Simple ways to determine and measure distances on the ground, by eye, by measured angular values ​​of local objects, by measuring in steps, by ear. Location orientation

Measuring distance is one of the most basic tasks in geodesy. There are different distances, as well as a large number of devices created to carry out this work. So, let's look at this issue in more detail.

Direct method for measuring distances

If you need to determine the distance to an object in a straight line and the area is accessible for research, use such a simple device for measuring distance as a steel tape measure.

Its length is from ten to twenty meters. A cord or wire can also be used, with white markings after two and red after ten meters. If it is necessary to measure curved objects, the old and well-known two-meter wooden compass (fathom) or, as it is also called, “Kovalyok”, is used. Sometimes it becomes necessary to make preliminary measurements of approximate accuracy. They do this by measuring the distance in steps (at the rate of two steps equal to the height of the person measuring minus 10 or 20 cm).

Measuring distances on the ground remotely

If the measurement object is in the line of sight, but in the presence of an insurmountable obstacle that makes direct access to the object impossible (for example, lakes, rivers, swamps, gorges, etc.), distance measurement is used remotely by the visual method, or rather by methods, since there is There are several varieties of them:

1. High precision measurements.
2. Low precision or approximate measurements.

The first includes measurements using special instruments, such as optical rangefinders, electromagnetic or radio rangefinders, light or laser rangefinders, ultrasonic rangefinders. The second type of measurement includes a method called geometric eye measurement. This includes determining distances based on the angular size of objects, constructing equal right-angled triangles, and the method of direct notching in many other geometric ways. Let's look at some of the methods for high-precision and approximate measurements.

Optical distance meter

Such distance measurements with millimeter accuracy are rarely needed in normal practice. After all, neither tourists nor military intelligence officers will carry large and heavy objects with them. They are mainly used when carrying out professional geodetic and construction work. A distance measuring device such as an optical range finder is often used. It can be either with a constant or variable parallax angle and can be an attachment to a regular theodolite.

Measurements are made using vertical and horizontal measuring rods that have a special installation level. of such a rangefinder is quite high, and the error can reach 1:2000. The measurement range is small and ranges only from 20 to 200-300 meters.

Electromagnetic and laser rangefinders

An electromagnetic distance meter belongs to the so-called pulse-type devices; the accuracy of their measurement is considered average and can have an error of 1.2 to 2 meters. But these devices have a great advantage over their optical counterparts, since they are optimally suited for determining the distance between moving objects. Their units of distance measurement can be calculated in both meters and kilometers, so they are often used when carrying out aerial photography.

As for the laser rangefinder, it is designed to measure not very large distances, has high accuracy and is very compact. This especially applies to modern portable devices. These devices measure the distance to objects at a distance of 20-30 meters and up to 200 meters, with an error of no more than 2-2.5 mm over the entire length.

Ultrasonic range finder

This is one of the simplest and most convenient devices. It is lightweight and easy to operate and refers to devices that can measure the area and angular coordinates of a single specified point on the ground. However, in addition to the obvious advantages, it also has disadvantages. Firstly, due to the short measuring range, the distance units of this device can only be calculated in centimeters and meters - from 0.3 to 20 meters. Also, the accuracy of the measurement may change slightly, since the speed of sound directly depends on the density of the medium, and, as is known, it cannot be constant. However, this device is great for quick, small measurements that do not require high precision.

Geometric eye methods for measuring distances

Above we discussed professional methods of measuring distances. What to do when you don’t have a special distance meter at hand? This is where geometry comes to the rescue. For example, if you need to measure the width of a water barrier, you can build two equilateral right triangles on its shore, as shown in the diagram.

In this case, the width of the river AF will be equal to DE-BF. Angles can be adjusted using a compass, a square piece of paper, or even using identical crossed branches. There shouldn't be any problems here.

You can also measure the distance to the target through an obstacle by also using the geometric straight-line method, constructing a right triangle with the vertex on the target and dividing it into two scalene triangles. There is a way to determine the width of an obstacle using a simple blade of grass or thread, or a method using an extended thumb...

It is worth considering this method in more detail, since it is the simplest. On the opposite side of the obstacle, a noticeable object is selected (you must know its approximate height), one eye is closed and the raised thumb of an outstretched hand is pointed at the selected object. Then, without removing your finger, close the open eye and open the closed one. The finger turns out to be shifted to the side in relation to the selected object. Based on the estimated height of the object, it is approximately how many meters the finger has visually moved. This distance is multiplied by ten to obtain the approximate width of the obstacle. In this case, the person himself acts as a stereophotogrammetric distance meter.

There are many geometric ways to measure distance. It would take a lot of time to talk about each one in detail. But they are all approximate and are only suitable for conditions where accurate measurement with instruments is impossible.

Let's remember: What methods do you know of determining distances between two objects?

Keywords:distance, step length, range finder, terrain pattern.

1. Methods for measuring distances. It takes a long time to measure the distance traveled on a hike or the distance between two distant objects with a tape measure or meter. In this case, it is more convenient to measure the distance in steps. To do this, you need to know the average length of your step. Let us remind you that to determine the average step length, you need to measure a distance on the ground using a tape measure, for example 50 m. Then walk this distance in a normal step, counting the number of steps. Let's say you walked a distance of 50 meters and took 70 steps. Therefore, your average stride length is approximately 71 cm (5,000 cm: 70 = 71 cm)

When measuring long distances, it is more convenient to count steps in pairs (for example, only under the left foot).

The distance can be determined less accurately by the time spent walking. So, if you walk 1 km in 15 minutes, then in 1 hour you will walk 4 km. You can determine the distance by eye.

Sometimes instruments called rangefinders are used to measure distances. The rangefinder is easy to make yourself (Fig. 16).

To use a rangefinder to determine the distance to an object, you need to hold it at arm’s length in front of your eyes and, moving it to the right or left, ensure that the entire person’s figure is visible through the slot. In this case, the base of the object should be at the bottom of the slot. Below it will be a number corresponding to the distance from the observer to the object. The figure shows that the distance in this example is 80 m.

Fig. 16. The simplest rangefinder (the drawing is made in full size). Draw the drawing onto a sheet of thick cardboard and cut out the painted part.

2. Types of terrain images. To decide where to build new factories, residential buildings, build roads, or plan the placement of crops and pastures, you need to have an image of the area. A small area can be drawn or photographed (Fig. 17).

Rice. 17. Photo of the area.

But there are other images of the earth’s surface, from which you can clearly see various objects (forests, rivers, villages, fields, etc.), find out their sizes and relative positions. These are aerial photographs (Fig. 18) and site plans (Fig. 19).

Rice. 18. Aerial photograph of the area. What objects can you distinguish from an aerial photograph of a site?

Rice. 19. Site plan. How is it different from an aerial photograph?

Aerial photographs are obtained by photographing the Earth's surface from aircraft.

1. How to determine the distance based on the time spent walking? 2. What is the simplest device that can be used to determine distance? 3. What types of terrain images do you know?

& 7. Site plan

At school, when studying geography and in the future, you will refer to the map to find out where different geographical objects are located and what their properties are. To do this, let’s first get acquainted with what a terrain plan and a geographical map are, and how people depict the surface of the Earth on them. Knowing how to use a plan is very important. So, for example, in an unfamiliar city, having a plan, you can find the desired street, theater, museum, monuments and other objects. Builders, using the area plan, decide where it is best to lay a new road and build settlements in newly developed areas.

Let's remember: What is azimuth? How to determine azimuth on the ground? How to determine the distance by the time spent walking?

Keywords: drawing, area plan, symbols.

1. Site plan. Site plans, like aerial photographs, show the area from above. But there are differences between a photograph, a drawing, an aerial photograph and a site plan.

The drawing and photograph of the area differs from the plan in that the drawing shows a side view of the area, and the plan shows a top view of the area.

In the photograph, all objects are depicted in their natural form, and on the plan they are depicted using conventional symbols.

The terrain can also be depicted using a drawing in which distances will be shown to scale.

Thus, LOCATION PLAN is a drawing of a small area of ​​the earth's surface, made to a certain scale and using conventional symbols. An integral part of the plan is symbols and scale.

2. Conventional signs. Objects and subjects on the terrain plan are depicted using conventional signs (Fig. 20).

Rice. 20. Conventional signs of the area plan. Do the symbols resemble the objects they represent?

Many symbols depict objects that occupy significant areas on the ground. These are fields, forests, swamps, bushes. The boundary between them is shown on site plans by small dots.

Small rivers and streams, roads, narrow streets are depicted by symbols in the form of lines. By their length you can find out the length of the depicted river or road. When applying symbols to the plan, you must adhere to certain rules.

Fig.21. Incorrect (A) and correct (B) representation of symbols on the plan.

*Conventional signs were already present on ancient plans. These were figures of animals and people, drawings of houses and fortress walls. The signs for the plans were different. On modern plans, the conventional signs do not change.

Developing conventional signs is a difficult task. Well-designed symbols help to better read the plan and map and make them easier to draw. Signs should be simple and clear.

1. What is called a site plan? 2. Find on the terrain plan (Fig. 19.) a meadow, mixed forest, thickets of bushes, ravines and other terrain objects.

3. Using fig. 21, determine what mistakes were made on the left plan in the depiction of conventional signs of meadows, swamps, cleared forests, and a single tree.

Practical work.

Build a table showing the differences in the depiction of the terrain in a drawing, photograph, or aerial photograph.

& 8. Scope of site plans.

Let's remember: How are objects indicated on the site plan? What is azimuth?

Keywords: scale, numerical scale, named scale, linear scale, orientation according to the terrain plan.

1. Types of scales. Suppose you need to depict on paper the distance from your school to your home. You already know that the distance from school to your home is 910 m. It is impossible to show this distance in full size on paper, so you need to draw it to scale. M a s t a b o m called a fraction in which the numerator is one, and the denominator is a number indicating how many times the distance on the plan is less than on the terrain itself. Let us agree that on paper we will depict all distances 10,000 times smaller than in reality, i.e. on a scale of 1: 10,000 (one ten-thousandth). This fraction can be written as 1/10,000. This means that 1 cm on paper will correspond to 10,000 cm (or 100 m) on the ground. Then the distance from school to your home will be 9 cm 1 mm.

This type of scale is called numbered

By the numerical scale they find out how many times all the distances on the plan are reduced. The larger the number in the denominator of the fraction, the greater the decrease. Now you can draw on paper the distance from your home to school.

The same scale can be written with the words “1 centimeter - 100m”. This scale is called named. It is convenient because you can immediately find out the distance on the ground from the line measured on the plan.

A linear scale is also placed on the plans.

LINEAR SCALE- This is a straight line divided into equal parts (usually centimeters). When drawing a linear scale, the zero is set at a distance of 1 cm from the left end of the segment, and the first centimeter is divided into smaller parts (2 mm each) (Fig. 22).

Rice. 22. Indication of scale on the site plan and on the map.

The linear scale is used to determine distances according to the plan using a measuring compass (see Fig. 23).

Rice. 23. The position of the measuring compass when measuring distances on a plan using a linear scale.

2. Determination of azimuth according to the terrain plan. On plans, the direction to the north is often indicated by an arrow. If the arrow is not shown, then it is considered that the upper edge of the plan is northern, the lower is southern, the right is eastern and the left is western. Let's assume that we need to go from the ferry on the Golubaya River to the dam on the Malinovka River (Fig. 24)

Rice. 24. Determination of azimuth according to the plan using a protractor.

To do this, you need to know in what azimuth you need to move from the ferry to get to the dam. This azimuth can be determined from the plan using a protractor (Fig. 24). What azimuth is this? On the ground, you find this azimuth using a compass and follow this azimuth to go in the right direction.

1. What is scale? 2. What types of scales are there? 3. What does the denominator of a numerical scale show? 4. When is it more convenient to use a named scale?

Practical work.

Draw on the drawing a distance of 300 m on a scale: 1 cm - 100 m, 1 cm - 30 m. Which scale is larger?

Draw a distance of 500 m on the drawing. Choose the scale yourself.

Read the scales 1:20,000 and 1:300,000. How many times are the distances reduced in the first and second cases? Convert these numerical scales to named ones. Express them using linear scales.

* The student depicted a distance of 1 km in the drawing with a segment 10 cm long. Determine what scale he chose to complete the task

* The student depicted a distance of 500 m on a drawing on a scale of 1 cm - 50 m. What is this distance in the drawing?

**The student walked from point A to point B along an azimuth of 360 degrees 100 m (conventionally reflect this distance in your notebook on a scale of 1:1000). From point B to point C, he walked the same distance along an azimuth of 90 degrees. From point B he traveled the same distance along an azimuth of 180 degrees. Draw the student’s path in a notebook and determine what distance and what azimuth he has left to go to point A.

Competition of experts . You've found a plan. The part of the sheet where the scale is located has not been preserved. How to determine the scale of this plan?

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.

Rice. 8. Determination of distances by the angular dimensions of an object (subject)

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):

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 using 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 on the ground a well-imagined constant measure (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, twilight, cloudy days, when the air is saturated with dust, observed objects seem further away than on 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, the usual error ranges from 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.

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. The average range of audibility of various sounds during the day on flat terrain, 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:

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Determination of distances by 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.

Another version of this method is shown in Fig. 10, b.

Point C is selected so that the angle ACB is equal to 60°.

It is known that the tangent of an angle of 60° is equal to 1/2, therefore, the width of the river is equal to twice the distance AC.
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.

Table 6

To approximate and measure distances on the ground, the following simplest methods are used: by eye, by measured angular values ​​of local objects, by measuring in steps, by time of movement, by the sound and flash of a shot, by ear.

The eye method is the main, simplest and fastest, most accessible to everyone in any conditions. However, an accurate eye gauge is not acquired immediately. It is developed through systematic training carried out in a variety of terrain conditions, at different times of the year and day.

To develop your eye, you need to practice determining distances by eye as often as possible, with the obligatory check of them in steps, on a map or in another way. Training should begin with short distances - 10, 50, 100 meters. Having mastered these distances well, you can move on to larger distances - 200, 400, 800, 1000 meters. Then you can easily determine long distances.

The accuracy of the visual method is indicated and influenced by such side effects as:

Larger objects always seem closer to smaller ones located at the same distance.
- The fewer intermediate objects there are between the eye and the observed object, the closer this object seems.
- 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.

Eye estimation of distances can be controlled when several people measure the same distance independently of each other. Taking the average of all these determinations gives the most accurate measurement. For a rough estimate of distances, the approximate data given in the table below is sometimes used.

Everyone can clarify and supplement this table in relation to their observations. The accuracy of the eye method depends on the training of the observer, on the magnitude of the distances being determined and on the observation conditions. For distances up to 1000 meters, it is necessary to achieve through training the determination of values ​​with an error of no more than 10-15%.

A method for determining and measuring distances on the ground from the measured angular values ​​of local objects.

If the linear magnitude of the observed object is known (height, width or length), then to determine the distance to it it is necessary to measure the angle (in thousandths) at which this object is visible. And by the ratio of the linear (known in advance) and angular (measured) values ​​of this object, you can determine the distance to it.

A method for determining and measuring distances on the ground using pairs of steps.

When measuring distances in steps, you need to practice walking at an even pace, especially in unfavorable conditions. On ups and downs, when moving along a hummocky meadow, in bushes, etc. In addition, you need to know the length of your step in meters. It is determined from measurements by line steps, the length of which is known in advance and must be at least 200-300 meters.

When measuring distances, steps are counted in pairs, usually under the left foot. After every hundred pairs of steps, the count starts again. In order not to lose count, it is useful to write every hundred pairs of steps on paper, or bend your fingers in sequence, or in any way. Errors in determining distances in steps, with an even, well-calibrated step, on average reach 2-4% of the measured distance.

A method for determining and measuring distances on the ground based on time and speed.

You can determine distances by the time of movement if you approximately know your average speed. So, for example, if the average walking speed is 5 km/h, when the ascents and descents are no more than 5 degrees, then after walking for 45 minutes, you can roughly say that you have covered 3.75 km.

A method for determining and measuring distances to firing guns.

Determination of distances to firing guns is based on the detection, at the moment of firing, of flash and smoke formation. Then, knowing that the speed of sound propagation in the air is 330 m/sec, that is, rounded 1 km per 3 seconds, we count the time in seconds from the moment of the flash to the moment of auditory perception of sound (or explosion) and, dividing it by three, determine the distance kilometers to the guns.

In the absence of a clock, you can count seconds by counting “to yourself” two-digit numbers (21, 22, 23, 24), starting from the moment of the flash from the shot until the sound from it arrives. Each of these numbers takes approximately one second to count. The skills of such counting, commensurate with the movement of the second hand, are acquired quite quickly after 2-3 trainings in counting two-digit numbers.

A method for determining and measuring distances by ear.

At night, in conditions of poor visibility, distances often have to be estimated by ear. To do this, you need to be able to determine their sources by the nature of sounds and know from what approximately distances these sounds can be heard at night. With normal hearing and favorable acoustic conditions, the hearing range can be approximately considered as given in the table below.

These data vary depending on the specific conditions in which the observation is made, and therefore must be taken into account by each observer on the basis of his personal experience.

Based on materials from the book “Map and Compass are My Friends.”
Klimenko A.I.

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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 “thousandths” formula, then angular values ​​can be measured using improvised objects, a ruler, binoculars, a compass, a tower inclinometer, observation and aiming devices and other 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 be a good goniometric device if you know how many “thousandths” they contain, but in this case it is necessary 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 based on 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