The movement of a bullet in the air. Sniper training. Internal and external ballistics. Shape, properties and types of trajectory
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 fast rotational movement. 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;
· impact point – 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 trajectories;
· trajectory 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 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 at 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 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 firing 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. Corner longest range, flooring,
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 value of the angle of greatest range for small arms 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. What flatter trajectory, the larger 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 different tactical properties of flat and mounted trajectories can be taken into account when organizing a fire system. The flatness of the trajectory affects the range direct shot, affected and covered space.
Aiming (aiming) a weapon at a target.
The goal of any shooting is to hit the target in the shortest time and with the least amount 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 weapon bore the necessary position in space 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 of aiming problems of any type 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.
1.1.1. Shot. Shot periods and their characteristics.
With a shot is called the ejection of a bullet from the bore of a weapon by the energy of gases formed during the combustion of a powder charge.
When a small weapon is fired, the following phenomenon occurs. 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 penetrates through the seed holes in the bottom of the cartridge case to the powder charge and ignites it. When a charge burns, it forms a large number of highly heated gases that create high pressure on the bottom of the bullet, the bottom and walls of the cartridge case, as well as on the walls of the barrel and the bolt. As a result of the pressure of the gases on the bottom of the bullet, it moves from its place and crashes into the rifling - rotating along them, it moves along the barrel with a continuously increasing speed and is thrown out.
When a powder charge is burned, approximately 25-35% of the released energy is spent on communicating with the bullet forward movement(main job); 15-25% of energy - for performing secondary work (plunging in and overcoming the friction of a bullet when moving along the bore; heating the walls of the barrel, cartridge case and bullet; moving moving parts of the weapon, gaseous and unburnt parts of gunpowder); about 40% of the energy is not used and is lost after the bullet leaves the barrel.
The shot occurs in a very short period of time (0.001 - 0.06 seconds).
When firing, there are four consecutive periods(Fig. 116):
Preliminary;
First or main;
The third or aftereffect period of gases.
Preliminary period lasts from the beginning of the combustion of the powder charge until the bullet casing completely cuts into the rifling of the barrel. 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. It reaches 250-500 kg/cm depending on the rifling design, the weight of the bullet and the hardness of its shell. 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 boost pressure is reached in the barrel bore.
First or main period lasts from the beginning of the bullet's movement until the moment complete combustion powder charge. During this period, combustion of the powder charge occurs in a rapidly changing volume.
At the beginning of the period, when the speed of the bullet moving along the bore is still low, the number of gases grows faster than the volume of the bullet space (the space between the bottom of the bullet and the bottom of the cartridge case), the gas pressure quickly increases and reaches greatest value. This pressure is called maximum pressure. It is created in small arms when a bullet travels 4-6 cm. Then, due to the rapid increase in the speed of the bullet, the volume of the bullet space increases faster than the influx new gases, and the pressure begins to drop. By the end of the period it is 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.
The second 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, however, highly compressed and heated gases expand and, putting pressure on the bullet, increase its speed. The decrease in pressure in the second period occurs quite quickly and at the muzzle - muzzle pressure - is 300-900 kg/cm for various types of weapons. The speed of the bullet at the moment it leaves the barrel (muzzle speed) is slightly less than the initial speed. For some types of small arms, especially short-barreled ones (for example, a Makarov pistol), there is no second period, since complete combustion of the powder charge does not actually occur by the time the bullet leaves the barrel.
Rice. 116 - Shot periods
The third period, or the period of aftereffect of gases, lasts from the moment the bullet leaves the barrel until the moment 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/sec continue to affect the bullet and impart additional speed to it. The bullet reaches its highest (maximum) speed at the end of the third period at a distance of several tens of centimeters from the muzzle of the barrel
This period ends at the moment when the pressure of the powder gases at the bottom of the bullet is balanced by air resistance.
1.1.2. Initial and maximum speed. Initial bullet speed
(v o) - the speed of the bullet at the muzzle of the barrel. For initial speed
a conditional velocity is accepted, which is slightly greater than the muzzle and less than the maximum. It is determined experimentally with subsequent calculations. The magnitude of the muzzle velocity is indicated in the shooting tables and in the combat characteristics of the weapon. The initial speed is one of the most important characteristics combat properties of weapons. As the initial speed increases, the bullet's flight range, the range of a direct shot, the lethal and penetrating effect of the bullet increases, and the influence of external conditions
for her flight.
The magnitude of the initial bullet speed depends on:
1) Barrel lengths.
2) Bullet weight.
3) Weight, temperature and humidity of the powder charge, shape and size of the powder grains and loading density.
1) The longer the barrel, the longer the time the powder gases act on the bullet and the greater the initial speed of the bullet.
2) With a constant barrel length and constant weight of the powder charge, the lower the weight of the bullet, the greater the initial speed. A change in the weight of the powder charge leads to a change in the amount of powder gases, and, consequently, to a change in the maximum pressure in the barrel bore and the initial velocity of the bullet. 3) What more weight
powder charge, the greater the maximum pressure and initial velocity of the bullet. The length of the barrel and the weight of the powder charge increase when designing the weapon to the most rational dimensions.
In this regard, it is necessary to take into account range corrections for air and charge temperatures (charge temperature is approximately equal to air temperature).
As the humidity of the powder charge increases, its burning rate and the initial speed of the bullet decrease. The shape and size of the gunpowder have a significant impact on the burning rate of the powder charge, and therefore on the initial speed of the bullet. They are selected accordingly when designing weapons.
Loading density is called the ratio of the weight of the charge to the volume of the cartridge case with the bullet inserted (charge combustion chamber). When the bullet is seated deeply, the loading density increases significantly, which can lead to a sharp surge in pressure when fired and, as a result, to rupture of the barrel, so such cartridges cannot be used when shooting. As the loading density decreases (increases), the initial bullet speed increases (decreases).
The bullet reaches its highest (maximum) speed at the end of the third period at a distance of several tens of centimeters from the muzzle of the barrel.
1.1.3 Weapon recoil and departure angle (Fig. 117).
Recoil is the backward movement of the weapon (barrel) during a shot.. Recoil is felt in the form of a push to the shoulder, arm or ground. The recoil action of a weapon is characterized by the amount of speed and energy it has when moving backwards.
The recoil speed of a weapon is approximately the same number of times less than the initial speed of a bullet, how many times the bullet is lighter than the weapon. The recoil energy of hand-held small arms usually does not exceed 2 kgm and is perceived painlessly by the shooter.
When firing from an automatic weapon, the design of which is based on the principle of using recoil energy, part of it is spent on imparting movement to moving parts and on reloading the weapon. Recoil energy is generated when firing from such a weapon or from an automatic weapon, the design of which is based on the principle of using the energy of powder gases discharged through a hole in the barrel wall.
The pressure force of the powder gases (recoil force) and the recoil resistance force (butt stop, handle, center of gravity of the weapon, etc.) are not located on the same straight line and are directed in opposite directions. They form a pair of forces, under the influence of which the muzzle of the weapon barrel is deflected upward.
The amount of deflection of the muzzle of the barrel of this weapon the larger the leverage of this pair of forces.
In addition, when fired, the barrel of the weapon makes oscillatory movements - vibrates.
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, right, left). The magnitude of this deviation increases when the shooting rest is used incorrectly, the weapon is dirty, etc.
In an automatic weapon that has a gas outlet in the barrel, as a result of gas pressure on the front wall of the gas chamber, the muzzle of the weapon barrel, when fired, is slightly deflected in the direction opposite to the location of the gas outlet.
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.
The departure angle is considered positive when the axis of the barrel bore at the moment the bullet leaves is above its position before the shot, and negative when it is below.
The influence of the take-off angle on the shooting of each weapon is eliminated when it is brought back to normal combat.
In order to reduce the harmful effects of recoil on shooting results, some types of small arms (for example, a Kalashnikov assault rifle) use special devices - compensators. The gases flowing from the bore, hitting the walls of the compensator, slightly lower the muzzle of the barrel to the left and down.
1.2. Basic terms and concepts of the theory of external ballistics
External ballistics is a science that studies the movement of a bullet (grenade) after the action of powder gases on it ceases.
1.2.1. Bullet flight path and its elements
Trajectory called a curved line described by the center of gravity of a bullet (grenade) in flight (Fig. 118) .
A bullet (grenade) when flying in the air is subject to two forces :
Gravity
Forces of resistance.
The force of gravity causes the bullet (grenade) to gradually lower, and the force of air resistance continuously slows down the movement of the bullet (grenade) and tends to overturn it.
As a result of the action of these forces, the speed of the bullet (grenade) gradually decreases, and its trajectory is shaped like an unevenly curved line.
Air resistance to the flight of a bullet (grenade) is caused by the fact that air is elastic medium and therefore part of the bullet’s energy is expended on movement in this environment.
The force of air resistance is caused by three main reasons (Fig. 119):
1) Air friction.
2) Formation of vortices.
3) Formation of a ballistic wave.
Air particles in contact with a moving bullet (grenade), due to internal cohesion (viscosity) and adhesion to its surface, create friction and reduce the speed of the bullet (grenade).
The layer of air adjacent to the surface of the bullet (grenade), in which the movement of particles changes from the speed of the bullet (grenade) to zero, is called the boundary layer, and this layer of air, flowing around the bullet, breaks away from its surface and does not have time to immediately close behind the bottom part.
A rarefied space is formed behind the bottom of the bullet, resulting in a pressure difference between the head and bottom parts. This difference creates a force directed in the direction opposite to the movement of the bullet and reducing its flight speed. Air particles, trying to fill the vacuum formed behind the bullet, create a vortex.
When flying, a bullet (grenade) collides with air particles and causes them to vibrate. As a result, the air density in front of the bullet (grenade) increases and sound waves are formed. Therefore, the flight of a bullet (grenade) is accompanied by a characteristic sound. When the speed of a bullet (grenade) is less than the speed of sound, the formation of these waves has little effect on its flight, since the waves propagate faster than the speed of the bullet (grenade).
When the bullet's flight speed is greater than the speed of sound, the sound waves collide with each other to create a wave of highly compressed air - a ballistic wave, which slows down the bullet's flight speed, since the bullet spends part of its energy creating this wave.
The resultant (total) of all forces, resulting from the influence of air on the flight of a bullet (grenade), constitutes the force of air resistance. The point of application of the resistance force is called the center of resistance. The effect of drag on the flight of a bullet (grenade) is very great. It causes a decrease in the speed and range of a bullet (grenade).
To study the trajectory of a bullet (grenade), the following definitions are adopted (Fig. 120)
1) Center of the muzzle of the barrel called departure point. The departure point is the beginning of the trajectory.
2) The horizontal plane passing through the departure point, called the weapon horizon. The weapon horizon 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.
3) A straight line, which is a continuation of the axis of the barrel of the aimed weapon, called the elevation line.
4) The vertical plane passing through the elevation line, called the shooting plane.
5) The angle between the elevation line and the horizon of the weapon, called elevation angle. If this angle is negative, then it is called the declination (decrease) angle.
6) A straight line, which is a continuation of the axis of the barrel bore at the moment the bullet leaves, called the throwing line.
7) The angle between the throwing line and the horizon of the weapon is called throwing angle.
8) The angle between the elevation line and the throwing line , is called the departure angle.
9) The point of intersection of the trajectory with the horizon of the weapon called the point of impact.
10) The angle between the tangent to the trajectory at the point of impact and the horizon of the weapon, called the angle of incidence.
11) Distance from the point of departure to the point of impact is called the full horizontal range.
12) Speed of the bullet (grenade) at the point of impact called final speed.
13) Time of movement of a bullet (grenade) from the point of departure to the point of impact called total flight time.
14) Highest point trajectory called the vertex of the trajectory.
15) The part of the trajectory from the departure point to the top is called the ascending branch; part of the trajectory from the top to the point of fall called the outgoing branch of the trajectory.
16) The point on or off the target at which the weapon is aimed, called the aiming point.
17) A straight line running 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, called the line of sight.
18) The angle between the elevation line and the aiming line, called the aiming angle.
19) The angle between the aiming line and the horizon of the weapon, called the target elevation angle.
20) Distance from the departure point to the intersection of the trajectory with the aiming line called the target range.
21) The shortest distance from any point on the trajectory to the aiming line is called the excess of the trajectory above the aiming line.
23) Distance from the departure point to the target along the target line called slant range.
24) Point of intersection of the trajectory with the target surface (ground, obstacle) called the meeting point.
25) The angle between the tangent to the trajectory and the tangent to the surface of the target (ground, obstacle) at the meeting point, called the meeting angle.
The trajectory of a bullet in the air has the following properties:
The descending branch is shorter and steeper than the ascending one;
The angle of incidence is greater than the angle of throwing;
The final speed of the bullet is less than the initial speed;
The lowest bullet flight speed when shooting at high throwing angles is at
descending branch of the trajectory, and when shooting at small throwing angles - at the point
The time it takes a bullet to travel along the ascending branch of the trajectory is less than along the descending branch.
1.2.2. Trajectory shape and its practical significance(Fig. 121)
The shape of the trajectory depends on the elevation angle. As the elevation angle increases, the trajectory height and the full horizontal flight range of the bullet (grenade) 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.
Elevation angle, at which the total horizontal flight range of a bullet (grenade) becomes greatest, called the angle of greatest range. The value of the angle of greatest range for bullets various types arms is about 35 degrees.
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Rice. 121 Trajectory shapes |
Trajectories, obtained with 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 hinged .
When firing from the same weapon (at the same initial speeds), you can get two trajectories with the same horizontal range: flat and mounted
Trajectories having the same horizontal range at different elevation angles, are called conjugate.
When firing from small arms and grenade launchers, only flat trajectories are used .
The flatter the trajectory, the greater the 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 result).
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 magnitude of the angle of incidence - the smaller the angle of incidence, the more flat the trajectory.
The flat trajectory affects the range of a direct shot, hit, covered and dead space.
1.2.3. Direct shot (Fig. 122).
Straight shot- a shot in which the trajectory does not rise above the aiming line above the target along its entire length.
Within the range of a direct shot, during tense moments of battle, shooting can be carried out without rearranging the sight, while the aiming point in height is usually selected at the lower edge of the target.
The range of a direct shot depends on:
Target heights;
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. The direct shot range can be determined from 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.
1.2.4. The affected space (the depth of the affected space) (Fig. 123).
When shooting at targets located at a distance greater than the direct shot range, the trajectory near its apex rises above the target and the target is at
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.
Target space (depth of target space) – the distance on the ground over which the downward branch of the trajectory does not exceed the target height.
The depth of the affected space depends on:
From the height of the target (the higher the target, the higher it will be);
From the flatness of the trajectory (the flatter it will be, the greater
trajectory);
From the angle of inclination of the terrain (on the front slope it decreases, on the reverse slope
increases).
In the case when the target is located on a slope or there is an elevation angle of the target, the depth of the affected space is determined using the above methods, and the result obtained must be multiplied by the ratio of the angle of incidence to the angle of encounter.
The magnitude of the meeting angle depends on the direction of the slope:
On an oncoming slope, the meeting angle is equal to the sum of the angles of incidence and slope;
On the reverse slope - the differences between these angles;
In this case, the magnitude of the meeting angle also depends on the target elevation angle:
With a negative target elevation angle, the meeting angle increases by the amount of the elevation angle
With a positive target elevation angle, it decreases by its value.
The target space to some extent compensates for errors made when choosing a sight, and allows you to round up the measured distance to the target.
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, if possible, coincides with the extension of the aiming line.
1.2.5. Covered space (Fig. 123).
Covered space- 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.
Dead (not affected) space- part of the covered space in which the target cannot be hit with a given trajectory.
The greater the height of the cover, the lower the height of the target and the flatter the trajectory, the greater the dead space. The other part of the covered space in which the target can be hit is the target space.
The depth of the covered space (SC) can be determined from tables of the excess of trajectories above the line of sight. By selection, an excess is found that corresponds to the height of the shelter and the distance to it. After finding the excess, the corresponding setting of the sight and firing range is determined. The difference between a certain firing range and the distance to cover represents the depth of the covered space.
The depth of the dead space is equal to the difference between the covered and affected space.
Knowing the amount of covered 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.
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Rice. 123 – Covered, dead and target space |
1.2.6. The influence of shooting conditions on the flight of a bullet (grenade).
The following are accepted as normal (tabular) conditions:
A) Meteorological conditions:
Atmospheric (barometric) pressure at the horizon of the weapon is 750 mm Hg. ;
The air temperature on the horizon of the weapon is + 15 degrees. WITH. ;
Relative humidity air 50% (relative humidity
is the ratio of the amount of water vapor contained in the air to
the largest amount of water vapor that can be contained in the air
at a given temperature);
There is no wind (the atmosphere is motionless);
B) Ballistic conditions:
The weight of the bullet (grenade), initial speed and angle of departure are equal to the values
indicated in the shooting tables;
Charge temperature + 15 degrees. S.;t
The shape of the bullet (grenade) corresponds to the established drawing;
The height of the front sight is set based on the data of bringing the weapon to normal combat; - the height (divisions) of the sight correspond to the table aiming angles.
B) Topographic conditions:
The target is on the weapon's horizon;
There is no lateral tilt of the weapon;
If shooting conditions deviate from normal, it may be necessary to determine and take into account corrections for the firing range and direction.
Influence of atmospheric pressure
1) With increase atmospheric pressure The air density increases, and as a result, the force of air resistance increases and the flight range of a bullet (grenade) decreases.
2) As atmospheric pressure decreases, the density and force of air resistance decrease, and the bullet’s flight range increases.
Effect of temperature
1) As the temperature rises, the density of the air decreases, and as a result, the force of air resistance decreases and the range of the bullet increases.
2) As the temperature decreases, the density and force of air resistance increase and the flight range of a bullet (grenade) decreases.
As the temperature of the powder charge increases, the burning rate of the powder, the initial speed and the flight range of the bullet (grenade) increase.
When shooting in summer conditions, corrections for changes in air temperature and powder charge are insignificant and practically not taken into account. When shooting in winter (in conditions low temperatures) these amendments must be taken into account, guided by the rules specified in the shooting manuals.
Wind influence
1) With a tailwind, the speed of a bullet (grenade) relative to the air decreases. As the speed of the bullet relative to the air decreases, the force of air resistance decreases. Therefore, with a tailwind, the bullet will fly further than with no wind.
2) In a headwind, the speed of the bullet relative to the air will be greater than in a calm environment, therefore, the force of air resistance will increase and the bullet’s flight range will decrease
Longitudinal (tailwind, headwind) wind has an insignificant effect on the flight of a bullet, and in the practice of shooting from small arms, corrections for such wind are not introduced.
When firing a grenade launcher, adjustments for strong longitudinal winds should be taken into account.
3) Side wind puts pressure on lateral surface bullet and deflects it away from the firing plane depending on its direction. Crosswind has a significant impact, especially on grenade flight, and must be taken into account when firing grenade launchers and small arms.
4) The wind blowing at an acute angle to the shooting plane simultaneously influences both the change in the bullet’s flight range and its lateral deflection.
Effect of air humidity
Changes in air humidity have an insignificant effect on air density and, consequently, on the flight range of a bullet (grenade), so it is not taken into account when shooting.
Effect of scope installation
When shooting with one sight setting (with one aiming angle), but at different angles of the target, as a result of a number of reasons, incl. Changes in air density at different altitudes, and consequently in the force of air resistance, change the value of the inclined (sighting range of a bullet (grenade).
When shooting at small elevation angles of the target (up to +_ 15 degrees), this flight range of the bullet (grenade) changes very slightly, therefore equality of the inclined and full horizontal flight range of the bullet is allowed, i.e. constancy of the shape (rigidity) of the trajectory (Fig. 124).
Basic concepts are presented: periods of a shot, elements of a bullet’s flight path, direct shot, etc.
In order to master the technique of shooting from any weapon, you need to know a number of theoretical principles, without which not a single shooter will be able to show high results and his training will be ineffective.
Ballistics is the science of projectile movement. In turn, ballistics is divided into two parts: internal and external.
Internal ballistics
Internal ballistics studies the phenomena occurring in the barrel bore during a shot, the movement of the projectile along the bore, the nature of the thermo- and aerodynamic dependencies accompanying this phenomenon, both in the bore and beyond during the aftereffect of powder gases.
Internal ballistics solves the most rational use energy of the powder charge during the shot so that the projectile given weight and caliber to communicate a certain initial velocity (V0) while maintaining the strength of the barrel. This provides the initial data for external ballistics and weapon design.
With a shot is called the ejection of a bullet (grenade) from the bore of a weapon by the energy of gases formed during the combustion of a powder charge.
When the firing pin strikes the primer of a live cartridge sent into the chamber, the percussion composition of the primer explodes and a flame is formed, which penetrates through the seed holes in the bottom of the cartridge case to the powder charge and ignites it. When a powder (combat) charge burns, a large amount of highly heated gases are formed, creating high pressure in the barrel bore on the bottom of the bullet, the bottom and walls of the cartridge case, as well as on the walls of the barrel and the bolt.
As a result of the gas pressure on the bottom of the bullet, it moves from its place and crashes into the rifling; rotating along them, moves along the barrel bore with a continuously increasing speed and is thrown out in the direction of the axis of the barrel bore. The gas pressure on the bottom of the cartridge case causes the weapon (barrel) to move backward.
When fired from an automatic weapon, the design of which is based on the principle of using the energy of powder gases discharged through a hole in the barrel wall - sniper rifle Dragunov, part of the powder gases, in addition, after passing through it into the gas chamber, strikes the piston and throws the pusher with the bolt back.
When a powder charge is burned, approximately 25-35% of the released energy is spent on imparting forward motion to the bullet (the main work); 15-25% of energy - for performing secondary work (plunging in and overcoming the friction of a bullet when moving along the bore; heating the walls of the barrel, cartridge case and bullet; moving the moving part of the weapon, the gaseous and unburnt part of the gunpowder); about 40% of the energy is not used and is lost after the bullet leaves the bore.
The shot occurs in a very short period of time (0.001-0.06 s.). When firing, there are four consecutive periods:
- preliminary
- first or main
- second
- third, or period of last gases
Preliminary period lasts from the beginning of the combustion of the powder charge until the bullet casing completely cuts into the rifling of the barrel. 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; it reaches 250 - 500 kg/cm2 depending on the rifling design, the weight of the bullet and the hardness of its shell. 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 boost pressure is reached in the barrel bore.
First or main period lasts from the beginning of the bullet’s movement until the complete combustion of the powder charge. During this period, combustion of the powder charge occurs in a rapidly changing volume. At the beginning of the period, when the speed of the bullet moving 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 cartridge case), the gas pressure quickly increases and reaches its highest value - a rifle cartridge of 2900 kg/cm2. This pressure is called maximum pressure. It is created in small arms when a bullet travels 4 - 6 cm. Then due to fast speed As the bullet moves, the volume of the behind-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 constantly increases and by the end of the period reaches approximately 3/4 of the initial speed. The powder charge is completely burned shortly before the bullet leaves the barrel.
Second period lasts until the powder charge is completely burned until the bullet leaves the barrel. With the beginning of this period, the influx of powder gases stops, however, highly compressed and heated gases expand and, putting pressure on the bullet, increase its speed. The pressure drop in the second period occurs quite quickly and at the muzzle the muzzle pressure is 300 - 900 kg/cm2 for various types of weapons. The speed of the bullet at the moment it leaves the barrel (muzzle speed) is slightly less than the initial speed.
The third period, or the period after the action of gases lasts from the moment the bullet leaves the barrel 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 affect the bullet and impart additional speed to it. The bullet reaches its highest (maximum) speed at the end of the third period at a distance of several tens of centimeters from the muzzle of the barrel. This period ends at the moment when the pressure of the powder gases at the bottom of the bullet is balanced by air resistance.
Initial bullet speed and its practical significance
Initial speed called the speed of the bullet at the muzzle of the barrel. The initial speed is taken to be a conditional speed, which is slightly greater than the muzzle and less than the maximum. It is determined experimentally with subsequent calculations. The magnitude of the muzzle velocity is indicated in the shooting tables and in the combat characteristics of the weapon.
Initial speed is one of the most important characteristics of the combat properties of a weapon. As the initial speed increases, the bullet's flight range, direct shot range, lethal and penetrating effect of the bullet increases, and the influence of external conditions on its flight decreases. The magnitude of the initial bullet speed depends on:
- barrel length
- bullet weight
- weight, temperature and humidity of the powder charge
- shapes and sizes of gunpowder grains
- loading density
The longer the trunk, those longer time The powder gases act on the bullet and the greater the initial speed. With a constant barrel length and constant weight of the powder charge, the lower the bullet weight, the greater the initial velocity.
Changing the weight of the powder charge leads to a change in the amount of powder gases, and consequently to a change in the maximum pressure in the barrel bore and the initial velocity of the bullet. The greater the weight of the powder charge, the greater the maximum pressure and muzzle velocity.
With increasing temperature of the powder charge The burning rate of the gunpowder increases, and therefore the maximum pressure and initial speed increase. When the charge temperature decreases the initial speed decreases. An increase (decrease) in the initial speed causes an increase (decrease) in the range of the bullet. In this regard, it is necessary to take into account range corrections for air and charge temperatures (charge temperature is approximately equal to air temperature).
With increasing humidity of the powder charge its burning speed and the initial speed of the bullet decrease.
Shapes and sizes of gunpowder have a significant impact on the burning rate of the powder charge, and therefore on the initial speed of the bullet. They are selected accordingly when designing weapons.
Loading density is called the ratio of the weight of the charge to the volume of the cartridge case with the bullet inserted (charge combustion chamber). When the bullet is seated deeply, the loading density increases significantly, which can lead to a sharp surge in pressure when fired and, as a result, to rupture of the barrel, so such cartridges cannot be used for shooting. As the loading density decreases (increases), the initial bullet speed increases (decreases).
Recoil called the backward movement of the weapon during a shot. Recoil is felt in the form of a push to the shoulder, arm or ground. The recoil effect of a weapon is approximately as many times less than the initial speed of a bullet, as many times the bullet is lighter than the weapon. The recoil energy of hand-held small arms usually does not exceed 2 kg/m and is perceived painlessly by the shooter.
The recoil force and the recoil resistance force (butt support) are not located on the same straight line and are directed in opposite directions. They form a pair of forces, under the influence of which the muzzle of the weapon barrel is deflected upward. The greater the leverage of this pair of forces, the greater the deflection of the muzzle of a given weapon. In addition, when fired, the barrel of the weapon makes oscillatory movements - vibrates. 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, right, left).
The magnitude of this deviation increases when the shooting rest is used incorrectly, the weapon is dirty, etc.
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 the departure angle.
The departure angle is considered positive when the axis of the barrel bore at the moment the bullet leaves is above its position before the shot, negative when it is below. The influence of the take-off angle on shooting is eliminated when it is brought to normal combat. However, if the rules for placing a weapon are violated, the use of a stop, as well as the rules for caring for and preserving the weapon, 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, compensators are used.
So, the phenomena of a shot, the initial speed of a bullet, and the recoil of a weapon have great importance when shooting and affect the flight of the bullet.
External ballistics
This is a science that studies the movement of a bullet after the action of powder gases on it ceases. The main task of external ballistics is the study of the properties of the trajectory and patterns of flight of a bullet. External ballistics provides data for compiling shooting tables, calculating weapon sight scales, and developing shooting rules. Conclusions from external ballistics are widely used in combat when choosing a sight and aiming point depending on the firing range, wind direction and speed, air temperature and other shooting conditions.
The trajectory of a bullet and its elements. Trajectory properties. Types of trajectory and their practical significance
Trajectory called the curved line described by the center of gravity of the bullet in flight.
When flying in the air, a bullet is subject to 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. As a result of the action of these forces, 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 part of the bullet’s energy is expended on movement in this medium.
The force of air resistance is caused by three main reasons: air friction, the formation of vortices and the formation of a ballistic wave.
The shape of the trajectory depends on the elevation angle. 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.
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 bullets of various types of weapons is about 35°.
Trajectories obtained at elevation angles less than the angle of greatest range are called flat. Trajectories obtained at elevation angles greater than the angle largest angle longest range are called mounted. When firing from the same weapon (at the same initial speeds), you can get two trajectories with the same horizontal range: flat and mounted. Trajectories that have the same horizontal range and swarms of different elevation angles are called conjugated.
When shooting from small arms, only flat trajectories are used. The flatter the trajectory, the greater the area over which the target can be hit with one sight setting (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 magnitude of the angle of incidence: the smaller the angle of incidence, the more flat the trajectory. The flatness of the trajectory affects the range of the direct shot, the target, covered and dead space.
Path elements
Departure point- center of the muzzle of the 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 the declination (decrease) angle.
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.
Final speed- the speed of the bullet (grenade) at the point of impact.
Full time flight- time of movement of a bullet (grenade) 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 the horizon of the weapon.
Ascending branch of the trajectory- part of the trajectory from the point of departure to the top, and from the top to the point of fall - the descending branch of the trajectory.
Aiming point (aims)- 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 the 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 degrees.
Direct shot, striking and dead space most closely related to issues of shooting practice. The main objective of studying these issues is to gain solid knowledge in the use of a direct shot and the target space to perform fire missions in combat.
Direct shot, its definition and practical use in a combat situation
A shot in which the trajectory does not rise above the aiming line above the target throughout its entire length is called direct shot. Within the range of a direct shot, during tense moments of battle, shooting can be carried out without rearranging the sight, while the vertical aiming point is usually selected at the lower edge of the target.
The range of a direct shot depends on 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.
The range of a direct shot can be determined from tables by comparing the height of the target with the values of the greatest elevation of the trajectory above the aiming line or with the height of the trajectory.
Direct sniper shot in an urban environment
The installation height 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 the aiming line - the optical axis of the optical sight. The height of the aiming line at the middle of a distance of 200 meters 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, the height of the bullet trajectory will be 3 cm, and the height of the aiming line will be 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 a distance of 80 meters 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 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 scope “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 method described above can be useful in street battles, when the distances in the city are approximately 150-250 meters and everything is done quickly, on the run.
Target space, its definition and practical use in a combat situation
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.
The distance on the ground over which the descending branch of the trajectory does not exceed the target height, called target space(depth of affected space).
The depth of the affected space depends on the height of the target (it will be greater, the higher the target), on the flatness of the trajectory (it will be greater, the flatter the trajectory) and on the angle of inclination of the terrain (on the forward slope it decreases, on the reverse slope it increases).
The depth of the 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 at 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 space, its definition and practical use in a combat situation.
Covered space, its definition and practical use in a combat situation
The space behind cover that cannot be penetrated by a bullet, from its crest to the meeting point is called covered space.
The greater the height of the shelter and the flatter the trajectory, the larger the covered space. The depth of the covered space can be determined from tables of trajectory elevation above the aiming line. By selection, an excess is found that corresponds to the height of the shelter and the distance to it. After finding the excess, the corresponding 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 definition and practical use in a combat situation
The part of the covered space in which the target cannot be hit with a given trajectory is called dead (not affected) space.
The greater the height of the cover, the lower the height of the target and the flatter the trajectory, the greater the dead space. The other part of the covered space in which the target can be hit is the target space. The depth of the dead space is equal to the difference between the covered and affected space.
Knowing the size of the affected space, covered space, and dead space allows you to correctly use shelters for protection from enemy fire, as well as take measures to reduce dead spaces by correctly choosing firing positions and firing at targets from weapons with a more forward trajectory.
Derivation phenomenon
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 air resistance on more than one side and therefore deviates from the firing plane more and more in the direction of rotation. This deflection of a rotating bullet away from the firing plane is called derivation. This is a rather complex physical process. Derivation increases disproportionately to the flight distance of the bullet, as a result of which the latter takes more and more to the side and its trajectory in plan is a curved line. When the barrel is cut to the right, the derivation takes the bullet to the right, and when the barrel is cut to the left, to the left.
| Distance, m | Derivation, cm | thousandths |
| 100 | 0 | 0 |
| 200 | 1 | 0 |
| 300 | 2 | 0,1 |
| 400 | 4 | 0,1 |
| 500 | 7 | 0,1 |
| 600 | 12 | 0,2 |
| 700 | 19 | 0,2 |
| 800 | 29 | 0,3 |
| 900 | 43 | 0,5 |
| 1000 | 62 | 0,6 |
At firing distances up to 300 meters inclusive, derivation has no practical significance. This is especially typical for the SVD rifle, in which the PSO-1 optical sight is specially shifted to the left by 1.5 cm. At the same time, the barrel is slightly turned to the left and the bullets move slightly (1 cm) to the left. This is not of fundamental importance. At a distance of 300 meters, the force of derivation returns the bullets to the aiming point, that is, in the center. And already at a distance of 400 meters, the bullets begin to move thoroughly to the right, therefore, in order not to turn the horizontal flywheel, aim at the enemy’s left (away from you) eye. Derivation will move the bullet 3-4 cm to the right, and it will hit the enemy on the bridge of the nose. At a distance of 500 meters, aim at the left (from you) side of the enemy’s head between the eye and ear - this will be approximately 6-7 cm. At a distance of 600 meters, aim at the left (from you) side of the enemy’s head. Derivation will move the bullet to the right by 11-12 cm. At a distance of 700 meters, take the visible gap between the aiming point and the left edge of the head, somewhere above the center of the shoulder strap on the enemy’s shoulder. At 800 meters - correct the horizontal corrections by 0.3 thousandths with the flywheel (move the reticle to the right, midpoint hits move to the left), at 900 meters - 0.5 thousandths, at 1000 meters - 0.6 thousandths.
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 shooting 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 the trajectory height and flight range of a bullet on the 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 condensation of air particles in front of the bullet head and the rarefied zone 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 excessively high 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 area of rarefied space behind the bullet is smaller, the more its tail is beveled; 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 equipped with blunt-pointed bullets: this is more convenient for reloading weapons, and also helps preserve them 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: a heavy bullet with an initial speed of about 770 m/sec has a maximum flight range of 5100 m, while a light bullet with an initial speed of 865 m/sec has only 3400 m.
2.3.6 Dependence of the trajectory on meteorological conditions
Continuously changing during shooting weather conditions can have a significant impact on the flight of a bullet. However, certain knowledge and practical experience help to significantly reduce their harmful effect on shooting accuracy.
Since sport shooting distances are relatively short and the bullet travels 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.
The 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 initial material and help the shooter navigate difficult shooting conditions 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 line of fire. 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. Therefore, 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. Therefore, the lower the air temperature, the slower the process is underway increase in 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, somewhat different from the trajectories of other bullets. This phenomenon is called natural dispersion.
With a significant number of shots, the trajectories in their totality form sheaf, which, when meeting 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). The trajectory located in the middle of the sheaf and passing through the midpoint of impact is 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.
With a large number of shots, the dispersion of bullets obeys a certain dispersion law, 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 cartridges 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.
With a shot is called the ejection of a bullet from the barrel under the influence of powder gases formed during the combustion of a powder charge. The impact of the firing pin on the cartridge primer produces a flame that ignites the powder charge. In this case, a large amount of highly heated gases is formed, which create high pressure, acting in all directions with equal force. At a gas pressure of 250–500 kg/cm2, the bullet moves and crashes into the rifling of the barrel, receiving a rotational movement. The gunpowder continues to burn, therefore, the amount of gases increases. Then, due to a rapid increase in the speed of the bullet, the volume of the behind-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 barrel continues to increase, since the gases, although to a lesser extent, still put pressure on it. The bullet moves along the bore with continuously increasing speed and is thrown outward along the axis of the bore. The entire firing process occurs 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 speed.
Initial bullet speed is the speed at which the bullet leaves the barrel. The magnitude of the initial 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. Increasing the initial speed increases the range of the bullet, its penetrating and lethal effect, and reduces the influence of external conditions on its flight. The backward movement of the weapon while firing is called recoil. The pressure of the powder gases in the barrel bore acts in all directions with equal force. The gas pressure on the bottom of the bullet causes it to move forward, and the pressure on the bottom of the cartridge case is transferred to the bolt and causes the weapon to move backward. During recoil, a pair of forces is formed, under the influence of which the muzzle of the weapon is deflected upward. The recoil force acts along the axis of the barrel, and the butt rest on the shoulder and the center of gravity of the weapon are located below the direction of this force, so when firing, the muzzle of the weapon is deflected upward.
Recoil small arms are felt as a push into the shoulder, arm or into the ground. The recoil action of a weapon is characterized by the amount of speed and energy it has when moving backwards. The recoil speed of a weapon is approximately the same number of times less than the initial speed of a bullet, how many times the bullet is lighter than the weapon. The recoil energy of a Kalashnikov assault rifle is low and is perceived painlessly by the shooter. Holding the weapon correctly and uniformly reduces the impact of recoil and improves shooting performance. The presence of muzzle brakes-compensators or compensators in weapons improves the results of burst fire and reduces recoil.
At the moment of firing, the barrel of the weapon, depending on the angle of elevation, occupies a certain position. The flight of a bullet in the air begins in a straight line, representing a continuation of the axis of the barrel bore at the moment the bullet leaves. This line is called throwing line. When flying in the air, a bullet is acted upon by two forces: gravity and air resistance. The force of gravity deflects the bullet more and more downward from the throwing line, and the force of air resistance slows down the movement of the bullet. Under the influence of these two forces, the bullet continues to fly along a curve located below the throwing line. Path shape depends on the magnitude of the elevation angle and the initial speed of the bullet, it affects the range of a direct shot, covered, targeted and dead space. 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 height continues to increase, and the total horizontal range decreases.
The elevation angle at which the total horizontal range of the bullet becomes greatest is called angle of greatest range. The maximum range angle for bullets of various types of weapons is about 35°. Trajectories obtained at elevation angles less 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 aiming line above the target along its entire length.
Direct shot range depends on the height of the target and the flatness of the trajectory. The higher the target and the flatter the trajectory, the greater the direct shot range and, therefore, the distance at which the target can be hit with one sight setting. Practical significance direct shot lies in the fact that in tense moments of 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 cover that cannot be penetrated by a bullet, from its crest to the meeting point is called covered space.
The higher the shelter and the flatter the trajectory, the larger the covered space. The part of the covered space in which the target cannot be hit with a given trajectory is called dead (unhittable) space. The greater the height of the shelter, the lower the height of the target, and the flatter the trajectory, the greater it is. The other part of the covered space in which the target can be hit is the target space.
Shot periodization
The shot occurs in a very short period of time (0.001-0.06 s.). When firing, there are four consecutive periods:
- preliminary;
- first, or main;
- second;
- third, or period of last gases.
Preliminary period lasts from the beginning of the combustion of the powder charge until the bullet casing completely cuts into the rifling of the barrel. 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; it reaches 250 - 500 kg/cm 2 depending on the rifling design, the weight of the bullet and the hardness of its shell (for example, for small arms chambered for the 1943 model cartridge, the boost 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 boost pressure is reached in the barrel bore.
First or main period lasts from the beginning of the bullet’s movement until the complete combustion of the powder charge. During this period, combustion of the powder charge occurs in a rapidly changing volume. At the beginning of the period, when the speed of the bullet moving 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 cartridge case), the gas pressure quickly increases and reaches its greatest value (for example, in small arms chambered for the sample cartridge 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. Then, due to the rapid movement of the bullet, the volume of the behind-the-bullet space increases faster than the influx of new gases, and the pressure begins to drop, 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 of the initial speed. The powder charge is completely burned shortly before the bullet leaves the barrel.
Second period lasts until the powder charge is completely burned until the bullet leaves the barrel. With the beginning of this period, the influx of powder gases stops, however, highly compressed and heated gases expand and, putting pressure on the bullet, increase its speed. The pressure decline 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 a Simonov self-loading carbine - 390 kg/cm 2, for a Goryunov heavy machine gun - 570 kg/cm 2 ). The speed of the bullet at the moment it leaves the barrel (muzzle speed) is slightly less than the initial speed.