How to find scale in geography. Scales of topographic maps and plans Topographic maps 1,100,000

Topographic map - a geographical map of universal purpose, which shows the area in detail. A topographic map contains information about reference geodetic points, relief, hydrography, vegetation, soils, economic and cultural objects, roads, communications, boundaries and other terrain objects. The completeness of the content and the accuracy of topographic maps make it possible to solve technical problems.

The science of creating topographic maps is topography.

All geographical maps, depending on the scale, are conventionally divided into the following types:

topographic plans - up to 1:5 000 inclusive;
large-scale topographic maps - from 1:10,000 to 1:200,000 inclusive;
medium-scale topographic maps - from 1:200,000 (not including) to 1:1,000,000 inclusive;
small-scale topographic maps - less than (less than) 1:1,000,000.

The smaller the denominator of the numerical scale, the larger the scale. Plans are made on a large scale, and maps are made on a small scale. The maps take into account the "sphericity" of the Earth, but the plans do not. Because of this, plans should not be made for areas larger than 400 km² (i.e. land plots larger than 20x20 km). The main difference between topographic maps (in the narrow, strict sense) is their large scale, namely the scale of 1:200,000 and larger (the first two points, more strictly - the second point: from 1:10,000 to 1:200,000 inclusive).

The most detailed geographical objects and their outlines are depicted on large-scale (topographic) maps. When the scale of the map is reduced, the details have to be excluded and generalized. Individual objects are replaced by their collective values. Selection and generalization become apparent when comparing a multi-scale image of a settlement, which is given in the form of separate buildings on a scale of 1:10,000, quarters on a scale of 1:50,000, and a punchson on a scale of 1:100,000. Selecting and summarizing content when compiling geographical maps called cartographic generalization. It aims to preserve and highlight on the map the typical features of the depicted phenomena in accordance with the purpose of the map.

Secrecy

Topographic maps of the territory of Russia up to a scale of 1:50,000 inclusive are secret, topographic maps of a scale of 1:100,000 are intended for official use (DSP), smaller scale 1:100,000 are unclassified.

Those working with maps up to a scale of 1:50,000 are required, in addition to a permit (license) from the Federal Service for State Registration, Cadastre and Cartography or a certificate from a self-regulatory organization (SRO), to obtain permission from the FSB, since such maps constitute a state secret. For the loss of a map at a scale of 1:50,000 or larger, in accordance with Article 284 of the Criminal Code of the Russian Federation “Loss of documents containing state secrets”, a penalty of up to three years in prison is provided.

At the same time, after 1991, secret maps of the entire territory of the USSR, stored in the headquarters of military districts located outside of Russia, appeared on free sale. Since the leadership of, for example, Ukraine or Belarus does not need to maintain the secrecy of maps of foreign territories.

The problem of the existing secrecy on the maps became acute in February 2005 in connection with the launch of the project Google Maps, allowing anyone to use color satellite images high resolution(up to several meters), although in Russia any space image with a resolution of more than 10 meters is considered secret and requires an order from the FSB for a declassification procedure.

In other countries this problem allowed by the fact that not areal, but object secrecy is used. With object secrecy, the free distribution of large-scale topographic maps and photographs of strictly defined objects, for example, areas of military operations, military bases and training grounds, and parking of warships, is prohibited. For this, a technique has been developed for creating topographic maps and plans of any scale, which do not have a secrecy stamp and are intended for open use.

Scales of topographic maps and plans

map scale- this is the ratio of the length of the segment on the map to its actual length on the ground.

Scale(from German - measure and Stab - stick) - the ratio of the length of a segment on a map, plan, aerial or space image to its actual length on the ground.

Numerical scale- scale, expressed as a fraction, where the numerator is one, and the denominator is a number showing how many times the image is reduced.

Named (verbal) scale- type of scale, a verbal indication of what distance on the ground corresponds to 1 cm on a map, plan, photograph.

Linear scale - an auxiliary measuring ruler applied to maps to facilitate the measurement of distances.

The named scale is expressed by named numbers denoting the lengths of mutually corresponding segments on the map and in nature.

For example, there are 5 kilometers in 1 centimeter (5 km in 1 cm).

Numerical scale - a scale expressed as a fraction in which: the numerator is equal to one, and the denominator is equal to the number showing how many times the linear dimensions on the map are reduced.

The scale of the plan is the same at all its points.

The scale of the map at each point has its own particular value, depending on the latitude and longitude of the given point. Therefore, its strict numerical characteristic is a particular scale - the ratio of the length of an infinitely small segment D / on the map to the length of the corresponding infinitesimal segment on the surface of the ellipsoid of the globe. However, for practical measurements on the map, its main scale is used.

Scale expression forms

The designation of the scale on maps and plans has three forms: numerical, named and linear scales.

The numerical scale is expressed as a fraction, in which the numerator is one, and the denominator M is a number showing how many times the dimensions on the map or plan are reduced (1: M)

In Russia, for topographic maps, standard numerical scales are accepted:

For special purposes, topographic maps are also created at scales of 1: 5,000 and 1: 2,000.

Main scales topographic plans in Russia are:

1:5000, 1:2000, 1:1000 and 1:500.

However, in land management practice, land use plans are most often drawn up on a scale of 1: 10,000 and 1:25,000, and sometimes 1: 50,000.

When comparing different numerical scales, the smaller one is the one with the larger denominator M, and, conversely, the smaller the denominator M, the larger the scale of the plan or map.

Thus, scale 1:10,000 is larger than scale 1:100,000, and scale 1:50,000 is smaller than scale 1:10,000.

Named Scale

Since the lengths of lines on the ground are usually measured in meters, and on maps and plans - in centimeters, it is convenient to express the scales in verbal form, for example:

There are 50 meters in one centimeter. This corresponds to a numerical scale of 1: 5000. Since 1 meter is equal to 100 centimeters, the number of meters of terrain contained in 1 cm of a map or plan is easily determined by dividing the denominator of the numerical scale by 100.

Linear scale

It is a graph in the form of a straight line segment, divided into equal parts with signed values of the lengths of the terrain lines commensurate with them. The linear scale allows you to measure or build distances on maps and plans without calculations.

Scale Accuracy

The limiting possibility of measuring and constructing segments on maps and plans is limited to 0.01 cm. The corresponding number of meters of terrain on the map or plan scale is the ultimate graphic accuracy of this scale. Since the accuracy of the scale expresses the length horizontal terrain line in meters, then to determine it, the denominator of the numerical scale should be divided by 10,000 (1 m contains 10,000 segments of 0.01 cm each). So, for a map with a scale of 1: 25,000, the scale accuracy is 2.5 m; for map 1: 100,000-10 m, etc.

Topographic map scales

Below are the numerical scales of maps and their corresponding named scales:

Scale 1: 100,000
1 mm on the map - 100 m (0.1 km) on the ground

1 cm on the map - 1000 m (1 km) on the ground

10 cm on the map - 10000 m (10 km) on the ground
Scale 1:10000
1 mm on the map - 10 m (0.01 km) on the ground

1 cm on the map - 100 m (0.1 km) on the ground

10 cm on the map - 1000m (1 km) on the ground
Scale 1:5000
1 mm on the map - 5 m (0.005 km) on the ground

1 cm on the map - 50 m (0.05 km) on the ground

10 cm on the map - 500 m (0.5 km) on the ground
Scale 1:2000
1 mm on the map - 2 m (0.002 km) on the ground

1 cm on the map - 20 m (0.02 km) on the ground

10 cm on the map - 200 m (0.2 km) on the ground
Scale 1:1000
1 mm on the map - 100 cm (1 m) on the ground

1 cm on the map - 1000cm (10 m) on the ground

10 cm on the map - 100 m on the ground
Scale 1:500
1 mm on the map - 50 cm (0.5 meters) on the ground

1 cm on the map - 5 m on the ground

10 cm on the map - 50 m on the ground
Scale 1:200
1 mm on the map -0.2 m (20 cm) on the ground

1 cm on the map - 2 m (200 cm) on the ground

10 cm on the map - 20 m (0.2 km) on the ground
Scale 1:100
1 mm on the map - 0.1 m (10 cm) on the ground

1 cm on the map - 1 m (100 cm) on the ground

10 cm on the map - 10m (0.01 km) on the ground

To convert a numerical scale into a named one, you need to convert the number in the denominator and corresponding to the number of centimeters into kilometers (meters). For example, 1:100,000 in 1 cm is 1 km.

To convert a named scale into a numerical scale, you need to convert the number of kilometers to centimeters. For example, in 1 cm - 50 km 1: 5,000,000.

Nomenclature of topographic plans and maps

Nomenclature - a system of marking and notation of topographic plans and maps.

The division of a multi-sheet map into separate sheets according to a certain system is called the layout of the map, and the designation of a sheet of a multi-sheet map is called nomenclature. In cartographic practice, the following map layout systems are used:

along the lines of the cartographic grid of meridians and parallels;
along the lines of a rectangular coordinate grid;
along auxiliary lines parallel to the middle meridian of the map and a line perpendicular to it, etc.

The most widespread in cartography is the layout of maps along the lines of meridians and parallels, since in this case the position of each sheet of the map on earth's surface precisely determined by the values of the geographical coordinates of the corners of the frame and the position of its lines. Such a system is universal, convenient for depicting any areas of the globe, except for the polar regions. It is used in Russia, USA, France, Germany and many other countries of the world.

The basis of the nomenclature of maps in the territory Russian Federation international layout of map sheets at a scale of 1:1 000000 is required. To obtain one sheet of a map of this scale Earth divided by meridians and parallels into columns and rows (belts).

Meridians are drawn every 6°. The count of the columns from 1 to 60 goes from the 180° meridian from 1 to 60 from west to east, counterclockwise. The columns coincide with the zones of the rectangular layout, but their numbers differ by exactly 30. So for zone 12, the column number is 42.

Column numbers

Parallels are drawn every 4 °. The account of belts from A to W goes from the equator to the north and south.

Row numbers

Map sheet 1:1,000,000 contains 4 map sheets 1:500,000, denoted by capital letters A, B, C, D; 36 map sheets 1:200,000, designated from I to XXXVI; 144 sheets of a 1:100,000 map, labeled 1 to 144.

A card sheet 1:100,000 contains 4 sheets of a card 1:50,000, which are indicated by capital letters A, B, C, D.

A map sheet 1:50,000 is divided into 4 map sheets 1:25,000, which are indicated by lowercase letters a, b, c, d.

Within the map sheet 1:1,000,000, the arrangement of numbers and letters when designating map sheets 1:500,000 and larger is made from left to right in rows and in the direction to south pole. The initial row is adjacent to the northern frame of the sheet.

The disadvantage of this layout system is the change in the linear dimensions of the northern and southern frames of the map sheets depending on the geographical latitude. As a result, as they move away from the equator, the sheets take the form of narrower and narrower strips, elongated along the meridians. Therefore, topographic maps of Russia at all scales from 60 to 76 ° northern and southern latitudes are published in double longitude, and in the range from 76 to 84 ° - quadruple (on a scale of 1: 200,000 - tripled) in longitude sheets.

The nomenclature of map sheets at scales 1:500,000, 1:200,000, and 1:100,000 is composed of the nomenclature of a map sheet at 1:1,000,000, followed by the addition of map sheet designations of the corresponding scales. The nomenclatures of double, triple or quadruple sheets contain the designations of all individual sheets are presented in the table:

Nomenclature of sheets of topographic maps for the northern hemisphere.

1:1 000 000	N-37	P-47.48	T-45,46,47,48
1:500 000	N-37-B	R-47-A,B	T-45-A,B,46-A,B
1:200 000	N-37-IV	P-47-I, II	T-47-I,II,III
1:100 000	N-37-12	P-47-9.10	T-47-133, 134,135,136
1:50 000	N-37-12-A	P-47-9-A,B	T-47-133-A,B, 134-A.B
1:25 000	N-37-12-A-a	R-47-9-A-a, b	T-47-12-A-a, b, B-a, b

On the sheets of the southern hemisphere, the signature (JP) is placed to the right of the nomenclature.

N37

On sheets of topographic maps of the entire scale range, along with nomenclature, their code numbers (ciphers) are placed, which are necessary for accounting maps using automated means. The coding of the nomenclature consists in replacing letters and Roman numerals with Arabic numerals in it. In this case, the letters are replaced by their serial numbers in alphabetical order. The numbers of belts and columns of the map 1:1,000,000 are always indicated by two-digit numbers, for which zero is assigned to single-digit numbers in front. The numbers of sheets of the map 1:200,000 within the framework of the sheet of the map 1:1,000,000 are also indicated by two-digit numbers, and the numbers of sheets of the map 1:100,000 are three-digit (one or two zeros are assigned to single-digit and two-digit numbers in front, respectively).

Knowing the nomenclature of maps and the system of its construction, it is possible to determine the scale of the map and the geographical coordinates of the corners of the sheet frame, that is, to determine which part of the earth's surface the this sheet cards. Conversely, knowing the scale of a map sheet and the geographic coordinates of the corners of its frame, one can determine the nomenclature of this sheet.

To select the necessary sheets of topographic maps for a specific area and quickly determine their nomenclature, there are special prefabricated tables:

Prefabricated tables are small-scale schematic blank maps, divided by vertical and horizontal lines into cells, each of which corresponds to a specific map sheet of the corresponding scale. The scale, the signatures of the meridians and parallels, the designations of the columns and belts of the map layout 1: 1,000,000, as well as the number of sheets of maps of a larger scale within the sheets of a millionth map, are indicated on the prefabricated tables. Prefabricated tables are used in the preparation of applications for required cards, as well as for the geographical accounting of topographic maps in the troops and warehouses, the preparation of documents on the cartographic security of territories. A strip or area of operations of troops (traffic route, area of exercises, etc.) is applied to the combined table of maps, then the nomenclature of sheets covering the strip (area) is determined. For example, in an application for map sheets 1:100,000 of the region shaded in the figure, O-36-132, 144, 0-37-121, 133 are written; N-36-12, 24; N "37-1, 2, 13, 14.

Enlargement or reduction of an image on paper is characterized by scale. On a geographical map, the image of the area is represented by a reduction scale.

Numerical Scale map is expressed as a ratio of 1 to a number showing how many times the real segment has been reduced.

Most geographical maps are made on a scale of 1:20,000,000 or 1:25,000,000. This scale indicates that 1 cm on the map corresponds to 20,000,000 cm = 200 km or 25,000,000 cm = 25 km on the ground, since in scale records, the dimension of the units of the map and the terrain must match.

If the scale is 1:20,000,000 on the map, then by measuring the distance between points in centimeters and multiplying it by 20,000,000, you will get the real distance between points in centimeters.

To simplify calculations, you can immediately translate the scale into kilometers or meters on the ground.

For example, the distance between city A and city B was 3.5 cm on the map, the map scale was 1:25,000,000.

Decision:
1) 25,000,000 cm = 250 km
2) 3.5 * 250 = 875 (km)

In addition to the numerical scale, the map can also be given linear scale.

The first square on the left shows the scale (1 cm on the map is equal to 200 m on the ground). Having attached a ruler to the map, we immediately determine from it how many meters this segment will be on the ground.

Scale is the ratio of 2 linear dimensions, which is used when creating drawings and models and allows you to show large objects in a reduced form, and small objects in an enlarged one. In other words, this is the ratio of the length of the segment on the map to the true length on the ground. Different practical situations may require you to know how to find the scale.

When does scaling become necessary?

How to find the scale

It mostly happens in the following situations:

when using the card;
when making a drawing;
in the manufacture of models of various objects.

Scale types

Under the numerical scale it is necessary to understand the scale expressed as a fraction.

Its numerator is one, and the denominator is a number showing how many times the image is smaller than the real object.

A linear scale is a ruler that you can see on maps. This segment is divided into equal parts, signed by the values of their respective distances on the real terrain. A linear scale is convenient in that it provides the ability to measure and build distances on plans and maps.

A named scale is a verbal description of what distance in reality corresponds to one centimeter on the map.

For example, there are 100,000 centimeters in one kilometer. In this case, the numerical scale would look like this: 1:100000.

How to find the map scale?

Take, for example, a school atlas and look at any of its pages.

At the bottom, you can see a ruler that indicates how much distance in the real area corresponds to one centimeter on your map.

The scale in atlases is usually indicated in centimeters, which will need to be converted to kilometers.

For example, when you see the inscription 1:9 500 000, you will understand that 95 kilometers of real terrain corresponds to only 1 cm of the map.

If, for example, you know that the distance between your city and the neighboring one is 40 km, then you can simply measure the gap between them on the map with a ruler and determine the ratio.

So, if by measuring you got a distance of 2 cm, then you get a scale of 2:40=2:4000000=1:2000000. As you can see, finding the scale is not difficult at all.

Other Uses for Scale

When making models of aircraft, tanks, ships, cars and other objects, certain scaling standards are used. For example, it can be a scale of 1:24, 1:48, 1:144.

At the same time, the manufactured models must be smaller than their prototypes exactly by the specified number of times.

Scaling may be needed, for example, when enlarging a picture. In this case, the image is divided into cells of a certain size, for example, 0.5 cm. A sheet of paper will also need to be drawn into cells, but already enlarged by the required number of times (for example, the length of their sides can be one and a half centimeters, if the picture needs to be enlarged 3 times) .

By applying the contours of the original drawing to the lined sheet, it will be possible to obtain an image that is very close to the original.

Map scale. The scale of topographic maps is the ratio of the length of the line on the map to the length of the horizontal projection of the corresponding terrain line. On flat territories, at small angles of inclination of the physical surface, the horizontal projections of the lines differ very little from the lengths of the lines themselves, and in these cases, the ratio of the line length on the map to the length of the corresponding terrain line, i.e.

the degree of reduction in the length of lines on the map relative to their length on the ground. The scale is indicated under the southern frame of the map sheet in the form of a ratio of numbers (numerical scale), as well as in the form of named and linear (graphic) scales.

Numerical scale(M) is expressed as a fraction, where the numerator is one, and the denominator is a number indicating the degree of reduction: M \u003d 1 / m. So, for example, on a map on a scale of 1:100,000, the lengths are reduced by a factor of 100,000 compared to their horizontal projections (or reality).

Obviously, the larger the scale denominator, the greater the reduction in length, the smaller the image of objects on the map, i.e. the smaller the scale of the map.

Named Scale- an explanation indicating the ratio of the lengths of the lines on the map and on the ground.

At M= 1:100,000, 1 cm on the map corresponds to 1 km.

Linear scale serves to determine the lengths of lines in kind from maps. This is a straight line divided into equal segments corresponding to the "round" decimal numbers of the distances of the terrain (Fig. 5).

Rice. 5. Designation of the scale on the topographic map: a - the base of the linear scale: b - the smallest division of the linear scale; scale accuracy 100 m.

Scale value - 1 km

Segments a to the right of zero are called scale base. The distance on the ground corresponding to the base is called linear scale value. To improve the accuracy of determining distances, the leftmost segment of the linear scale is divided into smaller parts in, called the smallest divisions of the linear scale.

The distance on the ground, expressed by one such division, is the accuracy of a linear scale. As can be seen in Figure 5, with a numerical map scale of 1:100,000 and a linear scale base of 1 cm, the scale value will be 1 km, and the scale accuracy (at the smallest division of 1 mm) will be 100 m.

The accuracy of measurements on maps and the accuracy of graphic constructions on paper are related both to the technical capabilities of measurements and to the resolution of human vision. The accuracy of constructions on paper (graphic accuracy) is considered to be equal to 0.2 mm.

The resolution of normal vision is close to 0.1 mm.

Ultimate Accuracy map scale - a segment on the ground corresponding to 0.1 mm on the scale of this map. At a map scale of 1:100,000, the maximum accuracy will be 10 m; at a map scale of 1:10,000, it will be 1 m.

Obviously, the possibilities of depicting contours in their actual outlines on these maps will be very different.

The scale of topographic maps largely determines the selection and detail of the display of the objects depicted on them.

With zoom out, i.e. with an increase in its denominator, the detail of the image of terrain objects is lost.

Maps of different scales are needed to meet the diverse needs of the sectors of the national economy, science and defense of the country. For the state topographic maps of the USSR, a number of standard scales, based on the metric decimal system of measures (Table.

Table 1. Scales of topographic maps of the USSR
Numerical scale	Map name	1 cm on the map corresponds to the distance on the ground	1 cm2 on the map corresponds to the area on the ground
1:5 000	five thousandth	50 m	0.25 ha
1:10 000	ten thousandth	100 m	1 ha
1:25 000	twenty-five thousandth	250 m	6.25 ha
1:50 000	fifty thousandth	500 m	25 ha
1:100 000	hundred thousandth	1 km	1 km2
1:200 000	two hundred thousandth	2 km	4 km2
1:500 000	five hundred thousandth	5 km	25 km2
1:1 000 000	millionth	10 km	100 km2

In the complex of maps named in Table.

1, there are actually topographic maps at scales of 1:5000-1:200,000 and survey topographic maps at scales of 1:500,000 and 1:1,000,000. maps are used for general familiarization with the terrain, for orientation when moving at high speed.

Measuring distances and areas using maps.

When measuring distances on maps, it should be remembered that the result is the length of horizontal projections of lines, and not the length of lines on the earth's surface. However, at small angles of inclination, the difference in the length of the inclined line and its horizontal projection is very small and may not be taken into account. So, for example, at an inclination angle of 2°, the horizontal projection is shorter than the line itself by 0.0006, and at 5°, by 0.0004 of its length.

When measuring from distance maps in mountainous areas, the actual distance on a sloping surface can be calculated

according to the formula S = d cos α, where d is the length of the horizontal projection of the line S, α is the angle of inclination.

The angles of inclination can be measured from a topographic map by the method specified in §11. Corrections for the lengths of oblique lines are also given in the tables.

Rice. 6. The position of the measuring compass when measuring distances on the map using a linear scale

To determine the length of a straight line segment between two points, a given segment is taken from the map into the compass-measuring solution, transferred to the linear scale of the map (as shown in Figure 6) and the line length is obtained, expressed in land measures (meters or kilometers).

Similarly, the lengths of broken lines are measured, taking each segment separately into the compass solution and then summing up their lengths. Measuring distances along curved lines (roads, borders, rivers, etc.)

etc.) are more complex and less precise. Very smooth curves are measured as broken lines, having previously been divided into straight segments. Winding lines are measured with a small constant solution of a compass, rearranging it (“stepping”) along all the bends of the line. Obviously, finely sinuous lines should be measured with a very small compass opening (2-4 mm).

Knowing what length the compass solution corresponds to on the ground, and counting the number of its installations along the entire line, its total length is determined. For these measurements, a micrometer or a spring compass is used, the solution of which is regulated by a screw passed through the legs of the compass.

7. Curvimeter

It should be borne in mind that any measurements are inevitably accompanied by errors (errors). According to their origin, errors are divided into gross blunders (arise due to the inattention of the person making the measurements), systematic errors (due to errors in measuring instruments, etc.), random errors that cannot be fully taken into account (their reasons are not clear).

Obviously, the true value of the measured quantity remains unknown due to the influence of measurement errors. Therefore, its most probable value is determined. This value is the arithmetic average of all individual measurements x - (a1+a2+ …+аn):n=∑a/n , where x is the most probable value of the measured value, a1, a2 … an are the results of individual measurements; 2 - sum sign, n - number of measurements.

The more measurements, the closer the probable value to the true value of A. If we assume that the value of A is known, then the difference between this value and the measurement a will give the true measurement error Δ=A-a.

The ratio of the measurement error of any quantity A to its value is called the relative error -. This error is expressed as a proper fraction, where the denominator is the proportion of the error from the measured value, i.e. ∆/A = 1/(A:∆).

So, for example, when measuring the lengths of curves with a curvimeter, a measurement error of the order of 1-2% occurs, i.e., it will be 1/100 - 1/50 of the length of the measured line. Thus, when measuring a line with a length of 10 cm, a relative error of 1-2 mm is possible.

This value on different scales gives different errors in the lengths of the measured lines. So, on a 1:10,000 scale map, 2 mm corresponds to 20 m, and on a 1:1,000,000 scale map it will be 200 m.

It follows that more accurate measurement results are obtained when using maps of large scales.

Determination of areas plots on 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 a rectangle on the map are reduced by n times, then the area of this figure will decrease by n2 times.

For a map with a scale of 1:10,000 (1 cm - 100 m), the area scale will be equal to (1:10,000)2 or 1 cm2-(100 m)2, i.e. in 1 cm2 - 1 ha, and on a map with a scale of 1: 1,000,000 in 1 cm2 - 100 km2.

To measure areas on maps, graphical and instrumental methods are used. The use of one or another measurement method is dictated by the shape of the area being measured, the given accuracy of the measurement results, the required speed of obtaining data, and the availability of the necessary instruments.

8. Straightening the curvilinear boundaries of the site and breaking down its area into simple geometric figures: dots indicate cut-off areas, hatching - attached areas

When measuring the area of a site with rectilinear boundaries, the site is divided into simple geometric shapes, 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.

plan scale

An object with a curvilinear contour is 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. 8). The measurement results will be approximate to some extent.

Rice. 9. Square grid palette superimposed on the measured figure. Plot area Р=a2n, a - side of the square, expressed on the scale of the map; n is the number of squares that fall within the contour of the measured area

Measurement of the areas of areas with a complex irregular configuration is often carried out using pallets and planimeters, which gives the most accurate results.

A grid palette (Fig. 9) is a transparent plate (made of plastic, organic glass or tracing paper) with an engraved or drawn grid of squares. 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, the area of \u200b\u200bone cell is determined in land measures, i.e.

the price of the division of the palette.

Rice. 10. Dot palette - a modified square palette. Р=a2n

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.

10). 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.

11. Palette consisting of a system parallel lines. The area of the figure is equal to the sum of the lengths of the segments (middle dashed), cut off by the contour of the area, multiplied by the distance between the lines of the palette.

Equidistant parallel lines are engraved on the parallel palette. The measured area will be divided into a series of trapeziums with the same height when the palette is applied to it (Fig. 11). Segments of parallel lines inside the contour in the middle between the lines are the middle lines of the trapezoid. Having measured all the middle lines, multiply their sum by the length of the gap between the lines and get the area of \u200b\u200bthe entire plot (taking into account the areal scale).

Measurement of the areas of significant areas is carried out on maps using a planimeter.

The most common is the polar planimeter, which is not very difficult to work with. However, the theory of this device is quite complex and is discussed in surveying manuals.

12. Polar planimeter

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How to find the scale of the map

A topographic map is a projection of a real ground mathematical model onto a plane in a reduced form.

The amount of relief image decreases and is called the denominator of the scale. In other words, the map scale is the ratio of the distance between two objects measured along it to the distance between the same objects measured on the ground. Knowing the scale of the map, you can always calculate the actual size and distance between objects located on the earth's surface.

instructions

An indispensable condition for the publication of any topographic map or graph is a sign of its scale, without which it loses its meaning and becomes just a beautiful picture. Usually the scale of the map is indicated in its description - legends or taken to the border. You can indicate it in your head as well with explanatory inscriptions. Sometimes on popular schematic diagrams, the scale is written directly on the map itself. Take a close look at the map and look for "Criterion 1:" or "M 1:".
If the map is cropped and there is no border processing, you can specify the desired scale on another map of the same area, the scale of which is known.
Find a pair of identical feature points in the field on both maps. These can be structures or industrial buildings, road intersections, characteristic characteristics of the area, which are reflected on one and on the other map. Measure the distance between them on both charts and calculate the ratio between the scales - the number of times the desired scale is smaller or larger than the one specified for the other map.
Keep in mind that the scale is usually an integer multiple of 100 or 1000 values.
If you get a scale value, it's not the result of a measurement error, so your map's scale brings that value.
If there is no other card, high tech will be available. Use one of the map services available in Yandex or Google.
Finding a distance on the map

Their base is converted into flat images, mostly maps. Find them in the area shown on your map of unknown magnitude and at two locations you have chosen as a feature.

Use the Ruler tool to determine the distance between these points in spatial images in the selected units. If you know the distance on the map and the distance in the field, specify the map scale and convert it to an integer greater than 100 or 1000.

Geography lesson in grade 6 on the topic “Scale. Scale types»

According to the scale maps are divided into three groups: small-scale (1:1,000,000, 1:500,000, 1:300,000, 1:200,000); medium scale (1:100000, 1:50000, 1:25000); large scale (1:10000, 1:5000, 1:2000, 1:1000, 1:500).

Large-scale topographic maps are the most accurate and suitable for detailed design.

Small-scale maps are intended: for a general study of the area in the general design of the development of the national economy, for accounting for the resources of the earth's surface and water space, for the preliminary design of large engineering facilities, for the needs of the country's defense.

Medium-scale maps have more detailed content and higher accuracy; designed for detailed design in agriculture, design of roads, highways, power lines, for preliminary development of planning and development of rural settlements, to determine mineral reserves.

Large-scale maps and plans are drawn up for more accurate detailed design (technical design, irrigation, drainage and landscaping, development master plans cities, design of engineering networks and communications, etc.).

The more demanding the survey tasks, the larger the required scale, but this is associated with high costs, so large-scale surveys must have an engineering justification.

Sheets of maps are published in a unified system of markings and nomenclature and represent a horizontal projection of a spheroid trapezoid - a certain area of the earth's surface.

The nomenclature of topographic maps is usually called the designation of its individual sheets (trapezoids). The nomenclature of trapezoids is based on a map sheet at a scale of 1:1000000, called the international map.

Scale types

The scale can be written in numbers or words, or depicted graphically.

Numerical.
Named.
Graphic.

Numerical scale

The numerical scale is signed with numbers at the bottom of the plan or map.

For example, the scale "1: 1000" means that all distances on the plan are reduced by 1000 times. 1 cm on the plan corresponds to 1000 cm on the ground, or, since 1000 cm = 10 m, 1 cm on the plan corresponds to 10 m on the ground.

Named Scale

The named scale of a plan or map is indicated by words.

For example, it may be written "in 1 cm - 10 m."

Linear scale

It is most convenient to use the scale depicted as a straight line segment divided into equal parts, usually centimeters (Fig. 15). Such a scale is called linear, it is also shown at the bottom of the map or plan.

Please note that when drawing a linear scale, zero is set, retreating 1 cm from the left end of the segment, and the first centimeter is divided into five parts (2 mm each).

Near each centimeter it is signed what distance it corresponds to on the plan.

One centimeter is divided into parts, next to which it is written what distance on the map they correspond to. A compass or ruler measures the length of any segment on the plan and, applying this segment to a linear scale, determines its length on the ground.

Application and use of scale

Knowing the scale, it is possible to determine the distances between geographical objects, to measure the objects themselves.

If the distance from the road to the river on a plan with a scale of 1: 1000 (“in 1 cm - 10 m”) is 3 cm, then on the ground it is 30 m.

Material from the site http://wikiwhat.ru

Suppose, from one object to another, 780 m. It is impossible to show this distance on paper in full size, so you have to draw it to scale. For example, if all distances are shown 10,000 times smaller than in reality, i.e.

e. 1 cm on paper will correspond to 10 thousand cm (or 100 m) on the ground. Then, on a scale, the distance in our example from one object to another will be 7 cm and 8 mm.

Pictures (photos, drawings)

On this page, material on the topics:

What does the scale show
Report geographical scale
Scale definition of coroicre
Scale 1:10 abstract
Causes of the Revolution in Europe 1848-184

Questions for this article:

What is scale?
What does scale show?
What can be measured with a scale?
How big is the lake, if in captivity with a scale of 1: 2000 (“in 1 cm - 20 m”) its length is 5 cm?
What does scale 1:5000, 1:50000 mean?
Which one is bigger? What scale is more convenient for a plan of a land plot, and which one is more convenient for a plan of a large city?

Material from the site http://WikiWhat.ru

Each card has scale- a number that shows how many centimeters on the ground correspond to one centimeter on the map.

map scale usually listed on it. Record 1: 100,000,000 means that if the distance between two points on the map is 1 cm, then the distance between the corresponding points on its terrain is 100,000,000 cm.

May be listed in numerical form as a fraction– numerical scale (for example, 1: 200,000). And it can be marked in linear form: as a simple line or strip divided into units of length (usually kilometers or miles).

The larger the scale of the map, the more detailed the elements of its content can be depicted on it, and vice versa, the smaller the scale, the more extensive space can be shown on the map sheet, but the terrain on it is depicted with less detail.

Scale is a fraction whose numerator is one. To determine which of the scales is larger and by how many times, let's recall the rule for comparing fractions with the same numerators: of two fractions with the same numerators, the one with the smaller denominator is larger.

The ratio of the distance on the map (in centimeters) to the corresponding distance on the ground (in centimeters) is equal to the scale of the map.

How does this knowledge help us in solving problems in mathematics?

Example 1

Let's look at two cards. A distance of 900 km between points A and B corresponds on one map to a distance of 3 cm. A distance of 1,500 km between points C and D corresponds to a distance of 5 cm on another map. Let us prove that the scales of the maps are the same.

Decision.

Find the scale of each map.

900 km = 90,000,000 cm;

the scale of the first map is: 3: 90,000,000 = 1: 30,000,000.

1500 km = 150,000,000 cm;

the scale of the second map is: 5: 150,000,000 = 1: 30,000,000.

Answer. The scales of the maps are the same, i.e. are equal to 1:30,000,000.

Example 2

The scale of the map is 1: 1,000,000. Let's find the distance between points A and B on the ground, if on the map
AB = 3.42 cm?

Decision.

Let's make an equation: the ratio of AB \u003d 3.42 cm on the map to the unknown distance x (in centimeters) is equal to the ratio between the same points A and B on the ground to the map scale:

3.42: x = 1: 1,000,000;

x 1 \u003d 3.42 1,000,000;

x \u003d 3,420,000 cm \u003d 34.2 km.

Answer: the distance between points A and B on the ground is 34.2 km.

Example 3

The scale of the map is 1: 1,000,000. The distance between points on the ground is 38.4 km. What is the distance between these points on the map?

Decision.

The ratio of the unknown distance x between points A and B on the map to the distance in centimeters between the same points A and B on the ground is equal to the scale of the map.

38.4 km = 3,840,000 cm;

x: 3,840,000 = 1: 1,000,000;

x \u003d 3,840,000 1: 1,000,000 \u003d 3.84.

Answer: the distance between points A and B on the map is 3.84 cm.

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Scales of topographic maps and plans

map scale- this is the ratio of the length of the segment on the map to its actual length on the ground.
Scale(from German - measure and Stab - stick) - the ratio of the length of a segment on a map, plan, aerial or space image to its actual length on the ground.
Numerical scale- scale, expressed as a fraction, where the numerator is one, and the denominator is a number showing how many times the image is reduced.
Named (verbal) scale- type of scale, a verbal indication of what distance on the ground corresponds to 1 cm on a map, plan, photograph.
Linear scale- an auxiliary measuring ruler applied to maps to facilitate the measurement of distances.

The named scale is expressed by named numbers denoting the lengths of mutually corresponding segments on the map and in nature.

For example, there are 5 kilometers in 1 centimeter (5 km in 1 cm).

The scale of the plan is the same at all its points.

Scale expression forms

The designation of the scale on maps and plans has three forms: numerical, named and linear scales. The numerical scale is expressed as a fraction, in which the numerator is one, and the denominator M is a number showing how many times the dimensions on the map or plan are reduced (1: M)

In Russia, topographic maps have standard numerical scales: 1:1,000,000; 1:500,000; 1: 300,000; 1: 200,000; 1: 100,000; 1:50,000; 1: 25,000; 1:10,000.

For special purposes, topographic maps are also created on a scale of 1: 5,000 and 1: 2,000. The main scales of topographic plans in Russia are: 1: 5000, 1: 2000, 1: 1000 and 1: 500.

However, in land management practice, land use plans are most often drawn up on a scale of 1: 10,000 and 1:25,000, and sometimes 1: 50,000.

When comparing different numerical scales, the smaller one is the one with the larger denominator M, and, conversely, the smaller the denominator M, the larger the scale of the plan or map.

Thus, scale 1:10,000 is larger than scale 1:100,000, and scale 1:50,000 is smaller than scale 1:10,000. Named Scale

Since the lengths of lines on the ground are usually measured in meters, and on maps and plans - in centimeters, it is convenient to express the scales in verbal form, for example:

Linear scale

Scale Accuracy

The limiting possibility of measuring and constructing segments on maps and plans is limited to 0.01 cm. The corresponding number of meters of terrain on the map or plan scale is the ultimate graphic accuracy of this scale. Since the accuracy of the scale expresses the length of the horizontal laying of the terrain line in meters, then to determine it, the denominator of the numerical scale should be divided by 10,000 (1 m contains 10,000 segments of 0.01 cm each). So, for a map with a scale of 1: 25,000, the scale accuracy is 2.5 m; for map 1: 100,000-10 m, etc.

Topographic map scales

Below are the numerical map scales and their corresponding named scales:

1. Scale 1: 100,000

1 mm on the map - 100 m (0.1 km) on the ground

1 cm on the map - 1000 m (1 km) on the ground

10 cm on the map - 10000 m (10 km) on the ground

2. Scale 1:10000

1 mm on the map - 10 m (0.01 km) on the ground

1 cm on the map - 100 m (0.1 km) on the ground

10 cm on the map - 1000m (1 km) on the ground

3. Scale 1:5000

1 mm on the map - 5 m (0.005 km) on the ground

1 cm on the map - 50 m (0.05 km) on the ground

10 cm on the map - 500 m (0.5 km) on the ground

4. Scale 1:2000

1 mm on the map - 2 m (0.002 km) on the ground

1 cm on the map - 20 m (0.02 km) on the ground

10 cm on the map - 200 m (0.2 km) on the ground

5. Scale 1:1000

1 mm on the map - 100 cm (1 m) on the ground

1 cm on the map - 1000cm (10 m) on the ground

10 cm on the map - 100 m on the ground

6. Scale 1:500

1 mm on the map - 50 cm (0.5 meters) on the ground

1 cm on the map - 5 m on the ground

10 cm on the map - 50 m on the ground

7. Scale 1:200

1 mm on the map -0.2 m (20 cm) on the ground

1 cm on the map - 2 m (200 cm) on the ground

10 cm on the map - 20 m (0.2 km) on the ground

8. Scale 1:100

1 mm on the map - 0.1 m (10 cm) on the ground

1 cm on the map - 1 m (100 cm) on the ground

10 cm on the map - 10m (0.01 km) on the ground

To convert a named scale into a numerical scale, you need to convert the number of kilometers to centimeters. For example, in 1 cm - 50 km 1: 5,000,000.

Nomenclature of topographic plans and maps

Nomenclature - a system of marking and notation of topographic plans and maps.

The division of a multi-sheet map into separate sheets according to a certain system is called the layout of the map, and the designation of a sheet of a multi-sheet map is called nomenclature.

In cartographic practice, the following map layout systems are used:
along the lines of the cartographic grid of meridians and parallels;
along the lines of a rectangular coordinate grid;
along auxiliary lines parallel to the middle meridian of the map and a line perpendicular to it, etc.

The most widespread in cartography is the layout of maps along the lines of meridians and parallels, since in this case the position of each sheet of the map on the earth's surface is precisely determined by the values of the geographical coordinates of the corners of the frame and the position of its lines. Such a system is universal, convenient for depicting any areas of the globe, except for the polar regions. It is used in Russia, USA, France, Germany and many other countries of the world.

The nomenclature of maps on the territory of the Russian Federation is based on the international layout of map sheets at a scale of 1:1 000000. To obtain one sheet of a map of this scale, the globe is divided by meridians and parallels into columns and rows (belts).

Column numbers

Parallels are drawn every 4 °. The account of belts from A to W goes from the equator to the north and south.
Row numbers

Map sheet 1:1,000,000 contains 4 map sheets 1:500,000, denoted by capital letters A, B, C, D; 36 map sheets 1:200,000, designated from I to XXXVI; 144 sheets of a 1:100,000 map, labeled 1 to 144.

A card sheet 1:100,000 contains 4 sheets of a card 1:50,000, which are indicated by capital letters A, B, C, D.

A map sheet 1:50,000 is divided into 4 map sheets 1:25,000, which are indicated by lowercase letters a, b, c, d.

Within the map sheet 1:1,000,000, the arrangement of numbers and letters when designating map sheets 1:500,000 and larger is made from left to right along the rows and towards the South Pole. The initial row is adjacent to the northern frame of the sheet.

1:1 000 000
1:500 000		T-45-A,B,46-A,B
1:200 000
1:100 000		T-47-133, 134,135,136
1:50 000		T-47-133-A,B, 134-A.B
1:25 000	R-47-9-A-a, b	T-47-12-A-a, b, B-a, b

How to find scale in geography. Scales of topographic maps and plans Topographic maps 1,100,000

Secrecy

Scales of topographic maps and plans

Scale expression forms

Named Scale

Linear scale

Scale Accuracy

Nomenclature of topographic plans and maps

How to find the scale

Scale types

How to find the map scale?

Other Uses for Scale

plan scale

How to find the scale of the map

instructions

Finding a distance on the map

Geography lesson in grade 6 on the topic “Scale. Scale types»

Scale types

Numerical scale

Named Scale

Linear scale

Application and use of scale

Pictures (photos, drawings)

What does the scale show

Report geographical scale

Scale definition of coroicre

Scale 1:10 abstract

Causes of the Revolution in Europe 1848-184

What is scale?

What does scale show?

What can be measured with a scale?

How big is the lake, if in captivity with a scale of 1: 2000 (“in 1 cm - 20 m”) its length is 5 cm?

What does scale 1:5000, 1:50000 mean? Which one is bigger? What scale is more convenient for a plan of a land plot, and which one is more convenient for a plan of a large city?

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What does scale 1:5000, 1:50000 mean?
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