Internal ballistics. Shot and its periods. External ballistics. Trajectory and its elements. Excess of the bullet's flight path above the aiming point. Trajectory shape Determination of the full horizontal range of a bullet
To successfully master shooting techniques from any small arms, it is necessary to have a good knowledge of the laws of ballistics and a number of basic concepts related to it. Not a single sniper could or will do without this; without studying this discipline, a sniping training course is of little use.
Ballistics is the science of the movement of bullets and projectiles fired from small arms when fired. Ballistics is divided into external And internal.
Internal ballistics
Internal ballistics studies the processes occurring in the bore of a weapon during a shot, the movement of a bullet along the bore and the accompanying aero and thermodynamic dependencies both in the bore and beyond until the end of the aftereffect of the powder gases.
Besides, internal ballistics studies the issues most rational use energy of a powder charge during a shot in order to impart an optimal initial velocity to a bullet of a given caliber and weight while maintaining the strength of the weapon barrel: this provides initial data for both external ballistics and weapon design.
Shot
Shot- this is the ejection of a bullet from the bore of a weapon under the influence of the energy of gases formed during the combustion of the powder charge of the cartridge.
Shot dynamics. When the firing pin hits the primer of a live cartridge sent into the chamber, the percussion composition of the primer explodes, and a flame is formed, which is transferred to the powder charge through the seed holes in the bottom of the cartridge case and ignites it. With the simultaneous combustion of a combat (powder) charge, a large amount of heated powder gases is formed, which creates high pressure on the bottom of the bullet, the bottom and walls of the cartridge case, as well as on the walls of the bore and bolt.
Under strong pressure of the powder gases at the bottom of the bullet, it is separated from the cartridge case and crashes into the channels (rifling) of the weapon barrel and, rotating along them with an ever-increasing speed, is thrown out in the direction of the axis of the barrel channel.
In turn, the pressure of the gases on the bottom of the cartridge case causes the weapon (weapon barrel) to move backward: this phenomenon is called return. How larger caliber weapon and, accordingly, the ammunition (cartridge) for it - the greater the recoil force (see below).
When fired from automatic weapons, the principle of operation of which is based on the use of the energy of powder gases removed through a hole in the wall of the barrel, as for example in the SVD, part of the powder gases, after passing into the gas chamber, hits the piston and throws the pusher with the bolt back.
The shot occurs in an ultra-short period of time: from 0.001 to 0.06 seconds and is divided into four consecutive periods:
- preliminary
- first (main)
- second
- third (period of aftereffect of powder gases)
Preliminary shot period. It lasts from the moment the cartridge’s powder charge ignites until the bullet completely pierces the rifling of the barrel. During this period, gas pressure is created in the barrel bore sufficient to move the bullet from its place and overcome the resistance of its shell to cut into the rifling of the barrel bore. This type of pressure is called boost pressure, which reaches a value of 250 - 600 kg/cm² depending on the weight of the bullet, the hardness of its shell, caliber, barrel type, number and type of rifling.
First (main) shot period. Lasts from the moment the bullet begins to move along the bore of the weapon until the complete combustion of the powder charge of the cartridge. During this period, the combustion of the powder charge occurs in rapidly changing volumes: at the beginning of the period, when the speed of the bullet along the barrel is still relatively low, the amount of gases grows faster than the volume of the bullet space (the space between the bottom of the bullet and the bottom of the case), the gas pressure quickly rises and reaches greatest value- 2900 kg/cm² for a 7.62 mm rifle cartridge: this pressure is called maximum pressure. It is created in small arms when a bullet travels 4 - 6 cm.
Then, due to a very rapid increase in the speed of the bullet, the volume of the behind-the-bullet space increases faster than the influx of new gases, as a result of which the pressure begins to fall: by the end of the period it is equal to approximately 2/3 of the maximum pressure. The speed of the bullet constantly increases and by the end of the period reaches approximately 3/4 initial speed. The powder charge is completely burned shortly before the bullet leaves the barrel.
Second shot period. Lasts from the moment the powder charge is completely burned until the bullet leaves the barrel. With the beginning of this period, the influx of powder gases stops, but highly heated, compressed gases expand and, putting pressure on the bullet, significantly increase its speed. The pressure drop in the second period occurs quite quickly and the muzzle pressure at the muzzle of the weapon is 300 - 1000 kg/cm² for various types of weapons. Muzzle velocity, that is, the speed of the bullet at the moment it leaves the barrel is slightly less than the initial speed.
The third period of the shot (the period of aftereffect of powder gases). Lasts from the moment the bullet leaves the bore of the weapon until the action of the powder gases on the bullet ceases. During this period, powder gases flowing from the barrel at a speed of 1200-2000 m/s continue to act on the bullet and impart additional speed to it. The bullet reaches its maximum speed at the end of the third period at a distance of several tens of centimeters from the muzzle of the weapon barrel. This period ends at the moment when the pressure of the powder gases at the bottom of the bullet is completely balanced by air resistance.
Initial bullet speed
Initial bullet speed- this is the speed of the bullet at the muzzle of the weapon barrel. The value of the initial bullet velocity is taken to be a conditional velocity that is less than the maximum, but greater than the muzzle, which is determined experimentally and relevant calculations.
This parameter is one of the most important characteristics of the combat properties of a weapon. The magnitude of the muzzle velocity is indicated in the shooting tables and in the combat characteristics of the weapon. As the initial speed increases, the bullet's flight range increases, the range direct shot, lethal and penetrating effect of the bullet, and also reduces the influence of external conditions on its flight. The magnitude of the initial bullet speed depends on:
- bullet weight
- barrel length
- temperature, weight and humidity of the powder charge
- size and shape of gunpowder grains
- loading density
Bullet weight. The smaller it is, the greater its initial speed.
Barrel length. The larger it is, the longer the period of time the powder gases act on the bullet, and accordingly, the greater its initial speed.
Temperature of the powder charge. As the temperature decreases, the initial velocity of the bullet decreases; with an increase, it increases due to the increase in the burning rate of the gunpowder and the pressure value. Under normal conditions weather conditions, the temperature of the powder charge is approximately equal to the air temperature.
Weight of the powder charge. The greater the weight of the powder charge of the cartridge, the greater the amount of powder gases affecting the bullet, the greater the pressure in the barrel and, accordingly, the speed of the bullet.
Humidity of the powder charge. When it increases, the burning rate of gunpowder decreases, and accordingly, the speed of the bullet decreases.
Size and shape of gunpowder grains. Gunpowder grains of various sizes and shapes have different speed combustion, and this has a significant impact on the initial velocity of the bullet. The optimal option is selected at the stage of weapon development and during its subsequent testing.
Loading density. This is the ratio of the weight of the powder charge to the volume of the cartridge case when the bullet is inserted: this space is called charge combustion chamber. If the bullet is seated too deeply in the cartridge case, the loading density increases significantly: when fired, this can lead to the rupture of the weapon barrel due to a sharp jump in pressure inside it, therefore such cartridges cannot be used for shooting. The higher the loading density, the lower the initial bullet speed; the lower the loading density, the higher the initial bullet speed.
Recoil
Recoil- This is the movement of the weapon back at the moment of the shot. It is felt as a push in the shoulder, arm, ground, or a combination of these sensations. The recoil effect of a weapon is approximately the same number of times less than the initial speed of the bullet, as the bullet is lighter than the weapon. The recoil energy of hand-held small arms usually does not exceed 2 kg/m and is perceived by the shooter painlessly.
The recoil force and the recoil resistance force (butt support) are not located on the same straight line: they are directed in opposite directions and form a pair of forces, under the influence of which the muzzle of the weapon barrel is deflected upward. The magnitude of the deflection of the muzzle of a given weapon is greater, the greater more shoulder this pair of forces. In addition, when fired, the barrel of the weapon vibrates, that is, it makes oscillatory movements. As a result of vibration, the muzzle of the barrel at the moment the bullet leaves can also deviate from its original position in any direction (up, down, left, right).
You should always remember that the magnitude of this deviation increases with improper use of the shooting rest, contamination of the weapon, or use of non-standard cartridges.
The combination of the influence of barrel vibration, weapon recoil and other reasons leads to the formation of an angle between the direction of the axis of the barrel bore before the shot and its direction at the moment the bullet leaves the bore: this angle is called departure angle.
Departure angle it is considered positive if the axis of the barrel bore at the moment the bullet leaves is above its position before the shot, negative - when below. The influence of the take-off angle on shooting is eliminated when it is brought to normal combat. But if the rules for caring for and preserving a weapon, the rules for attaching a weapon, or using a stop are violated, the value of the angle of departure and the engagement of the weapon changes. In order to reduce the harmful effects of recoil on shooting results, recoil compensators are used, located on the muzzle of the weapon barrel or removable and attached to it.
External ballistics
External ballistics studies the processes and phenomena accompanying the movement of a bullet that arise after the effect of powder gases on it ceases. The main task of this subdiscipline is to study the patterns of bullet flight and study the properties of its flight trajectory.
Also, this discipline provides data for developing shooting rules, compiling shooting tables and calculating weapon sight scales. Conclusions from external ballistics have long been widely used in combat when choosing a sight and aiming point depending on the firing range, wind speed and direction, air temperature and other shooting conditions.
This is a curved line described by the center of gravity of the bullet during flight.
The trajectory of a bullet, the flight of a bullet in space
When flying in space, two forces act on a bullet: gravity And air resistance force.
The force of gravity forces the bullet to gradually decrease horizontally towards the plane of the earth, and the force of air resistance permanently (continuously) slows down the flight of the bullet and tends to overturn it: as a result, the speed of the bullet gradually decreases, and its trajectory is shaped like an unevenly curved curved line.
Air resistance to the flight of a bullet is caused by the fact that air is an elastic medium and therefore some of the energy of the bullet is expended on movement in this medium.
Air resistance force caused by three main factors:
- air friction
- swirls
- ballistic wave
Shape, properties and types of trajectory
Path shape depends on the elevation angle. As the elevation angle increases, the trajectory height and the total horizontal range of the bullet increase, but this occurs up to a certain limit, after which the trajectory height continues to increase, and the total horizontal range begins to decrease.
The elevation angle at which the total horizontal range of the bullet becomes greatest is called angle of greatest range. The value of the angle of greatest range for bullets various types weapons is about 35°.
mounted trajectory- this is the trajectory obtained at elevation angles larger than the angle of greatest range.
Flat trajectory- trajectory obtained at elevation angles smaller than the angle of greatest range.
Conjugate trajectory- a trajectory having the same horizontal range at different elevation angles.
When firing from a weapon of the same model (at the same initial bullet speeds), you can get two flight trajectories with the same horizontal range: mounted and flat.
When shooting from small arms, only flat trajectories. The flatter the trajectory, the greater the distance a target can be hit with one sight setting and the less impact an error in determining the sight setting has on the shooting results: this is the practical significance of the trajectory.
The flatness of the trajectory is characterized by its greatest excess above the aiming line. At a given range, the trajectory is flatter the less it rises above the aiming line. In addition, the flatness of the trajectory can be judged by the angle of incidence: the trajectory is more flat, the smaller the angle of incidence.
The flatness of the trajectory affects the range of a direct shot, hit, covered and dead space.
Departure point- the center of the muzzle of the weapon barrel. The departure point is the beginning of the trajectory.
Weapon Horizon- horizontal plane passing through the departure point.
Elevation line- a straight line, which is a continuation of the axis of the barrel of the aimed weapon.
Firing plane- a vertical plane passing through the elevation line.
Elevation angle- the angle between the elevation line and the horizon of the weapon. If this angle is negative, then it is called declination angle (declination).
Throwing line- a straight line, which is a continuation of the axis of the barrel bore at the moment the bullet leaves.
Throwing angle
Departure angle- the angle between the elevation line and the throwing line.
Drop point- the point of intersection of the trajectory with the horizon of the weapon.
Angle of incidence- the angle between the tangent to the trajectory at the point of impact and the horizon of the weapon.
Full horizontal range- the distance from the point of departure to the point of impact.
Ultimate speed b is the speed of the bullet at the point of impact.
Total flight time- time of movement of a bullet from the point of departure to the point of impact.
Top of the trajectory- the highest point of the trajectory above the horizon of the weapon.
Path height- the shortest distance from the top of the trajectory to weapon horizon.
Ascending branch of the trajectory- part of the trajectory from the departure point to the top.
Descending branch of the trajectory- part of the trajectory from the top to the point of fall.
Aiming point (aiming point)- a point on the target (outside it) at which the weapon is aimed.
Line of sight- a straight line running from the shooter’s eye through the middle of the sight slot at a level with its edges and the top of the front sight to the aiming point.
Aiming angle- the angle between the elevation line and the aiming line.
Target elevation angle- the angle between the aiming line and the horizon of the weapon. This angle is considered positive (+) when the target is above, and negative (-) when the target is below the weapon's horizon.
Sighting range- the distance from the departure point to the intersection of the trajectory with the aiming line. The excess of the trajectory above the aiming line is the shortest distance from any point on the trajectory to the aiming line.
Target line- a straight line connecting the departure point to the target.
Slant range- the distance from the departure point to the target along the target line.
Meeting point- the point of intersection of the trajectory with the target surface (ground, obstacle).
Meeting angle- the angle between the tangent to the trajectory and the tangent to the surface of the target (ground, obstacle) at the meeting point. The meeting angle is taken to be the smaller of the adjacent angles, measured from 0 to 90°.
Direct shot, covered space, target space, dead space
This is a shot in which the trajectory does not rise above the aiming line above the target throughout its entire length.
Direct shot range depends on two factors: the height of the target and the flatness of the trajectory. The higher the target and the flatter the trajectory, the greater the range of a direct shot and the greater the area over which the target can be hit with one sight setting.
Also, the direct shot range can be determined from shooting tables by comparing the target height with the values of the greatest elevation of the trajectory above the aiming line or with the trajectory height.
Within the range of a direct shot, in tense moments of battle, shooting can be carried out without rearranging the sight values, while the vertical aiming point is usually selected at the lower edge of the target.
Practical use
The height of installation of optical sights above the bore of a weapon is on average 7 cm. At a distance of 200 meters and sight “2” the greatest excesses of the trajectory, 5 cm at a distance of 100 meters and 4 cm at 150 meters, practically coincide with aiming line - optical axis of the optical sight. Line of sight height at the middle of a distance of 200 meters it is 3.5 cm. There is a practical coincidence of the bullet trajectory and the aiming line. The difference of 1.5 cm can be neglected. At a distance of 150 meters, the height of the trajectory is 4 cm, and the height of the optical axis of the sight above the horizon of the weapon is 17-18 mm; the difference in height is 3 cm, which also does not play a practical role.
At a distance of 80 meters from the shooter bullet trajectory height will be 3 cm, and sighting line height- 5 cm, the same difference of 2 cm is not decisive. The bullet will land only 2 cm below the aiming point.
The vertical dispersion of bullets of 2 cm is so small that it is of no fundamental importance. Therefore, when shooting with the “2” division of the optical sight, starting from 80 meters of distance and up to 200 meters, aim at the bridge of the enemy’s nose - you will hit there ±2/3 cm higher and lower throughout this distance.
At a distance of 200 meters, the bullet will hit exactly the aiming point. And even further, at a distance of up to 250 meters, aim with the same sight “2” at the enemy’s “top”, at the upper cut of the cap - the bullet drops sharply after 200 meters of distance. At 250 meters, aiming this way, you will hit 11 cm lower - on the forehead or bridge of the nose.
The above method of firing can be useful in street battles, when the distances in the city that are relatively open for viewing are approximately 150-250 meters.
Target space
Target space- this is the distance on the ground over which the descending branch of the trajectory does not exceed the target height.
When shooting at targets located at a distance greater than the direct shot range, the trajectory near its top rises above the target and the target in some area will not be hit with the same sight setting. However, there will be a space (distance) near the target at which the trajectory does not rise above the target and the target will be hit by it.
Depth of affected space depends on:
- target height (the higher the height, the greater the value)
- flatness of the trajectory (the flatter the trajectory, the greater the value)
- angle of inclination of the terrain (on the forward slope it decreases, on the reverse slope it increases)
Depth of affected space can be determined from tables of trajectory elevation above the aiming line by comparing the excess of the descending branch of the trajectory by the corresponding firing range with the target height, and if the target height is less than 1/3 of the trajectory height, then in the form of a thousandth.
To increase the depth of the affected area on sloping terrain the firing position must be chosen so that the terrain at the enemy’s location coincides, if possible, with the line of sight.
Covered, target and dead space
Covered space- this is the space behind cover that cannot be penetrated by a bullet, from its crest to the meeting point.
The greater the height of the shelter and the flatter the trajectory, the larger the covered space. Depth of covered space can be determined from tables of trajectory elevation above the aiming line: by selection, the elevation is found corresponding to the height of the shelter and the distance to it. After finding the excess, the corresponding sight setting and firing range are determined.
The difference between a certain firing range and the distance to cover represents the depth of the covered space.
Dead space- this is part of the covered space in which the target cannot be hit with a given trajectory.
The greater the height of the shelter, the lower the height of the target and the flatter the trajectory, the greater the dead space.
Ptarget space- this is a part of the covered space in which the target can be hit. The depth of dead space is equal to the difference between the covered and affected space.
Knowing the size of the target space, covered space, and dead space allows you to correctly use shelters to protect against enemy fire, as well as take measures to reduce dead spaces by the right choice firing positions and firing at targets from weapons with a more advanced trajectory.
This is a rather complicated process. Due to the simultaneous impact of rotational motion on the bullet, which gives it a stable position in flight, and air resistance, which tends to tip the bullet head back, the axis of the bullet deviates from the direction of flight in the direction of rotation.
As a result of this, the bullet encounters greater air resistance on one of its sides, and therefore deviates from the firing plane more and more in the direction of rotation. This deviation of a rotating bullet away from the firing plane is called derivation.
It increases disproportionately to the flight distance of the bullet, as a result of which the latter deviates more and more away from the intended target and its trajectory is a curved line. The direction of deflection of the bullet depends on the direction of the rifling of the weapon's barrel: when the barrel is rifled on the left side, the deflection takes the bullet into left side, with right-handed - to the right.
At firing distances up to 300 meters inclusive, derivation has no practical significance.
| Distance, m | Derivation, cm | Thousands (horizontal sight correction) | Aiming point without corrections (SVD rifle) |
| 100 | 0 | 0 | sight center |
| 200 | 1 | 0 | Same |
| 300 | 2 | 0,1 | Same |
| 400 | 4 | 0,1 | enemy's left (from the shooter) eye |
| 500 | 7 | 0,1 | to the left side of the head between the eye and ear |
| 600 | 12 | 0,2 | left edge of the enemy's head |
| 700 | 19 | 0,2 | above the center of the shoulder strap on the enemy's shoulder |
| 800 | 29 | 0,3 | without corrections, accurate shooting is not possible |
| 900 | 43 | 0,5 | Same |
| 1000 | 62 | 0,6 | Same |
Flying a bullet in the air
Having flown out of the barrel, the bullet moves by inertia and is subject to the action of two forces: gravity and air resistance.
The force of gravity causes the bullet to gradually lower, and the force of air resistance continuously slows down the movement of the bullet and tends to knock it over. Part of the bullet's energy is spent on overcoming the force of air resistance.
The force of air resistance is caused by three main reasons: air friction, the formation of vortices and the formation of a ballistic wave (Fig. 4)
During flight, a bullet collides with air particles and causes them to vibrate. As a result, the air density in front of the bullet increases and sound waves are formed, a ballistic wave is formed. The force of air resistance depends on the shape of the bullet, flight speed, caliber, air density
Rice. 4. Formation of air resistance force
To prevent the bullet from tipping over under the influence of air resistance, it is given a rapid rotational movement using rifling in the barrel. Thus, as a result of the action of gravity and air resistance on the bullet, it will not move uniformly and rectilinearly, but will describe a curved line - a trajectory.
Trajectory called the curved line described by the center of gravity of the bullet in flight.
To study the trajectory, the following definitions were adopted (Fig. 5):
· departure point – the center of the muzzle of the barrel, where the center of gravity of the bullet is located at the moment of departure. The moment of departure is the passage of the bottom of the bullet through the muzzle of the barrel;
· weapon horizon – horizontal plane passing through the departure point;
· elevation line – a straight line, which is a continuation of the axis of the barrel bore at the moment of departure;
· shooting plane – vertical plane passing through the elevation line;
· throwing line – a straight line, which is a continuation of the axis of the barrel bore at the moment the bullet leaves;
· throwing angle – the angle between the throwing line and the horizon of the weapon;
· departure angle – the angle between the elevation line and the throwing line;
· point of impact - the point of intersection of the trajectory with the horizon of the weapon,
· corner falls – the angle at the point of impact between the tangent to the trajectory and the horizon of the weapon,
· full horizontal range – distance from the point of departure to the point of fall,
· top of the trajectory - highest point of the trajectory;
· trajectory height – the shortest distance from the top of the trajectory to the horizon of the weapon,
· ascending branch of the trajectory – part of the trajectory from the departure point to its top;
· descending branch of the trajectory – part of the trajectory from the top to the point of fall,
· meeting point – intersection of the trajectory with the target surface (ground, obstacles),
· meeting angle – the angle between the tangent to the trajectory and the tangent to the target surface at the meeting point;
· aiming point - the point on or off the target at which the weapon is aimed,
· aiming line - a straight line running from the shooter's eye through the middle of the sight slot and the top of the front sight to the aiming point,
· aiming angle – the angle between the aiming line and the elevation line;
· target elevation angle – the angle between the aiming line and the horizon of the weapon;
· sighting range – the distance from the departure point to the intersection of the trajectory with the aiming line;
· trajectory exceeding the aiming line – the shortest distance from any point of the trajectory to the aiming line;
· elevation angle – the angle between the elevation line and the horizon of the weapon. The shape of the trajectory depends on the elevation angle
Rice. 5. Elements of a bullet's flight path
The trajectory of a bullet in the air has the following properties:
· the descending branch is steeper than the ascending one;
· the angle of incidence is greater than the angle of throw;
· the final speed of the bullet is less than the initial one;
· lowest bullet flight speed when shooting at high throwing angles
· on the descending branch of the trajectory, and when shooting at small throwing angles - at the point of impact;
· the time of movement of a bullet along the ascending branch of the trajectory is less than
· descending;
· the trajectory of a rotating bullet due to its descent under the influence of gravity and derivation is a line of double curvature.
The shape of the trajectory depends on the elevation angle (Fig. 6). As the elevation angle increases, the trajectory height and the full horizontal range of the bullet increase, but this occurs to a certain limit. Beyond this limit, the trajectory altitude continues to increase, and the total horizontal range begins to decrease.
Rice. 6. Longest range angle, flat,
hinged and conjugate trajectories
The angle of elevation at which the total horizontal range of the bullet becomes greatest is called the angle of greatest range. The maximum range angle for small arms is 30-35 degrees, and for range artillery systems 45-56 degrees.
Trajectories obtained at elevation angles less than the angle of greatest range are called flat.
Trajectories obtained at elevation angles greater than the angle of greatest range are called mounted. When firing from the same weapon, you can get two trajectories with the same horizontal range - flat and mounted. Trajectories that have the same horizontal range at different elevation angles are called conjugated.
Flat trajectories allow you to:
1. It is good to hit openly located and fast-moving targets.
2. Successfully fire from guns at a long-term firing structure (DOS), a long-term firing point (DOT), from stone buildings at tanks.
3. The flatter the trajectory, the greater the area over which the target can be hit with one sight setting (the less impact errors in determining the sight setting have on the shooting results).
Mounted trajectories allow:
1. Hit targets behind cover and in deep folds of the terrain.
2. Destroy the ceilings of structures.
These various tactical properties of flat and mounted trajectories can be taken into account when organizing the fire system. The flatness of the trajectory affects the range of the direct shot, the affected and covered space.
Aiming (aiming) a weapon at a target.
The goal of any shooting is to hit the target in the most a short time and with the least expenditure of ammunition. This problem can be solved only in close proximity to the target and if the target is stationary. In most cases, hitting a target is associated with certain difficulties arising from the properties of the trajectory, meteorological and ballistic conditions shooting and the nature of the target.
Let the target be at point A - at some distance from the firing position. In order for the bullet to reach this point, the barrel of the weapon must be given a certain angle in the vertical plane (Fig. 7).
But the wind can cause lateral deflections of the bullet. Therefore, when aiming, it is necessary to take a lateral correction for the wind. Thus, in order for the bullet to reach the target and hit it or the desired point on it, it is necessary to give the axis of the barrel bore a certain position in space (in the horizontal and vertical plane) before firing.
Giving the axis of the bore of a weapon the position in space necessary for shooting is called aiming or pointing. Giving the axis of the weapon barrel the required position in the horizontal plane is called horizontal aiming, and in the vertical plane - vertical aiming.
Rice. 7. Aiming (aiming) using open sight:
O - front sight, a - rear sight, aO - aiming line; сС - axis of the barrel bore, оО - line parallel to the axis of the barrel bore: H - height of the sight, M - amount of movement of the rear sight;
a - aiming angle; Ub - lateral correction angle
Accurate solution to any type of aiming problem sighting devices depends on their correct alignment on the weapon. Alignment of sighting devices of small arms for shooting at ground targets carried out in the process of checking the combat of a weapon and bringing it to normal combat.
The bullet, having received a certain initial speed when leaving the bore, strives by inertia to maintain the magnitude and direction of this speed.
If the flight of a bullet took place in airless space, and gravity did not act on it, the bullet would move rectilinearly, uniformly and endlessly. However, a bullet flying in the air is subject to forces that change its flight speed and 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 barrel bore.
The line that a moving bullet describes in space (its center of gravity) is called trajectory.
Typically, ballistics considers the trajectory over weapon horizon- an imaginary infinite horizontal plane passing through the departure point (Fig. 5).
Rice. 5. Weapon Horizon
The movement of the bullet, and therefore 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 force of air resistance act on the bullet separately.
The action of gravity. Let's imagine that no force acts on the bullet after it leaves the barrel. In this case, as mentioned above, the bullet would move by inertia endlessly, uniformly and rectilinearly along the axis of the barrel 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 aimed directly at the target, the bullet, following in the direction of the axis of the barrel 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 freely falling body.
If we assume that the force of gravity acts on the bullet as it flies by inertia in airless space, then under the influence of this force the bullet will drop lower from the extension of the axis of the barrel bore - in the first second - by 4.9 m, in the second - by 19.6 m etc. In this case, if you point the barrel of a weapon at a target, the bullet will never hit it, since, being exposed to the force of gravity, it will fly under the target (Fig. 7).
Rice. 7. The movement of the bullet (if gravity acted on it,
but air resistance did not work)
It is quite obvious that in order for a 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 barrel bore and the horizon plane of the weapon make 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, which is affected by gravity, is a regular curve, which is called parabola. The highest point of the trajectory above the horizon of the weapon is called its top. The part of the curve from the departure point to the apex is called ascending branch. This bullet trajectory is characterized by the fact that the ascending and descending branches are exactly the same, and the throwing and falling angles are equal to each other.
Rice. 8. Elevation angle (bullet trajectory in airless space)
Action of air resistance force. At first glance, it seems unlikely that air, which has such a low density, could provide significant resistance to the movement of a 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 large - 3.5 kg.
Considering that the bullet weighs only a few grams, the large braking effect that air has on a flying bullet becomes quite obvious.
During flight, a bullet expends a significant portion of its energy to push apart air particles that interfere with its flight.
As a photograph of a bullet flying at supersonic speed (over 340 m/s) shows, an air compaction forms in front of its head (Fig. 9). From this compaction the head ballistic wave diverges in all directions. Air particles, sliding along the surface of the bullet and falling off its side walls, form a zone of rarefied space behind the bullet. In an effort to fill the void behind the bullet, air particles create turbulence, resulting in a tail wave trailing behind the bottom of the bullet.
The compaction of air in front of the bullet's head slows down its flight; the discharged zone behind the bullet sucks it in and thereby further enhances the 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 air resistance force.
Rice. 9. Photograph of a bullet flying at supersonic speed
(over 340 m/sec.)
The enormous influence that air resistance has 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 greatest horizontal flight range of 3400 m, and when firing in airless space it could fly 76 km.
Consequently, under the influence of air resistance, the trajectory of the bullet loses the shape of a regular parabola, taking on the shape of an asymmetrical curved line; the apex divides it into two unequal parts, of which the ascending branch is always longer and shallower 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 branch as 3:2.
Rotation of a bullet around its axis. It is known that a body acquires significant stability if it is given a rapid rotational movement around its axis. An example of the stability of a rotating body is the “top” toy. A non-rotating “top” will not stand on its pointed leg, but if the “top” is given a rapid rotational movement around its axis, it will stand stably on it (Fig. 10).
In order for the bullet to acquire the ability to combat the overturning effect of air resistance and maintain stability during flight, it is given a rapid rotational movement around its longitudinal axis. The bullet acquires this rapid rotational movement thanks to helical rifling in the bore of the weapon (Fig. 11). Under the influence of the pressure of the powder gases, the bullet moves forward along the barrel bore, simultaneously rotating around its longitudinal axis. Upon departure from the barrel, the bullet, by inertia, retains the resulting complex motion - translational and rotational.
Without going into details of the explanation of physical phenomena associated with the action of forces on a body experiencing complex motion, it is still necessary to say that a bullet during flight makes regular oscillations and its head describes a circle around the trajectory (Fig. 12). In this case, the longitudinal axis of the bullet seems to “follow” 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 will become obvious that the greater the speed of its movement and the longer the bullet, the more the air tends to knock it over. Therefore, the bullets of cartridges different types it is necessary to give different rotation speeds. Thus, a light bullet fired from a rifle has a rotation speed of 3604 rpm.
However, the rotational motion of the bullet, which is so necessary to give it stability during flight, also has its negative sides.
A rapidly rotating bullet, as already mentioned, is subject to a continuous overturning effect by the force of air resistance, due to which the head of the bullet describes a circle around the trajectory. As a result of the addition of these two rotational movements, a new movement arises, deflecting its head part away from the firing plane1 (Fig. 14). In this case, one side surface of the bullet is subjected to more particle pressure than the other. This unequal air pressure on the side surfaces of the bullet deflects it 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 quickly and progressively increases.
When shooting at short and medium distances, derivation does not have much practical significance for the shooter. So, at a firing range of 300 m, the derivation deviation is 2 cm, and at 600 m - 12 cm. Derivation has to be taken into account only when shooting with extreme precision at long distances, making appropriate adjustments to the installation of the sight, in accordance with the table of derivation deviations of the bullet for a certain range shooting.
2.3.4 Dependence of the trajectory shape on the throwing angle. Path elements
The angle formed by the horizon of the weapon and the continuation of the axis of the barrel bore before the shot is called elevation angle.
However, it is more correct to talk about the dependence of the horizontal firing range, and therefore the shape of the trajectory, on throwing angle, which is the algebraic sum of the elevation angle and the departure angle (Fig. 48).
Rice. 48 - Elevation angle and throwing angle
So, there is a certain relationship between the flight range of a bullet and the throwing angle.
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According to the laws of mechanics, the greatest horizontal flight range in airless space is achieved when the throwing angle is 45°. As the angle increases from 0 to 45°, the range of the bullet increases, and from 45 to 90° it decreases. The throwing angle at which the horizontal range of the bullet is greatest is called angle of greatest range.
When a bullet flies in the air, the angle of maximum range does not reach 45°. Its value for modern small arms ranges from 30-35°, depending on the weight and shape of the bullet.
Trajectories formed at throwing angles less than the angle of greatest range (0-35°) are called flat. Trajectories formed at throwing angles greater than the angle of greatest range (35-90°) are called mounted(Fig. 49).
Rice. 49 - Floor and mounted trajectories
When studying the movement of a bullet in the air, the designations of trajectory elements shown in Fig. are used. 50.
Rice. 50 - Trajectory and its elements:
departure point- center of the muzzle of the barrel; it is the beginning of the trajectory;
weapon horizon- horizontal plane passing through the departure point. In drawings and drawings depicting a trajectory from the side, the horizon looks like a horizontal line;
elevation line- a straight line, which is a continuation of the axis of the barrel of the aimed weapon;
throwing line- a straight line, which is a continuation of the axis of the barrel bore at the moment of the shot. Tangent to the trajectory at the departure point;
firing plane- vertical plane passing through the elevation line;
elevation angle- the angle formed by the elevation line and the horizon of the weapon;
throwing angle- the angle formed by the throwing line and the horizon of the weapon;
departure angle- the angle formed by the elevation line and the throwing line;
impact point- the point of intersection of the trajectory with the horizon of the weapon;
angle of incidence- the angle formed by the tangent to the trajectory at the point of impact and the horizon of the weapon;
horizontal range- distance from the point of departure to the point of impact;
top of trajectory- the highest point of the trajectory above the horizon of the weapon. The vertex divides the trajectory into two parts - the branches of the trajectory;
ascending branch of the trajectory- part of the trajectory from the departure point to the top;
descending branch of the trajectory- part of the trajectory from the top to the point of fall;
trajectory height- the distance from the top of the trajectory to the horizon of the weapon.
Since when sports shooting The distances for each type of weapon remain largely unchanged; many shooters do not even think about what elevation or throwing angle they should shoot at. In practice, it turned out to be much more convenient to replace the throwing angle with another, very similar to it - aiming angle(Fig. 51). Therefore, slightly departing from the presentation of issues of external ballistics, we give elements of weapon aiming (Fig. 52).
Rice. 51 - Line of sight and aiming angle
Rice. 52 - Elements of aiming a weapon at a target:
aiming line- a straight arrow passing from the eye through the slots of the sight and the top of the front sight to the aiming point;
aiming point- the point of intersection of the aiming line with the target or target plane (when moving the aiming point);
aiming angle- the angle formed by the aiming line and the elevation line;
target elevation angle- the angle formed by the aiming line and the horizon of the weapon;
elevation angle- algebraic sum of aiming angles and target elevation angle.
It does not hurt the shooter to know the degree of flatness of the trajectories of bullets used in sports shooting. Therefore, we present graphs characterizing the excess of the trajectory when shooting from various rifles, pistols and revolvers (Fig. 53-57).
Rice. 53 - Exceeding the trajectory above the aiming line when firing a 7.6 mm heavy bullet from a service rifle
Rice. 54 - Excess of the bullet trajectory above the aiming line when shooting from a small-caliber rifle (at V 0 =300 m/sec)
Rice. 55 - Excess of the bullet trajectory above the aiming line when firing from a small-caliber pistol (at V 0 =210 m/sec)
Rice. 56 - Excess of the bullet trajectory above the aiming line when shooting:
A- from a re-barreled revolver (at V 0 =260 m/sec); b- from a PM pistol (at V 0 =315 m/sec).
Rice. 57 - Excess of the bullet trajectory above the aiming line when shooting from a rifle with a 5.6 mm sporting and hunting cartridge (at V 0 = 880 m/sec)
2.3.5 Dependence of the trajectory shape on the initial velocity of the bullet, its shape and lateral load
While retaining their basic properties and elements, bullet trajectories can differ sharply from one another in their shape: be longer and shorter, have different slopes and curvatures. These varied changes depend on a number of factors.
Effect of initial speed. If two identical bullets are fired at the same throwing angle with different initial speeds, then the trajectory of the bullet with a higher initial speed will be higher than the trajectory of the bullet with a lower initial speed (Fig. 58).
Rice. 58 - Dependence of trajectory height and bullet flight range on initial speed
A bullet flying at a lower initial speed will take more time to reach the target, so under the influence of gravity it will have time to go down significantly more. It is also obvious that with an increase in speed, its flight range will also increase.
Effect of bullet shape. The desire to increase the range and accuracy of shooting required giving the bullet a shape that would allow it to maintain speed and stability in flight for as long as possible.
The concentration of air particles in front of the bullet head and the zone of rarefied space behind it are the main factors in the force of air resistance. The head wave, which sharply increases the deceleration of a bullet, occurs when its speed is equal to or exceeds the speed of sound (over 340 m/sec).
If the speed of a bullet is less than the speed of sound, then it flies at the very crest of the sound wave, without experiencing excessive air resistance. If it is greater than the speed of sound, the bullet overtakes all sound waves generated in front of its head. In this case, a head ballistic wave appears, which significantly slows down the flight of the bullet, causing it to quickly lose speed.
If you look at the outlines of the head wave and air turbulence that arise when bullets of different shapes move (Fig. 59), you can see that the sharper its shape, the less pressure on the head of the bullet. The rarefied space zone behind the bullet is smaller, the more beveled its tail part is; in this case, there will also be less turbulence behind the flying bullet.
Rice. 59 - The nature of the outlines of the head wave that occurs during the movement of bullets of different shapes
Both theory and practice have confirmed that the most streamlined shape of the bullet is the one outlined along the so-called curve of least resistance - cigar-shaped. Experiments show that the coefficient of air resistance, depending only on the shape of the bullet head, can change by one and a half to two times.
Different flight speeds have their own, most advantageous, bullet shape.
When shooting at short distances with bullets that have a low initial velocity, their shape has little effect on the shape of the trajectory. Therefore, revolver, pistol and small-caliber cartridges are loaded with blunt-pointed bullets: this is more convenient for reloading weapons, and also helps to preserve it from damage (especially non-sheathed ones - for small-caliber weapons).
Considering the dependence of shooting accuracy on the shape of the bullet, the shooter must protect the bullet from deformation and ensure that scratches, nicks, dents, etc. do not appear on its surface.
Influence lateral load . The heavier the bullet, the more kinetic energy it has, therefore, the less air resistance affects its flight. However, the ability of a bullet to maintain its speed depends not simply on its weight, but on the ratio of weight to area encountering air resistance. The ratio of the weight of a bullet to its largest cross-sectional area is called lateral load(Fig. 60).
Rice. 60 - Cross-sectional area of bullets:
A- to a 7.62 mm rifle; b- to a 6.5 mm rifle; V- to a 9 mm pistol; G- for a 5.6 mm rifle for target shooting “Running Deer”; d- for a 5.6 mm side-fire rifle (long cartridge).
The greater the weight of the bullet and the smaller the caliber, the greater the lateral load. Consequently, with the same caliber, the lateral load is greater for a longer bullet. A bullet with a greater lateral load has both a longer flight range and a flatter trajectory (Fig. 61).
Rice. 61 - The influence of the lateral load of a bullet on its flight range
However, there is a certain limit to increasing this load. First of all, as it increases (with the same caliber), it increases total weight bullets, and hence the recoil of the weapon. In addition, an increase in lateral load due to excessive elongation of the bullet will cause a significant tipping effect of its head part back by air resistance. This is what we proceed from when establishing the most advantageous dimensions of modern bullets. Thus, the lateral load of a heavy bullet (weight 11.75 g) for a service rifle is 26 g/cm 2 , and a small-caliber bullet (weight 2.6 g) is 10.4 g/cm 2 .
How great the influence of the lateral load of a bullet on its flight is can be seen from the following data: for a heavy bullet with an initial speed of the order of 770 m/sec, longest range flight 5100 m, for a light bullet at an initial speed of 865 m/sec - only 3400 m.
2.3.6 Dependence of the trajectory on meteorological conditions
Continuously changing meteorological conditions during shooting can have a significant impact on the flight of the bullet. However, certain knowledge and practical experience help to significantly reduce their harmful effect on shooting accuracy.
Since sport shooting distances are relatively short and the bullet travels over them in a very short time, some atmospheric factors, such as air density, will not have a significant effect on its flight. Therefore, in sports shooting it is necessary to take into account mainly the influence of wind and, to a certain extent, air temperature.
Wind influence. Headwinds and tailwinds have little effect on shooting accuracy, so shooters usually neglect their effect. Thus, when shooting at a distance of 600 m, a strong (10 m/sec) head or tail wind changes the height of the STP by only 4 cm.
A side wind significantly deflects the bullet to the side, even when shooting at close distances.
Wind is characterized by strength (speed) and direction.
The strength of the wind is determined by its speed in meters per second. In shooting practice, winds are distinguished: weak - 2 m/sec, moderate - 4-5 m/sec and strong - 8-10 m/sec.
The strength and direction of the wind are practically determined by the arrows based on various local characteristics: using a flag, by the movement of smoke, the vibration of grass, bushes and trees, etc. (Fig. 62).
Rice. 62 - Determining wind strength by flag and smoke
Depending on the strength and direction of the wind, you should either make a lateral correction of the sight, or move the point, aiming in the direction opposite to its direction (taking into account the deflection of bullets under the influence of the wind - mainly when shooting at figured targets). In table 8 and 9 show the deflection values of bullets under the influence of side winds.
Deflection of bullets under the influence of side winds when firing from 7.62 mm rifles
| Firing range, m | Heavy bullet deflection (11.8 g), cm | ||
|---|---|---|---|
| light wind (2 m/sec) | moderate wind (4 m/sec) | strong wind (8 m/sec) | |
| 100 | 1 | 2 | 4 |
| 200 | 4 | 8 | 18 |
| 300 | 10 | 20 | 41 |
| 400 | 20 | 40 | 84 |
| 500 | 34 | 68 | 140 |
| 600 | 48 | 100 | 200 |
| 700 | 70 | 140 | 280 |
| 800 | 96 | 180 | 360 |
| 900 | 120 | 230 | 480 |
| 1000 | 150 | 300 | 590 |
Deflection of bullets under the influence of side wind when shooting from a small-caliber rifle
As can be seen from these tables, when shooting at short distances, the deflection of bullets is almost proportional to the strength (speed) of the wind. From the table 8 also shows that when shooting from service and free rifles at 300 m, a side wind with a speed of 1 m/sec blows the bullet to the side by one dimension of target No. 3 (5 cm). These simplified data should be used in practice when determining the magnitude of wind corrections.
Oblique wind (at an angle to the shooting plane of 45, 135, 225 and 315°) deflects the bullet half as much as side wind.
However, during shooting, it is, of course, impossible to make corrections for the wind, so to speak, “formally,” guided solely by the data in the tables. This data should serve only as source material and help the shooter navigate difficult conditions shooting in the wind.
It practically rarely happens that on such a relatively small area of terrain as a shooting range, the wind always has the same direction, much less the same strength. It usually blows in gusts. Therefore, the shooter needs the ability to time the shot to the moment when the strength and direction of the wind become approximately the same as during previous shots.
Flags are usually hung at the shooting range so that the athlete can determine the strength and direction of the wind. You need to learn to correctly follow the indications of the flags. Flags should not be relied upon entirely if they are mounted high above the target line and firing line. You also cannot navigate by flags installed at the edge of the forest, steep cliffs, ravines and hollows, since the wind speed is different layers the atmosphere, as well as uneven terrain and obstacles are different. As an example in Fig. 63 provides approximate data on wind speed in summer on the plain at various heights from the ground. It is clear that the readings of flags mounted on a high bullet receiving shaft or on a high mast will not correspond to the true force of the wind, which acts directly on the bullet. You need to be guided by the readings of flags, paper ribbons, etc., installed at the same level at which the weapon is located during shooting.
Rice. 63 - Approximate data on wind speed in summer at various altitudes on the plain
It should also be borne in mind that the wind, bending around uneven terrain and obstacles, can create turbulence. If flags are installed along the entire shooting distance, they often show completely different, even opposite, wind directions. Therefore, you need to try to determine the main direction and strength of the wind along the entire shooting route, carefully observing individual local landmarks in the area of the terrain lying between the shooter and the target.
Naturally, making accurate wind corrections requires some experience. But experience does not come by itself. The shooter must constantly carefully observe and carefully study the influence of wind in general and at a given shooting range in particular, and systematically record the conditions under which shooting is carried out. Over time, he develops a subconscious feeling and experience that allows him to quickly navigate the meteorological situation and make the necessary adjustments to ensure accurate shooting in difficult conditions.
Effect of air temperature. The lower the air temperature, the greater its density. A bullet flying in denser air encounters a large number of air particles on its path, and therefore loses its initial speed faster. Consequently, in cold weather, at low temperatures, the firing range decreases and the STP decreases (Table 10).
Moving the average point of impact when shooting from a 7.62 mm rifle under the influence of changes in air temperature and powder charge every 10°
| Firing range, m | STP movement in height, cm | |
|---|---|---|
| light bullet (9.6 g) | heavy bullet (11.8 g) | |
| 100 | - | - |
| 200 | 1 | 1 |
| 300 | 2 | 2 |
| 400 | 4 | 4 |
| 500 | 7 | 7 |
| 600 | 12 | 12 |
| 700 | 21 | 19 |
| 800 | 35 | 28 |
| 900 | 54 | 41 |
| 1000 | 80 | 59 |
Temperature also affects the combustion process of the powder charge in the barrel of a weapon. As is known, with increasing temperature, the burning rate of a powder charge increases, since the heat consumption required to heat and ignite the powder grains decreases. Consequently, the lower the air temperature, the slower the process of increasing gas pressure. As a result, the initial speed of the bullet decreases.
It has been established that a change in air temperature by 1° changes the initial speed by 1 m/sec. Significant temperature fluctuations between summer and winter lead to changes in the initial speed within the range of 50-60 m/sec.
Taking this into account, for zeroing weapons, compiling appropriate tables, etc. take a certain “normal” temperature - +15°.
Considering the relationship between the temperature of the powder charge and the initial velocity of the bullet, the following must be kept in mind.
When shooting in large bursts for a long time, when the rifle barrel gets very hot, you should not allow the next cartridge to remain in the chamber for a long time: relatively heat the heated barrel, transmitted through the cartridge case to the powder charge, will lead to an acceleration of the ignition of the powder, which ultimately can lead to a change in the STP and upward “breaks” (depending on the duration of the cartridge’s stay in the chamber).
Therefore, if the shooter is tired and needs some rest before the next shot, then during such a break in shooting the cartridge should not be in the chamber; it should be removed or replaced altogether with another cartridge from the pack, that is, unheated.
2.3.7 Bullet dispersion
Even under the most favorable shooting conditions, each of the fired bullets describes its own trajectory, slightly different from the trajectories of other bullets. This phenomenon is called natural dispersion.
With a significant number of shots, the trajectories in their totality form sheaf, which, when meeting a target, produces a number of holes, more or less distant from each other. The area they occupy is called dispersion area(Fig. 64).
Rice. 64 - Sheaf of trajectories, average trajectory, dispersion area
All holes are located on the dispersion area around a certain point called center of dispersion or midpoint of impact (STP). A trajectory located in the middle of the sheaf and passing through midpoint hits are called average trajectory . When making adjustments to the installation of the sight during the shooting process, this average trajectory is always implied.
For different types of weapons and cartridges, there are certain standards for bullet dispersion, as well as standards for bullet dispersion according to factory specifications and tolerances for the production of certain types of weapons and batches of cartridges.
At large quantities shots, the dispersion of bullets obeys a certain law of dispersion, the essence of which is as follows:
— the holes are located unevenly across the dispersion area, most densely grouped around the STP;
— the holes are located symmetrically relative to the STP, since the probability of a bullet deflecting in any direction from the STP is the same;
— the dispersion area is always limited to a certain limit and has the shape of an ellipse (oval), elongated in height on a vertical plane.
By virtue of this law, in general, holes are located on the dispersion area naturally, and therefore, in symmetrical stripes of equal width, equally distant from the dispersion axes, the same and certain number of holes are contained, although the dispersion areas can have different sizes (depending on the type of weapon and cartridges). The measure of dispersion is: median deviation, core band and radius of the circle containing better half holes (P 50) or all hits (P 100). It should be emphasized that the law of dispersion fully manifests itself with a large number of shots. When shooting sports in relatively small series, the dispersion area approaches the shape of a circle, therefore the measure of dispersion is the value of the radius of the circle that contains 100% of the holes (P 100) or the better half of the holes (P 50) (Fig. 65). The radius of the circle containing all the holes is approximately 2.5 times larger than the radius of the circle containing the best half of them. During factory tests of cartridges, when shooting is carried out in small series (usually 20) of shots, a circle that includes all the holes - P 100 (the diameter that includes all the holes, see Fig. 16) also serves as a measure of dispersion.
Rice. 65 - Large and small radii of circles containing 100 and 50% hits
So, the natural dispersion of bullets is an objective process that operates independently of the will and desire of the shooter. This is partly true, and requiring weapons and ammunition to ensure that all bullets hit the same point is pointless.
At the same time, the shooter must remember that the natural dispersion of bullets is by no means an inevitable norm, once and for all established for a given type of weapon and certain shooting conditions. The art of marksmanship is to know the causes of natural bullet dispersion and reduce their impact. Practice has convincingly proven how important correct debugging of weapons and selection of cartridges, technical preparedness of the shooter and experience of shooting in adverse weather conditions are to reduce dispersion.
Ballistics is divided into internal (the behavior of the projectile inside the weapon), external (the behavior of the projectile along the trajectory) and barrier (the effect of the projectile on the target). This topic will cover the basics of internal and external ballistics. Barrier ballistics will be considered wound ballistics(the effect of a bullet on the client’s body). The existing section of forensic ballistics is discussed in the course of criminalistics and will not be covered in this manual.
Internal ballistics
Internal ballistics depend on the type of propellant used and the type of barrel.
Conventionally, trunks can be divided into long and short.
Long trunks (length more than 250 mm) serve to increase the initial speed of the bullet and its flatness along the trajectory. Accuracy increases (compared to short barrels). On the other hand, a long barrel is always more cumbersome than a short barrel.
Short trunks do not give the bullet the same speed and flatness than long ones. The bullet has greater dispersion. But a short-barreled weapon is convenient to carry, especially concealed, which is most suitable for self-defense weapons and police weapons. On the other hand, trunks can be divided into rifled and smooth.
Rifled barrels give the bullet greater speed and stability along the trajectory. Such trunks are widely used for bullet shooting. For shooting bullet hunting cartridges from smoothbore weapons Various threaded attachments are often used.
Smooth trunks. Such barrels help to increase the dispersion of damaging elements when firing. Traditionally used for shooting with shot (buckshot), as well as for shooting with special hunting cartridges at short distances.
There are four firing periods (Fig. 13).
Preliminary period (P) lasts from the beginning of the combustion of the powder charge until the bullet completely penetrates the rifling. During this period, gas pressure is created in the barrel bore, which is necessary to move the bullet from its place and overcome the resistance of its shell to cut into the rifling of the barrel. This pressure is called boost pressure and reaches 250-500 kg/cm2. 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 bullet’s movement until the complete combustion of the powder charge. At the beginning of the period, when the speed of the bullet along the barrel is still low, the volume of gases grows faster than the behind-the-bullet space. The 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 by the end of this period reaches approximately 3/4 of the initial speed.
Second period (2) lasts from the moment the powder charge is completely burned until the bullet leaves 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 end - the 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, since 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 action of the powder gases on it ceases. During this period, powder gases flowing from the barrel at a speed of 1200-2000 m/s continue to affect the bullet, giving it additional speed. The bullet reaches its highest speed at the end of the third period at a distance of several tens of centimeters from the muzzle of the barrel (for example, when shooting from 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. Then the bullet flies by inertia. This relates to the question of why a bullet fired from a TT pistol does not penetrate class 2 armor when shot at point-blank range and pierces it at a distance of 3-5 m.
As already mentioned, black and smokeless powder are used to load cartridges. Each of them has its own characteristics:
Black powder. This type of gunpowder burns very quickly. Its combustion is like an explosion. It is used for an instant surge in pressure in the barrel bore. This type of gunpowder is usually used for smooth barrels, since the friction of the projectile against the barrel walls in a smooth barrel is not so great (compared to a rifled barrel) and the residence time of the bullet in the barrel is less. Therefore, at the moment the bullet leaves the barrel, greater pressure is achieved. When using black powder in a rifled barrel, the first period of the shot is quite short, 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. The gas pressure curve has a very sharp peak of maximum pressure and a fairly sharp drop in pressure in the first period.
Smokeless powder. This type of powder burns more slowly than black 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 it takes for the bullet to fly down the barrel increases and by the time the bullet leaves, the powder charge is completely burned out. Due to this, the bullet is exposed to the full amount of gases, while the second period is selected to be quite small. On the gas pressure curve, the peak of maximum pressure is somewhat smoothed out, with a gentle decrease in pressure in the first period. In addition, it is useful to pay attention to some numerical methods for estimating intra-ballistic solutions.
1. Power coefficient(kM). Shows the energy that falls on one conventional cubic mm of bullet. Used to compare bullets of the same type of cartridge (for example, pistol). It is measured in Joules per millimeter cubed.
KM = E0/d 3, where E0 is muzzle energy, J, d is bullets, mm. For comparison: the power coefficient for the 9x18 PM cartridge is 0.35 J/mm 3; for cartridge 7.62x25 TT - 1.04 J/mm 3; for cartridge.45ASR - 0.31 J/mm 3. 2. Metal utilization factor (kme). Shows the shot energy per gram of weapon. Used to compare bullets from cartridges of the same type or to compare the relative shot energy of different cartridges. It is measured in Joules per gram. Often, the metal utilization rate is taken as a simplified version of calculating 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, respectively, is 0.37, 0.66 and 0.76 J/g.
External ballistics
First you need to imagine the full trajectory of the bullet (Fig. 14). 
In explanation of the figure, it should be noted that the line of departure of the bullet (throwing line) will be different than the direction of the barrel (elevation line). This occurs due to the occurrence of barrel vibrations when fired, 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 finishing of the barrel and the calculation of the internal ballistic characteristics of the weapon, the smaller the departure angle will be. Approximately the first two-thirds of the upward trajectory line can be considered straight. In view of this, three firing distances are distinguished (Fig. 15). Thus, the influence of third-party conditions on the trajectory is described by a simple quadratic equation, and in graphics it is a parabola. In addition to third-party conditions, the deviation of a bullet from its trajectory is also influenced by some design features bullets and cartridge. Below we will consider a complex of events; deflecting the bullet from its original trajectory. The ballistic tables of this topic contain data on the ballistics of the 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 once again that thanks 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 increases slightly 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 slightly shifted from the central axis of the bullet, so in the cross section you get a circle of bullet expansion - the average deviation of the bullet from the original trajectory. Taking into account this behavior of the bullet, its possible trajectory can be represented as a single-plane hyperboloid (Fig. 17). The displacement of a bullet from the main directrix due to a displacement of its axis of rotation is called dispersion. The bullet with full probability ends up in the circle of dispersion, diameter (by 
peppercorn) 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 dispersion radii for shooting at various distances.
Table 3
Diffusion
| Fire range (m) |
|
- Considering the size of the standard head target is 50x30 cm, and the chest target is 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 slightly from the firing plane. Moreover, in the case of right-hand rifling (the bullet rotates clockwise when viewed from behind), the bullet deflects to the right, in the case of left-hand rifling - to the left.
In table Figure 4 shows the magnitude of derivational deviations when firing at various ranges. - Table 4
- Derivation
- Fire range (m)
- Derivation (cm)
- 1000
- 1200
- It is easier to take into account 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 slightly by the amount of the derivational displacement of the bullet.
Bullet displacement by wind
- Among all the third-party conditions affecting the flight of a bullet (humidity, pressure, etc.), it is necessary to highlight the most serious factor - the influence of wind. The wind blows the bullet away quite seriously, especially at the end of the ascending branch of the trajectory and beyond.
The displacement of a bullet by a side wind (at an angle of 90 0 to the trajectory) of average force (6-8 m/s) is shown in table. 5. - Table 5
- Bullet displacement by wind
- Fire range (m)
- Offset (cm)
- To determine the displacement of a bullet by a strong wind (12-16 m/s), it is necessary to double the table values; for weak winds (3-4 m/s), the table values are divided in half. For wind blowing at an angle of 45° to the trajectory, the table values are also divided in half.
Bullet flight time
- Fire range (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 (dispersion, bullet flight time) on the firing range. Such a graph will make it easy to calculate intermediate values (for example, at 350 m), and will also allow you to guess the table values of the function.
In Fig. Figure 18 shows the simplest ballistic problem. - Shooting is carried out at a distance of 600 m, the wind blows from behind to the left at an angle of 45° to the trajectory.
Question: the diameter of the scattering circle and the displacement of its center from the target; flight time to target.
- Solution: The diameter of the scattering circle 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). The bullet's flight time is 1.07 s (flight time + 5% due to the direction of the wind in the direction of the bullet's flight) (see Table 6).
- Answer; the bullet will fly 600 m in 1.07 s, the diameter of the dispersion circle 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 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 conveniently determined by some mathematical formulas.
1. Usually used to determine the probability of penetration on various discs
- dancing different classes passive armor protection.
Penetration is a dimensionless quantity. - P = En / Epr,
- where En is the energy of the bullet at a given point of the trajectory, in J; Epr is the energy required to break through an obstacle, in J.
- Taking into account the standard EPR for body armor (BZh) (500 J for protection against pistol cartridges, 1000 J - from intermediate and 3000 J - from rifle cartridges) and sufficient energy to defeat a person (max 50 J), it is easy to calculate the probability of hitting the corresponding BZh with a bullet from one or another another cartridge. Thus, the probability of penetrating a standard pistol BZ with a bullet from a 9x18 PM cartridge will be equal to 0.56, and by a bullet from a 7.62x25 TT cartridge - 1.01. The probability of penetrating a standard assault rifle bullet with a 7.62x39 AKM cartridge will be 1.32, and with a 5.45x39 AK-74 cartridge bullet will be 0.87. The given numerical data are calculated for a distance of 10 m for pistol cartridges and 25 m for intermediate cartridges. 2. Impact coefficient (ky). Impact coefficient shows the energy of a bullet per square millimeter of its maximum cross-section. Impact factor 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 9x18 PM, 7.62x25 TT and .40 Auto cartridges 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 from 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? Clarification of this issue is the most important characteristic for choosing 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 (0B). Naturally, the enemy stops most reliably when the bullet hits a certain place on the human body (head, spine, kidneys), but some types of ammunition have a large 0B even when hitting secondary targets. In general, 0B is directly proportional to the caliber of the bullet, its mass and speed at the moment it hits the target. Also, 0B increases when using lead and expansion bullets. It must be remembered that an increase in 0B shortens the length of the wound channel (but increases its diameter) and reduces the effect of the bullet on a target protected by armor. One of the options for mathematical calculation of OM was proposed in 1935 by the American Yu. 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 the target, m/s; S - transverse area of the bullet, cm 2; k is the bullet shape coefficient (from 0.9 for full-shell bullets to 1.25 for hollow-point bullets). According to these calculations, at a distance of 15 m, bullets of 7.62x25 TT, 9x18 PM and .45 cartridges have a MR of 171, 250 in 640, respectively. For comparison: RP of a bullet of a 7.62x39 cartridge (AKM) = 470, and bullets of 7.62x54 ( OVD) = 650. Penetrating impact (PE). PT can be defined as the ability of a bullet to penetrate a target to its maximum depth. The penetrating ability is higher (all other things being equal) for bullets of small caliber and those that are slightly deformable in the body (steel, full-shell). High penetration improves the bullet's effect on targets protected by armor. In Fig. Figure 19 shows the effect of a standard PM jacketed bullet with a steel core. When a bullet hits the body, a wound channel and a wound cavity are formed. A wound channel is a channel pierced directly by a bullet. A wound cavity is a cavity of damage to fibers and vessels caused by tension and rupture of them by a bullet. Gunshot wounds are divided into through, blind, and secant.
Penetrating wounds
A perforation 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, smaller than the caliber of a bullet. With a direct hit, the edges of the wound are smooth, and with a hit through thick clothing at an angle, there will be a slight tear. Often the inlet closes up quite quickly. There are no traces of bleeding (except for damage to large vessels or when the wound is positioned below). The exit hole is large and can exceed the caliber of the bullet by orders of magnitude. The edges of the wound are torn, uneven, and spread to the sides. A rapidly developing tumor is observed. There is often severe bleeding. In non-fatal wounds, suppuration develops quickly. With fatal wounds, the skin around the wound quickly turns blue. Penetrating wounds are typical for bullets with a high penetrating effect (mainly for machine guns and rifles). When a bullet passes through soft tissue, the internal wound is axial, with minor damage to neighboring organs. When wounded by a bullet from a 5.45x39 (AK-74) cartridge, the steel core of the bullet in the body may come out of the shell. As a result, two wound channels appear and, accordingly, two exit holes (from the shell and the core). Such injuries are more oftenthey occur when ingested through thick clothing (peacoat). Often the wound channel from a bullet is blind. When a bullet hits a skeleton, a blind wound usually occurs, but with a high power of ammunition, a through wound is likely. In this case, large internal damage from fragments and parts of the skeleton is observed with an increase in the wound channel to the exit hole. In this case, the wound channel can “break” due to the ricochet of the bullet from the skeleton. Perforating head wounds are characterized by cracking or fracture of the skull bones, often in a non-axial wound channel. The skull cracks even when hit by 5.6 mm lead non-jacketed bullets, not to mention more powerful ammunition. In most cases, such injuries are fatal. With through wounds to the head, severe bleeding is often observed (prolonged flow of blood from the corpse), of course, when the wound is positioned on the side or below. The inlet is fairly smooth, but the outlet is uneven with a lot of cracking. A fatal wound quickly turns blue and swells. In case of cracking, damage to the scalp may occur. The skull is easily dented to the touch, and fragments can be felt. In case of wounds with sufficiently strong ammunition (bullets of 7.62x39, 7.62x54 cartridges) and wounds with expansive bullets, a very wide exit hole is possible with a long leakage of blood and brain matter.Blind wounds
Such wounds occur when hit by bullets from less powerful (pistol) ammunition, using hollow-point bullets, passing a bullet through the skeleton, or being wounded by a bullet at the end of its life. With such wounds, the entrance hole is also quite small and smooth. 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 not axial. This is observed when weaker ammunition hits the skeleton - the bullet moves away from the entrance hole plus damage from fragments of the skeleton and shell. When such bullets hit the skull, it becomes severely cracked. A large entrance hole is formed in the bone, and the intracranial organs are severely affected.Cutting wounds
Cutting wounds are observed when a bullet hits the body at an acute angle, damaging only the skin and external parts of the muscles. Most of the injuries are not dangerous. Characterized by skin rupture; the edges of the wound are uneven, torn, and often diverge greatly. Sometimes quite severe bleeding is observed, especially when large subcutaneous vessels rupture.
To solve the simplest ballistic tasks It is necessary to note the dependence of the bullet’s flight time on the firing range. Without taking this factor into account, it will be quite problematic to hit even a slowly moving target.
The bullet's flight time to the target is presented in table. 6.
Table 6Time of flight of a bullet to the target