Trajectories obtained at elevation angles smaller than the angle. Bullet flight trajectory, its elements, properties. Types of trajectories and their practical significance. Shape, properties and types of toolpath
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.
A distinction is made between internal ballistics, which studies the movement of a projectile in the gun channel, as opposed to external ballistics, which studies the movement of a 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 events 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. When a powder (or so-called combat) charge is burned, a large amount of highly heated gases are formed, which create in the bore high pressure on the bottom of the bullet, the bottom and walls of the sleeve, as well as on the walls of the barrel and the bolt. As a result of the pressure of gases on the 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 - for 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 the 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 to the moment complete combustion 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 inflow 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 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 external conditions for her 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 automatic weapons, the device of which is based on the principle of using recoil energy, part of it is spent on communicating movement to moving parts and reloading weapons. 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 amount of deflection of the muzzle of the barrel this weapon the more than more shoulder this pair of forces.
In addition, when fired, the barrel of the weapon makes 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.
Air resistance to the flight of a bullet is caused by the fact that air is elastic medium, so part of the energy of the bullet is expended in this environment, 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 angle longest range (the value of this angle is about 35°).
There are flat and mounted trajectories:
1. flat- called the trajectory obtained at elevation angles smaller angle the greatest range.
2. hinged- called the trajectory obtained at elevation angles of a large angle of greatest range.
Flat and hinged trajectories obtained by firing from the same weapon at the same initial speed 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 range direct shot, as well as the size of the affected and dead space.
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 setting of the sight): this is practical value trajectories.
2.3.4 Dependence of the shape of the trajectory on the angle of throw. Trajectory elements
The angle formed by the horizon of the weapon and the continuation of the axis of the bore before the shot is called elevation angle.
However, it is more correct to speak about the dependence of the horizontal firing range, and, consequently, the shape of the trajectory on throw angle, which is the algebraic sum of the elevation angle and the departure angle (Fig. 48).
Rice. 48 - Elevation and throw angle
So, there is a certain relationship between the range of a bullet and the angle of throw.
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According to the laws of mechanics, the greatest horizontal flight range in airless space is achieved when the throw angle is 45°. With an increase in the angle from 0 to 45 °, the range of the bullet increases, and from 45 to 90 ° it decreases. The angle of throw at which the horizontal range of the bullet is greatest is called farthest angle.
When flying a bullet in the air, the maximum range angle does not reach 45 °. Its value for modern small arms ranges from 30-35 °, depending on the weight and shape of the bullet.
Trajectories formed at throw angles less than the angle of greatest range (0-35 °) are called flat. Trajectories formed at throwing angles greater than the angle of greatest range (35-90 °) are called hinged(Fig. 49).
Rice. 49 - Flat and mounted trajectories
When studying the movement of a bullet in the air, the designations of the elements of the trajectory are used, indicated in Fig. fifty.
Rice. 50 - Trajectory and its elements:
departure point- the center of the muzzle of the barrel; it is the beginning of the trajectory;
weapon horizon is the horizontal plane passing through the departure point. In the drawings and figures depicting the trajectory from the side, the horizon has the form of a horizontal line;
elevation line- a straight line, which is a continuation of the axis of the bore of the aimed weapon;
throw line- a straight line, which is a continuation of the axis of the bore at the time of the shot. Tangent to the trajectory at the departure point;
firing plane- vertical plane passing through the line of elevation;
elevation angle- the angle formed by the line of elevation and the horizon of the weapon;
throw angle- the angle formed by the line of throw and the horizon of the weapon;
departure angle- the angle formed by the line of elevation and the line of throwing;
drop point- the point of intersection of the trajectory with the horizon of the weapon;
angle of incidence- the angle formed by the tangent to the trajectory at the point of impact and the horizon of the weapon;
horizontal range- distance from the point of departure to the point of fall;
vertex of the trajectory- the highest point of the trajectory above the horizon of the weapon. The vertex divides the trajectory into two parts - the branches of the trajectory;
ascending branch of the trajectory- part of the trajectory from the departure point to the top;
descending branch of the trajectory- part of the trajectory from the top to the point of fall;
trajectory height- distance from the top of the trajectory to the horizon of the weapon.
Since at sports shooting distances for each type of weapon remain basically the same, many shooters do not even think at what angle of elevation or throw to shoot. In practice, it turned out to be much more convenient to replace the throwing angle with another, very similar to it, - aiming angle(Fig. 51). Therefore, deviating somewhat from the presentation of questions external ballistics, we give the elements of aiming weapons (Fig. 52).
Rice. 51 - Line of sight and angle of aim
Rice. 52 - Elements of aiming weapons at the target:
line of sight- a straight line passing from the eye of the shooter through the slots of the sight and the top of the front sight to the aiming point;
aiming point- the point of intersection of the aiming line with the target or the plane of the target (when taking out the aiming point);
aiming angle- the angle formed by the aiming line and the elevation line;
target elevation angle- the angle formed by the aiming line and the horizon of the weapon;
elevation angle is the algebraic sum of the aiming angles and the elevation angle of the target.
The shooter does not interfere with knowing the degree of sloping trajectories of bullets used in sports shooting. Therefore, we present graphs characterizing the excess of the trajectory when firing from various rifles, pistols and revolvers (Fig. 53-57).
Rice. 53 - Exceeding the trajectory above the line of sight when firing a 7.6 mm heavy bullet from a service rifle
Rice. 54 - Exceeding the trajectory of a bullet above the line of sight when firing from a small-caliber rifle (at V 0 =300 m/s)
Rice. 55 - Exceeding the trajectory of a bullet above the aiming line when firing from a small-caliber pistol (at V 0 = 210 m/s)
Rice. 56 - Exceeding the trajectory of a bullet over the line of sight when firing:
a- from a revolver (at V 0 =260 m/s); b- from the PM gun (at V 0 =315 m/s).
Rice. 57 - Exceeding the trajectory of a bullet above the line of sight when firing from a rifle with a 5.6 mm sports and hunting cartridge (at V 0 = 880 m / s)
2.3.5 The dependence of the shape of the trajectory on the value of the muzzle velocity of the bullet, its shape and transverse load
While retaining their basic properties and elements, the trajectories of bullets can differ sharply from one another in their shape: be longer and shorter, have different slopes and curvature. These various changes depend on a number of factors.
Influence of initial speed. If two identical bullets are fired at the same throwing angle with different initial velocities, then the trajectory of the bullet with a higher initial velocity will be higher than the trajectory of the bullet with a lower initial velocity (Fig. 58).
Rice. 58 - Dependence of the height of the trajectory and the range of the bullet from the initial speed
A bullet flying at a lower initial speed will take longer to reach the target, so under the influence of gravity it will have time to go down much more. It is also obvious that with an increase in speed, the range of its flight will also increase.
Influence of bullet shape. The desire to increase the range and accuracy of shooting required to give the bullet a shape that would allow it to maintain speed and stability in flight as long as possible.
The condensation of air particles in front of the bullet head and the rarefied space zone behind it are the main factors in the air resistance force. The head wave, which sharply increases the deceleration of the bullet, occurs when its speed is equal to the speed of sound or exceeds it (over 340 m / s).
If the speed of the bullet is less than the speed of sound, then it flies at the very crest of the sound wave, without experiencing excessively high air resistance. If it is greater than the speed of sound, the bullet overtakes all sound waves formed in front of its head. In this case, a head ballistic wave occurs, which slows down the flight of the bullet much more, which is why it quickly loses speed.
If you look at the outlines of the bow wave and the air turbulence that arise when bullets of various shapes move (Fig. 59), it can be seen that the pressure on the head of the bullet is the less, the sharper its shape. The area of rarefied space behind the bullet is the smaller, the more its tail is bevelled; in this case, there will also be less turbulence behind the flying bullet.
Rice. 59 - The nature of the outlines of the bow wave that occurs when moving bullets of various shapes
Both theory and practice have confirmed that the most streamlined is the shape of the bullet, which is outlined by the so-called curve of least resistance - cigar-shaped. Experiments show that the coefficient of air resistance, depending only on the shape of the head of the bullet, can vary by one and a half to two times.
Different flight speeds correspond to their own, most advantageous, bullet shape.
When firing at short distances with bullets having a low initial velocity, their shape slightly affects the shape of the trajectory. Therefore, revolver, pistol and small-caliber cartridges they are equipped with blunt bullets: this is more convenient for reloading weapons, and also helps to preserve it from damage (especially shellless ones - to small-caliber weapons).
Given the dependence of shooting accuracy on the shape of the bullet, the shooter must protect the bullet from deformation, make sure that scratches, nicks, dents, etc. do not appear on its surface.
Influence transverse load . The heavier the bullet, the more kinetic energy it has, therefore, the less the force of air resistance affects its flight. However, the ability of a bullet to maintain its speed depends not just on its weight, but on the ratio of weight to the area that meets air resistance. The ratio of the bullet's weight to its largest cross-sectional area is called transverse load(Fig. 60).
Rice. 60 - Cross-sectional area of bullets:
a- to a 7.62 mm rifle; b- to a 6.5 mm rifle; in- to a 9 mm pistol; G- to a 5.6-mm rifle for shooting at a target "Running Deer"; d- to 5.6 mm side-firing rifle (long cartridge).
The transverse load is greater than more weight bullets and smaller caliber. Therefore, with the same caliber, the lateral load is greater for a longer bullet. A bullet with a larger transverse load has both a greater flight range and a more gentle trajectory (Fig. 61).
Rice. 61 - Influence of the transverse load of a bullet on the range of its flight
However, there is a certain limit to the increase in this load. First of all, with an increase in it (with the same caliber) increases total weight bullets, and hence the recoil of the weapon. In addition, an increase in the transverse load due to excessive elongation of the bullet will cause a significant tipping action of its head part back by the force of air resistance. From this they proceed, setting the most favorable dimensions of modern bullets. So, the transverse load of a heavy bullet (weight 11.75 g) for a service rifle is 26 g / cm 2, a small-caliber bullet (weight 2.6 g) - 10.4 g / cm 2.
How great is the influence of the lateral load of a bullet on its flight, can be seen from the following data: a heavy bullet with an initial velocity of about 770 m/s has the greatest flight range of 5100 m, a light bullet with an initial velocity of 865 m/s has only 3400 m.
2.3.6 Dependence of the trajectory on meteorological conditions
Continuously changing meteorological conditions during firing can have a significant impact on the flight of a bullet. However, certain knowledge and practical experience help to significantly reduce their harmful effect on shooting accuracy.
Since sport shooting distances are relatively short and the bullet travels them in a very short time, some atmospheric factors, such as air density, will not significantly affect its flight. Therefore, in sports shooting, it is necessary to take into account mainly the influence of wind and, to a certain extent, air temperature.
Wind influence. Headwinds and tailwinds have little effect on shooting accuracy, so shooters usually neglect their effect. So, when shooting at a distance of 600 m, a strong (10 m/sec) head or tail wind changes the STP in height by only 4 cm.
The side wind significantly deflects the bullet to the side, even when shooting at close range.
Wind is characterized by strength (speed) and direction.
The strength of the wind is measured by its speed in meters per second. In shooting practice, wind is distinguished: weak - 2 m / s, moderate - 4-5 m / s and strong - 8-10 m / s.
The strength and direction of the wind arrows are practically determined by various local features: with the help of a flag, by the movement of smoke, by the swaying of grass, bushes and trees, etc. (Fig. 62).
Rice. 62 - Determination of wind strength by flag and smoke
Depending on the strength and direction of the wind, one should either make a lateral correction of the sight, or make a point, aiming in the direction opposite to its direction (taking into account the deflection of bullets under the action of the wind - mainly when shooting at curly targets). In table. Figures 8 and 9 give the values of bullet deflections under the influence of crosswind.
Bullet deflection under the influence of crosswind when firing from rifles of caliber 7.62 mm
| Firing range, m | Heavy bullet deflection (11.8 g), cm | ||
|---|---|---|---|
| light wind (2 m/s) | moderate wind (4 m/s) | strong wind (8 m/s) | |
| 100 | 1 | 2 | 4 |
| 200 | 4 | 8 | 18 |
| 300 | 10 | 20 | 41 |
| 400 | 20 | 40 | 84 |
| 500 | 34 | 68 | 140 |
| 600 | 48 | 100 | 200 |
| 700 | 70 | 140 | 280 |
| 800 | 96 | 180 | 360 |
| 900 | 120 | 230 | 480 |
| 1000 | 150 | 300 | 590 |
Deflection of bullets under the influence of crosswind when firing from a small-caliber rifle
As can be seen from these tables, when shooting at short distances, the deflection of bullets is almost proportional to the strength (speed) of the wind. From Table. 8 also shows that when firing from service and free rifles at 300 m, a side wind with a speed of 1 m / s blows the bullet to the side by one dimension of the target No. 3 (5 cm). These simplified data should be used in practice when determining the value of wind corrections.
An oblique wind (at an angle to the firing plane of 45, 135, 225 and 315 °) deflects a bullet half as much as a side wind.
However, during firing, it is, of course, impossible to make a correction for the wind, so to speak, "formally" guided solely by the data of the tables. This data should only serve as source material and help the shooter navigate in difficult conditions shooting in the wind.
In practice, it rarely happens that in such a relatively small piece of terrain as a shooting range, the wind always had one direction, and even more so the same strength. It usually blows in gusts. Therefore, the shooter needs the ability to time the shot to the moment when the strength and direction of the wind become approximately the same as with previous shots.
Flags are usually posted at the shooting range so that the athlete can determine the strength and direction of the wind. You need to learn how to correctly follow the indications of the flags. Flags should not be relied entirely on when they are high above the target line and the line of fire. It is also impossible to navigate by the flags set at the edge of the forest, steep cliffs, ravines and hollows, since the wind speed in different layers atmosphere, as well as uneven terrain, obstacles is different. As an example, in fig. 63 gives approximate data on wind speed in summer on a plain at various heights from the ground. It is clear that the readings of flags mounted on a high bullet-receiving shaft or on a high mast will not correspond to the true force of the wind, which acts directly on the bullet. It is necessary to be guided by the indications of flags, paper ribbons, etc., set at the same level at which the weapon is located at the time of firing.
Rice. 63 - Approximate data on wind speed in summer at different heights on the plain
It must also be borne in mind that the wind, bending around uneven terrain, obstacles, can create turbulence. If the flags are placed along the entire shooting range, they often show a completely different, even opposite wind direction. Therefore, one should try to determine the main direction and strength of the wind along the entire shooting path, carefully observing individual local landmarks in the area between the shooter and the target.
Naturally, in order to make accurate corrections for the wind, some experience is needed. And experience does not come by itself. The shooter must constantly carefully observe and carefully study the effect of wind in general and on a given shooting range in particular, systematically record the conditions under which the shooting is carried out. Over time, he develops a subconscious feeling, gains experience that allows him to quickly navigate in the meteorological situation and make the necessary corrections to ensure accurate shooting in difficult conditions.
Influence of air temperature. The lower the air temperature, the greater its density. A bullet flying in denser air encounters a large number of its particles on its way, and therefore loses its initial velocity faster. Therefore, in cold weather, at low temperatures, the firing range decreases and the STP decreases (Table 10).
Moving the midpoint of impact when firing from a rifle of caliber 7.62 mm under the influence of changes in air temperature and powder load for every 10 °
| Firing range, m | Movement of the STP in height, cm | |
|---|---|---|
| light bullet (9.6 g) | heavy bullet (11.8 g) | |
| 100 | - | - |
| 200 | 1 | 1 |
| 300 | 2 | 2 |
| 400 | 4 | 4 |
| 500 | 7 | 7 |
| 600 | 12 | 12 |
| 700 | 21 | 19 |
| 800 | 35 | 28 |
| 900 | 54 | 41 |
| 1000 | 80 | 59 |
The temperature also affects the process of burning the powder charge in the barrel of a weapon. As is known, with an increase in temperature, the burning rate of the powder charge increases, since the heat consumption required to heat and ignite the powder grains decreases. Therefore, the lower the air temperature, the slower there is a process increase in gas pressure. As a result, the initial velocity of the bullet also decreases.
It has been established that a change in air temperature by 1° changes the initial velocity by 1 m/sec. Significant temperature fluctuations between summer and winter lead to changes in the initial speed in the range of 50-60 m/s.
Given this, for zeroing weapons, compiling relevant tables, etc. take a certain "normal" temperature - + 15 °.
Considering the relationship between the temperature of the powder charge and the initial velocity of the bullet, the following must be borne in mind.
During long-term shooting in large series, when the rifle barrel is very hot, one should not allow the next cartridge to stay in the chamber for a long time: relatively heat the heated barrel, being transmitted through the cartridge case to the powder charge, will cause the ignition of the powder to accelerate, which ultimately can lead to a change in the STP and “separations” upwards (depending on the length of time the cartridge stays in the chamber).
Therefore, if the shooter is tired and he needs some rest before the next shot, then during such a break in shooting, the cartridge should not be in the chamber; it should be removed or even replaced with another cartridge from the pack, that is, unheated.
2.3.7 Scattering bullets
Even under the most favorable shooting conditions, each of the fired bullets describes its own trajectory, somewhat different from the trajectories of other bullets. This phenomenon is called natural dispersion.
With a significant number of shots, the trajectories in their totality form sheaf, which, when meeting with the target, gives a series of holes, more or less distant from each other. The area they occupy is called scattering area(fig.64).
Rice. 64 - Sheaf of trajectories, average trajectory, scattering area
All holes are located on the dispersion area around a certain point, called scattering center or mid point of impact (STP). A trajectory in the middle of the sheaf and passing through middle point hit, called average trajectory . When making adjustments to the installation of the sight during the shooting process, it is always this average trajectory that is implied.
For different types of weapons and cartridges, there are certain bullet dispersion standards, as well as bullet dispersion standards according to factory specifications and tolerances for the production of certain types of weapons and batches of cartridges.
At in large numbers shots, the dispersion of bullets obeys a certain law of dispersion, the essence of which is as follows:
- holes are located unevenly on the dispersion area, most densely grouped around the STP;
- holes are located symmetrically relative to the STP, since the probability of a bullet deflecting in any direction from the STP is the same;
- the scattering area is always limited by a certain limit and has the shape of an ellipse (oval), elongated on a vertical plane in height.
By virtue of this law, as a whole, holes are located on the dispersion area in a regular manner, and therefore in symmetrical strips of equal width, equally distant from the dispersion axes, the same and a certain number of holes are located, although the dispersion areas may have different sizes (depending on the type of weapon and cartridges). The measure of dispersion are: the median deviation, the core band and the radius of the circle containing better half holes (P 50) or all hits (P 100). It should be emphasized that the law of dispersion fully manifests itself with a large number of shots. In sports shooting in relatively small series, the dispersion area approaches the shape of a circle, therefore, the radius of the circle containing 100% of holes (P 100) or the best half of the holes (P 50) (Fig. 65) serves as a measure of dispersion. The radius of the circle that contains all the holes is about 2.5 times the radius of the circle that contains the best half of them. During factory tests of cartridges, when shooting is carried out in small series (usually 20) shots, a circle that includes all holes - P 100 (diameter that includes all holes, see Fig. 16) also serves as a measure of dispersion.
Rice. 65 - Large and small radii of circles containing 100 and 50% hits
So, the natural dispersion of bullets is an objective process that operates independently of the will and desire of the shooter. This is partly true, and it makes no sense to demand from weapons and cartridges that all bullets hit the same point.
At the same time, the shooter must remember that the natural dispersion of bullets is by no means an inevitable norm, once and for all established for a given type of weapon and certain shooting conditions. The art of marksmanship is to know the causes of the natural dispersion of bullets and to reduce their influence. Practice has convincingly proved how important the correct debugging of weapons and the selection of cartridges, the technical preparedness of the shooter and the experience of shooting in adverse meteorological conditions are to reduce dispersion.
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 |
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 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 than the angle of greatest range (see Fig. trajectories 1 and 2).
Overhead trajectories are called trajectories obtained at elevation angles greater than the angle of greatest range (see Fig. trajectories 3 and 4).
Conjugate trajectories are 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.
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.
The bullet, having received a certain initial velocity upon departure from the bore, strives by inertia to maintain the magnitude and direction of this velocity.
If the flight of a bullet took place in an airless space, and it was not affected by gravity, the bullet would move in a straight line, uniformly and infinitely. However, a bullet flying in the air is subject to forces that change the speed of its flight and the direction of movement. These forces are gravity and air resistance (Fig. 4).
Rice. 4. Forces acting on a bullet during its flight
Due to the combined action of these forces, the bullet loses speed and changes the direction of its movement, moving in the air along a curved line passing below the direction of the axis of the bore.
The line that a moving bullet describes in space (its center of gravity) is called trajectory.
Usually ballistics considers the trajectory over arms horizon- an imaginary infinite horizontal plane passing through the departure point (Fig. 5).
Rice. 5. Horizon weapons
The movement of the bullet, and hence the shape of the trajectory, depends on many conditions. Therefore, in order to understand how the trajectory of a bullet is formed in space, it is necessary to consider first of all how the force of gravity and the drag force of the air medium act on the bullet separately.
The action of gravity. Let us imagine that no force acts on the bullet after it has left the bore. In this case, as mentioned above, the bullet would move by inertia infinitely, uniformly and rectilinearly in the direction of the axis of the bore; for every second it would fly the same distances with a constant speed equal to the initial one. In this case, if the barrel of the weapon were pointed directly at the target, the bullet, following the direction of the axis of the bore, would hit it (Fig. 6).
Rice. 6. The movement of a bullet by inertia (if there were no gravity and air resistance)
Let us now assume that only one force of gravity acts on the bullet. Then the bullet will begin to fall vertically down, like any free-falling body.
If we assume that gravity acts on the bullet during its flight by inertia in airless space, then under the influence of this force the bullet will fall lower from the continuation of the axis of the bore - in the first second - by 4.9 m, in the second - by 19.6 m etc. In this case, if you point the barrel of the weapon at the target, the bullet will never hit it, because, being subjected to the action of gravity, it will fly under the target (Fig. 7).
Rice. 7. The movement of the bullet (if gravity acted on it,
but no air resistance
It is quite obvious that in order for the bullet to fly a certain distance and hit the target, it is necessary to point the barrel of the weapon somewhere above the target. To do this, it is necessary that the axis of the bore and the plane of the horizon of the weapon make up a certain angle, which is called elevation angle(Fig. 8).
As can be seen from fig. 8, the trajectory of a bullet in airless space, on which the force of gravity acts, is a regular curve, which is called parabola. The most high point trajectory over the horizon of the weapon is called her summit. The part of the curve from the departure point to the apex is called ascending branch. Such a bullet trajectory is characterized by the fact that the ascending and descending branches are exactly the same, and the angle of throw and fall are equal to each other.
Rice. 8. Elevation (bullet trajectory in airless space)
The action of the air resistance force. At first glance, it seems unlikely that the air, which has such a low density, could provide significant resistance to the movement of the bullet and thereby significantly reduce its speed.
However, experiments have established that the force of air resistance acting on a bullet fired from a rifle of the 1891/30 model is a large value - 3.5 kg.
Considering that the bullet weighs only a few grams, it becomes quite obvious the great braking effect that air has on a flying bullet.
During the flight, the bullet spends a significant part of its energy on pushing the air particles that interfere with its flight.
As a photograph of a bullet flying at supersonic speed (over 340 m/s) shows, an air seal forms in front of its head (Fig. 9). From this seal, a head ballistic wave radiates in all directions. Air particles, sliding along the surface of the bullet and breaking off from its side walls, form a zone of rarefied space behind the bullet. In an effort to fill the resulting void behind the bullet, air particles create turbulence, as a result of which a tail wave stretches behind the bottom of the bullet.
The compaction of air ahead of the head of the bullet slows down its flight; the discharged zone behind the bullet sucks it in and thereby further enhances braking; the walls of the bullet experience friction against air particles, which also slows down its flight. The resultant of these three forces is the force of air resistance.
Rice. 9. Photograph of a bullet flying at supersonic speed
(over 340 m/s)
The great influence exerted by air resistance on the flight of a bullet can also be seen from the following example. A bullet fired from a Mosin rifle model 1891/30. or from sniper rifle Dragunov (SVD). Under normal conditions (with air resistance), it has the largest horizontal flight range of 3400 m, and when firing in a vacuum, it could fly 76 km.
Consequently, under the influence of the air resistance force, the trajectory of the bullet loses the shape of a regular parabola, acquiring the shape of an asymmetrical curved line; the top divides it into two unequal parts, of which the ascending branch is always longer and delayed than the descending one. When shooting at medium distances, you can conditionally take the ratio of the length of the ascending branch of the trajectory to the descending one as 3:2.
The rotation of the bullet around its axis. It is known that a body acquires considerable stability if it is given a rapid rotary motion around its axis. An example of the stability of a rotating body is a spinning top toy. A non-rotating “top” will not stand on its pointed leg, but if the “top” is given a quick rotational movement around its axis, it will stand steadily on it (Fig. 10).
In order for the bullet to acquire the ability to deal with the overturning effect of the force of air resistance, to maintain stability during flight, it is given a rapid rotational movement around its longitudinal axis. The bullet acquires this rapid rotational movement due to helical grooves in the bore of the weapon (Fig. 11). Under the action of the pressure of powder gases, the bullet moves forward along the bore, simultaneously rotating around its longitudinal axis. Upon departure from the barrel, the bullet by inertia retains the resulting complex movement - translational and rotational.
Without going into details of the explanation physical phenomena, associated with the action of forces on a body experiencing a complex movement, it must still be said that the bullet during flight makes regular oscillations and describes a circle around the trajectory with its head (Fig. 12). In this case, the longitudinal axis of the bullet, as it were, “follows” the trajectory, describing a conical surface around it (Fig. 13).
Rice. 12. Conical rotation of the bullet head
Rice. 13. Flight of a spinning bullet in the air
If we apply the laws of mechanics to a flying bullet, it becomes obvious that the greater the speed of its movement and the longer the bullet, the more the air tends to overturn it. Therefore, the bullets of cartridges different type it is necessary to give a different speed of rotation. Thus, a light bullet fired from a rifle has a rotation speed of 3604 rpm.
However, the rotational movement of the bullet, so necessary to give it stability during flight, has its negative sides.
As already mentioned, a rapidly rotating bullet is subjected to a continuous overturning force of air resistance, in connection with which the head of the bullet describes a circle around the trajectory. As a result of the addition of these two rotational movements, a new movement arises, deflecting its head part away from the firing plane1 (Fig. 14). In this case, one side surface of the bullet is subjected to particle pressure more than the other. This uneven air pressure side surfaces bullets and deflects them away from the firing plane. The lateral deviation of a rotating bullet from the firing plane in the direction of its rotation is called derivation(Fig. 15).
Rice. 14. As a result of two rotational movements, the bullet gradually turns the head to the right (in the direction of rotation)
Rice. 15. The phenomenon of derivation
As the bullet moves away from the muzzle of the weapon, the value of its derivational deviation increases rapidly and progressively.
When shooting at short and medium distances, derivation is not of great practical importance for the shooter. So, at a firing range at 300 m, the derivational deviation is 2 cm, and at 600 m - 12 cm. Derivation has to be taken into account only for particularly accurate shooting at long distances, making appropriate adjustments to the installation of the sight, in accordance with the table of derivational deviations of a bullet for a certain range shooting.
external ballistics. Trajectory and its elements. Exceeding the trajectory of the bullet above the point of aim. Trajectory shape
External ballistics
External ballistics is a science that studies the movement of a bullet (grenade) after the action of powder gases on it has ceased.
Having flown out of the bore under the action of powder gases, the bullet (grenade) moves by inertia. A grenade with a jet engine moves by inertia after the expiration of gases from the jet engine.
Bullet trajectory (side view)
Formation of air resistance force
Trajectory and its elements
A trajectory is a curved line described by the center of gravity of a bullet (grenade) in flight.
A bullet (grenade) when flying in the air is subject to the action of two forces: gravity and air resistance. The force of gravity causes the bullet (grenade) to gradually lower, and the force of air resistance continuously slows down the movement of the bullet (grenade) and tends to overturn it. As a result of the action of these forces, the speed of the bullet (grenade) gradually decreases, and its trajectory is an unevenly curved curved line in shape.
Air resistance to the flight of a bullet (grenade) is caused by the fact that air is an elastic medium and therefore part of the energy of the bullet (grenade) 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.
Air particles in contact with a moving bullet (grenade), due to internal adhesion (viscosity) and adhesion to its surface, create friction and reduce the speed of the bullet (grenade).
The layer of air adjacent to the surface of the bullet (grenade), in which the movement of particles changes from the speed of the bullet (grenade) to zero, is called the boundary layer. 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 rarefied space is formed behind the bottom of the bullet, as a result of which a pressure difference appears on the head and bottom parts. This difference creates a force directed 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.
A bullet (grenade) in flight collides with air particles and causes them to oscillate. As a result, air density increases in front of the bullet (grenade) and sound waves are formed. Therefore, the flight of a bullet (grenade) is accompanied by a characteristic sound. At a bullet (grenade) flight speed that is less than the speed of sound, the formation of these waves has little effect on its flight, since the waves propagate faster than the bullet (grenade) flight speed. When the speed of the bullet is higher than the speed of sound, a wave of highly compacted air is created from the incursion of sound waves against each other - a ballistic wave that slows down the speed of the bullet, since the bullet spends part of its energy to create this wave.
The resultant (total) of all forces resulting from the influence of air on the flight of a bullet (grenade) is the force of air resistance. The point of application of the resistance force is called the center of resistance.
The effect of the force of air resistance on the flight of a bullet (grenade) is very large; it causes a decrease in the speed and range of the bullet (grenade). For example, a bullet mod. 1930 at an angle of throw of 15 ° and an initial speed of 800 m / s in airless space would have flown at a distance of 32,620 m; the flight range of this bullet under the same conditions, but in the presence of air resistance, is only 3900 m.
The magnitude of the air resistance force depends on the flight speed, the shape and caliber of the bullet (grenade), as well as on its surface and air density.
The force of air resistance increases with the 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 an air seal in front of the head (ballistic wave), bullets with an elongated pointed head are advantageous. At subsonic grenade flight speeds, when the main cause of air resistance is the formation of rarefied space and turbulence, grenades with an elongated and narrowed tail are beneficial.
The effect of the force of air resistance on the flight of a bullet: CG - center of gravity; CA - center of air resistance
The smoother the surface of the bullet, the lower the friction force and. force of air resistance.
The variety of shapes of modern bullets (grenades) is largely determined by the need to reduce the force of air resistance.
Under the influence of initial perturbations (shocks) at the moment the bullet leaves the bore, an angle (b) is formed between the bullet axis and the tangent to the trajectory, and the air resistance force acts not along the bullet axis, but at an angle to it, trying not only to slow down the movement of the bullet, but and knock her over.
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.
For example, when fired from a Kalashnikov assault rifle, the speed of rotation of the bullet at the moment of departure from the bore is about 3000 revolutions per second.
During the flight of a rapidly rotating bullet in the air, the following phenomena occur. The force of air resistance tends to turn the bullet head up and back. But the head of the bullet, as a result of rapid rotation, according to the property of the gyroscope, tends to maintain the given position and deviates not upwards, but very slightly in the direction of its rotation at right angles to the direction of the air resistance force, i.e., to the right. As soon as the head of the bullet deviates to the right, the direction of the air resistance force will change - it tends to turn the head of the bullet to the right and back, but the head of the bullet will not turn to the right, but down, etc. Since the action of the air resistance force is continuous, but its direction relative to the bullet changes with each deviation of the bullet axis, then the head of the 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, or precessional, movement, and the bullet flies with its head part forward, that is, it seems to follow the change in the curvature of the trajectory.
Slow conical movement of the bullet
Derivation (Trajectory top view)
The effect of air resistance on the flight of a grenade
The axis of slow conical motion lags somewhat behind the tangent to the trajectory (located above the latter). Consequently, the bullet collides with the air flow more with its lower part and the axis of the slow conical movement deviates in the direction of rotation (to the right when the barrel is right-handed). The deviation of the bullet from the plane of fire in the direction of its rotation is called derivation.
Thus, the causes of derivation are: the rotational movement of the bullet, air resistance and the decrease under the action of gravity of the tangent to the trajectory. In the absence of at least one of these reasons, there will be no derivation.
In shooting charts, derivation is given as heading correction in thousandths. However, when shooting from small arms, the magnitude of the derivation is insignificant (for example, at a distance of 500 m it does not exceed 0.1 thousandth) and its effect on the results of shooting is practically not taken into account.
The stability of the grenade in flight is ensured by the presence of a stabilizer, which allows you to move the center of air resistance back, behind the center of gravity of the grenade.
As a result, the force of air resistance turns the axis of the grenade to a tangent to the trajectory, forcing the grenade to move forward.
To improve accuracy, some grenades are given slow rotation due to the outflow of gases. Due to the rotation of the grenade, the moments of forces that deviate the axis of the grenade act sequentially in different directions, so the shooting improves.
To study the trajectory of a bullet (grenade), the following definitions are adopted.
The center of the muzzle of the barrel is called the departure point. The departure point is the start of the trajectory.
Trajectory elements
The horizontal plane passing through the departure point is called the weapon's 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.
A straight line, which is a continuation of the axis of the bore of the aimed weapon, is called the line of elevation.
The vertical plane passing through the line of elevation is called the shooting plane.
The angle enclosed between the line of elevation and the horizon of the weapon is called the angle of elevation. If this angle is negative, then it is called the angle of declination (decrease).
The straight line, which is a continuation of the axis of the bore at the moment the bullet takes off, is called the line of throw.
The angle enclosed between the line of throw and the horizon of the weapon is called the angle of throw.
The angle enclosed between the line of elevation and the line of throw is called the departure angle.
The point of intersection of the trajectory with the horizon of the weapon is called the point of impact.
The angle enclosed between the tangent to the trajectory at the point of impact and the horizon of the weapon is called the angle of incidence.
The distance from the point of departure to the point of impact is called the full horizontal range.
The speed of a bullet (grenade) at the point of impact is called the final speed.
The time of movement of a bullet (grenade) from the point of departure to the point of impact is called the total flight time.
The highest point of the trajectory is called the vertex of the trajectory.
The shortest distance from the top of the trajectory to the horizon of the weapon is called the height of the trajectory.
The part of the trajectory from the departure point to the top is called the ascending branch; the part of the trajectory from the top to the point of fall is called the descending branch of the trajectory.
The point on or off the target at which the weapon is aimed is called the point of aim.
The straight line that runs from the shooter's eye through the middle of the sight slot (level with its edges) and the top of the front sight to the aiming point is called the aiming line.
The angle enclosed between the line of elevation and the line of sight is called the angle of aim.
The angle enclosed between the line of sight and the horizon of the weapon is called the elevation angle of the target. The target's elevation angle is considered positive (+) when the target is above the weapon's horizon, and negative (-) when the target is below the weapon's horizon. The elevation angle of the target can be determined using instruments or using the thousandth formula.
The distance from the departure point to the intersection of the trajectory with the aiming line is called the aiming range.
The shortest distance from any point of the trajectory to the line of sight is called the excess of the trajectory over the line of sight.
The straight line connecting the departure point with the target is called the target line. The distance from the departure point to the target along the target line is called the 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 the meeting point.
The angle enclosed between the tangent to the trajectory and the tangent to the target surface (ground, obstacles) at the meeting point is called the meeting angle. The smaller of the adjacent angles, measured from 0 to 90°, is taken as the meeting angle.
The trajectory of a bullet in the air has the following properties:
The descending branch is shorter and steeper than the ascending one;
The angle of incidence is greater than the angle of throw;
The final speed of the bullet is less than the initial one;
The lowest speed of 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 a bullet along the ascending branch of the trajectory is less than along the descending one;
The trajectory of a rotating bullet due to the drop of the bullet under the action of gravity and derivation is a line of double curvature.
Grenade trajectory (side view)
The trajectory of a grenade in the air can be divided into two sections: active - the flight of a grenade under the action of a reactive force (from the point of departure to the point where the action of the reactive force stops) and passive - the flight of a grenade by inertia. The shape of the trajectory of a grenade is about the same as that of a bullet.
Trajectory shape
The shape of the trajectory depends on the magnitude of the elevation angle. With an increase in the elevation angle, the height of the trajectory and the full horizontal range of the bullet (grenade) increase, but this occurs up to a known limit. Beyond this limit, the trajectory height continues to increase and the total horizontal range begins to decrease.
Angle of greatest range, flat, overhead and conjugate trajectories
The angle of elevation at which the full horizontal range of the bullet (grenade) becomes the greatest is called the angle of greatest range. The value of the angle of greatest range for bullets of various types of weapons is about 35°.
Trajectories obtained at elevation angles smaller than the angle of greatest range are called flat. Trajectories obtained at elevation angles greater than the angle of greatest range are called hinged.
When firing from the same weapon (with the same initial speeds) you can get two trajectories with the same horizontal range: flat and hinged. Trajectories that have the same horizontal range at different elevation angles are called conjugate.
When firing from small arms and grenade launchers, only flat trajectories are used. The flatter the trajectory, the greater the extent of the terrain, the target can be hit with one sight setting (the less impact on the results of shooting is caused by errors in determining the sight setting); this is the practical significance of the flat trajectory.
Exceeding the trajectory of a bullet above the aiming point
The flatness of the trajectory is characterized by its greatest exceeding the line of sight. 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.