external ballistics. Trajectory and its elements. Exceeding the trajectory of the bullet above the point of aim. Trajectory shape. Yuriev A.A. "Bullet sports shooting" Define the trajectory and characterize its elements
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 deals mainly with the study of 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 with)
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 - 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. eight.
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 a rotational motion with the help of rifling in the barrel 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 |
(dimensions and location of the leading belt, sending shells).
|
|
| 2. Variety of throwing angles |
|
|
| 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 departure point and middle point 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 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 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. Range 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.
Shot is called the ejection of a bullet from the bore under the action of powder gases formed during the combustion of a powder charge. From the impact of the striker on the primer of the cartridge, a flame arises that ignites the powder charge. This creates a large number of highly heated gases that create high pressure acting in all directions with the same force. At a gas pressure of 250-500 kg / cm 2, the bullet moves from its place and crashes into the rifling of the bore, receiving rotational motion. Gunpowder continues to burn, therefore, the amount of gases increases. Then, due to the rapid increase in the speed of the bullet, the volume of the bullet space increases faster than inflow new gases, and the pressure starts to drop. However, the speed of the bullet in the bore continues to increase, as the gases, although to a lesser extent, still put pressure on it. The bullet moves along the bore at a continuously increasing speed and is ejected outward in the direction of the axis of the bore. The entire firing process takes place in a very short period of time (0.001–0.06 s). Further, the flight of the bullet in the air continues by inertia and largely depends on its initial velocity.
muzzle velocity is the speed at which the bullet leaves the bore. The value of the muzzle velocity of a bullet depends on the length of the barrel, the mass of the bullet, the mass of the powder charge, and other factors. An increase in the initial speed increases the range of the bullet, its penetrating and lethal effect, reduces the impact external conditions for her flight. The movement of the weapon backwards while firing is called recoil. The pressure of powder gases in the bore acts in all directions with the same force. The pressure of the gases on the bottom of the bullet makes it move forward, and the pressure on the bottom of the cartridge case is transmitted to the bolt and causes the weapon to move backward. When recoil, a pair of forces is formed, under the influence of which the muzzle of the weapon deviates upward. The recoil force acts along the axis of the bore, and the butt stop in the shoulder and the center of gravity of the weapon are located below the direction of this force, therefore, when firing, the muzzle of the weapon deviates upward.
recoil small arms felt in the form of a push in the shoulder, arm or into the ground. The recoil action of a weapon is characterized by the amount of speed and energy that it has when moving backward. The recoil speed of the weapon is about as many times less than the initial speed of the bullet, how many times the bullet is lighter than the weapon. The recoil energy of the Kalashnikov assault rifle is small and is perceived painlessly by the shooter. Correct and uniform holding of the weapon reduces the impact of recoil and increases the effectiveness of shooting. The presence of muzzle brakes-compensators or compensators for weapons improves the results of firing bursts and reduces recoil.
At the time of the shot, the barrel of the weapon, depending on the elevation angle, occupies a certain position. The flight of a bullet in the air begins in a straight line, representing the continuation of the axis of the bore at the time of the bullet's departure. This line is called throw line. When flying in the air, two forces act on a bullet: gravity and air resistance. Gravity pushes the bullet further and further away from the line of throw, while air resistance slows the bullet down. Under the influence of these two forces, the bullet continues to fly along a curve located below the line of throw. Trajectory shape depends on the magnitude of the elevation angle and the initial velocity of the bullet, it affects the range of a direct shot, covered, hit and dead space. As the elevation angle increases, the height of the trajectory and the total horizontal range of the bullet increase, but this occurs up to a certain limit. Beyond this limit, the trajectory height continues to increase and the total horizontal range decreases.
The angle of elevation at which the full horizontal range of the bullet is greatest is called angle longest range . The value of the angle of greatest range for bullets various kinds arms is about 35°. Trajectories obtained at elevation angles, smaller angle the greatest range are called flat.
Straight shot called a shot in which the trajectory of the bullet does not rise above the line of sight above the target throughout its entire length.
Direct shot range depends on the height of the target and flatness of the trajectory. The higher the target and flatter trajectory, the longer the point-blank range and hence the distance at which the target can be hit with one sight setting. The practical significance of a direct shot lies in the fact that in tense moments of the battle, shooting can be carried out without rearranging the sight, while the aiming point in height will be selected along the lower edge of the target.
The space behind a cover that is not penetrated by a bullet, from its crest to the meeting point is called covered space.
The covered space is the greater, the higher the shelter and the flatter the trajectory. The part of the covered space on which the target cannot be hit with a given trajectory is called dead (non-hit) space. It is the greater, the greater the height of the shelter, the lower the height of the target and the flatter the trajectory. The other part of the covered space in which the target can be hit is the hit space.
Shot periodization
The shot occurs in a very short period of time (0.001-0.06 s.). When fired, four consecutive periods are distinguished:
- preliminary;
- first, or main;
- second;
- the third, or period of the last gases.
Preliminary period lasts from the beginning of the burning of the powder charge to the complete cutting of the shell of the bullet into the rifling of the barrel. During this period, the gas pressure is created in the barrel bore, which is necessary in order to move the bullet from its place and overcome the resistance of its shell to cutting into the rifling of the barrel. This pressure is called boost pressure; it reaches 250 - 500 kg / cm 2, depending on the rifling device, the weight of the bullet and the hardness of its shell (for example, for small arms chambered for the 1943 sample, the forcing pressure is about 300 kg / cm 2). It is assumed that the combustion of the powder charge in this period occurs in a constant volume, the shell cuts into the rifling instantly, and the movement of the bullet begins immediately when the forcing pressure is reached in the bore.
First or main period lasts from the beginning of the movement of the bullet to the moment complete combustion powder charge. During this period, the combustion of the powder charge occurs in a rapidly changing volume. At the beginning of the period, when the speed of the bullet along the bore is still low, the amount of gases grows faster than the volume of the bullet space (the space between the bottom of the bullet and the bottom of the case), the gas pressure rises rapidly and reaches largest(for example, for small arms chambered for a sample of 1943 - 2800 kg / cm 2, and for a rifle cartridge 2900 kg / cm 2). This pressure is called maximum pressure. It is created in small arms when a bullet travels 4 - 6 cm of the path. Then, due to the rapid speed of the movement of the bullet, the volume of the bullet space increases faster than the influx of new gases, and the pressure begins to fall, by the end of the period it is equal to approximately 2/3 of the maximum pressure. The speed of the bullet is constantly increasing and by the end of the period reaches approximately 3/4 of the initial speed. The powder charge completely burns out shortly before the bullet leaves the bore.
Second period lasts until the moment of complete combustion of the powder charge until the moment the bullet leaves the bore. With the beginning of this period, the influx of powder gases stops, however, highly compressed and heated gases expand and, putting pressure on the bullet, increase its speed. The pressure drop in the second period occurs quite quickly and at the muzzle, the muzzle pressure is 300 - 900 kg / cm 2 for various types of weapons (for example, for the Simonov self-loading carbine - 390 kg / cm 2, for easel machine gun Goryunov - 570 kg / cm 2). The speed of the bullet at the time of its departure from the bore (muzzle velocity) is somewhat less than the initial velocity.
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 focuses primarily on 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 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 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 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 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 when 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 value of the range of a 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. 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.
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 from the shooter's eye through the middle of the sight slot (level with its edges) and the top of the front sight to the aiming point |
|
|
aiming angle |
The angle enclosed between the line of elevation and the line of sight |
|
|
Target elevation angle |
The angle enclosed between the line of sight and the horizon of the weapon |
The target's elevation angle is considered positive (+) when the target is above the weapon's horizon, and negative (-) when the target is below the weapon's horizon. |
|
Sighting range |
Distance from the point of departure to the intersection of the trajectory with the line of sight |
|
|
Exceeding the trajectory above the line of sight |
The shortest distance from any point of the trajectory to the line of sight |
|
|
target line |
A straight line connecting the departure point with the target |
When firing direct fire, the target line practically coincides with the aiming line |
|
Slant Range |
Distance from point of origin to target along target line |
When firing direct fire, the slant range practically coincides with the aiming range. |
|
meeting point |
Intersection point of the trajectory with the target surface (ground, obstacles) |
|
|
Meeting angle |
The angle enclosed between the tangent to the trajectory and the tangent to the target surface (ground, obstacles) at the meeting point |
The smaller of the adjacent angles, measured from 0 to 90°, is taken as the meeting angle. |
|
Sighting line |
A straight line connecting the middle of the sight slot to the top of the front sight |
|
|
Aiming (pointing) |
Giving the axis of the bore of the weapon the position in space necessary for firing |
In order for the bullet to reach the target and hit it or the desired point on it |
|
Horizontal aiming |
Giving the axis of the bore the desired position in the horizontal plane |
|
|
vertical guidance |
Giving the axis of the bore the desired position in the vertical plane |
The trajectory of a bullet in the air has the following properties:
- the descending branch is shorter and steeper than the ascending one;
- the angle of incidence is greater than the angle of throw;
- the final speed of the bullet is less than the initial one;
- the lowest speed of the bullet when firing at high angles of throw - on the descending branch of the trajectory, and when firing at small angles of throw - at the point of impact;
- the time of movement of the bullet along the ascending branch of the trajectory is less than along the descending one;
- the trajectory of a rotating bullet due to the lowering of the bullet under the action of gravity and derivation is a line of double curvature.
Types of trajectories and their practical significance
When firing from any type of weapon with an increase in the elevation angle from 0° to 90°, the horizontal range first increases to a certain limit, and then decreases to zero (Fig. 5).
The 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 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.
A bullet, having received a certain initial speed, strive by inertia to maintain the magnitude and direction of this speed.
If the flight of a bullet was made in an airless space, and the force of gravity did not act on it, the bullet would move in a straight line, uniformly and infinitely. However, a bullet flying in the air is subject to forces that change the speed of its flight and the direction of movement. These forces are gravity and air resistance (Fig. 4).
Rice. 4. Forces acting on a bullet during its flight
Due to the combined action of these forces, the bullet loses speed and changes the direction of its movement, moving in the air along a curved line passing below the direction of the axis of the bore.
The line that a moving bullet describes in space (its center of gravity) is called trajectory.
Usually ballistics considers the trajectory over arms horizon- an imaginary infinite horizontal plane passing through the departure point (Fig. 5).
Rice. 5. Horizon weapons
The movement of the bullet, and hence the shape of the trajectory, depends on many conditions. Therefore, in order to understand how the trajectory of a bullet is formed in space, it is necessary to consider first of all how the force of gravity and the drag force of the air medium act on the bullet separately.
The action of gravity. Let us imagine that no force acts on the bullet after it has left the bore. In this case, as mentioned above, the bullet would move by inertia infinitely, uniformly and rectilinearly in the direction of the axis of the bore; for every second it would fly the same distances with a constant speed equal to the initial one. In this case, if the barrel of the weapon were pointed directly at the target, the bullet, following in the direction of the axis of the bore, would hit it (Fig. 6).
Rice. 6. The movement of a bullet by inertia (if there were no gravity and air resistance)
Let us now assume that only one force of gravity acts on the bullet. Then the bullet will begin to fall vertically down, like any free-falling body.
If we assume that gravity acts on the bullet during its flight by inertia in airless space, then under the influence of this force the bullet will fall lower from the continuation of the bore axis - in the first second - by 4.9 m, in the second - by 19.6 m etc. In this case, if you point the barrel of the weapon at the target, the bullet will never hit it, because, being subjected to the action of gravity, it will fly under the target (Fig. 7).
Rice. 7. The movement of the bullet (if gravity acted on it,
but no air resistance
It is quite obvious that in order for the bullet to fly a certain distance and hit the target, it is necessary to point the barrel of the weapon somewhere above the target. To do this, it is necessary that the axis of the bore and the plane of the horizon of the weapon make up a certain angle, which is called elevation angle(Fig. 8).
As can be seen from fig. 8, the trajectory of a bullet in airless space, on which the force of gravity acts, is a regular curve, which is called parabola. The 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 the photograph of a bullet flying at supersonic speed (over 340 m/s) shows, an air seal forms in front of its head (Fig. 9). From this seal, a head ballistic wave radiates in all directions. Air particles, sliding over the surface of the bullet and breaking off from its side walls, form a zone of rarefied space behind the bullet. In an effort to fill the resulting void behind the bullet, air particles create turbulence, as a result of which a tail wave stretches behind the bottom of the bullet.
The compaction of air ahead of the head of the bullet slows down its flight; the discharged zone behind the bullet sucks it in and thereby further enhances braking; the walls of the bullet experience friction against air particles, which also slows down its flight. The resultant of these three forces is the force of air resistance.
Rice. 9. Photograph of a bullet flying at supersonic speed
(over 340 m/s)
The great influence exerted by air resistance on the flight of a bullet can also be seen from the following example. A bullet fired from a Mosin rifle model 1891/30. or from sniper rifle Dragunov (SVD). Under normal conditions (with air resistance), it has the largest horizontal flight range of 3400 m, and when firing in a vacuum, it could fly 76 km.
Consequently, under the influence of the air resistance force, the trajectory of the bullet loses the shape of a regular parabola, acquiring the shape of an asymmetrical curved line; the top divides it into two unequal parts, of which the ascending branch is always longer and delayed than the descending one. When shooting at medium distances, you can conditionally take the ratio of the length of the ascending branch of the trajectory to the descending one as 3:2.
The rotation of the bullet around its axis. It is known that a body acquires considerable stability if it is given a rapid rotational 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 adding 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 magnitude of its derivational deviation increases rapidly and progressively.
When shooting at short and medium distances, derivation does not have much practical value 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.