Determination of distances without special means. Distance meter on the ground. Methods for measuring distance

Measure the corresponding segment using a ruler. It is preferable that it be made from sheet material that is as thin as possible. If the surface on which it is spread is not flat, a tailor's meter will help. And if you don’t have a thin ruler, and if you don’t mind piercing the card, it’s convenient to use a compass for measuring, preferably with two needles. Then you can transfer it to graph paper and measure the length of the segment along it.

Roads between two points are rarely straight. A convenient device - a curvimeter - will help you measure the length of the line. To use it, first rotate the roller to align the arrow with zero. If the curvimeter is electronic, it is not necessary to set it to zero manually - just press the reset button. Holding the roller, press it to the starting point of the segment so that the mark on the body (located above the roller) points directly to this point. Then move the roller along the line until the mark is aligned with the end point. Read the testimony. Please note that some curvimeters have two scales, one of which is graduated in centimeters, and the other in inches.

Find the scale indicator on the map - it is usually located in the lower right corner. Sometimes this indicator is a piece of calibrated length, next to which it is indicated what distance it corresponds to. Measure the length of this segment with a ruler. If it turns out, for example, that it has a length of 4 centimeters, and next to it it is indicated that it corresponds to 200 meters, divide the second number by the first, and you will find out that everyone on the map corresponds to 50 meters on the ground. On some, instead of a segment, there is a ready-made phrase, which may look, for example, as follows: “There are 150 meters in one centimeter.” The scale can also be specified as a ratio of the following form: 1:100000. In this case, we can calculate that a centimeter on the map corresponds to 1000 meters on the ground, since 100000/100 (centimeters in a meter) = 1000 m.

Multiply the distance measured with a ruler or curvimeter, expressed in centimeters, by the number of meters indicated on the map or calculated in one centimeter. The result will be the actual distance, expressed, respectively, in kilometers.

Any map is a miniature image of some territory. The coefficient showing how much the image is reduced in relation to the real object is called scale. Knowing it, you can determine distance By . For real existing maps on paper, the scale is a fixed value. For virtual electronic cards this value changes as the magnification of the map image on the monitor screen changes.

Instructions

If yours is based, then find it, which is called a legend. Most often, it is framed. The legend must indicate the scale of the map, which will tell you, measured in distance according to this will be in reality, at . So, if the scale is 1:15000, then this means that 1 cm per map equal to 150 meters on the ground. If the map scale is 1:200000, then 1 cm laid out on it is equal to 2 km in reality

That distance, which interests you. Please note that if you want to determine how quickly you will walk or get from one house to another in or from one settlement to another, then your route will consist of straight segments. You will not move in a straight line, but along a route that runs along streets and roads.

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Lesson questions:

1. Essence and methods of orientation.

When performing many combat missions, commanders' actions are inevitably related to terrain orientation. The ability to navigate is necessary, for example, on the march, in battle, in reconnaissance to maintain the direction of movement, target designation, drawing landmarks, targets and other objects on a map (terrain diagram), control of a unit and fire. Knowledge and skills in orienteering consolidated by experience help to perform more confidently and successfully combat missions in various combat conditions and on unfamiliar terrain.
Find your bearings- this means determining your location and directions to the sides of the horizon relative to surrounding local objects and relief forms, finding the indicated direction of movement and accurately maintaining it along the way. When orienting in a combat situation, the location of the unit relative to friendly and enemy troops, the location of landmarks, and the direction and depth of operations are also determined.
The essence of orientation. Terrain orientation can be general or detailed.
General orientation consists in approximate determination of one’s location, direction of movement and the time required to reach the final destination of movement. This type of orientation is most often used on the march, when the crew of the vehicle does not have a map, but uses only a pre-compiled diagram or list of settlements and other landmarks along the route. To maintain the direction of movement in this case, it is necessary to constantly monitor the time of movement, the distance traveled, determined by the speedometer of the car, and control the passage of settlements and other landmarks according to the diagram (list).
Detailed orientation is to accurately determine your location and direction of movement. It is used when orienting using a map, aerial photographs, land navigation instruments, when moving in azimuth, plotting explored objects and targets on a map or diagram, when determining achieved boundaries, and in other cases.
When navigating the terrain, the simplest elements are widely used. ways of orientation: using a compass, celestial bodies and signs of local objects, as well as a more complex method - orientation on a map.

2. Orientation on the terrain without a map: determining the sides of the horizon by celestial bodies and signs of local objects.

To find the direction according to the cardinal points, first determine the north-south direction; after which, facing north, the determiner will have to the right - east, to the left - west. The cardinal directions are usually found using a compass, and in the absence of one, using the Sun, Moon, stars and some signs of local objects.
2.1 Determination of directions to the sides of the horizon using celestial bodies
In the absence of a compass or in areas of magnetic anomalies, where the compass can give erroneous readings (readings), the sides of the horizon can be determined by the celestial bodies: during the day - by the Sun, and at night - by the North Star or the Moon.

According to the Sun
In the northern hemisphere, the sunrise and sunset locations by season are as follows:

• in winter the Sun rises in the southeast and sets in the southwest;
• in summer the Sun rises in the northeast and sets in the northwest;
• In spring and autumn, the Sun rises in the east and sets in the west.

The sun is approximately at 7.00 in the east, at 13.00 in the south, at 19.00 in the west. The position of the Sun at these hours will indicate the directions east, south and west, respectively.
The shortest shadow from local objects occurs at 13 o'clock, and the direction of the shadow from vertically located local objects at this time will point to the north.
To more accurately determine the sides of the horizon based on the Sun, wristwatches are used.

Table 1

2.2 Determination of directions to the sides of the horizon based on signs of local objects
If there is no compass and the heavenly bodies are not visible, then the sides of the horizon can be determined by some signs of local objects.

By melting snow
It is known that the southern side of objects heats up more than the northern side, and accordingly, the melting of snow on this side occurs faster. It's clearly visible in early spring and during thaws in winter on the slopes of ravines, holes near trees, snow stuck to stones.

By the shadow
At noon, the direction of the shadow (it will be the shortest) points north. Without waiting for the shortest shadow, you can navigate in the following way. Stick a stick about 1 meter long into the ground. Mark the end of the shadow. Wait 10-15 minutes and repeat the procedure. Draw a line from the first shadow position to the second and extend one step beyond the second mark. Place the toe of your left foot opposite the first mark, and the toe of your right foot at the end of the line you drew. You are now facing north.

For local subjects
It is known that the resin protrudes more on the southern half of the trunk coniferous tree, ants arrange their homes with south side tree or bush and make the southern slope of the anthill flatter than the northern one (Fig. 4).

Rice. 4. Determining the sides of the horizon based on local objects.

The bark of birch and pine on the northern side is darker than on the southern side, and tree trunks, stones, and rock ledges are more densely covered with moss and lichens. In large tracts of cultivated forest, the sides of the horizon can be determined by the clearings, which, as a rule, are cut strictly along the north-south and east-west lines, as well as by the inscriptions of block numbers on poles installed at the intersections of the clearings. On each such pillar, in its upper part and on each of the four faces, numbers are affixed - the numbering of the opposite forest blocks; the edge between the two edges with the smallest numbers shows the direction to the north (numbering of blocks forest areas in the CIS it goes from west to east and further to the south).

By buildings
Buildings that are quite strictly oriented along the horizon include churches, mosques, and synagogues.
Altars and chapels of Christian and Lutheran churches face east, bell towers face west.
The lowered edge of the lower crossbar of the cross on the dome Orthodox Church facing south, raised - to the north.
The altars of Catholic churches are located on the western side.
The doors of Jewish synagogues and Muslim mosques face approximately north, their opposite sides are directed: the mosques face Mecca in Arabia, lying on the Voronezh meridian, and the synagogues face Jerusalem in Palestine, lying on the Dnepropetrovsk meridian.
Shrines, pagodas, Buddhist monasteries facades face south.
The exit from the yurts is usually made to the south.
In houses rural areas more windows in living quarters are cut on the south side, and the paint on the walls of buildings on the south side fades more and has a faded color.

3. Determination of the sides of the horizon, magnetic azimuths, horizontal angles and compass direction.

3.1 Determination of directions to the sides of the horizon using a compass
Using a compass, you can most conveniently and quickly determine north, south, west and east (Fig. 5). To do this, you need to give the compass a horizontal position, release the arrow from the clamp, and let it calm down. Then the arrow-shaped end of the arrow will point north.

To determine the accuracy of the deviation of the direction of movement from the direction to the north or to determine the positions of terrain points in relation to the direction to the north and counting them, divisions are marked on the compass, of which the lower divisions are indicated in degree measures (the value of the division is 3 °), and the upper divisions of the protractor in tens of thousands. Degrees are counted clockwise from 0 to 360°, and protractor divisions are counted counterclockwise from 0 to 600°. The zero division is located at the letter “C” (north), and there is also a triangle glowing in the dark, which replaces the letter “C” in some compasses.
Under the letters “B” (east), “Y” (south), “3” (west) there are luminous dots. On the movable cover of the compass there is a sighting device (sight and front sight), against which luminous indicators are mounted, which serve to indicate the direction of movement at night. The most common compass in the army is the Andrianov system and the artillery compass.
When working with a compass, you should always remember that strong electromagnetic fields or nearby metal objects deflect the arrow from its correct position. Therefore, when determining compass directions, it is necessary to move 40-50 m away from power lines, railroad tracks, military vehicles and other large metal objects.
Determining directions to the sides of the horizon using a compass is performed as follows. The sighting device's front sight is placed on the zero scale division, and the compass is placed in a horizontal position. Then the brake of the magnetic needle is released and the compass is turned so that its northern end coincides with the zero reading. After this, without changing the position of the compass, a distant landmark is noticed by sighting through the rear sight and front sight, which is used to indicate the direction to the north.

Then, without changing the position of the compass, install the sighting device so that the line of sight through the rear sight and front sight coincides with the direction of the object. The scale reading against the front sight corresponds to the value of the determined magnetic azimuth of the direction to the local object.
The direction azimuth from the standing point to a local object is called direct magnetic azimuth. In some cases, for example, to find a return path, they use reverse magnetic azimuth, which differs from the straight line by 180°. To determine the reverse azimuth, you need to add 180° to the forward azimuth if it is less than 180°, or subtract 180° if it is greater than 180°.

3.3 Determination of horizontal angles using a compass
First, the front sight of the compass sighting device is set to zero on the scale. Then, by turning the compass in a horizontal plane, align the line of sight through the rear sight and front sight with the direction to the left object (landmark).
After this, without changing the position of the compass, the sighting device is moved to the direction of the right object and a reading is taken on the scale, which will correspond to the value of the measured angle in degrees.
When measuring an angle in thousandths The line of sight is first aligned with the direction towards the right object (landmark), since the count of thousandths increases counterclockwise.

4. Methods for determining distances on the ground and target designation.

4.1. Methods for determining distances on the ground
Very often it is necessary to determine the distances to various objects on the ground. Distances are most accurately and quickly determined using special instruments (rangefinders) and rangefinder scales of binoculars, stereo scopes, and sights. But due to the lack of instruments, distances are often determined using improvised means and by eye.
Common methods for determining the range (distances) to objects on the ground include the following: by the angular dimensions of the object; by linear dimensions of objects; eye; by visibility (discernibility) of objects; by sound, etc.

Determination of distances by angular dimensions objects (Fig. 8) is based on the relationship between angular and linear quantities. The angular dimensions of objects are measured in thousandths using binoculars, observation and aiming devices, a ruler, etc.
Some angular values ​​(in thousandths of the distance) are given in Table 2.
table 2

The distance to objects in meters is determined by the formula: , where B is the height (width) of the object in meters; Y is the angular magnitude of the object in thousandths.
For example (see Fig. 8): 1) the angular size of a landmark observed through binoculars (a telegraph pole with a support), whose height is 6 m, is equal to the small division of the binocular reticle (0-05). Therefore, the distance to the landmark will be equal to: .
2) the angle in thousandths, measured with a ruler located at a distance of 50 cm from the eye, (1 mm is equal to 0-02) between two telegraph poles 0-32 (telegraph poles are located at a distance of 50 m from each other). Therefore, the distance to the landmark will be equal to: .
3) tree height in thousandths, measured with a 0-21 ruler (true tree height 6 m). Therefore, the distance to the landmark will be equal to: .
Determining distances by linear dimensions of objects is as follows (Fig. 9). Using a ruler located at a distance of 50 cm from the eye, measure the height (width) of the observed object in millimeters. Then the actual height (width) of the object in centimeters is divided by that measured by a ruler in millimeters, the result is multiplied by a constant number 5 and the desired height of the object in meters is obtained.

For example, a distance between telegraph poles equal to 50 m (Fig. 8) is closed on the ruler by a segment of 10 mm. Therefore, the distance to the telegraph line is:
The accuracy of determining distances by angular and linear values ​​is 5-10% of the length of the measured distance. To determine distances based on the angular and linear dimensions of objects, it is recommended to remember the values ​​(width, height, length) of some of them, given in table. 3.
Table 3

Determining distances by eye
Eye-measuring- this is the easiest and fastest way. The main thing in it is the training of visual memory and the ability to mentally lay down a well-imagined constant measure on the ground (50, 100, 200, 500 meters). Having fixed these standards in memory, it is not difficult to compare with them and estimate distances on the ground.
When measuring distance by successively mentally setting aside a well-studied constant measure, one must remember that the terrain and local objects seem reduced in accordance with their distance, that is, when removed by half, the object will seem half as large. Therefore, when measuring distances, the mentally plotted segments (measures of terrain) will decrease according to the distance.
The following must be taken into account:

• the closer the distance, the clearer and sharper the visible object seems to us;
• the closer an object is, the larger it appears;
• larger objects seem closer than small objects located at the same distance;
• an object of a brighter color appears closer than an object of a dark color;
• brightly lit objects seem closer to dimly lit ones that are at the same distance;
• during fog, rain, at dusk, cloudy days, when the air is saturated with dust, the observed objects seem further away than in clear and sunny days;
• the sharper the difference in color of the object and the background against which it is visible, the more reduced the distances seem; for example, in winter a snow field seems to bring the darker objects on it closer;
• objects on flat terrain seem closer than on hilly terrain, distances defined across vast expanses of water seem especially shortened;
• folds of the terrain (river valleys, depressions, ravines), invisible or not fully visible to the observer, conceal the distance;
• when observing while lying down, objects seem closer than when observing while standing;
• when observed from the bottom up - from the bottom of the mountain to the top, objects seem closer, and when observed from top to bottom - further;
• when the sun is behind the soldier, the distance disappears; shines into the eyes - it seems larger than in reality;
• The fewer objects there are in the area under consideration (when observed through a body of water, a flat meadow, steppe, arable land), the smaller the distances seem.

The accuracy of the eye meter depends on the training of the soldier. For a distance of 1000 m common mistake fluctuates between 10-20%.

Determination of distances by visibility (discernibility) of objects
With the naked eye, you can approximately determine the distance to targets (objects) by the degree of their visibility. A soldier with normal visual acuity can see and distinguish some objects from the following maximum distances indicated in Table 4.
It must be borne in mind that the table indicates the maximum distances from which certain objects begin to be visible. For example, if a serviceman saw a pipe on the roof of a house, this means that the house is no more than 3 km away, and not exactly 3 km. It is not recommended to use this table as a reference. Each serviceman must individually clarify this data for himself.
Table 4

Orientation by sounds.
At night and in fog, when observation is limited or impossible at all (and in very rough terrain and in the forest, both at night and during the day), hearing comes to the aid of vision.
Military personnel must learn to determine the nature of sounds (that is, what they mean), the distance to the sources of sounds and the direction from which they come. If different sounds are heard, the soldier must be able to distinguish them from one another. The development of such an ability is achieved through long-term training (in the same way a professional musician distinguishes the voices of instruments in an orchestra).
Almost all sounds that indicate danger are made by humans. Therefore, if a soldier hears even the faintest suspicious noise, he should freeze in place and listen. If the enemy starts moving first, thereby giving away his location, then he will be the first to be detected.
Quietly summer night even an ordinary human voice in open space can be heard far away, sometimes half a kilometer. On a frosty autumn or winter night, all kinds of sounds and noises can be heard very far away. This applies to speech, steps, and the clinking of dishes or weapons. In foggy weather, sounds can also be heard far away, but their direction is difficult to determine. On the surface of calm water and in the forest, when there is no wind, sounds travel a very long distance. But the rain greatly muffles the sounds. The wind blowing towards the soldier brings sounds closer and away from him. It also carries sound to the side, creating misrepresentation about the location of its source. Mountains, forests, buildings, ravines, gorges and deep hollows change the direction of sound, creating an echo. They also generate echoes and water spaces, facilitating its spread over long distances.
The sound changes when its source moves on soft, wet or hard soil, along the street, along a country or field road, on pavement or soil covered with leaves. It must be taken into account that dry soil transmits sounds better than air. At night, sounds are transmitted especially well through the ground. That’s why they often listen by putting their ears to the ground or tree trunks. Average range The audibility of various sounds during the day on level ground, km (in summer), is given in Table 5.
Table 5

To listen to sounds while lying down, you need to lie on your stomach and listen while lying down, trying to determine the direction of the sounds. This is easier to do by turning one ear in the direction from which the suspicious noise is coming. To improve audibility, it is recommended to apply bent palms, a bowler hat, or a piece of pipe to the auricle.
To better listen to sounds, you can put your ear to a dry board placed on the ground, which acts as a sound collector, or to a dry log dug into the ground.

Determining distances using the speedometer. The distance traveled by a car is determined as the difference between the speedometer readings at the beginning and end of the journey. When driving on hard-surfaced roads it will be 3-5%, and on viscous soil 8-12% more than the actual distance. Such errors in determining distances using the speedometer arise from wheel slip (track slippage), tire tread wear and changes in tire pressure. If you need to determine the distance traveled by the car as accurately as possible, you need to make an amendment to the speedometer readings. This need arises, for example, when moving in azimuth or when orienting using navigation devices.
The amount of correction is determined before the march. For this purpose, a section of the road is selected, which in terms of the nature of the relief and soil cover is similar to the upcoming route. This section is passed at marching speed in the forward and reverse directions, taking speedometer readings at the beginning and end of the section. Based on the data obtained, the average length of the control section is determined and the value of the same section, determined from a map or on the ground with a tape (roulette), is subtracted from it. Dividing the result obtained by the length of the section measured on the map (on the ground) and multiplying by 100, the correction factor is obtained.
For example, if the average value of the control section is 4.2 km, and the measured value on the map is 3.8 km, then the correction factor is:
Thus, if the length of the route measured on the map is 50 km, then the speedometer will read 55 km, i.e. 10% more. The difference of 5 km is the magnitude of the correction. In some cases it may be negative.

Measuring distances in steps. This method is usually used when moving in azimuth, drawing up terrain diagrams, drawing individual objects and landmarks on a map (scheme), and in other cases. Steps are usually counted in pairs. When measuring a long distance, it is more convenient to count steps in threes, alternately under the left and right foot. After every hundred pairs or triplets of steps, a mark is made in some way and the countdown begins again.
When converting the measured distance in steps into meters, the number of pairs or triplets of steps is multiplied by the length of one pair or triple of steps.
For example, there are 254 pairs of steps taken between turning points on the route. The length of one pair of steps is 1.6 m. Then
Typically, the step of a person of average height is 0.7-0.8 m. The length of your step can be determined quite accurately using the formula: , where D is the length of one step in meters; P is a person’s height in meters.
For example, if a person is 1.72 m tall, then his step length will be equal to:
More precisely, the step length is determined by measuring some flat linear section of terrain, for example a road, with a length of 200-300 m, which is measured in advance with a measuring tape (tape measure, range finder, etc.).
When measuring distances approximately, the length of a pair of steps is taken to be 1.5 m.
The average error in measuring distances in steps, depending on driving conditions, is about 2-5% of the distance traveled.

Determination of distance by time and speed. This method is used to approximate the distance traveled, for which the average speed is multiplied by the time of movement. average speed pedestrian speed is about 5, and when skiing 8-10 km/h.
For example, if a reconnaissance patrol skied for 3 hours, then it covered about 30 km.

Determination of distances by the ratio of the speeds of sound and light. Sound travels in the air at a speed of 330 m/s, i.e. approximately 1 km per 3 s, and light travels almost instantly (300,000 km/h). Thus, the distance in kilometers to the place of the flash of the shot (explosion) is equal to the number of seconds that passed from the moment of the flash to the moment when the sound of the shot (explosion) was heard, divided by 3.
For example, an observer heard the sound of an explosion 11 seconds after the flash. The distance to the flash point will be:
Determining distances geometric constructions on the ground. This method can be used to determine the width of difficult or impassable terrain and obstacles (rivers, lakes, flooded areas, etc.). Figure 10 shows the determination of the river width by constructing an isosceles triangle on the ground.
Since in such a triangle the legs are equal, the width of the river AB is equal to the length of the leg AC.
Point A is selected on the ground so that a local object (point B) on the opposite bank can be seen from it, and a distance equal to its width can be measured along the river bank.

In both the first and second cases, the angle at point A should be equal to 90°.
Orientation by light very convenient for maintaining direction or for determining the position of an object on the ground. Moving at night towards a light source is most reliable. The distances at which light sources can be detected by the naked eye at night are given in Table 6.

Useful tips for tourists. How to determine distance by sound and eye. Ranging.

On a hike, especially in unknown terrain and with not very detailed map Often there is a need for orientation and determining the range to any objects or objects. And even a GPS receiver will not help you here, since it must also come with a map. And with them (on Russian territory) it’s very difficult. Linking the same coordinates with tourist map very conditional (+- kilometer).

Perhaps they will help you simple tips accumulated by many years of tourist experience of predecessors.

1. On open area settlements visible from 10-12 km.

2. Multi-storey buildings - 8-10 km.

3. Separate one-story (private) houses - 5-6 km.

4. The windows in the houses are visible from 4 km away.

5. Roof stove pipes - 3 km.

6. Individual trees are visible from 2 km away.

7. People (in the form of points) - 1.5 - 2 km.

8. The movement of a person's arms and legs is 700 meters.

9. Window frames - 500 meters.

10. Human head - 400 m.

11. Color and parts of clothing - 250-300 m.

12. Leaves on trees - 200 m.

13. Facial features and hands - 100 m.

14. Eyes in the form of dots - 60-80 m.

At night time:

1. A burning fire (of normal size) is visible at a distance of 6-8 km.

2. Light of an electric flashlight (regular) - 1.5 - 2 km.

3. Burning match - 1-1.5 km.

4. Cigarette fire - 400-500 m.

Determining distance by sound strongly depends on air density and also to a greater extent from its humidity. The higher the pressure and the higher the humidity, the farther sounds travel. This must be taken into account. For quiet place and at normal humidity:

1. Noise railway(of a running train) can be heard 5-10 km away.

2. Shot from a gun - 2-4 km.

3. A car horn, a tractor starter crackling, a loud whistle - 2-3 km.

4. Barking dogs - 1-2 km.

5. Car traffic on the highway is 1-2 km.

6. Human screams are unintelligible - 1 - 1.5 km.

7. The sound of a car engine revving - 0.5 - 1 km.

8. The sound of a falling tree (crackling) - 800 - 1000 meters.

9. Ax knock, knock on metal objects- 300-500 meters.

10. Calm conversation between people - 200 meters.

11. Low speech, cough - 50 - 100 meters.

Psychological adjustments that need to be taken into account:

2. The distance on a “smooth” surface (snow, water, flat field) seems less than actual. The width of the river from the flat bank is greater than from the cliff.

3. When looking from the bottom up, the slope appears less steep, and the distance to objects is less than actual.

4. Night any light seems significant (!) closer than the actual distance. During the day, light objects also appear closer.

5. Bare slopes appear steeper than those covered with vegetation.

6. Way back seems shorter. A smooth road seems shorter than a rough one.

A simple way to determine the distance to objects using the similar triangles method.

This method is based on a simple mathematical ratio of the sides of triangles and knowledge of a couple of quantities, such as: 1) The length of a person's thumb is approximately 6 cm (60 mm) and 2) The distance from the thumb to the person's eyes with an outstretched arm is approximately 60 cm. ( Of course, you can accurately measure your own parameters and make appropriate adjustments to the formula.By the way, instead of your thumb it is more convenient to use an ordinary match (length 45 mm)).

In order to accurately determine the distance to an object, you also need to know its dimensions, height, in particular.

For example, we need to determine the distance to a village. Average height house walls - approx. 3 meters. The roof is the same height. Those. The height of the house is about 6 meters. We stretch out our hand with our thumb up and evaluate which part of the finger “fits” the house. Let's say it's about 1/3 of a finger, i.e. 2 cm.

In such triangles, the true height will be as related to the true distance as the "projection" of the height will be to the distance to that projection from the viewpoint. (or vice versa).

Those. 6 meters height / X meters (distance) = 2 cm / 60 cm, or

X meters / 6 = 60/2

From here we get that X = 6 x 30, i.e. 180 meters to the house.

If you know the height of an object and have a ruler (tape measure) with you, then you can calculate distances very accurately (with sufficient accuracy for tourist purposes).

If the height of the object is unknown, even approximately, then a slightly more complex problem needs to be solved, which will allow us to calculate both the distance to the object and its height. To do this, you will need to take two measurements of the projection of the height of the object from two different points. After the first measurement, you need to approach the object at some distance (and remember this distance, let’s denote it “L”, the first projection “h1”, and the second “h2”).

I won’t bore you with mathematical calculations, but will immediately give you the formula:

X = (L x h1) / (h2 - h1) (h2 will be larger if you were moving closer to the object).

Well, now knowing the distance to the object it is easy to calculate its height (H):

H (m) = X x h2 / 0.6

These simple formulas will allow you to very accurately navigate the terrain and determine distances without a rangefinder.

DETERMINING DISTANCE - BY CONSTRUCTING SIMILAR TRIANGLES

When determining the distance to inaccessible objects, various techniques are used related to the construction of similar triangles.

Determination of distance by linear dimensions of objects. To measure the distance, the tourist, holding a ruler at arm's length, points it at an object (Fig. 56), the height (length) of which is approximately known to him. Thus, a person’s height in meters is 1.7, a bicycle wheel has a height of 0.75, a wooden communication line pole has a height of 5-7, a one-story house with a roof has a height of 7-8, a middle-aged forest has a height of 18-20; a car has a length of 4-4.5, a truck - 5-6, a railway passenger car - 24-25; The distance between communication line poles is on average 50-60 m, etc. Let's say we need to determine the distance to the communication line pole. On the ruler, his image took 20 mm. Taking the arm length of an adult to be approximately 60 cm, we create the proportion:

Length of the arm/distance to the pillar=size of the image on the ruler/height of the pillar

X=(0.6*6)/0.02=180

Thus, the distance to the post is 180 m.

Hiking standards. To take measurements along the route using the construction of similar triangles, it is useful for tourists to know some other hiking standards.
The length of the “quarter”, that is, the distance between the ends of the spaced thumb and little finger of an adult, is approximately 18-22 cm. The length of the index finger from the base of the thumb is 11-13 cm, from the base of the middle finger - 7-8 cm. The greatest distance between the ends of the large and index finger 16-18 cm, between the ends of the index and middle fingers - 8-10 cm. The distance from the eyes to the raised thumb of an outstretched hand is 60-70 cm. The width of the index finger is about 2 cm, the width of its nail is 1 cm. The width of the four fingers of the palm is 7 -8 cm.
Each tourist determines the specific length of these and other standards independently and writes it down in his hiking notebook.

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1. Measuring angles on the ground using available objects, rulers, binoculars, compass, observation and aiming devices

The location of the object (target) is usually determined in relation to the landmark that is closest to the object (target). It is enough to know two coordinates of the object (target): range, that is, the distance from the observer to the object (target), and the angle (to the right or left of the landmark) at which the object (target) is visible to us, and then the location of the object (target) will be completely determined exactly.
If distances to an object (target) are determined by direct measurement or calculation using the “thousandth” formula, then angular values ​​can be measured using improvised objects, rulers, binoculars, compass, tower inclinometer, observation and aiming devices and others measuring instruments.

1.1. Measuring angles on the ground using available objects.
Without measuring instruments, to approximately measure angles in thousandths on the ground, you can use improvised objects, the dimensions of which (in millimeters) are known in advance. This could be: a pencil, a cartridge, a matchbox, a front sight and a machine gun magazine, etc.
The palm, fist and fingers can also become a good goniometric device if you know how many “thousandths” they contain, but in this case you need to remember that different people have different arm lengths and different widths of the palm, fist and fingers. Therefore, before using his palm, fist and fingers to measure angles, each soldier must determine their “price” in advance.

The “price” of fingers, fist, pencil and matchbox in thousandths (“the price” of fingers and fist is individual for each serviceman)

To determine the angular value, you need to know that a segment of 1 mm, distant from the eye by 50 cm, corresponds to an angle of two thousandths (written: 0-02). For example, the width of a fist is 100 mm, therefore, its “price” in angular values ​​is equal to 2-00 (two hundred thousandths), and if, for example, the width of a pencil is 6 mm, then its “price” in angular values ​​will be equal to 0-12 (twelve thousandths). When measuring angles in thousandths, it is customary to name and write first the number of hundreds, and then tens and units of thousandths. If there are no hundreds or tens, zeros are called and written instead, for example: (see table).

1.2. Measuring angles on the ground using a ruler.
To measure angles in thousandths using a ruler, you need to hold it in front of you, at a distance of 50 cm from the eye, then one division (1 mm) will correspond to 0-02. When measuring an angle, you need to count the number of millimeters between objects (landmarks) on a ruler and multiply by 0-02.

Measuring angles using a ruler with millimeter divisions.

The result obtained will correspond to the value of the measured angle in thousandths. For example (see figure), for a segment of 32 mm the angular value will be 64 thousandths (0-64), for a segment of 21 mm - 42 thousandths (0-42). Remember that the accuracy of measuring angles using a ruler depends on your skill in placing the ruler exactly 50 cm from the eye. To do this, you can practice, or better yet, take measurements, using a rope (thread) with two knots, the distance between which is 50 cm. When you extend the ruler (hand) by 50 cm, one knot (rope) of the thread is clamped in the teeth, and the other - presses his finger against the ruler.

To measure an angle in degrees, the ruler is placed in front of you at a distance of 60 cm. In this case, 1 cm on the ruler will correspond to 1°.

1.3. Measuring angles on the ground using binoculars.
In the field of view of the binoculars there are two mutually perpendicular goniometric scales (grids). One of them is used to measure horizontal angles, the other is used to measure vertical angles.

Measuring angles with binoculars

The value of one large division corresponds to 0-10 (ten thousandths), and the value of a small division corresponds to 0-05 (five thousandths). To determine the angles to an object (target) on the ground using binoculars, you need to place the object (target) between the binocular scale divisions, count the number of scale divisions and find out its angular value. To measure the angle between two objects (for example, between a landmark and a target), you need to combine a scale stroke with one of them and count the number of divisions against the image of the second. By multiplying the number of divisions by the price of one division, we obtain the value of the measured angle in thousandths.

1.4. Measuring angles on the ground using a compass.
The compass scale can be graduated in degrees and protractor divisions. Don't go wrong with the numbers. Degrees in a circle - 360; Protractor divisions - 6000.
Measuring angles in thousandths using a compass is carried out as follows. First, the front sight of the compass sighting device is set to zero on the scale. Then, by turning the compass in a horizontal plane, align the line of sight through the rear sight and front sight with the direction to the right object (landmark).
After this, without changing the position of the compass, the sighting device is moved to the direction of the left object and a reading is taken on the scale, which will correspond to the value of the measured angle in thousandths. Indications are taken on a compass scale, graduated in protractor divisions.
When measuring an angle in degrees, the line of sight is first aligned with the direction to the left object (landmark), since the count of degrees increases clockwise, and readings are taken on a compass scale graduated in degrees.

1.5. Measuring angles on the ground using observation and aiming devices.
Observation and aiming devices have scales similar to those of binoculars, so angles are measured with these devices in the same way as with binoculars.

2. Determination of distances on the ground by the degree of visibility and audibility, by the linear and angular dimensions of objects, by the ratio of the speed of light and sound, time and speed of movement, in steps

2.1. Determining distances on the ground based on the degree of visibility of objects.
With the naked eye, you can approximately determine the distance to objects (targets) by the degree of their visibility.
A soldier with normal visual acuity can see and distinguish some objects from the following maximum distances indicated in the table.

Determination of distances by visibility (discernibility)
some objects

It must be borne in mind that the table indicates the maximum distances from which certain objects begin to be visible. For example, if a serviceman saw a pipe on the roof of a house, this means that the house is no more than 3 km away, and not exactly 3 km. It is not recommended to use this table as a reference. Each serviceman must individually clarify this data for himself.

2.2. Determining distances on the ground based on the degree of audibility of objects.
At night and in fog, when observation is limited or impossible at all (and in very rough terrain and in the forest, both at night and during the day), hearing comes to the aid of vision.
Military personnel must learn to determine the nature of sounds (that is, what they mean), the distance to the sources of sounds and the direction from which they come. If different sounds are heard, the soldier must be able to distinguish them from one another. The development of this ability is achieved through long-term training.
Almost all sounds that indicate danger are made by humans. Therefore, if a soldier hears even the faintest suspicious noise, he should freeze in place and listen. It is possible that an enemy is hiding not far from him. If the enemy starts moving first, thereby giving away his location, then he will be the first to die. If a scout does this, the same fate will befall him.
On a quiet summer night, even an ordinary human voice in an open space can be heard far away, sometimes half a kilometer. On a frosty autumn or winter night, all kinds of sounds and noises can be heard very far away. This applies to speech, steps, and the clinking of dishes or weapons. In foggy weather, sounds can also be heard far away, but their direction is difficult to determine. On the surface of calm water and in the forest, when there is no wind, sounds travel a very long distance. But the rain greatly muffles the sounds. The wind blowing towards the soldier brings sounds closer and away from him. It also carries sound away, creating a distorted picture of the location of its source. Mountains, forests, buildings, ravines, gorges and deep hollows change the direction of sound, creating an echo. They also generate echoes and water spaces, facilitating its spread over long distances.
The sound changes when its source moves on soft, wet or hard soil, along the street, along a country or field road, on pavement or soil covered with leaves. It must be taken into account that dry soil transmits sounds better than air. At night, sounds are transmitted especially well through the ground. That’s why they often listen by putting their ears to the ground or tree trunks.

Average range of audibility of various sounds
during the day on flat terrain, km (summer)

There are certain ways to help you listen at night, namely:

• lying down: put your ear to the ground;
• standing: lean one end of the stick to your ear, rest the other end on the ground;
• stand, slightly leaning forward, shifting the center of gravity of the body to one leg, with a half-open mouth - the teeth are a conductor of sound.

When sneaking up, a trained soldier lies down on his stomach and listens while lying down, trying to determine the direction of the sounds. This is easier to do by turning one ear in the direction from which the suspicious noise is coming. To improve audibility, it is recommended to apply bent palms, a bowler hat, or a piece of pipe to the auricle.
To better listen to sounds, a soldier can put his ear to a dry board placed on the ground, which acts as a sound collector, or to a dry log dug into the ground.
If necessary, you can make a homemade water stethoscope. To do this, use a glass bottle (or metal flask), filled with water up to the neck, which is buried in the ground until the water level in it. A tube (plastic) is tightly inserted into the cork, onto which a rubber tube is placed. The other end of the rubber tube, equipped with a tip, is inserted into the ear. To check the sensitivity of the device, you need to hit the ground with your finger at a distance of 4 m from it (the sound of the impact is clearly audible through the rubber tube).

2.3. Determination of distances on the ground by the linear dimensions of objects.
Determining distances based on the linear dimensions of objects is as follows: using a ruler located at a distance of 50 cm from the eye, measure the height (width) of the observed object in millimeters. Then the actual height (width) of the object in centimeters is divided by that measured by a ruler in millimeters, the result is multiplied by a constant number 5 and the desired height (width) of the object in meters is obtained.
For example, a telegraph pole 6 m high (see figure) covers a 10 mm segment on the ruler. Therefore, the distance to it is:

The accuracy of determining distances using linear values ​​is 5-10% of the length of the measured distance.

2.4. Determining distances on the ground based on the angular dimensions of objects.
To apply this method, you need to know the linear size of the observed object (its height, length or width) and the angle (in thousandths) at which this object is visible. The angular dimensions of objects are measured using binoculars, observation and aiming devices, and improvised means.
The distance to objects in meters is determined by the formula:

For example, the height of a railway booth is 4 meters, a soldier sees it at an angle of 25 thousandths. Then the distance to the booth will be:
.
Or a serviceman sees a Leopard-2 tank at a right angle from the side. The length of this tank is 7 meters 66 centimeters. Let's assume that the viewing angle is 40 thousandths. Therefore, the distance to the tank is 191.5 meters.
To determine the angular value using available means, you need to know that a segment of 1 mm, distant from the eye by 50 cm, corresponds to an angle of two thousandths (written 0-02). From here it is easy to determine the angular value for any segments.
For example, for a segment of 0.5 cm, the angular value will be 10 thousandths (0-10), for a segment of 1 cm - 20 thousandths (0-20), etc. The easiest way is to memorize the standard values ​​of thousandths.

Angular values ​​(in thousandths of distance)

The accuracy of determining distances by angular values ​​is 5-10% of the length of the measured distance.
To determine distances by the angular and linear dimensions of objects, it is recommended to remember the values ​​(width, height, length) of some of them, or to have this data at hand (on a tablet, in a notebook). The sizes of the most frequently encountered objects are shown in the table.

Linear dimensions of some objects

2.5. Determination of distances on the ground by the ratio of the speeds of sound and light.
Sound travels in the air at a speed of 330 m/s, i.e. approximately 1 km per 3 s, and light travels almost instantly (300,000 km/h).
Thus, for example, the distance in kilometers to the location of the flash of a shot (explosion) is equal to the number of seconds that passed from the moment of the flash to the moment when the sound of the shot (explosion) was heard, divided by 3.
For example, an observer heard the sound of an explosion 11 s after the flash. The distance to the flash point will be:

2.6. Determination of distances on the ground by time and speed.
This method is used to approximate the distance traveled, for which the average speed is multiplied by the time of movement. The average walking speed is about 5, and when skiing 8-10 km/h.
For example, if a reconnaissance patrol skied for 3 hours, then it covered about 30 km.

2.7. Determining distances on the ground in steps.
This method is usually used when moving in azimuth, drawing up terrain diagrams, drawing individual objects and landmarks on a map (scheme), and in other cases. Steps are usually counted in pairs. When measuring a long distance, it is more convenient to count steps in threes, alternately under the left and right foot. After every hundred pairs or triplets of steps, a mark is made in some way and the countdown begins again. When converting the measured distance in steps into meters, the number of pairs or triplets of steps is multiplied by the length of one pair or triple of steps.
For example, there are 254 pairs of steps taken between turning points on the route. The length of one pair of steps is 1.6 m. Then:

Typically, the step of a person of average height is 0.7-0.8 m. The length of your step can be determined quite accurately using the formula:

For example, if a person is 1.72 m tall, then his step length will be:

More precisely, the step length is determined by measuring some flat linear section of terrain, for example a road, with a length of 200-300 m, which is measured in advance with a measuring tape (tape measure, range finder, etc.).
When measuring distances approximately, the length of a pair of steps is taken to be 1.5 m.
The average error in measuring distances in steps, depending on driving conditions, is about 2-5% of the distance traveled.

3. Compliance with the standard: “Measuring distances (angles) on the ground using binoculars (ruler with millimeter divisions)”

3.1. Features of developing standards for military topography.
1. Standards for military topography during classes and training are practiced using serviceable training facilities.
2. The standard is considered fulfilled if the conditions for its implementation are met during work and there have been no violations of safety requirements, as well as charters, manuals, instructions and manuals.
3. If, when working out the standard, a student makes at least one mistake that could lead to injury (defeat) to personnel, breakdown of equipment, weapons or an accident, fulfillment of the standard is stopped and assessed "unsatisfactory".
4. For violation of the sequence of compliance with the standard, which did not lead to accidents, breakdown (damage) of equipment and weapons, as well as for every error leading to a violation of the conditions for fulfilling the standard, the requirements of charters, manuals, manuals, instructions, technological maps, the score is reduced by one point.
5. When standards are met by personnel wearing skin protective equipment (OZK, L-1, etc.), the time increases by 25%, and when working in respiratory protection equipment (gas mask, respirator) - by 10%, in addition to the standards, the implementation of which is provided only in protective equipment.
6. At an air temperature of minus 10° C and below, plus 30° C and above, with heavy rain, snowfall, altitude above 1500 m above sea level, the time to comply with standards increases to 20%, when operating at night, if the time is for night conditions not defined, it increases to 30%.
7. When units (military personnel) operate in muddy conditions, desert-sandy terrain, polar tundra, deep snow cover (30-50 cm - when operating on foot and on wheeled vehicles, 50-80 cm - when operating on tracked vehicles) , dense fog and heavy dust, the time to comply with the standards increases, the speed of movement is reduced by the decision of the lesson leader (inspector) by no less than 10%, but no more than 30% (taking into account the totality of negative conditions).
8. When working out standards on the ground, routes (directions) for unit actions are not laid out or designated in advance.
9. The time for fulfilling the standard by a military personnel (unit) is counted using a stopwatch from the moment the command is given “ To fulfill the standard - Get started"(or other established command, signal) until the standard is fulfilled by all military personnel (unit) and the commander (trainee) reports on its implementation or until actions begin in a new order.

3.2. The procedure for determining the assessment for meeting standards.
If a standard is practiced several times during the training process, then the grade for its implementation is determined based on the last result shown or on the result of a control attempt.
An individual assessment for a serviceman for fulfilling several standards for military medical training is determined by the marks received for fulfilling each standard, and is considered:

The grade for fulfilling single standards for the unit is derived from the individual assessments of students and is determined:

3.3. Conditions for fulfillment and guidelines for developing the standard.

The procedure for complying with the standard

We often hear that shooters simply do not know how to determine the distance to the target (target) at which they need to shoot. And this despite the fact that an optical sight is installed on the rifle or shotgun (carbine). In general, the topic of optical sights is very common in questions on forums and letters from readers. The main issues are reticles and distances to the object of observation. Which reticle is best for long range shooting? Why big ones? Yes, because at a distance of 10 to 20 m it is easier to use a red dot sight. I decided to organize some information regarding optics and distance.

A simple method for determining the distance to an object

In the picture below you can see the aiming reticle Rangefinder, or as it is popularly called - “crossbow net”. Sights with this type of reticle have become very popular among owners of weapons with optical sights. A convenient scale for calculating distances and at the same time auxiliary crosshairs allow you to very accurately calculate the distance to the target, making certain adjustments. The figure clearly shows how you can determine the distance to a target using the example of a 4x32 optical sight.

Visual determination of the distance to the target using an optical sight
(Rangefinder reticle, or crossbow reticle)

It is worth noting that the setup and preliminary calibration of each sight must be carried out separately. This should be done as follows:
- take a “standard” with a vertical and horizontal dimension of 50 cm (for example, a cardboard box),
- set the scope magnification to 4 (if you have a scope with variable magnification) and look at the “standard” through the optical sight from a distance of 30 m. Usually at this distance 0.5 meters of width is placed between the curves at the level of the central crosshair.

If the “standard” does not fit between the curves or, on the contrary, is much smaller, then you need to change the distance to the target until you achieve desired result. Remember this distance, or better yet, make a note to yourself so that later, when needed, you can quickly calculate the distance to the target.

In the same way, we find the distances corresponding to all other aiming marks on the reticle. After this, you can begin to zero in the sight. “Why not the other way around?” - you ask. Yes, because it is easier to sight the sight at already known distances. Now, looking at your hunting object through an optical sight, you will know exactly the distance to the target.

Such sights can be installed on air guns and firearms.

To approximately determine the distance, a sniper or shooter can use the following simplest methods.

An eye-based method for determining the distance to a target

To hit the target with the first shot, you need to know the distance to it. This is necessary for correct definition correction values ​​for side wind, air temperature, Atmosphere pressure and, most importantly, to install the correct sight and select the aiming point.

The ability to quickly and accurately determine the distance to stationary, moving, and emerging targets is one of the main conditions for the successful work of a sniper.

Rice. Proportional perception of the target by the sniper with the reticle of the PSO-1 sight for the development of automatic skills in determining the range

The main one, the simplest and fastest, most accessible to a sniper in any combat situation. However, a sufficiently accurate eye is not acquired immediately; it is developed through systematic training carried out in various terrain conditions, at different times of the year and day. To develop your eye, you need to more often practice estimating distances by eye, necessarily checking them in steps and on a map or in some other way.

First of all, you need to learn to mentally imagine and confidently distinguish several distances that are most convenient as standards on any terrain. You should start training with short distances (10, 50, 100 m). Having mastered these distances well, you can move successively to larger ones (200, 400, 800 m) up to the maximum range of actual fire sniper rifle. Having studied and consolidated these standards in visual memory, you can easily compare with them and evaluate other distances.

During such training, the main attention should be paid to taking into account side effects that affect the accuracy of the visual method of determining distances:
1. Larger objects seem closer than small ones located at the same distance.
2. Objects that are visible more sharply and clearly seem to be closer together, therefore:
- objects of bright colors (white, yellow, red) seem closer than objects of dark colors (black, brown, blue),
- brightly lit objects seem closer to dimly lit ones that are at the same distance,
- during fog, rain, at dusk, on cloudy days, when the air is saturated with dust, observed objects seem further away than on clear sunny days,
- the sharper the difference in the color of objects and the background against which they are visible, the more reduced the distances to these objects seem; for example, in winter, a snow field seems to bring all the darker objects on it closer.

3. The fewer intermediate objects are between the eye and the observed object, the closer this object seems, in particular:
- objects on level ground seem closer,
- distances defined through vast open water spaces seem especially shortened; the opposite shore always seems closer than in reality,
- folds of the terrain (ravines, hollows) crossing the measured line seem to reduce the distance,
- when observing while lying down, objects seem closer than when observing while standing.

4. When observed from bottom to top, from the bottom of the mountain to the top, objects appear closer, and when observed from top to bottom, they appear further away.

Visibility of objects at different distances:

Determining the distance to the target by angular dimensions

Determining the distance to a target by angular dimensions is possible if the observable linear value (height, width or length) of the object to which the distance is determined is known. The method comes down to measuring the angle in thousandths at which this object is visible.

The thousandth is 1/6000 part of the circular horizon, increasing in width in direct proportion to the increase in the distance to the reference point, which is the center of the circle. For those who have a hard time understanding, remember that the thousandth is in distance:

100 m = 10 cm,

200 m = 20 cm,

300 m = 30 cm,

400 m = 40 cm, etc.

Knowing the approximate linear dimensions of a target or landmark in meters and the angular magnitude of this object, you can determine the distance using the thousandth formula: D = (H x 1000)/U,
Where D- distance to target
1000 - a constant, unchangeable mathematical quantity that is always present in this formula
U- the angular magnitude of the target, that is, to put it simply, how many one-thousandth divisions on the scale of an optical sight or other device will the target occupy
IN- metric (that is, in meters) known width or height of the target.

For example, a target is detected. It is necessary to determine the distance to it. What are the actions?
1. Measure the target angle in thousand.
2. The size of the object located next to the target in meters, multiply by 1000
3. Divide the result obtained by the measured angle in thousand.

The metric parameters of some objects are:

The scales of open sights, optical sights and optical instruments available in service are graduated in thousandths and have a division value:

Thus, to determine the distance to an object using optics, it is necessary to place it between the scale divisions of the sight (device) and, having found out its angular value, calculate the distance using the above formula.

Example, you need to determine the distance to the target (chest or height target), which fits into one small side segment of the scale of the PSO-1 optical sight.

Solution, the width of the chest or height target (full-length infantryman) is 0.5 m. According to measurements using PSO-1, the target is covered by one division of the lateral correction scale, i.e. angle 1 thousandth.
Hence: D=(0.5 x 1000)/1=500m.

Measuring angles using improvised means

To measure angles with a ruler, you need to hold it in front of you, at a distance of 50 cm from the eye, then one of its divisions (1 mm) will correspond to 0-02.
The accuracy of measuring angles using this method depends on the skill in placing the ruler exactly 50 cm from the eye. You can practice this using a rope (thread) of this length.
To measure angles with improvised objects, you can use your finger, palm or any small object at hand ( matchbox, pencil, 7.62 mm sniper cartridge), the dimensions of which in millimeters, and therefore in thousandths, are known. To measure the angle, such a measure is also placed at a distance of 50 cm from the eye, and from it the desired angle value is determined by comparison.

The angular dimensions of some objects are:

Having acquired skills in measuring angles, you should proceed directly to determining distances based on the measured angular dimensions of objects.
Determining distances by the angular dimensions of objects gives accurate results only if the actual dimensions of the observed objects are well known, and angular measurements are made carefully using measuring instruments (binoculars, stereo scopes).