming line and the shooting line is called the aiming angle. This aiming angle is obtained by setting the slot of the sight (or front sight) in height corresponding to the firing range.

The point of intersection of the descending branch of the trajectory with the line of sight is called the point of incidence. The distance from the point of departure to the point of impact is called the target range. The angle between the tangent to the trajectory at the point of incidence and the line of sight is called the angle of incidence.

When positioning weapons and targets at the same height the aiming line coincides with the horizon of the weapon, and the aiming angle coincides with the elevation angle. When positioning the target above or below the horizon weapon between the aiming line and the horizon line, the elevation angle of the target is formed. The elevation angle of the target is considered positive if the target is above the weapon's horizon and negative if the target is below the weapon's horizon.

The elevation angle of the target and the aiming angle together make up the elevation angle. With a negative elevation angle of the target, the line of fire can be directed below the horizon of the weapon; in this case, the elevation angle becomes negative and is called the declination angle.

At its end, the trajectory of the bullet intersects either with the target (obstacle) or with the surface of the earth. The point of intersection of the trajectory with the target (obstacle) or the surface of the earth is called the meeting point. The possibility of ricochet depends on the angle at which the bullet hits the target (obstacle) or the ground, their mechanical characteristics, and the material of the bullet. The distance from the departure point to the rendezvous point is called the actual range. A shot in which the trajectory does not rise above the aiming line above the target throughout the aiming range is called a direct shot.

From the foregoing, it is clear that before practical shooting the weapon must be shot (otherwise it must be brought to a normal battle). Zeroing should be carried out with the same ammunition and under the same conditions that will be typical for subsequent firing. Be sure to take into account the size of the target, the shooting position (lying, kneeling, standing, from unstable positions), even the thickness of clothing (when zeroing in a rifle).

The line of sight, passing from the shooter's eye through the top of the front sight, the top edge of the rear sight and the target, is a straight line, while the trajectory of the bullet's flight is an unevenly curved downward line. The line of sight is located 2-3 cm above the barrel in the case of an open sight and much higher in the case of an optical one.

In the simplest case, if the line of sight is horizontal, the trajectory of the bullet crosses the line of sight twice: on the ascending and descending parts of the trajectory. The weapon is usually zeroed (adjusted sights) at a horizontal distance at which the descending part of the trajectory intersects the line of sight.

It may seem that there are only two distances to the target - where the trajectory crosses the line of sight - at which a hit is guaranteed. So sports shooting fired at a fixed distance of 10 meters, at which the trajectory of the bullet can be considered straight.

For practical shooting (for example, hunting), the firing range is usually much longer and the curvature of the trajectory has to be taken into account. But here the arrow plays into the hands of the fact that the size of the target (slaughter place) in height in this case can reach 5-10 cm or more. If we choose such a horizontal range of sighting of the weapon that the height of the trajectory at a distance does not exceed the height of the target (the so-called direct shot), then aiming at the edge of the target, we will be able to hit it throughout the firing distance.

Point-blank range, at which the height of the trajectory does not rise above the line of sight above the height of the target, is very important characteristic any weapon, which determines the flatness of the trajectory.
The aiming point is usually the lower edge of the target or its center. It is more convenient to aim under the edge when the entire target is visible when aiming.

When shooting, it is usually necessary to introduce vertical corrections if:

Target size is smaller than usual.
the shooting distance is greater than the sighting distance of the weapon.
the shooting distance is closer than the first point of intersection of the trajectory with the line of sight (typical for shooting with a telescopic sight).

Horizontal corrections usually have to be introduced during shooting in windy weather or when shooting at a moving target. Usually, corrections for open sights are introduced by firing ahead (moving the aiming point to the right or left of the target), and not by adjusting the sights.

Bullet flight trajectory, its elements, properties. Types of trajectories and their practical significance

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

A bullet flying through the air is subjected to two forces: gravity and air resistance. The force of gravity causes the bullet to gradually descend, and the force of air resistance continuously slows down the movement of the bullet and tends to knock it over.

As a result of the action of these forces, the bullet's flight speed gradually decreases, and its trajectory is an unevenly curved curved line in shape.

Parameter trajectories	Parameter characteristic	Note
Departure point	Center of muzzle	The departure point is the start of the trajectory
Weapon Horizon	Horizontal plane passing through the departure point	The horizon of the weapon looks like a horizontal line. The trajectory crosses the horizon of the weapon twice: at the point of departure and at the point of impact
elevation line	A straight line that is a continuation of the axis of the bore of the aimed weapon
Shooting plane	The vertical plane passing through the line of elevation
Elevation angle	The angle enclosed between the line of elevation and the horizon of the weapon	If this angle is negative, then it is called the angle of declination (decrease)
Throw line	Straight line, a line that is a continuation of the axis of the bore at the time of the bullet's departure
Throwing angle	The angle enclosed between the line of throw and the horizon of the weapon
Departure angle	The angle enclosed between the line of elevation and the line of throw
drop point	Point of intersection of the trajectory with the horizon of the weapon
Angle of incidence	The angle enclosed between the tangent to the trajectory at the point of impact and the horizon of the weapon
Total horizontal range	Distance from departure point to drop point
Ultimate speed	Bullet speed at point of impact
Total flight time	The time it takes for a bullet to travel from point of departure to point of impact
Top of the path	The highest point of the trajectory
Trajectory height	The shortest distance from the top of the trajectory to the horizon of the weapon
Ascending branch	Part of the trajectory from the departure point to the summit
descending branch	Part of the trajectory from the top to the point of impact
Aiming point (aiming)	The point on or off the target at which the weapon is aimed
line of sight	A straight line passing from the shooter's eye through the middle of the sight slot (level with its edges) and the top of the front sight to the aiming point
aiming angle	The angle enclosed between the line of elevation and the line of sight
Target elevation angle	The angle enclosed between the line of sight and the horizon of the weapon	The target's elevation angle is considered positive (+) when the target is above the weapon's horizon, and negative (-) when the target is below the weapon's horizon.
Sighting range	Distance from the point of departure to the intersection of the trajectory with the line of sight
Exceeding the trajectory above the line of sight	The shortest distance from any point of the trajectory to the line of sight
target line	A straight line connecting the departure point with the target	When firing direct fire, the target line practically coincides with the aiming line
Slant Range	Distance from point of origin to target along target line	When firing direct fire, the slant range practically coincides with the aiming range.
meeting point	Intersection point of the trajectory with the target surface (ground, obstacles)
Meeting angle	The angle enclosed between the tangent to the trajectory and the tangent to the target surface (ground, obstacles) at the meeting point	The smaller of the adjacent angles, measured from 0 to 90°, is taken as the meeting angle.
Sighting line	A straight line connecting the middle of the sight slot to the top of the front sight
Aiming (pointing)	Giving the axis of the bore of the weapon the position in space necessary for firing	In order for the bullet to reach the target and hit it or the desired point on it
Horizontal aiming	Giving the axis of the bore the desired position in the horizontal plane
vertical guidance	Giving the axis of the bore the desired position in the vertical plane

The trajectory of a bullet in the air has the following properties:
- the descending branch is shorter and steeper than the ascending one;
- the angle of incidence is greater than the angle of throw;
- the final speed of the bullet is less than the initial one;
- the smallest bullet flight speed when firing at high angles of throw - on the descending branch of the trajectory, and when firing at small angles of throw - at the point of impact;
- the time of movement of the bullet along the ascending branch of the trajectory is less than along the descending one;
- the trajectory of a rotating bullet due to the lowering of the bullet under the action of gravity and derivation is a line of double curvature.

Types of trajectories and their practical significance

When firing from any type of weapon with an increase in the elevation angle from 0° to 90°, the horizontal range first increases to a certain limit, and then decreases to zero (Fig. 5).

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

The angle of greatest range divides all the trajectories into two types: into the trajectories flat and hinged (Fig. 6).

Flat trajectories are called trajectories obtained at elevation angles smaller than the angle of greatest range (see Fig. trajectories 1 and 2).

Overhead trajectories are called trajectories obtained at elevation angles greater than the angle of greatest range (see Fig. trajectories 3 and 4).

Conjugate trajectories are called trajectories obtained at the same horizontal range by two trajectories, one of which is flat, the other is hinged (see Fig. trajectories 2 and 3).

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

The flatness of the trajectory is characterized by its greatest excess over the aiming line. At a given range, the trajectory is all the more flat, the less it rises above the aiming line. In addition, the flatness of the trajectory can be judged by the magnitude of the angle of incidence: the trajectory is the more flat, the smaller the angle of incidence. The flatness of the trajectory affects the value of the range of a direct shot, struck, covered and dead space.