Sniper training. Internal and external ballistics. Fundamentals of external ballistics, bullet rotation and derivation Line of elevation of the bullet trajectory
Ballistics is divided into internal (the behavior of the projectile inside the weapon), external (the behavior of the projectile on the trajectory) and barrier (the action of the projectile on the target). This topic will cover the basics of internal and external ballistics. From barrier ballistics will be considered wound ballistics(action of a bullet on the client's body). The section of forensic ballistics that also exists is considered in the course of forensic science and will not be covered in this manual.
Internal ballistics
Internal ballistics depends on the type of powder used and the type of barrel.
Conditionally trunks can be divided into long and short.
Long barrels (length over 250 mm) serve to increase the initial speed of the bullet and its flatness on the trajectory. Increases (compared to short barrels) accuracy. On the other hand, a long barrel is always more cumbersome than a short barrel.
Short barrels do not give the bullet that speed and flatness than long ones. The bullet has more dispersion. But short-barreled weapons are comfortable to wear, especially hidden, which is most appropriate for self-defense weapons and police weapons. On the other hand, trunks can be conditionally divided into rifled and smooth.
rifled barrels give the bullet greater speed and stability on the trajectory. Such trunks are widely used for bullet shooting. For firing bullet hunting cartridges from smoothbore weapons often used various threaded nozzles.
smooth trunks. Such barrels contribute to an increase in the dispersion of striking elements during firing. Traditionally used for shooting with shot (buckshot), as well as for shooting with special hunting cartridges at short distances.
There are four periods of the shot (Fig. 13).
Preliminary period (P) lasts from the beginning of the burning of the powder charge to the full penetration of the bullet into the rifling. 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 forcing pressure and reaches 250-500 kg/cm 2 . It is assumed that the combustion of the powder charge at this stage occurs in a constant volume.
First period (1) lasts from the beginning of the movement of the bullet until the 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 volume of gases grows faster than the bullet space. Gas pressure reaches its peak (2000-3000 kg/cm2). This pressure is called maximum pressure. Then, due to a rapid increase in the speed of the bullet and a sharp increase in the bullet space, the pressure drops somewhat and by the end of the first period it is approximately 2/3 of the maximum pressure. The speed of movement is constantly growing and reaches by the end of this period approximately 3/4 of the initial speed.
Second period (2) lasts from the moment of complete combustion of the powder charge to the departure of the bullet from the barrel. With the beginning of this period, the influx of powder gases stops, but highly compressed and heated gases expand and, putting pressure on the bottom of the bullet, increase its speed. The pressure drop in this period occurs quite quickly and at the muzzle - muzzle pressure - is 300-1000 kg/cm 2 . Some types of weapons (for example, Makarov, and most types of short-barreled weapons) do not have a second period, because by the time the bullet leaves the barrel, the powder charge does not completely burn out.
Third period (3) lasts from the moment the bullet leaves the barrel until the powder gases stop acting on it. During this period, powder gases flowing out of the bore at a speed of 1200-2000 m/s continue to act on the bullet, giving it additional speed. fastest speed the bullet reaches at the end of the third period at a distance of several tens of centimeters from the muzzle of the barrel (for example, when firing a pistol, a distance of about 3 m). This period ends at the moment when the pressure of the powder gases at the bottom of the bullet is balanced by air resistance. Further, the bullet flies already by inertia. This is to the question of why a bullet fired from a TT pistol does not pierce armor of the 2nd class when fired at close range and pierces it at a distance of 3-5 m.
As already mentioned, smoky and smokeless powders are used to equip cartridges. Each of them has its own characteristics:
black powder. This type of powder burns very quickly. Its burning is like an explosion. It is used to instantly release pressure in the bore. Such gunpowder is usually used for smooth barrels, since the friction of the projectile against the walls of the barrel in a smooth barrel is not so great (compared to a rifled barrel) and the time the bullet stays in the bore is less. Therefore, at the moment the bullet leaves the barrel, more pressure is reached. When using black powder in a rifled barrel, the first period of the shot is short enough, due to which the pressure on the bottom of the bullet decreases quite significantly. It should also be noted that the gas pressure of burnt black powder is approximately 3-5 times less than that of smokeless powder. On the gas pressure curve there is a very sharp peak of maximum pressure and a rather sharp drop in pressure in the first period.
Smokeless powder. Such powder burns more slowly than smoky powder, and is therefore used to gradually increase the pressure in the bore. In view of this, for rifled weapons smokeless powder is used as standard. Due to screwing into the rifling, the time for the bullet to fly along the barrel increases and by the time the bullet takes off, the powder charge completely burns out. Due to this, the full amount of gases acts on the bullet, while the second period is chosen to be sufficiently small. On the gas pressure curve, the maximum pressure peak is somewhat smoothed, with a gentle pressure drop in the first period. In addition, it is useful to pay attention to some numerical methods for estimating intraballistic solutions.
1. Power factor(kM). Shows the energy that falls on one conventional cubic mm of a bullet. Used to compare bullets of the same type of cartridges (for example, pistol). It is measured in joules per millimeter cubed.
KM \u003d E0 / d 3, where E0 - muzzle energy, J, d - bullets, mm. For comparison: the power factor for the 9x18 PM cartridge is 0.35 J/mm 3 ; for cartridge 7.62x25 TT - 1.04 J / mm 3; for cartridge.45ACP - 0.31 J / mm 3. 2. Metal utilization factor (kme). Shows the energy of the shot, which falls on one gram of the weapon. Used to compare bullets of cartridges for one sample or to compare the relative energy of a shot for different cartridges. Measured in Joules per gram. Often, the metal utilization coefficient is taken as a simplified version of the calculation of the recoil of a weapon. kme=E0/m, where E0 is the muzzle energy, J, m is the mass of the weapon, g. For comparison: the metal utilization coefficient for the PM pistol, machine gun and rifle is 0.37, 0.66 and 0.76 J/g, respectively.
External ballistics
First you need to imagine the full trajectory of the bullet (Fig. 14). 
In explanation to the figure, it should be noted that the line of departure of the bullet (line of throwing) will be different than the direction of the barrel (line of elevation). This is due to the occurrence of barrel vibrations during the shot, which affect the trajectory of the bullet, as well as due to the recoil of the weapon when fired. Naturally, the departure angle (12) will be extremely small; moreover, the better the manufacture of the barrel and the calculation of the intra-ballistic characteristics of the weapon, the smaller the departure angle will be. Approximately the first two thirds of the ascending line of the trajectory can be considered a straight line. In view of this, three firing distances are distinguished (Fig. 15). Thus, the influence of external conditions on the trajectory is described by a simple quadratic equation, and in the graph is a parabola. In addition to third-party conditions, the deviation of the bullet from the trajectory is also affected by some design features bullets and cartridge. The complex of events will be considered below; deflecting the bullet from its original trajectory. The ballistic tables of this topic contain data on the ballistics of a 7.62x54R 7H1 cartridge bullet when fired from an SVD rifle. In general, the influence of external conditions on the flight of a bullet can be shown by the following diagram (Fig. 16).
Diffusion
It should be noted again that due to the rifled barrel, the bullet acquires rotation around its longitudinal axis, which gives greater flatness (straightness) to the flight of the bullet. Therefore, the distance of dagger fire is somewhat increased compared to a bullet fired from a smooth barrel. But gradually towards the distance of the mounted fire, due to the already mentioned third-party conditions, the axis of rotation is somewhat shifted from the central axis of the bullet, therefore, in the cross section, a circle of bullet expansion is obtained - the average deviation of the bullet from the original trajectory. Given this behavior of the bullet, its possible trajectory can be represented as a one-plane hyperboloid (Fig. 17). The displacement of a bullet from the main directrix due to the displacement of its axis of rotation is called dispersion. The bullet with full probability is in the circle of dispersion, the diameter (according to 
list) which is determined for each specific distance. But the specific point of impact of the bullet inside this circle is unknown.
In table. 3 shows the dispersion radii for firing at various distances.
Table 3
Diffusion
| Range of fire (m) |
|
- Given the size of a standard head target 50x30 cm, and a chest target 50x50 cm, it can be noted that the maximum distance of a guaranteed hit is 600 m. At a greater distance, dispersion does not guarantee the accuracy of the shot.
Derivation
- Due to complex physical processes, a rotating bullet in flight deviates somewhat from the plane of fire. Moreover, in the case of right-handed rifling (the bullet rotates clockwise when viewed from behind), the bullet deviates to the right, in the case of left-handed rifling - to the left.
In table. 4 shows the values of derivational deviations when firing at different ranges. - Table 4
- Derivation
- Range of fire (m)
- Derivation (cm)
- 1000
- 1200
- It is easier to take into account the derivational deviation when shooting than dispersion. But, taking into account both of these values, it should be noted that the center of dispersion will shift somewhat by the value of the derivational displacement of the bullet.
Bullet displacement by wind
- Among all the external conditions affecting the flight of a bullet (humidity, pressure, etc.), it is necessary to single out the most serious factor - the influence of wind. The wind blows the bullet quite seriously, especially at the end of the ascending branch of the trajectory and beyond.
The displacement of the bullet by a side wind (at an angle of 90 0 to the trajectory) of medium force (6-8 m / s) is shown in Table. 5. - Table 5
- Bullet displacement by wind
- Range of fire (m)
- Displacement (cm)
- To determine the displacement of the bullet by a strong wind (12-16 m/s), it is necessary to double the values of the table, for a weak wind (3-4 m/s), the table values are divided in half. For wind blowing at an angle of 45° to the path, the table values are also divided in half.
bullet flight time
- Range of fire (m)
- Flight time (s)
- 0,15
- 0,28
- 0,42
- 0,60
- 0,80
- 1,02
- 1,26
Solution of ballistic problems
- To do this, it is useful to make a graph of the dependence of the displacement (scattering, bullet flight time) on the firing range. Such a graph will allow you to easily calculate intermediate values (for example, at 350 m), and also allow you to assume out-of-table values of the function.
On fig. 18 shows the simplest ballistic problem. - Shooting is carried out at a distance of 600 m, the wind at an angle of 45 ° to the trajectory blows from behind-left.
Question: the diameter of the circle of dispersion and the offset of its center from the target; flight time to the target.
- Solution: The diameter of the circle of dispersion is 48 cm (see Table 3). The derivational shift of the center is 12 cm to the right (see Table 4). The displacement of the bullet by the wind is 115 cm (110 * 2/2 + 5% (due to the direction of the wind in the direction of the derivational displacement)) (see Table 5). Bullet flight time - 1.07 s (flight time + 5% due to wind direction in the direction of bullet flight) (see table 6).
- Answer; the bullet will fly 600 m in 1.07 s, the diameter of the circle of dispersion will be 48 cm, and its center will shift to the right by 127 cm. Naturally, the answer data is quite approximate, but their discrepancy with the real data is no more than 10%.
Barrier and wound ballistics
Barrier ballistics
- The impact of a bullet on obstacles (as, indeed, everything else) is quite convenient to determine by some mathematical formulas.
1. It is usually used to determine the probability of penetration on various dis
- dances different classes passive armor protection.
Penetration is a dimensionless quantity. - P \u003d En / Epr,
- where En is the energy of the bullet at a given point in the trajectory, in J; Epr is the energy required to break through the barrier, in J.
- Taking into account the standard Epr for body armor (BZ) (500 J for protection against pistol cartridges, 1000 J - from intermediate and 3000 J - from rifle cartridges) and sufficient energy to hit a person (max 50 J), it is easy to calculate the probability of hitting the corresponding BZ with a bullet of one or more another patron. So, the probability of penetrating a standard pistol BZ with a 9x18 PM cartridge bullet will be 0.56, and with a 7.62x25 TT cartridge bullet - 1.01. The probability of penetrating a standard machine-gun BZ with a 7.62x39 AKM cartridge bullet will be 1.32, and with a 5.45x39 AK-74 cartridge bullet - 0.87. The given numerical data are calculated for a distance of 10 m for pistol cartridges and 25 m for intermediate ones. 2. Coefficient, impact (ky). The impact coefficient shows the energy of the bullet, which falls on the square millimeter of its maximum section. Impact ratio is used to compare cartridges of the same or different classes. It is measured in J per square millimeter. ky=En/Sp, where En is the energy of the bullet at a given point of the trajectory, in J, Sn is the area of the maximum cross-section of the bullet, in mm 2. Thus, the impact coefficients for bullets of cartridges 9x18 PM, 7.62x25 TT and .40 Auto at a distance of 25 m will be equal to 1.2, respectively; 4.3 and 3.18 J / mm 2. For comparison: at the same distance, the impact coefficient of bullets of 7.62x39 AKM and 7.62x54R SVD cartridges are respectively 21.8 and 36.2 J/mm 2 .
Wound ballistics
How does a bullet behave when it hits a body? The clarification of this question is the most important characteristic to select weapons and ammunition for a particular operation. There are two types of impact of a bullet on a target: stopping and penetrating, in principle, these two concepts have an inverse relationship. Stopping effect (0V). Naturally, the enemy stops as reliably as possible when the bullet hits a certain place on the human body (head, spine, kidneys), but some types of ammunition have a large 0V when it hits secondary targets. In the general case, 0V is directly proportional to the caliber of the bullet, its mass and speed at the moment of impact with the target. Also, 0V increases when using lead and expansive bullets. It must be remembered that an increase in 0V reduces the length of the wound channel (but increases its diameter) and reduces the effect of a bullet on a target protected by armored clothing. One of the variants of the mathematical calculation of OM was proposed in 1935 by the American J. Hatcher: 0V = 0.178*m*V*S*k, where m is the mass of the bullet, g; V is the speed of the bullet at the moment of meeting with the target, m/s; S is the transverse area of the bullet, cm 2; k is the bullet shape factor (from 0.9 for full-shell to 1.25 for expansion bullets). According to such calculations, at a distance of 15 m, bullets of cartridges 7.62x25 TT, 9x18 PM and .45 have OB, respectively, 171, 250 in 640. For comparison: OB bullets of the cartridge 7.62x39 (AKM) \u003d 470, and bullets 7.62x54 ( ATS) = 650. Penetrating effect (PV). PV can be defined as the ability of a bullet to penetrate maximum depth to the target. Penetration is higher (ceteris paribus) for bullets of small caliber and weakly deformed in the body (steel, full-shell). The high penetrating effect improves the action of the bullet against armored targets. On fig. 19 shows the action of a standard PM jacketed bullet with a steel core. When a bullet enters the body, a wound channel and a wound cavity are formed. Wound channel - a channel pierced directly by a bullet. Wound cavity - a cavity of damage to fibers and blood vessels caused by tension and rupture of their bullet. Gunshot wounds are divided into through, blind, secant.
through wounds
A penetrating wound occurs when a bullet passes through the body. In this case, the presence of inlet and outlet holes is observed. The entrance hole is small, less than the caliber of the bullet. With a direct hit, the edges of the wound are even, and with a hit through tight clothing at an angle - with a slight tear. Often the inlet is quickly tightened. There are no traces of bleeding (except for the defeat of large vessels or when the wound is at the bottom). The exit hole is large, it can exceed the caliber of the bullet by orders of magnitude. The edges of the wound are torn, uneven, diverging to the sides. A rapidly developing tumor is observed. There is often heavy bleeding. With non-fatal wounds, suppuration quickly develops. With fatal wounds, the skin around the wound quickly turns blue. Through wounds are typical for bullets with a high penetrating effect (mainly for submachine guns and rifles). When a bullet passed through soft tissues, the internal wound was axial, with slight damage to neighboring organs. When wounded by a bullet cartridge 5.45x39 (AK-74), the steel core of the bullet in the body can come out of the shell. As a result, there are two wound channels and, accordingly, two outlets (from the shell and the core). Such injuries are most oftenth occur when it enters through dense clothing (pea jacket). Often the wound channel from the bullet is blind. When a bullet hits a skeleton, a blind wound usually occurs, but with a high power of the ammunition, a through wound is also likely. In this case, there are large internal injuries from fragments and parts of the skeleton with an increase in the wound channel to the outlet. In this case, the wound channel can "break" due to the ricochet of the bullet from the skeleton. Penetrating wounds to the head are characterized by cracking or fracture of the bones of the skull, often with a non-axial wound channel. The skull cracks even when hit by 5.6 mm lead-free jacketed bullets, not to mention more powerful ammunition. In most cases, these wounds are fatal. With penetrating wounds to the head, severe bleeding is often observed (prolonged leakage of blood from the corpse), of course, when the wound is located on the side or below. The inlet is quite even, but the outlet is uneven, with many cracks. A mortal wound quickly turns blue and swells. In case of cracking, violations of the skin of the head are possible. To the touch, the skull easily misses, fragments are felt. In case of wounds with sufficiently strong ammunition (bullets of cartridges 7.62x39, 7.62x54) and wounds with expansive bullets, a very wide exit hole with a long outflow of blood and brain matter is possible.Blind wounds
Such wounds occur when bullets from less powerful (pistol) ammunition hit, using expansive bullets, passing a bullet through the skeleton, and being wounded by a bullet at the end. With such wounds, the inlet is also quite small and even. Blind wounds are usually characterized by multiple internal injuries. When wounded by expansive bullets, the wound channel is very wide, with a large wound cavity. Blind wounds are often non-axial. This is observed when weaker ammunition hits the skeleton - the bullet goes away from the inlet, plus damage from fragments of the skeleton, the shell. When such bullets hit the skull, the latter cracks heavily. A large inlet is formed in the bone, and the intracranial organs are severely affected.Cutting wounds
Cutting wounds are observed when a bullet enters the body at an acute angle with a violation of only the skin and external parts of the muscles. Most of the injuries are harmless. Characterized by rupture of the skin; the edges of the wound are uneven, torn, often strongly divergent. Quite severe bleeding is sometimes observed, especially when large subcutaneous vessels rupture.
To solve the simplest ballistic tasks It should be noted that the time of flight of a bullet depends on the firing range. Without taking into account this factor, it will be quite problematic to hit even a slowly moving target.
The time of flight of a bullet to the target is presented in Table. 6.
Table 6Bullet time to target
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 elevation angle at which the greatest range is obtained is called the angle longest range. The value of the angle of greatest range for bullets various kinds weapons is about 35 °.
The angle of greatest range divides all the trajectories into two types: into the trajectories flat and hinged (Fig. 6). 
Flat trajectories are called trajectories obtained at elevation angles, smaller angle longest range (see Fig. trajectories 1 and 2).
Overhead trajectories are called trajectories obtained at elevation angles greater than the angle of greatest range (see Fig. trajectories 3 and 4).
Conjugate trajectories are trajectories obtained at the same horizontal range by two trajectories, one of which is flat, the other is hinged (see Fig. trajectories 2 and 3).
When firing from small arms and grenade launchers, only flat trajectories are used. How flatter trajectory, the greater the extent of the terrain, the target can be hit with one sight setting (the less impact on the results of shooting has an error in determining the sight setting): this is the practical significance of the trajectory.
The flatness of the trajectory is characterized by its greatest excess over the aiming line. At a given range, the trajectory is all the more flat, the less it rises above the aiming line. In addition, the flatness of the trajectory can be judged by the magnitude of the angle of incidence: the trajectory is the more flat, the smaller the angle of incidence. The flatness of the trajectory affects the range direct shot, struck, covered and dead space.
The trajectory of a bullet is understood as a line drawn in space by its center of gravity.
This trajectory is formed under the influence of the inertia of the bullet, the forces of gravity and air resistance acting on it.
The inertia of a bullet is formed while it is in the bore. Under the influence of the energy of powder gases, the speed and direction are set to the bullet forward movement. And if external forces did not act on it, then according to the first law of Galileo - Newton, it would rectilinear motion in a given direction at a constant speed to infinity. In this case, in every second it would pass a distance equal to the initial speed of the bullet (see Fig. 8).
However, due to the fact that the forces of gravity and air resistance act on the bullet in flight, they together, in accordance with the fourth law of Galileo - Newton, impart to it an acceleration equal to the vector sum of the accelerations arising from the actions of each of these forces separately.
Therefore, in order to understand the features of the formation of the flight path of a bullet in the air, it is necessary to consider how the force of gravity and the force of air resistance act separately on the bullet.
Rice. 8. The movement of a bullet by inertia (in the absence of the influence of gravity
and air resistance)
The force of gravity acting on the bullet gives it an acceleration equal to the acceleration of free fall. This force is directed vertically downward. In this regard, the bullet under the action of gravity will constantly fall to the ground, and the speed and height of its fall will be determined, respectively, by formulas 6 and 7:
where: v - bullet fall speed, H - bullet fall height, g - free fall acceleration (9.8 m/s2), t - bullet fall time in seconds.
If the bullet flew out of the bore without having the kinetic energy given by the pressure of the powder gases, then, in accordance with the above formula, it would fall vertically down: in one second by 4.9 m; two seconds later at 19.6 m; after three seconds at 44.1 m; four seconds later at 78.4 m; after five seconds at 122.5 m, etc. (see fig. 9).
Rice. 9. The fall of a bullet without kinetic energy in a vacuum
under the influence of gravity
When a bullet with a given kinetic energy moves by inertia, under the action of gravity, it will move a given distance down relative to the line that is a continuation of the axis of the bore. By constructing parallelograms, the lines of which will be the values of the distances covered by the bullet by inertia and under the action of gravity in
corresponding time intervals, we can determine the points that the bullet will pass in these time intervals. Connecting them with a line, we get the trajectory of the bullet in airless space (see Fig. 10).
Rice. 10. The trajectory of a bullet in a vacuum
This trajectory is a symmetrical parabola, the highest point of which is called the vertex of the trajectory; its part, located from the point of departure of the bullet to the top, is called the ascending branch of the trajectory; and the part located after the top is descending. In vacuum, these parts will be the same.
In this case, the height of the top of the trajectory and, accordingly, its figure will depend only on the initial velocity of the bullet and the angle of its departure.
If the force of gravity acting on the bullet is directed vertically downward, then the force of air resistance is directed in the direction opposite to the movement of the bullet. It continuously slows down the movement of the bullet and tends to overturn it. To overcome the force of air resistance, part of the kinetic energy of the bullet is expended.
The main causes of air resistance are: its friction against the surface of the bullet, the formation of a vortex, the formation of a ballistic wave (see Fig. 11).
Rice. 11. Causes of air resistance
The bullet in flight collides with air particles and causes them to oscillate, as a result of which the density of the air in front of the bullet increases, and sound waves are formed that cause a characteristic sound and a ballistic wave. In this case, the layer of air flowing around the bullet does not have time to close behind its bottom part, as a result of which a rarefied space is created there. The difference in air pressure exerted on the head and bottom parts of the bullet forms a force directed to the side opposite to the direction of its flight and reduces its speed. In this case, air particles, trying to fill the rarefied space formed behind the bottom of the bullet, create a vortex.
The air resistance force is the sum of all the forces generated due to the influence of air on the flight of a bullet.
The center of drag is the point at which the force of air resistance is applied to the bullet.
The force of air resistance depends on the shape of the bullet, its diameter, flight speed, air density. With an increase in the speed of the bullet, its caliber and air density, it increases.
Under the influence of air resistance, the flight path of the bullet loses its symmetrical shape. The speed of a bullet in the air decreases all the time as it moves away from the point of departure, so the average speed of a bullet on the ascending branch of the trajectory is greater than on the descending one. In this regard, the ascending branch of the flight path of a bullet in the air is always longer and flatter than the descending one; when shooting at medium distances, the ratio of the length of the ascending branch of the trajectories to the length of the descending one is conditionally taken as 3: 2 (see Fig. 12).
Rice. 12. The trajectory of a bullet in the air
Rotation of a bullet around its axis
When a bullet is flying in the air, the force of its resistance constantly strives to overturn it. It manifests itself in the following way. The bullet, moving by inertia, constantly strives to maintain the position of its axis, given direction barrel of the weapon. At the same time, under the influence of gravity, the direction of the bullet's flight constantly deviates from its axis, which is characterized by an increase in the angle between the axis of the bullet and the tangent to its flight path (see Fig. 13).
Rice. 13. The effect of the force of air resistance on the flight of a bullet: CG - center of gravity, CA - center of air resistance
The action of the air resistance force is directed opposite to the direction of the bullet and parallel to its tangent trajectory, i.e. from below at an angle to the axis of the bullet.
Based on the shape of the bullet, air particles hit the surface of its head at an angle close to a straight line, and into the surface of the tail at a fairly sharp angle (see Fig. 13). In this regard, at the head of the bullet there is a compacted air, and at the tail - a rarefied space. Therefore, the air resistance in the head of the bullet significantly exceeds its resistance in the tail. As a result, the speed of the head section decreases faster than the speed of the tail section, which causes the head of the bullet to tip back (bullet rollover).
Rolling the bullet backwards causes it to rotate erratically in flight, with a significant decrease in its flight range and accuracy of hitting the target.
In order for the bullet not to tip over in flight under the action of air resistance, it is given a quick rotary motion around the longitudinal axis. This rotation is formed due to the helical cutting in the bore of the weapon.
The bullet, passing through the bore, under the pressure of powder gases, enters the rifling and fills them with its body. In the future, like a bolt in a nut, it simultaneously moves forward and rotates around its axis. At the exit from the bore, the bullet retains both translational and rotational motion by inertia. At the same time, the rotation speed of the bullet reaches very high values, for the Kalashnikov 3000 assault rifle, and for sniper rifle Dragunov - about 2600 rpm.
Bullet rotation speed can be calculated by the formula:
where Vvr - rotation speed (rpm), Vo - muzzle velocity (mm/s), Lnar - rifling stroke length (mm).
During the flight of a bullet, the force of air resistance tends to tip the bullet head up and back. But the head of the bullet, rotating rapidly, according to the property of the gyroscope, tends to maintain its position and deviate not upwards, but slightly in the direction of its rotation - to the right, at right angles to the direction of the air resistance force. When the head part is deflected to the right, the direction of the air resistance force changes, which now tends to turn the head part of the bullet to the right and back. But as a result of rotation, the head of the bullet does not turn to the right, but down and further to its description full circle(see fig. 14).
Rice. 14. Conical rotation of the bullet head
Thus, the head of a flying and rapidly rotating bullet describes a circle, and its axis is a cone with a vertex at the center of gravity. There is a so-called slow conical movement, in which the bullet flies head first in accordance with the change in the curvature of the trajectory (see Fig. 15).
Rice. 15. Flight of a spinning bullet in the air
The axis of slow conical rotation is located above the tangent to the flight path of the bullet, so the lower part of the bullet is in more subject to the pressure of the oncoming air flow than the top. In this regard, the axis of slow conical rotation deviates in the direction of rotation, i.e. to the right. This phenomenon is called derivation (see Fig. 16).
Derivation is the deviation of the bullet from the plane of fire in the direction of its rotation.
The plane of fire is understood as a vertical plane in which lies the axis of the bore of the weapon.
The reasons for the derivation are: the rotational movement of the bullet, air resistance and the constant decrease under the action of gravity of the tangent to the bullet's flight path.
In the absence of at least one of these reasons, there will be no derivation. For example, when shooting vertically up and vertically down, there will be no derivation, since the air resistance force in this case is directed along the bullet axis. There will be no derivation when shooting in an airless space due to the lack of air resistance and when shooting from a smooth-bore weapon due to the lack of bullet rotation.
Rice. 16. The phenomenon of derivation (view of the trajectory from above)
During the flight, the bullet deviates more and more to the side, while the degree of increase in derivational deviations significantly exceeds the degree of increase in the distance traveled by the bullet.
Derivation is not of great practical importance for the shooter when shooting at close and medium distances, it must be taken into account only for particularly accurate shooting at long distances, making certain adjustments to the installation of the sight in accordance with the table of derivational deviations for the corresponding firing range.
Bullet trajectory characteristics
To study and describe the flight path of a bullet, the following indicators characterizing it are used (see Fig. 17).
The departure point is located in the center of the muzzle of the barrel, is the beginning of the bullet's flight path.
The weapon's horizon is the horizontal plane passing through the departure point.
The line of elevation is a straight line that is a continuation of the axis of the bore of the weapon aimed at the target.
The elevation angle is the angle enclosed between the elevation line and the horizon of the weapon. If this angle is negative, for example, when
shooting down from a significant hill, it is called the angle of declination (or descent).
Rice. 17. Bullet trajectory indicators
The line of throw is a straight line, which is a continuation of the axis of the bore at the time of the bullet's departure.
The throw angle is the angle between the throw line and the weapon's horizon.
The departure angle is the angle enclosed between the line of elevation and the line of throw. Represents the difference between the values of the angles of throw and elevation.
Point of impact - is the point of intersection of the trajectory with the horizon of the weapon.
The angle of incidence is the angle at the point of impact between the tangent to the bullet's flight path and the weapon's horizon.
The final velocity of the bullet is the velocity of the bullet at the point of impact.
The total flight time is the time it takes the bullet to travel from the point of departure to the point of impact.
Full horizontal range is the distance from the point of departure to the point of impact.
The vertex of the trajectory is its highest point.
The height of the trajectory is the shortest distance from its top to the horizon of the weapon.
The ascending branch of the trajectory is the part of the trajectory from the departure point to its top.
The descending branch of the trajectory is the part of the trajectory from its top to the point of fall.
The meeting point is a point lying at the intersection of the bullet's flight path with the target surface (ground, obstacles).
The meeting angle is the angle between the tangent to the bullet's flight path and the tangent to the target surface at the meeting point.
The point of aim (aiming) is the point on or off the target at which the weapon is aimed.
The line of sight is a straight line from the shooter's eye through the middle of the sight slit and the top of the front sight to the point of aim.
The angle of aim is the angle between the line of sight and the line of elevation.
Target elevation angle is the angle between the line of sight and the horizon of the weapon.
Sighting range is the distance from the point of departure to the intersection of the trajectory with the line of sight.
The excess of the trajectory over the line of sight is the shortest distance from any point of the trajectory to the line of sight.
When shooting at close range, the values of the excess of the trajectory over the aiming line will be quite low. But when firing at long distances, they reach significant values (see Table 1).
Table 1
Exceeding the trajectory above the aiming line when firing from a Kalashnikov assault rifle (AKM) and a Dragunov sniper rifle (SVD) at distances of 600 m or more
| For 7.62mm AKM | |||||||||||||||||||||
| Range, m | 100 | 200 | 300 | 400 | 500 | 600 | 700 | 800 | 900 | 1000 | |||||||||||
| Aim | meters | ||||||||||||||||||||
| 6 | 0,98 | 1,8 | 2,2 | 2,1 | 1,4 | 0 | -2,7 | -6,4 | - | - | |||||||||||
| 7 | 1,3 | 2,5 | 3,3 | 3,6 | 3,3 | 2,1 | colspan=2 bgcolor=white>0-3,5 | -8,4 | - | ||||||||||||
| 8 | 1,8 | 3,4 | 4,6 | 5,4 | 5,5 | 4,7 | 3,0 | 0 | -4,5 | -10,5 | |||||||||||
| For SVD using an optical sight | |||||||||||||||||||||
| Range, | 100 | 200 | 300 | 400 | 500 | 600 | 700 | 800 | 900 | 1000 | 1100 | 1200 | 1300 | 1400 | |||||||
| Aim | meters | ||||||||||||||||||||
| 6 | 0,53 | 0,95 | 1,2 | 1,1 | 0,74 | 0 | -1,3 | - | - | - | - | - | - | - | |||||||
| 7 | 0,71 | 1,3 | 1,7 | 1,9 | 1,6 | 1,0 | 0 | -1,7 | - | - | - | - | - | - | |||||||
| 8 | 0,94 | 1,8 | 2,4 | 2,7 | 2,8 | 2,4 | 1,5 | 0 | -2,2 | - | - | - | - | - | |||||||
| 9 | 1,2 | 2,2 | 3,1 | 3,7 | 4,0 | 3,9 | 2,3 | 2,0 | 0 | -2,9 | - | - | - | - | |||||||
| 10 | 1,5 | 2,8 | 4,0 | 4,9 | 5,4 | 5,7 | 5,3 | 4,3 | 2,6 | 0 | -3,7 | - | - | - | |||||||
| 11 | 1,8 | 3,5 | 5,0 | 6,2 | 7,1 | 7,6 | 7,7 | 7,1 | 5,7 | 3,4 | 0 | -4,6 | - | - | |||||||
| 12 | 2,2 | 4,3 | 6,2 | 7,8 | 9,1 | 10,0 | 10,5 | 10,0 | 9,2 | 7,3 | 4,3 | 0 | -5,5 | - | |||||||
| 13 | 2,6 | 5,1 | 7,4 | 9,5 | 11 | 12,5 | 13,5 | 13,5 | 13,0 | 11,5 | 8,9 | 5,1 | 0 | -6,6 | |||||||
Note: The number of units in the scope value corresponds to the number of hundreds of meters of shooting distance for which the scope is designed.
(6 - 600 m, 7 - 700 m, etc.).
From Table. 1 shows that the excess of the trajectory above the aiming line when firing from the AKM at a distance of 800 m (sight 8) exceeds 5 meters, and when firing from the SVD at a distance of 1300 m (sight 13) - the bullet trajectory rises above the aiming line by more than 13 meters.
Aiming (weapon aiming)
In order for the bullet to hit the target as a result of the shot, it is first necessary to give the axis of the barrel bore an appropriate position in space.
Giving the axis of the bore of a weapon the position necessary to hit a given target is called aiming or aiming.
This position must be given both in the horizontal plane and in the vertical. Giving the axis of the bore the required position in the vertical plane is a vertical pickup, giving it the desired position in the horizontal plane is a horizontal pickup.
If the aiming reference is a point on or near the target, such aiming is called direct. When shooting from small arms, direct aiming is used, performed using a single sighting line.
The sight line is a straight line connecting the middle of the sight slot to the top of the front sight.
To carry out aiming, it is necessary first, by moving the rear sight (slot of the sight), to give the aiming line such a position in which between it and the axis of the bore, an aiming angle is formed in the vertical plane corresponding to the distance to the target, and in the horizontal plane - an angle equal to the lateral correction, taking into account crosswind speed, derivation and lateral movement speed of the target (see Fig. 18).
After that, directing the sighting line to the area, which is the aiming reference point, by changing the position of the barrel of the weapon, the axis of the bore is given the desired position in space.
In this case, in weapons with a permanent rear sight, as, for example, in most pistols, to give the necessary position of the bore in the vertical plane, an aiming point is selected corresponding to the distance to the target, and the aiming line is directed to this point. In weapons with a sight slot fixed in the side position, as in a Kalashnikov assault rifle, to give the necessary position of the bore in the horizontal plane, the aiming point is selected corresponding to the side correction, and the aiming line is directed to this point.
Rice. 18. Aiming (weapon aiming): O - front sight; a - rear sight; aO - aiming line; сС - the axis of the bore; oO - a line parallel to the axis of the bore;
H - sight height; M - the amount of movement of the rear sight; a - aiming angle; Ub - angle of lateral correction
Bullet trajectory shape and its practical significance
The shape of the trajectory of a bullet in the air depends on the angle at which it is fired in relation to the horizon of the weapon, its initial velocity, kinetic energy and shape.
To produce a targeted shot, the weapon is aimed at the target, while the aiming line is directed to the aiming point, and the axis of the bore in the vertical plane is brought to a position corresponding to the required elevation line. Between the axis of the bore and the horizon of the weapon, the required elevation angle is formed.
When fired, under the action of the recoil force, the axis of the barrel bore is shifted by the value of the departure angle, while it goes into a position corresponding to the throw line and forms a throw angle with the horizon of the weapon. At this angle, the bullet flies out of the bore of the weapon.
Due to the insignificant difference between the angle of elevation and the angle of throwing, they are often identified, while, however, it is more correct in this case talk about the dependence of the trajectory of a bullet on the angle of throw.
With an increase in the angle of throw, the height of the trajectory of the flight of the bullet and the total horizontal range increase to a certain value given angle, after which the trajectory height continues to increase, and the total horizontal range decreases.
The angle of throw at which the full horizontal range of the bullet is greatest is called the angle of greatest range.
In accordance with the laws of mechanics in an airless space, the angle of greatest range will be 45 °.
When a bullet is flying in air, the relationship between the angle of throw and the shape of the bullet's flight path is similar to the dependence of these characteristics observed when a bullet is flying in airless space, but due to the influence of air resistance, the maximum range angle does not reach 45 °. Depending on the shape and mass of the bullet, its value varies between 30 - 35 °. For calculations, the angle of the greatest firing range in the air is assumed to be 35°.
The flight paths of a bullet that occur at angles of throw smaller than the angle of greatest range are called flat.
The flight paths of a bullet that occur at angles of throw of a large angle of greatest range are called hinged (see Fig. 19).
Rice. 19. Angle of greatest range, flat and overhead trajectories
Flat trajectories are used when firing direct fire at fairly short distances. When firing from small arms, only this type of trajectory is used. The flatness of the trajectory is characterized by its maximum excess over the aiming line. The less the trajectory rises above the aiming line at a given firing range, the more flat it is. Also, the flatness of the trajectory is estimated by the angle of incidence: the smaller it is, the flatter the trajectory.
The flatter the trajectory used when shooting, the greater the distance the target can be hit with one set of
intact, i.e. errors in the installation of the sight have a lesser effect on the effectiveness of shooting.
Mounted trajectories are not used when firing from hand-held small arms, in turn, they are widely used in firing shells and mines at long distances outside the line of sight of the target, which in this case is set by coordinates. Mounted trajectories are used when firing from howitzers, mortars and other types of artillery weapons.
Due to the peculiarities of this type of trajectory, these types of weapons can hit targets located in cover, as well as behind natural and artificial barriers (see Fig. 20).
Trajectories that have the same horizontal range at different throw angles are called conjugate. One of these trajectories will be flat, the second hinged.
Conjugated trajectories can be obtained when firing from one weapon, using throwing angles greater and less than the angle of greatest range.
Rice. 20. Features of the use of hinged trajectories
A shot in which the excess of the trajectory over the line of sight throughout its entire length does not reach values greater than the height of the target is considered a direct shot (see Fig. 21).
The practical significance of a direct shot lies in the fact that, within its range, in tense moments of the battle, it is allowed to fire without rearranging the sight, while the aiming point in height, as a rule, is chosen at the lower edge of the target.
The range of a direct shot depends, firstly, on the height of the target and, secondly, on the flatness of the trajectory. The higher the target and the flatter the trajectory, the greater the range of a direct shot and the greater the distance the target can be hit with one sight setting.
Rice. 21. Direct shot
The range of a direct shot can be determined from the tables, comparing the height of the target with the values of the greatest excess of the trajectory above the aiming line or with the height of the trajectory.
When shooting at a target that is at a distance greater than the range of a direct shot, the trajectory near the top rises above the target, and the target in a certain area will not be hit with this setting of the sight. In this case, there will be a space near the target, on which the descending branch of the trajectory will lie within its height.
The distance at which the descending branch of the trajectory is within the height of the target is called the affected space (see Fig. 22).
The depth (length) of the affected space directly depends on the height of the target and the flatness of the trajectory. It also depends on the angle of inclination of the terrain: when the terrain rises up, it decreases, when it slopes down, it increases.
Rice. 22. Affected space with a depth equal to the segment AC, for the target
height equal to segment AB
If the target is behind cover, impenetrable by a bullet, then the possibility of hitting it depends on where it is located.
The space behind the shelter from its crest to the meeting point is called the covered space (see Fig. 23). The covered space will be the greater, the greater the height of the shelter and the flatter the trajectory of the bullet.
The part of the covered space in which the target cannot be hit with a given trajectory is called dead (non-hit) space. Dead space will be the greater, the greater the height of the shelter, the lower the height of the target and the flatter the trajectory. The part of the covered space in which the target can be hit is the hit space.
Thus, the depth of the dead space is the difference between the covered and affected space.
Rice. 23. Covered, dead and affected space
The shape of the trajectory also depends on the muzzle velocity of the bullet, its kinetic energy and shape. Consider how these indicators affect the formation of the trajectory.
The further speed of its flight directly depends on the initial speed of the bullet, the value of its kinetic energy, with equal shapes and sizes, provides a smaller degree of speed reduction under the action of air resistance.
Thus, a bullet fired at the same elevation (throw) angle, but with a higher initial velocity or with a higher kinetic energy, will have a higher speed during further flight.
If we imagine a certain horizontal plane at some distance from the departure point, then at the same value elevation angle-
When thrown (thrown), a bullet with a higher speed will reach it faster than a bullet with a lower speed. Accordingly, a slower bullet, having reached this plane and spending more time on it, will have time to go down more under the action of gravity (see Fig. 24).
Rice. 24. The dependence of the trajectory of the flight of a bullet on its speed
In the future, the trajectory of a bullet with lower speed characteristics will also be located below the trajectory of a faster bullet, and under the influence of gravity, it will drop faster in time and closer in distance from the point of departure to the level of the weapon’s horizon.
Thus, the muzzle velocity and kinetic energy of the bullet directly affect the height of the trajectory and the full horizontal range of its flight.
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 point the gun so that the axis of the bore is directed at the target, then we will not hit the target, since the flight path 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 with Latin letter c)
the angle between the target line and the fall line is called (see Fig. 2).
Meeting angle (Greek mu)
is the angle between the line of incidence and the tangent to the target surface at the meeting point (see Fig. 2).
The value of the value of this angle greatly affects the resistance of the armor of the ship, which is fired at, to penetration by shells. Obviously, the closer this angle is to 90 degrees, the higher the probability of penetration, and the opposite is also true.
Shooting plane
called the vertical plane passing through the line of elevation. When the ship fires at sea targets, the aiming line is directed along the horizon, in this case the elevation angle equal to the angle aiming. When a ship fires at coastal and air targets, the elevation angle is equal to the sum of the aiming angle and the elevation angle of the target (see Fig. 3). When firing a coastal battery at sea targets, the elevation angle is equal to the difference between the aiming angle and the elevation angle of the target (see Fig. 4). Thus, the magnitude of the elevation angle is equal to the algebraic sum of the aiming angle and the elevation angle of the target. If the target is above the horizon, the target elevation angle is "+", if the target is below the horizon, the target elevation angle is "-".
The influence of air resistance on the trajectory of the projectile
Rice. 5. Changing the trajectory of the projectile from air resistance
The flight path of a projectile in airless space is a symmetrical curved line, called a parabola in mathematics. The ascending branch coincides in shape with the descending branch and, therefore, the angle of incidence is equal to the angle of elevation.
When flying in the air, the projectile spends part of its speed to overcome air resistance. Thus, two forces act on the projectile in flight - the force of gravity and the force of air resistance, which reduces the speed and range of the projectile, as illustrated in Fig. 5. The magnitude of the air resistance force depends on the shape of the projectile, its size, flight speed and air density. The longer and more pointed the head of the projectile, the less air resistance. The shape of the projectile is especially affected at flight speeds exceeding 330 meters per second (that is, at supersonic speeds).
Rice. 6. Short-range and long-range projectiles
On fig. 6, on the left, is a short-range, old-style projectile and a more oblong, pointed, long-range projectile on the right. It can also be seen that a long-range projectile has a conical narrowing at the bottom. The fact is that a rarefied space and turbulence are formed behind the projectile, which significantly increase air resistance. By narrowing the bottom of the projectile, a decrease in the amount of air resistance resulting from rarefaction and turbulence behind the projectile is achieved.
The force of air resistance is proportional to the speed of its flight, but not directly proportional. Dependence is formalized more difficult. Due to the action of air resistance, the ascending branch of the projectile's flight path is longer and delayed than the descending one. The angle of incidence is greater than the angle of elevation.
In addition to reducing the range of the projectile and changing the shape of the trajectory, the force of air resistance tends to overturn the projectile, as can be seen from Fig. 7.
Rice. 7. Forces acting on a projectile in flight
Therefore, a non-rotating elongated projectile will roll over under the action of air resistance. In this case, the projectile can hit the target in any position, including sideways or bottom, as shown in Fig. 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 to 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 point of departure and the middle point of fall is called average trajectory
.
The scattering area has the shape of an ellipse, so the scattering area is called scattering ellipse
.
The intensity with which 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.
Taking into account the fact that the dispersion ellipse has a large length and a small width, we can conclude that at a shallow target depth, fewer projectiles hit the target than at a large depth. That is, the greater the depth of the target, the easier it is to hit it. With an increase in the firing range, the affected target space decreases, as the angle of incidence increases.
Straight shot a shot is called, in which the entire distance from the point of departure to the point of impact is the affected space (see Fig. 13).
Rice. 13. Direct shot
This is obtained if the height of the trajectory does not exceed the height of the target. The range of a direct shot depends on the steepness of the trajectory and the height of the target.
Range of a direct shot (or range of flattening) called the distance at which the height of the trajectory does not exceed the height of the target.
The most important works on ballistics
17th century
- - Tartaglia theory,
- 1638- labor Galileo Galilei about the parabolic motion of a body thrown at an angle.
- 1641- a student of Galileo - Toricelli, developing the parabolic theory, derives an expression for horizontal range, which later formed the basis of artillery firing tables.
- 1687- Isaac Newton proves the influence of air resistance on a thrown body, introducing the concept of the shape factor of the body, and also drawing a direct dependence of the movement resistance on the cross section (caliber) of the body (projectile).
- 1690— Ivan Bernoulli mathematically describes main task ballistics, solving the problem of determining the motion of a ball in a resisting medium.
18th century
- 1737- Bigot de Morogues (1706-1781) published a theoretical study of the issues internal ballistics, which laid the foundation for the rational design of tools.
- 1740- the Englishman Robins learned to determine the initial velocities of the projectile and proved that the parabola of the projectile flight 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 velocities 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 the influx of new gases, and the pressure begins to fall. However, the speed of the bullet in the bore continues to increase, as the gases, although to a lesser extent, still put pressure on it. The bullet moves along the bore at a continuously increasing speed and is ejected outward in the direction of the axis of the bore. The entire firing process takes place in a very short period of time (0.001–0.06 s). Further, the flight of the bullet in the air continues by inertia and largely depends on its initial velocity.
muzzle velocity is the speed at which the bullet leaves the bore. The value of the muzzle velocity of a bullet depends on the length of the barrel, the mass of the bullet, the mass of the powder charge, and other factors. An increase in the initial speed increases the range of the bullet, its penetrating and lethal effect, reduces the impact external conditions for her flight. The movement of the weapon backwards while firing is called recoil. The pressure of powder gases in the bore acts in all directions with the same force. The pressure of the gases on the bottom of the bullet makes it move forward, and the pressure on the bottom of the cartridge case is transmitted to the bolt and causes the weapon to move backward. When recoil, a pair of forces is formed, under the influence of which the muzzle of the weapon deviates upward. The recoil force acts along the axis of the bore, and the butt rest against the shoulder and the center of gravity of the weapon are located below the direction of this force, therefore, when firing, the muzzle of the weapon deviates upward.
recoil small arms is felt in the form of a push in the shoulder, arm or into the ground. The recoil action of a weapon is characterized by the amount of speed and energy that it has when moving backward. The recoil speed of the weapon is about as many times less than the initial speed of the bullet, how many times the bullet is lighter than the weapon. The recoil energy of the Kalashnikov assault rifle is small and is perceived painlessly by the shooter. Correct and uniform holding of the weapon reduces the impact of recoil and increases the effectiveness of shooting. The presence of muzzle brakes-compensators or compensators for weapons improves the results of firing bursts and reduces recoil.
At the time of the shot, the barrel of the weapon, depending on the elevation angle, occupies a certain position. The flight of a bullet in the air begins in a straight line, representing the continuation of the axis of the bore at the time of the bullet's departure. This line is called throw line. When flying in the air, two forces act on a bullet: gravity and air resistance. Gravity pushes the bullet further and further away from the line of throw, while air resistance slows the bullet down. Under the influence of these two forces, the bullet continues to fly along a curve located below the line of throw. Trajectory shape depends on the magnitude of the angle of elevation and the initial velocity of the bullet, it affects the value of the range of a direct shot, covered, affected and dead space. As the elevation angle increases, the height of the trajectory and the total horizontal range of the bullet increase, but this occurs up to a certain limit. Beyond this limit, the trajectory height continues to increase and the total horizontal range decreases.
The angle of elevation at which the full horizontal range of the bullet is greatest is called farthest angle. The value of the angle of greatest range for bullets of various types of weapons is about 35 °. Trajectories obtained at elevation angles smaller than the angle of greatest range are called flat.
Straight shot called a shot in which the trajectory of the bullet does not rise above the line of sight above the target throughout its entire length.
Direct shot range depends on the height of the target and flatness of the trajectory. The higher the target and the flatter the trajectory, the greater the range of a direct shot and, therefore, the distance at which the target can be hit with one sight setting. The practical significance of a direct shot lies in the fact that in tense moments of the battle, shooting can be carried out without rearranging the sight, while the aiming point in height will be selected along the lower edge of the target.
The space behind a cover that is not penetrated by a bullet, from its crest to the meeting point is called covered space.
The covered space is the greater, the higher the shelter and the flatter the trajectory. The part of the covered space on which the target cannot be hit with a given trajectory is called dead (non-hit) space. It is the greater, the greater the height of the shelter, the lower the height of the target and the flatter the trajectory. The other part of the covered space in which the target can be hit is the hit space.
Shot periodization
The shot occurs in a very short period of time (0.001-0.06 s.). When fired, four consecutive periods are distinguished:
- preliminary;
- first, or main;
- second;
- the third, or period of the last gases.
Preliminary period lasts from the beginning of the burning of the powder charge to the complete cutting of the shell of the bullet into the rifling of the barrel. During this period, the gas pressure is created in the barrel bore, which is necessary in order to move the bullet from its place and overcome the resistance of its shell to cutting into the rifling of the barrel. This pressure is called boost pressure; it reaches 250 - 500 kg / cm 2, depending on the rifling device, the weight of the bullet and the hardness of its shell (for example, for small arms chambered for the 1943 sample, the forcing pressure is about 300 kg / cm 2). It is assumed that the combustion of the powder charge in this period occurs in a constant volume, the shell cuts into the rifling instantly, and the movement of the bullet begins immediately when the forcing pressure is reached in the bore.
First or main period lasts from the beginning of the movement of the bullet until the moment of complete combustion of the powder charge. During this period, the combustion of the powder charge occurs in a rapidly changing volume. At the beginning of the period, when the speed of the bullet along the bore is still low, the amount of gases grows faster than the volume of the bullet space (the space between the bottom of the bullet and the bottom of the 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.