Bullet flight trajectory, its elements, properties. Types of trajectories and their practical significance. Sniper training. Internal and external ballistics The line of elevation of the trajectory of a grenade bullet is called
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 about the dependence of the horizontal firing range, and, consequently, the shape of the trajectory on 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.
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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 corner 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 at sports shooting distances for each type of weapon remain basically the same, many shooters do not even think at what angle of elevation or throw 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, somewhat deviating from the presentation of issues of 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 arrow passing from the eye through the slots of the sight and the top of the front sight in 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 higher initial velocity will be higher than the trajectory of the bullet with a smaller one. 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 condensation 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, the greater the weight of the bullet and the smaller the 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), the total weight of the bullet increases, 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 are practically determined by arrows by various local features: with the help of a flag, by the movement of smoke, by the vibration 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
| Firing range, m | Heavy bullet deflection (11.8 g), cm | ||
|---|---|---|---|
| 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 flags set at the edge of the forest, steep cliffs, ravines and hollows, since the wind speed in different layers of the atmosphere, as well as at 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 needed. 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 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 middle point hits when firing from a rifle of caliber 7.62 mm under the influence of changes in air temperature and powder outfit for every 10 °
| Firing range, m | Movement of the STP in height, cm | |
|---|---|---|
| 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 the process of increasing 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 be in the chamber for a long time: the relatively high temperature of the heated barrel, transmitted through the cartridge case to the powder charge, will cause the powder to ignite faster, which ultimately can lead to to a change in the STP and "separations" upwards (depending on the length of stay of the cartridge 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 way, 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, a 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 preparedness of the shooter and the experience of shooting in adverse meteorological conditions are to reduce dispersion.
Topic 3. Information from internal and external ballistics.
The essence of the phenomenon of a shot and its period
A shot is the ejection of a bullet (grenade) from the bore of a weapon by the energy of gases formed during the combustion of a powder charge.
When fired from small arms, the following phenomena occur.
From the impact of the striker on the primer of a live cartridge sent into the chamber, the percussion composition of the primer explodes and a flame forms, which through the seed holes in the bottom of the sleeve penetrates to the powder charge and ignites it. During the combustion of a powder (combat) charge, a large amount of highly heated gases are formed, which create high pressure in the bore on the bottom of the bullet, the bottom and walls of the sleeve, as well as on the walls of the barrel and the bolt.
As a result of the pressure of gases on the bottom of the bullet, it moves from its place and crashes into the rifling; rotating along them, it moves along the bore with a continuously increasing speed and is thrown outward, in the direction of the axis of the bore. The pressure of gases on the bottom of the sleeve causes the movement of the weapon (barrel) back. From the pressure of gases on the walls of the sleeve and barrel, they are stretched (elastic deformation), and the sleeve, tightly pressed against the chamber, prevents the breakthrough of powder gases towards the bolt. At the same time, when fired, an oscillatory movement (vibration) of the barrel occurs and it heats up. Hot gases and particles of unburned powder, flowing from the bore after the bullet, when they meet with air, generate a flame and shock wave; the latter is the source of sound when fired.
When fired from automatic weapons, the device of which is based on the principle of using the energy of powder gases vented through a hole in the barrel wall (for example, a Kalashnikov assault rifle and machine guns, a Dragunov sniper rifle, a Goryunov easel machine gun), part of the powder gases, in addition, after passing through the gas outlet bullet, rushes through it into gas chamber, hits the piston and throws the piston with the bolt carrier (pusher with bolt) back.
Until the bolt carrier (bolt stem) travels a certain distance to allow the bullet to exit the bore, the bolt continues to lock the bore. After the bullet leaves the barrel, it is unlocked; the bolt frame and the bolt, moving backward, compress the return (back-action) spring; the shutter at the same time removes the sleeve from the chamber. When moving forward under the action of a compressed spring, the bolt sends the next cartridge into the chamber and again locks the bore.
When fired from an automatic weapon, the device of which is based on the principle of using recoil energy (for example, a Makarov pistol, an automatic pistol of Stechkin, an automatic rifle of the 1941 model), the gas pressure through the bottom of the sleeve is transmitted to the bolt and causes the bolt with the sleeve to move back. This movement begins at the moment when the pressure of the powder gases on the bottom of the sleeve overcomes the inertia of the shutter and the force of the reciprocating mainspring. The bullet by this time is already flying out of the bore. Moving back, the bolt compresses the reciprocating mainspring, then, under the action of the energy of the compressed spring, the bolt moves forward and sends the next cartridge into the chamber.
In some types of weapons (for example, the Vladimirov heavy machine gun, the easel machine gun of the 1910 model), under the action of the pressure of powder gases on the bottom of the sleeve, the barrel first moves back along with the bolt (lock) coupled to it.
After passing a certain distance, ensuring the departure of the bullet from the bore, the barrel and bolt disengage, after which the bolt moves to its rearmost position by inertia and compresses (stretches) the return spring, and the barrel returns to the front position under the action of the spring.
Sometimes, after the striker hits the primer, the shot will not follow, or it will happen with some delay. In the first case, there is a misfire, and in the second, a protracted shot. The cause of a misfire is most often dampness of the percussion composition of the primer or powder charge, as well as a weak impact of the striker on the primer. Therefore, it is necessary to protect the ammunition from moisture and keep the weapon in good condition.
A protracted shot is a consequence of the slow development of the process of ignition or ignition of a powder charge. Therefore, after a misfire, you should not immediately open the shutter, as a protracted shot is possible. If a misfire occurs when firing from mounted grenade launcher, wait at least one minute before discharging it.
During the combustion of a powder charge, approximately 25 - 35% of the energy released is spent on communicating the progressive motion of the pool (the main work);
15 - 25% of energy - for secondary work (cutting and overcoming the friction of a bullet when moving along the bore; heating the walls of the barrel, cartridge case and bullet; moving the moving parts of the weapon, gaseous and unburned parts of gunpowder); about 40% of the energy is not used and is lost after the bullet leaves the bore.
The shot occurs in a very short period of time (0.001 0.06 sec). When fired, four consecutive periods are distinguished: preliminary; first, or main; second; the third, or period of aftereffect of gases (see Fig. 30).
Preliminary period lasts from the beginning of the burning of the powder charge to the complete cutting of the shell of the bullet into the rifling of the barrel. During this period, the gas pressure is created in the barrel bore, which is necessary in order to move the bullet from its place and overcome the resistance of its shell to cutting into the rifling of the barrel. This pressure is called forcing pressure; it reaches 250 - 500 kg / cm 2, depending on the rifling device, the weight of the bullet and the hardness of its shell (for example, for small arms chambered for the 1943 sample, the forcing pressure is about 300 kg / cm 2). It is assumed that the combustion of the powder charge in this period occurs in a constant volume, the shell cuts into the rifling instantly, and the movement of the bullet begins immediately when the forcing pressure is reached in the bore.
First, or main period lasts from the beginning of the movement of the bullet until the moment of complete combustion of the powder charge. During this period, the combustion of the powder charge occurs in a rapidly changing volume. At the beginning of the period, when the speed of the bullet along the bore is still low, the amount of gases grows faster than the volume of the bullet space (the space between the bottom of the bullet and the bottom of the case), the gas pressure rises rapidly and reaches largest(for example, for small arms chambered for the sample of 1943 - 2800 kg / cm 2, and for a rifle cartridge - 2900 kg / cm 2). This pressure is called maximum pressure. It is created in small arms when a bullet travels 4-6 cm of the path. Then, due to the rapid increase in the speed of the bullet, the volume of the bullet space increases faster than the influx of new gases, and the pressure begins to fall, by the end of the period it is equal to about 2/3 of the maximum pressure. The speed of the bullet is constantly increasing and by the end of the period reaches approximately 3/4 of the initial speed. The powder charge completely burns out shortly before the bullet leaves the bore.
Second period lasts from the moment of complete combustion of the powder charge until the moment the bullet leaves the barrel. With the beginning of this period, the influx of powder gases stops, however, highly compressed and heated gases expand and, putting pressure on the bullet, increase its speed. The pressure drop in the second period occurs quite quickly and at the muzzle - muzzle pressure- is 300 - 900 kg / cm 2 for various types of weapons (for example, for Simonov's self-loading carbine 390 kg / cm 2, for easel machine gun Goryunov - 570 kg / cm 2). The speed of the bullet at the time of its departure from the bore (muzzle velocity) is somewhat less than the initial velocity.
For some types of small arms, especially short-barreled ones (for example, the Makarov pistol), there is no second period, since the complete combustion of the powder charge does not actually occur by the time the bullet leaves the barrel.
The third period, or the period of aftereffect of gases lasts from the moment the bullet leaves the bore until the moment the powder gases act on the bullet. During this period, powder gases flowing out of the bore at a speed of 1200 - 2000 m / s continue to act on the bullet and give it additional speed. The bullet reaches its greatest (maximum) speed at the end of the third period at a distance of several tens of centimeters from the muzzle of the barrel. This period ends at the moment when the pressure of the powder gases at the bottom of the bullet is balanced by air resistance.
muzzle velocity
Initial speed (v0) called the speed of the bullet at the muzzle of the barrel.
For the initial speed, the conditional speed is taken, which is slightly more than the muzzle and less than the maximum. It is determined empirically with subsequent calculations. The value of the initial velocity of the bullet is indicated in the firing tables and in the combat characteristics of the weapon.
The initial speed is one of the most important characteristics 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 the bullet, and also the influence of external conditions on its flight is reduced.
The value of the muzzle velocity depends on the length of the barrel; bullet weight; weight, temperature and humidity of the powder charge, shape and size of powder grains and charge density.
The longer the stem, the more time powder gases act on the bullet and the greater the initial velocity.
With a constant barrel length and a constant weight of the powder charge, the initial velocity is greater, the lower the weight of the bullet.
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. 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 increase during the design of the weapon to the most rational dimensions.
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. As the charge temperature decreases, the initial speed decreases. An increase (decrease) in initial velocity causes an increase (decrease) in the range of the bullet. In this regard, it is necessary to take into account range corrections for air and charge temperature (charge temperature is approximately equal to air temperature).
With 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, consequently, on the muzzle velocity of the bullet. They are selected accordingly when designing weapons.
The charge density is the ratio of the weight of the charge to the volume of the sleeve with the inserted pool (charge combustion chambers). With a deep landing of a bullet, the charge density increases significantly, which can lead to a sharp pressure jump when fired and, as a result, to a rupture of the barrel, so such cartridges cannot be used for shooting. With a decrease (increase) in the charge density, the initial velocity of the bullet increases (decreases).
Weapon recoil and launch angle
recoil called 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 kg / m and is perceived by the shooter painlessly.
When firing from an automatic weapon, 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 the weapon. Therefore, the recoil energy when fired from such a weapon is less than when fired from non-automatic 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 (see Fig. 31).
Rice. 31. Weapon recoil
Throwing the muzzle of the weapon barrel up when fired as a result of recoil.
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.
For automatic weapons 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 deviates slightly when fired 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 (y). 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 value of the departure angle is given in the firing tables.
The influence of the departure angle on firing for each weapon is eliminated when it is brought to normal combat. However, in case of violation of the rules for laying weapons, using the stop, as well as the rules for caring for weapons and saving them, the value of the angle of departure and the battle of the weapon change. To ensure the uniformity of the departure angle and reduce the effect of recoil on the results of shooting, it is necessary to strictly follow the shooting techniques and the rules for caring for weapons specified in the manuals on shooting.
In order to reduce the harmful effect of recoil on the results of firing, in some samples of small arms (for example, the Kalashnikov assault rifle), special devices are used - 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.
Features of a shot from hand-held anti-tank grenade launchers
Hand-held anti-tank grenade launchers are dynamo-reactive weapons. When fired from a grenade launcher, part of the powder gases is thrown back through the open breech of the barrel, the resulting reactive force balances the recoil force; the other part of the powder gases puts pressure on the grenade, as in conventional weapons (dynamic action), and gives it the necessary initial speed.
The reactive force when fired from a grenade launcher is formed as a result of the outflow of powder gases through the breech breech. In connection with this, that the area of the bottom of the grenade, which is, as it were, the front wall of the barrel, is larger than the area of \u200b\u200bthe nozzle that blocks the path of gases back, an excess pressure force of powder gases (reactive force) appears, directed in the direction opposite to the outflow of gases. This force compensates for the recoil of the grenade launcher (it is practically absent) and gives the grenade initial speed.
When a grenade jet engine acts in flight, due to the difference in the areas of its front wall and the back wall, which has one or more nozzles, the pressure on the front wall is greater and the generating reactive force increases the speed of the grenade.
The magnitude of the reactive force is proportional to the amount of outflowing gases and the speed of their outflow. The rate of outflow of gases when fired from a grenade launcher is increased with the help of a nozzle (a narrowing and then expanding hole).
Approximately, the value of the reactive force is equal to one tenth of the amount of outflowing gases in one second, multiplied by the speed of their expiration.
The nature of the change in gas pressure in the bore of the grenade launcher is influenced by low loading densities and the outflow of powder gases, therefore, the value of the maximum gas pressure in the grenade launcher barrel is 3-5 times less than in the barrel of small arms. The powder charge of a grenade burns out by the time it leaves the barrel. The charge of the jet engine ignites and burns out when the grenade is flying in the air at some distance from the grenade launcher.
Under the action of the reactive force of the jet engine, the speed of the grenade increases all the time and reaches the greatest value on the trajectory at the end of the outflow of powder gases from the jet engine. Top speed the flight of a grenade is called the maximum speed.
bore wear
In the process of firing, the barrel is subject to wear. The causes of barrel wear can be divided into three main groups - chemical, mechanical and thermal.
As a result of chemical causes, carbon deposits form in the bore, which has big influence for bore wear.
Note. Nagar consists of soluble and insoluble substances. Soluble substances are salts formed during the explosion of the shock composition of the primer (mainly potassium chloride). Insoluble substances of soot are: ash formed during the combustion of a powder charge; tompak, plucked from the shell of a bullet; copper, brass, melted from a sleeve; lead smelted from the bottom of the bullet; iron, melted from the barrel and torn off the bullet, etc. Soluble salts, absorbing moisture from the air, form a solution that causes rust. Insoluble substances in the presence of salts increase rusting.
If, after firing, all the powder deposits are not removed, then the bore for a short time in the places where the chrome is chipped will be covered with rust, after the removal of which traces remain. With the repetition of such cases, the degree of damage to the trunk will increase and may reach the appearance of shells, i.e., significant depressions in the walls of the trunk canal. Immediate cleaning and lubrication of the bore after shooting protects it from rust damage.
The causes of a mechanical nature - impacts and friction of the bullet on the rifling, improper cleaning (cleaning the barrel without using a muzzle lining or cleaning from the breech without a cartridge case inserted into the chamber with a hole drilled in its bottom), etc. - lead to erasing of the rifling fields or rounding corners of the rifling fields, especially their left side, chipping and chipping of chrome in the places of the grid of the ramp.
The reasons for the thermal nature - the high temperature of the powder gases, the periodic expansion of the bore, and its return to its original state - lead to the formation of a fire grid and the contents of the surfaces of the walls of the bore in places where the chromium is chipped.
Under the influence of all these reasons, the bore expands and its surface changes, as a result of which the breakthrough of powder gases between the bullet and the walls of the bore increases, the initial velocity of the bullet decreases and the dispersion of bullets increases. To increase the life of the barrel for firing, it is necessary to follow the established rules for cleaning and inspecting weapons and ammunition, to take measures to reduce the heating of the barrel during firing.
The strength of the barrel is the ability of its walls to withstand a certain pressure of powder gases in the bore. Since the pressure of the gases in the bore during the shot is not the same throughout its entire length, the walls of the barrel are made of different thicknesses - thicker in the breech and thinner towards the muzzle. At the same time, the barrels are made of such a thickness that they can withstand pressure 1.3 - 1.5 times the maximum.
Fig 32. Bloating the trunk
If the pressure of the gases for some reason exceeds the value for which the strength of the barrel is calculated, then the barrel may swell or burst.
Bloating of the trunk can occur in most cases from foreign objects (tow, rags, sand) entering the trunk (see Fig. 32). When moving along the bore, the bullet, having met a foreign object, slows down the movement and therefore the space behind the bullet increases more slowly than with a normal shot. But since the burning of the powder charge continues and the flow of gases increases intensively, increased pressure is created at the point where the bullet slows down; when the pressure exceeds the value for which the strength of the barrel is calculated, swelling and sometimes rupture of the barrel is obtained.
Measures to prevent barrel wear
In order to prevent swelling or rupture of the barrel, you should always protect the bore from foreign objects getting into it, be sure to inspect it before shooting and, if necessary, clean it.
With prolonged use of the weapon, as well as with insufficient preparation for firing, an increased gap between the bolt and the barrel may form, which allows the cartridge case to move backward when fired. But since the walls of the sleeve under the pressure of gases are tightly pressed against the chamber and the friction force prevents the movement of the sleeve, it stretches and, if the gap is large, breaks; a so-called transverse rupture of the sleeve occurs.
In order to avoid case ruptures, it is necessary to check the gap size when preparing the weapon for firing (for weapons with gap regulators), keep the chamber clean and not use contaminated cartridges for firing.
The survivability of the barrel is the ability of the barrel to withstand a certain number of shots, after which it wears out and loses its qualities (the spread of bullets increases significantly, the initial speed and stability of the flight of bullets decrease). The survivability of chrome-plated small arms barrels reaches 20 - 30 thousand shots.
The increase in barrel survivability is achieved proper care for weapons and observance of the regime of fire.
The mode of fire is the maximum number of shots that can be fired in a certain period of time without compromising the material part of the weapon, safety and without compromising shooting results. Each type of weapon has its own fire mode. In order to comply with the fire regime, it is necessary to change the barrel or cool it after a certain number of shots. Failure to comply with the fire regime leads to excessive heating of the barrel and, consequently, to its premature wear, as well as to sharp decline shooting results.
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.
Formation of the flight path of a bullet (grenade)
trajectory called a curved line, described by the center of gravity of a bullet (grenade) in flight (see Fig. 33).
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.
Rice. 33. Bullet trajectory (side view)
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 (grenade) is expended on movement in this medium.
Rice. 34. Formation of resistance force
The force of air resistance is caused by three main causes: air friction, the formation of vortices and the formation of a ballistic wave (see Fig. 34).
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 force of air resistance. The point of application of the resistance force is called 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 150 and an initial speed of 800 m / s. in airless space it would fly to a distance of 32620 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 smoother the surface of the bullet, the lower the friction force and the air resistance force (see Fig. 35).
Rice. 35. The effect of air resistance force on the flight of a bullet:
CG - center of gravity; CA - center of air resistance
The variety of shapes of modern bullets (grenades) is largely determined by the need to reduce the force of air resistance.
Under the influence of initial perturbations (shocks) at the moment the bullet leaves the bore, an angle (b) is formed between the bullet axis and the tangent to the trajectory, and the air resistance force acts not along the bullet axis, but at an angle to it, trying not only to slow down the movement of the bullet, but and knock her over.
In order to prevent the bullet from tipping over under the action of air resistance, it is given a rapid rotational movement with the help of rifling in the bore. For example, when fired from a Kalashnikov assault rifle, the speed of rotation of the bullet at the moment of departure from the bore is about 3000 revolutions per second.
During the flight of a rapidly rotating bullet in the air, the following phenomena occur. The force of air resistance tends to turn the bullet head up and back. But the head of the bullet, as a result of rapid rotation, according to the property of the gyroscope, tends to maintain the given position and deviates not upwards, but very slightly in the direction of its rotation at right angles to the direction of the air resistance force, i.e. to the right.
As soon as the head of the bullet deviates to the right, the direction of the air resistance force will change - it tends to turn the head of the bullet to the right and back, but the head of the bullet does not turn to the right, but down, etc.
Since the action of the air resistance force is continuous, and its direction relative to the bullet changes with each deviation of the bullet axis, 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, as if following a change in the curvature of the trajectory.
The deviation of a bullet from the plane of fire in the direction of its rotation is called derivation. The axis of slow conical motion lags somewhat behind the tangent to the trajectory (located above the latter) (see Fig. 36).
Rice. 36. Slow conical movement of a bullet
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 with right-hand cutting of the barrel) (see Fig. 37).
Rice. 37. Derivation (view of the trajectory from above)
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.
Rice. 38. The effect of the force of air resistance on the flight of a 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 (see Fig. 38).
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 accuracy of fire improves.
To study the trajectory of a bullet (grenade), the following definitions were adopted (see Fig. 39).
The center of the muzzle of the barrel is called the departure point. The departure point is the start of the trajectory.
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.
Rice. 39. Trajectory elements
The angle enclosed between the line of throw and the horizon of the weapon is called the throw angle (6).
The angle enclosed between the line of elevation and the line of throwing is called the departure angle (y).
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 (6).
The distance from the point of departure to the point of impact is called the full horizontal range (X).
The speed of the bullet (grenade) at the point of impact is called the final speed (v).
The time of movement of a bullet (grenade) from the point of departure to the point of impact is called total flight time (T).
The highest point of the trajectory is called the top of the path. The shortest distance from the top of the trajectory to the horizon of the weapon is called trajectory height (U).
The part of the trajectory from the departure point to the top is called ascending branch; the part of the trajectory from the top to the point of fall is called descending branch trajectories.
The point on or off the target at which the weapon is aimed is called aiming point (aiming).
A straight line passing from the shooter's eye through the middle of the sight slot (at the level with its edges) and the top of the front sight to the aiming point is called aiming line.
The angle enclosed between the line of elevation and the line of sight is called aiming angle (a).
The angle enclosed between the line of sight and the horizon of the weapon is called target elevation angle (E). 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
where e is the elevation angle of the target in thousandths;
AT- excess of the target above the horizon of the weapon in meters; D - firing range in meters.
The distance from the departure point to the intersection of the trajectory with the aiming line is called aiming range (d).
The shortest distance from any point of the trajectory to the line of sight is called exceeding the trajectory above the line of sight.
The line joining the departure point with the target is called target line.
The distance from the departure point to the target along the target line is called obliquerange. 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 meeting point. The angle enclosed between the tangent to the trajectory and the tangent to the surface of the target (ground, obstacles) at the meeting point is called meeting angle. The meeting angle is taken as the smaller of the adjacent angles, measured from 0 to 90 degrees.
The trajectory of a bullet in the air is following properties: descending branch is shorter and steeper ascending;
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 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 that 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.
The trajectory of a grenade in the air can be divided into two sections (see Fig. 40): 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- flight grenades by inertia. The shape of the trajectory of a grenade is about the same as that of a bullet.
Rice. 40. Grenade trajectory (side view)
The shape of the trajectory and its practical value
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 (see Figure 40).
The elevation angle at which the full horizontal range of the bullet (grenade) becomes the greatest is called farthest angle. The value of the angle of greatest range for a bullet various kinds arms is about 35 degrees.
Trajectories (see Fig. 41) 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 mounted.
When firing from the same weapon (at the same initial speeds), you can get two trajectories with the same horizontal range: flat and mounted. Trajectories having the same horizontal range at different elevation angles are called conjugated.
Rice. 41. Angle of greatest range, flat, hinged and conjugate trajectories
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 results of shooting have errors in determining the setting of the sight); this is the practical significance of the flat 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.
Example. Compare the flatness of the trajectory when firing from a Goryunov heavy machine gun and a Kalashnikov light machine gun with a 5 sight at a distance of 500 m.
Solution: From the table of excess of average trajectories over the aiming line and the main table, we find that when firing from an easel machine gun at 500 m with a sight 5, the greatest excess of the trajectory over the aiming line is 66 cm and the angle of incidence is 6.1 thousandth; when firing from a light machine gun - respectively 121 cm and 12 thousandths. Consequently, the trajectory of a bullet when firing from an easel machine gun is flatter than the trajectory of a bullet when firing from a light machine gun.
direct shot
The flatness of the trajectory affects the value of the range of a direct shot, struck, covered and dead space.
A shot in which the trajectory does not rise above the aiming line above the target throughout its entire length is called a direct shot (see Fig. 42).
Within the range of a direct shot in tense moments of the battle, shooting can be carried out without rearranging the sight, while the aiming point in height, as a rule, is chosen at the lower edge of the target.
The range of a direct shot depends on the height of the target and the flatness of the trajectory. The higher the target and the flatter the trajectory, the greater the range of a direct shot and the greater the extent of the terrain, the target can be hit with one sight setting.
The range of a direct shot can be determined from 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.
When firing at targets located at a distance greater than the range of a direct shot, the trajectory near its top rises above the target and the target in some area will not be hit with the same sight setting. However, there will be such a space (distance) near the target in which the trajectory does not rise above the target and the target will be hit by it.
Rice. 42. Direct shot
Affected, covered and dead space The distance on the ground during which the descending branch of the trajectory does not exceed the height of the target is called the affected space (the depth of the affected space).
Rice. 43. Dependence of the depth of the affected space on the height of the target and flatness of the trajectory (angle of incidence)
The depth of the affected space depends on the height of the target (it will be the greater, the higher the target), on the flatness of the trajectory (it will be the greater, the flatter the trajectory) and on the angle of the terrain (on the front slope it decreases, on the reverse slope it increases) ( see Fig. 43).
Depth of affected area (Ppr) can determine from the tables the excess of trajectories over the aiming line by comparing the excess of the descending branch of the trajectory by the corresponding firing range with the target height, and in the event that the target height is less than 1/3 of the trajectory height - according to the thousandth formula:
where Ppr- depth of the affected space in meters;
Vts- target height in meters;
os is the angle of incidence in thousandths.
Example. Determine the depth of the affected space when firing from the Goryunov heavy machine gun at the enemy infantry (target height 0 = 1.5 m) at a distance of 1000 m.
Decision. According to the table of excesses of average trajectories above the aiming line, we find: at 1000 m, the excess of the trajectory is 0, and at 900 m - 2.5 m (more than the height of the target). Consequently, the depth of the affected space is less than 100 m. To determine the depth of the affected space, we make up the proportion: 100 m corresponds to an excess of the trajectory of 2.5 m; X m corresponds to an excess of the trajectory of 1.5 m:
Since the height of the target is less than the height of the trajectory, the depth of the affected space can also be determined using the thousandth formula. From the tables we find the angle of incidence Os \u003d 29 thousandths.
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 opposite slope - the difference of these angles. In this case, the value of the meeting angle also depends on the target elevation angle: with a negative target elevation angle, the encounter angle increases by the value of the target elevation angle, with a positive target elevation angle, 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.
The space behind a cover that is not penetrated by a bullet, from its crest to the meeting point is called covered space(see fig. 44). The covered space will be the greater, the greater the height of the shelter and the flatter the trajectory.
The part of the covered space in which the target cannot be hit with a given trajectory is called dead (unaffected) space.
Rice. 44. Covered, dead and affected space
Dead space will be the greater, the greater the height of the shelter, the lower the height of the target and the flatter the trajectory. The other part of the covered space in which the target can be hit is the hit space.
Depth of 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 the firing range are determined. The difference between a certain range of fire and the range to cover is the depth of the covered space.
Influence of firing conditions on the flight of a bullet (grenade)
The tabular trajectory data corresponds to normal firing conditions.
The following are accepted as normal (table) conditions.
a) Meteorological conditions:
atmospheric (barometric) pressure on the horizon of the weapon 750 mm Hg. Art.;
air temperature on the weapon horizon + 15 WITH;
relative air humidity 50% ( relative humidity called the ratio of the amount of water vapor contained 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 WITH; 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;
heights (divisions) of the sight correspond to the tabular aiming angles.
c) Topographic conditions:
the target is on the horizon of the weapon;
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.
With an increase in atmospheric pressure, the air density increases, and as a result, the air resistance force increases and the flight range of a bullet (grenade) decreases. On the contrary, with a decrease in atmospheric pressure, the density and force of air resistance decrease, and the range of the bullet increases. For every 100 m elevation, atmospheric pressure decreases by an average of 9 mm.
When shooting from small arms on flat terrain, range corrections for changes in atmospheric pressure are insignificant and are not taken into account. In mountainous conditions, at an altitude of 2000 m above sea level, these corrections must be taken into account when shooting, guided by the rules specified in the manuals on shooting.
As the temperature rises, the air density decreases, and as a result, the air resistance force decreases and the range of the bullet (grenade) increases. On the contrary, 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.
With a tailwind, the speed of the bullet (grenade) relative to the air decreases. For example, if the speed of the bullet relative to the ground is 800 m/s, and the speed of the tailwind is 10 m/s, then the velocity of the bullet relative to the air will be 790 m/s (800-10).
As the speed of the bullet relative to the air decreases, the force of air resistance decreases. Therefore, with a fair wind, the bullet will fly further than with no wind.
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 grenade launchers, corrections for strong longitudinal wind should be taken into account.
The side wind exerts pressure on the side surface of the bullet and deflects it away from the firing plane depending on its direction: the wind from the right deflects the bullet to the left side, the wind from the left - to the right side.
The grenade on the active part of the flight (when the jet engine is running) deviates to the side where the wind is blowing from: with the wind from the right - to the right, with the wind from the left - to the left. This phenomenon is explained by the fact that the side wind turns the tail of the grenade in the direction of the wind, and the head part against the wind and under the action of a reactive force directed along the axis, the grenade deviates from the firing plane in the direction from which the wind blows. On the passive part of the trajectory, the grenade deviates to the side where the wind blows.
Crosswind has a significant effect, especially on the flight of a grenade (see Fig. 45), and must be taken into account when firing grenade launchers and small arms.
The wind blowing at an acute angle to the firing plane has both an effect on the change in the range of the bullet and on its lateral deflection. 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.
When firing with one sight setting (with one aiming angle), but at different target elevation angles, as a result of a number of reasons, including changes in air density at different heights, and therefore the air resistance force / the value of the slant (sighting) flight range changes bullets (grenades).
When firing at large target elevation angles, the slant range of the bullet changes significantly (increases), therefore, when shooting in the mountains and at air targets, it is necessary to take into account the correction for the target elevation angle, guided by the rules specified in the shooting manuals.
scattering phenomenon
When firing from the same weapon, with the most careful observance of the accuracy and uniformity of the shot, each bullet (grenade) due to a number random reasons describes its trajectory and has its own point of fall (meeting point), which does not coincide with others, as a result of which bullets (grenades) are scattered.
The phenomenon of scattering of bullets (grenades) when firing from the same weapon in almost the same conditions is called natural dispersion of bullets (grenades) and also dispersion of trajectories.
The set of trajectories of bullets (grenades obtained as a result of their natural dispersion) is called a sheaf of trajectories (see Fig. 47). The trajectory passing in the middle of the bundle of trajectories is called the middle trajectory. Tabular and calculated data refer to the average trajectory.
The point of intersection of the average trajectory with the surface of the target (obstacle) is called the middle point of impact or the center of dispersion.
The area on which the meeting points (holes) of bullets (grenades) are located, obtained by crossing a sheaf of trajectories with any plane, is called the scattering area.
The scattering area is usually elliptical in shape. When shooting from small arms at close range, the scattering area in the vertical plane may be in the form of a circle.
Mutually perpendicular lines drawn through the center of dispersion (middle point of impact) so that one of them coincides with the direction of fire are called axes scattering.
The shortest distances from meeting points (holes) to dispersion axes are called deviations
Causes scattering
The causes causing dispersion of bullets (grenades) can be summarized in three groups:
the reasons causing a variety of initial speeds;
reasons causing a variety of throwing angles and shooting directions;
reasons causing a variety of conditions for the flight of a bullet (grenade). The reasons for the variety of initial speeds are:
diversity in the weight of powder charges and bullets (grenades), in the shape and size of bullets (grenades) and shells, in the quality of gunpowder, in the charge density, etc., as a result of inaccuracies (tolerances) in their manufacture; a variety of temperatures, charges, depending on the air temperature and the unequal time spent by the cartridge (grenade) in the barrel heated during firing;
variety in the degree of heating and in the quality condition of the trunk. These reasons lead to fluctuations in the initial speeds, and therefore in the ranges of the bullets (grenades), i.e., they lead to the dispersion of bullets (grenades) in range (height) and depend mainly on ammunition and weapons.
The reasons for the variety of throwing angles and shooting directions are:
variety in horizontal and vertical aiming of weapons (mistakes in aiming);
a variety of launch angles and lateral displacements of the weapon, resulting from a non-uniform preparation for firing, unstable and non-uniform retention of automatic weapons, especially during burst firing, improper use of stops and unsmooth trigger release;
angular oscillations of the barrel when firing with automatic fire, arising from the movement and impact of moving parts and the recoil of the weapon.
These reasons lead to the dispersion of bullets (grenades) in the lateral direction and range (height), have the greatest impact on the magnitude of the dispersion area and mainly depend on the skill of the shooter.
The reasons causing a variety of conditions for the flight of a bullet (grenade) are:
variety in atmospheric conditions, especially in the direction and speed of the wind between shots (bursts);
variety in the weight, shape and size of bullets (grenades), leading to a change in the magnitude of the air resistance force.
These reasons lead to an increase in dispersion in the lateral direction and in range (altitude) and mainly depend on the external conditions of firing and ammunition.
With each shot, all three groups of causes act in different combinations. This leads to the fact that the flight of each bullet (grenades) occurs along a trajectory different from the trajectories of other bullets (grenades).
It is impossible to completely eliminate the causes that cause dispersion, therefore, it is impossible to eliminate the dispersion itself. However, knowing the reasons on which the dispersion depends, it is possible to reduce the influence of each of them and thereby reduce the dispersion, or, as they say, increase the accuracy of fire.
Reducing the dispersion of bullets (grenades) is achieved by excellent training of the shooter, careful preparation of weapons and ammunition for shooting, skillful application of the rules of shooting, proper preparation for shooting, uniform application, accurate aiming (aiming), smooth trigger release, steady and uniform holding of the weapon when shooting, and proper care of weapons and ammunition.
Scattering law
At large numbers shots (more than 20) in the location of the meeting points on the dispersion area, a certain pattern is observed. Dispersion of bullets (grenades) obeys normal law random errors, which in relation to the dispersion of bullets (grenades) is called the law of dispersion. This law is characterized by the following three provisions (see Fig. 48):
1) Meeting points (holes) on the scattering area are unevenly denser towards the center of dispersion and less often towards the edges of the dispersion area.
2) On the scattering area, you can determine the point that is the center of dispersion (middle point of impact). Relative to which the distribution of meeting points (holes) symmetrical: the number of meeting points on both sides of the scattering axes, consisting in absolute limits (bands), is the same, and each deviation from the scattering axis in one direction corresponds to the same deviation in the opposite direction.
3) The meeting points (holes) in each particular case do not occupy an unlimited, but a limited area.
Thus, the scattering law in general view can be formulated like this: with a sufficiently large number of shots fired under practically identical conditions, the dispersion of bullets (grenades) is uneven, symmetrical and not limitless.
Rice. 48. Scattering pattern
Determination of the midpoint of impact
With a small number of holes (up to 5), the position of the midpoint of the hit is determined by the method of successive division of the segments (see Fig. 49). For this you need:
Rice. 49. Determination of the position of the midpoint of the hit by the method of successive division of segments: a) By 4 holes, b) By 5 holes.
connect two holes (meeting points) with a straight line and divide the distance between them in half;
connect the resulting point with the third hole (meeting point) and divide the distance between them into three equal parts;
since the holes (meeting points) are located more densely towards the dispersion center, the division closest to the first two holes (meeting points) is taken as the middle point of hit of the three holes (meeting points); the found middle point of impact for three holes (meeting points) is connected with the fourth hole (meeting point) and the distance between them is divided into four equal parts;
the division closest to the first three holes (meeting points) is taken as the midpoint of the four holes (meeting points).
For four holes (meeting points), the middle point of impact can also be determined as follows: connect the adjacent holes (meeting points) in pairs, connect the midpoints of both lines again and divide the resulting line in half; the division point will be the mid-point of impact. If there are five holes (meeting points), the average point of impact for them is determined in a similar way.
Rice. 50. Determining the position of the midpoint of the hit by drawing dispersion axes. BBi- axis of scattering in height; BBi- dispersion axis in the lateral direction
With a large number of holes (meeting points), based on the symmetry of dispersion, the average point of impact is determined by the method of drawing the axes of dispersion (see Fig. 50). For this you need:
count the right or left half of the breakdowns and (meeting points) in the same order and separate it with the dispersion axis in the lateral direction; the intersection of the dispersion axes is the midpoint of impact. The mid-point of impact can also be determined by the method of calculation (calculation). for this you need:
draw a vertical line through the left (right) hole (meeting point), measure the shortest distance from each hole (meeting point) to this line, add up all the distances from the vertical line and divide the sum by the number of holes (meeting points);
draw a horizontal line through the lower (upper) hole (meeting point), measure the shortest distance from each hole (meeting point) to this line, add up all the distances from the horizontal line and divide the sum by the number of holes (meeting points).
The resulting numbers determine the distance of the midpoint of impact from the specified lines.
The probability of hitting and hitting the target. The concept of the reality of shooting. The reality of the shooting
In the conditions of a fleeting tank firefight, as already mentioned, it is very important to inflict the greatest losses on the enemy in the shortest time and with minimal ammunition consumption.
There is a concept shooting reality, characterizing the results of firing and their compliance with the assigned fire task. In combat conditions, a sign of the high reality of shooting is either the visible defeat of the target, or the weakening of the enemy's fire, or the violation of his battle order, or the withdrawal of manpower into cover. However, the expected reality of the shooting can be assessed even before the opening of fire. To do this, the probability of hitting the target, the expected consumption of ammunition to obtain the required number of hits, and the time required to solve the fire mission are determined.
Hit Probability- this is a value that characterizes the possibility of hitting a target under certain firing conditions and depends on the size of the target, the size of the dispersion ellipse, the position of the average trajectory relative to the target, and, finally, the direction of fire relative to the front of the target. It is expressed either fractional number, or as a percentage.
The imperfection of human vision and sighting devices does not allow, after each shot, the barrel of the weapon to be ideally accurately restored to its previous position. Dead moves and backlashes in the guidance mechanisms also cause the displacement of the barrel of the weapon at the time of the shot in the vertical and horizontal planes.
As a result of the difference in the ballistic shape of the projectiles and the state of its surface, as well as the change in the atmosphere during the time from shot to shot, the projectile can change the direction of flight. And this leads to dispersion both in range and in direction.
With the same dispersion, the probability of hitting, if the center of the target coincides with the center of dispersion, the greater, the more larger size goals. If, however, shooting is carried out at targets of the same size and the average trajectory passes through the target, the probability of hitting is greater, the smaller the dispersion area. The probability of hitting the higher, the closer the center of dispersion is located to the center of the target. When firing at targets that have a large extent, the probability of hitting is higher if the longitudinal axis of the dispersion ellipse coincides with the line of the greatest extent of the target.
In quantitative terms, the hit probability can be calculated in various ways, including by the dispersion core, if the target area does not go beyond it. As already noted, the dispersion core contains the best (in terms of accuracy) half of all holes. Obviously, the probability of hitting the target will be less than 50 percent. as many times as the area of the target is less than the area of the core.
The area of the dispersion core is easy to determine from the special shooting tables available for each type of weapon.
The number of hits required to reliably hit a particular target is usually a known value. So, one direct hit is enough to destroy an armored personnel carrier, two or three hits are enough to destroy a machine-gun trench, etc.
Knowing the probability of hitting a particular target and the required number of hits, it is possible to calculate the expected consumption of projectiles to hit the target. So, if the probability of hitting is 25 percent, or 0.25, and three direct hits are needed to reliably hit the target, then to find out the consumption of shells, the second value is divided by the first.
The balance of time during which the firing task is performed includes the time for preparing the firing and the time for the firing itself. The time for preparing the shooting is determined practically and depends not only on design features weapons, but also the training of the shooter or crew members. To determine the time to fire, the amount of expected ammunition consumption is divided by the rate of fire, i.e., by the number of bullets, shells fired per unit of time. To the figure thus obtained, add the time to prepare for shooting.
trajectory called the curved line described by the center of gravity of the bullet in flight.
A bullet flying through the air is subjected to two forces: gravity and air resistance. The force of gravity causes the bullet to gradually descend, and the force of air resistance continuously slows down the movement of the bullet and tends to 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. Air resistance to the flight of a bullet is caused by the fact that air is an elastic medium and therefore part of the energy of the bullet is expended on movement in this medium.
The force of air resistance is caused by three main causes: air friction, the formation of vortices and the formation of a ballistic wave.
The shape of the trajectory depends on the magnitude of the elevation angle. As the elevation angle increases, the height of the trajectory and the total horizontal range of the bullet increase, but this occurs up to a certain limit. Beyond this limit, the trajectory height continues to increase and the total horizontal range begins to decrease.
The angle of elevation at which the full horizontal range of the bullet is at its greatest is called the angle of greatest range. The value of the angle of greatest range for bullets of various types of weapons is about 35°.
Trajectories obtained at elevation angles, smaller angle longest range are called flat. Trajectories obtained at elevation angles greater than the angle largest angle longest range are called mounted. When firing from the same weapon (at the same initial speeds), you can get two trajectories with the same horizontal range: flat and mounted. Trajectories having the same horizontal range and swarms of different elevation angles are called conjugated.
When shooting from small arms, only flat trajectories are used. The flatter the trajectory, the greater the extent of the terrain, the target can be hit with one sight setting (the less impact on the shooting results is the error in determining the sight setting): this is the practical significance of the trajectory.
The flatness of the trajectory is characterized by its greatest excess over the aiming line. At a given range, the trajectory is all the more flat, the less it rises above the aiming line. In addition, the flatness of the trajectory can be judged by the magnitude of the angle of incidence: the trajectory is the more flat, the smaller the angle of incidence. The flatness of the trajectory affects the value of the range of a direct shot, struck, covered and dead space.
Trajectory elements
Departure point- the center of the muzzle of the barrel. The departure point is the start of the trajectory.
Weapon horizon is the horizontal plane passing through the departure point.
elevation line- a straight line, which is a continuation of the axis of the bore of the aimed weapon.
Shooting plane- a vertical plane passing through the line of elevation.
Elevation angle- the angle enclosed between the line of elevation and the horizon of the weapon. If this angle is negative, then it is called the angle of declination (decrease).
Throw line- a straight line, which is a continuation of the axis of the bore at the time of the bullet's departure.
Throwing angle
Departure angle- the angle enclosed between the line of elevation and the line of throwing.
drop point- the point of intersection of the trajectory with the horizon of the weapon.
Angle of incidence- the angle enclosed between the tangent to the trajectory at the point of impact and the horizon of the weapon.
Total horizontal range- the distance from the point of departure to the point of fall.
final speed- the speed of the bullet (grenade) at the point of impact.
Total flight time- the time of movement of a bullet (grenade) from the point of departure to the point of impact.
Top of the path- the highest point of the trajectory above the horizon of the weapon.
Trajectory height- the shortest distance from the top of the trajectory to the horizon of the weapon.
Ascending branch of the trajectory- part of the trajectory from the departure point to the top, and from the top to the drop point - the descending branch of the trajectory.
Aiming point (aiming)- the point on the target (outside it) at which the weapon is aimed.
line of sight- a straight line passing from the shooter's eye through the middle of the sight slot (at the level with its edges) and the top of the front sight to the aiming point.
aiming angle- the angle enclosed between the line of elevation and the line of sight.
Target elevation angle- the angle enclosed between the aiming line and the horizon of the weapon. This angle is considered positive (+) when the target is higher and negative (-) when the target is below the weapon's horizon.
Sighting range- distance from the departure point to the intersection of the trajectory with the line of sight. The excess of the trajectory over the line of sight is the shortest distance from any point of the trajectory to the line of sight.
target line- a straight line connecting the departure point with the target.
Slant Range- distance from the departure point to the target along the target line.
meeting point- point of intersection of the trajectory with the surface of the target (ground, obstacles).
Meeting angle- the angle enclosed between the tangent to the trajectory and the tangent to the target surface (ground, obstacles) at the meeting point. The meeting angle is taken as the smaller of the adjacent angles, measured from 0 to 90 degrees.
Flight of a bullet in the air
Having flown out of the bore, the bullet moves by inertia and is subjected to the action of two forces of 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. To overcome the force of air resistance, part of the energy of the bullet is expended
The force of air resistance is caused by three main reasons: air friction, the formation of eddies, and the formation of a ballistic wave (Fig. 4)
The bullet collides with air particles during flight and causes them to oscillate. As a result, the air density in front of the bullet increases and sound waves are formed, a ballistic wave is formed. The force of air resistance depends on the shape of the bullet, flight speed, caliber, air density
Rice. 4. Formation of air resistance force
In order to prevent the bullet from tipping over under the action of air resistance, it is given a rapid rotational movement with the help of rifling in the bore. Thus, as a result of the action of gravity and air resistance on the bullet, it will not move uniformly and rectilinearly, but will describe a curved line - a trajectory.
trajectory called the curved line described by the center of gravity of the bullet in flight.
To study the trajectory, the following definitions are adopted (Fig. 5):
· departure point - the center of the muzzle of the barrel, in which the center of gravity of the bullet is located at the time of departure. The moment of departure is the passage of the bottom of the bullet through the muzzle of the barrel;
· weapon horizon - a horizontal plane passing through the departure point;
· elevation line - a straight line, which is a continuation of the axis of the bore at the moment of departure;
· shooting plane - a vertical plane passing through the line of elevation;
· throw line - a straight line, which is a continuation of the axis of the bore at the time of the bullet's departure;
· throw 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 throwing;
· drop point - the point of intersection of the trajectory with the horizon of the weapon,
· injection fall – the angle at the point of impact between the tangent to the trajectory and the horizon of the weapon,
· full horizontal range - distance from point of departure to point of fall,
· top of the trajectory 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 of the trajectory - part of the trajectory from the departure point to its top;
· descending branch of the trajectory - part of the trajectory from the top to the point of fall,
· meeting point - intersection of the trajectory with the surface of the target (ground, obstacles),
· meeting angle - the angle enclosed between the tangent to the trajectory and the tangent to the target surface at the meeting point;
· aiming point - the point on or off the target at which the weapon is aimed,
· line of sight - a straight line from the shooter's eye through the middle of the sight slot and the top of the front sight to the aiming point,
· aiming angle - the angle enclosed between the aiming line and the elevation line;
· target elevation angle the angle enclosed between the aiming line and the horizon of the weapon;
· aiming range - distance from the point of departure to the intersection of the trajectory with the line of sight;
· excess of the trajectory over the aiming line - the shortest distance from any point of the trajectory to the line of sight;
· elevation angle - the angle enclosed between the line of elevation and the horizon of the weapon. The shape of the trajectory depends on the elevation angle
Rice. 5. Bullet trajectory elements
The trajectory of a bullet in the air has the following properties:
The descending branch is steeper than the ascending one;
the angle of incidence is greater than the angle of throw;
The final velocity of the bullet is less than the initial one;
The lowest speed of a bullet when shooting at high angles of throw
on the descending branch of the trajectory, and when firing at small throwing angles - at the point of impact;
the time of movement of the bullet along the ascending branch of the trajectory is less than
descending;
· the trajectory of a rotating bullet due to the decrease under the action of gravity and derivation is a line of double curvature.
The shape of the trajectory depends on the magnitude of the elevation angle (Fig. 6). As the elevation angle increases, the height of the trajectory and the total horizontal range of the bullet increase, but this occurs up to a certain limit. Beyond this limit, the trajectory height continues to increase and the total horizontal range begins to decrease.
Rice. 6. Angle of greatest reach, flat,
hinged and conjugate trajectories
The angle of elevation at which the full horizontal range of the bullet is at its greatest is called the angle of greatest range. The value of the angle of greatest range for small arms is 30-35 degrees, and for the range of artillery systems 45-56 degrees.
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 mounted. When firing from the same weapon, 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 conjugated.
Flat trajectories allow:
1. It is good to hit openly located and fast moving targets.
2. Successfully fire from guns at a long-term firing structure (DOS), a long-term firing point (DOT), from stone buildings at tanks.
3. 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).
Mounted trajectories allow:
1. Hit targets behind cover and in deep terrain.
2. Destroy the ceilings of structures.
These different tactical properties of flat and overhead trajectories can be taken into account when organizing a fire system. The flatness of the trajectory affects the range of a direct shot, the affected and covered space.
Aiming (aiming) weapons at the target.
The objective of any shooting is to hit the target in the shortest possible time and with the least expenditure of ammunition. This problem can be solved only in close proximity to the target and if the target is motionless. In most cases, hitting a target is associated with certain difficulties arising from the properties of the trajectory, meteorological and ballistic conditions shooting and the nature of the target.
Let the target be at point A - at some distance from the firing position. In order for the bullet to reach this point, the barrel of the weapon must be given a certain angle in the vertical plane (Fig. 7).
But from the wind, lateral deflections of the bullet can occur. Therefore, when aiming, it is necessary to take a lateral correction for the wind. Thus, in order for the bullet to reach the target and hit it or the desired point on it, it is necessary to give the axis of the bore a certain position in space (in the horizontal and vertical plane) before firing.
Giving the axis of the bore of a weapon the position in space necessary for firing is called aiming or pointing. Giving the axis of the bore of the weapon the required position in the horizontal plane is called horizontal pickup, and in the vertical plane - vertical pickup.
Rice. 7. Aiming (aiming) with open sight:
O - front sight, a - rear sight, aO - aiming line; сС - the axis of the bore, оО - a line parallel to the axis of the bore: H - the height of the sight, M - the amount of movement of the rear sight;
a - aiming angle; Ub - angle of lateral correction
Accurate solution of aiming problems of any type sights depends on the correct alignment of them on the weapon. Alignment of sights of small arms for shooting at ground targets carried out in the process of checking the combat of the weapon and bringing it to normal combat.
The bullet, having received a certain initial velocity upon departure from the bore, strives by inertia to maintain the magnitude and direction of this velocity.
If the flight of a bullet was made in an airless space, and the force of gravity did not act on it, the bullet would move in a straight line, uniformly and infinitely. However, a bullet flying in the air is subject to forces that change the speed of its flight and the direction of movement. These forces are gravity and air resistance (Fig. 4).
Rice. 4. Forces acting on a bullet during its flight
Due to the combined action of these forces, the bullet loses speed and changes the direction of its movement, moving in the air along a curved line passing below the direction of the axis of the bore.
The line that a moving bullet describes in space (its center of gravity) is called trajectory.
Usually ballistics considers the trajectory over arms horizon- an imaginary infinite horizontal plane passing through the departure point (Fig. 5).
Rice. 5. Horizon weapons
The movement of the bullet, and hence the shape of the trajectory, depends on many conditions. Therefore, in order to understand how the trajectory of a bullet is formed in space, it is necessary to consider first of all how the force of gravity and the drag force of the air medium act on the bullet separately.
The action of gravity. Let us imagine that no force acts on the bullet after it has left the bore. In this case, as mentioned above, the bullet would move by inertia infinitely, uniformly and rectilinearly in the direction of the axis of the bore; for every second it would fly the same distances with a constant speed equal to the initial one. In this case, if the barrel of the weapon were pointed directly at the target, the bullet, following in the direction of the axis of the bore, would hit it (Fig. 6).
Rice. 6. The movement of a bullet by inertia (if there were no gravity and air resistance)
Let us now assume that only one force of gravity acts on the bullet. Then the bullet will begin to fall vertically down, like any free-falling body.
If we assume that gravity acts on the bullet during its flight by inertia in airless space, then under the influence of this force the bullet will fall lower from the continuation of the axis of the bore - in the first second - by 4.9 m, in the second - by 19.6 m etc. In this case, if you point the barrel of the weapon at the target, the bullet will never hit it, because, being subjected to the action of gravity, it will fly under the target (Fig. 7).
Rice. 7. The movement of the bullet (if gravity acted on it,
but no air resistance
It is quite obvious that in order for the bullet to fly a certain distance and hit the target, it is necessary to point the barrel of the weapon somewhere above the target. To do this, it is necessary that the axis of the bore and the plane of the horizon of the weapon make up a certain angle, which is called elevation angle(Fig. 8).
As can be seen from fig. 8, the trajectory of a bullet in airless space, on which the force of gravity acts, is a regular curve, which is called parabola. The most high point trajectory over the horizon of the weapon is called her summit. The part of the curve from the departure point to the apex is called ascending branch. Such a bullet trajectory is characterized by the fact that the ascending and descending branches are exactly the same, and the angle of throw and fall are equal to each other.
Rice. 8. Elevation (bullet trajectory in airless space)
The action of the air resistance force. At first glance, it seems unlikely that the air, which has such a low density, could provide significant resistance to the movement of the bullet and thereby significantly reduce its speed.
However, experiments have established that the force of air resistance acting on a bullet fired from a rifle of the 1891/30 model is a large value - 3.5 kg.
Considering that the bullet weighs only a few grams, it becomes quite obvious the great braking effect that air has on a flying bullet.
During the flight, the bullet spends a significant part of its energy on pushing the air particles that interfere with its flight.
As a photograph of a bullet flying at supersonic speed (over 340 m/s) shows, an air seal forms in front of its head (Fig. 9). From this seal, a head ballistic wave radiates in all directions. Air particles, sliding over the surface of the bullet and breaking off from its side walls, form a zone of rarefied space behind the bullet. In an effort to fill the resulting void behind the bullet, air particles create turbulence, as a result of which a tail wave stretches behind the bottom of the bullet.
The compaction of air ahead of the head of the bullet slows down its flight; the discharged zone behind the bullet sucks it in and thereby further enhances braking; the walls of the bullet experience friction against air particles, which also slows down its flight. The resultant of these three forces is the force of air resistance.
Rice. 9. Photograph of a bullet flying at supersonic speed
(over 340 m/s)
The great influence exerted by air resistance on the flight of a bullet can also be seen from the following example. A bullet fired from a Mosin rifle model 1891/30. or from sniper rifle Dragunov (SVD). Under normal conditions (with air resistance), it has the largest horizontal flight range of 3400 m, and when firing in a vacuum, it could fly 76 km.
Consequently, under the influence of the air resistance force, the trajectory of the bullet loses the shape of a regular parabola, acquiring the shape of an asymmetrical curved line; the top divides it into two unequal parts, of which the ascending branch is always longer and delayed than the descending one. When shooting at medium distances, you can conditionally take the ratio of the length of the ascending branch of the trajectory to the descending one as 3:2.
The rotation of the bullet around its axis. It is known that a body acquires considerable stability if it is given a rapid rotational motion around its axis. An example of the stability of a rotating body is a spinning top toy. A non-rotating “top” will not stand on its pointed leg, but if the “top” is given a quick rotational movement around its axis, it will stand steadily on it (Fig. 10).
In order for the bullet to acquire the ability to deal with the overturning effect of the force of air resistance, to maintain stability during flight, it is given a rapid rotational movement around its longitudinal axis. The bullet acquires this rapid rotational movement due to helical grooves in the bore of the weapon (Fig. 11). Under the action of the pressure of powder gases, the bullet moves forward along the bore, simultaneously rotating around its longitudinal axis. Upon departure from the barrel, the bullet by inertia retains the resulting complex movement - translational and rotational.
Without going into details of the explanation of the physical phenomena associated with the action of forces on a body experiencing complex motion, it is nevertheless necessary to say that a bullet during flight makes regular oscillations and describes circles around the trajectory with its head (Fig. 12). In this case, the longitudinal axis of the bullet, as it were, “follows” the trajectory, describing a conical surface around it (Fig. 13).
Rice. 12. Conical rotation of the bullet head
Rice. 13. Flight of a spinning bullet in the air
If we apply the laws of mechanics to a flying bullet, it becomes obvious that the greater the speed of its movement and the longer the bullet, the more the air tends to overturn it. Therefore, the bullets of cartridges different type it is necessary to give a different speed of rotation. Thus, a light bullet fired from a rifle has a rotation speed of 3604 rpm.
However, the rotational movement of the bullet, so necessary to give it stability during flight, has its negative sides.
As already mentioned, a rapidly rotating bullet is subjected to a continuous overturning force of air resistance, in connection with which the head of the bullet describes a circle around the trajectory. As a result of the addition of these two rotational movements, a new movement arises, deflecting its head part away from the firing plane1 (Fig. 14). In this case, one side surface of the bullet is subjected to particle pressure more than the other. This uneven air pressure side surfaces bullets and deflects them away from the firing plane. The lateral deviation of a rotating bullet from the firing plane in the direction of its rotation is called derivation(Fig. 15).
Rice. 14. As a result of two rotational movements, the bullet gradually turns the head to the right (in the direction of rotation)
Rice. 15. The phenomenon of derivation
As the bullet moves away from the muzzle of the weapon, the value of its derivational deviation increases rapidly and progressively.
When shooting at short and medium distances, derivation is not of great practical importance for the shooter. So, at a firing range at 300 m, the derivational deviation is 2 cm, and at 600 m - 12 cm. Derivation has to be taken into account only for particularly accurate shooting at long distances, making appropriate adjustments to the installation of the sight, in accordance with the table of derivational deviations of a bullet for a certain range shooting.