How to calculate the required area on the maps. Map measurement of distances, areas and angles

Topic 7. MEASUREMENT OF DISTANCES AND AREA ON TOPOGRAPHIC MAP

7.1. TECHNIQUE FOR MEASURING AND PUTTING DISTANCES ON A MAP

To measure distances on a map, a millimeter or scale ruler, a compass-meter are used, and a curvimeter is used to measure curved lines.

7.1.1. Measuring distances with a millimeter ruler

With a millimeter ruler, measure the distance between the given points on the map with an accuracy of 0.1 cm. Multiply the resulting number of centimeters by the value of the named scale. For flat terrain, the result will correspond to the distance on the ground in meters or kilometers.
Example. On a map of scale 1: 50,000 (in 1 cm - 500 m) the distance between two points is 3.4 cm. Determine the distance between these points.
Solution. Named scale: in 1 cm 500 m. The distance on the ground between the points will be 3.4 × 500 = 1700 m.
At angles of inclination of the earth's surface more than 10º, it is necessary to introduce an appropriate correction (see below).

7.1.2. Measuring distances with a compass

When measuring distance in a straight line, the needles of the compass are set at the end points, then, without changing the solution of the compass, the distance is read off on a linear or transverse scale. In the case when the opening of the compass exceeds the length of the linear or transverse scale, the integer number of kilometers is determined by the squares of the coordinate grid, and the remainder - by the usual scale order.

Rice. 7.1. Measuring distances with a compass-meter on a linear scale.

To get the length broken line sequentially measure the length of each of its links, and then summarize their values. Such lines are also measured by increasing the compass solution.
Example. To measure the length of a polyline ABCD(Fig. 7.2, A), the legs of the compass are first placed at points A And IN. Then, rotating the compass around the point IN. move the back leg from the point A exactly IN" lying on the continuation of the line sun.
Front leg from point IN transferred to a point WITH. The result is a solution of the compass B "C"=AB+sun. Moving the back leg of the compass in the same way from the point IN" exactly WITH", and the front of WITH V D. get a solution of the compass
C "D \u003d B" C + CD, the length of which is determined using a transverse or linear scale.

Rice. 7.2. Line length measurement: a - broken line ABCD; b - curve A1B1C1;
B"C" - auxiliary points

Long curves measured along the chords with compass steps (see Fig. 7.2, b). The step of the compass, equal to an integer number of hundreds or tens of meters, is set using a transverse or linear scale. When rearranging the legs of the compass along the measured line in the directions shown in fig. 7.2, b arrows count steps. The total length of the line A 1 C 1 is the sum of the segment A 1 B 1 equal to the step value multiplied by the number of steps, and the remainder B 1 C 1 measured on a transverse or linear scale.

7.1.3. Measuring distances with a curvimeter

Curved segments are measured with a mechanical (Fig. 7.3) or electronic (Fig. 7.4) curvimeter.

Rice. 7.3. Curvimeter mechanical

First, turning the wheel by hand, set the arrow to zero division, then roll the wheel along the measured line. The reading on the dial against the end of the arrow (in centimeters) is multiplied by the scale of the map and the distance on the ground is obtained. The digital curvimeter (Fig. 7.4.) is a high-precision, easy-to-use device. Curvimeter includes architectural and engineering functions and has a convenient display for reading information. This unit can process metric and Anglo-American (feet, inches, etc.) values, allowing you to work with any maps and drawings. You can enter the most commonly used type of measurement and the instrument will automatically translate scale measurements.

Rice. 7.4. Curvimeter digital (electronic)

To improve the accuracy and reliability of the results, it is recommended that all measurements be carried out twice - in the forward and reverse directions. In case of insignificant differences in the measured data, the arithmetic mean of the measured values is taken as the final result.
The accuracy of measuring distances by these methods using a linear scale is 0.5 - 1.0 mm on a map scale. The same, but using a transverse scale, is 0.2 - 0.3 mm per 10 cm of line length.

7.1.4. Converting horizontal distance to slant range

It should be remembered that as a result of measuring distances on maps, the lengths of horizontal projections of lines (d) are obtained, and not the lengths of lines on the earth's surface (S)(Fig. 7.5).

Rice. 7.5. Slant Range ( S) and horizontal spacing ( d)

The actual distance on an inclined surface can be calculated using the formula:

Where d- the length of the horizontal projection of the line S;
α - the angle of inclination of the earth's surface.

The length of the line on the topographic surface can be determined using the table ( table 7.1) relative values of corrections to the length of the horizontal laying (in%) .

Table 7.1

Tilt angle

Rules for using the table

1. The first line of the table (0 tens) shows the relative values of the corrections at inclination angles from 0° to 9°, the second - from 10° to 19°, the third - from 20° to 29°, the fourth - from 30° up to 39°.
2. To determine the absolute value of the correction, you must:
a) in the table, by the angle of inclination, find the relative value of the correction (if the angle of inclination of the topographic surface is not given by an integer number of degrees, then the relative value of the correction must be found by interpolation between the tabular values);
b) calculate the absolute value of the correction to the length of the horizontal span (i.e., multiply this length by the relative value of the correction and divide the resulting product by 100).
3. To determine the length of a line on a topographic surface, the calculated absolute value of the correction must be added to the length of the horizontal distance.

Example. On the topographic map, the length of the horizontal distance is 1735 m, the angle of inclination of the topographic surface is 7°15′. In the table, the relative values of the corrections are given for whole degrees. Therefore, for 7°15" it is necessary to determine the nearest larger and nearest smaller multiples of one degree - 8º and 7º:
for 8° relative correction value 0.98%;
for 7° 0.75%;
difference in tabular values in 1º (60') 0.23%;
the difference between the specified angle of inclination of the earth's surface 7 ° 15 "and the nearest smaller tabular value of 7º is 15".
We make proportions and find the relative amount of the correction for 15 ":

For 60' the correction is 0.23%;
For 15′ the correction is X%
X% = = 0,0575 ≈ 0,06%

Relative correction value for tilt angle 7°15"
0,75%+0,06% = 0,81%
Then you need to determine the absolute value of the correction:
= 14.05 m » 14 m.
The length of the inclined line on the topographic surface will be:
1735 m + 14 m = 1749 m.

At small angles of inclination (less than 4° - 5°), the difference in the length of the inclined line and its horizontal projection is very small and may not be taken into account.

7.2. MEASUREMENT OF AREA BY MAP

The determination of the areas of plots from topographic maps is based on the geometric relationship between the area of the figure and its linear elements. The area scale is equal to the square of the linear scale.
If the sides of the rectangle on the map are reduced to n times, then the area of this figure will decrease in n 2 times. For a map with a scale of 1:10,000 (in 1 cm 100 m), the area scale will be (1: 10,000) 2, or in 1 cm 2 there will be 100 m × 100 m = 10,000 m 2 or 1 ha, and on a map of scale 1 : 1,000,000 in 1 cm 2 - 100 km 2.
To measure areas on maps, graphic, analytical and instrumental methods are used. The use of one or another measurement method is determined by the shape of the measured area, the given accuracy of the measurement results, the required speed of obtaining data, and the availability of the necessary instruments.

7.2.1. Measuring the area of a parcel with straight boundaries

When measuring the area of a plot with rectilinear borders the site is divided into simple geometric figures, the area of each of them is measured geometrically and, summing up the areas of individual sections calculated taking into account the scale of the map, the total area of the object is obtained.

7.2.2. Measuring the area of a plot with a curved contour

Object with curvilinear contour they are divided into geometric shapes, having previously straightened the boundaries in such a way that the sum of the cut-off sections and the sum of the excesses mutually compensate each other (Fig. 7.6). The measurement results will be approximate to some extent.

Rice. 7.6. Straightening curvilinear site boundaries and
breakdown of its area into simple geometric shapes

7.2.3. Measurement of the area of a plot with a complex configuration

Measurement of plot areas, having a complex irregular configuration, more often produced using pallets and planimeters, which gives the most accurate results. grid palette is a transparent plate with a grid of squares (Fig. 9.9).

Rice. 7.7. Square Mesh Palette

The palette is placed on the measured contour and the number of cells and their parts inside the contour is counted. The proportions of incomplete squares are estimated by eye, therefore, to improve the accuracy of measurements, palettes with small squares (with a side of 2 - 5 mm) are used. Before working on this map, determine the area of one cell.
The area of the plot is calculated by the formula:

P \u003d a 2 n,

Where: A - the side of the square, expressed on the scale of the map;
n- the number of squares that fall within the contour of the measured area

To improve accuracy, the area is determined several times with an arbitrary permutation of the palette used in any position, including rotation relative to its original position. The arithmetic mean of the measurement results is taken as the final value of the area.

In addition to grid palettes, dot and parallel palettes are used, which are transparent plates with engraved dots or lines. Points are placed in one of the corners of the cells of the grid palette with a known division value, then the grid lines are removed (Fig. 7.8).

Rice. 7.8. dot palette

The weight of each point is equal to the price of the division of the palette. The area of the measured area is determined by counting the number of points inside the contour, and multiplying this number by the weight of the point.
Equidistant parallel lines are engraved on the parallel palette (Fig. 7.9). The measured area, when applied to it with a palette, will be divided into a series of trapezoids with the same height h. Segments of parallel lines inside the contour (in the middle between the lines) are the middle lines of the trapezoid. To determine the area of a plot using this palette, it is necessary to multiply the sum of all measured middle lines by the distance between the parallel lines of the palette h(taking into account the scale).

P = h∑ l

Fig 7.9. Palette consisting of a system
parallel lines

Measurement areas of significant plots made on cards with the help of planimeter .

Rice. 7.10. polar planimeter

The planimeter is used to determine areas mechanically. The polar planimeter is widely used (Fig. 7.10). It consists of two levers - pole and bypass. Determining the contour area with a planimeter comes down to the following steps. After fixing the pole and setting the needle of the bypass lever at the starting point of the circuit, a reading is taken. Then the bypass spire is carefully guided along the contour to the starting point and a second reading is taken. The difference in readings will give the area of the contour in divisions of the planimeter. Knowing the absolute value of the division of the planimeter, determine the area of the contour.
The development of technology contributes to the creation of new devices that increase labor productivity in calculating areas, in particular, the use of modern devices, among which - electronic planimeters .

Rice. 7.11. Electronic planimeter

7.2.4. Calculating the area of a polygon from the coordinates of its vertices
(analytical way)

This method allows you to determine the area of a plot of any configuration, i.e. with any number of vertices whose coordinates ( x,y) are known. In this case, the numbering of the vertices should be done in a clockwise direction.
As can be seen from fig. 7.12, area S polygon 1-2-3-4 can be considered as the difference in areas S" figures 1y-1-2-3-3y And S" figures 1y-1-4-3-3y
S = S" - S".

Rice. 7.12. To the calculation of the area of a polygon by coordinates.

In turn, each area S" And S" is the sum of the areas of trapezoids, the parallel sides of which are the abscissas of the corresponding vertices of the polygon, and the heights are the differences in the ordinates of the same vertices, i.e.
S" = sq. 1u-1-2-2u + pl. 2y-2-3-3y,
S" \u003d pl 1y-1-4-4y + pl. 4y-4-3-3y
or:

2S " = (x 1+ x 2)(at 2 – at 1) + (x 2+ x 3 ) (at 3 - at 2)
2S" = (x 1+ x 4)(at 4 – at 1) + (x 4+ x 3)(at 3 - at 4).
Thus,
2S = (x 1+ x 2)(at 2 – at 1) + (x 2+ x 3 ) (at 3 - 2) - (x 1+ x 4)(at 4 – at 1) - (x 4+ x 3)(at 3 - at 4).

Expanding the brackets, we get
2S = x 1 y 2 – x 1 y 4 + x 2 y 3 - x 2 y 1 + x 3 y 4 - x 3 y 2 +x 4 1 - x 4 y 3

From here
2S = x 1 (y 2 - at 4) + x 2 (y 3 - at 1)+ x 3 (y 4 - at 2 ) + x 4 (at 1 - at 3 ) (7.1)
2S = y 1 (x 4 - X 2) + y 2 (x 1 - X 3 )+ y 3 (x 2 - X 4 )+ y 4 (x 3 - x 1) (7.2)

Let us represent expressions (7.1) and (7.2) in general form, denoting by i serial number ( i = 1, 2, ..., P) polygon vertices:
2S = (7.3)
2S = (7.4)

Hence, twice the area of the polygon is equal to either the sum of the products of each abscissa and the difference between the ordinates of the next and previous vertices of the polygon, or the sum of the products of each ordinate and the difference of the abscissas of the previous and subsequent vertices of the polygon.

An intermediate control of calculations is the satisfaction of the following conditions:
= 0 or = 0

Coordinate values and their differences are usually rounded to tenths of a meter, and products to whole square meters.
Complex formulas for calculating the area of a plot can be easily solved using spreadsheets MicrosoftXL . An example for a polygon (polygon) of 5 points is given in tables 7.2, 7.3.
In table 7.2 we enter the initial data and formulas.

Table 7.2.


				y i (x i-1 - x i+1)





	Double area in m2			SUM(D2:D6)
	Area in hectares

In table 7.3 we see the results of the calculations.

Table 7.3.

				y i (x i-1 -x i+1)






	Double area in m2
	Area in hectares

7.3. EYE MEASUREMENTS ON THE MAP

In the practice of cartometric work, eye measurements are widely used, which give approximate results. However, the ability to visually determine distances, directions, areas, steepness of the slope and other characteristics of objects on the map contributes to mastering the skills of correctly understanding the cartographic image. The accuracy of eye measurements increases with experience. Eye skills prevent gross miscalculations in instrument measurements.
For determining lengths of linear objects on the map, one should visually compare the size of these objects with segments of a kilometer grid or divisions of a linear scale.
For determining area of objects as a kind of palette, squares of a kilometer grid are used. Each square of the grid of maps of scales 1:10,000 - 1:50,000 on the ground corresponds to 1 km 2 (100 ha), scale 1:100,000 - 4 km 2, 1:200,000 - 16 km 2.
The accuracy of quantitative determinations on the map, with the development of the eye, is 10-15% of the measured value.

Questions and tasks for self-control

Explain how to measure on a straight line map.

Explain the order of measurement on the polyline map.

Explain the measurement procedure on the map of a curved winding line using a measuring compass.

Explain the measurement procedure on the map of a curved winding line using an odometer.

How can one visually determine the length of a linear object using a topographic map?

What area on the ground corresponds to one square of the coordinate grid of the map at a scale of 1:25,000?

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METHODOLOGICAL INSTRUCTIONS FOR LABORATORY WORKS

ON THE COURSE "GEODESY Part 1"

7. MEASUREMENT OF AREA ACCORDING TO A PLAN OR MAP

To solve a number of engineering problems, it is required to determine according to the plan or map the areas of various areas of the terrain. The determination of areas can be done graphically. analytical and mechanical methods.

7.1. Graphical method for determining the area

The graphical method serves to determine the area of small areas (up to 10-15 cm 2) according to a plan or map and is used in two versions: a) with a breakdown of the intended area into geometric shapes; b) about using palettes.

In the first version, the area of the site is divided into the simplest geometric figures: triangles, rectangles, trapezoids (Fig. 19, a), the corresponding elements of these figures (base lengths and heights) are measured, and the areas of these figures are calculated using geometric formulas. The area of the entire plot is determined as the sum of the areas of individual figures. The division of the plot into figures should be carried out in such a way that the figures are as large as possible, and their sides coincide as closely as possible with the contour of the plot.

For control, the area of the site is divided into other geometric shapes and the area is re-determined. The relative discrepancy in the results of double determinations of the total area of the plot should not exceed 1: 200.

For small areas (2-3 cm 2) with pronounced curvilinear boundaries, it is advisable to determine the area with using a square palette(Fig. І9, b). The palette can be made on tracing paper, drawing it with a grid of squares with sides of 2-5 mm. Knowing the length of the side of the scale of the plan, you can calculate the area of the square of the palette IKB.

To determine the area of the site, the tent is arbitrarily placed on the plan and the number of full squares is counted. N 1 located within the contour of the plot. Then evaluate by eye (in tenths) each incomplete square and find the total number N 2 for all incomplete squares on the boundaries of the contour. Then the total area of the measured area S= sKB *(N 1 + N 2 ). For control, the tent is deployed at about 45 A and the area is re-determined. The relative error in determining the area with a square palette is 1: 50 - 1: 100. When determining areas, several larger areas (up to 10 cm 2) can be used linear palette(Fig. 19, c), which can be made on tracing paper, drawing a series of parallel lines at regular intervals (2-5 mm). The palette is superimposed on this area in such a way that the extreme points of the area (points m and n in Fig. 19, c) are located in the middle between the parallel lines of the palette. Then measure the length of the lines using compass-measuring instruments and a scale ruler. l 1 , l 2 ….., l n , which are the middle lines of the trapezoid, into which the area of this section is divided using a palette. Then the plot area S= a(l 1 + l 2 +……+ l n ), Where a- step of the linear palette, i.e. distance between parallel lines. For control, the palette is drawn 60-90 about relative to the original position and the area of the site is re-determined. The relative error in determining the area of a linear tent depends on its pitch and is 1: 50 - 1: 100
7.2. Analytical method for determining the area If enough points are collected along the contour of the area of the measured area to approximate this area with the required accuracy by the polygon formed by these points (Fig. 19, a), and then measure the coordinates on the map X And at all points, then the area of the site can be determined analytically. For a polygon about the number of vertices n when they are digitized clockwise, the area will be determined by the formulas For control, calculations are made using both formulas. The accuracy of the analytical method depends on the density of the set of points along the contour of the measured area. With a significant number of points, it is advisable to carry out calculations using computers or microcalculators = 7.3. Mechanical way to determine the area using a planimeter A planimeter is a mechanical device for measuring area. In engineering and geodetic practice, with the help of a planimeter, according to plans or maps, the areas of sufficiently large areas are measured. Of the numerous designs of planimeters, polar planimeters are the most widely used. The polar planimeter (Fig. 20) consists of two levers - pole 1 and bypass 4. In the lower part of the load 2, fixed at one end of the pole lever, there is a needle - the pole of the planimeter. At the second end of the pole arm there is a pin with a spherical head, which is inserted into a special socket in the carriage 5 of the bypass arm. At the end of the bypass lever there is a lens 3, on which a circle with a bypass point in the center is applied. Carriage 5 has a counting mechanism, consisting of a counter 6 of whole revolutions of the counting wheel and the counting wheel 7 itself. For readings on the counting wheel, there is a special device - vernier 8. When traversing the contour of the bypass lens 3, the rim of the counting wheel and roller 9 rolls or slides on paper , forming together with the bypass point three control points of the planimeter. In modern planimeters, a carriage with a counting mechanism can move along the bypass lever, thereby changing its length, and fixed in a new position. The circumference of the counting wheel is divided into 100 parts, every tenth stroke is digitized. The countdown on the planimeter consists of four digits: the first digit is the smallest digit of the revolution counter closest to the index (thousands of divisions of the planimeter), the second and third digits are hundreds and tens of divisions on the counting wheel, preceding the zero stroke of the vernier; the fourth digit is the number of the vernier stroke that matches the nearest stroke of the counting wheel (division units). Before measuring the area of the site, the planimeter is installed on the map so that its pole is located outside the measured area, and the pole and bypass arms form an approximately right angle. In this case, the place for fixing the pole is chosen so that during the bypass of the entire figure, the angle between the bypass and pole levers is not less than 30° and not more than 150°. By aligning the bypass point of the planimeter with some starting point of the contour of the site, the initial reading is taken by the counting mechanism no and smoothly outline the entire contour in a clockwise direction. Returning to the starting point, take the final count n. Count difference ( n -no) expresses the area of the figure in planimeter divisions. Then the area of the measured area Where µ is the division price of the planimeter, i.e. the area corresponding to one division of the planimeter. To control and improve the accuracy of the measurement results, the area of the plot is measured at two positions of the planimeter pole relative to the counting mechanism: "left pole" and "right pole". Before measuring areas, it is necessary to determine the division valueplanimeter µ . To do this, choose a figure whose area is ½ O known in advance (for example, one or more grid squares). In order to obtain higher accuracy, this figure is circled along the contour 4 times: 2 times in the "pole right" position and 2 times in the "pole left" position. With each bypass, the initial and final readings are taken and their difference is calculated (n i- n oi) . Differences between the values of the differences at the "pole to the right" and "pole to the left" should not exceed 2 divisions with a figure area of up to 200 division, 3 divisions - with an area of \u200b\u200bthe figure from 200 to 2000 division and 4 divisions - with an area of \u200b\u200bthe figure over 2000 divisions of the planimeter. If the discrepancies do not exceed the allowable, then calculate the averagereading difference (n- no) cfand calculate the division value of the planimeter using the formula / (n - n o ) Wed The division price is calculated with an accuracy of 3-4 significant figures. The table (p. 39) shows an example of recording the results of measurements of the division value of the planimeter and determining the area of the site on the map. The accuracy of determining areas with a polar planimeter depends on the size of the measured areas. The smaller the area of the site, the greater the relative error of its determination. Planimeter is recommended to measure the area of plots on the plan (map) not less than 10-12 cm 2 . Under favorable measurement conditions, the relative error in determining areas using a planimeter is approximately 1: 400. 8. MAP DESCRIPTION When conducting engineering and geodetic surveys, the preparation of technical documentation requires the performer to have a good knowledge of the symbols and the main patterns of the placement of natural objects (for example, mutual consistency of relief, hydrography, vegetation, settlements, road network, etc.). Often in this case, it becomes necessary to describe certain sections of the map. It is recommended to use the following scheme to describe the map section. I. The name (nomenclature) of the map. 2. Imprint: 2.1. Where, when and by whom the map was compiled and published. 2.2. On what cartographic materials it is made. 3.1. Map scale. 3.2. Longitudes and latitudes of the map frames. 3.3. Kilometer grid, the frequency of its lines and their digitization. 3.4. Location on the map of the described area. 3.5. Geodetic basis on the described map participation (types of reference marks, their number). 4. Physical and geographical elements: hydrography (seas, rivers, lakes, canals, irrigation and drainage systems); relief, its character, dominant heights and lowest places, their marks; vegetation cover. 5. Socio-economic elements: settlements, means of communication, means of communication, industry, agriculture and forestry, elements of culture. As an example, the following description of one of the sections of the map at a scale of 1: 25,000 is given. I. Map U-34-37-V-in (Snov). 2. Imprint: 2.1. The map was prepared for publication in 1981 by the GUGK and printed in 1982. Filmed by A.P. Ivanov. 2.2. The map was compiled based on the materials of the aerial photographic survey of 1980. 3. Mathematical elements of the map: 3.1. Map scale 1: 25,000. 3.2. The map sheet is bounded in longitude by the meridians 18 o 00' 00'' (in the west) and І8°07'"W0'' (in the east) and in latitude by the parallels 54 o 40' 00'' (in the south) and 54°45 '00'' (in the north). 3.3. The map shows a kilometer grid of rectangular coordinates (every 1 km). The grid squares on the map have side dimensions of 40 mm (on the map scale, 1 cm corresponds to 250 m on the ground). The map sheet contains 9 horizontal lines of the kilometer grid (from x = 6065 km in the south to x = 6073 km in the north) and 8 vertical grid lines (from y = 4307 km in the west to y = 4314 km in the east). 3.4. The described section of the map occupies four squares of the kilometer grid (from x 1 = 6068 km to x 2 = 6070 km and from y 1 = 4312 km to y 2 = 4314 km) to the east of the central section of the map. Determining the area of a plot with a planimeter

Pole position		Number			countdowns				Difference r=n-n0			Medium r cp		Relative error (rpp- rpl)/ r cp		Value of division µ= s o/ r cp	contour area S= µ * r cp
					n 0		n
1. Determination of the division price of the planimeter (S o \u003d 4 km 2 \u003d 400 ha)
PP			2	0112 0243		6414 6549				6302 6306			6304	1:3152 0.06344 ha/div.
PL			2	0357 0481		6662 6788				6305 6307			6306
2. Determining the area of the plot
PP PL	2				0068 0106			0912 0952			846				1:472 0.06344 ha/div. 59.95ha

3.5. On the described section of the map there is one point of the geodetic network, installed on Mount Mikhalinskaya. 4. Physical-geographical elements. In the northeast corner of the described section, the Sot River flows, over 250 m wide. The direction of its flow is from the northwest to the southeast, the flow velocity is 0.1 m/s. On the western bank of the river, a permanent riverside signaling sign has been installed. The banks of the river are swampy, covered with meadow vegetation. In addition, there are some shrubs on the eastern bank of the river. In the described section, two streams flow into the Sot River, flowing along the bottom of the ravines that go to the river. In addition to the indicated ravines, another ravine leads to the cancer, and in the southwestern part of the site there are two ravines covered with continuous vegetation. The terrain is hilly, with height differences over 100 m. The dominant heights are Mount Bolshaya Mikhalinskaya with a peak elevation of 213.8 m in the western part of the site and Mount Mikhalinskaya with a peak elevation of 212.8 m in the southern part of the site. From these heights, the relief rises to the river (with a water edge mark of about 108.2 m). In the northern section, the coast is steep (with a cliff height of up to 10 m). Some lowering of the relief is also observed from the indicated heights to the southwest. In the southern part of the site there is the Severny forest, which occupies about 0.25 km 2 and is located in the saddle between the indicated heights and to the east of the saddle. The predominant tree species in the forest is pine, the average height of trees is about 20 m, the average thickness of trees is 0.20 m, the distance between trees is 6 m. On the western slope of Mount Mikhalinskaya there is a separate tree, which has the value of a landmark. 5. Socio-economic elements. There are no settlements on the described site, but immediately beyond its borders in the southwest there is the settlement of Mihalino, with 33 houses. Partially the gardens of this settlement fall on the plot area. There are three dirt (country) roads on the site. One of them runs from the west to the southwest of the site, the other goes from the southwest to the north and passes at the very edge of the site into a field road. At the point of this transition, the road forks and from the north to the southeast there is a third unpaved (sifted local) road. From this third road in the southeast, another sex road branches off in a southerly direction. There are no other socio-economic elements in this section of the map.
9. PREPARATION OF THE REPORT The report on laboratory work on a topographic map consists of an explanatory note and graphic documents. The explanatory note contains a write-off of the performed laboratory work, an explanation of the results obtained. An explanatory note is drawn up on separate sheets of writing paper (standard format 210 x 297 mm). Each laboratory work must have the name and information about the card on which it was performed, and the date the work was completed. The explanatory note must have a title page, on which it is necessary to indicate the name of the faculty, group, the name of the student who completed the work, the name of the teacher who issued the task and checks the work, the date the work was completed. Graphic documents are a copy and a topographic profile. These documents are enclosed in an explanatory note. A copy of the map is drawn in ink on tracing paper, while copying the marginal design of the map (decorative and degree frames, signatures), the kilometer grid. On a copy of the map on tracing paper, copies are also made of those sections of the map that are necessary to illustrate the solution of a particular problem, for example, when designing a line of a given slope, when determining the boundaries of a catchment area, when describing a map section. The topographic profile is drawn in ink on graph paper, and the profile line must necessarily be shown on a copy of the map and the horizontal lines directly adjacent (1 cm in each direction) to the profile line must be copied on it. Other graphic diagrams and figures illustrating the solution of tasks on the topographic map may be placed in the text of the explanatory note. All drawings must be made neatly, without blots, in compliance with the dimensions, symbols and fonts. The pages of the explanatory note should be numbered, and the note itself should have a table of contents. The reading is submitted to the teacher for verification, after which it is defended by the student in class.

1.1 Map scales

map scale shows how many times the length of the line on the map is less than the corresponding length on the ground. It is expressed as a ratio of two numbers. For example, a scale of 1:50,000 means that all terrain lines are shown on the map with a reduction of 50,000 times, i.e. 1 cm on the map corresponds to 50,000 cm (or 500 m) on the ground.

Rice. 1. Registration of numerical and linear scales on topographic maps and city plans

The scale is indicated under the lower side of the map frame in numerical terms (numerical scale) and in the form of a straight line (linear scale), on the segments of which the corresponding distances on the ground are signed (Fig. 1). The scale value is also indicated here - the distance in meters (or kilometers) on the ground, corresponding to one centimeter on the map.

It is useful to remember the rule: if you cross out the last two zeros on the right side of the ratio, then the remaining number will show how many meters on the ground correspond to 1 cm on the map, that is, the scale value.

When comparing several scales, the larger one will be the one with the smaller number on the right side of the ratio. Let's assume that there are maps of 1:25000, 1:50000 and 1:100000 scales for the same area. Of these, the 1:25000 scale will be the largest, and the 1:100,000 scale will be the smallest.
The larger the scale of the map, the more detailed the terrain is shown on it. With a decrease in the scale of the map, the number of terrain details applied to it also decreases.

The detail of the image of the area on topographic maps depends on its nature: the less details the area contains, the more fully they are displayed on maps of smaller scales.

In our country and many other countries, the main scales of topographic maps are: 1:10000, 1:25000, 1:50000, 1:100000, 1:200000, 1:500000 and 1:1000000.

The cards used in the troops are divided into large scale, medium scale and small scale.

map scale	Card name	Map classification
		scale	by main purpose
1:10 000 (in 1 cm 100 m)	ten thousandth	large scale	tactical
1:25 000 (in 1 cm 250 m)	twenty-five thousandth
1:50 000 (in 1 cm 500 m)	five thousandth
1:100,000 (in 1 cm 1 km)	hundred thousandth	medium scale
1:200,000 (in 1 cm 2 km)	two hundred thousandth		operational
1:500,000 (in 1 cm 5 km)	five hundred thousandth	small scale
1:1 000 000 (in 1 cm 10 km)	millionth

1.2. Measurement on a map of straight and winding lines

To determine the distance between points of the terrain (objects, objects) on the map, using a numerical scale, it is necessary to measure the distance between these points in centimeters on the map and multiply the resulting number by the scale value.

For example, on a map with a scale of 1:25000, we measure the distance between the bridge and the windmill with a ruler (Fig. 2); it is equal to 7.3 cm, multiply 250 m by 7.3 and get the desired distance; it is equal to 1825 meters (250x7.3=1825).

Rice. 2. Determine the distance between points on the map using a ruler.

A small distance between two points in a straight line is easier to determine using a linear scale (Fig. 3). To do this, it is enough to apply a compass-meter, the solution of which is equal to the distance between given points on the map, to a linear scale and take a reading in meters or kilometers. On fig. 3 the measured distance is 1070 m.

Rice. 3. Measurement on a map of distances with a compass-meter on a linear scale

Rice. 4. Measurement on the map of distances with a compass-meter along winding lines

Large distances between points along straight lines are usually measured using a long ruler or measuring compass.

In the first case, a numerical scale is used to determine the distance on the map using a ruler (see Fig. 2).

In the second case, the “step” solution of the measuring compass is set so that it corresponds to an integer number of kilometers, and an integer number of “steps” is set aside on the segment measured on the map. The distance that does not fit into an integer number of “steps” of the measuring compass is determined using a linear scale and added to the resulting number of kilometers.

In the same way, distances are measured along winding lines (Fig. 4). In this case, the "step" of the measuring compass should be taken as 0.5 or 1 cm, depending on the length and degree of sinuosity of the measured line.

Rice. 5. Distance measurements with a curvimeter

To determine the length of the route on the map, a special device is used, called a curvimeter (Fig. 5), which is especially convenient for measuring winding and long lines.

The device has a wheel, which is connected by a gear system with an arrow.

When measuring the distance with a curvimeter, you need to set its arrow to division 99. Keeping the curvimeter in a vertical position, guide it along the line being measured, without tearing it off the map along the route so that the scale readings increase. Bringing to the end point, count the measured distance and multiply it by the denominator of the numerical scale. (In this example 34x25000=850000, or 8500 m)

1.3. The accuracy of measuring distances on the map. Distance corrections for slope and tortuosity of lines

Map Distance Accuracy depends on the scale of the map, the nature of the measured lines (straight, winding), the chosen measurement method, the terrain and other factors.

The most accurate way to determine the distance on the map is in a straight line.

When measuring distances using a measuring compass or a ruler with millimeter divisions, the average measurement error on flat terrain usually does not exceed 0.7-1 mm on the map scale, which is 17.5-25 m for a 1:25000 scale map, scale 1:50000 - 35-50 m, scale 1:100000 - 70-100 m.

In mountainous areas, with a large steepness of the slopes, errors will be greater. This is explained by the fact that when surveying the terrain, it is not the length of the lines on the surface of the Earth that is plotted on the map, but the length of the projections of these lines on the plane.

For example, With a slope slope of 20 ° (Fig. 6) and a distance on the ground of 2120 m, its projection on the plane (distance on the map) is 2000 m, i.e. 120 m less.

It has been calculated that at an inclination angle (slope slope) of 20°, the obtained result of measuring the distance on the map should be increased by 6% (add 6 m per 100 m), by 15% at an inclination angle of 30°, and by 23 at an angle of 40°. %.

Rice. 6. Projection of the slope length on a plane (map)

When determining the length of the route on the map, it should be borne in mind that the distances along the roads, measured on the map using a compass or curvimeter, in most cases are shorter than the actual distances.

This is explained not only by the presence of descents and ascents on the roads, but also by some generalization of the meanders of the roads on the maps.

Therefore, the result of measuring the length of the route obtained from the map should be multiplied by the coefficient indicated in the table, taking into account the nature of the terrain and the scale of the map.

1.4. The simplest ways to measure areas on a map

An approximate estimate of the size of the areas is made by eye on the squares of the kilometer grid available on the map. Each square of the grid of maps at scales 1:10000 - 1:50000 on the ground corresponds to 1 km2, a square of the grid of maps at a scale of 1 : 100000 - 4 km2, to the square of the grid of maps at a scale of 1:200000 - 16 km2.

Areas are measured more accurately palette, which is a sheet of transparent plastic with a grid of squares with a side of 10 mm applied to it (depending on the scale of the map and the required measurement accuracy).

Having superimposed such a palette on the measured object on the map, it first calculates the number of squares that completely fit inside the contour of the object, and then the number of squares intersected by the contour of the object. Each of the incomplete squares is taken as half a square. As a result of multiplying the area of one square by the sum of the squares, the area of \u200b\u200bthe object is obtained.

Using squares of scales 1:25,000 and 1:50,000, it is convenient to measure the areas of small areas with an officer's ruler, which has special rectangular cutouts. The areas of these rectangles (in hectares) are indicated on the ruler for each hart scale.

2. Azimuths and directional angle. Magnetic declination, meridian convergence and direction correction

true azimuth(Ai) - horizontal angle measured clockwise from 0° to 360° between the north direction of the true meridian of a given point and the direction to the object (see Fig. 7).

Magnetic azimuth(Am) - horizontal angle measured clockwise from 0e to 360° between the north direction of the magnetic meridian of the given point and the direction to the object.

Directional angle(α; DN) - horizontal angle measured clockwise from 0° to 360° between the north direction of the vertical grid line of the given point and the direction to the object.

Magnetic declination(δ; Sk) - the angle between the northern direction of the true and magnetic meridians at a given point.

If the magnetic needle deviates from the true meridian to the east, then the declination is east (taken into account with the + sign), if the magnetic needle deviates to the west, it is western (taken into account with the - sign).

Rice. 7. Angles, directions and their relationship on the map

convergence of meridians(γ; Sat) - the angle between the northern direction of the true meridian and the vertical line of the coordinate grid at a given point. When the grid line deviates to the east, the approach of the meridian is east (taken into account with the + sign), when the grid line deviates to the west, it is western (taken into account with the - sign).

Direction correction(PN) - the angle between the northern direction of the vertical grid line and the direction of the magnetic meridian. It is equal to the algebraic difference between the magnetic declination and the approach of the meridians:

3. Measurement and construction of directional angles on the map. Transition from directional angle to magnetic azimuth and vice versa

On the ground using a compass (compass) measure magnetic azimuths directions, from which they then move to directional angles.

On the map on the contrary, they measure directional angles and from them they pass to the magnetic azimuths of directions on the ground.

Rice. 8. Changing the directional angles on the map with a protractor

Directional angles on the map are measured with a protractor or a chordogonometer.

Measurement of directional angles with a protractor is carried out in the following sequence:

the landmark on which the directional angle is measured is connected by a straight line to the standing point so that this straight line is greater than the radius of the protractor and intersects at least one vertical line of the coordinate grid;
combine the center of the protractor with the intersection point, as shown in Fig. 8 and count the value of the directional angle along the protractor. In our example, the directional angle from point A to point B is 274° (Fig. 8, a), and from point A to point C - 65° (Fig. 8, b).

In practice, it often becomes necessary to determine the magnetic AM from a known directional angle ά, or, conversely, the angle ά to a known magnetic azimuth.

Transition from directional angle to magnetic azimuth and vice versa

The transition from the directional angle to the magnetic azimuth and back is performed when it is necessary to find the direction on the ground using a compass (compass), the directional angle of which is measured on the map, or vice versa, when it is necessary to plot the direction on the map, the magnetic azimuth of which is measured, on the terrain with compass.

To solve this problem, it is necessary to know the magnitude of the deviation of the magnetic meridian of a given point from the vertical kilometer line. This value is called the directional correction (PN).

Rice. 10. Determination of the correction for the transition from the directional angle to the magnetic azimuth and vice versa

The direction correction and its constituent angles - the convergence of the meridians and the magnetic declination - are indicated on the map under the south side of the frame in the form of a diagram that looks like the one shown in fig. 9.

convergence of meridians(g) - the angle between the true meridian of the point and the vertical kilometer line depends on the distance of this point from the axial meridian of the zone and can have a value from 0 to ±3°. The diagram shows the average convergence of meridians for a given sheet of the map.

Magnetic declination(d) - the angle between the true and magnetic meridians is indicated on the diagram for the year of surveying (updating) the map. The text placed next to the diagram provides information about the direction and magnitude of the annual change in magnetic declination.

To avoid errors in determining the magnitude and sign of the direction correction, the following method is recommended.

Draw an arbitrary direction OM from the top of the corners in the diagram (Fig. 10) and designate the directional angle ά and the magnetic azimuth Am of this direction with arcs. Then it will immediately be seen what the magnitude and sign of the direction correction are.

If, for example, ά = 97°12", then Am = 97°12" - (2°10"+10°15") = 84°47 " .

4. Preparation on the data map for movement in azimuths

Movement in azimuths- this is the main way of orienting in terrain poor in landmarks, especially at night and with limited visibility.

Its essence lies in maintaining on the ground the directions given by magnetic azimuths, and the distances determined on the map between the turning points of the intended route. The directions of movement are maintained with the help of a compass, distances are measured in steps or on a speedometer.

The initial data for movement in azimuths (magnetic azimuths and distances) are determined on the map, and the time of movement is determined according to the standard and drawn up in the form of a diagram (Fig. 11) or entered in a table (Table 1). Data in this form is issued to commanders who do not have topographic maps. If the commander has his own work map, then he draws up the initial data for movement in azimuths directly on the work map.

Rice. 11. Scheme for movement in azimuth

The route of movement in azimuths is chosen taking into account the terrain, its protective and camouflage properties, so that it provides a quick and covert exit to the specified point in a combat situation.

The route usually includes roads, clearings and other linear landmarks that make it easier to maintain the direction of movement. Turning points are chosen from landmarks that are easily identifiable on the ground (for example, tower-type buildings, road intersections, bridges, overpasses, geodetic points, etc.).

It has been experimentally established that the distances between landmarks at the turning points of the route should not exceed 1 km when driving during the day on foot, and when driving by car - 6–10 km.

For movement at night, landmarks are marked along the route more often.

In order to provide a secret exit to the specified point, the route is planned along hollows, vegetation massifs and other objects that provide movement masking. It is necessary to avoid movement on the crests of hills and open areas.

The distances between the landmarks chosen on the route at the turning points are measured along straight lines using a measuring compass and a linear scale, or perhaps more precisely, with a ruler with millimeter divisions. If the route is planned along a hilly (mountainous) area, then a relief correction is introduced into the distances measured on the map.

Table 1

5. Compliance with regulations

no.	Name of the standard	Conditions (order) for fulfilling the standard	Category of trainees	Time estimate
no.	Name of the standard	Conditions (order) for fulfilling the standard	Category of trainees	"excellent"	"hor."	"ud."
1	Determining the direction (azimuth) on the ground	A direction azimuth (landmark) is given. Indicate the direction corresponding to the given azimuth on the ground, or determine the azimuth to the specified landmark. The time to fulfill the standard is counted from the setting of the task to the report on the direction (azimuth value). Compliance with the standard is assessed "unsatisfactory" if the error in determining the direction (azimuth) exceeds 3° (0-50).	Serviceman	40 s	45 s	55 s
5	Preparing data for moving along azimuths	On the M 1:50000 map, two points are indicated at a distance of at least 4 km. Study the terrain on the map, outline the route of movement, select at least three intermediate landmarks, determine the directional angles and the distances between them. Draw up a scheme (table) of data for movement along azimuths (translate directional angles into magnetic azimuths, and distances into pairs of steps). Errors that reduce the rating to "unsatisfactory": the error in determining the directional angle exceeds 2°; distance measurement error exceeds 0.5 mm on the map scale; corrections for convergence of meridians and declination of the magnetic needle were not taken into account or incorrectly introduced. The time to fulfill the standard is counted from the moment the card is issued to the presentation of the scheme (table).	officers	8 min	9 min	11 min

When creating topographic maps, the linear dimensions of all terrain objects projected onto a level surface are reduced by a certain number of times. The degree of such reduction is called the scale of the map. The scale of the map can be expressed in numerical form (numerical scale) or in graphical form (linear, transverse scales), in the form of a graph.

Distances on a map are usually measured using a numerical or linear scale. More accurate measurements are made using a transverse scale.

On the scale of the linear scale, the segments corresponding to the distances on the ground in meters or kilometers are digitized. This makes it easier to measure distances as no calculations are required.

Determination of distances and areas on the map. Measurement of distances.

When using a numerical scale, the distance measured on the map in centimeters is multiplied by the denominator of the numerical scale in meters.

For example, the distance from the GGS point elev. 174.3 (square 3909) to the fork in the road (square 4314) on the map is 13.96 cm, on the ground it will be: 13.96 x 500 = 6980 m. (map scale 1: 50,000 U-34-85 -A).

If the distance measured on the ground must be plotted on the map, then it must be divided by the denominator of the numerical scale. For example, the distance measured on the ground is 1550 m, on a map at a scale of 1: 50,000 it will be 3.1 cm.

Measurements on a linear scale are performed using a measuring compass. With a compass solution, two contour points on the map are connected, between which it is necessary to determine the distance, then applied to a linear scale and the distance on the ground is obtained. Curvilinear sections are determined in parts or using a curvimeter.

Determination of areas.

The area of a piece of terrain is determined from the map most often by counting the squares of the coordinate grid covering this area. The size of the shares of squares is determined by eye or using a special palette. Each square formed by the lines of the coordinate grid corresponds to: 1: 25,000 and 1: 50,000 - 1 km.sq., 1: 100,000 - 4 km.sq., 1: 200,000 - 16 km.sq.

It is useful to remember that the following 2 x 2 mm ratios are appropriate for scales:

1: 25,000 - 0.25 ha = 0.0025 km2

1: 50,000 - 1 ha = 0.01 km2

1: 100,000 - 4 ha = 0.04 km2

1: 200,000 - 16 ha = 0.16 km2

The determination of the areas of individual plots is carried out during the alienation of land plots for the Ministry of Defense.

The accuracy of determining distances on the map. Correction for route length.

The accuracy of measuring lines, areas on a topographic map. You can buy truck tractors and trucks at the best prices on the website auto-holland.ru. All trucks have passed pre-sale preparation and inspection control (instrumental, computer and visual).

The accuracy of measuring lines and areas primarily depends on the scale of the map. The larger the scale of the map, the more accurately the lengths of lines and areas are determined from it. At the same time, the accuracy depends not only on the accuracy of measurements, but also on the error of the map itself, which is inevitable when it is compiled and printed. Errors can reach 0.5 mm for flat areas, and up to 0.7 mm in mountains. The source of measurement errors is also the deformation of the map and the measurements themselves.

Absolutely with the same error, flat rectangular coordinates are determined from topographic maps of the above scales.

Distance correction for line slope.

For example, the distance between two points, measured on the map, on a terrain with an inclination angle of 12 degrees is 9270 m. The actual distance between these points will be 9270 x 1.02 = 9455 m. Thus, when measuring distances on the map, it is necessary to introduce corrections for the slope lines (relief).

Long-range straight-line distances in one six-degree zone can be calculated using the formula:

This method of determining the distance is used mainly in the preparation of artillery firing and when launching missiles at ground targets.

Measuring distances on the map. Study of the area. Reading the map along the route

Study of the terrain

According to the relief and local objects depicted on the map, one can judge the suitability of a given area for organizing and conducting combat, for using military equipment in combat, for conditions of observation, firing, orientation, camouflage, and also for cross-country ability.

The presence on the map of a large number of settlements and individual tracts of forest, cliffs and gullies, lakes, rivers and streams indicates rugged terrain and limited visibility, which will impede the movement of military and transport equipment off-road, create difficulties in organizing observation. At the same time, the rugged nature of the terrain creates good conditions for sheltering and protecting units from the effects of enemy weapons of mass destruction, and forests can be used to mask unit personnel, military equipment, etc.

According to the nature of the layout, size and font of the signature of the settlements, it can be said that some settlements belong to cities, others to urban-type settlements, and still others to rural-type settlements. The orange color of the quarters indicates the predominance of fire-resistant buildings. The closely spaced black rectangles inside the quarters indicate the dense nature of the development, and the yellow fill indicates the non-fire resistance of the buildings.

A settlement may have a weather station, a power station, a radio tower, a fuel depot, a factory with a pipe, a railway station, a flour mill, and other facilities. Some of these local items can serve as good reference points.

The map may show a relatively developed network of roads of various classes. If there is a signature on the conventional sign of the highway, for example, 10 (14) B. This means that the covered part of the road has a width of 10 m, and from ditch to ditch - 14 m, the pavement is cobblestone. A single-track (double-track) railway can pass through the area. Studying the route of movement along the railway, you can find on the map separate sections of roads that pass along an embankment or in a recess with a specified depth.

With a more detailed study of the roads, it is possible to establish: the presence and characteristics of bridges, embankments, excavations and other structures; the presence of difficult areas, steep descents and ascents; the possibility of exit from the roads and traffic next to them.

Water surfaces are depicted on maps in blue or cyan, so they stand out clearly from the conventional signs of other local objects.

By the nature of the font of the signature of the river, one can judge its navigability. The arrow and the number on the river indicate in which direction it flows and at what speed. The signature, for example: means that the width of the river in this place is 250 m, the depth is 4.8 m, and the bottom soil is sandy. If there is a bridge across the river, then its description is given next to the image of the bridge.

If the river is shown on the map with one line, then this indicates that the width of the river does not exceed 10 m, if the river is shown in two lines, and its width is not indicated on the map, its width can be determined from the indicated characteristics of the bridges.

If the river is fordable, then the symbol of the ford indicates the depth of the ford and the bottom soil.

When studying the soil and vegetation cover, it is possible to find on the map areas of forest of various sizes. Explanatory symbols on the green fill of the forest area may indicate a mixed composition of tree species, deciduous or coniferous forest. The caption, for example: , indicates that the average height of trees is 25 m, their thickness is 30 cm, the average distance between them is 5 m, which allows us to conclude that vehicles and tanks cannot move through the forest off-road.

The study of the relief on the map begins with determining the general nature of the irregularities of the section of the terrain on which the combat mission is to be carried out. For example, if the map shows a hilly terrain with relative heights of 100-120 m, and the distance between contour lines (layout) is from 10 to 1 mm, this indicates a relatively small steepness of slopes (from 1 to 10 °).

A detailed study of the terrain on the map is associated with solving problems of determining the heights and mutual excess of points, the type, direction of the steepness of the slopes, the characteristics (depth, width and length) of hollows, ravines, gullies and other details of the relief.

Measuring distances on the map

Measurement on a map of straight and winding lines

Example, on a map with a scale of 1:25000, we measure the distance between the bridge and the windmill with a ruler; it is equal to 7.3 cm, multiply 250 m by 7.3 and get the desired distance; it is equal to 1825 meters (250x7.3=1825).

Determine the distance between points on the map using a ruler

A small distance between two points in a straight line is easier to determine using a linear scale. To do this, it is enough to apply a compass-meter, the solution of which is equal to the distance between given points on the map, to a linear scale and take a reading in meters or kilometers. In the figure, the measured distance is 1070 m.

Large distances between points along straight lines are usually measured using a long ruler or measuring compass.

In the first case, a numerical scale is used to determine the distance on the map using a ruler.

In the same way, distances are measured along winding lines. In this case, the "step" of the measuring compass should be taken as 0.5 or 1 cm, depending on the length and degree of sinuosity of the measured line.

To determine the length of the route on the map, a special device is used, called a curvimeter, which is especially convenient for measuring winding and long lines.

The device has a wheel, which is connected by a gear system with an arrow.

The accuracy of measuring distances on the map. Distance corrections for slope and tortuosity of lines

The accuracy of determining distances on the map depends on the scale of the map, the nature of the measured lines (straight, winding), the chosen method of measurement, the terrain and other factors.

The most accurate way to determine the distance on the map is in a straight line.

For example, With a slope of 20 ° and a distance on the ground of 2120 m, its projection on the plane (distance on the map) is 2000 m, i.e., 120 m less.

This is explained not only by the presence of descents and ascents on the roads, but also by some generalization of the meanders of the roads on the maps.

The simplest ways to measure areas on a map

An approximate estimate of the size of the areas is made by eye on the squares of the kilometer grid available on the map. Each square of the grid of maps of scales 1:10000 - 1:50000 corresponds to 1 km2 on the ground, the square of the grid of maps of scale 1:100000 - 4 km2, the square of the grid of maps of scale 1:200000 - 16 km2.

More precisely, areas are measured with a palette, which is a sheet of transparent plastic with a grid of squares with a side of 10 mm applied to it (depending on the scale of the map and the required measurement accuracy).

Reading the map along the route

Reading a map means correctly and fully perceiving the symbolism of its conventional signs, quickly and accurately recognizing from them not only the type and varieties of the depicted objects, but also their characteristic properties.

The study of the area on the map (reading the map) includes determining its general nature, the quantitative and qualitative characteristics of individual elements (local objects and landforms), as well as determining the degree of influence of the given area on the organization and conduct of combat.

When studying the area on the map, it should be remembered that since its creation, changes may have occurred on the area that are not reflected on the map, i.e., the content of the map to some extent will not correspond to the actual state of the area at the moment. Therefore, the study of the area on the map is recommended to start with familiarization with the map itself.

Introduction to the map. When familiarizing with the map, according to the information placed in the marginal design, the scale, the height of the relief section and the time the map was created are determined. Data on the scale and height of the relief section will allow you to establish the degree of detail of the image on this map of local objects, forms and details of the relief. Knowing the scale value, you can quickly determine the size of local objects or their distance from each other.

Information about the time the map was created will make it possible to preliminarily determine whether the content of the map corresponds to the actual state of the area.

Then they read and, if possible, remember the declination of the magnetic needle, the direction corrections. Knowing the direction correction from memory, you can quickly convert directional angles into magnetic azimuths or orient the map on the ground along the kilometer grid line.

General rules and sequence of studying the area on the map. The sequence and degree of detail of the study of the terrain is determined by the specific conditions of the combat situation, the nature of the subunit's combat mission, as well as seasonal conditions and the tactical and technical data of the military equipment used in the performance of the assigned combat mission. When organizing defense in a city, it is important to determine the nature of its planning and development, to identify durable buildings with basements and underground structures. In the case when the route of movement of the unit passes through the city, it is not necessary to study the features of the city in such detail. When organizing an offensive in the mountains, the main objects of study are passes, mountain passes, gorges and gorges with adjacent heights, the forms of slopes and their influence on the organization of the fire system.

The study of the terrain, as a rule, begins with determining its general nature, and then studies in detail individual local objects, forms and details of the relief, their influence on the conditions of observation, camouflage, maneuverability, protective properties, conditions of firing and orientation.

Determining the general nature of the terrain is aimed at identifying the most important features of the relief and local objects that have a significant impact on the fulfillment of the task. When determining the general nature of the area on the basis of familiarization with the relief, settlements, roads, hydrographic network and vegetation cover, the variety of the area, the degree of its ruggedness and closeness are revealed, which makes it possible to preliminarily determine its tactical and protective properties.

The general character of the area is determined by a cursory survey on the map of the entire area under study.

At first glance at the map, one can say that there are settlements and individual tracts of forest, cliffs and gullies, lakes, rivers and streams indicating rough terrain and limited visibility, which inevitably makes it difficult for military and transport equipment to move off-road, creates difficulties in organizing observation . At the same time, the rugged nature of the terrain creates good conditions for sheltering and protecting units from the effects of enemy weapons of mass destruction, and forests can be used to mask unit personnel, military equipment, etc.

So, as a result of determining the general nature of the terrain, a conclusion is made about the availability of the area and its individual directions for the actions of units on vehicles, and also outline the lines and objects that should be studied in more detail, given the nature of the combat mission to be performed on this area of the terrain.
A detailed study of the terrain is aimed at determining the qualitative characteristics of local objects, forms and details of the relief within the boundaries of the unit's actions or along the forthcoming route of movement. Based on the receipt of such data on the map and taking into account the relationship of topographical elements of the terrain (local objects and relief), an assessment is made of the conditions of passability, camouflage and surveillance, orientation, firing, and the protective properties of the terrain are determined.

The definition of the qualitative and quantitative characteristics of local objects is carried out on the map with a relatively high accuracy and great detail.

When studying the map of settlements, the number of settlements, their type and dispersal are determined, the degree of habitation of a particular section (district) of the area is determined. The main indicators of the tactical and protective properties of settlements are their area and configuration, the nature of planning and development, the presence of underground structures, the nature of the terrain on the outskirts of the settlement.

Reading the map, according to the conventional signs of settlements, they establish the presence, type and location of them in a given area, determine the nature of the outskirts and layout, building density and fire resistance of buildings, the location of streets, main thoroughfares, the presence of industrial facilities, outstanding buildings and landmarks.

When studying the map of the road network, the degree of development of the road network and the quality of the roads are specified, the conditions for the passability of the area and the possibility of the effective use of vehicles are determined.

With a more detailed study of roads, the following are established: the presence and characteristics of bridges, embankments, excavations and other structures; the presence of difficult areas, steep descents and ascents; the possibility of exit from the roads and traffic next to them.

When studying dirt roads, special attention is paid to identifying the carrying capacity of bridges and ferry crossings, since on such roads they are often not designed for the passage of heavy wheeled and tracked vehicles.

By studying hydrography, the presence of water bodies is determined on the map, and the degree of indentation of the terrain is clarified. The presence of water bodies creates good conditions for water supply and transportation by waterways.

Water surfaces are depicted on maps in blue or cyan, so they stand out clearly from the conventional signs of other local objects. When studying the map of rivers, canals, streams, lakes and other water barriers, the width, depth, speed of the current, the nature of the soil of the bottom, banks and the surrounding area are determined; the presence and characteristics of bridges, dams, locks, ferry crossings, fords and areas suitable for forcing are established.

When studying the soil and vegetation cover, the presence and characteristics of forest and shrub massifs, swamps, solonchaks, sands, stony placers and those elements of the soil and vegetation cover that can have a significant impact on the conditions of passability, camouflage, observation and the possibility of shelter are established on the map.

The characteristics of the forest plot studied on the map allow us to conclude that it can be used for the covert and dispersed location of units, as well as the forest's passability along roads and clearings. Good landmarks in the forest for determining your location and orienting yourself on the move are the forester's house and clearings.

The characteristics of swamps are determined by the outlines of conventional signs. However, when determining the passability of swamps on the map, the time of year and weather conditions should be taken into account. During the period of rains and mudslides, swamps, shown on the map as passable by a symbol, in reality may turn out to be difficult to pass. In winter, during severe frosts, impassable swamps can become easily passable.

The study of the relief on the map begins with determining the general nature of the irregularities of the section of the terrain on which the combat mission is to be carried out. At the same time, the presence, location and interconnection of the typical forms and relief details most characteristic of a given area are established, their influence on the conditions of passability, observation, firing, camouflage, orientation and organization of protection against weapons of mass destruction is determined in general terms. The general nature of the relief can be quickly determined by the density and outline of contour lines, elevation marks and conventional signs of relief details.

A detailed study of the terrain on the map is associated with solving problems of determining the heights and mutual elevation of points, the type and direction of the steepness of the slopes, the characteristics (depth, width and length) of hollows, ravines, gullies and other details of the relief.

Naturally, the need to solve specific tasks will depend on the nature of the assigned combat mission. For example, the definition of fields of invisibility will be required when organizing and conducting surveillance reconnaissance; determination of the steepness, height and length of the slopes will be required when determining the terrain conditions and choosing a route, etc.