Bullet trajectory and its elements. internal ballistics. Hinged trajectories allow
Flight of a bullet in the air
Having flown out of the bore, the bullet moves by inertia and is subjected to the action of two forces of gravity and air resistance
The force of gravity causes the bullet to gradually descend, and the force of air resistance continuously slows down the movement of the bullet and tends to knock it over. To overcome the force of air resistance, part of the energy of the bullet is expended
The force of air resistance is caused by three main reasons: air friction, the formation of eddies, and the formation of a ballistic wave (Fig. 4)
The bullet collides with air particles during flight and causes them to oscillate. As a result, the air density increases in front of the bullet and 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
In order for the bullet not to tip over under the action of air resistance, it is given a quick rotary motion. 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 are adopted (Fig. 5):
· departure point - the center of the muzzle of the barrel, in which the center of gravity of the bullet is located at the time of departure. The moment of departure is the passage of the bottom of the bullet through the muzzle of the barrel;
· weapon horizon - a horizontal plane passing through the departure point;
· elevation line - a straight line, which is a continuation of the axis of the bore at the moment of departure;
· shooting plane - a vertical plane passing through the line of elevation;
· throw line - a straight line, which is a continuation of the axis of the bore at the time of the bullet's departure;
· throw angle - the angle enclosed between the line of throw and the horizon of the weapon;
· departure angle - the angle enclosed between the line of elevation and the line of throwing;
· drop point - the point of intersection of the trajectory with the horizon of the weapon,
· injection fall – the angle at the point of impact between the tangent to the trajectory and the horizon of the weapon,
· full horizontal range - distance from point of departure to point of fall,
· top of the trajectory highest point trajectories;
· trajectory height - the shortest distance from the vertex of the trajectory to horizon arms,
· 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 surface of the target (ground, obstacles),
· meeting angle - the angle enclosed 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,
· line of sight - a straight line from the shooter's eye through the middle of the sight slot and the top of the front sight in aiming point,
· aiming angle - the angle enclosed between the aiming line and the elevation line;
· target elevation angle the angle enclosed between the aiming line and the horizon of the weapon;
· aiming range - distance from the point of departure to the intersection of the trajectory with the line of sight;
· excess of the trajectory over the aiming line - the shortest distance from any point of the trajectory to the line of sight;
· elevation angle - the angle enclosed between the line of elevation and the horizon of the weapon. The shape of the trajectory depends on the elevation angle
Rice. 5. Bullet trajectory elements
The trajectory of a bullet in the air is following properties:
The descending branch is steeper than the ascending one;
the angle of incidence is greater than the angle of throw;
The final velocity of the bullet is less than the initial one;
The lowest speed of a bullet when shooting at high angles of throw
on the descending branch of the trajectory, and when firing at small throwing angles - at the point of impact;
the time of movement of the bullet along the ascending branch of the trajectory is less than
descending;
· the trajectory of a rotating bullet due to the decrease under the action of gravity and derivation is a line of double curvature.
The shape of the trajectory depends on the magnitude of the elevation angle (Fig. 6). As the elevation angle increases, the height of the trajectory and the total horizontal range of the bullet increase, but this occurs up to a certain limit. Beyond this limit, the trajectory height continues to increase and the total horizontal range begins to decrease.
Rice. 6. Angle of greatest reach, flat,
hinged and conjugate trajectories
The angle of elevation at which the full horizontal range of the bullet is at its 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, smaller angle longest 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 having the same horizontal range at different elevation angles are called conjugated.
Flat trajectories allow:
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. Than flatter trajectory, the greater the extent of the terrain, the target can be hit with one sight setting (the less impact on the results of shooting is caused by errors in determining the sight setting).
Mounted trajectories allow:
1. Hit targets behind cover and in deep terrain.
2. Destroy the ceilings of structures.
These different tactical properties of flat and overhead 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) weapons at the target.
The task of any shooting is to hit the target in the most a short 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 motionless. 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 from the wind, lateral deflections of the bullet can occur. 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 bore a certain position in space (in the horizontal and vertical plane) before firing.
Giving the axis of the bore of a weapon the position in space necessary for firing is called aiming or pointing. Giving the axis of the bore of the weapon the required position in the horizontal plane is called horizontal pickup, and in the vertical plane - vertical pickup.
Rice. 7. Aiming (aiming) with open sight:
O - front sight, a - rear sight, aO - aiming line; сС - the axis of the bore, оО - a line parallel to the axis of the bore: H - the height of the sight, M - the amount of displacement of the rear sight;
a - aiming angle; Ub - angle of lateral correction
Accurate solution of aiming problems of any type sights depends on the correct alignment of them on the weapon. Alignment of sights of small arms for shooting at ground targets carried out in the process of checking the combat of the weapon and bringing it to normal combat.
Shot is called the ejection of a bullet from the bore under the action of powder gases formed during the combustion of a powder charge. From the impact of the striker on the primer of the cartridge, a flame arises that ignites the powder charge. This creates a large number of highly heated gases that create high pressure acting in all directions with the same force. At a gas pressure of 250-500 kg / cm 2, the bullet moves from its place and crashes into the rifling of the bore, receiving rotational motion. Gunpowder continues to burn, therefore, the amount of gases increases. Then, due to the rapid increase in the speed of the bullet, the volume of the bullet space increases faster than inflow new gases, and the pressure starts to drop. However, the speed of the bullet in the bore continues to increase, as the gases, although to a lesser extent, still put pressure on it. The bullet moves along the bore at a continuously increasing speed and is ejected outward in the direction of the axis of the bore. The entire firing process takes place in a very short period of time (0.001–0.06 s). Further, the flight of the bullet in the air continues by inertia and largely depends on its initial velocity.
muzzle velocity is the speed at which the bullet leaves the bore. The value of the muzzle velocity of a bullet depends on the length of the barrel, the mass of the bullet, the mass of the powder charge, and other factors. An increase in the initial speed increases the range of the bullet, its penetrating and lethal effect, reduces the impact external conditions for her flight. The movement of the weapon backwards while firing is called recoil. The pressure of powder gases in the bore acts in all directions with the same force. The pressure of the gases on the bottom of the bullet makes it move forward, and the pressure on the bottom of the cartridge case is transmitted to the bolt and causes the weapon to move backward. When recoil, a pair of forces is formed, under the influence of which the muzzle of the weapon deviates upward. The recoil force acts along the axis of the bore, and the butt stop in the shoulder and the center of gravity of the weapon are located below the direction of this force, therefore, when firing, the muzzle of the weapon deviates upward.
recoil small arms is felt in the form of a push in the shoulder, arm or into the ground. The recoil action of a weapon is characterized by the amount of speed and energy that it has when moving backward. The recoil speed of the weapon is approximately as many times less than the initial speed of the bullet, how many times the bullet is lighter than the weapon. The recoil energy of the Kalashnikov assault rifle is small and is perceived painlessly by the shooter. Correct and uniform holding of the weapon reduces the impact of recoil and increases the effectiveness of shooting. The presence of muzzle brakes-compensators or compensators for weapons improves the results of firing bursts and reduces recoil.
At the time of the shot, the barrel of the weapon, depending on the elevation angle, occupies a certain position. The flight of a bullet in the air begins in a straight line, representing the continuation of the axis of the bore at the time of the bullet's departure. This line is called throw line. When flying in the air, two forces act on a bullet: gravity and air resistance. Gravity pushes the bullet further and further away from the line of throw, while air resistance slows the bullet down. Under the influence of these two forces, the bullet continues to fly along a curve located below the line of throw. Trajectory shape depends on the magnitude of the elevation angle and the initial velocity of the bullet, it affects the range of a direct shot, covered, hit and dead space. As the elevation angle increases, the height of the trajectory and the total horizontal range of the bullet increase, but this occurs up to a certain limit. Beyond this limit, the trajectory height continues to increase and the total horizontal range decreases.
The angle of elevation at which the full horizontal range of the bullet is greatest is called farthest angle. The value of the angle of greatest range for bullets various kinds arms is about 35°. Trajectories obtained at elevation angles smaller than the angle of greatest range are called flat.
Straight shot called a shot in which the trajectory of the bullet does not rise above the line of sight above the target throughout its entire length.
Direct shot range depends on the height of the target and flatness of the trajectory. The higher the target and the flatter the trajectory, the greater the range of a direct shot and, therefore, the distance at which the target can be hit with one sight setting. The practical significance of a direct shot lies in the fact that in tense moments of the battle, shooting can be carried out without rearranging the sight, while the aiming point in height will be selected along the lower edge of the target.
The space behind a cover that is not penetrated by a bullet, from its crest to the meeting point is called covered space.
The covered space is the greater, the higher the shelter and the flatter the trajectory. The part of the covered space on which the target cannot be hit with a given trajectory is called dead (non-hit) space. It is the greater, the greater the height of the shelter, the lower the height of the target and the flatter the trajectory. The other part of the covered space in which the target can be hit is the hit space.
Shot periodization
The shot occurs in a very short period of time (0.001-0.06 s.). When fired, four consecutive periods are distinguished:
- preliminary;
- first, or main;
- second;
- the third, or period of the last gases.
Preliminary period lasts from the beginning of the burning of the powder charge to the complete cutting of the shell of the bullet into the rifling of the barrel. During this period, the gas pressure is created in the barrel bore, which is necessary in order to move the bullet from its place and overcome the resistance of its shell to cutting into the rifling of the barrel. This pressure is called boost pressure; it reaches 250 - 500 kg / cm 2, depending on the rifling device, the weight of the bullet and the hardness of its shell (for example, for small arms chambered for the 1943 sample, the forcing pressure is about 300 kg / cm 2). It is assumed that the combustion of the powder charge in this period occurs in a constant volume, the shell cuts into the rifling instantly, and the movement of the bullet begins immediately when the forcing pressure is reached in the bore.
First or main period lasts from the beginning of the movement of the bullet to the moment complete combustion powder charge. During this period, the combustion of the powder charge occurs in a rapidly changing volume. At the beginning of the period, when the speed of the bullet along the bore is still low, the amount of gases grows faster than the volume of the bullet space (the space between the bottom of the bullet and the bottom of the case), the gas pressure rises rapidly and reaches largest(for example, for small arms chambered for a sample of 1943 - 2800 kg / cm 2, and for a rifle cartridge 2900 kg / cm 2). This pressure is called maximum pressure. It is created in small arms when a bullet travels 4 - 6 cm of the path. Then due to fast speed movement of the bullet, the volume of the bullet space increases faster than the influx of new gases, and the pressure begins to fall, by the end of the period it is equal to approximately 2/3 of the maximum pressure. The speed of the bullet is constantly increasing and by the end of the period reaches approximately 3/4 of the initial speed. The powder charge completely burns out shortly before the bullet leaves the bore.
Second period lasts until the moment of complete combustion of the powder charge until the moment the bullet leaves the bore. With the beginning of this period, the influx of powder gases stops, however, highly compressed and heated gases expand and, putting pressure on the bullet, increase its speed. The pressure drop in the second period occurs quite quickly and at the muzzle, the muzzle pressure is 300 - 900 kg / cm 2 for various types of weapons (for example, for the Simonov self-loading carbine - 390 kg / cm 2, for the Goryunov easel machine gun - 570 kg / cm 2 ). The speed of the bullet at the time of its departure from the bore (muzzle velocity) is somewhat less than the initial velocity.
To successfully master the technique of shooting from any small arms, it is necessary to master the knowledge of the laws of ballistics and a number of basic concepts related to it. Not a single sniper could and does not do without this, and without studying this discipline, a sniping training course is of little use.
Ballistics is the science of the movement of bullets and projectiles fired from small arms when fired. Ballistics is subdivided into external and internal.
Internal ballistics
Internal ballistics studies the processes occurring in the bore of a weapon during a shot, the movement of a bullet along the bore and the aero- and thermodynamic dependences accompanying this phenomenon both in the bore and outside it until the end of the aftereffect of powder gases.
In addition, internal ballistics studies the issues of the most rational use the energy of the powder charge during the shot so that the bullet of a given caliber and weight is given the optimal initial speed while respecting the strength of the weapon barrel: this provides initial data for both external ballistics and weapon design.
Shot
Shot- this is the ejection of a bullet from the bore of a weapon under the influence of the energy of gases formed during the combustion of the powder charge of the cartridge.
Shot dynamics. When the striker hits the primer of a live cartridge sent into the chamber, the percussion composition of the primer explodes, and a flame is formed, which is transmitted through the seed holes in the bottom of the sleeve to the powder charge and ignites it. With the simultaneous combustion of a combat (powder) charge, a large amount of heated powder gases are formed, which create high pressure on the bottom of the bullet, the bottom and walls of the sleeve, as well as on the walls of the bore and the bolt.
Under strong pressure of powder gases on the bottom of the bullet, it is separated from the cartridge case and crashes into the channels (rifling) of the weapon barrel and, rotating along them at a constantly increasing speed, is thrown outward in the direction of the axis of the barrel bore.
In turn, the pressure of gases on the bottom of the sleeve causes the movement of the weapon (the barrel of the weapon) back: this phenomenon is called bestowal. The larger the caliber of the weapon and, accordingly, the ammunition (cartridge) for it, the greater the recoil force (see below).
When fired from automatic weapons, the principle of operation of which is based on the use of powder gases energy removed through a hole in the barrel wall, as, for example, in SVD, part of the powder gases, after passing into the gas chamber, hits the piston and throws the pusher with the shutter back.
The shot occurs in an ultra-short period of time: from 0.001 to 0.06 seconds and is divided into four consecutive periods:
- preliminary
- first (main)
- second
- third (aftereffect period of powder gases)
Pre-shot period. It lasts from the moment the powder charge of the cartridge ignites until the moment the bullet completely cuts into the rifling of the barrel bore. During this period, sufficient gas pressure is created in the bore to move the bullet from its place and overcome the resistance of its shell to cutting into the rifling of the bore. This type of pressure is called boost pressure, which reaches a value of 250 - 600 kg / cm², depending on the weight of the bullet, the hardness of its shell, caliber, barrel type, number and type of rifling.
First (main) shot period. It lasts from the moment the bullet begins to move along the bore of the weapon until the moment of complete combustion of the powder charge of the cartridge. During this period, the combustion of the powder charge occurs in rapidly changing volumes: at the beginning of the period, when the speed of the bullet along the bore is still relatively low, the amount of gases grows faster than the volume of the bullet space (the space between the bottom of the bullet and the bottom of the cartridge case), the gas pressure rapidly rises and reaches its maximum value - 2900 kg / cm² for a 7.62 mm rifle cartridge: this pressure is called maximum pressure. It is created in small arms when a bullet travels 4 - 6 cm of the path.
Then, due to a very rapid increase in the speed of the bullet, the volume of the bullet space increases faster than the influx of new gases, as a result of which the pressure begins to fall: by the end of the period it is equal to approximately 2/3 of the maximum pressure. The speed of the bullet is constantly increasing and by the end of the period reaches approximately 3/4 of the initial speed. The powder charge completely burns out shortly before the bullet leaves the bore.
Second shot period. It lasts from the moment of complete combustion of the powder charge until the moment the bullet leaves the barrel. With the beginning of this period, the influx of powder gases stops, but highly heated, compressed gases expand and, putting pressure on the bullet, significantly increase its speed. The pressure drop in the second period occurs quite quickly and the muzzle pressure at the muzzle of the weapon barrel is 300 - 1000 kg / cm² for various types of weapons. muzzle velocity, that is, the speed of the bullet at the time of its departure from the bore is slightly less than the initial speed.
The third period of the shot (the period of aftereffect of powder gases). It lasts from the moment the bullet leaves the bore of the weapon until the moment the action of the powder gases on the bullet ceases. During this period, powder gases flowing out of the bore at a speed of 1200-2000 m/s continue to act on the bullet and impart additional speed to it. Max Speed the bullet reaches at the end of the third period at a distance of several tens of centimeters from the muzzle of the weapon barrel. This period ends at the moment when the pressure of the powder gases at the bottom of the bullet is fully balanced by the air resistance.
muzzle velocity
muzzle velocity- this is the speed of the bullet at the muzzle of the barrel of the weapon. For the value of the initial speed of the bullet, the conditional speed is taken, which is less than the maximum, but more than the muzzle, which is determined empirically and by the corresponding calculations.
This option is one of the most important characteristics combat properties of weapons. The value of the initial velocity of the bullet is indicated in the firing tables and in the combat characteristics of the weapon. With an increase in the initial speed, the range of the bullet, the range of a direct shot, the lethal and penetrating effect of the bullet increases, and the influence of external conditions on its flight also decreases. The muzzle velocity of a bullet depends on:
- bullet weight
- barrel length
- temperature, weight and humidity of the powder charge
- sizes and shapes of powder grains
- loading density
Bullet weight. The smaller it is, the greater its initial speed.
Barrel length. The larger it is, the longer the period of time the powder gases act on the bullet, respectively, the greater its initial speed.
Powder charge temperature. With a decrease in temperature, the initial velocity of the bullet decreases, with an increase, it increases due to an increase in the burning speed of the gunpowder and the pressure value. Under normal weather conditions, the temperature of the powder charge is approximately equal to the air temperature.
Powder charge weight. How more weight powder charge of the cartridge, the greater the amount of powder gases acting on the bullet, the greater the pressure in the bore and, accordingly, the speed of the bullet.
Powder charge moisture content. With its increase, the burning rate of gunpowder decreases, respectively, the speed of the bullet decreases.
The size and shape of the grains of gunpowder. Gunpowder grains of various sizes and shapes have different speed combustion, and this has a significant impact on the initial velocity of the bullet. The best option is selected at the stage of weapon development and during its subsequent tests.
Loading density. This is the ratio of the weight of the powder charge to the volume of the cartridge case with the bullet inserted: this space is called charge combustion chamber. If the bullet is too deep into the cartridge case, the loading density increases significantly: when fired, this can lead to a rupture of the weapon barrel due to a sharp pressure surge inside it, therefore such cartridges cannot be used for firing. The greater the loading density, the lower the muzzle velocity, the lower the loading density, the greater the muzzle velocity.
recoil
recoil- This is the movement of the weapon back at the time of the shot. It is felt as a push in the shoulder, arm, ground, or a combination of these sensations. The recoil action of the weapon is about as many times less than the initial velocity of the bullet, how 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 by the shooter painlessly.
The recoil force and the recoil resistance force (butt stop) are not located on the same straight line: they are directed in opposite directions and form a pair of forces, under the influence of which the muzzle of the weapon barrel deviates upward. The amount of deflection of the muzzle of the barrel this weapon the more than more shoulder this pair of forces. In addition, when fired, the barrel of the weapon vibrates, that is, it makes oscillatory movements. As a result of vibration, the muzzle of the barrel at the moment the bullet takes off can also deviate from its original position in any direction (up, down, left, right).
It should always be remembered that the value of this deviation increases if the firing stop is used incorrectly, the weapon is contaminated, or non-standard cartridges are used.
The combination of the influence of barrel vibration, weapon recoil and other causes leads to the formation of an angle between the direction of the axis of the bore before the shot and its direction at the moment the bullet leaves the bore: this angle is called departure angle.
Departure angle it is considered positive if the axis of the bore at the time of the bullet's departure is higher than its position before the shot, negative - when it is lower. The influence of the departure angle on shooting is eliminated when it is brought to normal combat. But in case of violation of the rules for caring for a weapon and its conservation, the rules for applying a weapon, using an emphasis, the value of the angle of departure and the battle of the weapon change. In order to reduce the harmful effect of recoil on the results of shooting, recoil compensators are used, located on the muzzle of the weapon barrel or removable, attached to it.
External ballistics
External ballistics studies the processes and phenomena accompanying the movement of a bullet that occur after the effect of powder gases on it stops. The main task of this sub-discipline is to study the patterns of bullet flight and the study of the properties of the trajectory of its flight.
Also, this discipline provides data for developing shooting rules, compiling shooting tables and calculating weapon sight scales. Conclusions from external ballistics have long been widely used in combat when choosing a sight and aiming point depending on the firing range, wind speed and direction, air temperature and other firing conditions.
This is the curved line described by the bullet's center of gravity during flight.
Bullet flight path, bullet flight in space
When flying in space, two forces act on a bullet: gravity and air resistance force.
The force of gravity causes the bullet to gradually descend horizontally towards the plane of the ground, and the force of air resistance permanently (continuously) slows down the flight of the bullet and tends to overturn it: as a result, the speed of the bullet gradually decreases, and its trajectory is an unevenly curved curved line in shape.
Air resistance to the flight of a bullet is caused by the fact that air is elastic medium and therefore some part of the energy of the bullet is expended on movement in this medium.
Force of air resistance caused by three main factors:
- air friction
- swirls
- ballistic wave
Shape, properties and types of toolpath
Trajectory shape depends on the elevation angle. As the elevation angle increases, the trajectory height and total horizontal range of the bullet increase, but this happens up to a certain limit, after which the trajectory height continues to increase, and the total horizontal range begins to decrease.
The angle of elevation at which the full horizontal range of the bullet is greatest is called farthest angle. The value of the angle of greatest range for bullets of various types of weapons is about 35 °.
Hinged trajectory is the trajectory obtained at elevation angles greater than the angle of greatest range.
Flat trajectory- trajectory obtained at elevation angles smaller than the angle of greatest range.
Conjugate trajectory- a trajectory having the same horizontal range at different elevation angles.
When firing from weapons of the same model (with the same initial speeds bullets), you can get two flight paths with the same horizontal range: hinged and flat.
When shooting from small arms, only flat trajectories. The flatter the trajectory, the greater the distance the target can be hit with one sight setting and the less impact on the results of shooting has an error in determining the sight setting: this is practical value trajectories.
The flatness of the trajectory is characterized by its greatest excess over the aiming line. At a given range, the trajectory is all the more flat, the less it rises above the aiming line. In addition, the flatness of the trajectory can be judged by angle of incidence: the trajectory is more flat, the smaller the angle of incidence.
The flatness of the trajectory affects the value of the range of a direct shot, struck, covered and dead space.
Departure point- the center of the muzzle of the barrel of the weapon. The departure point is the start of the trajectory.
Weapon horizon is the horizontal plane passing through the departure point.
elevation line- a straight line that is a continuation of the axis of the bore of the aimed weapon.
Shooting plane- a vertical plane passing through the line of elevation.
Elevation angle- the angle enclosed between the line of elevation and the horizon of the weapon. If this angle is negative, then it is called angle of declination (descent).
Throw line- a straight line, which is a continuation of the axis of the bore at the time of the bullet's departure.
Throwing angle
Departure angle- the angle enclosed between the line of elevation and the line of throwing.
drop point- the point of intersection of the trajectory with the horizon of the weapon.
Angle of incidence- the angle enclosed between the tangent to the trajectory at the point of impact and the horizon of the weapon.
Total horizontal range- the distance from the point of departure to the point of fall.
Final speed b is the speed of the bullet at the point of impact.
Total flight time- the time of movement of the bullet from the point of departure to the point of impact.
Top of the path- the highest point of the trajectory above the horizon of the weapon.
Trajectory height- the shortest distance from the top of the trajectory to the horizon of the weapon.
Ascending branch of the trajectory- part of the trajectory from the departure point to the top.
Descending branch of the trajectory- part of the trajectory from the top to the point of fall.
Aiming point (sighting point)- the point on the target (outside it) at which the weapon is aimed.
line of sight- a straight line passing from the shooter's eye through the middle of the sight slot at a level with its edges and the top of the front sight to the aiming point.
aiming angle- the angle enclosed between the line of elevation and the line of sight.
Target elevation angle- the angle enclosed between the aiming line and the horizon of the weapon. This angle is considered positive (+) when the target is higher and negative (-) when the target is below the weapon's horizon.
Sighting range- distance from the departure point to the intersection of the trajectory with the line of sight. The excess of the trajectory over the line of sight is the shortest distance from any point of the trajectory to the line of sight.
target line- a straight line connecting the departure point with the target.
Slant Range- distance from the departure point to the target along the target line.
meeting point- point of intersection of the trajectory with the surface of the target (ground, obstacles).
Meeting angle- the angle enclosed between the tangent to the trajectory and the tangent to the target surface (ground, obstacles) at the meeting point. The smaller of the adjacent angles, measured from 0 to 90°, is taken as the meeting angle.
Direct shot, covered area, hit area, dead space
This is a shot in which the trajectory does not rise above the line of sight above the target for its entire length.
Direct shot range depends on two factors: the height of the target and the flatness of the trajectory. The higher the target and the flatter the trajectory, the greater the range of a direct shot and the greater the extent of the terrain, the target can be hit with one sight setting.
Also, the range of a direct shot can be determined from shooting tables by comparing the height of the target with the values of the greatest excess of the trajectory above the aiming line or with the height of the trajectory.
Within the range of a direct shot, in tense moments of the battle, shooting can be carried out without rearranging the sight values, while the aiming point in height, as a rule, is selected at the lower edge of the target.
Practical use
The installation height of optical sights above the bore of the weapon is on average 7 cm. At a distance of 200 meters and the 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 line of sight - optical axis of the optical sight. Line of sight height at the middle of the distance of 200 meters is 3.5 cm. There is a practical coincidence of the trajectory of the bullet and the line of sight. A difference of 1.5 cm can be neglected. At a distance of 150 meters, the height of the trajectory is 4 cm, and the height of the optical axis of the sight above the horizon of the weapon is 17-18 mm; the difference in height is 3 cm, which also does not play a practical role.
At a distance of 80 meters from the shooter bullet trajectory height will be 3 cm, and aiming line height- 5 cm, the same difference of 2 cm is not decisive. The bullet will fall only 2 cm below the aiming point.
The vertical spread of bullets of 2 cm is so small that it is of no fundamental importance. Therefore, when shooting with division "2" of the optical sight, starting from 80 meters of distance and up to 200 meters, aim at the bridge of the nose of the enemy - you will get there and get ± 2/3 cm higher lower throughout this distance.
At a distance of 200 meters, the bullet will hit exactly the aiming point. And even further, at a distance of up to 250 meters, aim with the same sight "2" at the enemy's "top", at the upper cut of the cap - the bullet drops sharply after 200 meters of distance. At 250 meters, aiming in this way, you will fall 11 cm lower - in the forehead or bridge of the nose.
The above method of firing can be useful in street battles, when relatively open distances in the city are approximately 150-250 meters.
Affected space
Affected space is the distance on the ground during which the descending branch of the trajectory does not exceed the height of the target.
When shooting at targets located at a distance greater than the range of a direct shot, 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 such a space (distance) near the target in which the trajectory does not rise above the target and the target will be hit by it.
Depth of affected space depends on:
- target height (the higher the height, the greater the value)
- flatness of the trajectory (the flatter the trajectory, the greater the value)
- the angle of inclination of the terrain (on the front slope it decreases, on the reverse slope it increases)
Depth of affected area can be determined from the tables of the excess of the trajectory above the aiming line by comparing the excess of the descending branch of the trajectory by the corresponding firing range with the height of the target, 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 space on sloping terrain the firing position must be chosen so that the terrain in the enemy's disposition coincides, if possible, with the aiming line.
Covered, affected and dead space
covered space- this is the space behind the shelter that is not penetrated by a bullet, from its crest to the meeting point.
The greater the height of the shelter and the flatter the trajectory, the greater the covered space. Depth of covered area can be determined from the tables of the excess of the trajectory 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 setting of the sight and the firing range are determined.
The difference between a certain range of fire and the range to cover is the depth of the covered space.
Dead space- this is the part of the covered space in which the target cannot be hit with a given trajectory.
The greater the height of the shelter, the lower the height of the target and the flatter the trajectory - the greater the dead space.
Pimaginable space- this is the part of the covered area in which the target can be hit. 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, dead space allows you to correctly use shelters to protect against enemy fire, as well as take measures to reduce dead spaces through right choice firing positions and firing at targets with weapons with a more trajectory.
This is a rather complicated process. Due to the simultaneous impact on the bullet of rotational motion, 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 more air resistance on one of its sides, and therefore deviates from the firing plane more and more in the direction of rotation. Such a deviation of a rotating bullet away from the plane of fire is called derivation.
It increases disproportionately to the flight distance of the bullet, as a result of which the latter deviates more and more to the side of the intended target and its trajectory is a curved line. The direction of the bullet deflection depends on the direction of the rifling of the barrel of the weapon: with left-sided rifling of the barrel, the derivation takes the bullet into left side, with right-handed - to the right.
At firing distances up to 300 meters inclusive, derivation has no practical significance.
| Distance, m | Derivation, cm | Thousandths (horizontal adjustment of the sight) | Aiming point without corrections (SVD rifle) |
| 100 | 0 | 0 | sight center |
| 200 | 1 | 0 | Same |
| 300 | 2 | 0,1 | Same |
| 400 | 4 | 0,1 | left (from the shooter) eye of the enemy |
| 500 | 7 | 0,1 | on the left side of the head between the eye and ear |
| 600 | 12 | 0,2 | left side of the enemy's head |
| 700 | 19 | 0,2 | over the center of the epaulette on the opponent's shoulder |
| 800 | 29 | 0,3 | without corrections, accurate shooting is not performed |
| 900 | 43 | 0,5 | Same |
| 1000 | 62 | 0,6 | Same |
trajectory called the curved line described by the center of gravity of the bullet in flight.
Rice. 3. Trajectory
Rice. 4. Bullet trajectory parameters
A bullet flying through the air is subjected to two forces: gravity and air resistance. The force of gravity causes the bullet to gradually descend, and the force of air resistance continuously slows down the movement of the bullet and tends to knock it over.
As a result of the action of these forces, the bullet's flight speed gradually decreases, and its trajectory is an unevenly curved curved line in shape.
| Parameter trajectories |
Parameter characteristic | Note |
| Departure point | Center of muzzle | The departure point is the start of the trajectory |
| Weapon horizon | Horizontal plane passing through the departure point | The horizon of the weapon looks like a horizontal line. The trajectory crosses the horizon of the weapon twice: at the point of departure and at the point of impact |
| elevation line | A straight line that is a continuation of the axis of the bore of the aimed weapon | |
| Shooting plane | The vertical plane passing through the line of elevation | |
| Elevation angle | The angle enclosed between the line of elevation and the horizon of the weapon | If this angle is negative, then it is called the angle of declination (decrease) |
| Throw line | Straight line, a line that is a continuation of the axis of the bore at the time of the bullet's departure | |
| Throwing angle | The angle enclosed between the line of throw and the horizon of the weapon | |
| Departure angle | The angle enclosed between the line of elevation and the line of throw | |
| drop point | Point of intersection of the trajectory with the horizon of the weapon | |
| Angle of incidence | The angle enclosed between the tangent to the trajectory at the point of impact and the horizon of the weapon | |
| Total horizontal range | Distance from departure point to drop point | |
| Ultimate speed | Bullet speed at point of impact | |
| Total flight time | The time it takes for a bullet to travel from point of departure to point of impact | |
| Top of the path | The highest point of the trajectory | |
| Trajectory height | The shortest distance from the top of the trajectory to the horizon of the weapon | |
| Ascending branch | Part of the trajectory from the departure point to the summit | |
| descending branch | Part of the trajectory from the top to the point of impact | |
| Aiming point (aiming) | The point on or off the target at which the weapon is aimed | |
| line of sight | A straight line from the shooter's eye through the middle of the sight slot (level with its edges) and the top of the front sight to the aiming point | |
| aiming angle | The angle enclosed between the line of elevation and the line of sight | |
| Target elevation angle | The angle enclosed between the line of sight and the horizon of the weapon | The target's elevation angle is considered positive (+) when the target is above the weapon's horizon, and negative (-) when the target is below the weapon's horizon. |
| Sighting range | Distance from the point of departure to the intersection of the trajectory with the line of sight | |
| Exceeding the trajectory above the line of sight | The shortest distance from any point of the trajectory to the line of sight | |
| target line | A straight line connecting the departure point with the target | When firing direct fire, the target line practically coincides with the aiming line |
| Slant Range | Distance from point of origin to target along target line | When firing direct fire, the slant range practically coincides with the aiming range. |
| meeting point | Intersection point of the trajectory with the target surface (ground, obstacles) | |
| Meeting angle | The angle enclosed between the tangent to the trajectory and the tangent to the target surface (ground, obstacles) at the meeting point | The smaller of the adjacent angles, measured from 0 to 90°, is taken as the meeting angle. |
| Sighting line | A straight line connecting the middle of the sight slot to the top of the front sight | |
| Aiming (pointing) | Giving the axis of the bore of the weapon the position in space necessary for firing | In order for the bullet to reach the target and hit it or the desired point on it |
| Horizontal aiming | Giving the axis of the bore the desired position in the horizontal plane | |
| vertical guidance | Giving the axis of the bore the desired position in the vertical plane |
The trajectory of a bullet in the air has the following properties:
- the descending branch is shorter and steeper than the ascending one;
- the angle of incidence is greater than the angle of throw;
- the final speed of the bullet is less than the initial one;
- the lowest speed of the bullet when firing at high angles of throw - on the descending branch of the trajectory, and when firing at small angles of throw - at the point of impact;
- the time of movement of the bullet along the ascending branch of the trajectory is less than along the descending one;
- the trajectory of a rotating bullet due to the lowering of the bullet under the action of gravity and derivation is a line of double curvature.
Types of trajectories and their practical significance.
When firing from any type of weapon with an increase in the elevation angle from 0° to 90°, the horizontal range first increases to a certain limit, and then decreases to zero (Fig. 5).
The angle of elevation at which longest range, is called farthest angle. The value of the angle of greatest range for bullets of various types of weapons is about 35 °.
The angle of greatest range divides all trajectories into two types: on trajectories flooring and hinged(Fig. 6).
Rice. 5. The affected area and the largest horizontal and aiming ranges when shooting at different elevation angles. 
Rice. 6. Angle of greatest range. flat, hinged and conjugate trajectories Flat trajectories call the trajectories obtained at elevation angles smaller than the angle of greatest range (see figure, trajectories 1 and 2).
Hinged trajectories call the trajectories obtained at elevation angles greater than the angle of greatest range (see figure, trajectories 3 and 4).
Conjugate trajectories are called trajectories obtained with the same horizontal range two trajectories, one of which is flat, the other is hinged (see Fig. trajectories 2 and 3).
When firing from small arms and grenade launchers, only flat trajectories are used. The flatter the trajectory, the greater the extent of the terrain, the target can be hit with one sight setting (the less impact on the shooting results is the error in determining the sight setting): this is the practical significance of the trajectory.
The flatness of the trajectory is characterized by its greatest excess over the aiming line. At a given range, the trajectory is all the more flat, the less it rises above the aiming line. In addition, the flatness of the trajectory can be judged by the magnitude of the angle of incidence: the trajectory is the more flat, the smaller the angle of incidence. The flatness of the trajectory affects the value of the range of a direct shot, struck, covered and dead space.
Read full synopsisRice. 1. Artillery battleship"Marat"
Ballistics(from the Greek βάλλειν - to throw) - the science of the movement of bodies thrown in space, based on mathematics and physics. It deals mainly with the study of the movement of projectiles fired from firearms, rocket projectiles and ballistic missiles.
Basic concepts
Rice. 2. Elements of firing naval artillery
The main objective of shooting is to hit the target. To do this, the tool must be given a strictly defined position in the vertical and horizontal planes. If we aim the gun so that the axis of the bore is directed at the target, then we will not hit the target, since the trajectory of the projectile will always pass below the direction of the axis of the bore, the projectile will not reach the target. To formalize the terminological apparatus of the subject under consideration, we introduce the main definitions used when considering the theory of artillery firing.
Departure point
called the center of the muzzle of the gun.
drop point
called the point of intersection of the trajectory with the horizon of the gun.
horizon guns
called the horizontal plane passing through the departure point.
Elevation line
called the continuation of the axis of the bore of the pointed gun.
Throwing line
OB is the continuation of the axis of the bore at the time of the shot. At the moment of the shot, the gun shudders, as a result of which the projectile is thrown not along the line of elevation of the OA, but along the line of throwing of the OV (see Fig. 2).
Goal line
OC is the line connecting the gun to the target (see Fig. 2).
Line of sight (sight)
called the line running from the gunner's eye through the optical axis of the sight to the aiming point. When firing direct fire, when the line of sight is directed at the target, the line of sight coincides with the line of the target.
Falling line is called the tangent to the trajectory at the point of incidence.
Rice. 3. Shooting at an overlying target
Rice. 4. Shooting at the underlying target
Elevation (greek phi)
called the angle between the line of elevation and the horizon of the gun. If the bore axis is directed below the horizon, then this angle is called the angle of descent (see Fig. 2).
The firing range of the gun depends on the elevation angle and firing conditions. Therefore, in order to throw the projectile to the target, it is necessary to give the gun such an elevation angle at which the firing range will correspond to the distance to the target. The firing tables indicate which aiming angles must be given to the gun in order for the projectile to fly to the desired range.
Throwing angle (Greek theta zero)
the angle between the line of throw and the horizon of the gun is called (see Fig. 2).
Departure angle (Greek gamma)
called the angle between the line of throw and the line of elevation. In naval artillery, the departure angle is small and is sometimes not taken into account, assuming that the projectile is thrown at an elevation angle (see Fig. 2).
Aiming angle (Greek alpha)
the angle between the line of elevation and the line of sight is called (see Fig. 2).
Target elevation angle (greek epsilon)
called the angle between the line of the target and the horizon of the gun. When a ship fires at sea targets, the elevation angle of the target is equal to zero, since the target line is directed along the horizon of the gun (see Fig. 2).
Incident angle (Greek theta s Latin letter with)
the angle between the target line and the fall line is called (see Fig. 2).
Meeting angle (Greek mu)
is the angle between the line of incidence and the tangent to the target surface at the meeting point (see Fig. 2).
The value of the value of this angle greatly affects the resistance of the armor of the ship, which is fired at, to penetration by shells. Obviously, the closer this angle is to 90 degrees, the higher the probability of penetration, and the opposite is also true.
Shooting plane
called the vertical plane passing through the line of elevation. When the ship fires at sea targets, the aiming line is directed along the horizon, in this case the elevation angle equal to the angle aiming. When a ship fires at coastal and air targets, the elevation angle is equal to the sum of the aiming angle and the elevation angle of the target (see Fig. 3). When firing a coastal battery at sea targets, the elevation angle is equal to the difference between the aiming angle and the elevation angle of the target (see Fig. 4). Thus, the magnitude of the elevation angle is equal to the algebraic sum of the aiming angle and the elevation angle of the target. If the target is above the horizon, the target elevation angle is "+", if the target is below the horizon, the target elevation angle is "-".
The influence of air resistance on the trajectory of the projectile
Rice. 5. Changing the trajectory of the projectile from air resistance
The flight path of a projectile in airless space is a symmetrical curved line, called a parabola in mathematics. The ascending branch coincides in shape with the descending branch and, therefore, the angle of incidence is equal to the angle of elevation.
When flying in the air, the projectile spends part of its speed to overcome air resistance. Thus, two forces act on the projectile in flight - the force of gravity and the force of air resistance, which reduces the speed and range of the projectile, as illustrated in Fig. 5. The magnitude of the air resistance force depends on the shape of the projectile, its size, flight speed and air density. The longer and more pointed the head of the projectile, the less air resistance. The shape of the projectile is especially affected at flight speeds exceeding 330 meters per second (that is, at supersonic speeds).
Rice. 6. Short-range and long-range projectiles
On fig. 6, on the left, is a short-range, old-style projectile and a more oblong, pointed, long-range projectile on the right. It can also be seen that a long-range projectile has a conical narrowing at the bottom. The fact is that a rarefied space and turbulence are formed behind the projectile, which significantly increase air resistance. By narrowing the bottom of the projectile, a decrease in the amount of air resistance resulting from rarefaction and turbulence behind the projectile is achieved.
The force of air resistance is proportional to the speed of its flight, but not directly proportional. Dependence is formalized more difficult. Due to the action of air resistance, the ascending branch of the projectile's flight path is longer and delayed than the descending one. The angle of incidence is greater than the angle of elevation.
In addition to reducing the range of the projectile and changing the shape of the trajectory, the force of air resistance tends to overturn the projectile, as can be seen from Fig. 7.
Rice. 7. Forces acting on a projectile in flight
Therefore, a non-rotating elongated projectile will roll over under the action of air resistance. In this case, the projectile can hit the target in any position, including sideways or bottom, as shown in Fig. eight.
Rice. 8. Rotation of a projectile in flight under the influence of air resistance
So that the projectile does not roll over in flight, it is given a rotational motion with the help of rifling in the barrel bore.
If we consider the effect of air on a rotating projectile, we can see that this leads to a lateral deviation of the trajectory from the plane of fire, as shown in Fig. nine.
Rice. 9. Derivation
derivation called the deviation of the projectile from the plane of fire due to its rotation. If the rifling twists from left to right, then the projectile deflects to the right.
The influence of the angle of elevation and the initial velocity of the projectile on the range of its flight
The range of a projectile depends on the elevation angles at which it is thrown. An increase in the flight range with an increase in the elevation angle occurs only up to a certain limit (40-50 degrees), with a further increase in the elevation angle, the range begins to decrease.
Range limit angle
called the elevation angle at which the greatest firing range is obtained for a given initial velocity and projectile. When firing in an airless space, the greatest range of the projectile is obtained at an elevation angle of 45 degrees. When firing in the air, the maximum range angle differs from this value and is not the same for different guns (usually less than 45 degrees). For ultra-long-range artillery, when the projectile flies for a significant part of the path high altitude in highly rarefied air, the maximum range angle is more than 45 degrees.
For a gun of this type and when firing a certain type of ammunition, each elevation angle corresponds to a strictly defined range of the projectile. Therefore, in order to throw the projectile at the distance we need, it is necessary to give the gun an elevation angle corresponding to this distance.
The trajectories of projectiles fired at elevation angles smaller than the maximum range angle are called flat trajectories
.
The trajectories of projectiles fired at elevation angles greater than the maximum range angle are called " hinged trajectories" .
Projectile dispersion
Rice. 10. Dispersion of projectiles
If several shots are fired from the same gun, with the same ammunition, with the same direction of the gun barrel, under the same, at first glance, conditions, then the shells will not hit the same point, but will fly along different trajectories, forming a bundle of trajectories, as illustrated in fig. 10. This phenomenon is called projectile dispersion .
The reason for the dispersion of projectiles is the impossibility of achieving exactly the same conditions for each shot. The table shows the main factors that cause projectile dispersion and possible ways reduce this dispersion.
| The main groups of causes of dispersion | Conditions that give rise to the causes of dispersion | Control measures to reduce dispersion |
|---|---|---|
| 1. Variety of starting speeds |
(dimensions and location of the leading belt, sending shells).
|
|
| 2. Variety of throwing angles |
|
|
| 3. A variety of conditions in the flight of a projectile |
Variety of influence of the air environment (density, wind). |
The area on which projectiles fired from a gun with the same direction of the barrel bore fall is called scattering area
.
The middle of the scattering area is called midpoint of fall
.
An imaginary trajectory passing through the departure point and middle point fall is called average trajectory
.
The scattering area has the shape of an ellipse, so the scattering area is called scattering ellipse
.
The intensity with which projectiles hit different points of the dispersion ellipse is described by a two-dimensional Gaussian (normal) distribution law. From here, if we follow exactly the laws of probability theory, we can conclude that the scattering ellipse is an idealization. The percentage of shells hitting inside the ellipse is described by the three-sigma rule, namely, the probability of shells hitting the ellipse, the axis of which is equal to three times square root from the variances of the corresponding one-dimensional Gaussian distribution laws is 0.9973.
Due to the fact that the number of shots from one gun, especially large caliber, as already mentioned above, due to wear often does not exceed one thousand, this inaccuracy can be neglected and it can be assumed that all shells fall into the dispersion ellipse. Any section of a beam of projectile flight paths is also an ellipse. The dispersion of projectiles in range is always greater than in the lateral direction and in height. The value of the median deviations can be found in the main shooting table and the size of the ellipse can be determined from it.
Rice. 11. Shooting at a target with no depth
Affected space is the space over which the trajectory passes through the target.
According to fig. 11, the affected space is equal to the distance along the horizon AC from the base of the target to the end of the trajectory passing through the top of the target. Each projectile that fell outside the affected space either passed above the target or fell before it. The affected space is limited by two trajectories - the OA trajectory passing through the base of the target, and the OS trajectory passing through the top point of the target.
Rice. 12. Shooting at a target with depth
In case the target to be hit has depth, the amount of space to hit is increased by the value of the target's depth, as illustrated in Fig. 12. The depth of the target will depend on the size of the target and its position relative to the plane of fire. Consider the most likely target for naval artillery - an enemy ship. In such a case, if the target is coming from us or towards us, the depth of the target is equal to its length, when the target is perpendicular to the plane of fire, the depth is equal to the width of the target, as illustrated in the figure.
Given the fact that the scattering ellipse has great length and a small width, it can be concluded that at a shallow target depth, fewer projectiles hit the target than at a large depth. That is, than more depth target, the easier it is to hit. With an increase in the firing range, the affected target space decreases, as the angle of incidence increases.
Straight shot a shot is called, in which the entire distance from the point of departure to the point of impact is the affected space (see Fig. 13).
Rice. 13. Direct shot
This is obtained if the height of the trajectory does not exceed the height of the target. The range of a direct shot depends on the steepness of the trajectory and the height of the target.
Range of a direct shot (or range of flattening) called the distance at which the height of the trajectory does not exceed the height of the target.
The most important works on ballistics
17th century
- - Tartaglia theory,
- 1638- labor Galileo Galilei about the parabolic motion of a body thrown at an angle.
- 1641- a student of Galileo - Toricelli, developing the parabolic theory, derives an expression for horizontal range, which later formed the basis of artillery firing tables.
- 1687- Isaac Newton proves the influence of air resistance on a thrown body, introducing the concept of the shape factor of the body, and also drawing a direct dependence of the movement resistance on the cross section (caliber) of the body (projectile).
- 1690— Ivan Bernoulli mathematically describes main task ballistics, solving the problem of determining the motion of a ball in a resisting medium.
18th century
- 1737- Bigot de Morogues (1706-1781) published a theoretical study of internal ballistics, which laid the foundation for the rational design of guns.
- 1740- the Englishman Robins learned to determine the initial speeds of the projectile and proved that the projectile flight parabola has a double curvature - its descending branch is shorter than the ascending one, in addition, he empirically concluded that the air resistance to the flight of projectiles at initial speeds above 330 m / s increases abruptly and should calculated using a different formula.
- Second half of the 18th century
- Daniel Bernoulli deals with the issue of air resistance to the movement of projectiles;
- mathematician Leonhard Euler develops the work of Robins, Euler's work on the internal and external ballistics form the basis for the creation of artillery firing tables.
- Mordashev Yu. N., Abramovich I. E., Mekkel M. A. Textbook of deck artillery commander. M.: Military publishing house of the Ministry armed forces Union of the SSR. 1947. 176 p.