Terms

The flight path of a bullet, its elements and properties. Fundamentals of external ballistics, bullet rotation and derivation. Fundamentals of external ballistics

Ballistics is divided into internal (the behavior of the projectile inside the weapon), external (the behavior of the projectile on the trajectory) and barrier (the action of the projectile on the target). This topic will cover the basics of internal and external ballistics. From barrier ballistics will be considered wound ballistics(action of a bullet on the client's body). Existing also section forensic ballistics considered in the course of criminology and will not be covered in this manual.

Internal ballistics

Internal ballistics depends on the type of powder used and the type of barrel.

Conditionally trunks can be divided into long and short.

Long barrels (length over 250 mm) serve to increase the initial speed of the bullet and its flatness on the trajectory. Increases (compared to short barrels) accuracy. On the other hand, a long barrel is always more cumbersome than a short barrel.

Short barrels do not give the bullet that speed and flatness than long ones. The bullet has more dispersion. But short-barreled weapons are comfortable to wear, especially hidden, which is most appropriate for self-defense weapons and police weapons. On the other hand, trunks can be conditionally divided into rifled and smooth.

rifled barrels give the bullet greater speed and stability on the trajectory. Such barrels are widely used for bullet shooting. For firing bullet hunting cartridges from smoothbore weapons often used various threaded nozzles.

smooth trunks. Such barrels contribute to an increase in the dispersion of striking elements during firing. Traditionally used for shooting with shot (buckshot), as well as for shooting with special hunting cartridges at short distances.

There are four periods of the shot (Fig. 13).

Preliminary period (P) lasts from the beginning of the burning of the powder charge to the full penetration of the bullet into the rifling. 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 and reaches 250-500 kg/cm 2 . It is assumed that the combustion of the powder charge at this stage occurs in a constant volume.

First period (1) lasts from the beginning of the movement of the bullet to complete combustion powder charge. At the beginning of the period, when the speed of the bullet along the bore is still low, the volume of gases grows faster than the bullet space. Gas pressure reaches its peak (2000-3000 kg/cm2). This pressure is called maximum pressure. Then, due to a rapid increase in the speed of the bullet and a sharp increase in the bullet space, the pressure drops somewhat and by the end of the first period is approximately 2/3 of the maximum pressure. The speed of movement is constantly growing and reaches by the end of this period approximately 3/4 of the initial speed.
Second period (2) lasts from the moment of complete combustion of the powder charge to the departure of the bullet from the barrel. With the beginning of this period, the influx of powder gases stops, but highly compressed and heated gases expand and, putting pressure on the bottom of the bullet, increase its speed. The pressure drop in this period occurs quite quickly and at the muzzle - muzzle pressure - is 300-1000 kg/cm 2 . Some types of weapons (for example, Makarov, and most types of short-barreled weapons) do not have a second period, because by the time the bullet leaves the barrel, the powder charge does not completely burn out.

Third period (3) lasts from the moment the bullet leaves the barrel until the powder gases stop acting on it. During this period, powder gases flowing out of the bore at a speed of 1200-2000 m/s continue to act on the bullet, giving it additional speed. The bullet reaches its highest speed at the end of the third period at a distance of several tens of centimeters from the muzzle of the barrel (for example, when firing from a pistol, a distance of about 3 m). This period ends at the moment when the pressure of the powder gases at the bottom of the bullet is balanced by air resistance. Further, the bullet flies already by inertia. This is to the question of why a bullet fired from a TT pistol does not pierce armor of the 2nd class when fired at close range and pierces it at a distance of 3-5 m.

As already mentioned, smoky and smokeless powders are used to equip cartridges. Each of them has its own characteristics:

black powder. This type of powder burns very quickly. Its burning is like an explosion. It is used to instantly release pressure in the bore. Such gunpowder is usually used for smooth barrels, since the friction of the projectile against the walls of the barrel in a smooth barrel is not so great (compared to a rifled barrel) and the time the bullet stays in the bore is less. Therefore, at the moment the bullet leaves the barrel, more pressure is reached. When using black powder in a rifled barrel, the first period of the shot is short enough, due to which the pressure on the bottom of the bullet decreases quite significantly. It should also be noted that the gas pressure of burnt black powder is approximately 3-5 times less than that of smokeless powder. On the gas pressure curve there is a very sharp peak of maximum pressure and a rather sharp drop in pressure in the first period.

Smokeless powder. Such powder burns more slowly than smoky powder, and is therefore used to gradually increase the pressure in the bore. In view of this, for rifled weapons smokeless powder is used as standard. Due to screwing into the rifling, the time for the bullet to fly along the barrel increases and by the time the bullet takes off, the powder charge completely burns out. Due to this, the full amount of gases acts on the bullet, while the second period is chosen to be sufficiently small. On the gas pressure curve, the maximum pressure peak is somewhat smoothed, with a gentle pressure drop in the first period. In addition, it is useful to pay attention to some numerical methods for estimating intraballistic solutions.

1. Power factor(kM). Shows the energy that falls on one conventional cubic mm of a bullet. Used to compare bullets of the same type of cartridges (for example, pistol). It is measured in joules per millimeter cubed.

KM \u003d E0 / d 3, where E0 - muzzle energy, J, d - bullets, mm. For comparison: the power factor for the 9x18 PM cartridge is 0.35 J/mm 3 ; for cartridge 7.62x25 TT - 1.04 J / mm 3; for cartridge.45ACP - 0.31 J / mm 3. 2. Metal utilization factor (kme). Shows the energy of the shot, which falls on one gram of the weapon. Used to compare bullets of cartridges for one sample or to compare the relative energy of a shot for different cartridges. Measured in Joules per gram. Often, the metal utilization coefficient is taken as a simplified version of the calculation of the recoil of a weapon. kme=E0/m, where E0 is the muzzle energy, J, m is the mass of the weapon, g. For comparison: the metal utilization coefficient for the PM pistol, machine gun and rifle is 0.37, 0.66 and 0.76 J/g, respectively.

External ballistics

First you need to imagine the full trajectory of the bullet (Fig. 14).
In explanation to the figure, it should be noted that the line of departure of the bullet (line of throwing) will be different than the direction of the barrel (line of elevation). This is due to the occurrence of barrel vibrations during the shot, which affect the trajectory of the bullet, as well as due to the recoil of the weapon when fired. Naturally, the departure angle (12) will be extremely small; moreover, the better the manufacture of the barrel and the calculation of the intra-ballistic characteristics of the weapon, the smaller the departure angle will be. Approximately the first two thirds of the ascending line of the trajectory can be considered a straight line. In view of this, three firing distances are distinguished (Fig. 15). Thus, the influence of external conditions on the trajectory is described by a simple quadratic equation, and in the graph is a parabola. In addition to third-party conditions, the deviation of the bullet from the trajectory is also affected by some design features bullets and cartridge. The complex of events will be considered below; deflecting the bullet from its original trajectory. The ballistic tables of this topic contain data on the ballistics of a 7.62x54R 7H1 cartridge bullet when fired from an SVD rifle. In general, the influence of external conditions on the flight of a bullet can be shown by the following diagram (Fig. 16).

Diffusion

It should be noted again that due to the rifled barrel, the bullet acquires rotation around its longitudinal axis, which gives greater flatness (straightness) to the flight of the bullet. Therefore, the distance of dagger fire is somewhat increased compared to a bullet fired from a smooth barrel. But gradually towards the distance of the mounted fire, due to the already mentioned third-party conditions, the axis of rotation is somewhat shifted from the central axis of the bullet, therefore, in the cross section, a circle of expansion of the bullet is obtained - the average deviation of the bullet from the original trajectory. Given this behavior of the bullet, its possible trajectory can be represented as a one-plane hyperboloid (Fig. 17). The displacement of a bullet from the main directrix due to the displacement of its axis of rotation is called dispersion. The bullet with full probability is in the circle of dispersion, the diameter (according to
list) which is determined for each specific distance. But the specific point of impact of the bullet inside this circle is unknown.

In table. 3 shows the dispersion radii for firing at various distances.

Table 3

Diffusion

Range of fire (m)	Diffusion Diameter (cm)

Given the size of a standard head target 50x30 cm, and a chest target 50x50 cm, it can be noted that the maximum distance of a guaranteed hit is 600 m. At a greater distance, dispersion does not guarantee the accuracy of the shot.
Derivation
Due to complex physical processes, a rotating bullet in flight deviates somewhat from the plane of fire. Moreover, in the case of right-handed rifling (the bullet rotates clockwise when viewed from behind), the bullet deviates to the right, in the case of left-handed rifling - to the left.
In table. 4 shows the values of derivational deviations when firing at different ranges.
Table 4
Derivation
Range of fire (m)
Derivation (cm)
1000
1200
- It is easier to take into account the derivational deviation when shooting than dispersion. But, taking into account both of these values, it should be noted that the center of dispersion will shift somewhat by the value of the derivational displacement of the bullet.
- Bullet displacement by wind
- Among all the external conditions affecting the flight of a bullet (humidity, pressure, etc.), it is necessary to single out the most serious factor - the influence of wind. The wind blows the bullet quite seriously, especially at the end of the ascending branch of the trajectory and beyond.
  The displacement of the bullet by a side wind (at an angle of 90 0 to the trajectory) of medium force (6-8 m / s) is shown in Table. 5.
- Table 5
- Bullet displacement by wind
- Range of fire (m)
  
  Displacement (cm)
  - To determine the displacement of the bullet by a strong wind (12-16 m/s), it is necessary to double the values of the table, for a weak wind (3-4 m/s), the table values are divided in half. For wind blowing at an angle of 45° to the path, the table values are also divided in half.
  - bullet flight time
  - - Range of fire (m)
      
      Flight time (s)
      
      0,15
      
      0,28
      
      0,42
      
      0,60
      
      0,80
      
      1,02
      
      1,26
      Solution of ballistic problems
    - To do this, it is useful to make a graph of the dependence of the displacement (scattering, bullet flight time) on the firing range. Such a graph will allow you to easily calculate intermediate values (for example, at 350 m), and also allow you to assume out-of-table values of the function.
      On fig. 18 shows the simplest ballistic problem.
    - Shooting is carried out at a distance of 600 m, the wind at an angle of 45 ° to the trajectory blows from behind-left.
      Question: the diameter of the circle of dispersion and the offset of its center from the target; flight time to the target.
    - Solution: The diameter of the circle of dispersion is 48 cm (see Table 3). The derivational shift of the center is 12 cm to the right (see Table 4). The displacement of the bullet by the wind is 115 cm (110 * 2/2 + 5% (due to the direction of the wind in the direction of the derivational displacement)) (see Table 5). Bullet flight time - 1.07 s (flight time + 5% due to wind direction in the direction of bullet flight) (see table 6).
    - Answer; the bullet will fly 600 m in 1.07 s, the diameter of the circle of dispersion will be 48 cm, and its center will shift to the right by 127 cm. Naturally, the answer data is quite approximate, but their discrepancy with the real data is no more than 10%.
    - Barrier and wound ballistics
    - Barrier ballistics
    - The impact of a bullet on obstacles (as, indeed, everything else) is quite convenient to determine by some mathematical formulas.
    1. Penetration of barriers (P). Penetration determines how likely it is to break through one or another obstacle. In this case, the total probability is taken as
    1. It is usually used to determine the probability of penetration on various dis
  - dances different classes passive armor protection.
    Penetration is a dimensionless quantity.
  - P \u003d En / Epr,
  - where En is the energy of the bullet at a given point in the trajectory, in J; Epr is the energy required to break through the barrier, in J.
  - Taking into account the standard Epr for body armor (BZ) (500 J for protection against pistol cartridges, 1000 J - from intermediate and 3000 J - from rifle cartridges) and sufficient energy to hit a person (max 50 J), it is easy to calculate the probability of hitting the corresponding BZ with a bullet of one or more another patron. So, the probability of penetrating a standard pistol BZ with a 9x18 PM cartridge bullet will be 0.56, and with a 7.62x25 TT cartridge bullet - 1.01. The probability of penetrating a standard machine-gun BZ with a 7.62x39 AKM cartridge bullet will be 1.32, and with a 5.45x39 AK-74 cartridge bullet - 0.87. The given numerical data are calculated for a distance of 10 m for pistol cartridges and 25 m for intermediate ones. 2. Coefficient, impact (ky). The impact coefficient shows the energy of the bullet, which falls on the square millimeter of its maximum section. Impact ratio is used to compare cartridges of the same or different classes. It is measured in J per square millimeter. ky=En/Sp, where En is the energy of the bullet at a given point of the trajectory, in J, Sn is the area of the maximum cross-section of the bullet, in mm 2. Thus, the impact coefficients for bullets of cartridges 9x18 PM, 7.62x25 TT and .40 Auto at a distance of 25 m will be equal to 1.2, respectively; 4.3 and 3.18 J / mm 2. For comparison: at the same distance, the impact coefficient of bullets of 7.62x39 AKM and 7.62x54R SVD cartridges are respectively 21.8 and 36.2 J/mm 2 .
    Wound ballistics
    How does a bullet behave when it hits a body? The clarification of this issue is the most important characteristic for the choice of weapons and ammunition for a particular operation. There are two types of impact of a bullet on a target: stopping and penetrating, in principle, these two concepts have an inverse relationship. Stopping effect (0V). Naturally, the enemy stops as reliably as possible when the bullet hits a certain place on the human body (head, spine, kidneys), but some types of ammunition have a large 0V when it hits secondary targets. In the general case, 0V is directly proportional to the caliber of the bullet, its mass and speed at the moment of impact with the target. Also, 0V increases when using lead and expansive bullets. It must be remembered that an increase in 0V reduces the length of the wound channel (but increases its diameter) and reduces the effect of a bullet on a target protected by armored clothing. One of the variants of the mathematical calculation of OM was proposed in 1935 by the American J. Hatcher: 0V = 0.178*m*V*S*k, where m is the mass of the bullet, g; V is the speed of the bullet at the moment of meeting with the target, m/s; S is the transverse area of the bullet, cm 2; k is the bullet shape factor (from 0.9 for full-shell to 1.25 for expansion bullets). According to such calculations, at a distance of 15 m, bullets of cartridges 7.62x25 TT, 9x18 PM and .45 have OB, respectively, 171, 250 in 640. For comparison: OB bullets of the cartridge 7.62x39 (AKM) \u003d 470, and bullets 7.62x54 ( ATS) = 650. Penetrating effect (PV). PV can be defined as the ability of a bullet to penetrate maximum depth to the target. Penetration is higher (ceteris paribus) for bullets of small caliber and weakly deformed in the body (steel, full-shell). The high penetrating effect improves the action of the bullet against armored targets. On fig. 19 shows the action of a standard PM jacketed bullet with a steel core. When a bullet enters the body, a wound channel and a wound cavity are formed. Wound channel - a channel pierced directly by a bullet. Wound cavity - a cavity of damage to fibers and blood vessels caused by tension and rupture of their bullet. Gunshot wounds are divided into through, blind, secant.
    
    through wounds
    A penetrating wound occurs when a bullet passes through the body. In this case, the presence of inlet and outlet holes is observed. The entrance hole is small, less than the caliber of the bullet. With a direct hit, the edges of the wound are even, and with a hit through tight clothing at an angle - with a slight tear. Often the inlet is quickly tightened. There are no traces of bleeding (except for the defeat of large vessels or when the wound is at the bottom). The exit hole is large, it can exceed the caliber of the bullet by orders of magnitude. The edges of the wound are torn, uneven, diverging to the sides. A rapidly developing tumor is observed. There is often heavy bleeding. With non-fatal wounds, suppuration quickly develops. With fatal wounds, the skin around the wound quickly turns blue. Through wounds are typical for bullets with a high penetrating effect (mainly for submachine guns and rifles). When a bullet passed through soft tissues, the internal wound was axial, with slight damage to neighboring organs. When wounded by a bullet cartridge 5.45x39 (AK-74), the steel core of the bullet in the body can come out of the shell. As a result, there are two wound channels and, accordingly, two outlets (from the shell and the core). Such injuries are most oftenth occur when it enters through dense clothing (pea jacket). Often the wound channel from the bullet is blind. When a bullet hits a skeleton, a blind wound usually occurs, but with a high power of the ammunition, a through wound is also likely. In this case, there are large internal injuries from fragments and parts of the skeleton with an increase in the wound channel to the outlet. In this case, the wound channel can "break" due to the ricochet of the bullet from the skeleton. Penetrating wounds to the head are characterized by cracking or fracture of the bones of the skull, often with a non-axial wound channel. The skull cracks even when hit by 5.6 mm lead-free jacketed bullets, not to mention more powerful ammunition. In most cases, these wounds are fatal. With penetrating wounds to the head, severe bleeding is often observed (prolonged leakage of blood from the corpse), of course, when the wound is located on the side or below. The inlet is quite even, but the outlet is uneven, with many cracks. A mortal wound quickly turns blue and swells. In case of cracking, violations of the skin of the head are possible. To the touch, the skull easily misses, fragments are felt. In case of wounds with sufficiently strong ammunition (bullets of cartridges 7.62x39, 7.62x54) and wounds with expansive bullets, a very wide exit hole with a long outflow of blood and brain matter is possible.
    Blind wounds
    Such wounds occur when bullets from less powerful (pistol) ammunition hit, using expansive bullets, passing a bullet through the skeleton, and being wounded by a bullet at the end. With such wounds, the inlet is also quite small and even. Blind wounds are usually characterized by multiple internal injuries. When wounded by expansive bullets, the wound channel is very wide, with a large wound cavity. Blind wounds are often non-axial. This is observed when weaker ammunition hits the skeleton - the bullet goes away from the inlet, plus damage from fragments of the skeleton, the shell. When such bullets hit the skull, the latter cracks heavily. A large inlet is formed in the bone, and the intracranial organs are severely affected.
    Cutting wounds
    Cutting wounds are observed when a bullet enters the body at an acute angle with a violation of only the skin and external parts of the muscles. Most of the injuries are harmless. Characterized by rupture of the skin; the edges of the wound are uneven, torn, often strongly divergent. Quite severe bleeding is sometimes observed, especially when large subcutaneous vessels rupture.

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 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 greatest is called the angle longest range. The value of the angle of greatest range for bullets various kinds 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 of 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 and swarms of different elevation angles are called conjugated.

When firing 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 range 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.

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.

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 farthest angle.

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

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

Rice. 49 - Flat and mounted trajectories

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

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

Since the distances for each type of weapon remain basically the same in sports shooting, many shooters do not even think at what angle of elevation or throw they need to shoot. In practice, it turned out to be much more convenient to replace the throwing angle with another, very similar to it, - aiming angle(Fig. 51). Therefore, 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 line passing from the eye of the shooter through the slots of the sight and the top of the front sight to the aiming point;
aiming point- the point of intersection of the aiming line with the target or the plane of the target (when taking out the aiming point);
aiming angle- the angle formed by the aiming line and the elevation line;
target elevation angle- the angle formed by the aiming line and the horizon of the weapon;
elevation angle is the algebraic sum of the aiming angles and the elevation angle of the target.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

2.3.6 Dependence of the trajectory on meteorological conditions

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

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

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

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

Wind is characterized by strength (speed) and direction.

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

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

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

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

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

Table 8

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

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

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

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

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

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

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

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

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

Naturally, in order to make accurate corrections for the wind, some experience is 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 the shooting is carried out. Over time, he develops a subconscious feeling, gains experience that allows him to quickly navigate in the meteorological situation and make the necessary corrections to ensure accurate shooting in difficult conditions.

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

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

Table 10

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

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

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

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

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

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

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

2.3.7 Scattering bullets

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

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

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

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

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

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

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

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

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

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

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

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

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

The basic concepts are presented: periods of a shot, elements of the trajectory of a bullet, a direct shot, etc.

In order to master the technique of shooting from any weapon, it is necessary to know a number of theoretical provisions, without which not a single shooter will be able to show high results and his training will be ineffective.
Ballistics is the science of the movement of projectiles. In turn, ballistics is divided into two parts: internal and external.

Internal ballistics

Internal ballistics studies the phenomena that occur in the bore during a shot, the movement of a projectile along the bore, the nature of the thermo- and aerodynamic dependences accompanying this phenomenon, both in the bore and outside it during the aftereffect of powder gases.
Internal ballistics solves the most rational use the energy of the powder charge during the shot so that the projectile given weight and caliber to report a certain initial speed (V0) while respecting the strength of the barrel. This provides input for external ballistics and weapon design.

Shot is called 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.
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 is formed, which through the seed holes in the bottom of the cartridge case 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 barrel 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.
When fired from automatic weapons, the device of which is based on the principle of using the energy of powder gases discharged through a hole in the barrel wall - sniper rifle Dragunov, part of the powder gases, in addition, after passing through it into the gas chamber, hits the piston and throws the pusher with the shutter back.
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 - to perform secondary work (cutting and overcoming the friction of a bullet when moving along the bore; heating the walls of the barrel, cartridge case and bullet; moving the moving part of the weapon, the gaseous and unburned part of the 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 s.). When fired, four consecutive periods are distinguished:

preliminary
first or main
second
the third, or period of the last gases

Preliminary period lasts from the beginning of the burning of the powder charge to the complete cutting of the shell of the bullet into the rifling of the barrel. During this period, 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 boost pressure; it reaches 250 - 500 kg / cm2, depending on the rifling device, the weight of the bullet and the hardness of its shell. It is assumed that the combustion of the powder charge in this period occurs in a constant volume, the shell cuts into the rifling instantly, and the movement of the bullet begins immediately when the forcing pressure is reached in the bore.

First or main period lasts from the beginning of the movement of the bullet 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- rifle cartridge 2900 kg / cm2. 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 speed of the movement 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 approximately 2/3 of the maximum pressure. The speed of the bullet is constantly increasing and by the end of the period reaches approximately 3/4 of the initial speed. The powder charge completely burns out shortly before the bullet leaves the bore.

Second period lasts until the moment of complete combustion of the powder charge until the moment the bullet leaves the bore. With the beginning of this period, the influx of powder gases stops, however, highly compressed and heated gases expand and, putting pressure on the bullet, increase its speed. The pressure drop in the second period occurs quite quickly and at the muzzle, the muzzle pressure is 300 - 900 kg/cm2 for various types of weapons. The speed of the bullet at the time of its departure from the bore (muzzle velocity) is somewhat less than the initial velocity.

The third period, or the period after the action of gases lasts from the moment the bullet leaves the bore until the moment the powder gases act on the bullet. During this period, the powder gases flowing out of the bore at a speed of 1200 - 2000 m / s continue to act on the bullet and 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.

The muzzle velocity of a bullet and its practical significance

initial speed 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 of the combat properties of weapons. With an increase in the initial speed, the range of the bullet, the range of a direct shot, the lethal and penetrating effect of the bullet increases, and the influence of external conditions for her flight. The muzzle velocity of a bullet depends on:

barrel length
bullet weight
weight, temperature and humidity of the powder charge
shape and size of powder grains
loading density

The longer the trunk topics more time powder gases act on the bullet and the greater the initial velocity. With a constant barrel length and constant weight powder charge, the initial velocity is greater, the lower the weight of the bullet.
Powder charge weight change 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.
With an increase in the temperature of the powder charge the burning rate of gunpowder increases, and therefore the maximum pressure and initial speed increase. When the charge temperature drops initial speed is reduced. 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 increasing moisture content of the powder charge the speed of its burning and the initial speed of the bullet are reduced.
Shapes and sizes of gunpowder have a significant effect on the burning rate of the powder charge, and consequently, on the initial velocity of the bullet. They are selected accordingly when designing weapons.
Loading density is the ratio of the weight of the charge to the volume of the sleeve with the inserted pool (charge combustion chamber). With a deep landing of a bullet, the loading density increases significantly, which can lead to a sharp pressure jump when fired and, as a result, to a rupture of the barrel, so such cartridges cannot be used for shooting. With a decrease (increase) in the loading density, the initial velocity of the bullet increases (decreases).
recoil is called the movement of the weapon back during the shot. Recoil is felt in the form of a push to the shoulder, arm or ground. The recoil action of the weapon is about as many times less than the initial velocity 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.

The recoil force and the recoil resistance force (butt stop) are not located on the same straight line and are directed in opposite directions. They form a pair of forces, under the influence of which the muzzle of the weapon barrel deviates upward. The magnitude of the deviation of the muzzle of the barrel of a given weapon is the greater, 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 magnitude of this deviation increases with improper use of the firing stop, contamination of the weapon, etc.
The combination of the influence of barrel vibration, weapon recoil and other causes leads to the formation of an angle between the direction of the axis of the bore before the shot and its direction at the moment the bullet leaves the bore. This angle is called the departure angle.
The departure angle is considered positive when the axis of the bore at the time of the bullet's departure is higher than its position before the shot, negative - when it is lower. The influence of the departure angle on shooting 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 departure angle and the weapon’s combat change. In order to reduce the harmful effect of recoil on the results of shooting, compensators are used.
So, the phenomena of a shot, the initial velocity of a bullet, the recoil of a weapon are of great importance when shooting and affect the flight of a bullet.

External ballistics

This is a science that studies the movement of a bullet after the action of powder gases on it has ceased. The main task of external ballistics is the study of the properties of the trajectory and the laws of bullet flight. External ballistics provides data for compiling shooting tables, calculating weapon sight scales, and developing shooting rules. Conclusions from external ballistics are widely used in combat when choosing a sight and aiming point depending on the firing range, wind direction and speed, air temperature and other firing conditions.

Bullet trajectory and its elements. Trajectory properties. Types of trajectory and their practical significance

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

Direct shot, hit and dead space most closely related to issues of shooting practice. The main task of studying these issues is to gain solid knowledge in the use of a direct shot and the affected space to perform fire missions in combat.

Direct shot its definition and practical use in a combat situation

A shot in which the trajectory does not rise above the aiming line above the target for its entire length is called direct shot. 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, 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 tables by comparing the height of the target with the values of the greatest excess of the trajectory above the line of sight or with the height of the trajectory.

Direct sniper shot in urban environments
The installation height of optical sights above the bore of the weapon is on average 7 cm. At a distance of 200 meters and the sight "2" the greatest excesses of the trajectory, 5 cm at a distance of 100 meters and 4 cm - at 150 meters, practically coincide with the aiming line - the optical axis of the optical sight. The height of the line of sight at the middle of the distance of 200 meters is 3.5 cm. There is a practical coincidence of the trajectory of the bullet and the line of sight. A difference of 1.5 cm can be neglected. At a distance of 150 meters, the height of the trajectory is 4 cm, and the height of the optical axis of the sight above the horizon of the weapon is 17-18 mm; the difference in height is 3 cm, which also does not play a practical role.

At a distance of 80 meters from the shooter, the height of the trajectory of the bullet will be 3 cm, and the height of the sighting line will be 5 cm, the same difference of 2 cm is not decisive. The bullet will fall only 2 cm below the aiming point. The vertical spread of bullets of 2 cm is so small that it is of no fundamental importance. Therefore, when shooting with division "2" of the optical sight, starting from 80 meters of distance and up to 200 meters, aim at the bridge of the nose of the enemy - you will get there and get ± 2/3 cm higher lower throughout this distance. At 200 meters, the bullet will hit exactly the aiming point. And even further, at a distance of up to 250 meters, aim with the same sight "2" at the enemy's "top", at the upper cut of the cap - the bullet drops sharply after 200 meters of distance. At 250 meters, aiming in this way, you will fall 11 cm lower - in the forehead or bridge of the nose.
The above method can be useful in street battles, when the distances in the city are about 150-250 meters and everything is done quickly, on the run.

Affected space, its definition and practical use in a combat situation

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.

The distance on the ground during which the descending branch of the trajectory does not exceed the height of the target, called the affected space(the depth of the affected space).
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).
The depth of the affected space can be determined from the tables of the excess of the trajectory above the aiming line by comparing the excess of the descending branch of the trajectory by the corresponding firing range with the height of the target, and if the target height is less than 1/3 of the trajectory height, then in the form of a thousandth.
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 coincides, if possible, with the aiming line. Covered space its definition and practical use in a combat situation.

Covered space, its definition and practical use in a combat situation

The space behind a cover that is not penetrated by a bullet, from its crest to the meeting point is called covered space.
The covered space will be the greater, the greater the height of the shelter and the flatter the trajectory. The depth of the covered space can be determined from the tables of excess trajectory 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.

Dead space of its definition and practical use in a combat situation

The part of the covered space in which the target cannot be hit with a given trajectory is called dead (not 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. The depth of the dead space is equal to the difference between the covered and affected space.

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

The phenomenon of derivation

Due to the simultaneous impact on the bullet of rotational motion, which gives it a stable position in flight, and air resistance, which tends to tip the bullet head back, the axis of the bullet deviates from the direction of flight in the direction of rotation. As a result, the bullet encounters air resistance on more than one of its sides and therefore deviates from the firing plane more and more in the direction of rotation. Such a deviation of a rotating bullet away from the plane of fire is called derivation. This is a rather complex physical process. The derivation increases disproportionately to the flight distance of the bullet, as a result of which the latter takes more and more to the side and its trajectory in plan is a curved line. With the right cut of the barrel, the derivation takes the bullet to the right side, with the left - to the left.

Distance, m	Derivation, cm	thousandths
100	0	0
200	1	0
300	2	0,1
400	4	0,1
500	7	0,1
600	12	0,2
700	19	0,2
800	29	0,3
900	43	0,5
1000	62	0,6

At firing distances up to 300 meters inclusive, derivation has no practical significance. This is especially true for the SVD rifle, in which the PSO-1 optical sight is specially shifted to the left by 1.5 cm. The barrel is slightly turned to the left and the bullets go slightly (1 cm) to the left. It is of no fundamental importance. At a distance of 300 meters, the derivation force of the bullet returns to the aiming point, that is, in the center. And already at a distance of 400 meters, the bullets begin to thoroughly divert to the right, therefore, in order not to turn the horizontal flywheel, aim at the enemy’s left (away from you) eye. By derivation, the bullet will be taken 3-4 cm to the right, and it will hit the enemy in the bridge of the nose. At a distance of 500 meters, aim at the enemy’s left (from you) side of the head between the eye and ear - this will be approximately 6-7 cm. At a distance of 600 meters - at the left (from you) edge of the enemy’s head. Derivation will take the bullet to the right by 11-12 cm. At a distance of 700 meters, take a visible gap between the aiming point and the left edge of the head, somewhere above the center of the epaulette on the shoulder of the enemy. At 800 meters - give an amendment with the flywheel of horizontal corrections by 0.3 thousandth (set the grid to the right, move the middle point of impact to the left), at 900 meters - 0.5 thousandth, at 1000 meters - 0.6 thousandth.

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

Fundamentals of external ballistics

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

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

Note that airguns usually give a light bullet a small or average speed(from 100 to 380 m / s), so the curvature of the trajectory of the bullet from different influences greater than for firearms.

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

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

Due to the rotation of the bullet in flight

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

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

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

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

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

Normal weather conditions are: air temperature - plus 15 ° C, humidity - 50%, pressure - 750 mm Hg. An excess of air temperature above normal leads to an increase in the trajectory at the same distance, and a decrease in temperature leads to a decrease in the trajectory. High humidity leads to a decrease in the trajectory, and low humidity leads to an increase in the trajectory. Recall that atmospheric pressure varies 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 you to take into account the influence of weather conditions, derivation, relative position of the shooter and target in height, bullet speed and other factors on the bullet's flight path. Unfortunately, such tables are not published for pneumatic weapons, therefore, lovers of shooting at extreme distances or at small targets are forced to compile such tables themselves - their completeness and accuracy are the key to success in hunting or competitions.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Range of fire (m)	Flight time (s)
	0,15
	0,28
	0,42
	0,60
	0,80
	1,02
	1,26

The flight path of a bullet, its elements and properties. Fundamentals of external ballistics, bullet rotation and derivation. Fundamentals of external ballistics

Internal ballistics

External ballistics

Diffusion

Derivation

Bullet displacement by wind

bullet flight time

Solution of ballistic problems

Barrier and wound ballistics

Barrier ballistics

Wound ballistics

through wounds

Blind wounds

Cutting wounds

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

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

2.3.6 Dependence of the trajectory on meteorological conditions

2.3.7 Scattering bullets

Internal ballistics

The muzzle velocity of a bullet and its practical significance

External ballistics

Bullet trajectory and its elements. Trajectory properties. Types of trajectory and their practical significance

Trajectory elements

Direct shot its definition and practical use in a combat situation

Affected space, its definition and practical use in a combat situation

Covered space, its definition and practical use in a combat situation

Dead space of its definition and practical use in a combat situation

The phenomenon of derivation

Due to the rotation of the bullet in flight