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 a 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 influence of external forces on the ship - wind and current.

To be sure of the safe movement of your ship, you need to know the ship’s place on the map, which determines its position relative to the dangers in a given navigation area.

Navigation deals with the development of the fundamentals of navigation, it studies:

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

Methods for calculating and plotting a ship's path on nautical charts;

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

§ 19. Basic information about navigation.

1. Basic points, circles, lines and planes

Our earth has the shape of a spheroid with a semi-major axis OE equal to 6378 km, and the minor axis 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 occupying 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 earth's imaginary axis of rotation are called poles - north, or north, and south, or south.

Meridians are large 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 in countless numbers. The equator, meridians and parallels form the earth's geographic coordinate grid.

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

The latitude difference (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 prime meridian to the meridian of a given place. Otherwise: the longitude of a place is measured by the arc of the equator, enclosed between the plane of the prime meridian and the plane of the meridian of a given place.

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

The prime meridian is the 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; eastern - 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

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

Let us assume that at the point A is the observer's eye, line ZABC- vertical, HH 1 - the plane of the true horizon, and 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 A. The intersection of this vertical plane with the surface of the earth gives on it a great circle P N BEP SQ, 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 N.S. Line O.W. 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 well-defined position anywhere on earth, except for the poles, thanks to which different directions along the horizon can be determined relative to these points.

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

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

Rice. 38. Observer's true horizon

3. Visible horizon, visible horizon range

The expanse of water visible from a vessel is limited by a circle formed by the apparent intersection of the vault of heaven with the surface of the water. This circle is called the observer's apparent horizon. 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 should always know how far he can see 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 height of the observer's eye is 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 geographic 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 of the water surface. If we place an observer at point B of the water surface, then he could see lighthouse C , located at a distance d 2 from it ; therefore the observer located at the point A, will see the beacon from a distance equal to D n :

D n= d 1+d 2.

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

Dn = 2.08(+).

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

Solution. D n = l 2.6 miles, or 23.3 km.

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

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

Solution. Dn= 15.1 miles (dashed line in Fig. 40).

On maps, directions, in navigation manuals, in the descriptions of signs and lights, the visibility range is given for the height of the observer's eye 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 that indicated in manuals or on the map (see Table 1).

Example. The map indicates the visibility range of the lighthouse at 16 miles. This means that an observer will see this lighthouse 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 correspondingly decrease by the difference in the horizon visibility range for heights 5 and 3 m. Horizon visibility range for height 5 m equal to 4.7 miles; for height 3 m- 3.6 miles, difference 4.7 - 3.6=1.1 miles.

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

Rice. 40. Struisky's nomogram

Methods for determining range to targets:

Direct measurement of the terrain in pairs of steps.

First, the lesson leader should help each cadet determine the size of his step. To do this, the teacher marks a 100-meter segment with flags on level ground and orders the students to walk it two to three times, at a normal pace, counting each time to the right or left. left leg, how many pairs of steps are there?

Let’s assume that with three measurements the cadets obtained 66,67,68 pairs of steps. The arithmetic mean of these numbers is 67 pairs of steps.

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

After this, the teacher moves on to teaching cadets how to measure distances by direct measurements. To do this, he points to one of the students an object and orders him to measure the distance to it in steps. The next student is given a different object, etc. In this case, each student must act independently and take measurements both when moving to the object and back.

This method of determining the range to a target (object) is used under certain conditions - outside of contact with the enemy and when there is time.

By eye over sections of terrain:

When determining the range over sections of terrain, you need some kind of familiar range, which is firmly entrenched in visual memory mentally postpone from yourself to the goal (it should be taken into account that as the distance increases, the apparent value of the segment in the future is constantly reduced).

From landmarks (local items):

If a target is detected nearby local subject(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 visible size of the target with the visible dimensions of this target imprinted in memory at certain ranges.

Calculation method (using the thousandth formula):

┌───────────────┐

│ B x 1000 │

│ D = ──────── │

└───────────────┘

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

Solution: D = ────────── = 560 m.

Using hiding value 0 2 sighting devices small arms.

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

┌────────────┐

│ D x R │

│ K= ────── │

└────────────┘

K - covering value of the sighting device;

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

P is the size of the sighting device;

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

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

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 equal to 30 cm.

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

For example, at D=300 M - K=90 cm; at 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 completely closed by the front sight

(i.e. the front sight is closed to the example- (i.e. the front sight is closed to the

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

K=30cm by D=100M, then in the corresponding range

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

target - approximately 100 m. D = 3 x 100 = 300 m.

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

According to the rangefinder scale of aiming devices:

The range on the rangefinder scale is determined only to those targets whose height corresponds to the number indicated under the horizontal line of the rangefinder scale. In addition, it must be taken into account that the range to the target can be determined only 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/sec, i.e. almost instantly), and then we hear the sound. Speed ​​of sound propagation in air = 340 m/s. For example, we noticed a shot from a recoilless rifle, mentally calculate how long it will take for the sound of this shot to reach (for example, 2 seconds), respectively, the range to the target will be equal to:

D = 340m/s x 2s = 680 m.

According to the map.

Having determined the standing point and position of the target, knowing the scale of the map, you can determine the distance to the target.

Methods for determining the direction and speed of a target:

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

It could be:

Frontal - from 0° to 30° (180°-150°);

Flank - from 60° to 120°;

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

The target's speed of movement is determined visually by eye external signs and the way the target moves. It is generally accepted:

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

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

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

Tanks attacking leading edge defense - 10 - 15km/h;

Motorcycle - 15 - 20 km/h;

Equipment afloat when crossing a water obstacle - 6 - 8 km/h.

3. Purpose, performance characteristics, general device, order incomplete disassembly and assemblies after partial disassembly of the PM 9 mm MAKAROV PISTOL (PM)

The 9-mm Makarov pistol (Fig. 5.1) is a personal weapon of attack and defense, designed to defeat the enemy at short distances.

Rice. 5.1. General form 9 mm Makarov pistol

Application of the thousandths formula in shooting practice

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

D is the distance to the object in meters;
Y is the angle at which the object is visible in thousandths;
B is the metric (that is, in meters) known width or height of the target.

1000 - constant, unchangeable mathematical quantity, always present in this formula.

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

For example, you need to determine the distance to the target (chest or height target), which fits into 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 height of the target (full-length infantryman), 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 covered by an angle of 2 thousandths. Hence:

But the width of a live target may be different. Therefore, the sniper usually measures the width of the shoulders in different times year (by clothing) and only then accepts it as a constant value. It is necessary to measure and know the basic 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 viewed critically. Despite laser rangefinders, the determination of ranges in 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. There have been numerous cases when telegraph poles were secretly 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 shortfall.

Angular values ​​in thousandths of available objects and devices

To measure the angular values ​​of targets in thousandths, the most commonly used objects are used, which in combat practice are often at hand. Such objects and means are details open sights, sighting threads, marks, reticles optical sights and other optical instruments, as well as everyday items that are always available to a military personnel - cartridges, matches, ordinary scale metric rulers.

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

As mentioned earlier, the width of the aiming stump covers an angle of 2 thousandths in the projection onto the target. The horizontal threads cover the angles in their thickness by also 2 thousandths. Sight base

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

For PSO-1:
A - main square for shooting up to 1000 m,
B - three additional squares for shooting at distances of 1100, 1200, 1300 m;
B - the width of the lateral correction scale from 10 to 10 thousandths corresponds to 0-20 (twenty thousandths),
G - from the center (main square) right-left to the number 10 corresponds to 0.10 (ten thousandths) The height of the extreme vertical mark 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 mark on the lateral correction scale 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;
F - the number 1.7 shows that at this level of the scale the height includes average height person 170 cm.

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

The height of the small risk is 2.5 thousandths.
The height of the large risk is 5 thousandths.
Cross bars - 5 thousandths.

When using improvised means to determine 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 rifle cartridge and matches close the angles indicated below in projection onto the target.

1 centimeter of an ordinary scale ruler (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 a goniometric distance of 50 cm for possible determination of distances based on the angular values ​​of available objects. Usually for this purpose they measure 50 cm on the rifle and mark it.