External and internal ballistics determination. Formation of the trajectory of the bullet. Methods for determining the midpoint of impact

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 topple it.

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	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 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 value.

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 corner 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 largest horizontal and aiming ranges when shooting 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 are called trajectories obtained with the same horizontal range 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.

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To successfully master the technique of shooting from any small arms, it is necessary to master the knowledge of the laws of ballistics and a number of basic concepts related to it. Not a single sniper could and does not do without this, and without studying this discipline, a sniping training course is of little use.

Ballistics is the science of the movement of bullets and projectiles fired from small arms when fired. Ballistics is subdivided into external And internal.

Internal ballistics

Internal ballistics studies the processes occurring in the bore of a weapon during a shot, the movement of a bullet along the bore and the aero- and thermodynamic dependences accompanying this phenomenon both in the bore and outside it until the end of the aftereffect of powder gases.

Besides, internal ballistics studies issues most rational use the energy of the powder charge during the shot so that the bullet of a given caliber and weight is given the optimal initial speed while respecting the strength of the weapon barrel: this provides initial data for both external ballistics and weapon design.

Shot

Shot- this is the ejection of a bullet from the bore of a weapon under the influence of the energy of gases formed during the combustion of the powder charge of the cartridge.

Shot dynamics. When the striker hits the primer of a live cartridge sent into the chamber, the percussion composition of the primer explodes, and a flame is formed, which is transmitted through the seed holes in the bottom of the sleeve to the powder charge and ignites it. With the simultaneous combustion of a combat (powder) charge, a a large number of heated powder gases, which create high pressure on the bottom of the bullet, the bottom and walls of the sleeve, as well as on the walls of the bore and the bolt.

Under strong pressure of powder gases on the bottom of the bullet, it is separated from the cartridge case and crashes into the channels (rifling) of the weapon barrel and, rotating along them at a constantly increasing speed, is thrown outward in the direction of the axis of the barrel bore.

In turn, the pressure of gases on the bottom of the sleeve causes the movement of the weapon (the barrel of the weapon) back: this phenomenon is called bestowal. How more caliber weapons and, accordingly, ammunition (cartridge) under it - the greater the recoil force (see below).

When fired from automatic weapons, the principle of operation of which is based on the use of powder gases energy removed through a hole in the barrel wall, as, for example, in SVD, part of the powder gases, after passing into the gas chamber, hits the piston and throws the pusher with the shutter back.

The shot occurs in an ultra-short period of time: from 0.001 to 0.06 seconds and is divided into four consecutive periods:

preliminary
first (main)
second
third (aftereffect period of powder gases)

Pre-shot period. It lasts from the moment the powder charge of the cartridge ignites until the moment the bullet completely cuts into the rifling of the barrel bore. During this period, sufficient gas pressure is created in the bore to move the bullet from its place and overcome the resistance of its shell to cutting into the rifling of the bore. This type of pressure is called boost pressure, which reaches a value of 250 - 600 kg / cm², depending on the weight of the bullet, the hardness of its shell, caliber, barrel type, number and type of rifling.

First (main) shot period. It lasts from the moment the bullet begins to move along the bore of the weapon until the moment complete combustion powder charge of the cartridge. During this period, the combustion of the powder charge occurs in rapidly changing volumes: at the beginning of the period, when the speed of the bullet along the bore is still relatively 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 rapidly rises and reaches largest- 2900 kg/cm² for a 7.62 mm rifle cartridge: 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 a very rapid increase in the speed of the bullet, the volume of the bullet space increases faster than inflow new gases, as a result of which 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 shot period. It lasts from the moment of complete combustion of the powder charge until the moment the bullet leaves the barrel. With the beginning of this period, the influx of powder gases stops, but highly heated, compressed gases expand and, putting pressure on the bullet, significantly increase its speed. The pressure drop in the second period occurs quite quickly and the muzzle pressure at the muzzle of the weapon barrel is 300 - 1000 kg / cm² for various types of weapons. muzzle velocity, that is, the speed of the bullet at the time of its departure from the bore is slightly less than the initial speed.

The third period of the shot (the period of aftereffect of powder gases). It lasts from the moment the bullet leaves the bore of the weapon until the moment the action of the powder gases on the bullet ceases. During this period, 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 speed at the end of the third period at a distance of several tens of centimeters from the muzzle of the weapon barrel. This period ends at the moment when the pressure of the powder gases at the bottom of the bullet is fully balanced by the air resistance.

muzzle velocity

muzzle velocity- this is the speed of the bullet at the muzzle of the barrel of the weapon. For the value of the initial speed of the bullet, the conditional speed is taken, which is less than the maximum, but more than the muzzle, which is determined empirically and by the corresponding calculations.

This option is one of the most important characteristics combat properties of weapons. The value of the initial velocity of the bullet is indicated in the firing tables and in the combat characteristics of the weapon. 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:

bullet weight
barrel length
temperature, weight and humidity of the powder charge
sizes and shapes of powder grains
loading density

Bullet weight. The smaller it is, the greater its initial speed.

Barrel length. The larger it is, the longer the period of time the powder gases act on the bullet, respectively, the greater its initial speed.

Powder charge temperature. With a decrease in temperature, the initial velocity of the bullet decreases, with an increase, it increases due to an increase in the burning speed of the gunpowder and the pressure value. Under normal weather conditions, the temperature of the powder charge is approximately equal to the air temperature.

Powder charge weight. How more weight powder charge of the cartridge, the greater the amount of powder gases acting on the bullet, the greater the pressure in the bore and, accordingly, the speed of the bullet.

Powder charge moisture content. With its increase, the burning rate of gunpowder decreases, respectively, the speed of the bullet decreases.

The size and shape of the grains of gunpowder. Gunpowder grains of various sizes and shapes have different speed combustion, and this has a significant impact on the initial velocity of the bullet. The best option is selected at the stage of weapon development and during its subsequent tests.

Loading density. This is the ratio of the weight of the powder charge to the volume of the cartridge case with the bullet inserted: this space is called charge combustion chamber. If the bullet is too deep into the cartridge case, the loading density increases significantly: when fired, this can lead to a rupture of the weapon barrel due to a sharp pressure surge inside it, therefore such cartridges cannot be used for shooting. The greater the loading density, the lower the muzzle velocity, the lower the loading density, the greater the muzzle velocity.

recoil

recoil- This is the movement of the weapon back at the time of the shot. It is felt as a push in the shoulder, arm, ground, or a combination of these sensations. The recoil action of the weapon is about as many times less than the initial velocity of the bullet, how many times the bullet is lighter than the weapon. The recoil energy of hand-held small arms usually does not exceed 2 kg / m and is perceived by the shooter painlessly.

The recoil force and the recoil resistance force (butt stop) are not located on the same straight line: they are directed in opposite directions and 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 vibrates, that is, it makes oscillatory movements. 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, left, right).

It should always be remembered that the value of this deviation increases if the firing stop is used incorrectly, the weapon is contaminated, or non-standard cartridges are used.

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 departure angle.

Departure angle it is considered positive if the axis of the bore at the time of the bullet's departure is higher than its position before the shot, negative - when it is lower. The influence of the departure angle on shooting is eliminated when it is brought to normal combat. But in case of violation of the rules for caring for a weapon and its conservation, the rules for applying a weapon, using an emphasis, the value of the angle of departure and the battle of the weapon change. In order to reduce the harmful effect of recoil on the results of shooting, recoil compensators are used, located on the muzzle of the weapon barrel or removable, attached to it.

External ballistics

External ballistics studies the processes and phenomena accompanying the movement of a bullet that occur after the effect of powder gases ceases on it. The main task of this sub-discipline is to study the patterns of bullet flight and the study of the properties of the trajectory of its flight.

Also, this discipline provides data for developing shooting rules, compiling shooting tables and calculating weapon sight scales. Conclusions from external ballistics have long been widely used in combat when choosing a sight and aiming point depending on the firing range, wind speed and direction, air temperature and other firing conditions.

This is the curved line described by the bullet's center of gravity during flight.

Bullet flight path, bullet flight in space

When flying in space, two forces act on a bullet: the force of gravity And air resistance force.

The force of gravity causes the bullet to gradually descend horizontally towards the plane of the ground, and the force of air resistance permanently (continuously) slows down the flight of the bullet and tends to overturn it: as a result, the speed of the bullet 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 some part of the energy of the bullet is expended on movement in this medium.

Force of air resistance caused by three main factors:

air friction
swirls
ballistic wave

Shape, properties and types of toolpath

Trajectory shape depends on the elevation angle. As the elevation angle increases, the trajectory height and full horizontal range of the bullet increase, but this happens up to a certain limit, after which the trajectory height continues to increase, and the total horizontal range begins to decrease.

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

Hinged trajectory is the trajectory obtained at elevation angles greater than the angle of greatest range.

Flat trajectory- trajectory obtained at elevation angles smaller than the angle of greatest range.

Conjugate trajectory- a trajectory having the same horizontal range at different elevation angles.

When firing from weapons of the same model (with the same initial speeds bullets), you can get two flight paths with the same horizontal range: hinged and flat.

When shooting from small arms, only flat trajectories. The flatter the trajectory, the greater the distance the target can be hit with one sight setting, and 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 angle of incidence: the trajectory is 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.

Departure point- the center of the muzzle of the barrel of the weapon. 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 that 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 angle of declination (descent).

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 b is the speed of the bullet at the point of impact.

Total flight time- the time of movement of the bullet from the point of departure to the point of impact.

Top of the path- the highest point of the trajectory above the horizon of the weapon.

Trajectory height- the shortest distance from the top of the trajectory to the horizon of the weapon.

Ascending branch of the trajectory- part of the trajectory from the departure point to the top.

Descending branch of the trajectory- part of the trajectory from the top to the point of fall.

Aiming point (sighting point)- 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 a 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 smaller of the adjacent angles, measured from 0 to 90°, is taken as the meeting angle.

Direct shot, covered area, hit area, dead space

This is a shot in which the trajectory does not rise above the line of sight above the target for its entire length.

Direct shot range depends on two factors: the height of the target and the flatness of the trajectory. The higher the target and the flatter the trajectory, the greater the range of a direct shot and the greater the extent of the terrain, the target can be hit with one sight setting.

Also, the range of a direct shot can be determined from shooting tables by 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.

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

Practical use

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

At a distance of 80 meters from the shooter bullet trajectory height will be 3 cm, and aiming line height- 5 cm, the same difference of 2 cm is not decisive. The bullet will fall only 2 cm below the aiming point.

The vertical spread of bullets of 2 cm is so small that it is of no fundamental importance. Therefore, when shooting with division "2" of the optical sight, starting from 80 meters of distance and up to 200 meters, aim at the bridge of the nose of the enemy - you will get there and get ± 2/3 cm higher lower throughout this distance.

At a distance of 200 meters, the bullet will hit exactly the aiming point. And even further, at a distance of up to 250 meters, aim with the same sight "2" at the enemy's "top", at the upper cut of the cap - the bullet drops sharply after 200 meters of distance. At 250 meters, aiming in this way, you will fall 11 cm lower - in the forehead or bridge of the nose.

The above method of firing can be useful in street battles, when relatively open distances in the city are approximately 150-250 meters.

Affected space

Affected space is the distance on the ground during which the descending branch of the trajectory does not exceed the height of the target.

When shooting at targets located at a distance greater than the range of a direct shot, the trajectory near its top rises above the target and the target in some area will not be hit with the same sight setting. However, there will be such a space (distance) near the target in which the trajectory does not rise above the target and the target will be hit by it.

Depth of affected space depends on:

target height (the higher the height, the greater the value)
flatness of the trajectory (the flatter the trajectory, the greater the value)
the angle of inclination of the terrain (on the front slope it decreases, on the reverse slope it increases)

Depth of affected area can be determined from the tables of the excess of the trajectory above the aiming line by comparing the excess of the descending branch of the trajectory by the corresponding firing range with the height of the target, and if the target height is less than 1/3 of the trajectory height, then in the form of a thousandth.

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

Covered, affected and dead space

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

The greater the height of the shelter and the flatter the trajectory, the greater the covered space. Depth of covered space can be determined from the tables of the excess of the trajectory above the aiming line: by selection, an excess is found that corresponds to the height of the shelter and the distance to it. After finding the excess, the corresponding setting of the sight and the firing range are determined.

The difference between a certain range of fire and the range to cover is the depth of the covered space.

Dead space- this is the part of the covered space in which the target cannot be hit with a given trajectory.

The greater the height of the shelter, the lower the height of the target and the flatter the trajectory - the greater the dead space.

Pimaginable space- this is the part of the covered area in which the target can be hit. The depth of the dead space is equal to the difference between the covered and affected space.

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

This is a rather complicated process. Due to the simultaneous impact on the bullet of rotational motion, which gives it a stable position in flight and air resistance, which tends to tip the bullet head back, the axis of the bullet deviates from the direction of flight in the direction of rotation.

As a result of this, the bullet encounters more air resistance on one of its sides, and therefore deviates from the firing plane more and more in the direction of rotation. Such a deviation of a rotating bullet away from the plane of fire is called derivation.

It increases disproportionately to the flight distance of the bullet, as a result of which the latter deviates more and more to the side of the intended target and its trajectory is a curved line. The direction of the bullet deflection depends on the direction of the rifling of the barrel of the weapon: with left-sided rifling of the barrel, the derivation takes the bullet into left side, with right-handed - to the right.

At firing distances up to 300 meters inclusive, derivation has no practical significance.

Distance, m	Derivation, cm	Thousandths (horizontal adjustment of the sight)	Aiming point without corrections (SVD rifle)
100	0	0	sight center
200	1	0	Same
300	2	0,1	Same
400	4	0,1	left (from the shooter) eye of the enemy
500	7	0,1	on the left side of the head between the eye and ear
600	12	0,2	left side of the enemy's head
700	19	0,2	over the center of the epaulette on the opponent's shoulder
800	29	0,3	without corrections, accurate shooting is not performed
900	43	0,5	Same
1000	62	0,6	Same

Internal and external ballistics.

Shot and its periods. The initial speed of the bullet.

Lesson number 5.

"RULES FOR SHOOTING FROM SMALL ARMS"

1. Shot and its periods. The initial speed of the bullet.

Internal and external ballistics.

2. Shooting rules.

Ballistics is the science of the movement of bodies thrown in space. It deals mainly with the study of the movement of projectiles fired from firearms, rocket projectiles and ballistic missiles.

Distinguish between internal ballistics, which deals with the study of the movement of a projectile in the gun channel, as opposed to external ballistics, investigating the movement of the projectile after exiting the gun.

We will consider ballistics as the science of the movement of a bullet when fired.

Internal ballistics is a science that studies the processes that take place when a shot is fired and, in particular, when a bullet moves along a barrel bore.

A shot is 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 phenomena occur. 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 penetrates through the hole in the bottom of the sleeve to the powder charge and ignites it. During the combustion of a powder (or so-called combat) charge, a large amount of highly heated gases are formed, which create high pressure in the barrel bore on the bottom of the bullet, the bottom and walls of the sleeve, as well as on the walls of the barrel and the bolt. As a result of the pressure of gases on the bullet, it moves from its place and crashes into the rifling; rotating along them, it moves along the bore with a continuously increasing speed and is thrown outward in the direction of the axis of the bore. The pressure of gases on the bottom of the sleeve causes recoil - the movement of the weapon (barrel) back. From the pressure of gases on the walls of the sleeve and the barrel, they are stretched (elastic deformation) and the sleeves, tightly pressed against the chamber, prevent the breakthrough of powder gases towards the bolt. At the same time, when fired, an oscillatory movement (vibration) of the barrel occurs and it heats up.

During the combustion of a powder charge, approximately 25-30% 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 passes in a very short period of time: 0.001‑0.06 seconds. When fired, four periods are distinguished:

Preliminary;

First (or main);

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 bore. 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 (depending on the rifling device, the weight of the bullet and the hardness of its shell) is called forcing pressure and reaches 250-500 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 (main) period lasts from the beginning of the movement of the bullet until the moment of complete combustion of the powder charge. 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 its maximum value. This pressure is called maximum pressure. It is created in small arms when a bullet travels 4-6 cm of the path. Then, due to the rapid 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, 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 3/4 of the initial speed. The powder charge completely burns out shortly before the bullet leaves the bore.

Second period lasts from the moment of complete combustion of the powder charge until the moment the bullet leaves the barrel. With the beginning of this period, the influx of powder gases stops, however, highly compressed and heated gases expand and, putting pressure on the bullet, increases its speed. The speed of the bullet at the exit from the bore ( muzzle velocity) is slightly less than the initial speed.

initial speed called the speed of the bullet at the muzzle of the barrel, i.e. at the time of its departure from the bore. It is measured in meters per second (m/s). The initial speed of caliber bullets and projectiles is 700‑1000 m/s.

The value of the initial speed is one of the most important characteristics of the combat properties of weapons. For the same bullet an increase in the initial speed leads to an increase in the flight range, penetrating and lethal action of the bullet, as well as to reduce the influence of external conditions on its flight.

Bullet penetration is characterized by its kinetic energy: the depth of penetration of a bullet into an obstacle of a certain density.

When firing from AK74 and RPK74, a bullet with a steel core of 5.45 mm cartridge pierces:

o steel sheets with thickness:

2 mm at a distance of up to 950 m;

3 mm - up to 670 m;

5 mm - up to 350 m;

o steel helmet (helmet) - up to 800 m;

o earthen barrier 20-25 cm - up to 400 m;

o pine beams 20 cm thick - up to 650 m;

o brickwork 10-12 cm - up to 100 m.

Bullet lethality characterized by its energy (live force of impact) at the moment of meeting with the target.

Bullet energy is measured in kilogram-force-meters (1 kgf m is the energy required to do the work of lifting 1 kg to a height of 1 m). To inflict damage on a person, an energy equal to 8 kgf m is needed, to inflict the same defeat on an animal - about 20 kgf m. The bullet energy of the AK74 at 100 m is 111 kgf m, and at 1000 m it is 12 kgf m; the lethal effect of the bullet is maintained up to a range of 1350 m.

The value of the muzzle velocity of a bullet depends on the length of the barrel, the mass of the bullet and the properties of the powder. The longer the stem, the more time powder gases act on the bullet and the greater the initial velocity. With a constant barrel length and a constant mass of the powder charge, the initial velocity is greater, the smaller the mass of the bullet.

Some types of small arms, especially short-barreled ones (for example, the Makarov pistol), do not have a second period, because. complete combustion of the powder charge by the time the bullet leaves the bore does not occur.

The third period (the period of aftereffect of gases) lasts from the moment the bullet leaves the bore until the moment the action of the powder gases on the bullet ceases. During this period, powder gases flowing out of the bore at a speed of 1200-2000 m/s continue to act on the bullet and give it additional speed. The bullet reaches its greatest (maximum) speed at the end of the third period at a distance of several tens of centimeters from the muzzle of the barrel.

Hot powder gases escaping from the barrel after the bullet, when they meet with air, cause shock wave, which is the source of the sound of the shot. The mixing of hot powder gases (among which there are oxides of carbon and hydrogen) with atmospheric oxygen causes a flash, observed as a shot flame.

The pressure of the powder gases acting on the bullet ensures that it is given translational speed, as well as rotational speed. The pressure acting in the opposite direction (on the bottom of the sleeve) creates a recoil force. The movement of a weapon under the influence of recoil force is called bestowal. When shooting from small arms, the recoil force is felt in the form of a push to the shoulder, arm, acts on the installation or the ground. The recoil energy is greater than more powerful weapon. For hand-held small arms, the recoil usually does not exceed 2 kg / m and is perceived by the shooter painlessly.

Rice. 1. Throwing the muzzle of the weapon barrel up when fired

as a result of the action of recoil.

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.

When firing from an automatic weapon, 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 the weapon. Therefore, the recoil energy when fired from such a weapon is less than when fired from non-automatic weapons or from automatic weapons, the device of which is based on the principle of using the energy of powder gases discharged through holes 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. The resulting dynamic pair of forces leads to the angular displacement of the weapon. Deviations can also occur due to the influence of the action of small arms automation and the dynamic bending of the barrel as the bullet moves along it. These reasons lead 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 - departure angle. The magnitude of the deviation of the muzzle of the barrel of a given weapon is the greater, the greater the shoulder of this pair of forces.

In addition, when fired, the barrel of the weapon makes an oscillatory movement - 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. The departure angle is considered positive when the axis of the bore at the time of the bullet's departure is higher than its position before the shot, negative when it is lower. The value of the departure angle is given in the firing tables.

The influence of the departure angle on firing for each weapon is eliminated when bringing him to a normal fight (see 5.45mm Kalashnikov manual... - Chapter 7). However, in case of violation of the rules for laying the weapon, using the stop, as well as the rules for caring for the weapon and saving it, the value of the launch angle and the weapon's combat change.

In order to reduce the harmful effect of recoil on the results, in some samples of small arms (for example, the Kalashnikov assault rifle), special devices are used - compensators.

Muzzle brake-compressor is a special device on the muzzle of the barrel, acting on which, the powder gases after the bullet takes off, reduce the recoil speed of the weapon. In addition, 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.

In the AK74, the muzzle brake compensator reduces recoil by 20%.

1.2. external ballistics. Bullet flight path

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

Having flown out of the bore under the action of powder gases, the bullet moves by inertia. In order to determine how the bullet moves, it is necessary to consider the trajectory of its movement. trajectory called the curved line described by the center of gravity of the bullet during flight.

A bullet flying through the air is subjected to two forces: gravity and air resistance. The force of gravity causes it to gradually decrease, and the force of air resistance continuously slows down the movement of the bullet and tends to overturn it. As a result of the action of these forces, the bullet's flight speed gradually decreases, and its trajectory is an unevenly curved curve in shape.

The resistance of air to the flight of a bullet is caused by the fact that air is an elastic medium, therefore, part of the energy of the bullet is expended in this medium, which is caused by three main reasons:

Air friction

The formation of swirls

formation of a ballistic wave.

The resultant of these forces is the air resistance force.

Rice. 2. Formation of air resistance force.

Rice. 3. The action of the force of air resistance on the flight of a bullet:

CG - center of gravity; CS is the center of air resistance.

Air particles in contact with a moving bullet create friction and reduce the speed of the bullet. The air layer adjacent to the surface of the bullet, in which the movement of particles changes depending on the speed, is called the boundary layer. This layer of air, flowing around the bullet, breaks away from its surface and does not have time to immediately close behind the bottom.

A discharged 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 in the direction 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.

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 a sound wave is formed. Therefore, the flight of a bullet is accompanied by a characteristic sound. When the speed of the bullet is less than the speed of sound, the formation of these waves has little effect on its flight, because. waves propagate faster speed bullet flight. 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, because. the bullet spends some of its energy creating this wave.

The effect of the force of air resistance on the flight of a bullet is very large: it causes a decrease in speed and range. For example, a bullet at an initial speed of 800 m/s in airless space would fly to a distance of 32,620 m; the flight range of this bullet in the presence of air resistance is only 3900 m.

The magnitude of the air resistance force mainly depends on:

§ bullet speed;

§ the shape and caliber of the bullet;

§ from the surface of the bullet;

§ air density

and increases with an increase in the speed of the bullet, its caliber and air density.

At supersonic bullet speeds, when the main cause of air resistance is the formation of air compaction in front of the head (ballistic wave), bullets with an elongated pointed head are advantageous.

Thus, the force of air resistance reduces the speed of the bullet and overturns it. As a result of this, the bullet begins to “tumble”, the air resistance force increases, the flight range decreases and its effect on the target decreases.

The stabilization of the bullet in flight is ensured by giving the bullet a rapid rotational movement around its axis, as well as by the tail of the grenade. Departure rotation speed rifled weapons is: bullets 3000-3500 rpm, turning feathered grenades 10-15 rpm. Due to the rotational movement of the bullet, the impact of air resistance and gravity, the bullet deviates to the right side from the vertical plane drawn through the axis of the bore, - firing plane. The deviation of a bullet from it when flying in the direction of rotation is called derivation.

Rice. 4. Derivation (view of the trajectory from above).

As a result of the action of these forces, the bullet flies in space along an unevenly curved curve called trajectory.

Let's continue consideration of elements and definitions of a trajectory of a bullet.

Rice. 5. Trajectory elements.

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

The horizontal plane passing through the departure point is called weapon horizon. In the drawings depicting the weapon and the trajectory from the side, the horizon of the weapon appears as a horizontal line. The trajectory crosses the horizon of the weapon twice: at the point of departure and at the point of impact.

pointed weapons , is called elevation line.

The vertical plane passing through the line of elevation is called shooting plane.

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

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

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

The angle enclosed between the line of elevation and the line of throw is called departure angle.

The point of intersection of the trajectory with the horizon of the weapon is called drop point.

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

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

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

The time it takes for a bullet to travel from point of departure to point of impact is called full time flight.

The highest point of the trajectory is called the top of the path.

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

The part of the trajectory from the departure point to the top is called ascending branch, the part of the trajectory from the top to the point of fall is called descending branch of the trajectory.

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

The straight line from the shooter's eye to the aiming point is called aiming line.

The distance from the departure point to the intersection of the trajectory with the aiming line is called target range.

The angle enclosed between the line of elevation and the line of sight is called aiming angle.

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

The line joining the departure point with the target is called target line.

The distance from the departure point to the target along the target line is called slant range. When firing direct fire, the target line practically coincides with the aiming line, and the slant range - with the aiming range.

The point of intersection of the trajectory with the surface of the target (ground, obstacles) is called meeting point.

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

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 increases. But this happens to a certain limit. Beyond this limit, the trajectory height continues to increase and the total horizontal range begins to decrease.

The angle of elevation at which the full horizontal range of the bullet is greatest is called farthest angle(the value of this angle is about 35°).

There are flat and mounted trajectories:

1. flat- called the trajectory obtained at elevation angles smaller than the angle of greatest range.

2. hinged- called the trajectory obtained at elevation angles of a large angle of greatest range.

Floor and hinged trajectory, obtained by firing from the same weapon at the same muzzle velocity and having the same total horizontal range, are called - conjugate.

Rice. 6. Angle of greatest range,

flat, hinged and conjugate trajectories.

The trajectory is flatter if it rises less above the line of the target, and the smaller the angle of incidence. The flatness of the trajectory affects the value of the range of a direct shot, as well as the amount of affected and dead space.

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 results of shooting has an error in determining the setting of the sight): this is the practical significance of the trajectory.

Rice. 1. Artillery battleship"Marat"

Ballistics(from the Greek βάλλειν - to throw) - the science of the movement of bodies thrown in space, based on mathematics and physics. It focuses primarily on the movement of projectiles fired from firearms, rocket projectiles and ballistic missiles.

Basic concepts

Rice. 2. Elements of firing naval artillery

The main objective of shooting is to hit the target. To do this, the tool must be given a strictly defined position in the vertical and horizontal planes. If we aim the gun so that the axis of the bore is directed at the target, then we will not hit the target, since the trajectory of the projectile will always pass below the direction of the axis of the bore, the projectile will not reach the target. To formalize the terminological apparatus of the subject under consideration, we introduce the main definitions used when considering the theory of artillery firing.
Departure point called the center of the muzzle of the gun.

drop point called the point of intersection of the trajectory with the horizon of the gun.

horizon guns called the horizontal plane passing through the departure point.

Elevation line called the continuation of the axis of the bore of the pointed gun.

Throwing line OB is the continuation of the axis of the bore at the time of the shot. At the moment of the shot, the gun shudders, as a result of which the projectile is thrown not along the line of elevation of the OA, but along the line of throwing of the OV (see Fig. 2).

Goal line OC is the line connecting the gun to the target (see Fig. 2).

Line of sight (sight) called the line running from the gunner's eye through the optical axis of the sight to the aiming point. When firing direct fire, when the line of sight is directed at the target, the line of sight coincides with the line of the target.

Falling line is called the tangent to the trajectory at the point of incidence.

Rice. 3. Shooting at an overlying target

Rice. 4. Shooting at the underlying target

Elevation (greek phi) called the angle between the line of elevation and the horizon of the gun. If the bore axis is directed below the horizon, then this angle is called the angle of descent (see Fig. 2).

The firing range of the gun depends on the elevation angle and firing conditions. Therefore, in order to throw the projectile to the target, it is necessary to give the gun such an elevation angle at which the firing range will correspond to the distance to the target. The firing tables indicate which aiming angles must be given to the gun in order for the projectile to fly to the desired range.

Throwing angle (Greek theta zero) the angle between the line of throw and the horizon of the gun is called (see Fig. 2).

Departure angle (Greek gamma) called the angle between the line of throw and the line of elevation. In naval artillery, the departure angle is small and is sometimes not taken into account, assuming that the projectile is thrown at an elevation angle (see Fig. 2).

Aiming angle (Greek alpha) the angle between the line of elevation and the line of sight is called (see Fig. 2).

Target elevation angle (greek epsilon) called the angle between the line of the target and the horizon of the gun. When a ship fires at sea targets, the elevation angle of the target is equal to zero, since the target line is directed along the horizon of the gun (see Fig. 2).

Incident angle (Greek theta s Latin letter from) the angle between the target line and the fall line is called (see Fig. 2).

Meeting angle (Greek mu) is the angle between the line of incidence and the tangent to the target surface at the meeting point (see Fig. 2).
The value of the value of this angle greatly affects the resistance of the armor of the ship, which is fired at, to penetration by shells. Obviously, the closer this angle is to 90 degrees, the higher the probability of penetration, and the opposite is also true.
Shooting plane called the vertical plane passing through the line of elevation. When the ship fires at sea targets, the aiming line is directed along the horizon, in this case the elevation angle equal to the angle aiming. When a ship fires at coastal and air targets, the elevation angle is equal to the sum of the aiming angle and the elevation angle of the target (see Fig. 3). When firing a coastal battery at sea targets, the elevation angle is equal to the difference between the aiming angle and the elevation angle of the target (see Fig. 4). Thus, the magnitude of the elevation angle is equal to the algebraic sum of the aiming angle and the elevation angle of the target. If the target is above the horizon, the target elevation angle is "+", if the target is below the horizon, the target elevation angle is "-".

The influence of air resistance on the trajectory of the projectile

Rice. 5. Changing the trajectory of the projectile from air resistance

The flight path of a projectile in airless space is a symmetrical curved line, called a parabola in mathematics. The ascending branch coincides in shape with the descending branch and, therefore, the angle of incidence is equal to the angle of elevation.

When flying in the air, the projectile spends part of its speed to overcome air resistance. Thus, two forces act on the projectile in flight - the force of gravity and the force of air resistance, which reduces the speed and range of the projectile, as illustrated in Fig. 5. The magnitude of the air resistance force depends on the shape of the projectile, its size, flight speed and air density. The longer and more pointed the head of the projectile, the less air resistance. The shape of the projectile is especially affected at flight speeds exceeding 330 meters per second (that is, at supersonic speeds).

Rice. 6. Short-range and long-range projectiles

On fig. 6, on the left, is a short-range, old-style projectile and a more oblong, pointed, long-range projectile on the right. It can also be seen that a long-range projectile has a conical narrowing at the bottom. The fact is that a rarefied space and turbulence are formed behind the projectile, which significantly increase air resistance. By narrowing the bottom of the projectile, a decrease in the amount of air resistance resulting from rarefaction and turbulence behind the projectile is achieved.

The force of air resistance is proportional to the speed of its flight, but not directly proportional. Dependence is formalized more difficult. Due to the action of air resistance, the ascending branch of the projectile's flight path is longer and delayed than the descending one. The angle of incidence is greater than the angle of elevation.

In addition to reducing the range of the projectile and changing the shape of the trajectory, the force of air resistance tends to overturn the projectile, as can be seen from Fig. 7.

Rice. 7. Forces acting on a projectile in flight

Therefore, a non-rotating elongated projectile will roll over under the action of air resistance. In this case, the projectile can hit the target in any position, including sideways or bottom, as shown in Fig. 8.

Rice. 8. Rotation of a projectile in flight under the influence of air resistance

So that the projectile does not roll over in flight, it is given rotary motion using rifling in the bore.

If we consider the effect of air on a rotating projectile, we can see that this leads to a lateral deviation of the trajectory from the plane of fire, as shown in Fig. nine.

Rice. 9. Derivation

derivation called the deviation of the projectile from the plane of fire due to its rotation. If the rifling twists from left to right, then the projectile deflects to the right.

The influence of the angle of elevation and the initial velocity of the projectile on the range of its flight

The range of a projectile depends on the elevation angles at which it is thrown. An increase in the flight range with an increase in the elevation angle occurs only up to a certain limit (40-50 degrees), with a further increase in the elevation angle, the range begins to decrease.

Range limit angle called the elevation angle at which the greatest firing range is obtained for a given initial velocity and projectile. When firing in an airless space, the greatest range of the projectile is obtained at an elevation angle of 45 degrees. When firing in the air, the maximum range angle differs from this value and is not the same for different guns (usually less than 45 degrees). For ultra-long-range artillery, when the projectile flies for a significant part of the path high altitude in highly rarefied air, the maximum range angle is more than 45 degrees.

For a gun of this type and when firing a certain type of ammunition, each elevation angle corresponds to a strictly defined range of the projectile. Therefore, in order to throw the projectile at the distance we need, it is necessary to give the gun an elevation angle corresponding to this distance.

The trajectories of projectiles fired at elevation angles smaller than the maximum range angle are called flat trajectories .

The trajectories of projectiles fired at elevation angles greater than the maximum range angle are called " hinged trajectories" .

Projectile dispersion

Rice. 10. Dispersion of projectiles

If several shots are fired from the same gun, with the same ammunition, with the same direction of the gun barrel, under the same, at first glance, conditions, then the shells will not hit the same point, but will fly along different trajectories, forming a bundle of trajectories, as illustrated in fig. 10. This phenomenon is called projectile dispersion .

The reason for the dispersion of projectiles is the impossibility of achieving exactly the same conditions for each shot. The table shows the main factors that cause projectile dispersion and possible ways reduce this dispersion.

The main groups of causes of dispersion	Conditions that give rise to the causes of dispersion	Control measures to reduce dispersion
1. Variety of starting speeds	A variety of properties of gunpowder (composition, moisture and solvent content). Variety of charge weights. Variety of charge temperatures. Variety of loading density. (dimensions and location of the leading belt, sending shells). A variety of shapes and weights of projectiles.	Storage in a sealed container. Each shooting should be carried out with charges of one batch. Maintaining the proper temperature in the cellar. Load uniformity. Each shooting is carried out with shells of the same weight mark.
2. Variety of throwing angles	A variety of elevation angles (dead moves in the aiming device and in the vertical guidance mechanism). Variety of launch angles. Variety of guidance.	Careful maintenance of the material. Good gunner training.
3. A variety of conditions in the flight of a projectile	Variety of influence of the air environment (density, wind).

The area on which projectiles fired from a gun with the same direction of the barrel bore fall is called scattering area .

The middle of the scattering area is called midpoint of fall .

An imaginary trajectory passing through the point of departure and the middle point of fall is called average trajectory .

The scattering area has the shape of an ellipse, so the scattering area is called scattering ellipse .

The intensity with which the projectiles hit different points of the dispersion ellipse is described by a two-dimensional Gaussian (normal) distribution law. From here, if we follow exactly the laws of probability theory, we can conclude that the scattering ellipse is an idealization. The percentage of shells hitting inside the ellipse is described by the three-sigma rule, namely, the probability of shells hitting the ellipse, the axis of which is equal to three times square root from the variances of the corresponding one-dimensional Gaussian distribution laws is 0.9973.
Due to the fact that the number of shots from one gun, especially a large caliber, as already mentioned above, due to wear often does not exceed one thousand, this inaccuracy can be neglected and it can be assumed that all shells fall into the dispersion ellipse. Any section of a beam of projectile flight paths is also an ellipse. The dispersion of projectiles in range is always greater than in the lateral direction and in height. The value of the median deviations can be found in the main shooting table and the size of the ellipse can be determined from it.

Rice. 11. Shooting at a target with no depth

Affected space is the space over which the trajectory passes through the target.

According to fig. 11, the affected space is equal to the distance along the horizon AC from the base of the target to the end of the trajectory passing through the top of the target. Each projectile that fell outside the affected space either passed above the target or fell before it. The affected space is limited by two trajectories - the OA trajectory passing through the base of the target, and the OS trajectory passing through the top point of the target.

Rice. 12. Shooting at a target with depth

In case the target to be hit has depth, the amount of space to hit is increased by the value of the target's depth, as illustrated in Fig. 12. The depth of the target will depend on the size of the target and its position relative to the plane of fire. Consider the most likely target for naval artillery - an enemy ship. In such a case, if the target is coming from us or towards us, the depth of the target is equal to its length, when the target is perpendicular to the plane of fire, the depth is equal to the width of the target, as illustrated in the figure.

Given the fact that the scattering ellipse has great length and a small width, it can be concluded that at a shallow target depth, fewer projectiles hit the target than at a large depth. That is, than more depth target, the easier it is to hit. With an increase in the firing range, the affected target space decreases, as the angle of incidence increases.

Straight shot a shot is called, in which the entire distance from the point of departure to the point of impact is the affected space (see Fig. 13).

Rice. 13. Direct shot

This is obtained if the height of the trajectory does not exceed the height of the target. The range of a direct shot depends on the steepness of the trajectory and the height of the target.

Range of a direct shot (or range of flattening) called the distance at which the height of the trajectory does not exceed the height of the target.

The most important works on ballistics

17th century

- Tartaglia theory,
1638- labor Galileo Galilei about the parabolic motion of a body thrown at an angle.
1641- a student of Galileo - Toricelli, developing the parabolic theory, derives an expression for horizontal range, which later formed the basis of artillery firing tables.
1687- Isaac Newton proves the influence of air resistance on a thrown body, introducing the concept of the shape factor of the body, and also drawing a direct dependence of the movement resistance on the cross section (caliber) of the body (projectile).
1690— Ivan Bernoulli mathematically describes main task ballistics, solving the problem of determining the motion of a ball in a resisting medium.

18th century

1737- Bigot de Morogues (1706-1781) published a theoretical study of internal ballistics, which laid the foundation for the rational design of guns.
1740- the Englishman Robins learned to determine the initial speeds of the projectile and proved that the projectile flight parabola has a double curvature - its descending branch is shorter than the ascending one, in addition, he empirically concluded that the air resistance to the flight of projectiles at initial speeds above 330 m / s increases abruptly and should calculated using a different formula.
Second half of the 18th century
Daniel Bernoulli deals with the issue of air resistance to the movement of projectiles;
mathematician Leonhard Euler develops the work of Robins, Euler's work on internal and external ballistics forms the basis for the creation of artillery firing tables.
Mordashev Yu. N., Abramovich I. E., Mekkel M. A. Textbook of deck artillery commander. M.: Military publishing house of the Ministry armed forces Union of the SSR. 1947. 176 p.

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).

Hinged 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. 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.