Bullet trajectory and its elements. Trajectory properties. Types of trajectory and their practical significance. Information on ballistics: internal and external ballistics. wound ballistics Bullet trajectory elements
Ballistics studies the throwing of a projectile (bullet) from a barreled weapon. Ballistics is divided into internal, which studies the phenomena occurring in the barrel at the time of the shot, and external, which explains the behavior of the bullet after leaving the barrel.
Fundamentals of external ballistics
Knowledge of external ballistics (hereinafter referred to as ballistics) allows the shooter even before the shot with sufficient practical application know exactly where the bullet will hit. The accuracy of a shot is influenced by a lot of interrelated factors: the dynamic interaction of parts and parts of the weapon between themselves and the body of the shooter, gas and bullets, bullets with bore walls, bullets with environment after departure from the trunk and much more.
After leaving the barrel, the bullet does not fly in a straight line, but along the so-called ballistic trajectory close to a parabola. Sometimes at short shooting distances, the deviation of the trajectory from a straight line can be neglected, but at large and extreme shooting distances (which is typical for hunting), knowledge of the laws of ballistics is absolutely necessary.
Note that air guns usually give a light bullet a low or medium speed (from 100 to 380 m / s), so the curvature of the trajectory of the bullet from different influences greater than for firearms.
|
|
There are two main forces acting on a bullet that has flown out of the barrel at a certain speed in flight: gravity and air resistance force. The action of gravity is directed downward, it causes the bullet to descend continuously. The action of the air resistance force is directed towards the movement of the bullet, it causes the bullet to continuously reduce its flight speed. All this leads to a downward deviation of the trajectory.
To increase the stability of the bullet in flight on the surface of the bore rifled weapons there are spiral grooves (rifling) that give the bullet rotary motion and thereby prevent it from tumbling in flight.
Due to the rotation of the bullet in flight
Due to the rotation of the bullet in flight, the force of air resistance acts unevenly on different parts of the bullet. As a result, the bullet encounters more air resistance on one of the sides and in flight deviates more and more from the plane of fire in the direction of its rotation. This phenomenon is called derivation. The action of derivation is uneven and intensifies towards the end of the trajectory.
Powerful air rifles can give the bullet an initial velocity higher than the sound one (up to 360-380 m/s). The speed of sound in air is not constant (it depends on atmospheric conditions, height above sea level, etc.), but it can be taken equal to 330-335 m/s. Light bullets for pneumatics with small transverse load experience strong perturbations and deviate from their trajectory, overcoming sound barrier. Therefore, it is advisable to shoot heavier bullets with an initial velocity approaching to the speed of sound.
The trajectory of a bullet is also affected by weather conditions - wind, temperature, humidity and air pressure.
The wind is considered weak at its speed of 2 m/s, medium (moderate) - at 4 m/s, strong - at 8 m/s. Side moderate wind, acting at an angle of 90° to the trajectory, already has a very significant effect on a light and "low-velocity" bullet fired from an airgun. The impact of a wind of the same strength, but blowing at an acute angle to the trajectory - 45 ° or less - causes half the deflection of the bullet.
The wind blowing along the trajectory in one direction or another slows down or speeds up the speed of the bullet, which must be taken into account when shooting at a moving target. When hunting, the wind speed can be estimated with acceptable accuracy using a handkerchief: if you take a handkerchief by two corners, then with a light wind it will sway slightly, with a moderate one it will deviate by 45 °, and with a strong one it will develop horizontally to the surface of the earth.
Normal weather conditions are: air temperature - plus 15 ° C, humidity - 50%, pressure - 750 mm Hg. An excess of air temperature above normal leads to an increase in the trajectory at the same distance, and a decrease in temperature leads to a decrease in the trajectory. High humidity leads to a decrease in the trajectory, and low humidity leads to an increase in the trajectory. Recall that atmospheric pressure varies not only from the weather, but also from the height above sea level - the higher the pressure, the lower the trajectory.
Each "long-range" weapon and ammunition has its own correction tables, which allow taking into account the influence of weather conditions, derivation, relative position of the shooter and target in height, bullet speed and other factors on the bullet's flight path. Unfortunately, such tables are not published for pneumatic weapons, therefore, lovers of shooting at extreme distances or at small targets are forced to compile such tables themselves - their completeness and accuracy are the key to success in hunting or competitions.
When evaluating the results of firing, it must be remembered that from the moment of firing until the end of its flight, some random (not taken into account) factors act on the bullet, which leads to small deviations in the trajectory of the bullet from shot to shot. Therefore, even under "ideal" conditions (for example, when the weapon is rigidly fixed in the machine, constancy external conditions etc.) bullet hits on the target look like an oval, thickening towards the center. Such random deviations are called deviation. The formula for its calculation is given below in this section.
And now consider the trajectory of the bullet and its elements (see Figure 1).
The straight line representing the continuation of the axis of the bore before the shot is called the shot line. The straight line, which is a continuation of the axis of the barrel when the bullet leaves it, is called the line of throw. Due to the vibrations of the barrel, its position at the time of the shot and at the moment the bullet leaves the barrel will differ by the angle of departure.
As a result of the action of gravity and air resistance, the bullet does not fly along the line of throw, but along an unevenly curved curve passing below the line of throw.
The start of the trajectory is the departure point. The horizontal plane passing through the departure point is called the weapon's horizon. The vertical plane passing through the point of departure along the line of throw is called the shooting plane.
To throw a bullet to any point on the horizon of the weapon, it is necessary to direct the throwing line above the horizon. The angle formed by the line of fire and the horizon of the weapon is called the angle of elevation. The angle formed by the line of throw and the horizon of the weapon is called the angle of throw.
The point of intersection of the trajectory with the horizon of the weapon is called the (table) point of incidence. The horizontal distance from the departure point to the (table) drop point is called the horizontal range. The angle between the tangent to the trajectory at the point of impact and the horizon of the weapon is called the (table) angle of incidence.
The highest point of the trajectory above the weapon's horizon is called the trajectory apex, and the distance from the weapon's horizon to the trajectory's apex is called the trajectory height. The top of the trajectory divides the trajectory into two unequal parts: the ascending branch is longer and gentler and the descending branch is shorter and steeper.
Considering the position of the target relative to the shooter, three situations can be distinguished:
Shooter and target are on the same level.
- the shooter is located below the target (shoots up at an angle).
- the shooter is located above the target (shoots down at an angle).
In order to direct the bullet to the target, it is necessary to give the axis of the bore a certain position in the vertical and horizontal plane. Giving the desired direction to the axis of the bore in the horizontal plane is called horizontal pickup, and giving direction in the vertical plane is called vertical pickup.
Vertical and horizontal aiming is carried out using sighting devices. Mechanical sights rifled weapons consist of a front sight and a rear sight (or diopter).
The straight line connecting the middle of the slot in the rear sight with the top of the front sight is called the aiming line.
tip small arms using sighting devices not from the horizon of the weapon, but relative to the location of the target. In this regard, the elements of pickup and trajectory receive the following designations (see Figure 2).
The point at which the weapon is aimed is called the aiming point. The straight line connecting the shooter's eye, the middle of the rear sight slot, the top of the front sight and the aiming point is called the aiming line.
The angle formed by the aiming line and the shooting line is called the aiming angle. This aiming angle is obtained by setting the slot of the sight (or front sight) in height corresponding to the firing range.
The point of intersection of the descending branch of the trajectory with the line of sight is called the point of incidence. The distance from the point of departure to the point of impact is called the target range. The angle between the tangent to the trajectory at the point of incidence and the line of sight is called the angle of incidence.
When positioning weapons and targets at the same height the aiming line coincides with the horizon of the weapon, and the aiming angle coincides with the elevation angle. When positioning the target above or below the horizon weapon between the aiming line and the horizon line, the elevation angle of the target is formed. The elevation angle of the target is considered positive if the target is above the weapon's horizon and negative if the target is below the weapon's horizon.
The elevation angle of the target and the aiming angle together make up the elevation angle. With a negative elevation angle of the target, the line of fire can be directed below the horizon of the weapon; in this case, the elevation angle becomes negative and is called the declination angle.
At its end, the trajectory of the bullet intersects either with the target (obstacle) or with the surface of the earth. The point of intersection of the trajectory with the target (obstacle) or the surface of the earth is called the meeting point. The possibility of ricochet depends on the angle at which the bullet hits the target (obstacle) or the ground, their mechanical characteristics, and the material of the bullet. The distance from the departure point to the rendezvous point is called the actual range. A shot in which the trajectory does not rise above the line of sight above the target throughout effective range, is called a direct shot.
From the foregoing, it is clear that before practical shooting the weapon must be shot (otherwise it must be brought to a normal battle). Zeroing should be carried out with the same ammunition and under the same conditions that will be typical for subsequent firing. Be sure to take into account the size of the target, the shooting position (lying, kneeling, standing, from unstable positions), even the thickness of clothing (when zeroing in a rifle).
The line of sight, passing from the shooter's eye through the top of the front sight, the top edge of the rear sight and the target, is a straight line, while the trajectory of the bullet's flight is an unevenly curved downward line. The line of sight is located 2-3 cm above the barrel in the case of an open sight and much higher in the case of an optical one.
In the simplest case, if the line of sight is horizontal, the trajectory of the bullet crosses the line of sight twice: on the ascending and descending parts of the trajectory. The weapon is usually zeroed (adjusted sights) at a horizontal distance at which the descending part of the trajectory intersects the line of sight.
It may seem that there are only two distances to the target - where the trajectory crosses the line of sight - at which a hit is guaranteed. So sports shooting fired at a fixed distance of 10 meters, at which the trajectory of the bullet can be considered straight.
For practical shooting (for example, hunting), the firing range is usually much longer and the curvature of the trajectory has to be taken into account. But here the arrow plays into the hands of the fact that the size of the target (slaughter place) in height in this case can reach 5-10 cm or more. If we choose such a horizontal range of sighting of the weapon that the height of the trajectory at a distance does not exceed the height of the target (the so-called direct shot), then aiming at the edge of the target, we will be able to hit it throughout the firing range.
Range direct shot, at which the height of the trajectory does not rise above the aiming line above the height of the target, very important characteristic any weapon, which determines the flatness of the trajectory.
The aiming point is usually the lower edge of the target or its center. It is more convenient to aim under the edge when the entire target is visible when aiming.
When shooting, it is usually necessary to introduce vertical corrections if:
- Target size is smaller than usual.
- the shooting distance is greater than the sighting distance of the weapon.
- the shooting distance is closer than the first point of intersection of the trajectory with the line of sight (typical for shooting with a telescopic sight).
Horizontal corrections usually have to be introduced during shooting in windy weather or when shooting at a moving target. Usually corrections for open sights are introduced by firing ahead (by moving the aiming point to the right or left of the target), and not by adjusting the sights.
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 | Nai highest point trajectories | |
| Trajectory height | The shortest distance from the top of the trajectory to the horizon of the weapon | |
| Ascending branch | Part of the trajectory from the departure point to the summit | |
| descending branch | Part of the trajectory from the top to the point of impact | |
| Aiming point (aiming) | The point on or off the target at which the weapon is aimed | |
| line of sight | A straight line passing from the shooter's eye through the middle of the sight slot (level with its edges) and the top of the front sight to the aiming point | |
| aiming angle | The angle enclosed between the line of elevation and the line of sight | |
| Target elevation angle | The angle enclosed between the line of sight and the horizon of the weapon | The target's elevation angle is considered positive (+) when the target is above the weapon's horizon, and negative (-) when the target is below the weapon's horizon. |
| Sighting range | Distance from the point of departure to the intersection of the trajectory with the line of sight | |
| Exceeding the trajectory above the line of sight | The shortest distance from any point of the trajectory to the line of sight | |
| target line | A straight line connecting the departure point with the target | When firing direct fire, the target line practically coincides with the aiming line |
| Slant Range | Distance from point of origin to target along target line | When firing direct fire, the slant range practically coincides with the aiming range. |
| meeting point | Intersection point of the trajectory with the target surface (ground, obstacles) | |
| Meeting angle | The angle enclosed between the tangent to the trajectory and the tangent to the target surface (ground, obstacles) at the meeting point | The smaller of the adjacent angles, measured from 0 to 90°, is taken as the meeting angle. |
| Sighting line | A straight line connecting the middle of the sight slot to the top of the front sight | |
| Aiming (pointing) | Giving the axis of the bore of the weapon the position in space necessary for firing | In order for the bullet to reach the target and hit it or the desired point on it |
| Horizontal aiming | Giving the axis of the bore the desired position in the horizontal plane | |
| vertical guidance | Giving the axis of the bore the desired position in the vertical plane |
The trajectory of a bullet in the air has the following properties:
- the descending branch is shorter and steeper than the ascending one;
- the angle of incidence is greater than the angle of throw;
- the final speed of the bullet is less than the initial one;
- the 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 value.
When firing from any type of weapon with an increase in the elevation angle from 0° to 90°, the horizontal range first increases to a certain limit, and then decreases to zero (Fig. 5).
The elevation angle at which the greatest range is obtained is called farthest angle. The value of the angle of greatest range for bullets various kinds 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 greatest horizontal and aiming ranges when firing 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 the trajectories obtained at the same horizontal range are called two trajectories, one of which is flat, the other is mounted (see Fig. trajectories 2 and 3).
When firing from small arms and grenade launchers, only flat trajectories are used. How flatter trajectory, the greater the extent of the terrain, the target can be hit with one sight setting (the less impact on the results of shooting has an error in determining the sight setting): this is the practical significance of the trajectory.
The flatness of the trajectory is characterized by its greatest excess over the aiming line. At a given range, the trajectory is all the more flat, the less it rises above the aiming line. In addition, the flatness of the trajectory can be judged by the magnitude of the angle of incidence: the trajectory is the more flat, the smaller the angle of incidence. The flatness of the trajectory affects the range of a direct shot, struck, covered and dead space.
Read full synopsisThe bullet, having received a certain initial velocity upon departure from the bore, strives by inertia to maintain the magnitude and direction of this velocity.
If the bullet's flight took place in an airless space, and the force of gravity did not act on it, the bullet would move in a straight line, uniformly and infinitely. However, a bullet flying in the air is subject to forces that change the speed of its flight and the direction of movement. These forces are gravity and air resistance (Fig. 4).
Rice. 4. Forces acting on a bullet during its flight
Due to the combined action of these forces, the bullet loses speed and changes the direction of its movement, moving in the air along a curved line passing below the direction of the axis of the bore.
The line that a moving bullet describes in space (its center of gravity) is called trajectory.
Usually ballistics considers the trajectory over arms horizon- an imaginary infinite horizontal plane passing through the departure point (Fig. 5).
Rice. 5. Horizon weapons
The movement of the bullet, and hence the shape of the trajectory, depends on many conditions. Therefore, in order to understand how the trajectory of a bullet is formed in space, it is necessary to consider first of all how the force of gravity and the drag force of the air medium act on the bullet separately.
The action of gravity. Let us imagine that no force acts on the bullet after it has left the bore. In this case, as mentioned above, the bullet would move by inertia infinitely, uniformly and rectilinearly in the direction of the axis of the bore; for every second it would fly the same distances with a constant speed equal to the initial one. In this case, if the barrel of the weapon were pointed directly at the target, the bullet, following in the direction of the axis of the bore, would hit it (Fig. 6).
Rice. 6. The movement of a bullet by inertia (if there were no gravity and air resistance)
Let us now assume that only one force of gravity acts on the bullet. Then the bullet will begin to fall vertically down, like any free-falling body.
If we assume that gravity acts on the bullet during its flight by inertia in airless space, then under the influence of this force the bullet will fall lower from the continuation of the bore axis - in the first second - by 4.9 m, in the second - by 19.6 m etc. In this case, if you point the barrel of the weapon at the target, the bullet will never hit it, because, being subjected to the action of gravity, it will fly under the target (Fig. 7).
Rice. 7. The movement of the bullet (if gravity acted on it,
but no air resistance
It is quite obvious that in order for the bullet to fly a certain distance and hit the target, it is necessary to point the barrel of the weapon somewhere above the target. To do this, it is necessary that the axis of the bore and the plane of the horizon of the weapon make up a certain angle, which is called elevation angle(Fig. 8).
As can be seen from fig. 8, the trajectory of a bullet in airless space, on which the force of gravity acts, is a regular curve, which is called parabola. The highest point of the trajectory above the horizon of the weapon is called its summit. The part of the curve from the departure point to the apex is called ascending branch. Such a bullet trajectory is characterized by the fact that the ascending and descending branches are exactly the same, and the angle of throw and fall are equal to each other.
Rice. 8. Elevation (bullet trajectory in airless space)
The action of the air resistance force. At first glance, it seems unlikely that the air, which has such a low density, could provide significant resistance to the movement of the bullet and thereby significantly reduce its speed.
However, experiments have established that the force of air resistance acting on a bullet fired from a rifle of the 1891/30 model is a large value - 3.5 kg.
Considering that the bullet weighs only a few grams, it becomes quite obvious the great braking effect that air has on a flying bullet.
During the flight, the bullet spends a significant part of its energy on pushing the air particles that interfere with its flight.
As a photograph of a bullet flying at supersonic speed (over 340 m/s) shows, an air seal forms in front of its head (Fig. 9). From this seal, a head ballistic wave radiates in all directions. Air particles, sliding over the surface of the bullet and breaking off from its side walls, form a zone of rarefied space behind the bullet. In an effort to fill the resulting void behind the bullet, air particles create turbulence, as a result of which a tail wave stretches behind the bottom of the bullet.
The compaction of air ahead of the head of the bullet slows down its flight; the discharged zone behind the bullet sucks it in and thereby further enhances braking; the walls of the bullet experience friction against air particles, which also slows down its flight. The resultant of these three forces is the force of air resistance.
Rice. 9. Photograph of a bullet flying at supersonic speed
(over 340 m/s)
The great influence exerted by air resistance on the flight of a bullet can also be seen from the following example. A bullet fired from a Mosin rifle model 1891/30. or from sniper rifle Dragunov (SVD). Under normal conditions (with air resistance), it has the largest horizontal flight range of 3400 m, and when firing in a vacuum, it could fly 76 km.
Consequently, under the influence of the air resistance force, the trajectory of the bullet loses the shape of a regular parabola, acquiring the shape of an asymmetrical curved line; the top divides it into two unequal parts, of which the ascending branch is always longer and delayed than the descending one. When shooting at medium distances, you can conditionally take the ratio of the length of the ascending branch of the trajectory to the descending one as 3:2.
The rotation of the bullet around its axis. It is known that a body acquires considerable stability if it is given a rapid rotational motion around its axis. An example of the stability of a rotating body is a spinning top toy. A non-rotating “top” will not stand on its pointed leg, but if the “top” is given a quick rotational movement around its axis, it will stand steadily on it (Fig. 10).
In order for the bullet to acquire the ability to deal with the overturning effect of the force of air resistance, to maintain stability during flight, it is given a rapid rotational movement around its longitudinal axis. The bullet acquires this rapid rotational movement due to helical grooves in the bore of the weapon (Fig. 11). Under the action of the pressure of powder gases, the bullet moves forward along the bore, simultaneously rotating around its longitudinal axis. Upon departure from the barrel, the bullet by inertia retains the resulting complex movement - translational and rotational.
Without going into details of the explanation physical phenomena, associated with the action of forces on a body experiencing a complex movement, it must still be said that the bullet during flight makes regular oscillations and describes a circle around the trajectory with its head (Fig. 12). In this case, the longitudinal axis of the bullet, as it were, “follows” the trajectory, describing a conical surface around it (Fig. 13).
Rice. 12. Conical rotation of the bullet head
Rice. 13. Flight of a spinning bullet in the air
If we apply the laws of mechanics to a flying bullet, it becomes obvious that the greater the speed of its movement and the longer the bullet, the more the air tends to overturn it. Therefore, the bullets of cartridges different type it is necessary to give a different speed of rotation. Thus, a light bullet fired from a rifle has a rotation speed of 3604 rpm.
However, the rotational movement of the bullet, so necessary to give it stability during flight, has its negative sides.
As already mentioned, a rapidly rotating bullet is subjected to a continuous overturning force of air resistance, in connection with which the head of the bullet describes a circle around the trajectory. As a result of the addition of these two rotational movements, a new movement arises that deflects its head part away from the firing plane1 (Fig. 14). In this case, one side surface of the bullet is subjected to particle pressure more than the other. Such unequal air pressure on the side surfaces of the bullet deflects it away from the plane of fire. The lateral deviation of a rotating bullet from the firing plane in the direction of its rotation is called derivation(Fig. 15).
Rice. 14. As a result of two rotational movements, the bullet gradually turns the head to the right (in the direction of rotation)
Rice. 15. The phenomenon of derivation
As the bullet moves away from the muzzle of the weapon, the magnitude of its derivational deviation increases rapidly and progressively.
When shooting at short and medium distances, derivation is not of great practical importance for the shooter. So, at a firing range at 300 m, the derivational deviation is 2 cm, and at 600 m - 12 cm. Derivation has to be taken into account only for particularly accurate shooting at long distances, making appropriate adjustments to the installation of the sight, in accordance with the table of derivational deviations of a bullet for a certain range shooting.
The trajectory of a bullet is understood as a line drawn in space by its center of gravity.
This trajectory is formed under the influence of the inertia of the bullet, the forces of gravity and air resistance acting on it.
The inertia of a bullet is formed while it is in the bore. Under the influence of the energy of powder gases, the speed and direction are set to the bullet forward movement. And if external forces did not act on it, then according to the first law of Galileo - Newton, it would rectilinear motion in a given direction at a constant speed to infinity. In this case, in every second it would pass a distance equal to the initial speed of the bullet (see Fig. 8).
However, due to the fact that the forces of gravity and air resistance act on the bullet in flight, they together, in accordance with the fourth law of Galileo - Newton, impart to it an acceleration equal to the vector sum of the accelerations arising from the actions of each of these forces separately.
Therefore, in order to understand the features of the formation of the flight path of a bullet in the air, it is necessary to consider how the force of gravity and the force of air resistance act separately on the bullet.
Rice. 8. The movement of a bullet by inertia (in the absence of the influence of gravity
and air resistance)
The force of gravity acting on the bullet imparts to it an acceleration equal to the acceleration of free fall. This force is directed vertically downward. In this regard, the bullet under the action of gravity will constantly fall to the ground, and the speed and height of its fall will be determined, respectively, by formulas 6 and 7:
where: v - bullet fall speed, H - bullet fall height, g - free fall acceleration (9.8 m/s2), t - bullet fall time in seconds.
If the bullet flew out of the bore without having the kinetic energy given by the pressure of the powder gases, then, in accordance with the above formula, it would fall vertically down: in one second by 4.9 m; two seconds later at 19.6 m; after three seconds at 44.1 m; four seconds later at 78.4 m; after five seconds at 122.5 m, etc. (see fig. 9).
Rice. 9. The fall of a bullet without kinetic energy in a vacuum
under the influence of gravity
When a bullet with a given kinetic energy moves by inertia, under the action of gravity, it will move a given distance down relative to the line that is a continuation of the axis of the bore. By constructing parallelograms, the lines of which will be the values of the distances covered by the bullet by inertia and under the action of gravity in
corresponding time intervals, we can determine the points that the bullet will pass in these time intervals. Connecting them with a line, we get the trajectory of the bullet in airless space (see Fig. 10).
Rice. 10. The trajectory of a bullet in a vacuum
This trajectory is a symmetrical parabola, the highest point of which is called the vertex of the trajectory; its part, located from the point of departure of the bullet to the top, is called the ascending branch of the trajectory; and the part located after the top is descending. In vacuum, these parts will be the same.
In this case, the height of the top of the trajectory and, accordingly, its figure will depend only on the initial velocity of the bullet and the angle of its departure.
If the force of gravity acting on the bullet is directed vertically downward, then the force of air resistance is directed in the direction opposite to the movement of the bullet. It continuously slows down the movement of the bullet and tends to overturn it. To overcome the force of air resistance, part of the kinetic energy of the bullet is expended.
The main causes of air resistance are: its friction against the surface of the bullet, the formation of a vortex, the formation of a ballistic wave (see Fig. 11).
Rice. 11. Causes of air resistance
The bullet in flight collides with air particles and causes them to oscillate, as a result of which the density of the air in front of the bullet increases, and sound waves are formed that cause a characteristic sound and a ballistic wave. In this case, the layer of air flowing around the bullet does not have time to close behind its bottom part, as a result of which a rarefied space is created there. The difference in air pressure exerted on the head and bottom parts of the bullet forms a force directed to the side opposite to the direction of its flight and reduces its speed. In this case, air particles, trying to fill the rarefied space formed behind the bottom of the bullet, create a vortex.
The air resistance force is the sum of all the forces generated due to the influence of air on the flight of a bullet.
The center of drag is the point at which the force of air resistance is applied to the bullet.
The force of air resistance depends on the shape of the bullet, its diameter, flight speed, air density. With an increase in the speed of the bullet, its caliber and air density, it increases.
Under the influence of air resistance, the flight path of the bullet loses its symmetrical shape. The speed of a bullet in the air decreases all the time as it moves away from the point of departure, so the average speed of a bullet on the ascending branch of the trajectory is greater than on the descending one. In this regard, the ascending branch of the flight path of a bullet in the air is always longer and flatter than the descending one; when shooting at medium distances, the ratio of the length of the ascending branch of the trajectories to the length of the descending one is conditionally taken as 3: 2 (see Fig. 12).
Rice. 12. The trajectory of a bullet in the air
Rotation of a bullet around its axis
When a bullet is flying in the air, the force of its resistance constantly strives to overturn it. It manifests itself in the following way. The bullet, moving by inertia, constantly strives to maintain the position of its axis, given direction barrel of the weapon. At the same time, under the influence of gravity, the direction of the bullet's flight constantly deviates from its axis, which is characterized by an increase in the angle between the axis of the bullet and the tangent to the trajectory of its flight (see Fig. 13).
Rice. 13. The effect of the force of air resistance on the flight of a bullet: CG - center of gravity, CA - center of air resistance
The action of the air resistance force is directed opposite to the direction of the bullet and parallel to its tangent trajectory, i.e. from below at an angle to the axis of the bullet.
Based on the features of the shape of the bullet, air particles hit the surface of its head at an angle close to a straight line, and into the surface of the tail at a fairly sharp angle (see Fig. 13). In this regard, at the head of the bullet there is a compacted air, and at the tail - a rarefied space. Therefore, the air resistance in the head of the bullet significantly exceeds its resistance in the tail. As a result, the speed of the head section decreases faster than the speed of the tail section, which causes the head of the bullet to tip back (bullet rollover).
Rolling the bullet backwards causes it to rotate erratically in flight, with a significant decrease in its flight range and accuracy of hitting the target.
In order to prevent the bullet from tipping over in flight under the action of air resistance, it is given a rapid rotational movement around the longitudinal axis. This rotation is formed due to the helical cutting in the bore of the weapon.
The bullet, passing through the bore, under the pressure of powder gases, enters the rifling and fills them with its body. In the future, like a bolt in a nut, it simultaneously moves forward and rotates around its axis. At the exit from the bore, the bullet retains both translational and rotational motion by inertia. At the same time, the rotation speed of the bullet reaches very high values, for the Kalashnikov 3000 assault rifle, and for the Dragunov sniper rifle - about 2600 revolutions per second.
Bullet rotation speed can be calculated by the formula:
where Vvr - rotation speed (rpm), Vo - muzzle velocity (mm/s), Lnar - rifling stroke length (mm).
During the flight of a bullet, the force of air resistance tends to tip the bullet head up and back. But the head of the bullet, rotating rapidly, according to the property of the gyroscope, tends to maintain its position and deviate not upwards, but slightly in the direction of its rotation - to the right, at right angles to the direction of the air resistance force. When the head part is deflected to the right, the direction of the air resistance force changes, which now tends to turn the head part of the bullet to the right and back. But as a result of rotation, the head of the bullet does not turn to the right, but down and further to its description full circle(see fig. 14).
Rice. 14. Conical rotation of the bullet head
Thus, the head of a flying and rapidly rotating bullet describes a circle, and its axis is a cone with a vertex at the center of gravity. There is a so-called slow conical movement, in which the bullet flies head first in accordance with the change in the curvature of the trajectory (see Fig. 15).
Rice. 15. Flight of a spinning bullet in the air
The axis of slow conical rotation is located above the tangent to the flight path of the bullet, so the lower part of the bullet is in more subject to the pressure of the oncoming air flow than the top. In this regard, the axis of slow conical rotation deviates in the direction of rotation, i.e. to the right. This phenomenon is called derivation (see Fig. 16).
Derivation is the deviation of the bullet from the plane of fire in the direction of its rotation.
The plane of fire is understood as a vertical plane in which lies the axis of the bore of the weapon.
The reasons for the derivation are: the rotational movement of the bullet, air resistance and the constant decrease under the action of gravity of the tangent to the bullet's flight path.
In the absence of at least one of these reasons, there will be no derivation. For example, when shooting vertically up and vertically down, there will be no derivation, since the air resistance force in this case is directed along the bullet axis. There will be no derivation when firing in a vacuum due to the lack of air resistance and when firing from smoothbore weapons due to the lack of rotation of the bullet.
Rice. 16. The phenomenon of derivation (view of the trajectory from above)
During the flight, the bullet deviates more and more to the side, while the degree of increase in derivational deviations significantly exceeds the degree of increase in the distance traveled by the bullet.
Derivation is not of great practical importance for the shooter when shooting at close and medium distances, it must be taken into account only for particularly accurate shooting at long distances, making certain adjustments to the installation of the sight in accordance with the table of derivational deviations for the corresponding firing range.
Bullet trajectory characteristics
To study and describe the flight path of a bullet, the following indicators characterizing it are used (see Fig. 17).
The departure point is located in the center of the muzzle of the barrel, is the beginning of the bullet's flight path.
The weapon's horizon is the horizontal plane passing through the departure point.
The line of elevation is a straight line that is a continuation of the axis of the bore of the weapon aimed at the target.
The elevation angle is the angle enclosed between the elevation line and the horizon of the weapon. If this angle is negative, for example, when
shooting down from a significant hill, it is called the angle of declination (or descent).
Rice. 17. Bullet trajectory indicators
The line of throw is a straight line, which is a continuation of the axis of the bore at the time of the bullet's departure.
The throw angle is the angle between the throw line and the weapon's horizon.
The departure angle is the angle enclosed between the line of elevation and the line of throw. Represents the difference between the values of the angles of throw and elevation.
Point of impact - is the point of intersection of the trajectory with the horizon of the weapon.
The angle of incidence is the angle at the point of impact between the tangent to the bullet's flight path and the weapon's horizon.
The final velocity of the bullet is the velocity of the bullet at the point of impact.
The total flight time is the time it takes the bullet to travel from the point of departure to the point of impact.
Full horizontal range is the distance from the point of departure to the point of impact.
The vertex of the trajectory is its highest point.
The height of the trajectory is the shortest distance from its top to the horizon of the weapon.
The ascending branch of the trajectory is the part of the trajectory from the departure point to its top.
The descending branch of the trajectory is the part of the trajectory from its top to the point of fall.
The meeting point is a point lying at the intersection of the bullet's flight path with the target surface (ground, obstacles).
The meeting angle is the angle between the tangent to the bullet's flight path and the tangent to the target surface at the meeting point.
The point of aim (aiming) is the point on or off the target at which the weapon is aimed.
The line of sight is a straight line from the shooter's eye through the middle of the sight slit and the top of the front sight to the point of aim.
The angle of aim is the angle between the line of sight and the line of elevation.
Target elevation angle is the angle between the line of sight and the horizon of the weapon.
Sighting range is the distance from the point of departure to the intersection of the trajectory with the line of sight.
The excess of the trajectory over the line of sight is the shortest distance from any point of the trajectory to the line of sight.
When shooting at close range, the values of the excess of the trajectory over the aiming line will be quite low. But when firing at long distances, they reach significant values (see Table 1).
Table 1
Exceeding the trajectory above the aiming line when firing from a Kalashnikov assault rifle (AKM) and a Dragunov sniper rifle (SVD) at distances of 600 m or more
| For 7.62mm AKM | |||||||||||||||||||||
| Range, m | 100 | 200 | 300 | 400 | 500 | 600 | 700 | 800 | 900 | 1000 | |||||||||||
| Aim | meters | ||||||||||||||||||||
| 6 | 0,98 | 1,8 | 2,2 | 2,1 | 1,4 | 0 | -2,7 | -6,4 | - | - | |||||||||||
| 7 | 1,3 | 2,5 | 3,3 | 3,6 | 3,3 | 2,1 | colspan=2bgcolor=white>0-3,5 | -8,4 | - | ||||||||||||
| 8 | 1,8 | 3,4 | 4,6 | 5,4 | 5,5 | 4,7 | 3,0 | 0 | -4,5 | -10,5 | |||||||||||
| For SVD using an optical sight | |||||||||||||||||||||
| Range, | 100 | 200 | 300 | 400 | 500 | 600 | 700 | 800 | 900 | 1000 | 1100 | 1200 | 1300 | 1400 | |||||||
| Aim | meters | ||||||||||||||||||||
| 6 | 0,53 | 0,95 | 1,2 | 1,1 | 0,74 | 0 | -1,3 | - | - | - | - | - | - | - | |||||||
| 7 | 0,71 | 1,3 | 1,7 | 1,9 | 1,6 | 1,0 | 0 | -1,7 | - | - | - | - | - | - | |||||||
| 8 | 0,94 | 1,8 | 2,4 | 2,7 | 2,8 | 2,4 | 1,5 | 0 | -2,2 | - | - | - | - | - | |||||||
| 9 | 1,2 | 2,2 | 3,1 | 3,7 | 4,0 | 3,9 | 2,3 | 2,0 | 0 | -2,9 | - | - | - | - | |||||||
| 10 | 1,5 | 2,8 | 4,0 | 4,9 | 5,4 | 5,7 | 5,3 | 4,3 | 2,6 | 0 | -3,7 | - | - | - | |||||||
| 11 | 1,8 | 3,5 | 5,0 | 6,2 | 7,1 | 7,6 | 7,7 | 7,1 | 5,7 | 3,4 | 0 | -4,6 | - | - | |||||||
| 12 | 2,2 | 4,3 | 6,2 | 7,8 | 9,1 | 10,0 | 10,5 | 10,0 | 9,2 | 7,3 | 4,3 | 0 | -5,5 | - | |||||||
| 13 | 2,6 | 5,1 | 7,4 | 9,5 | 11 | 12,5 | 13,5 | 13,5 | 13,0 | 11,5 | 8,9 | 5,1 | 0 | -6,6 | |||||||
Note: The number of units in the scope value corresponds to the number of hundreds of meters of shooting distance for which the scope is designed.
(6 - 600 m, 7 - 700 m, etc.).
From Table. 1 shows that the excess of the trajectory above the aiming line when firing from the AKM at a distance of 800 m (sight 8) exceeds 5 meters, and when firing from the SVD at a distance of 1300 m (sight 13) - the bullet trajectory rises above the aiming line by more than 13 meters.
Aiming (weapon aiming)
In order for the bullet to hit the target as a result of the shot, it is first necessary to give the axis of the barrel bore an appropriate position in space.
Giving the axis of the bore of a weapon the position necessary to hit a given target is called aiming or aiming.
This position must be given both in the horizontal plane and in the vertical. Giving the axis of the bore the required position in the vertical plane is a vertical pickup, giving it the desired position in the horizontal plane is a horizontal pickup.
If the aiming reference is a point on or near the target, such aiming is called direct. When shooting from small arms, direct aiming is used, performed using a single sighting line.
The sight line is a straight line connecting the middle of the sight slot to the top of the front sight.
To carry out aiming, it is necessary first, by moving the rear sight (slot of the sight), to give the aiming line such a position in which between it and the axis of the bore, an aiming angle is formed in the vertical plane corresponding to the distance to the target, and in the horizontal plane - an angle equal to the lateral correction, taking into account crosswind speed, derivation and lateral movement speed of the target (see Fig. 18).
After that, directing the sighting line to the area, which is the aiming reference point, by changing the position of the barrel of the weapon, the axis of the bore is given the desired position in space.
At the same time, in weapons with a permanent rear sight, as, for example, in most pistols, in order to give the necessary position of the bore in the vertical plane, the aiming point is selected corresponding to the distance to the target, and the aiming line is directed to given point. In weapons with a sight slot fixed in the side position, as in a Kalashnikov assault rifle, to give the necessary position of the bore in the horizontal plane, the aiming point is selected corresponding to the side correction, and the aiming line is directed to this point.
Rice. 18. Aiming (weapon aiming): O - front sight; a - rear sight; aO - aiming line; сС - the axis of the bore; oO - a line parallel to the axis of the bore;
H - sight height; M - the amount of movement of the rear sight; a - aiming angle; Ub - angle of lateral correction
Bullet trajectory shape and its practical significance
The shape of the trajectory of a bullet in the air depends on the angle at which it is fired in relation to the horizon of the weapon, its initial velocity, kinetic energy and shape.
To produce a targeted shot, the weapon is aimed at the target, while the aiming line is directed to the aiming point, and the axis of the bore in the vertical plane is brought to a position corresponding to the required elevation line. Between the axis of the bore and the horizon of the weapon, the required elevation angle is formed.
When fired, under the action of the recoil force, the axis of the barrel bore is shifted by the value of the departure angle, while it goes into a position corresponding to the throw line and forms a throw angle with the horizon of the weapon. At this angle, the bullet flies out of the bore of the weapon.
Due to the insignificant difference between the angle of elevation and the angle of throwing, they are often identified, while, however, it is more correct in this case talk about the dependence of the trajectory of a bullet on the angle of throw.
With an increase in the angle of throw, the height of the trajectory of the flight of the bullet and the total horizontal range increase to a certain value given angle, after which the trajectory height continues to increase, and the total horizontal range decreases.
The angle of throw at which the full horizontal range of the bullet is greatest is called the angle of greatest range.
In accordance with the laws of mechanics in an airless space, the angle of greatest range will be 45 °.
When a bullet is flying in air, the relationship between the angle of throw and the shape of the bullet's flight path is similar to the dependence of these characteristics observed when a bullet is flying in airless space, but due to the influence of air resistance, the maximum range angle does not reach 45 °. Depending on the shape and mass of the bullet, its value varies between 30 - 35 °. For calculations, the angle of the greatest firing range in the air is assumed to be 35°.
The flight paths of a bullet that occur at angles of throw smaller than the angle of greatest range are called flat.
The flight paths of a bullet that occur at angles of throw of a large angle of greatest range are called hinged (see Fig. 19).
Rice. 19. Angle of greatest range, flat and overhead trajectories
Flat trajectories are used when firing direct fire at fairly short distances. When firing from small arms, only this type of trajectory is used. The flatness of the trajectory is characterized by its maximum excess over the aiming line. The less the trajectory rises above the aiming line at a given firing range, the more flat it is. Also, the flatness of the trajectory is estimated by the angle of incidence: the smaller it is, the flatter the trajectory.
The flatter the trajectory used when shooting, the greater the distance the target can be hit with one set of
intact, i.e. errors in the installation of the sight have a lesser effect on the effectiveness of shooting.
Mounted trajectories are not used when firing from small arms, in turn, they have widespread in firing shells and mines over long distances out of line of sight of the target, which in this case is set by coordinates. Mounted trajectories are used when firing from howitzers, mortars and other types of artillery weapons.
Due to the peculiarities of this type of trajectory, these types of weapons can hit targets located in cover, as well as behind natural and artificial barriers (see Fig. 20).
Trajectories that have the same horizontal range at different throw angles are called conjugate. One of these trajectories will be flat, the second hinged.
Conjugated trajectories can be obtained when firing from one weapon, using throwing angles greater and smaller angle the greatest range.
Rice. 20. Features of the use of hinged trajectories
A shot in which the excess of the trajectory over the line of sight throughout its entire length does not reach values greater than the height of the target is considered a direct shot (see Fig. 21).
The practical significance of a direct shot lies in the fact that, within its range, in tense moments of the battle, it is allowed to fire without rearranging the sight, while the aiming point in height, as a rule, is chosen at the lower edge of the target.
The range of a direct shot depends, firstly, on the height of the target and, secondly, on the flatness of the trajectory. The higher the target and the flatter the trajectory, the greater the range of a direct shot and the greater the distance the target can be hit with one sight setting.
Rice. 21. Direct shot
The range of a direct shot can be determined from the tables, comparing the height of the target with the values of the greatest excess of the trajectory above the aiming line or with the height of the trajectory.
When shooting at a target that is at a distance greater than the range of a direct shot, the trajectory near the top rises above the target, and the target in a certain area will not be hit with this setting of the sight. In this case, there will be a space near the target, on which the descending branch of the trajectory will lie within its height.
The distance at which the descending branch of the trajectory is within the height of the target is called the affected space (see Fig. 22).
The depth (length) of the affected space directly depends on the height of the target and the flatness of the trajectory. It also depends on the angle of inclination of the terrain: when the terrain rises up, it decreases, when it slopes down, it increases.
Rice. 22. Affected space with a depth equal to the segment AC, for the target
height equal to segment AB
If the target is behind cover, impenetrable by a bullet, then the possibility of hitting it depends on where it is located.
The space behind the shelter from its crest to the meeting point is called the covered space (see Fig. 23). The covered space will be the greater, the greater the height of the shelter and the flatter the trajectory of the bullet.
The part of the covered space in which the target cannot be hit with a given trajectory is called dead (non-hit) space. Dead space will be the greater, the greater the height of the shelter, the lower the height of the target and the flatter the trajectory. The part of the covered space in which the target can be hit is the hit space.
Thus, the depth of the dead space is the difference between the covered and affected space.
Rice. 23. Covered, dead and affected space
The shape of the trajectory also depends on the muzzle velocity of the bullet, its kinetic energy and shape. Consider how these indicators affect the formation of the trajectory.
The further speed of its flight directly depends on the initial speed of the bullet, the value of its kinetic energy, with equal shapes and sizes, provides a smaller degree of speed reduction under the action of air resistance.
Thus, a bullet fired at the same elevation (throw) angle, but with a higher initial velocity or with a higher kinetic energy, will have a higher speed during further flight.
If we imagine a certain horizontal plane at some distance from the departure point, then at the same value elevation angle-
When thrown (thrown), a bullet with a higher speed will reach it faster than a bullet with a lower speed. Accordingly, a slower bullet, having reached this plane and spending more time on it, will have time to go down more under the action of gravity (see Fig. 24).
Rice. 24. The dependence of the trajectory of the flight of a bullet on its speed
In the future, the trajectory of a bullet with lower speed characteristics will also be located below the trajectory of a faster bullet, and under the influence of gravity, it will drop faster in time and closer in distance from the point of departure to the level of the weapon’s horizon.
Thus, the muzzle velocity and kinetic energy of the bullet directly affect the height of the trajectory and the full horizontal range of its flight.
The force of gravity causes the bullet (grenade) to gradually decrease, 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 unevenly curved in shape curved line.
Air resistance to the flight of a bullet (grenade) is caused by the fact that air is elastic medium, therefore, part of the energy of the bullet (grenade) is expended on movement in this medium.
The force of air resistance is caused by three main causes: air friction, the formation of vortices and the formation of a ballistic wave.
Air particles in contact with a moving bullet (grenade), due to internal adhesion (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. 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, as a result of which a pressure difference appears on the head and bottom parts. This difference creates a force directed in the direction opposite to the movement of the bullet, and reduces the speed of its flight. Air particles, trying to fill the rarefaction formed behind the bullet, create a vortex.
A bullet (grenade) in flight collides with air particles and causes them to oscillate. As a result, air density increases in front of the bullet (grenade) and sound waves are formed. Therefore, the flight of a bullet (grenade) is accompanied by a characteristic sound. At a bullet (grenade) flight speed that 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 bullet (grenade) flight speed. When the speed of the bullet is higher than the speed of sound, a wave of highly compacted air is created from the incursion of sound waves against each other - a ballistic wave that slows down the speed of the bullet, since the bullet spends part of its energy on creating this wave.
The resultant (total) of all forces resulting from the influence of air on the flight of a bullet (grenade) is the force of air resistance. The point of application of the resistance force is called the center of resistance.
The magnitude of the air resistance force depends on the flight speed, the shape and caliber of the bullet (grenade), as well as on its surface and air density.
The force of air resistance increases with the increase in the speed of the bullet, its caliber and air density.
At supersonic bullet speeds, when the main cause of air resistance is the formation of an air seal in front of the head (ballistic wave), bullets with an elongated pointed head are advantageous. At subsonic grenade flight speeds, when the main cause of air resistance is the formation of rarefied space and turbulence, grenades with an elongated and narrowed tail are beneficial.
The smoother the surface of the bullet, the lower the friction force and air resistance force.
The variety of forms of modern zero (grenades) "is largely determined by the need to reduce the force of air resistance.
The trajectory of a bullet in the air has the following properties:
1) the descending branch is shorter and steeper than the ascending one;
2) the angle of incidence is greater than the angle of throw;
3) the final speed of the bullet is less than the initial one;
4) 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;
5) the time of movement of the bullet along the ascending branch of the trajectory is less than but downward;
6) 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.
Trajectory elements: departure point, weapon horizon, line of elevation, elevation (declination), plane of fire, point of impact, full horizontal range.
The center of the muzzle of a barrel is called departure point. The departure point is the start of the trajectory.
The horizontal plane passing through the departure point is called arms horizon. In the drawings depicting the weapon and the trajectory from the side, the horizon of the weapon appears as a horizontal line. The trajectory crosses the horizon of the weapon twice: at the point of departure and at the point of impact.
A straight line, which is a continuation of the axis of the bore of a pointed weapon, is called elevation line.
The angle enclosed between the line of elevation and the horizon of the weapon is called elevation angle. If this angle is negative, then it is called the angle of declination (decrease).
The vertical plane passing through the line of elevation is called firing plane.
The point of intersection of the trajectory with the horizon of the weapon is called drop point.
The distance from the point of departure to the point of impact is called full horizontal range.
Trajectory elements: aiming point, aiming line, aiming angle, target elevation angle, effective range.
The point on or off the target at which the weapon is aimed is called aiming point(finds).
A straight line passing 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 is called line of sight.
The angle enclosed between the line of elevation and the line of sight is called aiming angle.
The angle enclosed between the line of sight and the horizon of the weapon is called target elevation angle.
The 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. The elevation angle of the target can be determined using instruments or using the thousandth formula:
where ε is the elevation angle of the target in thousandths;
B - the excess of the target above the horizon of the weapon in meters;
D - firing range in meters.
The distance from the departure point to the intersection of the trajectory with the aiming line is called effective range.
Direct shot, covered, hit and dead spaces and their practical significance
A shot in which the trajectory does not rise above the aiming line above the target along its entire length is called straight shot.
Within the range of a direct shot in tense moments of the battle, shooting can be carried out without rearranging the sight, while the aiming point in height, as a rule, is chosen at the lower edge of the target.
The range of a direct shot depends on the height of the target and the flatness of the trajectory. The higher the target and the closer 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.
The range of a direct shot can be determined from the tables by comparing the height of the target with the values \u200b\u200bof the greatest excess of the trajectory above the line of sight or with the height of the trajectory.
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.
The distance on the ground during which the descending branch of the trajectory does not exceed the height of the target is called affected space(the depth of the affected space).
The depth of the affected space depends on the height of the target (it will be the greater, the higher the target), on the flatness of the trajectory (it will be the greater than the flat trajectory) and on the angle of the terrain (on the front slope it decreases, on the reverse slope it increases).
The depth of the affected space (Ppr) can be determined from the tables of excess of the trajectory over 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 in the event that the target height is less than 1/3 of the trajectory height, according to the thousandth formula:
where PPR- the depth of the affected space in meters;
Vts- target height in meters;
θs is the angle of incidence in thousandths.
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 by the above methods, and the result obtained must be multiplied by the ratio of the angle of incidence to the angle of impact.
The value of the meeting angle depends on the direction of the slope:
On the opposite slope, the meeting angle is equal to the sum of the angles of incidence and slope, on the reverse slope - the difference of these angles.
In this case, the value of the meeting angle also depends on the target elevation angle: with a negative target elevation angle, the meeting angle increases by the value of the target elevation angle, with a positive target elevation angle, it decreases by its value.
The affected space to some extent compensates for the errors made when choosing a sight, and allows you to round the measured distance to the target up.
To increase the depth of the space to be struck on sloping terrain, the firing position must be chosen so that the terrain in the enemy's disposition coincides, if possible, with the continuation of the aiming line.
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 will be the greater, the greater the height of the shelter and the flatter the trajectory.
The part of the covered space in which the target cannot be hit with a given trajectory is called dead(unbeatable) space.
Dead space will be the greater, the greater the height of the shelter, the lower the height of the target and the flatter the trajectory. The other part of the covered space in which the target can be hit is the hit space.
The depth of the covered space (Pp) can be determined from the tables of excess trajectories over 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 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.
The depth of dead space (Mpr) is different from the difference between the covered and affected space.
From machine guns on machine tools, the depth of the covered space can be determined by the aiming angles.
To do this, you need to install a sight corresponding to the distance to the shelter, and aim the machine gun at the crest of the shelter. After that, without knocking down the machine gun, mark yourself with a sight under the base of the shelter. The difference between these sights, expressed in meters, is the depth of the covered space. It is assumed that the terrain behind the shelter is a continuation of the aiming line directed under the base of the shelter.
Knowing the size of the covered and 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.
The phenomenon and causes of dispersion of projectiles (bullets) during firing; dispersion law and its main provisions
When firing from the same weapon, with the most careful observance of the accuracy and uniformity of the production of shots, each bullet (grenade) due to a number random reasons describes its trajectory and has its own point of fall (meeting point), which does not coincide with others, as a result of which bullets (grenades) are scattered.
The phenomenon of scattering of bullets (grenades) when firing from the same weapon in almost identical conditions is called natural dispersion of bullets (grenades) or dispersion of trajectories.
The causes causing zero (garnet) scattering can be summarized in three groups:
The reasons causing a variety of initial speeds;
Causes causing a variety of throwing angles and shooting directions;
Reasons causing a variety of conditions for the flight of a bullet (grenade).
The reasons for the variety of initial speeds are:
Variety in the mass of powder charges and bullets (grenades), in the shape and size of bullets (grenades) and shells, in the quality of gunpowder, in loading density, etc. as a result of inaccuracies (tolerances) in their manufacture;
A variety of charge temperatures, depending on the air temperature and the unequal time spent by the cartridge (grenade) in the barrel heated during firing;
Variety in the degree of heating and in the quality of the barrel.
These reasons lead to fluctuations in the initial speeds, and consequently, in the flight ranges of bullets (grenades), i.e., they lead to dispersion of bullets (grenades) in range (altitude) and depend mainly on ammunition and weapons.
The reasons for the variety of throwing angles and shooting directions are:
Variety in horizontal and vertical aiming of weapons (mistakes in aiming);
A variety of launch angles and lateral displacements of weapons, resulting from a non-uniform preparation for firing, unstable and non-uniform retention automatic weapons, especially during burst firing, improper use of stops and clumsy trigger release;
Angular vibrations of the barrel when firing automatic fire, arising from the movement and impact of moving parts and the recoil of the weapon.
These reasons lead to the dispersion of bullets (grenades) in the lateral direction and range (height), have greatest influence on the size of the dispersion area and mainly depend on the skill of the shooter.
The reasons causing a variety of flight conditions for zeros (grenades) are:
Variety in atmospheric conditions, especially in the direction and speed of the wind between shots (bursts);
A variety in the mass, shape and size of bullets (grenades), leading to a change in the magnitude of the air resistance force.
These reasons lead to an increase in dispersion in the lateral direction, but the range (height) and in wasps iiobhom depend on the external shooting conditions and ammunition.
With each shot, all three groups of causes act in different combinations. This leads to the fact that the flight of each bullet (grenades) occurs along a trajectory that is different from the trajectory of other bullets (grenades).
It is impossible to completely eliminate the causes that cause dispersion, and therefore, it is impossible to eliminate the dispersion itself. However, knowing the reasons on which the dispersion depends, it is possible to reduce the influence of each of them and thereby reduce the dispersion or, as they say, increase the accuracy of fire.
Reducing the dispersion of bullets (grenades) is achieved by excellent training of the shooter, careful preparation weapons and ammunition for shooting, skillful application of the rules of shooting, correct preparation for shooting, uniform application, accurate aiming (aiming), smooth trigger release, steady and uniform holding of the weapon when shooting, as well as proper care of weapons and ammunition.
Scattering law
At large numbers shots (more than 20), a certain regularity is observed in the location of the meeting points on the dispersion area. Dispersion of bullets (grenades) obeys normal law random errors, which in relation to the dispersion of bullets (grenades) is called the law of dispersion.
This law is characterized by the following three provisions:
1) Meeting points (holes) on the scattering area are unevenly located - thicker towards the center of dispersion and less often towards the edges of the dispersion area.
2) On the scattering area, you can determine the point that is the center of dispersion (the middle point of impact), with respect to which the distribution of meeting points (holes) is symmetrical: the number of meeting points on both sides of the dispersion axes, which are equal in absolute value limits (bands), the same, and each deviation from the scattering axis in one direction corresponds to the same deviation in the opposite direction.
3) The meeting points (holes) in each particular case do not occupy an unlimited, but a limited area.
Thus, the scattering law in general view can be formulated as follows: with a sufficiently large number of shots fired under practically the same conditions, the dispersion of bullets (grenades) is uneven, symmetrical and not limitless.
Methods for determining the midpoint of impact
With a small number of holes (up to 5) position middle point hit is determined by the method of successive division of the segments.
For this you need:
Connect two holes (meeting points) with a straight line and divide the distance between them in half;
Connect the resulting point to the third hole (meeting point) and divide the distance between them into three equal parts; since the holes (meeting points) are located more densely towards the dispersion center, the division closest to the first two holes (meeting points) is taken as the middle point of hit of the three holes (meeting points);
The found middle point of impact for three holes (meeting points) is connected with the fourth hole (meeting point) and the distance between them is divided into four equal parts; the division closest to the first three holes (meeting points) is taken as the midpoint of the four holes (meeting points).
For four holes (meeting points), the middle point of impact can also be determined as follows: connect the adjacent holes (meeting points) in pairs, connect the midpoints of both lines again and divide the resulting line in half; the division point will be the mid-point of impact.
If there are five holes (meeting points), the average point of impact for them is determined in a similar way.
With a large number of holes (meeting points), based on the symmetry of dispersion, the average point of impact is determined by the method of drawing the dispersion axes.
The intersection of the dispersion axes is the midpoint of impact.
The mid-point of impact can also be determined by the method of calculation (calculation). For this you need:
Draw a vertical line through the left (right) hole (meeting point), measure the shortest distance from each hole (meeting point) to this line, add up all the distances from the vertical line and divide the sum by the number of holes (meeting points);
Draw a horizontal line through the lower (upper) hole (meeting point), measure the shortest distance from each hole (meeting point) to this line, add up all the distances from the horizontal line and divide the sum by the number of holes (meeting points).
The resulting numbers determine the distance of the midpoint of impact from the specified lines.
Normal (table) firing conditions; influence of firing conditions on the flight of a bullet (grenade).
The following are accepted as normal (table) conditions.
a) Meteorological conditions:
Atmospheric (barometric) pressure on the horizon of the weapon 750 mm Hg. Art.;
The air temperature at the weapon horizon is 4-15°С;
Relative humidity 50% ( relative humidity is the ratio of the amount of water vapor in the air to most water vapor that can be contained in the air at a given temperature);
There is no wind (the atmosphere is still).
b) Ballistic conditions:
Bullet (grenade) mass, muzzle velocity and departure angle are equal to the values indicated in the firing tables;
Charge temperature +15° С;
The shape of the bullet (grenade) corresponds to the established drawing;
The height of the front sight is set according to the data of bringing the weapon to normal combat; heights (divisions) of the aisle correspond to the tabular aiming angles.
c) Topographic conditions:
The target is on the weapon's horizon;
There is no lateral tilt of the weapon.
If the firing conditions deviate from normal, it may be necessary to determine and take into account corrections for the range and direction of fire.
With the increase atmospheric pressure the air density increases, and as a result, the air resistance force increases, the range of the bullet (grenade) decreases. On the contrary, with a decrease in atmospheric pressure, the density and force of air resistance decrease, and the range of the bullet increases.
For every 100 m elevation, atmospheric pressure decreases by an average of 9 mm.
When shooting from small arms on flat terrain, range corrections for changes in atmospheric pressure are insignificant and are not taken into account. In mountainous conditions, at an altitude of 2000 m above sea level, these corrections must be taken into account when shooting, guided by the rules specified in the manuals on shooting.
As the temperature rises, the air density decreases, and as a result, the air resistance force decreases, and the range of the bullet (grenade) increases. On the contrary, with a decrease in temperature, the density and force of air resistance increase, and the range of a bullet (grenade) decreases.
With an increase in the temperature of the powder charge, the burning rate of the powder, the initial speed and range of the bullet (grenade) increase.
When shooting in summer conditions, the corrections for changes in air temperature and powder charge are insignificant and are practically not taken into account; when shooting in winter (under conditions low temperatures) these amendments must be taken into account, guided by the rules specified in the manuals on shooting.
With a tailwind, the speed of the bullet (grenade) relative to the air decreases. For example, if the speed of the bullet relative to the ground is 800 m/s, and the speed of the tailwind is 10 m/s, then the velocity of the bullet relative to the air will be 790 m/s (800 - 10).
With a decrease in the flight speed zeros relative to the air, the air resistance force decreases. Therefore, with a fair wind, the bullet will fly further than with no wind.
With a headwind, the speed of the bullet relative to the air will be greater than with no wind, therefore, the air resistance force will increase, and the range of the bullet will decrease.
The longitudinal (tail, head) wind has little effect on the flight of a bullet, and in the practice of shooting from small arms, corrections for such a wind are not introduced. When firing from grenade launchers, corrections for strong longitudinal wind should be taken into account.
Side wind exerts pressure on side surface bullet and deflects it away from the plane of fire depending on its direction: the wind from the right deflects the bullet into left side, wind from left to right.
The grenade in the active part of the flight (when the jet engine is running) deviates to the side where the wind is blowing from: with the wind from the right - to the right, with the wind - the tear - to the left. This phenomenon is explained by the fact that the side wind turns the tail of the grenade in the direction of the wind, and the head part against the wind and under the action of a reactive force directed along the axis, the grenade deviates from the firing plane in the direction from which the wind blows. On the passive part of the trajectory, the grenade deviates to the side where the wind blows.
Crosswind has a significant effect, especially on the flight of a grenade, and must be taken into account when firing grenade launchers and small arms.
The wind blowing at an acute angle to the firing plane simultaneously affects the change in the range of the bullet and its lateral deflection.
Changes in air humidity have little effect on air density and, consequently, on the range of a bullet (grenade), so it is not taken into account when shooting.
When firing with one sight setting (with one aiming angle), but at different target elevation angles, as a result of a number of reasons, including changes in air density at different heights, and, consequently, the air resistance force, the value of the slant (sighting) flight range changes bullets (grenades).
When firing at small target elevation angles (up to ± 15 °), this bullet (grenade) flight range changes very slightly, therefore, equality of the inclined and full horizontal ranges the flight of a bullet, i.e., the invariance of the shape (rigidity) of the trajectory.
When firing at large target elevation angles, the slant range of the bullet changes significantly (increases), therefore, when shooting in the mountains and at air targets, it is necessary to take into account the correction for the target elevation angle, guided by the rules specified in the shooting manuals.