Formula 1000 for determining distance. Application of the "thousandth" formula in shooting practice. Visibility of objects at different distances

Chapter VII. Navigation.

Navigation is the basis of the science of navigation. The navigational method of navigation is to navigate the ship from one place to another in the most advantageous, shortest and safest way. This method solves two problems: how to direct the ship along the chosen path and how to determine its place in the sea based on the elements of the ship's movement and observations of coastal objects, taking into account the impact on the ship of external forces - wind and current.

To be sure of the safety of the movement of your vessel, you need to know the position of the vessel on the map, which determines its position in relation to dangers in a given navigation area.

Navigation develops the basics of navigation, it studies:

Dimensions and surface of the earth, methods of depicting the earth's surface on maps;

Ways of calculating and laying the path of the vessel on sea charts;

Methods for determining the position of a vessel at sea by coastal objects.

§ 19. Basic information about navigation.

1. Basic points, circles, lines and planes

Our earth is shaped like a spheroid with a major semi-axis OE equal to 6378 km, and the minor semiaxis OR 6356 km(Fig. 37).

Rice. 37. Determining the coordinates of a point on the earth's surface

In practice, with some assumption, the earth can be considered a ball rotating around an axis that occupies a certain position in space.

To determine points on the earth's surface, it is customary to mentally divide it into vertical and horizontal planes that form lines with the earth's surface - meridians and parallels. The ends of the imaginary axis of rotation of the earth are called the poles - north, or nordic, and south, or south.

Meridians are great circles passing through both poles. Parallels are small circles on the earth's surface parallel to the equator.

The equator is a large circle whose plane passes through the center of the earth perpendicular to its axis of rotation.

Both meridians and parallels on the earth's surface can be imagined innumerable. The equator, meridians and parallels form a grid of geographic coordinates of the earth.

Location of any point BUT on the earth's surface can be determined by its latitude (f) and longitude (l) .

The latitude of a place is the arc of the meridian from the equator to the parallel of the given place. Otherwise: the latitude of a place is measured by the central angle enclosed between the plane of the equator and the direction from the center of the earth to the given place. Latitude is measured in degrees from 0 to 90° from the equator to the poles. When calculating, it is considered that the northern latitude f N has a plus sign, the southern latitude - f S minus sign.

The difference in latitude (f 1 - f 2) is the meridian arc enclosed between the parallels of these points (1 and 2).

The longitude of a place is the arc of the equator from the zero meridian to the meridian of the given place. Otherwise: the longitude of a place is measured by the arc of the equator enclosed between the zero meridian plane and the meridian plane of the given place.

The difference in longitudes (l 1 -l 2) is the arc of the equator enclosed between the meridians of the given points (1 and 2).

Prime meridian - Greenwich meridian. From it, longitude is measured in both directions (east and west) from 0 to 180 °. Western longitude is measured on the map to the left of the Greenwich meridian and is taken with a minus sign in calculations; east - to the right and has a plus sign.

The latitude and longitude of any point on earth are called the geographic coordinates of that point.

2. Division of the true horizon

The mentally imaginary horizontal plane passing through the eye of the observer is called the plane of the true horizon of the observer, or the true horizon (Fig. 38).

Let's assume that at the point BUT is the eye of the observer, the line ZABC- vertical, HH 1 - the plane of the true horizon, and the line P NP S - the axis of rotation of the earth.

Of the many vertical planes, only one plane in the drawing will coincide with the axis of rotation of the earth and the point BUT. The intersection of this vertical plane with the earth's surface gives a large circle P N BEP SQ on it, called the true meridian of the place, or the meridian of the observer. The plane of the true meridian intersects with the plane of the true horizon and gives the north-south line on the latter NS. Line ow, perpendicular to the line of true north-south is called the line of true east and west (east and west).

Thus, the four main points of the true horizon - north, south, east and west - occupy a quite definite position anywhere on earth, except for the poles, due to which, with respect to these points, various directions along the horizon can be determined.

Directions N(north), S (south), O(East), W(west) are called the main points. The entire circumference of the horizon is divided into 360°. The division is made from the point N in a clockwise direction.

Intermediate directions between the main points are called quarter points and are called NO, SO, SW, NW. Major and quarter rhumbs have the following values ​​in degrees:

Rice. 38. True horizon of the observer

3. Visible horizon, range of the visible horizon

The body of water visible from the vessel is limited by a circle formed by the apparent intersection of the firmament with the surface of the water. This circle is called the visible horizon of the observer. The range of the visible horizon depends not only on the height of the observer's eyes above the water surface, but also on the state of the atmosphere.

Figure 39. Object visibility range

The boatmaster must always know how far he sees the horizon in different positions, for example, standing at the helm, on deck, sitting, etc.

The range of the visible horizon is determined by the formula:

d=2.08

or, approximately, for an observer's eye height of less than 20 m by formula:

d=2,

where d is the range of the visible horizon in miles;

h is the height of the observer's eye, m.

Example. If the observer's eye height h = 4 m, then the range of the visible horizon is 4 miles.

The visibility range of the observed object (Fig. 39), or, as it is called, the geographical range D n , is the sum of the ranges of the visible horizon with the height of this object H and the height of the observer's eye A.

Observer A (Fig. 39), located at a height h, from his ship can see the horizon only at a distance d 1, i.e. to point B on the water surface. If, however, an observer is placed at point B on the water surface, then he could see lighthouse C , located at a distance d 2 from it ; therefore, the observer located at the point BUT, will see the beacon from a distance equal to D n :

Dn=d1+d2.

The visibility range of objects located above the water level can be determined by the formula:

Dn = 2.08( + ).

Example. Beacon height H = 1b.8 m, height of the observer's eye h = 4 m.

Decision. D n \u003d l 2.6 miles, or 23.3 km.

The visibility range of an object is also determined approximately according to the Struisky nomogram (Fig. 40). By applying a ruler so that the heights corresponding to the eye of the observer and the observed object are connected by one straight line, the visibility range is obtained on the middle scale.

Example. Find the visibility range of an object with a height above sea level in 26.2 m at an observer's eye height above sea level of 4.5 m.

Decision. D n= 15.1 miles (dashed line in Fig. 40).

On maps, sailing directions, in navigation aids, in the description of signs and lights, the visibility range is given for the observer's eye height of 5 m from the water level. Since on a small boat the observer's eye is located below 5 m, for him, the visibility range will be less than indicated in the manuals or on the map (see Table 1).

Example. The map indicates the visibility range of the lighthouse at 16 miles. This means that the observer will see this beacon from a distance of 16 miles if his eye is at a height of 5 m above sea level. If the observer's eye is at a height of 3 m, then the visibility will decrease accordingly by the difference in the visibility range of the horizon for heights 5 and 3 m. Horizon visibility range for altitude 5 m equals 4.7 miles; for height 3 m- 3.6 miles, difference 4.7 - 3.6=1.1 miles.

Consequently, the visibility range of the beacon will not be equal to 16 miles, but only 16 - 1.1 = 14.9 miles.

Rice. 40. Struisky's nomogram

Ways to determine the range to targets:

Direct measurement of the area in pairs of steps.

First, the leader of the lesson should help each cadet determine the size of his step. To do this, the teacher on a flat area marks a 100-meter segment with flags and orders the students to walk it two or three times, with the usual step, counting each time under the right or left foot, how many pairs of steps are obtained.

Let's assume that cadets obtained 66,67,68 pairs of steps during a three-time measurement. The arithmetic mean of these numbers is 67 pairs of steps.

Consequently, the length of one pair of steps of this cadet will be 100:67=1.5m.

After that, the teacher proceeds to teaching cadets how to measure distances by direct sounding. To do this, he points out to one of the trainees an object and orders to measure the distance to it in steps. Another subject is indicated to the next cadet, and so on. In this case, each trainee must act independently and measure both when moving to the subject and back.

This method of determining the range to the target (object) is used under certain conditions - out of contact with the enemy and in the presence of time.

Visually by segments of the terrain:

When determining the range by segments of the terrain, it is necessary to mentally set aside some familiar range that is firmly entrenched in visual memory from oneself to the target (it should be borne in mind that with increasing range, the apparent value of the segment in the future is constantly decreasing).

From landmarks (local items):

If the target is detected near a local object (landmark), the range to which is known, then when determining the range to the target, it is necessary to take into account its distance from the local object (landmark).

According to the degree of visibility and apparent size of objects:

When determining the range by the degree of visibility and the apparent size of the target, it is necessary to compare the apparent size of the target with the visible sizes of the given target imprinted in the memory at certain ranges.

Method of calculation (according to the formula "thousandth"):

┌───────────────┐

│ V x 1000 │

│ D = ──────── │

└───────────────┘

An enemy tank 2.8 m high is visible at an angle of 0-05. Determine the distance to the target (D).

Solution: D = ───────────= 560 m.

With the help of covering value 0 2 sighting devices of small arms.

To determine the covering value of the sighting device, the formula is used:

┌────────────┐

│ D x R │

│ K \u003d ────── │

└────────────┘

K - covering value of the sighting device;

D - range to the target (a 100 M site is taken);

P is the size of the sighting device;

d is the distance from the eye to the aiming device.

Example: - Calculate the covering value of the front sight AK-74;

100000mm x 2mm

K = ─────────────────= 303.3 mm or 30 cm.

Thus, the covering value of the AK-74 front sight at a distance of 100 m will be 30 cm.

At other ranges, the covering value of the AK-74 front sight will be as many times greater than the one obtained, as the range to the target is more than 100 M.

For example, at D=300 M - K=90 cm; on D=400 M - K=1.2 M, etc. Thus, knowing the size of the target, you can determine the range to it:

Target width - 50 cm, target Target width - 1 m, target

half closed by the front sight fully closed by the front sight

(i.e., the front sight is closed by an example- (i.e., the front sight is closed when-

but - 25 cm), as measured 3 times 30 cm)

K = 30cm at D = 100M, then in the range, respectively

In this case, the distance to the target will be equal to:

targets - approximately 100 m. D \u003d 3 x 100 \u003d 300 m.

In the same way, using this formula, you can calculate the covering value of any sighting device of various types of small arms, substituting only the corresponding values.

According to the rangefinder scale of aiming devices:

The distance on the rangefinder scale is determined only to those targets whose height corresponds to the figure indicated under the horizontal line of the rangefinder scale. In addition, it must be taken into account that the range to the target can only be determined when the target is completely visible in height, otherwise the measured range will be overestimated.

Comparing the speeds of light and sound.

The bottom line is that first we see the flash of a shot (the speed of light = 300,000 km / s, i.e. almost instantly), and then we hear the sound. Sound propagation speed in air = 340 m/s. For example, we noticed a shot of a recoilless gun, we mentally calculate after what time the sound from this shot will reach (for example, 2 seconds), respectively, the range to the target will be equal to:

D \u003d 340m / s x 2s \u003d 680 m.

On the map.

By determining the standing point and position of the target, knowing the scale of the map, you can determine the range to the target.

Ways to determine the direction and speed of the target:

The direction of movement of the target is determined by eye according to its heading angle (the angle between the directions of movement of the target and the direction of fire).

It can be:

Frontal - from 0° to 30° (180°-150°);

Flanking - from 60° to 120°;

Oblique - from 30° to 60° (120° - 150°).

The speed of the target is determined visually by eye according to external signs and the method of movement of the target. It is considered to be:

The speed of the walking target is 1.5 - 2 m / s;

The speed of the running target - 2 - 3 m / s;

Tanks in cooperation with infantry - 5 - 6 km / h;

Tanks when attacking the front line of defense - 10 - 15 km / h;

Motocel - 15 - 20 km / h;

Equipment afloat when forcing a water barrier - 6 - 8 km / h.

3. Purpose, performance characteristics, general arrangement, procedure for incomplete disassembly and assembly after incomplete disassembly of the PM 9mm Makarov pistol (PM)

The 9mm Makarov pistol (Fig. 5.1) is a personal offensive and defensive weapon designed to engage the enemy at short distances.

Rice. 5.1. General view of the 9mm Makarov pistol

Application of the "thousandth" formula in shooting practice

To determine firing distances using the “thousandth” formula, it is necessary to know exactly in advance the width or height of the object (target) to which the distance is determined, determine the angular magnitude of this object in thousandths using the available optical instruments, and then calculate the distance using the formula, where:

D - distance to the object in meters;
Y is the angle at which the object is seen in thousandths;
B is the metric (i.e. in meters) known width or height of the target.

1000 is a constant unchanging mathematical value that is always present in this formula.

Determining the distance in this way, you need to know or imagine the linear dimensions of the target, its width or height. Linear data (dimensions) of objects and targets (in meters) in infantry combined arms practice are as follows.

For example, you need to determine the distance to the target (chest or growth target), which fits in two small side segments of the scale of the PSO-1 optical sight, or is equal to the thickness of the aiming stump of the PU sight, or is equal to the thickness of the front sight of an open rifle sight. The width of the chest or growth target (infantryman in full growth), as can be seen from the table. 6 is equal to 0.5 m. According to all measurements of the above sighting devices (see below), the target is closed by an angle of 2 thousandths. Hence:

But the width of the live target may be different. Therefore, the sniper usually measures the width of the shoulders at different times of the year (by clothes) and only then accepts it as a constant value. It is necessary to measure and know the main dimensions of the human figure, the linear dimensions of the main military equipment, vehicles and everything that can be "attached" to on the side occupied by the enemy. And at the same time, all this should be treated critically. Despite laser rangefinders, the determination of ranges in the combat practice of the armies of all countries is carried out according to the above formula. Everyone knows about it and everyone uses it, and therefore they try to mislead the enemy. Repeatedly there were cases when telegraph poles were covertly increased by 0.5 m at night - during the day this gave the enemy an error in calculating the range of 50-70 meters of undershoot.

Angular values ​​\u200b\u200bin thousandths of improvised objects and devices

To measure the angular values ​​of targets in thousandths, the most commonly used items are used, which in combat practice are often at hand. Such items and means are parts of open sights, aiming threads, marks, reticles of optical sights and other optical devices, as well as everyday items that a soldier always has - cartridges, matches, ordinary scale metric rulers.

As mentioned earlier, the front sight in width closes an angle of 2 thousandths in projection onto the target. In height, the fly closes 3 thousandths. The base of the sight - the width of the slot - closes 6 thousandths.

As mentioned earlier, the aiming stump in width closes an angle of 2 thousandths in the projection onto the target. Horizontal threads close the corners in their thickness also by 2 thousandths.

A - the distance between the threads - closes 7 thousandths.

For PSO-1:
A - the main square for shooting up to 1000 m,
B - three additional squares for shooting at a distance of 1100, 1200, 1300 m;
B - the width of the scale of lateral corrections from 10 to 10 thousandths corresponds to 0-20 (twenty thousandths),
D - from the center (main square) to the right and left to the number 10 corresponds to 0.10 (ten thousandths) The height of the extreme vertical risk at the number 10 is 0.02 (two thousandths);
D - the distance between two small divisions is 0.01-1 (one thousandth), the height of one small risk on the scale of lateral corrections is 0.01 (one thousandth);
E - numbers on the rangefinder scale 2, 4, 6, 8, 10 correspond to distances of 200, 400, 600, 800 and 1000 m;
W - the figure 1.7 shows that at this level of the scale in height, the average height of a person is 170 cm.

Measurements in thousandths of binocular and periscope reticle:
- from a small risk to a large risk (small distances), an angle of 0.05 (five thousandths) is covered;
- from a big risk to a big risk, an angle of 0.10 (ten thousandths) is covered.

The height of the small risk is 2.5 thousandths.
The height of the big risk is 5 thousandths.
The crossbars of the crosses are 5 thousandths.

When using improvised means to determine the angular values, they are placed at a distance of 50 cm from the eye. This distance has been verified over many decades. At a distance of 50 cm from the eye, the rifle cartridge and matches close the angles indicated below in the projection onto the target.

1 centimeter of an ordinary scale ruler (it is better if it is made of transparent material) at a distance of 50 cm from the eye covers an angle of 20 thousandths; 1 millimeter, respectively, 2 thousandths.

Prudent shooters determine in advance for themselves a goniometric distance of 50 cm for a possible determination of distances by the angular values ​​of improvised objects. Usually for this they measure 50 cm on a rifle and make a risk.