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The trajectory in the air has the following property. Yuriev A.A. "Bullet sports shooting". Hinged trajectories allow

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.


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

Full time flight

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 horizon arms

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 in 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 the 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 the trajectories into two types: into the trajectories flat and hinged (Fig. 6).

Flat trajectories are called trajectories obtained at elevation angles, smaller angle longest 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).

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

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

trajectory called the curved line described by the center of gravity of the bullet in flight.
A bullet flying through the air is subjected to two forces: gravity and air resistance. The force of gravity causes the bullet to gradually descend, and the force of air resistance continuously slows down the movement of the bullet and tends to knock it over. As a result of the action of these forces, the bullet's flight speed gradually decreases, and its trajectory is an unevenly curved curved line in shape. Air resistance to the flight of a bullet is caused by the fact that air is elastic medium and therefore part of the energy of the bullet is expended on movement in this medium.

The force of air resistance is caused by three main causes: air friction, the formation of vortices and the formation of a ballistic wave.
The shape of the trajectory depends on the magnitude of the elevation angle. As the elevation angle increases, the height of the trajectory and the total horizontal range of the bullet increase, but this occurs up to a certain limit. Beyond this limit, the trajectory height continues to increase and the total horizontal range begins to decrease.

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

Trajectories obtained at elevation angles smaller than the angle of greatest range are called flat. Trajectories obtained at elevation angles greater than the angle largest angle longest range are called mounted. When firing from the same weapon (at the same initial speeds), you can get two trajectories with the same horizontal range: flat and mounted. Trajectories having the same horizontal range and swarms of different elevation angles are called conjugated.

When shooting from small arms, only flat trajectories are used. The flatter the trajectory, the greater the extent of the terrain, the target can be hit with one sight setting (the less impact on the shooting results is the error in determining the sight setting): this is the practical significance of the trajectory.
The flatness of the trajectory is characterized by its greatest excess over the aiming line. At a given range, the trajectory is all the more flat, the less it rises above the aiming line. In addition, the flatness of the trajectory can be judged by the magnitude of the angle of incidence: the trajectory is the more flat, the smaller the angle of incidence. The flatness of the trajectory affects the value of the range of a direct shot, struck, covered and dead space.

Trajectory elements

Departure point- the center of the muzzle of the barrel. The departure point is the start of the trajectory.
Weapon horizon is the horizontal plane passing through the departure point.
elevation line- a straight line, which is a continuation of the axis of the bore of the aimed weapon.
Shooting plane- a vertical plane passing through the line of elevation.
Elevation angle- the angle enclosed between the line of elevation and the horizon of the weapon. If this angle is negative, then it is called the angle of declination (decrease).
Throw line- a straight line, which is a continuation of the axis of the bore at the time of the bullet's departure.
Throwing angle
Departure angle- the angle enclosed between the line of elevation and the line of throwing.
drop point- the point of intersection of the trajectory with the horizon of the weapon.
Angle of incidence- the angle enclosed between the tangent to the trajectory at the point of impact and the horizon of the weapon.
Total horizontal range- the distance from the point of departure to the point of fall.
final speed- the speed of the bullet (grenade) at the point of impact.
Total flight time- the time of movement of a bullet (grenade) from the point of departure to the point of impact.
Top of the path - highest point trajectories over the horizon of the weapon.
Trajectory height- the shortest distance from the top of the trajectory to the horizon of the weapon.
Ascending branch of the trajectory- part of the trajectory from the departure point to the top, and from the top to the drop point - the descending branch of the trajectory.
Aiming point (aiming)- the point on the target (outside it) at which the weapon is aimed.
line of sight- a straight line passing from the shooter's eye through the middle of the sight slot (at the level with its edges) and the top of the front sight to the aiming point.
aiming angle- the angle enclosed between the line of elevation and the line of sight.
Target elevation angle- the angle enclosed between the aiming line and the horizon of the weapon. This angle is considered positive (+) when the target is higher and negative (-) when the target is below the weapon's horizon.
Sighting range- distance from the departure point to the intersection of the trajectory with the line of sight. The excess of the trajectory over the line of sight is the shortest distance from any point of the trajectory to the line of sight.
target line- a straight line connecting the departure point with the target.
Slant Range- distance from the departure point to the target along the target line.
meeting point- point of intersection of the trajectory with the surface of the target (ground, obstacles).
Meeting angle- the angle enclosed between the tangent to the trajectory and the tangent to the target surface (ground, obstacles) at the meeting point. The meeting angle is taken as the smaller of the adjacent angles, measured from 0 to 90 degrees.

The trajectory of a bullet is understood as a 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 a bullet is formed while it is in the bore. Under the influence of the energy of powder gases, the speed and direction are set to the bullet forward movement. And if external forces did not act on it, then according to the first law of Galileo - Newton, it would rectilinear motion in a given direction at a constant speed to infinity. At the same time, in every second it would cover a distance equal to initial speed bullets (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 features of the formation of the flight path of a bullet 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. The movement of a bullet by inertia (in the absence of the influence of gravity

and air resistance)

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

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

If the bullet flew out of the bore without having the kinetic energy given by the pressure of the powder gases, then, in accordance with the above formula, it would fall vertically down: in one second by 4.9 m; two seconds later 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 without kinetic energy in a vacuum

under the influence of gravity

When a bullet with a given kinetic energy moves by inertia, under the action of gravity, it will move a given distance down relative to the line that is a continuation of the axis of the bore. By constructing parallelograms, the lines of which will be the values ​​of the distances covered by the bullet by inertia and under the action of gravity in

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

Rice. 10. The trajectory of a bullet in a vacuum

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 vacuum, these parts will be the same.

In this case, the height of the top of the trajectory and, accordingly, its figure will depend only on the initial velocity 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 overturn it. To overcome the force of air resistance, part of the kinetic energy of the bullet is expended.

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

Rice. 11. Causes of air resistance

The bullet in flight collides with air particles and causes them to oscillate, as a result of which the density of the air in front of the bullet increases, and sound waves are formed that cause 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 parts of the bullet forms a force directed to the side 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 air resistance force is the sum of all the forces generated due to the influence of air on the flight of a bullet.

The center of drag is the point at which the force of air resistance is applied to the bullet.

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

Under the influence of air resistance, the flight path of the bullet loses its symmetrical shape. The speed of a bullet in the air decreases all the time as it moves away from the point of departure, so the average speed of a bullet on the ascending branch of the trajectory is greater than on the descending one. In this regard, the ascending branch of the flight path of a bullet in the air is always longer and flatter than the descending one; when shooting at medium distances, the ratio of the length of the ascending branch of the trajectories to the length of the descending one is conditionally taken 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 is flying in the air, the force of its resistance constantly strives to overturn it. It manifests itself in the following way. The bullet, moving by inertia, constantly strives to maintain the position of its axis, given direction barrel of the weapon. At the same time, under the influence of gravity, the direction of the bullet's flight constantly deviates from its axis, which is characterized by an increase in the angle between the axis of the bullet and the tangent to the trajectory of its flight (see Fig. 13).

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

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

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

Rolling the bullet backwards causes it to rotate erratically in flight, with a significant decrease in its flight range and accuracy of hitting the target.

In order for the bullet not to tip over in flight under the action of air resistance, it is given a quick rotary motion around the longitudinal axis. This rotation is formed due to the helical cutting 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. In the future, like a bolt in a nut, it simultaneously moves forward and rotates around its axis. At the exit from the bore, the bullet retains both translational and rotational motion by inertia. At the same time, the rotation speed of the bullet reaches very high values, for the Kalashnikov 3000 assault rifle, and for sniper rifle Dragunov - about 2600 rpm.

Bullet rotation speed can be calculated by the formula:

where Vvr - rotation speed (rpm), Vo - muzzle velocity (mm/s), Lnar - rifling stroke length (mm).

During the flight of a bullet, the force of air resistance tends to tip the bullet head up and back. But the head of the bullet, rotating rapidly, according to the property of the gyroscope, tends to maintain its position and deviate not upwards, but slightly in the direction of its rotation - to the right, at right angles 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 to its description full 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 a vertex at the center of gravity. There is a so-called slow conical movement, in which the bullet flies head first 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 flight path of the bullet, so the lower part of the bullet is in more subject to the pressure of the oncoming air flow than the top. 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 the bullet from the plane of fire in the direction of its rotation.

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

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

In the absence of at least one of these reasons, there will be no derivation. For example, when shooting vertically up and vertically down, there will be no derivation, since the air resistance force in this case is directed along the axis of the bullet. There will be no derivation when firing in a vacuum due to the lack of air resistance and when firing from smoothbore weapons due to the lack of rotation of the bullet.

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

During the flight, the bullet deviates more and more to the side, while the degree of increase in derivational deviations significantly exceeds the degree of increase in the distance traveled 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 for particularly accurate shooting at long distances, making certain adjustments to the installation of the sight in accordance with the table of derivational deviations for the corresponding firing range.

Bullet trajectory characteristics

To study and describe the flight path 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, is the beginning of the bullet's flight path.

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

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

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

Rice. 17. Bullet trajectory indicators

The line of throw is a straight line, which is a continuation of the axis of the bore at the time of the bullet's departure.

The throw angle is the angle between the throw line and the weapon's horizon.

The departure angle is the angle enclosed between the line of elevation and the line of throw. Represents the difference between the values ​​of the angles of throw and elevation.

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 weapon's horizon.

The final velocity of the bullet is the velocity of the bullet at the point of impact.

The total flight time is the time it takes the bullet to travel from the point of departure to the point of impact.

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

The vertex of the 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 top.

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

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

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 point of aim (aiming) is the point on or off 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 slit and the top of the front sight to the point of aim.

The angle of aim is the angle between the line of sight and the line of elevation.

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

Sighting range is the distance from the point of departure to the intersection of the trajectory with the line of sight.

The excess of the trajectory over the line of sight is the shortest distance from any point of the trajectory to the line of sight.

When shooting at close range, the values ​​of the excess of the trajectory over the aiming line will be quite low. But when firing 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 7.62mm 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 scope value corresponds to the number of hundreds of meters of shooting distance for which the scope is designed.

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

From Table. 1 shows that the excess of the trajectory above the aiming line when firing from the AKM at a distance of 800 m (sight 8) exceeds 5 meters, and when firing from the 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 the bullet to hit the target as a result of the shot, it is first necessary to give the axis of the barrel bore an appropriate position in space.

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

This position must be given both in the horizontal plane and in the vertical. Giving the axis of the bore the required position in the vertical plane is a vertical pickup, giving it the desired position in the horizontal plane is a horizontal pickup.

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, performed using a single sighting line.

The sight line is a 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 (slot of the sight), to give the aiming line such a position in which between it and the axis of the bore, an aiming angle is formed in the vertical plane corresponding to the distance to the target, and in the horizontal plane - an angle equal to the lateral correction, taking into account crosswind speed, derivation and lateral movement speed of the target (see Fig. 18).

After that, by directing the sighting line to the area, which is the aiming guideline, by changing the position of the weapon barrel, the axis of the bore is given the desired position in space.

At the same time, in weapons with a permanent rear sight, as, for example, in most pistols, in order to give the necessary position of the bore in the vertical plane, the aiming point is selected corresponding to the distance to the target, and the aiming line is directed to given point. In weapons with a sight slot fixed in the side position, as in a Kalashnikov assault rifle, to give the necessary position of the bore in the horizontal plane, the aiming point is selected corresponding to the side correction, and the aiming line is directed to this point.

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

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

Bullet trajectory shape and its practical significance

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

To produce 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 bore in the vertical plane is brought to a position corresponding to the required elevation line. Between the axis of the bore and the horizon of the weapon, the required elevation angle is formed.

When fired, under the action of the recoil force, the axis of the barrel bore is shifted by the value of the angle of departure, while it goes into a position corresponding to the line of throw and forms a throw angle with the horizon of the weapon. At this angle, the bullet flies out of the bore of the weapon.

Due to the insignificant difference between the angle of elevation and the angle of throwing, they are often identified, while, however, it is more correct in this case talk about the dependence of the trajectory of a bullet on the angle of throw.

With an increase in the angle of throw, the height of the trajectory of the flight of the bullet and the total horizontal range increase to a certain value given angle, after which the trajectory height continues to increase, and the total horizontal range decreases.

The angle of throw at which the full horizontal range of the bullet is greatest is called the angle of greatest range.

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

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

The flight paths of a bullet that occur at angles of throw smaller than the angle of greatest range are called flat.

The flight paths of a bullet that occur at angles of throw of a large angle of greatest range are called hinged (see Fig. 19).

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

Flat trajectories are used when firing direct fire at fairly short distances. When firing from small arms, only this type of trajectory is used. The flatness of the trajectory is characterized by its maximum excess over 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 estimated 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 set of

intact, i.e. errors in the installation of the sight have a lesser effect on the effectiveness of shooting.

Mounted trajectories are not used when firing from small arms, in turn, they have widespread in firing shells and mines over long distances out of line of sight of the target, which in this case is set 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 throw angles are called conjugate. One of these trajectories will be flat, the second hinged.

Conjugated trajectories can be obtained when firing from one weapon, using throwing angles greater and less than the angle of greatest range.

Rice. 20. Features of the use of hinged trajectories

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

Practical value direct shot lies in the fact that within its range in tense moments of the battle, it is allowed to fire 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, 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 range of a direct shot and the greater the distance the target can be hit with one sight setting.

Rice. 21. Direct shot

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

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

The distance at which the descending branch of the trajectory is within the height of the target is called the affected 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 inclination of the terrain: when the terrain rises up, it decreases, when it slopes down, it increases.

Rice. 22. Affected space with a depth equal to the segment AC, for the target

height equal to segment AB

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

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

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

Thus, the depth of the 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 muzzle velocity of the bullet, its kinetic energy and shape. Consider how these indicators affect the formation of the trajectory.

The further speed of its flight directly depends on the initial speed of the bullet, the value of its kinetic energy, with equal shapes and sizes, provides a smaller degree of speed reduction under the action of air resistance.

Thus, a bullet fired at the same elevation (throw) angle, but with a higher initial velocity or with a higher kinetic energy, will have a higher speed during further flight.

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

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

Rice. 24. The dependence of the trajectory of the flight of a bullet on its speed

In the future, the trajectory of a bullet with lower speed characteristics will also be located below the trajectory 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 muzzle velocity and kinetic energy of the bullet directly affect the height of the trajectory and the full horizontal range of its flight.

Flight of a bullet in the air

Having flown out of the bore, the bullet moves by inertia and is subjected to the action of two forces of gravity and air resistance

The force of gravity causes the bullet to gradually descend, and the force of air resistance continuously slows down the movement of the bullet and tends to knock it over. To overcome the force of air resistance, part of the energy of the bullet is expended

The force of air resistance is caused by three main reasons: air friction, the formation of eddies, and the formation of a ballistic wave (Fig. 4)

The bullet collides with air particles during flight and causes them to oscillate. As a result, the air density increases in front of the bullet and sound waves are formed, a ballistic wave is formed. The force of air resistance depends on the shape of the bullet, flight speed, caliber, air density

Rice. 4. Formation of air resistance force

In order to prevent the bullet from tipping over under the action of air resistance, it is given a rapid rotational movement with the help of rifling in the bore. Thus, as a result of the action of gravity and air resistance on the bullet, it will not move uniformly and rectilinearly, but will describe a curved line - a trajectory.

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

To study the trajectory, the following definitions are adopted (Fig. 5):

· departure point - the center of the muzzle of the barrel, in which the center of gravity of the bullet is located at the time of departure. The moment of departure is the passage of the bottom of the bullet through the muzzle of the barrel;

· weapon horizon - a horizontal plane passing through the departure point;

· elevation line - a straight line, which is a continuation of the axis of the bore at the moment of departure;

· shooting plane - a vertical plane passing through the line of elevation;

· throw line - a straight line, which is a continuation of the axis of the bore at the time of the bullet's departure;

· throw angle - the angle enclosed between the line of throw and the horizon of the weapon;

· departure angle - the angle enclosed between the line of elevation and the line of throwing;

· drop point - the point of intersection of the trajectory with the horizon of the weapon,

· injection fall – the angle at the point of impact between the tangent to the trajectory and the horizon of the weapon,

· full horizontal range - distance from point of departure to point of fall,

· top of the trajectory the highest point of the trajectory;

· trajectory height - the shortest distance from the top of the trajectory to the horizon of the weapon,

· ascending branch of the trajectory - part of the trajectory from the departure point to its top;

· descending branch of the trajectory - part of the trajectory from the top to the point of fall,



· meeting point - intersection of the trajectory with the surface of the target (ground, obstacles),

· meeting angle - the angle enclosed between the tangent to the trajectory and the tangent to the target surface at the meeting point;

· aiming point - the point on or off the target at which the weapon is aimed,

· line of sight - a straight line from the shooter's eye through the middle of the sight slot and the top of the front sight to the aiming point,

· aiming angle - the angle enclosed between the aiming line and the elevation line;

· target elevation angle the angle enclosed between the aiming line and the horizon of the weapon;

· aiming range - distance from the point of departure to the intersection of the trajectory with the line of sight;

· excess of the trajectory over the aiming line - the shortest distance from any point of the trajectory to the line of sight;

· elevation angle - the angle enclosed between the line of elevation and the horizon of the weapon. The shape of the trajectory depends on the elevation angle

Rice. five. Bullet trajectory elements

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

The descending branch is steeper than the ascending one;

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

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

The lowest speed of a bullet when shooting at high angles of throw

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

the time of movement of the bullet along the ascending branch of the trajectory is less than

descending;

· the trajectory of a rotating bullet due to the decrease under the action of gravity and derivation is a line of double curvature.

The shape of the trajectory depends on the magnitude of the elevation angle (Fig. 6). As the elevation angle increases, the height of the trajectory and the total horizontal range of the bullet increase, but this occurs up to a certain limit. Beyond this limit, the trajectory height continues to increase and the total horizontal range begins to decrease.

Rice. 6. Angle of greatest reach, flat,

hinged and conjugate trajectories

The angle of elevation at which the full horizontal range of the bullet is at its greatest is called the angle of greatest range. The value of the angle of greatest range for small arms is 30-35 degrees, and for the range artillery systems 45-56 degrees.

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

Trajectories obtained at elevation angles greater than the angle of greatest range are called mounted. When firing from the same weapon, you can get two trajectories with the same horizontal range - flat and mounted. Trajectories having the same horizontal range at different elevation angles are called conjugated.

Flat trajectories allow:

1. It is good to hit openly located and fast moving targets.

2. Successfully fire from guns at a long-term firing structure (DOS), a long-term firing point (DOT), from stone buildings at tanks.

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

Mounted trajectories allow:

1. Hit targets behind cover and in deep terrain.

2. Destroy the ceilings of structures.

These different tactical properties of flat and overhead trajectories can be taken into account when organizing a fire system. The flatness of the trajectory affects the range of a direct shot, the affected and covered space.

Aiming (aiming) weapons at the target.

The task of any shooting is to hit the target in the most a short time and with the least amount of ammunition. This problem can be solved only in close proximity to the target and if the target is motionless. In most cases, hitting a target is associated with certain difficulties arising from the properties of the trajectory, meteorological and ballistic conditions shooting and the nature of the target.

Let the target be at point A - at some distance from the firing position. In order for the bullet to reach this point, the barrel of the weapon must be given a certain angle in the vertical plane (Fig. 7).

But from the wind, lateral deflections of the bullet can occur. Therefore, when aiming, it is necessary to take a lateral correction for the wind. Thus, in order for the bullet to reach the target and hit it or the desired point on it, it is necessary to give the axis of the bore a certain position in space (in the horizontal and vertical plane) before firing.

Giving the axis of the bore of a weapon the position in space necessary for firing is called aiming or pointing. Giving the axis of the bore of the weapon the required position in the horizontal plane is called horizontal pickup, and in the vertical plane - vertical pickup.

Rice. 7. Aiming (aiming) with open sight:

O - front sight, a - rear sight, aO - aiming line; сС - the axis of the bore, оО - a line parallel to the axis of the bore: H - the height of the sight, M - the amount of displacement of the rear sight;

a - aiming angle; Ub - angle of lateral correction

Accurate solution of aiming problems of any type sights depends on the correct alignment of them on the weapon. Alignment of sights of small arms for shooting at ground targets carried out in the process of checking the combat of the weapon and bringing it to normal combat.

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 barrel 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. This creates a large number of highly heated gases that 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 inflow new gases, and the pressure starts to drop. 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 effect, reduces the impact external conditions for her 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 rest against 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 angle of elevation and the initial velocity 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. The practical significance of a 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 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 amount of gases grows faster than the volume of the bullet space (the space between the bottom of the bullet and the bottom of the case), the gas pressure rises rapidly and reaches largest(for example, for small arms chambered for a sample of 1943 - 2800 kg / cm 2, and for a rifle cartridge 2900 kg / cm 2). This pressure is called maximum pressure. It is created in small arms when a bullet travels 4 - 6 cm of the path. Then due to 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 easel machine gun Goryunov - 570 kg / cm 2). The speed of the bullet at the time of its departure from the bore (muzzle velocity) is somewhat less than the initial velocity.