Definition of initial bullet speed. The trajectory of a bullet in the air and its shape; the influence of gravity and air resistance on the flight of a bullet; properties of the trajectory. The influence of air resistance on the trajectory of a projectile

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 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.

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 an insignificant effect on its flight, since the waves propagate faster speed flight of a 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 sequentially 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.

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

The shortest distance from the top of the trajectory to the horizon of the weapon is called the 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 one;

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 value of the angle of greatest range for bullets various types 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 having the same horizontal range at different elevation angles are called conjugate.

When firing from small arms and grenade launchers, only flat trajectories are used. How flatter trajectory, the 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.

A bullet, having received a certain initial speed when leaving the barrel bore, tends by inertia to maintain the magnitude and direction of this speed.

If the flight of a bullet took place in airless space, and it was not affected by gravity, the bullet would move straight, uniformly and endlessly. However, a bullet flying in the air is subject to forces that change its flight speed and direction of movement. These forces are gravity and air resistance (Fig. 4).

Rice. 4. Forces acting on a bullet during its flight

Due to the combined action of these forces, the bullet loses speed and changes the direction of its movement, moving in the air along a curved line passing below the direction of the axis of the barrel bore.

The line that a moving bullet describes in space (its center of gravity) is called trajectory.

Typically, ballistics considers the trajectory over weapon horizon- an imaginary infinite horizontal plane passing through the departure point (Fig. 5).

Rice. 5. Weapon Horizon

The movement of the bullet, and therefore the shape of the trajectory, depends on many conditions. Therefore, in order to understand how the trajectory of a bullet is formed in space, it is necessary to consider first of all how the force of gravity and the force of air resistance act on the bullet separately.

The action of gravity. Let's imagine that no force acts on the bullet after it leaves the barrel. In this case, as mentioned above, the bullet would move by inertia endlessly, uniformly and rectilinearly along the axis of the barrel bore; for every second it would fly the same distances with a constant speed equal to the initial one. In this case, if the barrel of the weapon were aimed directly at the target, the bullet, following in the direction of the axis of the barrel bore, would hit it (Fig. 6).

Rice. 6. The movement of a bullet by inertia (if there were no gravity and air resistance)

Let us now assume that only one force of gravity acts on the bullet. Then the bullet will begin to fall vertically down, like any freely falling body.

If we assume that the force of gravity acts on the bullet as it flies by inertia in airless space, then under the influence of this force the bullet will drop lower from the extension of the axis of the barrel bore - in the first second - by 4.9 m, in the second - by 19.6 m etc. In this case, if you point the barrel of a weapon at a target, the bullet will never hit it, since, being exposed to gravity, it will fly under the target (Fig. 7).

Rice. 7. The movement of the bullet (if gravity acted on it,

but air resistance did not work)

It is quite obvious that in order for a bullet to fly a certain distance and hit the target, it is necessary to point the barrel of the weapon somewhere above the target. To do this, it is necessary that the axis of the barrel bore and the horizon plane of the weapon make a certain angle, which is called elevation angle(Fig. 8).

As can be seen from Fig. 8, the trajectory of a bullet in airless space, which is affected by gravity, is a regular curve, which is called parabola. The highest point of the trajectory above the horizon of the weapon is called its top. The part of the curve from the departure point to the apex is called ascending branch. This bullet trajectory is characterized by the fact that the ascending and descending branches are exactly the same, and the throwing and falling angles are equal to each other.

Rice. 8. Elevation angle (bullet trajectory in airless space)

Action of air resistance force. At first glance, it seems unlikely that air, which has such a low density, could provide significant resistance to the movement of a bullet and thereby significantly reduce its speed.

However, experiments have established that the force of air resistance acting on a bullet fired from a rifle of the 1891/30 model is large - 3.5 kg.

Considering that the bullet weighs only a few grams, the large braking effect that air has on a flying bullet becomes quite obvious.

During flight, a bullet expends a significant portion of its energy to push apart air particles that interfere with its flight.

As a photograph of a bullet flying at supersonic speed (over 340 m/s) shows, an air compaction forms in front of its head (Fig. 9). From this compaction the head ballistic wave diverges in all directions. Air particles, sliding along the surface of the bullet and falling off its side walls, form a zone of rarefied space behind the bullet. In an effort to fill the void behind the bullet, air particles create turbulence, resulting in a tail wave trailing behind the bottom of the bullet.

The compaction of air in front of the bullet's head slows down its flight; the discharged zone behind the bullet sucks it in and thereby further enhances the braking; the walls of the bullet experience friction against air particles, which also slows down its flight. The resultant of these three forces is the air resistance force.

Rice. 9. Photograph of a bullet flying at supersonic speed

(over 340 m/sec.)

The enormous influence that air resistance has on the flight of a bullet can also be seen from the following example. A bullet fired from a Mosin rifle model 1891/30. or from sniper rifle Dragunov (SVD). Under normal conditions (with air resistance), it has the greatest horizontal flight range of 3400 m, and when firing in airless space it could fly 76 km.

Consequently, under the influence of air resistance, the trajectory of the bullet loses the shape of a regular parabola, taking on the shape of an asymmetrical curved line; the apex divides it into two unequal parts, of which the ascending branch is always longer and shallower than the descending one. When shooting at medium distances, you can conditionally take the ratio of the length of the ascending branch of the trajectory to the descending branch as 3:2.

Rotation of a bullet around its axis. It is known that a body acquires significant stability if it is given a rapid rotational movement around its axis. An example of the stability of a rotating body is the “top” toy. A non-rotating “top” will not stand on its pointed leg, but if the “top” is given a rapid rotational movement around its axis, it will stand stably on it (Fig. 10).

In order for the bullet to acquire the ability to combat the overturning effect of air resistance and maintain stability during flight, it is given a rapid rotational movement around its longitudinal axis. The bullet acquires this rapid rotational movement thanks to helical rifling in the bore of the weapon (Fig. 11). Under the influence of the pressure of the powder gases, the bullet moves forward along the barrel bore, simultaneously rotating around its longitudinal axis. Upon departure from the barrel, the bullet, by inertia, retains the resulting complex motion - translational and rotational.

Without going into detail the explanation physical phenomena associated with the action of forces on a body experiencing complex motion, it is still necessary to say that the bullet makes regular oscillations during flight and its head describes a circle around the trajectory (Fig. 12). In this case, the longitudinal axis of the bullet seems to “follow” the trajectory, describing a conical surface around it (Fig. 13).

Rice. 12. Conical rotation of the bullet head

Rice. 13. Flight of a spinning bullet in the air

If we apply the laws of mechanics to a flying bullet, it will become obvious that the greater the speed of its movement and the longer the bullet, the more strongly the air tends to knock it over. Therefore, the bullets of cartridges different types it is necessary to give different rotation speeds. Thus, a light bullet fired from a rifle has a rotation speed of 3604 rpm.

However, the rotational motion of the bullet, which is so necessary to give it stability during flight, also has its negative sides.

A rapidly rotating bullet, as already mentioned, is subject to a continuous tipping effect by the force of air resistance, due to which the head of the bullet describes a circle around the trajectory. As a result of the addition of these two rotational movements, a new movement arises, deflecting its head part away from the firing plane1 (Fig. 14). In this case, one side surface of the bullet is subjected to more particle pressure than the other. This unequal air pressure on the side surfaces of the bullet deflects it away from the firing plane. The lateral deviation of a rotating bullet from the firing plane in the direction of its rotation is called derivation(Fig. 15).

Rice. 14. As a result of two rotational movements, the bullet gradually turns the head to the right (in the direction of rotation)

Rice. 15. The phenomenon of derivation

As the bullet moves away from the muzzle of the weapon, the magnitude of its derivational deviation quickly and progressively increases.

When shooting at short and medium distances, derivation does not have a large practical significance for the shooter. So, at a firing range of 300 m, the derivation deviation is 2 cm, and at 600 m - 12 cm. Derivation has to be taken into account only when shooting with precision at long distances, making appropriate adjustments to the installation of the sight, in accordance with the table of derivational deviations of the bullet for a certain range shooting.

Ballistics is divided into internal (the behavior of the projectile inside the weapon), external (the behavior of the projectile along the trajectory) and barrier (the effect of the projectile on the target). This topic will cover the basics of internal and external ballistics. Barrier ballistics will be considered wound ballistics(the effect of a bullet on the client’s body). The existing section of forensic ballistics is discussed in the course of criminalistics and will not be covered in this manual.

Internal ballistics

Internal ballistics depend on the type of propellant used and the type of barrel.

Conventionally, trunks can be divided into long and short.

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

Short trunks do not give the bullet the same speed and flatness than long ones. The bullet has greater dispersion. But a short-barreled weapon is convenient to carry, especially concealed, which is most suitable for self-defense weapons and police weapons. On the other hand, trunks can be divided into rifled and smooth.

Rifled barrels give the bullet greater speed and stability along the trajectory. Such trunks are widely used for bullet shooting. For shooting bullet hunting cartridges from smoothbore weapons Various threaded attachments are often used.

Smooth trunks. Such barrels help to increase the dispersion of damaging elements when firing. Traditionally used for shooting with shot (buckshot), as well as for shooting with special hunting cartridges at short distances.

There are four firing periods (Fig. 13).

Preliminary period (P) lasts from the beginning of the combustion of the powder charge until the bullet completely penetrates the rifling. 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 and reaches 250-500 kg/cm2. 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 bullet’s movement until the complete combustion of the powder charge. At the beginning of the period, when the speed of the bullet along the barrel is still low, the volume of gases grows faster than the behind-the-bullet space. The 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 slightly and by the end of the first period it is approximately 2/3 of the maximum pressure. The speed of movement is constantly growing and by the end of this period reaches approximately 3/4 of the initial speed.
Second period (2) lasts from the moment the powder charge is completely burned until the bullet leaves the barrel. With the beginning of this period, the influx of powder gases stops, 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, since 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 action of the powder gases on it ceases. During this period, powder gases flowing from the barrel at a speed of 1200-2000 m/s continue to affect 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 shooting 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. Then the bullet flies by inertia. This relates to the question of why a bullet fired from a TT pistol does not penetrate class 2 armor when shot at point-blank range and pierces it at a distance of 3-5 m.

As already mentioned, black and smokeless powder are used to load cartridges. Each of them has its own characteristics:

Black powder. This type of gunpowder burns very quickly. Its combustion is like an explosion. It is used for an instant surge in pressure in the barrel bore. This type of gunpowder is usually used for smooth barrels, since the friction of the projectile against the barrel walls in a smooth barrel is not so great (compared to a rifled barrel) and the residence time of the bullet in the barrel is less. Therefore, at the moment the bullet leaves the barrel, greater pressure is achieved. When using black powder in a rifled barrel, the first period of the shot is quite short, 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. The gas pressure curve has a very sharp peak of maximum pressure and a fairly sharp drop in pressure in the first period.

Smokeless powder. This type of powder burns more slowly than black 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 it takes for the bullet to fly down the barrel increases and by the time the bullet leaves, the powder charge is completely burned out. Due to this, the bullet is exposed to the full amount of gases, while the second period is selected to be quite small. On the gas pressure curve, the peak of maximum pressure is somewhat smoothed out, with a gentle decrease in pressure in the first period. In addition, it is useful to pay attention to some numerical methods for estimating intra-ballistic solutions.

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

KM = E0/d 3, where E0 is muzzle energy, J, d is bullets, mm. For comparison: the power coefficient 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 shot energy per gram of weapon. Used to compare bullets from cartridges of the same type or to compare the relative shot energy of different cartridges. It is measured in Joules per gram. Often, the metal utilization rate is taken as a simplified version of calculating 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, respectively, is 0.37, 0.66 and 0.76 J/g.

External ballistics

First you need to imagine the full trajectory of the bullet (Fig. 14).
In explanation of the figure, it should be noted that the line of departure of the bullet (throwing line) will be different than the direction of the barrel (elevation line). This occurs due to the occurrence of barrel vibrations when fired, 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 finishing of the barrel and the calculation of the internal ballistic characteristics of the weapon, the smaller the departure angle will be. Approximately the first two-thirds of the upward trajectory line can be considered straight. 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 it is represented by a parabola. In addition to third-party conditions, the deviation of a bullet from its trajectory is also influenced by some design features of the bullet and cartridge. Below we will consider a complex of events; deflecting the bullet from its original trajectory. The ballistic tables of this topic contain data on the ballistics of the 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 once again that thanks 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 increases slightly 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 shifts somewhat from the central axis of the bullet, so in the cross section you get a circle of bullet expansion - the average deviation of the bullet from the original trajectory. Taking into account this behavior of the bullet, its possible trajectory can be represented as a single-plane hyperboloid (Fig. 17). The displacement of a bullet from the main directrix due to a displacement of its axis of rotation is called dispersion. The bullet with full probability ends up in the circle of dispersion, diameter (by
peppercorn) 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 dispersion radii for shooting at various distances.

Table 3

Diffusion

Fire range (m)	Dispersion Diameter(cm)

Considering the size of the standard head target is 50x30 cm, and the chest target is 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 slightly from the firing plane. Moreover, in the case of right-hand rifling (the bullet rotates clockwise when viewed from behind), the bullet deflects to the right, in the case of left-hand rifling - to the left.
In table Figure 4 shows the magnitude of derivational deviations when firing at various ranges.
Table 4
Derivation
Fire range (m)
Derivation (cm)
1000
1200
- It is easier to take into account 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 slightly by the amount of the derivational displacement of the bullet.
- Bullet displacement by wind
- Among all the third-party conditions affecting the flight of a bullet (humidity, pressure, etc.), it is necessary to highlight the most serious factor - the influence of wind. The wind blows the bullet away quite seriously, especially at the end of the ascending branch of the trajectory and beyond.
  The displacement of a bullet by a side wind (at an angle of 90 0 to the trajectory) of average force (6-8 m/s) is shown in table. 5.
- Table 5
- Bullet displacement by wind
- Fire range (m)
  
  Offset (cm)
  - To find out the bullet's displacement strong wind(12-16 m/s) it is necessary to double the table values; for weak winds (3-4 m/s) the table values are divided in half. For wind blowing at an angle of 45° to the trajectory, the table values are also divided in half.
  - Bullet flight time
  - - Fire range (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 (dispersion, bullet flight time) on the firing range. Such a graph will allow you to easily calculate intermediate values (for example, at 350 m), and will also allow you to assume table values of the function.
      In Fig. Figure 18 shows the simplest ballistic problem.
    - Shooting is carried out at a distance of 600 m, the wind blows from behind to the left at an angle of 45° to the trajectory.
      Question: the diameter of the scattering circle and the displacement of its center from the target; flight time to target.
    - Solution: The diameter of the scattering circle 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). The bullet's flight time is 1.07 s (flight time + 5% due to the direction of the wind in the direction of the bullet's flight) (see Table 6).
    - Answer; the bullet will fly 600 m in 1.07 s, the diameter of the dispersion circle 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 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 conveniently determined by some mathematical formulas.
    1. Penetration of barriers (P). Penetration determines how likely it is to break through a particular barrier. In this case, the total probability is taken as
    1. Usually used to determine the probability of penetration on various disks
  - dances of different classes of passive armor protection.
    Penetration is a dimensionless quantity.
  - P = En / Epr,
  - where En is the energy of the bullet at a given point of the trajectory, in J; Epr is the energy required to break through an obstacle, in J.
  - Taking into account the standard EPR for body armor (BZh) (500 J for protection against pistol cartridges, 1000 J - from intermediate and 3000 J - from rifle cartridges) and sufficient energy to defeat a person (max 50 J), it is easy to calculate the probability of hitting the corresponding BZh with a bullet from one or another another cartridge. Thus, the probability of penetrating a standard pistol BZ with a bullet from a 9x18 PM cartridge will be equal to 0.56, and by a bullet from a 7.62x25 TT cartridge - 1.01. The probability of penetrating a standard assault rifle bullet with a 7.62x39 AKM cartridge will be 1.32, and with a 5.45x39 AK-74 cartridge bullet will be 0.87. The given numerical data are calculated for a distance of 10 m for pistol cartridges and 25 m for intermediate cartridges. 2. Impact coefficient (ky). Impact coefficient shows the energy of a bullet per square millimeter of its maximum cross-section. Impact factor 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 9x18 PM, 7.62x25 TT and .40 Auto cartridges 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 from 7.62x39 AKM and 7.62x54R SVD cartridges are 21.8 and 36.2 J/mm 2 , respectively.
    Wound ballistics
    How does a bullet behave when it hits a body? Clarification of this issue is the most important characteristic for choosing 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 most reliably when the bullet hits a certain place on the human body (head, spine, kidneys), but some types of ammunition have a large 0B even when hitting secondary targets. In general, 0B is directly proportional to the caliber of the bullet, its mass and speed at the moment it hits the target. Also, 0B increases when using lead and expansion bullets. It must be remembered that an increase in 0B shortens the length of the wound channel (but increases its diameter) and reduces the effect of the bullet on a target protected by armor. One of the options for mathematical calculation of OM was proposed in 1935 by the American Yu. 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 the target, m/s; S - transverse area of the bullet, cm 2; k is the bullet shape coefficient (from 0.9 for full-shell bullets to 1.25 for hollow-point bullets). According to these calculations, at a distance of 15 m, bullets of 7.62x25 TT, 9x18 PM and .45 cartridges have a MR of 171, 250 in 640, respectively. For comparison: RP of a bullet of a 7.62x39 cartridge (AKM) = 470, and bullets of 7.62x54 ( OVD) = 650. Penetrating impact (PE). PT can be defined as the ability of a bullet to penetrate maximum depth on target. The penetrating ability is higher (all other things being equal) for bullets of small caliber and those that are slightly deformed in the body (steel, full-shell). High penetration improves the bullet's effect on targets protected by armor. In Fig. Figure 19 shows the effect of a standard PM jacketed bullet with a steel core. When a bullet hits the body, a wound channel and a wound cavity are formed. A wound channel is a channel pierced directly by a bullet. A wound cavity is a cavity of damage to fibers and blood vessels caused by tension and rupture by a bullet. Gunshot wounds are divided into through, blind, and secant.
    
    Penetrating wounds
    A perforation 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, smaller than the caliber of a bullet. With a direct hit, the edges of the wound are smooth, and with a hit through thick clothing at an angle, there will be a slight tear. Often the inlet closes up quite quickly. There are no traces of bleeding (except for damage to large vessels or when the wound is positioned below). The exit hole is large and can exceed the caliber of the bullet by orders of magnitude. The edges of the wound are torn, uneven, and spread to the sides. A rapidly developing tumor is observed. There is often severe bleeding. In non-fatal wounds, suppuration develops quickly. With fatal wounds, the skin around the wound quickly turns blue. Penetrating wounds are typical for bullets with a high penetrating effect (mainly for machine guns and rifles). When a bullet passes through soft tissue, the internal wound is axial, with minor damage to neighboring organs. When wounded by a bullet from a 5.45x39 (AK-74) cartridge, the steel core of the bullet in the body may come out of the shell. As a result, two wound channels appear and, accordingly, two exit holes (from the shell and the core). Such injuries are more oftenthey occur when ingested through thick clothing (peacoat). Often the wound channel from a bullet is blind. When a bullet hits a skeleton, a blind wound usually occurs, but with a high power of ammunition, a through wound is likely. In this case, large internal damage from fragments and parts of the skeleton is observed with an increase in the wound channel towards the exit hole. In this case, the wound channel can “break” due to the ricochet of the bullet from the skeleton. Perforating head wounds are characterized by cracking or fracture of the skull bones, often in a non-axial wound channel. The skull cracks even when hit by 5.6 mm lead non-jacketed bullets, not to mention more powerful ammunition. In most cases, such injuries are fatal. With through wounds to the head, severe bleeding is often observed (prolonged flow of blood from the corpse), of course, when the wound is positioned on the side or below. The inlet is fairly smooth, but the outlet is uneven, with a lot of cracking. A fatal wound quickly turns blue and swells. In case of cracking, damage to the scalp may occur. The skull is easily crushed to the touch, and fragments can be felt. In case of wounds with sufficiently strong ammunition (bullets of 7.62x39, 7.62x54 cartridges) and wounds with expansive bullets, a very wide exit hole is possible with a long leakage of blood and brain matter.
    Blind wounds
    Such wounds occur when hit by bullets from less powerful (pistol) ammunition, using hollow-point bullets, passing a bullet through the skeleton, or being wounded by a bullet at the end of its life. With such wounds, the entrance hole is also quite small and smooth. 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 not axial. This is observed when weaker ammunition hits the skeleton - the bullet moves away from the entrance hole plus damage from fragments of the skeleton and shell. When such bullets hit the skull, it becomes severely cracked. A large entrance hole is formed in the bone, and the intracranial organs are severely affected.
    Cutting wounds
    Cutting wounds are observed when a bullet hits the body at an acute angle, damaging only the skin and external parts of the muscles. Most of the injuries are not dangerous. Characterized by skin rupture; the edges of the wound are uneven, torn, and often diverge greatly. Sometimes quite severe bleeding is observed, especially when large subcutaneous vessels rupture.

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.

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 of greatest range.

When a bullet flies in the air, the angle of maximum range 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 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 issues of 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 shooting 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 speeds, then the trajectory of the bullet with a higher initial speed will be higher than the trajectory of the bullet with a lower initial speed (Fig. 58).

Rice. 58 - Dependence of the trajectory height and flight range of a bullet on the 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 area of rarefied space behind the bullet is smaller, the more its tail is beveled; 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.

Influence 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 greater the weight of the bullet and the smaller the caliber, the greater the lateral load. 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 tipping 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 meteorological conditions during shooting can have a significant impact on the flight of the 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

Table 8

Firing range, m	Heavy bullet deflection (11.8 g), cm
Firing range, m	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 initial 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 a forest, steep cliffs, ravines and hollows, since the wind speed in different layers of the atmosphere, as well as around uneven terrain and obstacles, is 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 a large number of air particles on its path, 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°

Table 10

Firing range, m	STP movement 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

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, it decreases and starting speed bullets.

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 heat 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, slightly 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 cartridges 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.

The trajectory of a bullet is understood as the line drawn in space by its center of gravity.

This trajectory is formed under the influence of the inertia of the bullet, the forces of gravity and air resistance acting on it.

The inertia of the bullet is formed while it is in the barrel. Under the influence of the energy of the powder gases, the bullet is given speed and direction forward movement. And if external forces did not act on it, then, according to the first Galileo-Newton law, it would perform rectilinear movement in a given direction at a constant speed to infinity. In this case, in every second it would cover a distance equal to the initial speed of the bullet (see Fig. 8).

However, due to the fact that the forces of gravity and air resistance act on the bullet in flight, they together, in accordance with the fourth law of Galileo - Newton, impart to it an acceleration equal to the vector sum of the accelerations arising from the actions of each of these forces separately.

Therefore, in order to understand the peculiarities of the formation of a bullet’s flight path in the air, it is necessary to consider how the force of gravity and the force of air resistance act separately on the bullet.

Rice. 8. Bullet movement by inertia (in the absence of gravity

and air resistance)

The force of gravity acting on a bullet gives it an acceleration equal to the acceleration of gravity. This force is directed vertically downwards. In this regard, the bullet, under the influence of gravity, will constantly fall towards the ground, and the speed and height of its fall will be determined according to formulas 6 and 7, respectively:

where: v - bullet falling speed, H - bullet falling height, g - free fall acceleration (9.8 m/s2), t - bullet falling time in seconds.

If a bullet flew out of the barrel without possessing kinetic energy given by the pressure of the powder gases, then, in accordance with the above formula, it would fall vertically down: after one second, 4.9 m; after two seconds at 19.6 m; after three seconds at 44.1 m; four seconds later at 78.4 m; after five seconds at 122.5 m, etc. (see Fig. 9).

Rice. 9. The fall of a bullet with no kinetic energy in a vacuum

under the influence of gravity

When a bullet with a given kinetic energy moves, by inertia, under the influence of gravity, it will shift a given distance downward relative to the line that is a continuation of the axis of the barrel bore. Having constructed parallelograms, the lines of which will be the distances covered by the bullet by inertia and under the influence of gravity in

corresponding time intervals, we can determine the points that the bullet will pass in these time intervals. By connecting them with a line, we obtain the trajectory of a bullet in airless space (see Fig. 10).

Rice. 10. The trajectory of a bullet in airless space

This trajectory is a symmetrical parabola, the highest point of which is called the vertex of the trajectory; its part located from the point of departure of the bullet to the top is called the ascending branch of the trajectory; and the part located after the top is descending. In airless space these parts will be the same.

In this case, the height of the top of the trajectory and, accordingly, its shape will depend only on the initial speed of the bullet and the angle of its departure.

If the force of gravity acting on the bullet is directed vertically downward, then the force of air resistance is directed in the direction opposite to the movement of the bullet. It continuously slows down the movement of the bullet and tends to knock it over. Part of the kinetic energy of the bullet is spent on overcoming the force of air resistance.

The main causes of air resistance are: its friction against the surface of the bullet, the formation of turbulence, and the formation of a ballistic wave (see Fig. 11).

Rice. 11. Causes of air resistance

A bullet in flight collides with air particles and causes them to vibrate, as a result of which the density of the air in front of the bullet increases, and sound waves are formed, causing a characteristic sound, and a ballistic wave. In this case, the layer of air flowing around the bullet does not have time to close behind its bottom part, as a result of which a rarefied space is created there. The difference in air pressure exerted on the head and bottom of the bullet forms a force directed in the direction opposite to the direction of its flight and reduces its speed. In this case, air particles, trying to fill the rarefied space formed behind the bottom of the bullet, create a vortex.

The force of air resistance is the sum of all forces generated due to the influence of air on the flight of a bullet.

The center of resistance is the point where air resistance forces are applied to the bullet.

The force of air resistance depends on the shape of the bullet, its diameter, flight speed, and air density. With an increase in the speed of a bullet, its caliber and air density, it increases.

Under the influence of air resistance, the bullet's flight path loses its symmetrical shape. The speed of a bullet in the air decreases all the time as it moves away from the departure point, so the average speed of a bullet on the ascending branch of the trajectory is greater than on the descending branch. In this regard, the ascending branch of the bullet’s flight trajectory in the air is always longer and more positioned than the descending one; when shooting at medium distances, the ratio of the length of the ascending branch of the trajectory to the length of the descending branch is conventionally accepted as 3:2 (see Fig. 12).

Rice. 12. The trajectory of a bullet in the air

Rotation of a bullet around its axis

When a bullet flies in the air, the force of its resistance constantly strives to knock it over. It shows up in the following way. The bullet, moving by inertia, constantly strives to maintain the position of its axis, given direction weapon barrel. At the same time, under the influence of gravity, the direction of flight of the bullet constantly deviates from its axis, which is characterized by an increase in the angle between the axis of the bullet and the tangent to its flight path (see Fig. 13).

Rice. 13. The effect of air resistance on the flight of a bullet: CG - center of gravity, CS - center of air resistance

The action of the air resistance force is directed opposite to the direction of movement of the bullet and parallel to the tangent of its trajectory, i.e. from below at an angle to the axis of the bullet.

Based on the shape of the bullet, air particles hit the surface of its head at an angle close to a straight line, and the surface of the tail at a fairly acute angle (see Fig. 13). In this regard, compressed air appears at the head of the bullet, and rarefied space at the tail. Therefore, the air resistance in the head of the bullet significantly exceeds its resistance in the tail. As a result, the head speed decreases faster than the tail speed, which causes the head of the bullet to tip back (bullet rollover).

Tipping the bullet back leads to its random rotation in flight, while its flight range and accuracy of hitting the target are significantly reduced.

To ensure that the bullet does not tip over in flight under the influence of air resistance, it is given a rapid rotational movement around the longitudinal axis. This rotation is formed due to the helical rifling in the bore of the weapon.

The bullet, passing through the bore, under the pressure of powder gases enters the rifling and fills them with its body. Subsequently, like a bolt in a nut, it simultaneously moves forward and rotates around its axis. At the exit from the barrel, the bullet, by inertia, retains both translational and rotational motion. At the same time, the rotation speed of the bullet reaches very high values, for a Kalashnikov assault rifle 3000, and for a Dragunov sniper rifle - about 2600 revolutions per second.

The speed of rotation of a bullet can be calculated using the formula:

where Vvr is the rotation speed (revolutions per second), Vo is the initial bullet speed (mm/s), bnar is the rifling stroke length (mm).

When a bullet flies, the force of air resistance tends to tip the bullet head up and back. But the head of the bullet, rotating quickly, according to the property of the gyroscope, tends to maintain its position and deviate not upward, but slightly in the direction of its rotation - to the right, at a right angle to the direction of the air resistance force. When the head part is deflected to the right, the direction of the air resistance force changes, which now tends to turn the head part of the bullet to the right and back. But as a result of rotation, the head of the bullet does not turn to the right, but down and further until it describes a complete circle (see Fig. 14).

Rice. 14. Conical rotation of the bullet head

Thus, the head of a flying and rapidly rotating bullet describes a circle, and its axis is a cone with its apex at the center of gravity. The so-called slow conical movement occurs, in which the bullet flies with its head forward in accordance with the change in the curvature of the trajectory (see Fig. 15).

Rice. 15. Flight of a spinning bullet in the air

The axis of slow conical rotation is located above the tangent to the bullet’s flight path, so the lower part of the bullet is in to a greater extent exposed to the pressure of the oncoming air flow than the upper one. In this regard, the axis of slow conical rotation deviates in the direction of rotation, i.e. to the right. This phenomenon is called derivation (see Fig. 16).

Derivation is the deviation of a bullet from the firing plane in the direction of its rotation.

The firing plane is understood as the vertical plane in which the axis of the weapon bore lies.

The reasons for derivation are: the rotational movement of the bullet, air resistance and the constant decrease under the influence of gravity of the tangent to the bullet’s flight path.

In the absence of at least one of these reasons, there will be no derivation. For example, when shooting vertically up and vertically downward, there will be no derivation, since the force of air resistance in this case is directed along the axis of the bullet. There will be no derivation when shooting in airless space due to the lack of air resistance and when shooting from a smooth-bore weapon due to the lack of bullet rotation.

Rice. 16. The phenomenon of derivation (top view of the trajectory)

During the flight, the bullet deflects more and more to the side, while the degree of increase in derivational deviations significantly exceeds the degree of increase in the distance covered by the bullet.

Derivation is not of great practical importance for the shooter when shooting at close and medium distances; it must be taken into account only when shooting with extreme precision at long distances, making certain adjustments to the installation of the sight in accordance with the table of derivation deviations for the corresponding firing range.

Characteristics of the bullet's flight path

To study and describe the flight trajectory of a bullet, the following indicators characterizing it are used (see Fig. 17).

The departure point is located in the center of the muzzle of the barrel and is the beginning of the bullet’s flight path.

The weapon's horizon is the horizontal plane passing through the launch point.

The elevation line is a straight line that is a continuation of the axis of the bore of the weapon aimed at the target.

The elevation angle is the angle between the elevation line and the horizon of the weapon. If this angle is negative, for example, when

When shooting down from a significant elevation, it is called the declination (or descent) angle.

Rice. 17. Bullet flight path indicators

The throwing line is a straight line, which is a continuation of the axis of the bore at the moment the bullet leaves.

The throwing angle is the angle between the throwing line and the horizon of the weapon.

The launch angle is the angle between the elevation line and the throwing line. Represents the difference between the throwing angles and elevation angles.

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

The angle of incidence is the angle at the point of impact between the tangent to the bullet's flight path and the horizon of the weapon.

The final speed of a bullet is the speed of the bullet at the point of impact.

The total flight time is the time the bullet travels from the point of departure to the point of impact.

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

The vertex of a trajectory is its highest point.

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

The ascending branch of the trajectory is the part of the trajectory from the departure point to its apex.

The descending branch of a trajectory is the part of the trajectory from its top to the point of fall.

The meeting point is the point lying at the intersection of the bullet’s flight path with the target surface (ground, obstacle).

The meeting angle is the angle between the tangent to the bullet's flight path and the tangent to the target surface at the meeting point.

The aiming (aiming) point is the point on or outside the target at which the weapon is aimed.

The line of sight is a straight line from the shooter's eye through the middle of the sight slot and the top of the front sight to the aiming point.

The aiming angle is the angle between the aiming line and the elevation line.

Target elevation angle is the angle between the line of sight and the horizon of the weapon.

The aiming range is 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.

When shooting at close distances, the values of the trajectory exceeding the aiming line will be quite low. But when shooting at long distances they reach significant values (see Table 1).

Table 1

Exceeding the trajectory above the aiming line when firing from a Kalashnikov assault rifle (AKM) and a Dragunov sniper rifle (SVD) at distances of 600 m or more

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For 7.62 mm AKM
Range, m		100		200		300		400		500		600		700		800		900		1000
Aim		meters
6		0,98		1,8		2,2		2,1		1,4		0		-2,7		-6,4		-		-
7		1,3		2,5		3,3		3,6		3,3		2,1		-3,5		-8,4		-
8		1,8		3,4		4,6		5,4		5,5		4,7		3,0		0		-4,5		-10,5
For SVD using an optical sight
Range,	100		200	300	400		500		600	700	800		900		1000	1100	1200		1300		1400
Aim	meters
6	0,53		0,95	1,2	1,1		0,74		0	-1,3	-		-		-	-	-		-		-
7	0,71		1,3	1,7	1,9		1,6		1,0	0	-1,7		-		-	-	-		-		-
8	0,94		1,8	2,4	2,7		2,8		2,4	1,5	0		-2,2		-	-	-		-		-
9	1,2		2,2	3,1	3,7		4,0		3,9	2,3	2,0		0		-2,9	-	-		-		-
10	1,5		2,8	4,0	4,9		5,4		5,7	5,3	4,3		2,6		0	-3,7	-		-		-
11	1,8		3,5	5,0	6,2		7,1		7,6	7,7	7,1		5,7		3,4	0	-4,6		-		-
12	2,2		4,3	6,2	7,8		9,1		10,0	10,5	10,0		9,2		7,3	4,3	0		-5,5		-
13	2,6		5,1	7,4	9,5		11		12,5	13,5	13,5		13,0		11,5	8,9	5,1		0		-6,6

Note: The number of units in the sight value corresponds to the number of hundreds of meters of shooting distance for which the sight is designed

(6 - 600 m, 7 - 700 m, etc.).

From the table 1 shows that the excess of the trajectory above the aiming line when firing from an AKM at a distance of 800 m (sight 8) exceeds 5 meters, and when firing from an SVD at a distance of 1300 m (sight 13) - the bullet trajectory rises above the aiming line by more than 13 meters.

Aiming (weapon aiming)

In order for a bullet to hit the target as a result of a shot, it is first necessary to give the axis of the barrel bore the appropriate position in space.

Giving the axis of the weapon's bore the position necessary to hit a given target is called aiming or aiming.

This position must be given both in the horizontal and vertical planes. Giving the axis of the barrel bore the required position in the vertical plane is vertical guidance, giving it the required position in the horizontal plane is horizontal guidance.

If the aiming reference is a point on or near the target, such aiming is called direct. When shooting from small arms, direct aiming is used, carried out using a single aiming line.

The sight line is the straight line connecting the middle of the sight slot to the top of the front sight.

To carry out aiming, it is necessary first by moving the rear sight (sight slot) to give the aiming line a position in which between it and the axis of the barrel bore an aiming angle corresponding to the distance to the target is formed in the vertical plane, and in the horizontal plane - an angle equal to the lateral correction, taking into account crosswind speed, deflection and lateral speed of the target (see Fig. 18).

After this, directing the aiming line to the area that is the aiming reference, by changing the position of the weapon barrel, the axis of the barrel bore is given the required position in space.

In this case, in weapons with a permanently mounted rear sight, such as most pistols, to give the required position of the barrel bore in the vertical plane, an aiming point is selected that corresponds to the distance to the target, and the aiming line is directed to this point. In a weapon with a sight slot fixed in a lateral position, as in a Kalashnikov assault rifle, to give the required position of the barrel bore in the horizontal plane, an aiming point corresponding to the lateral correction is selected, and the aiming line is directed to this point.

Rice. 18. Aiming (aiming weapons): O - front sight; a - rear sight; aO - aiming line; сС - bore axis; oo - line parallel to the axis of the barrel bore;

H - sight height; M is the amount of movement of the rear sight; a - aiming angle; Ub - lateral correction angle

The shape of the bullet's flight path and its practical significance

The shape of a bullet's trajectory in the air depends on the angle at which it is fired relative to the weapon's horizon, its initial velocity, kinetic energy, and shape.

To fire a targeted shot, the weapon is aimed at the target, while the aiming line is directed to the aiming point, and the axis of the barrel bore in the vertical plane is brought to a position corresponding to the required elevation line. The required elevation angle is formed between the axis of the barrel bore and the horizon of the weapon.

When fired, under the influence of the recoil force, the axis of the barrel bore shifts by the amount of the take-off angle, while it moves to a position corresponding to the throwing line and forms a throwing angle with the horizon of the weapon. It is at this angle that the bullet flies out of the weapon's barrel.

Due to the slight difference between the elevation angle and the throwing angle, they are often identified, however, it is more correct in in this case talk about the dependence of the bullet’s flight path on the throwing angle.

As the throwing angle increases, the height of the bullet's flight path and the total horizontal range increase up to a certain value of a given angle, after which the height of the trajectory continues to increase, and the total horizontal range decreases.

The throwing angle at which the total horizontal range of the bullet is greatest is called the angle of greatest range.

In accordance with the laws of mechanics in airless space, the angle of greatest range will be 45°.

When a bullet flies in the air, the relationship between the throwing angle and the shape of the bullet’s flight path is similar to the dependence of these characteristics observed when a bullet flies in airless space, but, due to the influence of air resistance, the angle of greatest range does not reach 45°. Depending on the shape and mass of the bullet, its value ranges from 30 to 35°. For calculations, the angle of maximum firing range in the air is assumed to be 35°.

Bullet flight trajectories that occur at throwing angles smaller than the angle of greatest range are called flat.

The bullet flight trajectories that arise at throwing angles greater than the angle of greatest range are called hinged (see Fig. 19).

Rice. 19. Angle of greatest range, flat and mounted trajectories

Flat trajectories are used when firing direct fire at fairly short distances. When shooting from hand-held small arms, only this type of trajectories is used. The flatness of the trajectory is characterized by its maximum excess above the aiming line. The less the trajectory rises above the aiming line at a given firing range, the more flat it is. Also, the flatness of the trajectory is assessed by the angle of incidence: the smaller it is, the flatter the trajectory.

The flatter the trajectory used when shooting, the greater the distance the target can be hit with one gun setting.

intact, i.e. Errors in sight installation have less impact on shooting performance.

Mounted trajectories are not used when shooting from hand-held small arms; in turn, they are widespread in shooting shells and mines over long distances beyond the line of sight of the target, which in this case is specified by coordinates. Mounted trajectories are used when firing from howitzers, mortars and other types of artillery weapons.

Due to the peculiarities of this type of trajectory, these types of weapons can hit targets located in cover, as well as behind natural and artificial barriers (see Fig. 20).

Trajectories that have the same horizontal range at different throwing angles are called conjugate. One of these trajectories will be flat, the second will be mounted.

Conjugate trajectories can be obtained when shooting from one weapon, using throwing angles larger and smaller angle greatest range.

Rice. 20. Features of the use of mounted trajectories

A shot in which the excess of the trajectory above the aiming line along its entire length does not reach values greater than the height of the target is considered a direct shot (see Fig. 21).

Practical significance direct shot lies in the fact that within its range, during intense moments of battle, shooting can be carried out without rearranging the sight, while the vertical aiming point is, as a rule, selected at the lower edge of the target.

The range of a direct shot depends, firstly, on the height of the target and, secondly, on the flatness of the trajectory. The higher the target and the flatter the trajectory, the greater the direct shot range and the greater the distance the target can be hit with one sight setting.

Rice. 21. Straight shot

The range of a direct shot can be determined from tables, comparing the height of the target with the values of the greatest elevation of the trajectory above the aiming line or with the height of the trajectory.

When shooting at a target at a distance exceeding the direct shot range, the trajectory near the apex rises above the target, and the target in a certain area will not be hit with a given sight setting. In this case, there will be a space near the target in which the descending branch of the trajectory will lie within its height.

The distance at which the downward branch of the trajectory is within the target height is called the target space (see Fig. 22).

The depth (length) of the affected space directly depends on the height of the target and the flatness of the trajectory. It also depends on the angle of the terrain: when the terrain rises up, it decreases, when it slopes down, it increases.

Rice. 22. The affected space with a depth equal to the segment AC for the target

height equal to segment AB

If the target is behind cover that is impenetrable to a bullet, then the possibility of hitting it depends on where it is located.

The space behind the cover from its crest to the meeting point is called covered space (see Fig. 23). The covered space will be greater, the greater the height of the shelter and the flatter the bullet's flight path.

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 cover, the lower the height of the target and the flatter the trajectory, the greater the dead space. The part of the covered space in which a target can be hit constitutes the target space.

Thus, the depth of dead space is the difference between the covered and affected space.

Rice. 23. Covered, dead and affected space

The shape of the trajectory also depends on the initial speed of the bullet, its kinetic energy and shape. Let's consider how these indicators influence the formation of the trajectory.

The further speed of its flight directly depends on the initial speed of the bullet; the magnitude of its kinetic energy, with equal shapes and sizes, ensures a lesser degree of speed reduction under the influence of air resistance.

Thus, a bullet fired at the same elevation (throwing) angle, but with a greater initial speed or with greater kinetic energy during further flight will have a greater speed of movement.

If we imagine a certain horizontal plane at some distance from the departure point, then when same value elevation angle

When throwing (throwing), a bullet with a higher speed will reach it faster than a bullet with a lower speed. Accordingly, a slower bullet, having reached a given plane and spending more time on it, will have time to fall down more under the influence of gravity (see Fig. 24).

Rice. 24. Dependence of a bullet’s flight path on its speed

In the future, the flight path of a bullet with lower speed characteristics will be located below the flight path of a faster bullet and, under the influence of gravity, it will drop faster in time and closer in distance from the point of departure to the level of the weapon’s horizon.

Thus, the initial speed and kinetic energy of the bullet directly affect the height of the trajectory and the full horizontal range of its flight.

Fire range (m)	Flight time (s)
	0,15
	0,28
	0,42
	0,60
	0,80
	1,02
	1,26

Definition of initial bullet speed. The trajectory of a bullet in the air and its shape; the influence of gravity and air resistance on the flight of a bullet; properties of the trajectory. The influence of air resistance on the trajectory of a projectile

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

Penetrating wounds

Blind wounds

Cutting wounds

2.3.4 Dependence of the trajectory shape on the throwing angle. Path elements

2.3.5 Dependence of the trajectory shape on the initial velocity of the bullet, its shape and lateral load

2.3.6 Dependence of the trajectory on meteorological conditions

2.3.7 Bullet dispersion