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The value of the initial velocity of the bullet depends on. Sniper training. Internal and external ballistics. Flat trajectories allow

The bullet, having received a certain initial velocity upon departure from the bore, strives by inertia to maintain the magnitude and direction of this velocity.

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

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

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

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

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

Rice. 5. Horizon weapons

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

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

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

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

If we assume that gravity acts on the bullet during its flight by inertia in airless space, then under the influence of this force the bullet will fall lower from the continuation of the bore axis - in the first second - by 4.9 m, in the second - by 19.6 m etc. In this case, if you point the barrel of the weapon at the target, the bullet will never hit it, because, being subjected to the action of gravity, it will fly under the target (Fig. 7).

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

but no air resistance

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

As can be seen from fig. 8, the trajectory of a bullet in airless space, on which the force of gravity acts, is a regular curve, which is called parabola. The highest point of the trajectory above the horizon of the weapon is called its summit. The part of the curve from the departure point to the apex is called ascending branch. Such a bullet trajectory is characterized by the fact that the ascending and descending branches are exactly the same, and the angle of throw and fall are equal to each other.

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

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

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

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

During the flight, the bullet spends a significant part of its energy on pushing the air particles that interfere with its flight.

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

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

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

(over 340 m/s)

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

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

The rotation of the bullet around its axis. It is known that a body acquires considerable stability if it is given a rapid rotary motion around its axis. An example of the stability of a rotating body is a spinning top toy. A non-rotating “top” will not stand on its pointed leg, but if the “top” is given a quick rotational movement around its axis, it will stand steadily on it (Fig. 10).

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

Without going into details of the explanation physical phenomena, associated with the action of forces on a body experiencing a complex movement, it must still be said that the bullet during flight makes regular oscillations and describes a circle around the trajectory with its head (Fig. 12). In this case, the longitudinal axis of the bullet, as it were, “follows” the trajectory, describing a conical surface around it (Fig. 13).

Rice. 12. Conical rotation of the bullet head

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

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

However, the rotational movement of the bullet, so necessary to give it stability during flight, has its negative sides.

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

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

Rice. 15. The phenomenon of derivation

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

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

trajectory called the curved line described by the center of gravity of the bullet in flight.

Rice. 3. Trajectory

Rice. 4. Bullet trajectory parameters

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

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

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

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

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

Types of trajectories and their practical significance.

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

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

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

Rice. 5. The affected area and the greatest horizontal and aiming ranges when firing at different elevation angles.

Rice. 6. Angle of greatest range. flat, hinged and conjugate trajectories

Flat trajectories are called trajectories obtained at elevation angles, smaller angle longest range (see figure, trajectories 1 and 2).

Hinged trajectories call the trajectories obtained at elevation angles greater than the angle of greatest range (see figure, trajectories 3 and 4).

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

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

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

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1.1.1. Shot. Shot periods and their characteristics.

Shot is called the ejection of a bullet from the bore of a weapon by the energy of gases formed during the combustion of a powder charge.

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

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

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

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

Preliminary;

First or main;

The third or period of aftereffect of gases.

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

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

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

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

Rice. 116 - Shot periods

The third period, or the period of aftereffect of gases, lasts from the moment the bullet leaves the bore until the moment the action of powder gases on the bullet ceases. During this period, the powder gases flowing out of the bore at a speed of 1200-2000 m/s continue to act on the bullet and impart additional speed to it. The bullet reaches its maximum (maximum) speed at the end of the third period at a distance of several tens of centimeters from the muzzle of the barrel. . This period ends at the moment when the pressure of the powder gases at the bottom of the bullet is balanced by air resistance.

1.1.2. Initial and maximum speed.

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

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

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

The muzzle velocity of a bullet depends on:

1) Barrel length.

2) Bullet weight.

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

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

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

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

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

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

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

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

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

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

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

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

When firing from automatic weapons, the device of which is based on the principle of using recoil energy - part of it is spent on communicating movement to moving parts and reloading weapons. Recoil energy is generated when firing from such weapons or from automatic weapons, the device of which is based on the principle of using the energy of powder gases discharged through a hole in the barrel wall.

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

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

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

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

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

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

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

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

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

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

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

1.2.1 Bullet flight path and its elements

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

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

gravity

Forces of resistance.

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

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

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

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

1) Air friction.

2) The formation of swirls.

3) The formation of a ballistic wave.

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

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

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

A bullet (grenade) in flight collides with air particles and causes them to oscillate. As a result, air density increases in front of the bullet (grenade) and sound waves are formed. Therefore, the flight of a bullet (grenade) is accompanied by a characteristic sound. At a bullet (grenade) flight speed that is less than the speed of sound, the formation of these waves has little effect on its flight, since the waves propagate faster than the bullet (grenade) flight speed.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Rice. 121 Trajectory shapes

Trajectories obtained with elevation angles less than the angle of greatest range, called flat.

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

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

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

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

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

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

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

1.2.3. Direct shot (Fig. 122).

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

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

The range of a direct shot depends on:

target heights;

Flatness of the trajectory;

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

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

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

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

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

The depth of the affected space depends on:

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

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

trajectory);

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

increases).

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

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

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

On the reverse slope - the difference of these angles;

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

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

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

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

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

1.2.5. Covered space (Fig. 123).

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

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

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

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

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

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

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

Rice. 123 - Covered, dead and affected space

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

The following are accepted as normal (table) conditions:

A) Meteorological conditions:

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

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

Relative Humidity air 50% (relative humidity

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

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

at a given temperature);

There is no wind (the atmosphere is still);

B) Ballistic conditions:

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

indicated in the shooting tables;

Charge temperature + 15 deg. S.;t

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

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

C) Topographic conditions:

The target is on the weapon's horizon;

There is no side slope of the weapon;

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

Influence of atmospheric pressure

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

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

Temperature effect

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

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

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

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

Wind influence

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

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

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

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

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

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

Influence of air humidity

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

Influence of sight installation

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

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

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

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

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

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

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

Types of trajectories and their practical significance

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

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

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

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

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

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

Shot is a complex set of physical and chemical phenomena. The firing event can be conditionally divided into two stages - the movement of the projectile in the gun bore and the complex of phenomena that occur after the projectile leaves the barrel.

Shot is called the ejection of a bullet from the bore under the action of powder gases formed during the combustion of a powder charge. From the impact of the striker on the primer of the cartridge, a flame arises that ignites the powder charge. In this case, a large amount of highly heated gases are formed, which create high pressure, acting in all directions with the same force. At a gas pressure of 250-500 kg / cm 2, the bullet moves from its place and crashes into the rifling of the bore, receiving rotational motion. Gunpowder continues to burn, therefore, the amount of gases increases. Then, due to the rapid increase in the speed of the bullet, the volume of the bullet space increases faster than the influx of new gases, and the pressure begins to fall. However, the speed of the bullet in the bore continues to increase, as the gases, although to a lesser extent, still put pressure on it. The bullet moves along the bore at a continuously increasing speed and is ejected outward in the direction of the axis of the bore. The entire firing process takes place in a very short period of time (0.001–0.06 s). Further, the flight of the bullet in the air continues by inertia and largely depends on its initial velocity.

muzzle velocity is the speed at which the bullet leaves the bore. The value of the muzzle velocity of a bullet depends on the length of the barrel, the mass of the bullet, the mass of the powder charge, and other factors. An increase in the initial speed increases the range of the bullet, its penetrating and lethal action, reduces the influence of external conditions on its flight. The movement of the weapon backwards while firing is called recoil. The pressure of powder gases in the bore acts in all directions with the same force. The pressure of the gases on the bottom of the bullet makes it move forward, and the pressure on the bottom of the cartridge case is transmitted to the bolt and causes the weapon to move backward. When recoil, a pair of forces is formed, under the influence of which the muzzle of the weapon deviates upward. The recoil force acts along the axis of the bore, and the butt stop in the shoulder and the center of gravity of the weapon are located below the direction of this force, therefore, when firing, the muzzle of the weapon deviates upward.

recoil small arms is felt in the form of a push in the shoulder, arm or into the ground. The recoil action of a weapon is characterized by the amount of speed and energy that it has when moving backward. The recoil speed of the weapon is about as many times less than the initial speed of the bullet, how many times the bullet is lighter than the weapon. The recoil energy of the Kalashnikov assault rifle is small and is perceived painlessly by the shooter. Correct and uniform holding of the weapon reduces the impact of recoil and increases the effectiveness of shooting. The presence of muzzle brakes-compensators or compensators for weapons improves the results of firing bursts and reduces recoil.

At the time of the shot, the barrel of the weapon, depending on the elevation angle, occupies a certain position. The flight of a bullet in the air begins in a straight line, representing the continuation of the axis of the bore at the time of the bullet's departure. This line is called throw line. When flying in the air, two forces act on a bullet: gravity and air resistance. Gravity pushes the bullet further and further away from the line of throw, while air resistance slows the bullet down. Under the influence of these two forces, the bullet continues to fly along a curve located below the line of throw. Trajectory shape depends on the magnitude of the elevation angle and the initial speed of the bullet, it affects the value of the range of a direct shot, covered, affected and dead space. As the elevation angle increases, the height of the trajectory and the total horizontal range of the bullet increase, but this occurs up to a certain limit. Beyond this limit, the trajectory height continues to increase and the total horizontal range decreases.

The angle of elevation at which the full horizontal range of the bullet is greatest is called farthest angle. The value of the angle of greatest range for bullets of various types of weapons is about 35 °. Trajectories obtained at elevation angles smaller than the angle of greatest range are called flat.

Straight shot called a shot in which the trajectory of the bullet does not rise above the line of sight above the target throughout its entire length.

Direct shot range depends on the height of the target and flatness of the trajectory. The higher the target and the flatter the trajectory, the greater the range of a direct shot and, therefore, the distance at which the target can be hit with one sight setting. Practical value direct shot lies in the fact that in tense moments of the battle, shooting can be carried out without rearranging the sight, while the aiming point in height will be selected along the lower edge of the target.

The space behind a cover that is not penetrated by a bullet, from its crest to the meeting point is called covered space.

The covered space is the greater, the higher the shelter and the flatter the trajectory. The part of the covered space on which the target cannot be hit with a given trajectory is called dead (non-hit) space. It is the greater, the greater the height of the shelter, the lower the height of the target and the flatter the trajectory. The other part of the covered space in which the target can be hit is the hit space.

Shot periodization

The shot occurs in a very short period of time (0.001-0.06 s.). When fired, four consecutive periods are distinguished:

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

Preliminary period lasts from the beginning of the burning of the powder charge to the complete cutting of the shell of the bullet into the rifling of the barrel. During this period, the gas pressure is created in the barrel bore, which is necessary in order to move the bullet from its place and overcome the resistance of its shell to cutting into the rifling of the barrel. This pressure is called boost pressure; it reaches 250 - 500 kg / cm 2, depending on the rifling device, the weight of the bullet and the hardness of its shell (for example, for small arms chambered for the 1943 sample, the forcing pressure is about 300 kg / cm 2). It is assumed that the combustion of the powder charge in this period occurs in a constant volume, the shell cuts into the rifling instantly, and the movement of the bullet begins immediately when the forcing pressure is reached in the bore.

First or main period lasts from the beginning of the movement of the bullet until the moment of complete combustion of the powder charge. During this period, the combustion of the powder charge occurs in a rapidly changing volume. At the beginning of the period, when the speed of the bullet along the bore is still low, the amount of gases grows faster than the volume of the bullet space (the space between the bottom of the bullet and the bottom of the cartridge case), the gas pressure rises rapidly and reaches its highest value (for example, in small arms chambered for sample 1943 - 2800 kg / cm 2, and under a rifle cartridge 2900 kg / cm 2). This pressure is called maximum pressure. It is created in small arms when a bullet travels 4 - 6 cm of the path. Then due to fast speed movement of the bullet, the volume of the bullet space increases faster than the influx of new gases, and the pressure begins to fall, by the end of the period it is equal to approximately 2/3 of the maximum pressure. The speed of the bullet is constantly increasing and by the end of the period reaches approximately 3/4 of the initial speed. The powder charge completely burns out shortly before the bullet leaves the bore.

Second period lasts until the moment of complete combustion of the powder charge until the moment the bullet leaves the bore. With the beginning of this period, the influx of powder gases stops, however, highly compressed and heated gases expand and, putting pressure on the bullet, increase its speed. The pressure drop in the second period occurs quite quickly and at the muzzle, the muzzle pressure is 300 - 900 kg / cm 2 for various types of weapons (for example, for the Simonov self-loading carbine - 390 kg / cm 2, for the Goryunov easel machine gun - 570 kg / cm 2 ). The speed of the bullet at the time of its departure from the bore (muzzle velocity) is somewhat less than the initial velocity.