Properties of a bullet's trajectory in the air. Fundamentals of external ballistics, bullet rotation and derivation. "Rules of shooting from small arms"
2.3.4 Dependence of the trajectory shape on the throwing angle. Path elements
The angle formed by the horizon of the weapon and the continuation of the axis of the barrel bore before the shot is called elevation angle.
However, it is more correct to talk about the dependence of the horizontal firing range, and therefore the shape of the trajectory, on throwing angle, which is the algebraic sum of the elevation angle and the departure angle (Fig. 48).
Rice. 48 - Elevation angle and throwing angle
So, there is a certain relationship between the flight range of a bullet and the throwing angle.
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According to the laws of mechanics, the greatest horizontal flight range in airless space is achieved when the throwing angle is 45°. As the angle increases from 0 to 45°, the range of the bullet increases, and from 45 to 90° it decreases. The throwing angle at which the horizontal range of the bullet is greatest is called angle longest range .
When a bullet flies in the air, the angle of maximum range does not reach 45°. Its size for modern small arms fluctuates between 30-35°, depending on the weight and shape of the bullet.
Trajectories formed at throwing 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 mounted(Fig. 49).
Rice. 49 - Floor and mounted trajectories
When studying the movement of a bullet in the air, the designations of trajectory elements shown in Fig. are used. 50.
Rice. 50 - Trajectory and its elements:
departure point- center of the muzzle of the barrel; it is the beginning of the trajectory;
weapon horizon- horizontal plane passing through the departure point. In drawings and drawings depicting a trajectory from the side, the horizon looks like a horizontal line;
elevation line- a straight line, which is a continuation of the axis of the barrel of the aimed weapon;
throwing line- a straight line, which is a continuation of the axis of the barrel bore at the moment of the shot. Tangent to the trajectory at the departure point;
firing plane- vertical plane passing through the elevation line;
elevation angle- the angle formed by the elevation line and the horizon of the weapon;
throwing angle- the angle formed by the throwing line and the horizon of the weapon;
departure angle- the angle formed by the elevation line and the throwing line;
impact 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 impact;
top of 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- the distance from the top of the trajectory to the horizon of the weapon.
Since the distances for each type of weapon remain largely the same in sport shooting, many shooters do not think at all about what elevation or throwing angle they should shoot at. 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, slightly departing from the presentation of questions external ballistics, we give elements of weapon aiming (Fig. 52).
Rice. 51 - Line of sight and aiming angle
Rice. 52 - Elements of aiming a weapon at a target:
aiming line- a straight arrow passing from the eye through the slots of the sight and the top of the front sight to the aiming point;
aiming point- the point of intersection of the aiming line with the target or target plane (when moving 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- algebraic sum of aiming angles and target elevation angle.
It does not hurt the shooter to know the degree of flatness of the trajectories of bullets used in sports shooting. Therefore, we present graphs characterizing the excess of the trajectory when shooting from various rifles, pistols and revolvers (Fig. 53-57).
Rice. 53 - Exceeding the trajectory above the aiming line when firing a 7.6 mm heavy bullet from a service rifle
Rice. 54 - Excess of the bullet trajectory above the aiming line when shooting from a small-caliber rifle (at V 0 =300 m/sec)
Rice. 55 - Excess of the bullet trajectory above the aiming line when firing from a small-caliber pistol (at V 0 =210 m/sec)
Rice. 56 - Excess of the bullet trajectory above the aiming line when shooting:
A- from a re-barreled revolver (at V 0 =260 m/sec); b- from a PM pistol (at V 0 =315 m/sec).
Rice. 57 - Excess of the bullet trajectory above the aiming line when shooting from a rifle with a 5.6 mm sporting and hunting cartridge (at V 0 = 880 m/sec)
2.3.5 Dependence of the trajectory shape on the initial velocity of the bullet, its shape and lateral load
While retaining their basic properties and elements, bullet trajectories can differ sharply from one another in their shape: be longer and shorter, have different slopes and curvatures. These varied changes depend on a number of factors.
Effect 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 the higher initial speed, will be higher than the trajectory of the bullet, which had a lower initial speed (Fig. 58).
Rice. 58 - Dependence of trajectory height and bullet flight range on initial speed
A bullet flying at a lower initial speed will take more time to reach the target, so under the influence of gravity it will have time to go down significantly more. It is also obvious that with an increase in speed, its flight range will also increase.
Effect of bullet shape. The desire to increase the range and accuracy of shooting required giving the bullet a shape that would allow it to maintain speed and stability in flight for as long as possible.
The condensation of air particles in front of the bullet head and the rarefied zone behind it are the main factors in the force of air resistance. The head wave, which sharply increases the deceleration of a bullet, occurs when its speed is equal to or exceeds the speed of sound (over 340 m/sec).
If the speed of a 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 generated in front of its head. In this case, a head ballistic wave appears, which significantly slows down the flight of the bullet, causing it to quickly lose speed.
If you look at the outlines of the head wave and air turbulence that arise when bullets of different shapes move (Fig. 59), you can see that the sharper its shape, the less pressure on the head of the bullet. The rarefied space zone behind the bullet is smaller, the more beveled its tail part is; in this case, there will also be less turbulence behind the flying bullet.
Rice. 59 - The nature of the outlines of the head wave that occurs during the movement of bullets of different shapes
Both theory and practice have confirmed that the most streamlined shape of the bullet is the one outlined along the so-called curve of least resistance - cigar-shaped. Experiments show that the coefficient of air resistance, depending only on the shape of the bullet head, can change by one and a half to two times.
Different flight speeds have their own, most advantageous, bullet shape.
When shooting at short distances with bullets that have a low initial velocity, their shape has little effect on the shape of the trajectory. Therefore, revolver, pistol and small-caliber cartridges are equipped with blunt-pointed bullets: this is more convenient for reloading weapons, and also helps preserve them from damage (especially non-sheathed ones - for small-caliber weapons).
Considering the dependence of shooting accuracy on the shape of the bullet, the shooter must protect the bullet from deformation and ensure that scratches, nicks, dents, etc. do not appear on its surface.
Effect of lateral load. The heavier the bullet, the more kinetic energy it has, therefore, the less air resistance affects its flight. However, the ability of a bullet to maintain its speed depends not simply on its weight, but on the ratio of weight to area encountering air resistance. The ratio of the weight of a bullet to its largest cross-sectional area is called lateral load(Fig. 60).
Rice. 60 - Cross-sectional area of bullets:
A- to a 7.62 mm rifle; b- to a 6.5 mm rifle; V- to a 9 mm pistol; G- for a 5.6 mm rifle for target shooting “Running Deer”; d- for a 5.6 mm side-fire rifle (long cartridge).
The lateral load is greater, the more more weight bullets and smaller caliber. Consequently, with the same caliber, the lateral load is greater for a longer bullet. A bullet with a greater lateral load has both a longer flight range and a flatter trajectory (Fig. 61).
Rice. 61 - The influence of the lateral load of a bullet on its flight range
However, there is a certain limit to increasing this load. First of all, as it increases (with the same caliber), it increases total weight bullets, and hence the recoil of the weapon. In addition, an increase in lateral load due to excessive elongation of the bullet will cause a significant tilting effect of its head part back by air resistance. This is what we proceed from when establishing the most advantageous dimensions of modern bullets. Thus, the lateral load of a heavy bullet (weight 11.75 g) for a service rifle is 26 g/cm 2 , and a small-caliber bullet (weight 2.6 g) is 10.4 g/cm 2 .
How great the influence of the lateral load of a bullet on its flight is can be seen from the following data: a heavy bullet with an initial speed of about 770 m/sec has a maximum flight range of 5100 m, while a light bullet with an initial speed of 865 m/sec has only 3400 m.
2.3.6 Dependence of the trajectory on meteorological conditions
Continuously changing during shooting weather conditions can have a significant impact on the flight of a bullet. 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 over them in a very short time, some atmospheric factors, such as air density, will not have a significant effect on 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. Thus, when shooting at a distance of 600 m, a strong (10 m/sec) head or tail wind changes the height of the STP by only 4 cm.
The side wind significantly deflects the bullet to the side, even when shooting at close distances.
Wind is characterized by strength (speed) and direction.
The strength of the wind is determined by its speed in meters per second. In shooting practice, winds are distinguished: weak - 2 m/sec, moderate - 4-5 m/sec and strong - 8-10 m/sec.
The strength and direction of the wind are practically determined by the arrows based on various local characteristics: using a flag, by the movement of smoke, the vibration of grass, bushes and trees, etc. (Fig. 62).
Rice. 62 - Determining wind strength by flag and smoke
Depending on the strength and direction of the wind, you should either make a lateral correction of the sight, or move the point, aiming in the direction opposite to its direction (taking into account the deflection of bullets under the influence of the wind - mainly when shooting at figured targets). In table 8 and 9 show the deflection values of bullets under the influence of side winds.
Deflection of bullets under the influence of side winds when firing from 7.62 mm rifles
| Firing range, m | Heavy bullet deflection (11.8 g), cm | ||
|---|---|---|---|
| light wind (2 m/sec) | moderate wind(4 m/sec) | strong wind (8 m/sec) | |
| 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 side wind when shooting 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 the table 8 also shows that when shooting from service and free rifles at 300 m, a side wind with a speed of 1 m/sec blows the bullet to the side by one dimension of target No. 3 (5 cm). These simplified data should be used in practice when determining the magnitude of wind corrections.
Oblique wind (at an angle to the shooting plane of 45, 135, 225 and 315°) deflects the bullet half as much as side wind.
However, during shooting, it is, of course, impossible to make corrections for the wind, so to speak, “formally,” guided solely by the data in the tables. This data should serve only as source material and help the shooter navigate difficult conditions shooting in the wind.
It practically rarely happens that on such a relatively small area of terrain as a shooting range, the wind always has the same direction, much less 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 during previous shots.
Flags are usually hung at the shooting range so that the athlete can determine the strength and direction of the wind. You need to learn to correctly follow the indications of the flags. Flags should not be relied upon entirely if they are mounted high above the target line and line of fire. You also cannot navigate by flags installed at the edge of the forest, steep cliffs, ravines and hollows, since the wind speed is different layers the atmosphere, as well as uneven terrain and obstacles are different. As an example in Fig. 63 provides approximate data on wind speed in summer on the 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. You need to be guided by the readings of flags, paper ribbons, etc., installed at the same level at which the weapon is located during shooting.
Rice. 63 - Approximate data on wind speed in summer at various altitudes on the plain
It should also be borne in mind that the wind, bending around uneven terrain and obstacles, can create turbulence. If flags are installed along the entire shooting distance, they often show completely different, even opposite, wind directions. Therefore, you need to try to determine the main direction and strength of the wind along the entire shooting route, carefully observing individual local landmarks in the area of the terrain lying between the shooter and the target.
Naturally, making accurate wind corrections requires some experience. But experience does not come by itself. The shooter must constantly carefully observe and carefully study the influence of wind in general and at a given shooting range in particular, and systematically record the conditions under which shooting is carried out. Over time, he develops a subconscious feeling and experience that allows him to quickly navigate the meteorological situation and make the necessary adjustments to ensure accurate shooting in difficult conditions.
Effect of air temperature. The lower the air temperature, the greater its density. A bullet flying in denser air encounters large number its particles, and therefore loses its initial speed faster. Therefore, in cold weather, at low temperatures, the firing range decreases and the STP decreases (Table 10).
Moving the average point of impact when shooting from a 7.62 mm rifle under the influence of changes in air temperature and powder charge every 10°
| Firing range, m | STP movement 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 |
Temperature also affects the combustion process of the powder charge in the barrel of a weapon. As is known, with increasing temperature, the burning rate of a 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 is underway increase in gas pressure. As a result, the initial speed of the bullet decreases.
It has been established that a change in air temperature by 1° changes the initial speed by 1 m/sec. Significant temperature fluctuations between summer and winter lead to changes in the initial speed within the range of 50-60 m/sec.
Taking this into account, for zeroing weapons, compiling appropriate 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 kept in mind.
When shooting in large bursts for a long time, when the rifle barrel gets very hot, you should not allow the next cartridge to remain in the chamber for a long time: relatively high temperature the heated barrel, transmitted through the cartridge case to the powder charge, will lead to an acceleration of the ignition of the powder, which ultimately can lead to a change in the STP and upward “breaks” (depending on the duration of the cartridge’s stay in the chamber).
Therefore, if the shooter is tired and 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 replaced altogether with another cartridge from the pack, that is, unheated.
2.3.7 Bullet dispersion
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 a target, produces a number of holes, more or less distant from each other. The area they occupy is called dispersion area(Fig. 64).
Rice. 64 - Sheaf of trajectories, average trajectory, dispersion area
All holes are located on the dispersion area around a certain point called center of dispersion or midpoint of impact (STP). A trajectory located in the middle of the sheaf and passing through midpoint hits are called average trajectory. When making adjustments to the installation of the sight during the shooting process, this average trajectory is always implied.
For different types of weapons and cartridges, there are certain standards for bullet dispersion, as well as standards for bullet dispersion 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:
— the holes are located unevenly across the dispersion area, most densely grouped around the STP;
— the 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 dispersion area is always limited to a certain limit and has the shape of an ellipse (oval), elongated in height on a vertical plane.
By virtue of this law, in general, holes are located on the dispersion area naturally, and therefore, in symmetrical stripes of equal width, equally distant from the dispersion axes, the same and certain number of holes are contained, although the dispersion areas can have different sizes (depending on the type of weapon and cartridges). The measure of dispersion is: median deviation, core band and 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. When shooting sports in relatively small series, the dispersion area approaches the shape of a circle, therefore the measure of dispersion is the value of the radius of the circle that contains 100% of the holes (P 100) or the better half of the holes (P 50) (Fig. 65). The radius of the circle containing all the holes is approximately 2.5 times larger than the radius of the circle containing the best half of them. During factory tests of cartridges, when shooting is carried out in small series (usually 20) of shots, a circle that includes all the holes - P 100 (the diameter that includes all the 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 requiring weapons and ammunition to ensure that all bullets hit the same point is pointless.
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 natural bullet dispersion and reduce their impact. Practice has convincingly proven how important correct debugging of weapons and selection of cartridges, technical preparedness of the shooter and experience of shooting in adverse weather conditions are to reduce dispersion.
Trajectory called a curved line described by the center of gravity of a bullet (grenade) in flight. When flying in the air, a bullet (grenade) is subject to 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 shaped like an unevenly curved curved line. 
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 spent on movement in this environment. The force of air resistance is caused by three main reasons: air friction, the formation of vortices and the formation of a ballistic wave. The shape of the trajectory depends on the elevation angle. As the elevation angle increases, the trajectory height and the full horizontal flight range of the bullet (grenade) increase, but this occurs to a certain limit. Beyond this limit, the trajectory altitude continues to increase, and the total horizontal range begins to decrease. The elevation angle at which the total horizontal flight range of a bullet (grenade) becomes greatest is called the angle of greatest range. The value of the angle of greatest range for bullets various types weapons is about 35°. 
Trajectories obtained at elevation angles smaller angles longest range are called flat. Trajectories obtained at elevation angles greater than the greatest 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 swarms at different elevation angles are called conjugated. When firing from small arms and grenade launchers, only flat trajectories are used. The flatter the trajectory, the greater the area over which the target can be hit with one sight setting (the less impact an error in determining the sight setting has on the shooting results): this is the practical significance of the trajectory. The flatness of the trajectory is characterized by its greatest excess above the aiming line. At a given range, the trajectory is flatter 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 smaller the angle of incidence, the more flat the trajectory. The flatness of the trajectory affects the range direct shot, affected, covered and dead space.
To study the trajectory of a bullet, the following definitions are adopted:
Departure point- center of the muzzle of the barrel. The departure point is the beginning of the trajectory. Weapon Horizon- horizontal plane passing through the departure point. Elevation line- a straight line, which is a continuation of the axis of the barrel of the aimed weapon. Firing plane- a vertical plane passing through the elevation line. Elevation angle- the angle between the elevation line and the horizon of the weapon. If this angle is negative, then it is called the declination (decrease) angle. Throwing line- a straight line, which is a continuation of the axis of the barrel bore at the moment the bullet leaves. Throwing angle Departure angle- the angle between the elevation line and the throwing line. Drop point- the point of intersection of the trajectory with the horizon of the weapon. Angle of incidence- the angle between the tangent to the trajectory at the point of impact and the horizon of the weapon. Full horizontal range- the distance from the point of departure to the point of impact. Final speed- the speed of the bullet (grenade) at the point of impact. Total flight time- time of movement of a bullet (grenade) from the point of departure to the point of impact. Top of the trajectory- the highest point of the trajectory above the horizon of the weapon. Path 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 point of departure to the top, and from the top to the point of fall - the descending branch of the trajectory. Aiming point (aims)- a point on the target (outside it) at which the weapon is aimed. Line of sight- a straight line running 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 between the elevation line and the aiming line. Target elevation angle- the angle between the aiming line and the horizon of the weapon. This angle is considered positive (+) when the target is above, and negative (-) when the target is below the weapon's horizon. Sighting range- the distance from the departure point to the intersection of the trajectory with the aiming line. The excess of the trajectory above the aiming line is the shortest distance from any point on the trajectory to the aiming line. Target line- a straight line connecting the departure point to the target. Slant range- the distance from the departure point to the target along the target line. Meeting point- the point of intersection of the trajectory with the target surface (ground, obstacle). Meeting angle- the angle between the tangent to the trajectory and the tangent to the surface of the target (ground, obstacle) at the meeting point. The meeting angle is taken to be the smaller of the adjacent angles, measured from 0 to 90 degrees.
2.6 Direct shot - a shot in which the top of the bullet’s flight path does not exceed the height of the target.
Within the range of a direct shot, during tense moments of battle, shooting can be carried out without rearranging the sight, while the vertical aiming point is usually selected at the lower edge of the target.
The procedure for partial disassembly of the AK-74:
We disconnect the magazine, remove the safety and twist the bolt carrier, perform a control release, right hand press the spring stop and remove the box cover, disconnect the frame with the piston, remove the bolt from the bolt frame, disconnect the gas tube, disconnect the muzzle brake-compensator, remove the ram.
2.7 The space behind cover that is not penetrated by a bullet, from its crest to the meeting point is called covered space
The part of the covered space in which the target cannot be hit with a given trajectory is called dead space (the more, the higher the height of the shelter)
The part of the covered space in which the target can be hit is called affected area
Derivation(from lat. derivatio- abduction, deflection) in military affairs - deviation of the flight path of a bullet or artillery shell (this applies only to rifled weapons or special ammunition for smooth-bore weapons) under the influence of rotation imparted by the rifling of the barrel, inclined nozzles or inclined stabilizers of the ammunition itself, that is, due to the gyroscopic effect and effect Magnus. The phenomenon of derivation during the movement of oblong projectiles was first described in the works of the Russian military engineer General N.V. Maievsky.
3.1 What statutes are included in the ovu of the Armed Forces of the Russian Federation,
Charter of the internal service of the armed forces of the Russian Federation
Disciplinary Charter of the Armed Forces of the Russian Federation
Charter of the garrison, commandant and guard services of the Armed Forces of the Russian Federation
Drill regulations of the Armed Forces of the Russian Federation
3.2 Military discipline is strict and precise observance by all military personnel of the order and rules established by law Russian Federation, general military regulations of the Armed Forces of the Russian Federation (hereinafter referred to as general military regulations) and orders of commanders (chiefs).
2. Military discipline is based on each serviceman’s awareness of military duty and personal responsibility for the defense of the Russian Federation. It is built on legal basis, respect for the honor and dignity of military personnel.
The main method of instilling discipline in military personnel is persuasion. However, this does not exclude the possibility of using coercive measures against those who are dishonest in fulfilling their military duty.
3. Military discipline obliges every serviceman:
be faithful to the Military Oath (obligation), strictly observe the Constitution of the Russian Federation, the laws of the Russian Federation and the requirements of general military regulations;
perform your military duty skillfully and courageously, conscientiously study military affairs, take care of state and military property;
to unquestioningly carry out assigned tasks in any conditions, including at the risk of life, to steadfastly endure the difficulties of military service;
be vigilant, strictly keep state secrets;
support the rules of relationships between military personnel determined by general military regulations, strengthen military camaraderie;
show respect to commanders (superiors) and each other, observe the rules of military greeting and military courtesy;
behave with dignity in public places, prevent yourself and restrain others from unworthy actions, help protect the honor and dignity of citizens;
comply with the norms of international humanitarian law in accordance with the Constitution of the Russian Federation.
4. Military discipline is achieved:
instilling in military personnel moral, psychological, combat qualities and conscious obedience to commanders (superiors);
knowledge and compliance by military personnel with the laws of the Russian Federation, other regulatory legal acts of the Russian Federation, the requirements of general military regulations and norms of international humanitarian law;
the personal responsibility of each military personnel for the performance of military service duties;
maintaining internal order in a military unit (unit) by all military personnel;
clear organization of combat training and full coverage of personnel;
the daily demands of commanders (chiefs) on subordinates and control over their performance, respect for the personal dignity of military personnel and constant care for them, the skillful combination and correct use of measures of persuasion, coercion and social influence of the team;
creation in the military unit (unit) of the necessary conditions for military service, life and a system of measures to limit the dangerous factors of military service.
5. The commander and deputy commander for educational work are responsible for the state of military discipline in a military unit (unit), who must constantly maintain military discipline, demand that subordinates observe it, encourage the worthy, and strictly but fairly punish the negligent.
Military discipline must be observed in the unit; it is a necessary condition for the functioning of the army.
The effectiveness of work to strengthen military discipline in the armed forces largely depends on the activities of the officer in charge, and the state of law and order and discipline among subordinates is the main criterion for assessing the daily activities of commanders.
28% of the death toll, goes by number suicide
Consistency and the habit of strict order.
Discipline is Teaching, science.
The characteristic features of military discipline are:
Unity of command
Strict regulation of all aspects of the life and activities of military personnel
Commitment and unconditional performance
Clear chain of command
The inevitability and severity of coercive measures against violators of military discipline.
For the formation of a team, the essential factors are:
High performance
Healthy public opinion (take into account the opinion of the team)
Sense of responsibility
General optimistic mood of the team
Willingness to overcome difficulties
Analysis of the state of military discipline:
Requirements for an officer: must think logically, formulate arguments correctly, reason, and draw conclusions.
Master the rules of formal logic
Stages of analytical work on studying the state of military discipline:
Making a plan
Collection of information
Data processing
Identification of the reasons for violation of military disciplines
3.3 Internal order and how it is achieved. Fire safety measures in V.Ch. and divisions
Internal order is strict adherence to the rules of accommodation, daily activities, and life of military personnel in a military unit (unit) determined by military regulations and the performance of daily duty.
Internal order is achieved:
deep understanding, conscious and accurate fulfillment by all military personnel of the duties defined by laws and military regulations;
targeted educational work, a combination of the high demands of commanders (superiors) with constant care for subordinates and the preservation of their health;
clear organization of combat training;
exemplary performance combat duty and daily duty service;
accurate implementation of the daily routine and work time regulations;
compliance with the rules of operation (use) of weapons, military equipment and other material resources; creating conditions in the locations of military personnel for their daily activities, life and everyday life that meet the requirements of military regulations;
compliance with requirements fire safety, as well as taking measures to protect the environment in the area where the military unit operates.
Fire safety measures:
The territory of the military unit must be constantly cleared of debris and dry grass.
military property must be equipped with lightning protection devices and other engineering systems that ensure its fire and explosion safety in accordance with the requirements of current standards and regulations.
Entrances to sources of fire water supply, to buildings and all passages through the territory must always be free for the movement of fire engines. Also, passages within the unit and subdivision must be unobstructed.
It is forbidden to light a fire and keep an open fire closer than 50m from the military unit. Use faulty equipment and use flammable materials. Telephone sets must have inscriptions indicating the telephone number of the nearest fire brigade, and on the territory of a military unit there must be sound alarms to sound a fire alarm. These and other fire safety standards must be checked daily by the duty officer.
An order is an order from a commander-in-chief addressed to subordinates and requiring the mandatory execution of certain actions, compliance with rules, or establishing some order of its issuance. In writing or by technical communication to one or a group of military personnel. Discussion of an order is not permissible. Failure to comply with an order given in the prescribed manner is a crime against military service.
An order is a form of communication by the commander of tasks to subordinates on private issues. Issued in writing or orally. Issued in writing by the chief of staff, is an administrative document and is issued from the estate of the unit commander
When giving orders, the commander must not abuse his official powers. Do not give orders that are not related to the conduct of military service.
The order is formulated clearly and concisely. Issued in order of subordination.
Completed unquestioningly accurately and on time.
The serviceman answers “yes.”
Unity of command
It consists of vesting the commander (chief) with full administrative power in relation to his subordinates and assigning personal responsibility to him for all aspects of the life and activities of the military unit, unit and each serviceman.
determines the construction of the army as a centralized military organism, the unity of training and education of personnel, organization and discipline and, ultimately, the high combat readiness of troops. It should be noted that it best ensures the unity of will and actions of all personnel, strict centralization, maximum flexibility and efficiency of troop leadership. Unity of command allows the commander to act boldly, decisively, and show broad initiative, placing on the commander personal responsibility for all aspects of the life of the troops, and contributes to the development of the necessary leadership qualities in officers. It creates conditions for high organization, strict military discipline and firm order.
External ballistics. Trajectory and its elements. Excess of the bullet's flight path above the aiming point. Path shape
External ballistics
External ballistics is a science that studies the movement of a bullet (grenade) after the action of powder gases on it ceases.
Having flown out of the barrel under the influence of powder gases, the bullet (grenade) moves by inertia. A grenade with a jet engine moves by inertia after the gases flow out of the jet engine.
Bullet trajectory (side view)
Formation of air resistance force
Trajectory and its elements
A trajectory is a curved line described by the center of gravity of a bullet (grenade) in flight.
When flying in the air, a bullet (grenade) is subject to 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 shaped like an unevenly curved curved line.
Air resistance to the flight of a bullet (grenade) is caused by the fact that air is an elastic medium and therefore part of the energy of the bullet (grenade) is expended on movement in this medium.
The force of air resistance is caused by three main reasons: air friction, the formation of vortices and the formation of a ballistic wave.
Air particles in contact with a moving bullet (grenade), due to internal cohesion (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 varies 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 part.
A rarefied space is formed behind the bottom of the bullet, resulting in a pressure difference between the head and bottom parts. This difference creates a force directed in the direction opposite to the movement of the bullet, and reduces its flight speed. Air particles, trying to fill the vacuum formed behind the bullet, create a vortex.
When flying, a bullet (grenade) collides with air particles and causes them to vibrate. As a result, the air density in front of the bullet (grenade) increases and sound waves are formed. Therefore, the flight of a bullet (grenade) is accompanied by a characteristic sound. When the speed of a bullet (grenade) 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 speed of the bullet (grenade). When the bullet's flight speed is greater than the speed of sound, the sound waves collide with each other to create a wave of highly compressed air - a ballistic wave that slows down the bullet's flight speed, since the bullet spends part of its energy creating this wave.
The resultant (total) of all forces generated as a result of the influence of air on the flight of a bullet (grenade) is the force of air resistance. The point of application of the resistance force is called the center of resistance.
The effect of air resistance on the flight of a bullet (grenade) is very great; it causes a decrease in the speed and range of a bullet (grenade). For example, a bullet arr. 1930, with a throwing angle of 15° and an initial speed of 800 m/sec in airless space, it would fly to a distance of 32,620 m; the flight range of this bullet under the same conditions, but in the presence of air resistance, is only 3900 m.
The magnitude of the air resistance force depends on the flight speed, shape and caliber of the bullet (grenade), as well as on its surface and air density.
The force of air resistance increases with increasing bullet speed, caliber and air density.
At supersonic bullet flight speeds, when the main cause of air resistance is the formation of air compaction in front of the warhead (ballistic wave), bullets with an elongated pointed head are advantageous. At subsonic flight speeds of a grenade, when the main cause of air resistance is the formation of rarefied space and turbulence, grenades with an elongated and narrowed tail section are advantageous.
The effect of air resistance on the flight of a bullet: CG - center of gravity; CS - center of air resistance
The smoother the surface of the bullet, the less frictional force. air resistance force.
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 disturbances (shocks) at the moment the bullet leaves the barrel, an angle (b) is formed between the axis of the bullet and the tangent to the trajectory, and the force of air resistance acts not along the axis of the bullet, but at an angle to it, trying not only to slow down the movement of the bullet, but and knock it over.
To prevent the bullet from tipping over under the influence of air resistance, it is given a fast rotational movement.
For example, when fired from a Kalashnikov assault rifle, the rotation speed of the bullet at the moment it leaves the barrel is about 3000 rpm.
When a rapidly rotating bullet flies through 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 its given position and will not deviate upward, but very slightly in the direction of its rotation at a right angle 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 action of the air resistance force will change - it tends to turn the head of the bullet to the right and back, but the rotation of the head of the bullet will not occur to the right, but down, etc. Since the action of the air resistance force is continuous, but its direction relative to the bullet changes with each deviation of the bullet’s axis, then the head of the bullet describes a circle, and its axis is a cone with its apex at the center of gravity. The so-called slow conical, or precessional, movement occurs, and the bullet flies with its head forward, i.e., as if following the change in the curvature of the trajectory.
Slow conical bullet motion
Derivation (top view of trajectory)
The effect of air resistance on the flight of a grenade
The axis of slow conical motion lags somewhat behind the tangent to the trajectory (located above the latter). Consequently, the bullet collides with the air flow more with its lower part and the axis of slow conical movement deviates in the direction of rotation (to the right with a right-hand rifling of the barrel). The deviation of a bullet from the firing plane in the direction of its rotation is called derivation.
Thus, the reasons for derivation are: the rotational movement of the bullet, air resistance and a decrease in the tangent to the trajectory under the influence of gravity. In the absence of at least one of these reasons, there will be no derivation.
In shooting tables, derivation is given as a direction correction in thousandths. However, when shooting from small arms, the amount of derivation is insignificant (for example, at a distance of 500 m it does not exceed 0.1 thousandths) and its influence on the shooting results is practically not taken into account.
The stability of the grenade in flight is ensured by the presence of a stabilizer, which allows the center of air resistance to be moved back, beyond the center of gravity of the grenade.
As a result, the force of air resistance turns the axis of the grenade to a tangent to the trajectory, forcing the grenade to move forward with its head.
To improve accuracy, some grenades are given a slow rotation due to the outflow of gases. Due to the rotation of the grenade, the moments of force deflecting the axis of the grenade act consistently in different directions, so shooting improves.
To study the trajectory of a bullet (grenade), the following definitions are adopted.
The center of the muzzle of the barrel is called the take-off point. The departure point is the beginning of the trajectory.
Path elements
The horizontal plane passing through the point of departure is called the horizon of the weapon. In drawings showing the weapon and 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.
The straight line, which is a continuation of the axis of the barrel of the aimed weapon, is called the elevation line.
The vertical plane passing through the elevation line is called the shooting plane.
The angle between the elevation line and the horizon of the weapon is called the elevation angle. If this angle is negative, then it is called the declination (decrease) angle.
The straight line, which is a continuation of the axis of the barrel bore at the moment the bullet leaves, is called the throwing line.
The angle between the throwing line and the horizon of the weapon is called the throwing angle.
The angle between the elevation line and the throwing line is called the launch angle.
The point of intersection of the trajectory with the weapon's horizon is called the point of impact.
The angle between the tangent to the trajectory at the point of impact and the horizon of the weapon is called the angle of incidence.
The distance from the point of departure to the point of impact is called the total horizontal range.
The speed of the bullet (grenade) at the point of impact is called the final speed.
The time it takes a bullet (grenade) to travel from the point of departure to the point of impact is called full time flight.
The highest point of the trajectory is called the trajectory vertex.
The shortest distance from the top of the trajectory to the horizon of the weapon is called the trajectory height.
The part of the trajectory from the departure point to the top is called the ascending branch; the part of the trajectory from the top to the falling point is called the descending branch of the trajectory.
The point on or off the target at which the weapon is aimed is called the aiming point.
A straight line running from the shooter's eye through the middle of the sight slot (level with its edges) and the top of the front sight to the aiming point is called the aiming line.
The angle between the elevation line and the aiming line is called the aiming angle.
The angle between the aiming line and the horizon of the weapon is called the target elevation angle. 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 thousandths formula.
The distance from the departure point to the intersection of the trajectory with the aiming line is called the aiming range.
The shortest distance from any point on the trajectory to the aiming line is called the excess of the trajectory above the aiming line.
The straight line connecting the departure point to the target is called the target line. The distance from the departure point to the target along the target line is called slant range. When firing direct fire, the target line practically coincides with the aiming line, and the slant range coincides with the aiming range.
The point of intersection of the trajectory with the surface of the target (ground, obstacle) is called the meeting point.
The angle between the tangent to the trajectory and the tangent to the surface of the target (ground, obstacle) at the meeting point is called the meeting angle. The meeting angle is taken to be the smaller of the adjacent angles, measured from 0 to 90°.
The trajectory of a bullet in the air has the following properties:
The descending branch is shorter and steeper than the ascending branch;
The angle of incidence is greater than the angle of throwing;
The final speed of the bullet is less than the initial speed;
The lowest flight speed of a bullet when shooting at large throwing angles is on the downward branch of the trajectory, and when shooting at small throwing angles - at the point of impact;
The time it takes a bullet to move along the ascending branch of the trajectory is less than along the descending branch;
The trajectory of a rotating bullet due to the lowering of the bullet under the influence of gravity and derivation is a line of double curvature.
Grenade trajectory (side view)
The trajectory of a grenade in the air can be divided into two sections: active - the flight of the grenade under the influence of reactive force (from the point of departure to the point where the action of the reactive force stops) and passive - the flight of the grenade by inertia. The shape of a grenade's trajectory is approximately the same as that of a bullet.
Path shape
The shape of the trajectory depends on the elevation angle. As the elevation angle increases, the trajectory height and the full horizontal flight range of the bullet (grenade) increase, but this occurs to a certain limit. Beyond this limit, the trajectory altitude continues to increase, and the total horizontal range begins to decrease.
Angle of greatest range, flat, mounted and conjugate trajectories
The elevation angle at which the total horizontal flight range of a bullet (grenade) becomes greatest is called the angle of greatest range. The maximum range angle for bullets of various types of weapons is about 35°.
Trajectories obtained at elevation angles less than the angle of greatest range are called flat. Trajectories obtained at elevation angles greater than the angle of greatest range are called hinged.
When firing from the same weapon (at the same initial speeds), you can get two trajectories with the same horizontal range: flat and mounted. Trajectories that have the same horizontal range at different elevation angles are called conjugate.
When firing from small arms and grenade launchers, only flat trajectories are used. How flatter trajectory, the larger the area the target can be hit with one sight setting (the less impact errors in determining the sight setting have on the shooting results); This is the practical significance of the flat trajectory.
Excess of the bullet's flight path above the aiming point
The flatness of the trajectory is characterized by its greatest elevation above the line of sight. At a given range, the trajectory is flatter 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 smaller the angle of incidence, the more flat the trajectory.
With a shot is called the ejection of a bullet from the barrel under the influence of powder gases formed during the combustion of a powder charge. The impact of the firing pin on the cartridge primer produces a flame that ignites the powder charge. In this case, a large number of highly heated gases are formed, which create high blood pressure, acting in all directions with equal force. At a gas pressure of 250–500 kg/cm2, the bullet moves and crashes into the rifling of the barrel, receiving a rotational movement. The gunpowder continues to burn, therefore, the amount of gases increases. Then, due to a rapid increase in the speed of the bullet, the volume of the bullet space increases faster than the influx new gases, and the pressure begins to drop. However, the speed of the bullet in the barrel continues to increase, since the gases, although to a lesser extent, still put pressure on it. The bullet moves along the bore with continuously increasing speed and is thrown outward along the axis of the bore. The entire firing process occurs in a very short period of time (0.001–0.06 s). Further, the flight of the bullet in the air continues by inertia and largely depends on its initial speed.
Initial bullet speed is the speed at which the bullet leaves the barrel. The magnitude of the initial velocity of a bullet depends on the length of the barrel, the mass of the bullet, the mass of the powder charge and other factors. Increasing the initial speed increases the range of the bullet, its penetrating and lethal effect, reduces the impact external conditions for her flight. The backward movement of the weapon while firing is called recoil. The pressure of the powder gases in the barrel bore acts in all directions with equal force. The gas pressure on the bottom of the bullet causes it to move forward, and the pressure on the bottom of the cartridge case is transferred to the bolt and causes the weapon to move backward. During recoil, a pair of forces is formed, under the influence of which the muzzle of the weapon is deflected upward. The recoil force acts along the axis of the barrel, and the butt rest on the shoulder and the center of gravity of the weapon are located below the direction of this force, so when firing, the muzzle of the weapon is deflected upward.
Recoil small arms are felt as a push into the shoulder, arm or into the ground. The recoil action of a weapon is characterized by the amount of speed and energy it has when moving backwards. The recoil speed of a weapon is approximately the same number of times less than the initial speed of a bullet, how many times the bullet is lighter than the weapon. The recoil energy of a Kalashnikov assault rifle is low and is perceived painlessly by the shooter. Holding the weapon correctly and uniformly reduces the impact of recoil and improves shooting performance. The presence of muzzle brakes-compensators or compensators in weapons improves the results of burst fire and reduces recoil.
At the moment of firing, the barrel of the weapon, depending on the angle of elevation, occupies a certain position. The flight of a bullet in the air begins in a straight line, representing a continuation of the axis of the barrel bore at the moment the bullet leaves. This line is called throwing line. When flying in the air, a bullet is acted upon by two forces: gravity and air resistance. The force of gravity deflects the bullet more and more downward from the throwing line, and the force of air resistance slows down the movement of the bullet. Under the influence of these two forces, the bullet continues to fly along a curve located below the throwing line. Path shape depends on the magnitude of the elevation angle and the initial speed of the bullet, it affects the range of a direct shot, covered, hit and dead space. As the elevation angle increases, the trajectory height and the full horizontal range of the bullet increase, but this occurs to a certain limit. Beyond this limit, the trajectory height continues to increase, and the total horizontal range decreases.
The elevation angle at which the total horizontal range of the bullet becomes greatest is called angle of greatest range. The maximum range angle for bullets of various types of weapons is about 35°. Trajectories obtained at elevation angles less than the angle of greatest range are called flat.
Straight shot is called a shot in which the trajectory of the bullet does not rise above the aiming line above the target along its entire length.
Direct shot range 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 direct shot range and, therefore, the distance at which the target can be hit with one sight setting. Practical significance direct shot lies in the fact that in tense moments of battle shooting can be carried out without rearranging the sight, while the aiming point in height will be selected along the lower edge of the target.
The space behind cover that cannot be penetrated by a bullet, from its crest to the meeting point is called covered space.
The higher the shelter and the flatter the trajectory, the larger the covered space. The part of the covered space in which the target cannot be hit with a given trajectory is called dead (unhittable) space. The greater the height of the shelter, the lower the height of the target, and the flatter the trajectory, the greater it is. The other part of the covered space in which the target can be hit is the target space.
Shot periodization
The shot occurs in a very short period of time (0.001-0.06 s.). When firing, there are four consecutive periods:
- preliminary;
- first, or main;
- second;
- third, or period of last gases.
Preliminary period lasts from the beginning of the combustion of the powder charge until the bullet shell completely cuts into the rifling of the barrel. During this period, gas pressure is created in the barrel bore, which is necessary to move the bullet from its place and overcome the resistance of its shell to cut into the rifling of the barrel. This pressure is called boost pressure; it reaches 250 - 500 kg/cm 2 depending on the rifling design, the weight of the bullet and the hardness of its shell (for example, for small arms chambered for the 1943 model cartridge, the boost 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 boost pressure is reached in the barrel bore.
First or main period lasts from the beginning of the bullet's movement until the moment complete combustion powder charge. During this period, combustion of the powder charge occurs in a rapidly changing volume. At the beginning of the period, when the speed of the bullet moving along the bore is still low, the amount of gases grows faster than the volume of the bullet space (the space between the bottom of the bullet and the bottom of the cartridge case), the gas pressure quickly increases and reaches greatest value(for example, for small arms chambered for the 1943 model - 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. Then due to fast speed As the bullet moves, the volume of the behind-the-bullet space increases faster than the influx of new gases, and the pressure begins to fall, by the end of the period it is equal to approximately 2/3 of the maximum pressure. The speed of the bullet constantly increases and by the end of the period reaches approximately 3/4 of the initial speed. The powder charge is completely burned shortly before the bullet leaves the barrel.
Second period lasts until the powder charge is completely burned until the bullet leaves the barrel. With the beginning of this period, the influx of powder gases stops, however, highly compressed and heated gases expand and, putting pressure on the bullet, increase its speed. The pressure decline in the second period occurs quite quickly and at the muzzle the muzzle pressure is 300 - 900 kg/cm 2 for various types of weapons (for example, for a Simonov self-loading carbine - 390 kg/cm 2, for heavy machine gun Goryunova - 570 kg/cm 2). The speed of the bullet at the moment it leaves the barrel (muzzle speed) is slightly less than the initial speed.
Ballistics studies throwing a projectile (bullet) from a barrel weapon. Ballistics is divided into internal, which studies the phenomena occurring in the barrel at the time of the shot, and external, which explains the behavior of the bullet after leaving the barrel.
Fundamentals of External Ballistics
Knowledge of external ballistics (hereinafter referred to as ballistics) allows the shooter, even before the shot, with sufficient practical application know exactly where the bullet will hit. The accuracy of a shot is influenced by a lot of interrelated factors: the dynamic interaction of parts and pieces of the weapon between themselves and the shooter’s body, gas and bullet, bullet with the walls of the barrel bore, bullet with environment after leaving the barrel and much more.
After leaving the barrel, the bullet does not fly in a straight line, but along a so-called ballistic trajectory, close to a parabola. Sometimes at short shooting distances the deviation of the trajectory from a straight line can be neglected, but at long and extreme shooting distances (which is typical for hunting), knowledge of the laws of ballistics is absolutely necessary.
Note that air guns usually give a light bullet a small or average speed(from 100 to 380 m/s), therefore, the curvature of the bullet’s flight path from different influences more significant than for firearms.
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A bullet fired from a barrel at a certain speed is affected by two main forces in flight: gravity and air resistance. The force of gravity is downward, causing the bullet to continuously descend. The action of the air resistance force is directed towards the movement of the bullet, it forces the bullet to continuously reduce its flight speed. All this leads to a downward deviation of the trajectory.
To increase the stability of the bullet in flight on the surface of the bore rifled weapons There are spiral grooves (rifling) that give the bullet a rotational motion and thereby prevent it from tumbling in flight.
Due to the rotation of the bullet in flight
Due to the rotation of the bullet in flight, the force of air resistance acts unevenly on different parts of the bullet. As a result, the bullet encounters greater air resistance on one side and, in flight, deviates more and more from the firing plane in the direction of its rotation. This phenomenon is called derivation. The effect of derivation is uneven and intensifies towards the end of the trajectory.
Powerful air rifles can give the bullet an initial speed higher than sound (up to 360-380 m/s). The speed of sound in air is not constant (depends on atmospheric conditions, altitude above sea level, etc.), but it can be taken equal to 330-335 m/s. Lightweight pneumatic bullets with low lateral load experience strong disturbances and deviate from their trajectory, overcoming sound barrier. Therefore, it is advisable to shoot heavier bullets with muzzle velocity approaching to the speed of sound.
The trajectory of a bullet is also affected by weather conditions - wind, temperature, humidity and air pressure.
The wind is considered weak at a speed of 2 m/s, medium (moderate) at 4 m/s, strong at 8 m/s. A moderate side wind, acting at an angle of 90° to the trajectory, already has a very significant effect on a light and “low-speed” bullet fired from an air gun. The influence of wind of the same strength, but blowing at an acute angle to the trajectory - 45° or less - causes half the deflection of the bullet.
The wind blowing along the trajectory in one direction or another slows down or speeds up the speed of the bullet, which must be taken into account when shooting at a moving target. When hunting, the wind speed can be estimated with acceptable accuracy using a handkerchief: if you take the handkerchief by two corners, then in a weak wind it will sway slightly, in a moderate wind it will deviate by 45°, and in a strong wind it will develop horizontally to the surface of the earth.
Normal weather conditions are considered to be: air temperature - plus 15°C, humidity - 50%, pressure - 750 mm Hg. An excess of air temperature above normal leads to an increase in the trajectory at the same distance, and a decrease in temperature leads to a decrease in the trajectory. Increased humidity leads to a decrease in the trajectory, and decreased humidity leads to an increase in the trajectory. Let us recall that atmospheric pressure changes not only from the weather, but also from the height above sea level - the higher the pressure, the lower the trajectory.
Each “long-range” weapon and ammunition has its own correction tables that allow one to take into account the influence of weather conditions, derivations, the relative position of the shooter and the target in height, bullet speed and other factors on the bullet’s flight path. Unfortunately, such tables are not published for air guns, so those who like to shoot at extreme distances or at small targets are forced to compile such tables themselves - their completeness and accuracy are the key to success in hunting or competitions.
When assessing the results of shooting, you need to remember that from the moment the shot is fired until the end of its flight, some random (not taken into account) factors act on the bullet, which leads to slight deviations in the bullet’s flight path from shot to shot. Therefore, even under “ideal” conditions (for example, when the weapon is rigidly secured in the machine, constant external conditions, etc.), bullets hitting the target have the appearance of an oval, condensing towards the center. Such random deviations are called deviation. The formula for calculating it is given below in this section.
Now let’s look at the bullet’s flight path and its elements (see Figure 1).
The straight line representing the continuation of the bore axis before the shot is fired is called the shot line. The straight line, which is a continuation of the axis of the barrel when a bullet leaves it, is called the throwing line. Due to the vibrations of the barrel, its position at the moment of the shot and at the moment the bullet leaves the barrel will differ by the angle of departure.
As a result of gravity and air resistance, the bullet does not fly along the throwing line, but along an unevenly curved curve passing below the throwing line.
The beginning of the trajectory is the departure point. The horizontal plane passing through the point of departure is called the horizon of the weapon. The vertical plane passing through the point of departure along the throwing line is called the shooting plane.
To throw a bullet to any point on the horizon of the weapon, you need to direct the throwing line above the horizon. The angle made by the line of fire and the horizon of the weapon is called the elevation angle. The angle made by the throwing line and the horizon of the weapon is called the throwing angle.
The point of intersection of the trajectory with the horizon of the weapon is called the (tabular) point of impact. The horizontal distance from the departure point to the (tabular) impact point is called the horizontal range. The angle between the tangent to the trajectory at the point of impact and the horizon of the weapon is called the (tabular) angle of incidence.
The most high point The trajectory above the weapon horizon is called the trajectory apex, and the distance from the weapon horizon to the trajectory apex is the trajectory height. The top of the trajectory divides the trajectory into two unequal parts: the ascending branch is longer and flatter, and the descending branch is shorter and steeper.
Considering the position of the target relative to the shooter, three situations can be distinguished:
The shooter and target are located on the same level.
- the shooter is positioned below the target (shoots upward at an angle).
- the shooter is positioned above the target (shoots downward at an angle).
In order to direct the bullet at the target, it is necessary to give the axis of the barrel bore a certain position in the vertical and horizontal plane. Giving the desired direction to the axis of the barrel bore in the horizontal plane is called horizontal aiming, and giving direction in the vertical plane is called vertical aiming.
Vertical and horizontal aiming is done using sighting devices. Mechanical sights rifled weapons consist of a front sight and rear sight (or diopter).
The straight line connecting the middle of the rear sight slot to the top of the front sight is called the sighting line.
Aiming of small arms using sighting devices is carried out not from the horizon of the weapon, but relative to the location of the target. In this regard, the guidance and trajectory elements receive the following designations (see Figure 2).
The point at which the weapon is aimed is called the aiming point. The straight line connecting the shooter's eye, the middle of the rear sight slot, the top of the front sight and the aiming point is called the aiming line.
The angle formed by the aiming line and the shooting line is called the aiming angle. This aiming angle is obtained by setting the sight slot (or front sight) at a height corresponding to the firing range.
The point of intersection of the downward branch of the trajectory with the aiming line is called the point of incidence. The distance from the point of departure to the point of impact is called the target range. The angle between the tangent to the trajectory at the point of impact and the aiming line is called the angle of incidence.
When positioning the weapon and target at the same height the aiming line coincides with the horizon of the weapon, and the aiming angle coincides with the elevation angle. When the target is located above or below the horizon weapons, the target elevation angle is formed between the aiming line and the horizon line. The target elevation angle is calculated positive, if the target is above the weapon's horizon and negative, if the target is below the weapon's horizon.
The target elevation angle and the aiming angle together make up the elevation angle. With a negative target elevation angle, the shot line may be directed below the weapon's horizon; in this case, the elevation angle becomes negative and is called the declination angle.
At its end, the bullet’s trajectory intersects either with the target (obstacle) or with the surface of the earth. The point of intersection of the trajectory with the target (obstacle) or the surface of the earth is called the meeting point. The possibility of a rebound depends on the angle at which the bullet hits the target (obstacle) or the ground, their mechanical characteristics, and the material of the bullet. The distance from the departure point to the meeting point is called the actual range. A shot in which the trajectory does not rise above the aiming line above the target throughout the entire aiming range is called a direct shot.
From all of the above, it is clear that before practical shooting the weapon must be shot (otherwise it will lead to a normal battle). Sighting should be carried out with the same ammunition and under the same conditions that will be typical for subsequent shootings. It is imperative to take into account the size of the target, the shooting position (prone, kneeling, standing, from unstable positions), even the thickness of clothing (when zeroing the rifle).
The aiming line passing from the shooter's eye through the top of the front sight, the top edge of the rear sight and the target is a straight line, while the trajectory of the bullet is an unevenly curved line downwards. The aiming line is located 2-3 cm above the barrel in the case of an open sight and much higher in the case of an optical one.
In the simplest case, if the aiming line is horizontal, the bullet trajectory crosses the aiming line twice: on the ascending and descending parts of the trajectory. The weapon is usually zeroed (sights are adjusted) at the horizontal distance at which the downward part of the trajectory intersects the aiming line.
It may seem that there are only two distances to the target - where the trajectory intersects the line of sight - at which a hit is guaranteed. So sport shooting is carried out at a fixed distance of 10 meters, at which the trajectory of the bullet can be considered straight.
For practical shooting (for example, hunting), the firing range is usually much longer and the curvature of the trajectory must be taken into account. But here the arrow plays into the hands of the fact that the dimensions of the target (killing place) in height in this case can reach 5-10 cm or more. If we choose such a horizontal shooting range for the weapon that the height of the trajectory at a distance does not exceed the height of the target (the so-called direct shot), then by aiming at the edge of the target, we will be able to hit it throughout the entire firing distance.
The range of a direct shot, at which the trajectory height does not rise above the aiming line above the target height, is very important characteristic any weapon, determining the flatness of the trajectory.
The aiming point is usually chosen to be the bottom edge of the target or its center. It is more convenient to aim under the bleed, when the entire target is visible when aiming.
When shooting, it is usually necessary to introduce vertical corrections if:
- the target size is smaller than usual.
- The shooting distance exceeds the zeroing distance of the weapon.
- the firing distance is closer than the first point of intersection of the trajectory with the aiming line (typical for shooting with an optical sight).
Horizontal corrections usually have to be introduced during shooting in windy conditions or when shooting at a moving target. Usually amendments for open sights are introduced by shooting with anticipation (moving the aiming point to the right or left of the target), and not by adjusting the sights.