Project introduction topographic maps and plans. Presentation on the topic: Topographic maps and plans

1. Topographic maps and plans

1.1. Topographic maps and plans. General information.

Topographic maps depict significant areas of the Earth.

The spherical surface of the Earth cannot be depicted on flat paper without distortion, therefore, in order to minimize distortion, map projections are used when compiling maps. In our country, topographic maps are compiled in the Gauss-Kruger conformal transverse cylindrical projection. In this projection, the surface of the Earth's ellipsoid is projected onto a plane in parts or in six-degree or three-degree zones.

To do this, the entire Earth's ellipsoid is divided by meridians into six-degree zones extending from the north to the south pole. There are sixty zones in total.

The zones are absolutely identical and therefore it is sufficient to calculate the projection onto the plane of only one zone. The zone is projected first onto the surface of the cylinder, and then the latter is deployed onto the plane. The middle (axial) meridian of the zone is depicted on the plane by a straight line. The intersection of the images of the axial meridian and the equator is taken as the origin of coordinates in each zone, forming a rectangular coordinate grid.

Line length distortions on topographic maps increase with distance from the axial meridian and their maximum values will be at the edge of the zone. The magnitude of line length distortion in the Gauss-Kruger projection is expressed by the formula

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When tracing railways near the edge of the line zone, corrections should be introduced, calculated by formula (1.1), while it should be borne in mind that the lengths of the lines on the map are somewhat exaggerated and their values on the ellipsoid will be less, that is, the correction should be entered with a minus sign.

The coordinate system in each zone is the same. To establish the zone to which the point with the given coordinates belongs, the zone number is signed to the ordinate value on the left. The zones are numbered from the Greenwich meridian to the east, that is, the first zone will be limited by meridians with latitudes 0 and 6. In order not to have negative ordinates, the axial meridian points are conditionally signed with an ordinate equal to 500 km. Since the width of the zone for our latitudes is approximately 600 km, then from the axial meridian to the east and west, all points will have a positive ordinate.

Thus, a map is a reduced, generalized and constructed according to certain mathematical laws image of significant parts of the Earth's surface on a plane. There are survey maps compiled on a small scale. To solve engineering problems, large-scale maps are used with scales of 1:100,000, 1:50,000, 1:25,000, 1:10,000. Note that maps of a scale of 1:25,000 have been compiled for the entire territory of the Russian Federation. scales are drawn up for separate areas of the terrain, for example, in the territory of large cities, on mineral deposits and on other objects.

A topographic plan is a reduced and similar image on a plane of horizontal projections of contours and landforms without taking into account the sphericity of the Earth. Objects and contours of the area are depicted by conventional icons, relief by contour lines. The ratio of the length of the line segment on the plan to its horizontal location on the ground is called the scale. plan areas Sometimes they make plans without depicting the terrain, such plans are called situational or contour.

The area for which plans can be made, that is, not taking into account the curvature of the Earth, is 22 km 500 km2.

Usually plans are made on a scale of 1:500, 1:1000, 1:2000, 1:5000.

1.2. Scales of topographic plans and maps

Purpose of the assignment: learn how to build and apply graphs of various scales to solve problems related to scales.

Since on the map (plan) all terrain lines decrease by a certain number of times, therefore, in order to measure distances on the map and set their actual length, it is necessary to know the degree of their reduction - scale.

Scale serves two main purposes:

1) segments are plotted on a given scale on plans or maps, if the horizontal location of these segments on the ground is known;

2) the lengths of lines on the ground are determined by the measured segments of the same lines on the plan (map).

Scales are divided into numerical and graphic. For convenience, the numerical scale is written as a fraction, in the numerator of which one is put, and in the denominator the number m, showing how many times the images of the lines are reduced, i.e. their horizontal spacing on the map:

Numerical scale- the value is relative, independent of the system of linear measures, therefore, if the numerical scale of the map is known, then measurements can be made on it in any linear measures. For example, if a segment of 1 cm is measured on a 1:500 scale plan, then a line of 500 cm or 5 m will correspond to it on the ground. It is customary to express the lengths of lines on the plan in centimeters, and on the ground - in meters.

The most common plan scales are 1:500, 1:1000, 1:2000, 1:5000. When using a numerical scale, you have to perform calculations every time, which makes it difficult to use the scale. To avoid calculations, graphic scales are used.

Graphic scales are a graphical expression of a numerical scale and are divided into linear and transverse.

Linear scale is a straight line with a division scale (Fig. 1.1). To build a linear scale on a straight line, lay several times a segment of a certain length, called scale base. If, for example, the base of the scale is 2 cm, and the numerical scale is taken as 1:2000, then the scale base on the ground will correspond to a segment of 40 m (Fig. 1.1). We put 40 m at the end of the second segment, 80 m at the end of the third, and 120 m at the end of the fourth. Obviously, one tenth of the base will correspond to 4 m on the ground.

Rice. 1.1. Linear scale chart

In order to determine by a linear scale what length of a line on the ground corresponds to a certain length of a line taken on a plan, a line from the plan is taken with a meter solution, one leg of the meter is installed at the end of one of the bases (to the right of zero) of the scale so that the other the leg of the compass must be located within the first base, which is divided into n=10 equal parts.

If the leg of the meter falls between the strokes of a small division, then part of this division is estimated by eye.

For example, in Fig. 1.1, the length of the segment marked by the meter is 108.4 m on a scale of 1:2000. When plotting segments on the plan according to the known values of the horizontal distances of the terrain line, the problem is solved in a similar way, but in the reverse order. In order not to take small fractions of divisions of the base of a linear scale by eye, but to determine them with greater accuracy, a transverse scale is used.

Cross scale is a system of horizontal parallel lines drawn through 2–3 mm and divided by vertical lines into equal segments, the value of which is equal to the base of the scale. Such a scale is engraved on rulers called scale rulers, as well as on the rulers of some geodetic instruments. Consider the construction of the so-called normal transverse scale, suitable for any numerical scale.

On a horizontal line, lay a few segments (scale bases), 2 cm each. From the end points of the postponed segments, we restore the perpendiculars to the straight line. On the two extreme perpendiculars, we set aside 10 equal parts (2 mm each) and connect the ends of these parts with straight lines parallel to the base of the scale (Fig. 1.2). The leftmost base (its upper segment SD and lower - 0V) is divided into 10 equal parts and we draw oblique lines (transversals) in the following order:

We connect point 0 (zero) on the 0V segment with point 1 on the SD segment;

We connect point 1 on the 0V segment with point 2 on the SD segment, etc., as shown in fig. 1.2, a.

Consider a triangle OS1, which is shown in an enlarged form in Fig. 1.2, b. Let us determine in it the values of segments parallel to each other (a1c1, a2c2, a3c3, etc.). From the similarity of triangles OS1 and a1oc1 we have

https://pandia.ru/text/77/489/images/image010_62.gif" width="257 height=48" height="48"> scale base 0B.

In a similar way, we find a2c2=0.02, a3c3=0.03, ..., a9c9=0.09 scale bases 0B, i.e. each segment differs from the neighboring one by 0.01 scale bases.

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Rice. 1.2. Cross-Scale Plot

This property of the transverse scale makes it possible to measure and set aside segments up to 0.01 of the scale base without eye evaluation.

Thus, the value of the smallest segment on the graph of the transverse (linear) scale is the price of the smallest division of the scale graph.

A transverse scale with a base of 2 cm, on which the segments 0B and OS are divided into 10 equal parts, is called a normal centesimal transverse scale. The normal transverse scale is convenient for measuring and plotting distances at any numerical scale. For example, with a numerical scale of 1:5000, the base of the normal scale (2 cm) corresponds to 100 m on the ground, a tenth of it is 10 m, and a hundredth is 1 m.

When measured on a map at a scale of 1:50,000, the base of the normal scale (2 cm) corresponds to 1000 m on the ground, a tenth of it - 100 m, and a hundredth - 10 m, etc. As can be seen from the above examples, on the graph of a normal transverse scale for a numerical scale of 1:5000, the smallest segments up to 1 m can be measured, and for a numerical scale of 1:50,000 - up to 10 m, i.e., the accuracy is 10 times lower. Therefore, the accuracy of the graph of the transverse (linear) scale is the price of the smallest division of the graph on the scale of the plan or map. In addition, the human eye cannot distinguish very small divisions without the use of optical devices, and the compass, no matter how thin the points of its needles, does not make it possible to accurately establish the solution of the legs. As a result, the accuracy of laying and measuring segments on a scale is limited by a limit, which in topography is taken equal to 0.1 mm and is called the limiting graphic accuracy.

The distance on the ground corresponding to 0.1 mm on a map of a particular scale is called the maximum accuracy of the scale of this map or plan. In reality, the error in measuring distances on the map is much larger (errors in the scale reading, errors in the map itself, paper deformation, and other reasons affect). In practice, we can assume that the error in measuring distances on the map is about 5–7 times more than the limit values.

Let's consider how to apply scales using the example of a scale of 1:2000, where the base of the graph of a normal transverse scale of 2 cm corresponds to 40 m on the ground, a tenth of it is 4 m, and a hundredth is 0.4 m.

To determine the distance, the right leg of the meter is aligned on the bottom line of the scale with the vertical line separating its bases. In this case, the left leg of the meter should be on the bottom line of the leftmost base. Now, at the same time, the legs of the meter are lifted up until the left one is on any transversal. In this case, both legs of the meter should lie on the same horizontal line. The desired distance is obtained by summing integer bases of the scale, tenths and hundredths of the scale, for example, the distance between points X and Y consists of segments: 2 × 40 m + 6 × 4 m + 7 × 0.4 m = 80 m + 24 m + 2.8 m = 106.8 m (see Fig. 1.2, a).

Control questions:

1. What is called scale?

2. What are the scales?

3. What is a numerical scale?

4. What are the graphic scales?

5. What is the base of the scale chart?

6. What is called the accuracy of the graph of the transverse scale?

7. What is called the scale accuracy of a map or plan?

8. How to determine the accuracy of the scale?

1.3. Conventional signs of plans and maps

Maps and plans must be accurate and expressive. The accuracy of the map and plan depends on their scale, the accuracy of the geodetic instruments used in the survey, the methods of work and the experience of the work foreman.

The expressiveness of a map and a plan depends on a clear and distinct representation of terrain objects on them. For such an image of terrain objects in geodesy, special cartographic conventions have been developed, characterized by simplicity and clarity, which is achieved by combining only elementary geometric shapes, which to some extent resemble the appearance of the object itself in reality. The simplicity of conventional signs makes them easy to remember, which, in turn, makes it easier to read plans and maps.

Cartographic symbols (GOST 21667-76) are usually divided into areal, off-scale and linear.

Area signs are conventional signs used to fill in the areas of objects expressed on the scale of a plan or map.

According to a plan or map, it is possible to determine with the help of such a sign not only the location of an object, an object, but also its dimensions.

If an object on a given scale cannot be expressed by an area sign due to its smallness, then an off-scale symbol is used. Objects marked with such conventional signs take up more space on the plan than they should in terms of scale. Off-scale symbols are of great use on maps.

For the representation on maps and plans of objects of a linear nature, the lengths of which are expressed on a scale, linear symbols are used.

Such conventional signs on plans and maps are applied in full accordance with the scale and position of the horizontal projection of the length of the object, but its width is shown somewhat exaggerated. Most of the signatures on a topographic plan or map are placed parallel to the lower and upper frames. The inscriptions of rivers, streams, as well as mountain ranges are made along their directions.

The visibility of topographic maps, together with accuracy, is their most important indicator. It is achieved by the use of appropriate conventional signs and inscriptions that complement their content and are a kind of conventional sign.

The inscriptions not only indicate the name, but also reflect the nature (quality) of the given object. Therefore, inscriptions on maps and plans are used to indicate their own names of geographical objects, designate the type of object, and as explanatory inscriptions.

The choice of one or another font and the size of the inscription depend on the nature of the object being inscribed and the scale of the map.

Control questions:

1. What is the meaning of establishing uniform conventional signs?

2. What types of conventional signs exist?

3. How can tables of conventional signs be used to read plans and maps?

1.4. Nomenclature of topographic maps

The nomenclature is a system of marking and notation of sheets of topographic maps and plans.

Rice. 1.3. Nomenclature of map sheets at a scale of 1:1,000,000

The nomenclature is based on the international layout of map sheets at a scale of 1:1,000,000 (Fig. 1.3). A 1:1,000,000 scale map is an image on a plane of a spherical trapezoid formed by meridians and parallels. It measures 6° longitude and 4° latitude. To obtain these spherical trapezoids, the entire earth's surface is divided into columns by meridians located 6 ° apart in longitude, and into rows by parallels located 4 ° apart in latitude. The row and column designation defines a spherical trapezoid and a map sheet at a scale of 1:1,000,000.

Rows are indicated by capital letters of the Latin alphabet A, B, C, D, ..., starting from the equator in directions to the north and south (Table 1).

Table 1

Row designation	Latitude row boundaries	Row designation	Latitude row boundaries	Row designation	Latitude row boundaries

The columns are numbered in Arabic numerals 1, 2, ..., 60, starting from the meridian 180 ° in the direction from west to east. Each sheet of the map at a scale of 1:1000000 is assigned a nomenclature number, consisting of the letter of the corresponding row and the column number, for example, M-42.

For example, a map sheet at a scale of 1:1,000,000, on which Moscow is located (Fig. 1.3), has the nomenclature N-37.

For maps at a scale of 1:500000, a sheet at a scale of 1:1,000,000 is divided by a meridian and a parallel into 4 sheets, designating them in capital letters A, B, C, D. The nomenclature numbers of the map sheets are formed by adding the corresponding letter to the nomenclature number of the sheet at a scale of 1:1000000 (for example, M-42-G).

For maps at a scale of 1:200000, a sheet at a scale of 1:1,000,000 is divided into 36 sheets, numbered with Roman numerals I, II, ..., XXXVI.

For maps of scale 1: by dividing a sheet of scale 1:1000000 in latitude and longitude into 12 parts, they get the boundaries of 144 sheets (Fig. 1.4, a), which are numbered with the numbers 1, 2, ..., 144. The nomenclature of each sheet is made up of the nomenclature sheet scale 1:1000000 and sheet number. Sheet M-37-87 is highlighted in the figure.

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Nomenclature

Number of sheets

Sheet dimensions

(last

map sheet)

For plans of scales 1:5000 and 1:2000, two types of layout are used - trapezoidal, in which the frames of the plans are parallels and meridians, and rectangular, in which the frames are combined with grid lines of rectangular coordinates.

With a trapezoidal layout, the boundaries of sheets of plans at a scale of 1:5000 are obtained by dividing a sheet at a scale of 1:100000 into 256 parts (16´16), which are numbered from 1 to 256. The nomenclature, for example sheet No. 70, is written as M-37-87 (70) .

The layout of sheets at a scale of 1:2000 is obtained by dividing a sheet at a scale of 1:5000 into 9 parts (3´3) and denoted by the letters of the Russian alphabet, for example, M-37-87 (70-s).

Rectangular layout is used for plans of settlements and for plots with an area of less than 20 km2, as well as for plans of scales 1:1000 and 1:500.

When shooting a separate section, the plan can also be drawn up on a sheet of a non-standard format.

An example of a nomenclature definition:

Task. Find the nomenclature of a map sheet at a scale of 1:50,000 and the geographical coordinates of the corners of the trapezoid frames, if it is known that the point K located on this map sheet has the coordinates:

latitude https://pandia.ru/text/77/489/images/image016_51.gif" width="88" height="25 src=">.

Solution. Using the international layout of maps at a scale of 1: 1,000,000 in latitude and longitude of point K, given in Fig. 1.4, a map sheet is found within which it is located, and its nomenclature is written out. For our case, K is located on a map sheet at a scale of 1:1,000,000 with the nomenclature N - 44. Knowing that within this map sheet there are 144 map sheets at a scale of 1:100,000 (Fig. 1.5) and taking into account the size of the frames, we search for geographic point coordinates To its location within the map sheet at a scale of 1:100,000.

We find that point K is located on sheet 85 of the map at a scale of 1:100,000.

The nomenclature of this sheet will be N - We need to find the location of point K within the sheet of the map at a scale of 1:50,000. To do this, it is necessary to draw a diagram of the sheet N - Fig. 1.6), showing on it the location and designation of the sheets of the map at a scale of 1:50,000.

Rice. 1.5. Map 1:1

Rice. 1.6. Map 1:

Using the geographical coordinates of the corners of the frame of the map sheet at a scale of 1:50000, we find the position of point K. Point K is located in the northeast corner of the map sheet at a scale of 1:50,000. The nomenclature of this sheet will be N-B.

Control questions:

1. What is the nomenclature of maps?

2. What map scales are accepted in Russia?

3. What are the boundaries of the map sheet?

GENERAL INFORMATION

REAL ESTATE

MAP AND PLANS USED IN CREATING CADASTRE DOCUMENTATION

In the Federal Law of the Russian Federation “On State Registration of Rights to Real Estate and Transactions with It” (Article 12, paragraph 6), the following are named as real estate objects: land plots, buildings, structures, premises, apartments, as well as other real estate objects, strongly associated with the land; other objects that are part of buildings and structures. Geodetic, cartographic and other data are necessary in order to reliably determine the location of the boundary of the property, its area, as well as the qualitative characteristics of soils, vegetation, soil bearing capacity, etc.

When creating documentation of the real estate cadastre, you can use various cartographic materials presented in the form of: topographic maps and plans; plans (maps) of the boundaries of the land plot; maps (plans) of the land plot; cadastral plans of land plots; duty cadastral maps; digital terrain models; electronic maps (plans).

topographic map called a reduced, generalized image of the surface of the Earth, the surface of another celestial body or extraterrestrial space, built in a cartographic projection, showing the objects located on them in a certain system of conventional signs.

Topographic plan - a cartographic image on a plane in an orthogonal projection on a large scale of a limited area of the terrain, within which the curvature of the level surface is not taken into account.

On topographic maps and plans, all objects and areas of the terrain are displayed, provided for specific scales by the current conventional signs, which are a kind of language of maps (plans).

For topographic maps and plans, a unified system of conventional symbols is used, which is based on the following basic provisions:

each conventional sign always corresponds to a certain object or phenomenon of the earth's surface;

the symbol must be unique;

on maps (plans) of different scales, symbols of similar objects, if possible, should differ only in size;

the number of conventional symbols on topographic maps and plans on a small scale should be less than on maps and plans on a large scale (by replacing individual designations with their collective designations).

It is important that the tables of conventional signs have the meaning of state and industry standards. Fragment of the topographic scale plan

1:2000 compiled on settlement lands (built-up area) is shown in figure 5.1.

Symbols are divided into three groups of scales 1:500-1:5000; 1:10000; 1:25000-1:100000 and they are divided into scale, depicting the size and shape of objects on the earth's surface on the scale of this map, and off-scale, used to depict objects on the map (plan) that are not expressed on the scale of the map (plan).

Off-scale conventional signs are also used to depict linear objects (roads, small rivers, etc.), the width of which is not expressed on a scale. In this case, the geometric axis of the conventional sign must correspond to the position of the geometric axis of the terrain object, presented in the corresponding cartographic projection. Inscriptions and explanatory captions, which, as a rule, are transmitted in the form of generally accepted abbreviations, supplement the images of objects and phenomena with more detailed information.

All topographic maps (plans) show: geodetic points, settlements and individual buildings, industrial, agricultural and socio-cultural facilities, railways and structures attached to them, highways and dirt roads, hydrography, hydraulic and water transport facilities, public utilities and communications, other objects, as well as relief and vegetation.

We emphasize that topographic plans (maps) do not depict the boundaries of land plots and other real estate objects. Therefore, they cannot be fully used in the preparation of the relevant documents of the real estate cadastre.

For ease of use, topographic maps of large areas are published as separate sheets of a limited format, combined into a common multi-sheet map by a single layout system. For topographic maps, a trapezoidal (degree) marking system is used. In it, the frames of individual sheets are lines of meridians and parallels.

The layout is based on the division of the common earth ellipsoid by meridians through 6 ° in longitude (starting from the Greenwich meridian) and 4 ° in latitude (starting from the equator).

Each cell of the layout has its own nomenclature - a system of designations for individual sheets. The initial cell (6° in longitude and 4° in latitude) denotes a sheet of the International Map at a scale of 1:1000000.

Map sheets at a scale of 1:1000000, enclosed between adjacent parallels, form belts, which are denoted by capital letters of the Latin alphabet A, B,..., V, Z. There are 22 complete belts and one incomplete belt in the northern hemisphere. Sheets of map scale 1;1 000000, enclosed between adjacent meridians, make up columns, which are numbered in the direction from west to east with Arabic numerals 1,2,...,60.

The nomenclature of a map sheet at a scale of 1:1000000 consists of a letter denoting the corresponding zone, and a number - the number of the column, for example, N-37 (Fig. 5.2).

When moving to sheets of larger scales, the scale map sheet

1:1000000 is divided by meridians and parallels into parts so that map sheets of different scales would be approximately the same size.

So, dividing each side of the frame of the map at a scale of 1:1000000, for example N-37, into 12 parts, 144 sheets of a map at a scale of 1:100000 are obtained, each of which has dimensions: 30 "longitude and 20" latitude. They are numbered sequentially, denoted by the numbers 1,2, ..., 144. Thus, the map sheet 1:100000 with number 144 has the nomenclature N-37-144.

The number of sheets of topographic maps of a larger scale in a sheet of a topographic map of a smaller scale, as well as the corresponding dimensions and nomenclature of the last sheet of a topographic map, are given in Table 5.1.

Table 5.1

The layout and nomenclature of sheets of topographic plans (maps) of large scales 1:5000, 1:2000, 1:1000 and 1:500, compiled in the Gaussian projection in the local system of flat rectangular coordinates, differs from those set out earlier.

For plans of such scales, a rectangular layout is used, which is obtained as follows. A grid of flat rectangular coordinates on plans of scales 1:500 - 1:5000 is drawn every 10 cm. The layout is based on a sheet of a plan of scale 1:5000 with the dimensions of its frame 40 by 40 cm (2 by 2 km. on the ground). Frame sizes sheets of plans of other scales are 50 by 50 cm. Within the same coordinate zone, the numbers of belts and columns for sheets of a scale of 1: 5000 are numbered as shown in Figure 5.3

Rice. 5.2. Geodetic fragments of the frames of the N-37 map at a scale of 1:1000,000 and the nomenclature of sheets adjacent to it

The nomenclature of the plan sheet at a scale of 1:5000 consists of the number of the cadastral district (subject of the Russian Federation); numbers of the coordinate zone of the local coordinate system in the cadastral district; belt numbers; column numbers.

For example, the nomenclature of a plan sheet at a scale of 1:5000 for a cadastral district with number 17, coordinate zone 1, belt and column numbers 201 and 198, respectively, is written in the following form: 17-1-201-198. Note that the even lines of the kilometer grid of the local coordinate system are the frames of the sheets of plans at a scale of 1:5000.

One sheet of the plan in scale 1:5000 corresponds to 4 sheets of plans in scale 1:2000. And one sheet of the plan in scale 1:2000 - 4 sheets of the plan in scale 1:1000.

The nomenclature of the plan sheet at a scale of 1:2000 is obtained by adding one of the first four capital letters A, B, C, D of the Russian alphabet to the nomenclature of the plan sheet at a scale of 1:5000 (Fig. 5.4). The nomenclature of the plan sheet at a scale of 1:1000 consists of the nomenclature of the plan sheet at a scale of 1:2000 with the addition of one of four Roman numerals: I, II, III or IV. For example, 17-I-201-198-F-IV. To obtain a sheet of a plan at a scale of 1:500, a sheet of a plan at a scale of 1:2000 is divided into 16 parts, which are denoted by Arabic numerals from 1 to 16. With this in mind, the nomenclature of the last sheet of the plan at a scale of 1:500 is written in the following form:

17-I-201-198-G-16.

The content of topographic plans 1:500 - 1:5000 is distinguished by great detail compared to topographic maps of smaller scales. They show in particular detail the buildings, structures, public utilities and communications expressed on a large scale. These objects are usually plotted on plans by coordinates. For plans on a scale of 1:2000 inclusive, objects such as sheds on poles, basement hatches, electric lights on power poles, telephone booths, etc. are depicted.

An essential feature of the content of plans in scales of 1:500-1:5000 is an almost identical graphic representation of natural objects by conventional signs; hydrography, relief, vegetation, etc. For example, when displaying forests, they show on the plan the type of forest, the average height of trees, their thickness at chest height, and also highlight the contours of clearings, glades located among the forest, etc. The smallest area of \u200b\u200bthe contours depicted on the plans for economically valuable areas, is 20mm 2, and for areas that do not have economic importance - 50mm 2.

It was previously noted that topographic maps are created by moving from the earth's ellipsoid to the plane of the corresponding map projection. This transition is inevitably accompanied by distortions in the lengths of lines, areas and angles, and these distortions depend on the corresponding mathematical transition algorithm. In some projections, it is possible to avoid distortions of land areas, in others - distortions of horizontal angles, but the lengths of terrain lines will be distorted in all cartographic projections, except for their locations at individual points or lines, for example, the axial meridian of the zone. Let's consider this issue in more detail.

When presenting the results of converting the surface of a common earth ellipsoid (ball) into a plane, for example, in the form of topographic and special maps, as a rule, a reduced mathematical (or graphical) model of the surface of the ellipsoid (ball) is obtained. The degree of reduction of the entire mapped surface shows the main scale, which is signed on the map. Due to the presence of inevitable distortions in the lengths of the lines under the corresponding transformations, the main scale, in the general case, is stored on the map only at individual points or on a certain line of the map.

If the length of a small segment on the surface of an ellipsoid (ball) is S, and the length of its image in the map projection is equal to sr, then the image scale

t = Sr/S the length of the line (segment) in the cartographic projection will be expressed the more accurately, the smaller the value S. In this case, the image scale, for example, in the Gauss-Kruger projection, within the same zone is different and depends on the distance of the line from the axial meridian.

The change in scale is due to distortions in the lengths of the lines. Calculations show that those that are on the edge of the six-degree zone at the latitude of the equator receive the greatest distortion. On the territory of Russia, the relative distortion of line lengths in the six-degree zone reaches 0.00083, which is of no practical importance for small-scale mapping. However, when creating large-scale maps, for example, at a scale of 1:5000, such distortions must be taken into account. For this reason, three-degree zones are used in large-scale mapping. Distortions in line lengths lead to distortion of the areas of displayed figures (land plots). Correction Δ P in the area R land for the transition from the surface of the ball to the plane in the Gauss-Kruger projection can be calculated using the following approximate formula:

where Ym- the transformed ordinate of the midpoint of the land plot, R= 6371 km.

Calculations show that at a distance of 100 km from the axial meridian of the zone and the area of the land plot equal to 1000 ha, the correction Δ P= 0.25 ha, and at a distance of 200 km, the same correction will be equal to 0.98 ha.

When displaying information about the spatial position of land plots, it is important to choose a map projection that ensures optimal decision making. The choice of a specific type of cartographic projection depends on many factors: the geographical location of the depicted territory, its size and shape (configuration), the degree of display of territories adjacent to the mapped area, etc.

When choosing a map projection, it is necessary to take into account the purpose and specialization, as well as the scale and content of the map; the composition and content of the tasks that will be solved with its use, etc. The nature of distortions and the possibility of taking them into account when solving practical land cadastral problems is of no small importance.

To depict the spatial position of land plots and other real estate objects located in small areas, orthogonal map projections are often used - an image of a spatial object of the terrain (part of the earth's surface) on a plane by means of projecting rays perpendicular to the projection plane. As a rule, they serve as plumb lines. In this case, the level surface within the mapped territory is taken as a plane, and the plumb lines are taken as perpendicular to it. As a result of the corresponding transformations, an orthogonal projection of the part of the earth's surface depicted on the plane is obtained. Note that the orthogonal projection of the length of the line (segment) of the terrain on the horizontal plane is called the horizontal span, and the corresponding cartographic product is called the topographic plan of the area.

The terrain plan is characterized by the main properties:

distances on the plan are proportional to the horizontal lines of the terrain;

horizontal angles with a vertex at any point of the plan are equal to the corresponding horizontal angles on the ground;

the scale of the plan is a constant value and equal to the ratio of the length of the segment on the plan to its horizontal location on the ground.

Let us establish the dimensions of the land plot, the surface of which can be considered flat, and not spherical.

Let us assume that the Earth is a sphere with a radius R, on the surface of which there are two points A and V(Fig. 5.5). Draw a tangent to the surface of the ball at the point A and simultaneously perpendicular to the direction of the radius of the ball at this point. Denote the arc that subtends the points A and V as AB and the projection of this arc onto a plane - through S AB Then the difference Δ S equal to Δ S = SAB-AB there will be nothing more than a distortion of the arc length when it is displayed on a plane.

For the case under consideration, the value Δ S determine by the following approximate formula:

For arcs of various lengths, absolute Δ S and relative Δ S/AB the difference values are as follows.

When calculating, take the radius of the ball R= 6371 km.

When solving the vast majority of land cadastral tasks based on the use of topographic and geodetic data, the value of the relative distortion of line lengths less than 1:1000000 can be neglected. Based on this, we can conclude that an orthogonal cartographic projection can be chosen as a cartographic projection when displaying an area of the earth's surface with a size of less than 10 km 2, and in conditions of a flat relief of less than 20 km 2. In other words, the necessary cartographic information for solving the relevant land cadastral tasks in this case can be obtained based on the use of a topographic plan.

The accuracy of a map (plan) characterizes the degree of correspondence between the spatial position of terrain points and their representation on the map (plan).

As a numerical characteristic of the accuracy of maps (plans), the root-mean-square error t, the position of the contour point, is used, which for clear contours is assumed to be approximately 0.04 cm on the plan.

For contour points that limit areas of agricultural and forest land, as well as some water bodies, the value t t somewhat more than for clearly identifiable points in the terrain. This is explained by the fact that the contours of agricultural lands and a number of other natural objects, in addition to the variability of their position in time, have some uncertainty in their recognition on the ground, and in the case of using aerial photogeodetic methods for mapping (plans), on a photographic image. So, the degree of uncertainty of recognition on the ground of points belonging to the border of arable land with vegetation is characterized by a mean square error equal to 0.1 ... 0.2 m, and the boundaries of a plowed field (without vegetation) - 0.3 ... 0.4 m An even greater degree of recognition uncertainty on the ground has points belonging to the border of the forest (0.5 ... 2m), shrubs (3 ... 10m), wetlands (10m or more). This degree of uncertainty in point recognition affects the accuracy of the image of the boundaries of the corresponding terrain objects on the plan (map).

The numerical characteristics of the root-mean-square errors in the position of contour points m, on the plan for various objects are as follows:

Name of object t t , cm. on the plan

Corners of capital buildings, fences, centers of wells 0.02.-0.03

and points of other constants clearly identifiable
objects on the ground

Intersection points of asphalt roads, quarters 0.04...0.05

rural settlements, ditches and other

similar permanent points of objects

Points of the border of arable land, intersections of dirt roads, 0.06 ... 0.1

forest clearings and other slightly identifiable

objects

Border points of forest, shrub, meadow vegetation, 0.11...0D5

edges of ravines, water edges of rivers, streams, as well as other

variable, indistinctly identifiable terrain features

Let us consider another important question from a practical point of view - the rationale for choosing the scale of a topographic plan for its use for specific practical purposes.

The justification for choosing the scale of a topographic plan is understood as an operation aimed at a preliminary quantitative justification of the information content of the plan, i.e., its content with various information about the objects of the area, without compromising their readability and use for practical purposes.

One of the possible criteria for choosing the scale of the plan is the criterion of information redundancy, which involves the presentation of information about the area in the form of an appropriate contour information model and writes it as a function of two arguments. First - characteristic rq the information content of a topographic map or plan (inf. units/ha), which is understood as the amount of information sufficient for the consumer to calculate a specific land cadastral task. The second is the characteristic of scale-forming information capacity R m of a topographic map or plan (inf. units/ha). Attitude

is called the informative density of the topographic plan (map).

Information redundancy criterion G has the following form

At Q> 1 believe that the plan (map), due to its insufficiency, does not allow solving cadastral and other tasks, since many of the necessary terrain objects are not expressed in the accepted scale of the plan.

The value of scaling information capacity R m for topographic plans and maps at scales of 1:500, 1:1000, 1:2000, 1:5000 and 1:10000, respectively, are 500, 330, 110, 30 and 10 inf. unit / ha.

Information content characteristic R 0 , inf.unit/ha, can be calculated using the formula:

where TO- the number of information units, depending on the minimum area of the land plot R(m 2), which is required to be displayed on a plan or map, based on the information needs of consumers, equal to 3.0; 2.7; 2.5; 2.3 and 1.8 inf.un. respectively for the areas of land 1,5,10,20 and 100m 2 ; n and P - the average number of plots and objects of the terrain, which is required to be displayed accordingly with large-scale and off-scale conventional signs for solving the land cadastral problem.

Another criterion for choosing the scale of a topographic map or plan is the criterion for the permissible error in determining the area of a land plot from a map (plan). This criterion is essential for substantiating the choice of the scales of maps (plans) created for the purpose of using them to provide the cadastre of real estate objects with spatial data on land plots.

If the permissible error of the area of the land plot is given t P 0 , expressed as a percentage, then the calculated denominator of the scale M P topographic plan can be calculated by the formula:

where R- land area, ha.

For example, when t P 0 = 1 % and land area P = 0.25 ha, calculated denominator M R the scale of the plan is 1250. Taking into account the data obtained, the standard scale 1: M of the topographic plan for calculating the area of the land plot can be taken equal to 1: 1000.

EDUCATIONAL AND METHODOLOGICAL CENTER

METHODOLOGICAL DEVELOPMENT

To conduct initial training of rescuers

(t o p o gr a f i i )

TOPIC No. 2 “Topographic maps, terrain maps and plans”

G.Chelyabinsk

LEARNING OBJECTIVES: To study with students the scales of topographic maps,

give the basic concepts of orienting the map and topo-

graphic symbols used on the map.

M E S T O: Class.

TIME: 2 hours.

M E T O D: Practical lesson.

LEARNING QUESTIONS AND TIME CALCULATION

Introductory part - 5 min

1st educational question: Drawing up a plan and schemes.- 45 min

2nd educational question: Orientation on the map. - 30 minutes

Conclusion: - 10 min.

L I T E R A T U R A:

1. Textbook "Military topography" for cadets of educational units.

2. An officer's guide to military topography.

H O D A N I T I A:

Check for listeners

Announce the topic, purpose, training questions.

INTRODUCTION:

The actions of rescuers take place on the ground or are closely related to it. The knowledge, teachings and skills acquired during the study of topography are of great practical importance in the activities of rescuers.

Knowledge of the methods of studying the terrain, skills in orientation and movement on it in various conditions, day, night, with limited visibility, contribute to the correct use of favorable terrain properties to achieve success, help to quickly and confidently navigate and maintain a given direction when moving and maneuvering. The ability to use a topographic map makes it possible to study and evaluate the area in advance, to prepare the necessary data for the march.

With the help of the map, it is easier to make the most appropriate decision, setting tasks for subordinates.

1st educational question: Classification of topographic maps, schemes of local

sti and plans. Conditional signs.

TOPOGRAPHIC MAP - the main graphic document about the area, containing an accurate, detailed and visual representation of local objects and relief. On topographic maps, local objects are depicted by generally accepted conventional signs, and the relief is represented by horizontal lines.

Topographic maps are intended for the work of rescuers in the preparation, organization and conduct of work. They study and evaluate the terrain, solve various calculation problems related to determining distances, angles and areas, heights, elevations and mutual visibility of terrain points, steepness and types of slopes, etc. A march is planned and prepared for them

azimuth data.

The completeness, detail and accuracy of the depiction of the terrain on the map depend primarily on its scale.

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 50 m) on the ground.

The scale is indicated under the bottom 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. 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, i.e. scale value.

When comparing several scales, the larger one will be the one with the smaller number on the right side of the ratio. Suppose that there are maps of 1:25,000, 1:50,000 and 1:100,000 scales for the same area of the terrain. Of these, the scale of 1:25,000 will be the largest, and the scale of 1:100,000 will be the smallest.

For topographic maps, a scale range is set.

TOPOGRAPHIC PLANS.

Topographic plans can be created for large settlements and other objects of importance. They are a kind of topographic maps and differ from them in that they are published in separate sheets, the dimensions of which are determined by the boundaries of the plotted area (settlement, object). Plans have some features in the design.

Most often, plans are drawn up on a scale of 1:10,000 - 1:25,000, which allow you to show in great detail the nature of the depicted object and give detailed information about the qualitative and quantitative characteristics of local objects and relief details located both on the object itself and on the nearest approaches to him. According to the depicted area (object) of the area, the name of the plan is signed, for example, the Plan of the Zavodskaya station, the Plan of the camps, etc.

For ease of use and greater clarity, prominent buildings are distinguished on the plans of cities with special conventional signs and colors, lines of urban transport (metro, tram) are shown. To facilitate the purpose of indicating on the plan, conditional numbering of quarters and some local objects is given, and a brief reference-legend, a list of prominent buildings and an alphabetical street index are placed in the margins or on the back of the plan. A sample part of the city plan is given in Appendix 4.

Terrain map - a drawing in which the most characteristic local objects, as well as individual elements of the relief, are applied with approximate accuracy.

Local objects are depicted on the diagram by topographic symbols, elevations and depressions (heights, basins) - by several closed contour lines, and ridges and hollows - by fragments of contour lines that outline the configuration of these landforms. At the same time, in order to speed up the work, the outlines of the conventional signs of some local objects are simplified.

Drawing up schemes of the terrain by methods of visual survey. To carry out visual survey, you must have a compass, a target line, a pencil, an elastic band and a blank sheet of paper, reinforced on a rigid base (a piece of cardboard, plywood, etc.) In some cases, when shooting needs to be done quickly and no special care is required , it can be done with only a pencil and paper.

Let us consider some methods of visual survey used in the preparation of terrain maps.

Shooting from one point of standing is used when it is required to show a small area of the terrain located directly around the standing point or in a given sector on the drawing. In this case, shooting is performed by the circular sighting method in this sequence.

A standing point is applied to a sheet of paper so that the area to be removed fits on this sheet. For example, if we are standing in the center of the area being filmed, then the standing point should be marked in the center of the sheet of paper, if

we stand in one of the corners or on the edge of the site, then the dot on the paper should be placed in the corresponding corner or on the edge of the sheet of paper. Then, having oriented a sheet of paper relative to the area to be filmed, they fix it on some object (stump, bridge railing, trench parapet) and, without knocking down the position of the sheet, they shoot.

If you have to work holding a sheet of paper in your hand, then first draw a north-south direction on it. To do this, orienting a sheet of paper relative to the area to be filmed, put a compass on it, lower the arrow brake and, when the arrow calms down, draws a line parallel to the compass needle.

In the future, make sure that the direction of the compass needle exactly coincides with the drawn north-south line. When you need to orient the drawing again, for example, after a break in work, a compass is applied to it so that the divisions are 0 degrees (O) and 180 degrees. (S) coincided with the drawn north-south direction, then rotate the drawing until the port until the north end of the compass needle is against the division of 0 degrees (C). In this position, the drawing will be oriented, and you can continue working on it.

In order to put this or that object on the drawing, after orienting the sheet, attach a ruler (pencil) to the standing point indicated on it and turn it around the point until the direction of the ruler coincides with the direction of the object. With this position of the ruler, a straight line is drawn along it from the standing point, this line will be the direction in which the object drawn on the diagram is located. So sequentially point the ruler at all other objects and draw directions for each of them.

Then the distances to the objects are determined and they are laid out in the corresponding directions from the standing point on the scale of the drawing or approximately, keeping the approximate ratio of these distances in the drawing and on

Localities. The points obtained in the directions will indicate the location of objects in the drawing. In places of points, conventional signs of the applied objects are drawn, relative to which the rest of the terrain details are visually applied, located directly near the standing point, as well as located between the applied landmarks or near them. On the map of the area, individual trees, bushes near the road, a section of an improved dirt road, ruins, pits, etc. are marked in this way.

Shooting from multiple standing points performed when it is required to show a relatively large area of the terrain.

In this case, local objects are applied to the drawing by serifs, by measuring the distance, along the alignment, by the method of circular sighting, by the method of perpendiculars.

When preparing for shooting, it is necessary to fix a sheet of paper on which the shooting will be carried out on a solid base (tablet). A compass is attached to the same base so that the north-south line on the compass scale is approximately parallel to one of the sides of the tablet or sheet of paper.

For the speed and convenience of postponing distances measured in steps, it is necessary to make a scale of steps. Such a scale is built on a separate strip of paper or on the margin of the sheet on which the survey is being made.

The scale of steps is built like this. Let's assume that the survey is carried out to scale

1:10,000, i.e. 1 cm in the drawing corresponds to 100 m on the ground. The value of one pair of steps of the surveyor is 1.5 m. Therefore, 100 pairs of steps are equal to 150 m on the ground or 1.5 cm in the drawing. A segment of 1.5 cm is laid on a straight line three, four or more times. The number 0 is signed against the second division on the left, and the numbers 100, 200, 300, etc., are signed against subsequent divisions. Against the leftmost (first) division sign: 100 pairs of steps. Thus, a step scale is obtained, each major division of which

Corresponds to 100 pairs of steps. In order for the distances to be plotted with great accuracy, the leftmost segment is divided into 10 small divisions of 1.5 mm, each of which will be equal to 10 pairs of steps.

With such a scale, there is no need to convert pairs of steps into meters each time, it is enough to set aside the number of pairs of steps passed by the scale to get the distance on the survey scale, which is applied to the drawing.

The shooting is carried out bypassing the site along the roads, the river bank, the edge of the forest, along the communication line, etc. The directions along which the survey is carried out are called running lines, and the points at which the directions of new running lines are determined and drawn are called stations.

IMAGE OF LOCAL ITEMS ON

TOPOGRAPHIC MAP

Types of conventional signs of topographic maps. Local objects on topographic maps are depicted by conventional signs.

For ease of reading and memorization, many conventional signs have styles that resemble the view of the local objects depicted by them from above or from the side. For example, conventional signs of factories, oil rigs, isolated trees, and bridges are similar in shape to the appearance of the listed local objects.

Conventional signs depicting the same terrain elements on topographic maps of different scales are the same in their outline and differ only in size.

The relief on topographic maps is depicted by contour lines, and some of its details (cliffs, ravines, gullies, etc.) are depicted by appropriate symbols.

Conventional signs are usually divided into three main groups: large-scale, off-scale and explanatory.

large-scale Conventional signs depict those local objects and relief details that can be expressed in size on a map scale (lakes, forests, quarters of settlements, large rivers, ravines, etc.).

The contours (external boundaries) of such objects (objects) are shown on the map as solid lines or dotted lines in exact accordance with their actual outlines. Solid lines show the contours of lakes, wide rivers, ravines, quarters of settlements, dotted lines show the contours of forests, meadows, swamps. The area inside the contour of such conventional symbols on the map is usually covered with paint of the corresponding color or filled with additional

Signs (Tables 1, 4, and 5 of Appendix 3).

Scale conventional signs allow you to determine the actual length, width and area of depicted or objects on the map. For example, if the width of a river on a map at a scale of 1:50,000 is 2 mm, then its actual width on the ground is 100 m.

off-scale conventional signs are used to depict such local objects and relief details that, due to the small size of the area they occupy, cannot be expressed on a map scale. Such local objects are mines, radio masts, wells, tower-type structures, burial mounds, etc.

The exact position on the map of an object depicted by an off-scale conventional symbol is determined by the geometric center of the figure, the middle of the symbol base, the top of the right angle at the symbol base, and the geometric center of the lower figure.

An intermediate position between large-scale and off-scale conventional signs is occupied by conventional signs of roads, streams, gullies, water pipes, power lines and other linear local objects, in which only the length is expressed on a scale. Such conventional signs are usually called linear. Their exact position on the map is determined by the longitudinal axis of the object.

Explanatory conventional signs are used in combination with large-scale and non-scale ones; they serve to additionally characterize local objects and their varieties. For example, the image of a coniferous or deciduous tree in combination with a symbol of a forest shows the dominant tree species (see figure) in it, an arrow on a river indicates the direction of its flow, transverse strokes on a symbol of a railway show the number of tracks.

The maps contain signatures of their own names of settlements, rivers, lakes, mountains, forests and other objects, as well as explanatory signatures in the form of letters and numbers. They provide additional information about the quantitative and qualitative characteristics of local objects and relief. Letter explanatory signatures are most often given in abbreviated form according to the established list of conditional abbreviations (Appendix 5).

The image of the relief on topographic maps should make it possible to determine from the map

The image of the point of general and particular position on the diagram

Exceptional standard definition image, powerful zoom and convenient features

Find the appropriate definition of parallel, sequential, parallel-sequential type of movement of objects of labor

Laboratory work 1 Topic: Topographic maps and plans. Scales. Conditional signs. Linear measurements on topographic maps and plans Purpose: To get acquainted with topographic maps and plans, scales, types of symbols. Master the measurement and construction of segments using graphic scales Work plan: 1. Topographic plan and topographic map 2. Symbols 3. Scales, scale accuracy 4. Linear measurements on topographic plans and maps 5. Construction of segments of a given length using a transverse scale 6. Measuring the length of broken and curved segments 7. Homework (Individual settlement and graphic work)

1. Topographic plan and topographic map A topographic plan is a reduced and similar image on paper in conventional signs of horizontal projections of the contours of objects and the relief of a small area without taking into account the sphericity of the Earth. According to the content, plans are of two types: contour (situational) - they depict only local objects; topographic - local objects and relief are depicted.

1. Topographic plan and topographic map According to the content of the map, there are the following types: general geographical - they show the earth's surface in all its diversity; special purpose maps (soil maps, peat deposits maps, vegetation maps, etc.), on which individual elements are depicted with special completeness - soils, peat deposits, vegetation, etc. Maps are conditionally divided into three types according to the scale: small-scale (smaller than 1:); medium-scale (1: - 1:); large-scale (scale from 1: to 1:10,000); Scales of plans - larger than 1: Topographic map - a reduced generalized image in conventional symbols on paper of horizontal projections of the contours of artificial and natural objects and the relief of a significant area of the Earth, taking into account its sphericity.

2. Conventional signs Conventional signs, which are used to designate various terrain items on plans and maps, are the same for the whole of Russia and, according to the nature of the image, are divided into 2 groups. Scale (areal) symbols serve to depict objects that occupy a significant area and are expressed on the scale of a map or plan. An areal symbol consists of a boundary symbol of an object and icons that fill it or a symbol of color. At the same time, terrain objects are depicted in compliance with the scale, which makes it possible to determine from a plan or map not only the location of the object, but also its size and shape. Off-scale are called such conventional signs, by which objects of the area are depicted without observing the scale of the map or plan, which indicates only the nature and position of the object in space in its center (wells, geodesic signs, springs, pillars, etc.). These signs do not allow us to judge the size of the depicted local objects. For example, on a large-scale map, the city of Tomsk is represented as an outline (to scale); on the map of Russia as a point (out of scale).

2. Conventional signs According to the way they are depicted on the map, conventional signs are divided into 3 subgroups: A. Graphic conventional signs - lines of various configurations (solid, dotted, dash-dotted ...), as well as their combinations in the form of geometric shapes. Graphic conventions are used to depict objects of a linear type: roads, rivers, pipelines, power lines, etc., the width of which is less than the accuracy of the scale of this map. B. Color conventions: shading with color along the contour of the object; lines and objects of different colors. C. Explanatory symbols - supplement other symbols with digital data, explanatory inscriptions; are placed next to various objects to characterize their property or quality, for example: the width of the bridge, the type of trees, the average height and thickness of trees in the forest, the width of the carriageway and the total width of the road, etc. On topographic maps, conventional signs are indicated in a strictly defined sequence: Explanations for conventional signs are always given on the right and only on training maps.

3. Scales, scale accuracy When drawing up maps and plans, horizontal projections of segments are depicted on paper in a reduced form, i. on a scale. Scale of the map (plan) - the ratio of the length of the line on the map (plan) to the length of the horizontal projection of the terrain line:. (1) Scales are numerical and graphic. Numerical 1) In the form of a simple fraction:, (2) where m is the degree of reduction or the denominator of the numerical scale. 2) In the form of a named ratio, for example: in 1 cm 20 m, in 1 cm 10 m Using scales, you can solve the following problems. 1. According to the length of the segment on the plan of a given scale, determine the length of the line on the ground. 2. According to the length of the horizontal projection of the line, determine the length of the corresponding segment on the scale plan.

3. Scales, scale accuracy In order to avoid calculations and speed up work, as well as improve the accuracy of measurements on maps and plans, graphic scales are used: linear (Fig. 1.2) and transverse (Fig. 1.2). Linear scale - a graphic representation of a numerical scale in the form of a straight line. To build a linear scale on a straight line lay a series of segments of the same length. The original segment is called the base of the scale (O.M.). The base of the scale is the conditionally accepted length of the segments plotted on a linear scale from zero on the right side of the linear scale and one division on the left side, which in turn is divided into ten equal parts. (M = 1:10000). The linear scale allows you to evaluate the segment with an accuracy of 0.1 fractions of a base accurately and up to 0.01 fractions of a base per eye (for a given scale) m 200 base

3. Scales, scale accuracy For more accurate measurements, a transverse scale is used, which has an additional vertical construction on a linear scale. Transverse scale After setting aside the required number of scale bases (usually 2 cm long, and then the scale is called normal), restore the perpendiculars to the original line and divide them into equal segments (into m parts). If the base is divided into n equal parts and the division points of the upper and lower bases are connected by inclined lines as shown in the figure, then the segment. The transverse scale allows you to estimate the segment exactly at 0.01 shares of the base, and up to 0.001 shares of the base - by eye. base A e g 3 p 1 2 f d 0 B m n n c

3. Scales, scale accuracy The transverse scale is engraved on metal rulers, which are called scales. Before using the scale bar, you should evaluate the base and its shares according to the following scheme. Example: Let the numerical scale be 1:5000, the named ratio will be: in 1 cm 50 m. If the transverse scale is normal (base 2 cm), then: one whole scale base (r.m.) - 100 m; 0.1 scale base - 10 m; 0.01 scale base - 1 m; 0.001 scale base - 0.1 m.

3. Scales, scale accuracy Scale accuracy makes it possible to determine which objects of the area can be depicted on the plan and which are not due to their small size. The reverse question is also being solved: on what scale should the plan be drawn up so that objects having, for example, dimensions of 5 m, are depicted on the plan. In order to make a certain decision in a particular case, the concept of scale accuracy is introduced. In this case, they proceed from the physiological capabilities of the human eye. It is accepted that it is impossible to measure the distance using a compass and a scale ruler, more accurately than 0.1 mm, on this scale (this is the diameter of a circle from a sharply honed needle). Therefore, the maximum accuracy of the scale is understood as the length of the segment on the ground, corresponding to 0.1 mm on the plan of this scale. In practice, it is accepted that the length of a segment on a plan or map can be estimated with an accuracy of ± 0.2 mm. The horizontal distance on the ground, corresponding to a given scale of 0.2 mm on the plan, is called the graphic accuracy of the scale. Therefore, at this scale (1:2000), the smallest differences that can be identified graphically are 0.4 m. The accuracy of the transverse scale is the same as the accuracy of the graphical scale.

4. Linear measurements on topographic maps and plans Segments, the length of which is determined from a map or plan, can be rectilinear and curvilinear. It is possible to determine the linear dimensions of an object on a map or plan using: 1. a ruler and a numerical scale; By measuring the segment with a ruler, we get, for example, 98 mm, or on a scale of -980 m. When evaluating the accuracy of linear measurements, it should be taken into account that a segment with a length of at least 0.5 mm can be measured with a ruler - this is the magnitude of the error in linear measurements using a ruler 2. measuring compass and linear scale; 3. compass-measuring and transverse scale.

4. Linear measurements on topographic maps and plans of a measuring compass and a linear scale; The measurement of segments using a linear scale is carried out in the following order: take the segment to be measured into the solution of the measuring compass; attach the compass solution to the base of a linear scale, while combining its right leg with one of the strokes of the base so that the left leg fits on the base to the left of zero (on a fractional basis); count the number of integers and tenths of the scale base:

4. Linear measurements on topographic maps and plans of the measuring compass and transverse scale digitize the transverse scale (normal) on the map scale (in this case 1:10000): .0 7 o. m. 0.001 o.m. 0.8 o.m o.m.

5. Construction of segments of a given length using a transverse scale Let it be required to plot a segment on a map at a scale of 1:5000, the length of which is 173.3 m. 1. Make a painting in accordance with the scale of the map (1:5000): tenths, hundredths and thousandths of a scale base. 3. Dial on the measuring compass using a transverse scale the calculated number of whole, tenths, hundredths and thousandths of the scale bases. 4. Draw a segment on paper - pierce a sheet of paper and circle the resulting two points with circles. The diameter of the circles is 2-3 mm. Section length Fig. 6. Making a segment of a given length on paper

6. Measurement of the length of broken and curved segments Measurement of broken segments is carried out in parts or by the method of extension (Fig. 7): set the legs of the meter at points a and b, lay the ruler in the direction b-c, move the meter leg from point a to point a1, add a segment b-c, etc. a а1а1 а3а3 c e d b а2а2 7. Measurement of the length of broken segments by the method of extension Measurement of curved segments is possible in several ways:. 1.using curvimeter (approximate); 2. by extension; 3.constant solution meter.

7. Problem solving 1. The length of the line on the map (2.14 cm) and on the ground (4280.0 m) is known. Determine the numerical scale of the map. (2.48 cm; 620 m) 2. Write a named scale corresponding to the numerical scale 1:500, 1: (1:2000, 1:10000) 3. On the plan M 1:5000, display an object whose length on the ground is 30 m. Determine the length of the object on the plan in mm. 4. Determine the limiting and graphical accuracy of the scale 1:1000; 1: Using a measuring compass and a normal transverse scale, set aside a segment of 74.4 m on a sheet of paper on a scale of 1:2000. (1415 m on a scale of 1:25000) 6. Using a transverse scale, determine the distance between the absolute marks of the points - 129.2 and 122.1 (square of the training map). (141.4 and 146.4 (square 67-12). 7. Measure the length of the stream (to the Golubaya River) (square 64-11) using a curvimeter and a compass-measuring device with a solution of 1 mm. Compare the results. 8. Horizontal the distance between two points on the plan M 1:1000 is 2 cm. Determine the distance between these points on the ground.

References 1.Methodological guidelines for the implementation of laboratory work on the discipline "Geodesy and topography" for full-time students of the direction "Geophysical methods of prospecting and exploration of mineral deposits" and "Geophysical methods of well research". - Tomsk: ed. TPU, 2006 - 82 p. 2. Fundamentals of geodesy and topography: textbook / V.M. Perederin, N.V. Chukharev, N.A. Antropova. - Tomsk: Publishing House of the Tomsk Polytechnic University, p. 3. Symbols for topographic plans at scales 1:5000, 1:2000, 1:1000, 1:500 / Main Directorate of Geodesy and Cartography under the Council of Ministers of the USSR. – M.: Nedra, p.

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1 Ministry of Education and Science of the Russian Federation Altai State Technical University I.I. Polzunova I.V. Karelina, L.I. Khleborodova Topographic maps and plans. Solving problems on topographic maps and plans Guidelines for conducting laboratory work, practical exercises and for IWS students studying in the areas of "Construction" and "Architecture" Barnaul, 2013

2 UDC Karelina I.V., Khleborodova L.I. Topographic maps and plans. Solving problems on topographic maps and plans. Guidelines for conducting laboratory work, practical classes and for IWS students studying in the areas of "Construction" and "Architecture" / Alt. state tech. un-t im. I.I. Polzunov. - Barnaul: AltGTU, p. The guidelines consider solutions to a number of engineering tasks performed using maps: determining geographic and rectangular coordinates, orientation angles, building a profile along a given line, and determining slopes. The procedure for performing laboratory work (practical tasks) 1, 2 and tasks for the IWS are described in detail. Samples of their design are given. Methodical instructions were considered at a meeting of the department "Foundations, foundations, engineering geology and geodesy" of the Altai State Technical University named after. I.I. Polzunov. Protocol 2 dated

3 Introduction Maps and plans serve as a topographical basis necessary for a civil engineer in solving problems related to industrial and civil housing construction, the construction of agro-industrial, hydraulic, thermal power, road and other types of construction. According to topographic maps and plans, they solve a number of engineering problems: determining distances, marks, rectangular and geographical coordinates of points, reference angles, building a line profile in a given direction, etc. Having studied the conventional signs, you can determine the nature of the terrain, the characteristics of the forest, the number of settlements, etc. .d. The purpose of the guidelines is to teach students to solve problems on topographic maps and plans, which are necessary in engineering practice for builders. 1. Topographic plans and maps When depicting a small area of the earth's surface with a radius of up to 10 km, it is projected onto a horizontal plane. The resulting horizontal spacings are reduced and applied to paper, i.e. a topographic plan is obtained, a reduced and similar image of a small area of the terrain, built without taking into account the curvature of the Earth. Topographic plans are created on a large scale of 1:500, 1:1,000, 1:2,000, 1:5,000 and are used to draw up general plans, technical designs and drawings to support construction. Plans are limited to a square cm or cm, oriented to the north. When depicting large areas on a plane, they are projected onto a spherical surface, which is then deployed into a plane using imaging methods called map projections. Thus, a topographic map is obtained - a reduced, generalized and constructed according to certain mathematical laws image on the plane of a significant section of the earth's surface, taking into account the curvature of the earth. The boundaries of the map are the true meridians and parallels. A grid of geographic coordinates of the line of meridians and parallels, called a cartographic grid, and a grid of rectangular coordinates, called a coordinate grid, are applied to the map. Cards are conditionally divided into: 3

4 - large-scale - 1:10,000, 1:25,000, 1:50,000, 1:, - medium-scale - 1:, 1:, 1:, - small-scale - smaller 1: According to the content, maps are divided into geographical, topographic and special . 2. Scales Scale is the ratio of the length of a line on a plan or map to the horizontal location of the corresponding line on the ground. In other words, the scale is the degree of reduction of the horizontal distances of the corresponding segments on the ground when they are depicted on plans and maps. Scales can be expressed in both numerical and linear forms. The numerical scale is expressed as a fraction, the numerator of which is one, and the denominator is a number showing how many times the horizontal lines on the ground are reduced when they are transferred to a plan or map. In general terms, 1:M, where M is the denominator of the scale d M d where d m is the horizontal location of the line on the ground; d k (p) - the length of this line on the map or plan. For example, scales of 1:100 and 1:1000 indicate that the image on the plans is reduced in comparison with the natural one, respectively, by 100 and 1000 times. If on a scale plan of 1:5,000 the line ab = 5.3 cm (d p), then on the ground the corresponding segment AB (d m) will be equal to 4 m k (p), d m = M d p, AB = .3 cm \u003d cm \u003d 265 m. Numerical scales can be expressed in a named form. So scale 1: in the named form will be written: 1 cm of the plan corresponds to 100 m on the ground or 1 cm to 100 m. More simple, not requiring calculations, are graphic scales: linear and transverse (Figure 1).

5 Figure 1 Scales: a linear, b - transverse A linear scale is a graphic representation of a numerical scale. The linear scale is a scale in the form of a straight line segment, divided into equal parts - the base of the scale. As a rule, the base of the scale is taken equal to 1 cm. The ends of the bases are signed with numbers corresponding to distances on the ground. Figure 1-a shows a linear scale with a base of 1 cm for a numerical scale of 1: The left base is divided into 10 equal parts, called small divisions. A small division is equal to 0.1 parts of the base, i.e. 0.1 cm. The base of the scale will correspond to 10 m on the ground, a small 1 m. The distance taken from the map by the compass-measuring solution is transferred to a linear scale so that one needle of the measuring compass coincides with any whole stroke to the right of the zero stroke, and on the other, the number of small divisions of the left base is counted. In Figure 1-a, the distances measured on a 1:1,000 scale plan are 22 m and 15 m. It is built in the following way. On a straight line, the scale base is laid several times, usually equal to 2 cm. The leftmost base is divided into 10 equal parts, i.e. 5

6, the small division will be equal to 0.2 cm. The ends of the bases are signed, in the same way as when building a linear scale. From the ends of the bases, perpendiculars with a length of mm are restored. The extreme ones are divided into 10 parts and parallel lines are drawn through these points. The upper leftmost base is also divided into 10 parts. The division points of the upper and lower bases are connected by inclined lines as shown in Figure 1-b. The transverse scale is usually engraved on special metal rulers called scale bars. In figure 1-b, the transverse scale with a base of 2 cm has inscriptions corresponding to a numerical scale of 1:500. The segment ab is called the smallest division. Consider the triangle OAB and Oab (Figure 1-b). From the similarity of these triangles, we determine ab AB Ob ab, OB where AB = 0.2 cm; IN = 1 part; bo = 0.1 part. We substitute the values into the formula and get 0.2 cm 0.1 ab 0.02 cm, 1 i.e. the smallest division ab is 100 times smaller than the base of the CV (Figure 1-b). This scale is called normal or centesimal. The main elements of the transverse scale: - base = 2 cm or 1 cm, - small division = 0.2 cm or 0.1 cm, - smallest division = 0.02 cm or 0.01 cm. To determine the length of a segment on a plan or map remove this segment with a measuring compass and set it on a transverse scale so that the right needle is on one of the perpendiculars, and the left one is on one of the inclined lines. In this case, both needles of the measuring compass should be on the same horizontal line (Figure 1-b). Moving the meter up one division will correspond to a change in the length of the line by 0.02 cm on the scale of the plan or map. For a scale of 1:500 (Figure 1-b), this change is 0.1 m. For example, the distance taken into the solution of a measuring compass will correspond to 12.35 m. 6

7 The same line on a scale of 1:1,000 will correspond to 24.70 m, because on a scale of 1:1,000 (1 cm of the plan corresponds to 1000 cm or 10 m on the ground) the base of 2 cm corresponds to 20 m on the ground, the small division of 0.2 cm corresponds to 2 m on the ground, the smallest division of 0.02 cm corresponds to 0.2 m on the ground. In Figure 1-b, the line in the solution of the measuring compass consists of 1 base, 2 small divisions and 3.5 smallest divisions, i.e. m m + 3.5 0.2 m = .7 = 24.7 m. For the criterion the accuracy with which it is possible to determine the length of lines using a transverse scale, a value equal to 0.01 cm is taken - the smallest distance that the "naked" eye can distinguish. The distance on the ground corresponding to a given scale of 0.01 cm on a plan or map is called the graphic scale accuracy t or simply the scale accuracy t cm \u003d 0.01 cm M, where M is the denominator of the scale. So, for a scale of 1:1,000, the accuracy is t cm \u003d 0.01 cm 1000 \u003d 10 cm, for a scale of 1:500 5 cm, 1: cm, etc. This means that segments smaller than the specified ones will no longer be displayed on a plan or map of a given scale. The limiting accuracy t pr is equal to the triple accuracy of the scale t pr \u003d 3 t. With the help of the scale, two problems are solved: 1) the corresponding segments on the ground are determined from the measured segments on the plan or map; 2) according to the measured distances on the ground, find the corresponding segments on the plan or map. Let's consider the solution of the second problem. The length of the line CD d CD = 250.8 m was measured on the ground. Determine 7

8 the corresponding segment on the plan at a scale of 1:2,000, using a transverse scale. Solution: On this scale, the base corresponds to 40 m, the small division is 4 m, the smallest division is 0.4 m. In the length of the line CD, there are 6 whole bases, 2 integer small divisions, and 7 smallest divisions. 7 0.4 m = 240 m + 8 m + 2.8 m = 250.8 m. 3. Layout and nomenclature of maps The division of topographic maps into sheets is called layout. For ease of use of maps, each sheet of the map receives a specific designation. The designation system for individual sheets of topographic maps and plans is called the nomenclature. The layout and nomenclature of maps and plans are based on a map of scale 1: To obtain a sheet of such a map, the globe is divided by meridians through 6 in longitude into columns and parallels through 4 in latitude into rows (Figure 2-a). The dimensions of map sheet 1: are assumed to be the same for all countries. The columns are numbered in Arabic numerals from 1 to 60 from west to east, starting from the meridian with longitude 180. The rows are indicated by capital letters of the Latin alphabet from A to V, starting from the equator to the north and south poles (Figure 2-b). for the northern hemisphere of the Earth

9 on the plane Figure 2-b - Scheme of layout and nomenclature of sheets of maps of scale 1:

10 The nomenclature of such a sheet will consist of a letter denoting the row and column numbers. For example, the sheet nomenclature for Moscow is N-37, for Barnaul with geographic coordinates = 52 30 "N, = 83 45" E. - N-44. Each sheet of a map of scale 1: corresponds to 4 sheets of a map of scale 1:, denoted by capital letters of the Russian alphabet, which are attributed to the nomenclature of the millionth sheet (Figure 3). Nomenclature of the last sheet N-44-G. 56 N A C B D N-44-D Figure 3 Layout and nomenclature of map sheets at scale 1: Barnaul N Figure 4 Layout and nomenclature of map sheets at scale 1:

11 N А В a c d B D b Figure 5 Layout and nomenclature of map sheets in scale 1:50 000, 1: 25 00, 1: One map sheet 1: corresponds to 144 map sheets in scale 1:, which are indicated by Arabic numerals from 1 to 144 and follow the nomenclature for the millionth sheet (Figure 4). The nomenclature of the last sheet N One sheet of a map of scale 1: corresponds to 4 sheets of a map of a scale of 1:50,000, which are indicated by capital letters of the Russian alphabet A, B, C, D. The nomenclature of the last sheet N D (Figure 5). One sheet of a map of scale 1: corresponds to 4 sheets of a map of scale 1:25,000, which are indicated by lowercase letters of the Russian alphabet a, b, c, d (Figure 5). For example: N Г-б. One map sheet at scale 1: corresponds to 4 map sheets at a scale of 1:10,000, which are designated by Arabic numerals 1, 2, 3, 4 (Figure 5). For example: N Mr. Nomenclature of plans Sheet 1 of the map: corresponds to 256 sheets of the plan at a scale of 1:5,000, which are indicated by Arabic numerals from 1 to 256. These numbers are assigned in brackets to the nomenclature of sheet 1: For example, N (256). One sheet of a 1:5,000 scale plan corresponds to 9 sheets of a 1:2,000 scale plan, which are indicated by lowercase letters of the Russian alphabet a, b, c, d, e, f, g, h, i. For example: N (256th). When creating topographic plans for plots with an area of up to 20 km 2, a rectangular layout (conditional) can be applied. In this case, it is recommended to take a tablet as the basis for the layout - a sheet of the mass plan - 11

12 headquarters 1:5,000 with frame sizes cm or m and designate it with Arabic numerals, for example 4. One sheet of a 1:5,000 scale plan corresponds to 4 sheets of a 1:2,000 scale plan, which are indicated by capital letters of the Russian alphabet. The nomenclature of the last sheet of the scale plan 1: D (Figure 6). One sheet of the plan in scale 1:2,000 corresponds to 4 sheets in scale 1:1,000, which are indicated by Roman numerals I, II, III, IV. For example: 4-B-II. To determine the nomenclature of a sheet of a 1:500 scale plan, divide the sheet of a 1:2,000 scale plan into 16 sheets and designate them with Arabic numerals from 1 to 16. For example: 4-B Figure 6 :1 000 and 1:500 The order of numbering of tablets of scale 1:5 000 is established by the organizations issuing permission for the production of topographic and geodetic works. 5. Relief The set of irregularities in the physical surface of the Earth is called relief. To depict the relief on plans and maps, hatching, dotted lines, color gamut (coloring), hillshading are used, but the contour lines method is most often used (Figure 7). The essence of this method is as follows. The surface of a section of the Earth at regular intervals h is mentally cut by horizontal planes A, B, C, D, etc. The intersections of these planes with the Earth's surface form curved lines, which are called horizontals. In other words, a contour line is a closed curved line connecting

13 naming points of the earth's surface with the same heights. The resulting contours are projected onto the horizontal plane P, and then plotted on a plan or map on an appropriate scale. The distance between the secant planes h is called the height of the relief section. The lower the height of the relief section, the more detailed the relief will be. The height of the section, depending on the scale and relief, is assumed to be 0.25 m; 0.5 m; 1.0 m; 2.5 m; 5 m, etc. If at a given height of the section, changes in the relief are not captured by contour lines, then additional horizontal lines with half the height of the section, called semi-horizontal lines, are used, which are drawn by dotted lines. For the convenience of reading a map or plan, every fifth horizontal line is thickened (Figure 8-a). The distance between adjacent horizontals in plan ab = d (Figure 7) is called the laying of the contours. The more the laying, the less the steepness of the slope and vice versa. To some horizontal lines in the direction of the slope, dashes are placed, called berghstrich. If the bergstroke is located on the inside of a closed horizontal, then this indicates a decrease in relief, and on the outside - an increase in relief. In addition, the signatures of the contour lines indicating their marks are made so that the top of the numbers is directed towards the elevation of the relief (Figure 8-a). The relief of the Earth's surface is very diverse (Figure 8-a). Its main forms are distinguished: plain, mountain, hollow, ridge, hollow and saddle (Figure 8-b). Each landform has its own characteristics and corresponding names. a) b) Figure 8 The main landforms of the earth's surface 13

14 The mountain has its top, slopes and sole. The top of the mountain is the highest part of it. A peak is called a plateau if it is flat, and a peak or hill if it is pointed. The side surface of a mountain is called a slope or slope. The slopes of the mountains are gentle, sloping and steep, respectively, up to 5, 20 and 45. A very steep slope is called a cliff. The foot or sole of the mountain is the line separating the slopes and the plain. A hollow is a bowl-shaped concave part of the earth's surface. The basin has a bottom, its lowest part, slopes directed from the bottom in all directions, and a crevice - the line of transition of the slopes into the plain. A small hollow is called a depression. The ridge is a hill, elongated in one direction. The main elements of the ridge are the watershed line, slopes and soles. The watershed line runs along the ridge, connecting its highest points. A hollow, in contrast to a ridge, is a depression that extends in one direction. It has a spillway, slopes and a curb. The varieties of the hollow are the valley, the gorge, the ravine and the beam. Saddle - the bend of the ridge between two peaks. Some details of the relief (mounds, pits, quarries, talus, etc.) cannot be depicted by contour lines. Such objects are shown on maps and plans with special symbols. In addition to contour lines and conventional signs, the heights of characteristic points are signed on the map (Figure 8-a): on the tops of hills, on the bends of watersheds, on saddles. 6. Conventional signs The content of maps and plans is represented by graphic symbols - conventional signs. These symbols outwardly resemble the shape of the corresponding elements of the situation. The visibility of conventional signs reveals the semantic content of the depicted objects, allows you to read a map or plan. Conventional signs are divided into areal (scale), off-scale, linear and explanatory (Figure 9). Scale or outline conventional signs are such conventional signs with the help of which the elements of the situation, i.e. objects of the area are depicted on the scale of the plan in compliance with their actual dimensions. For example: the contour of meadows, forests, orchards, orchards, etc. The boundary of the contour is shown by a dotted line, and inside the contour - a conventional sign. Conventional off-scale signs are used to depict objects of the area that are not expressed on the scale of a map or plan. For example: a monument, a spring, a separate tree, etc. 14

15 Large-scale Fruit and berry orchard Linear Communication line Wasteland Meadow Power transmission line Main gas pipeline Shrub Clear-cutting Birch forest Kitchen garden U n-scale Kilometer pole Windmill Stand-alone broad-leaved tree Figure 9 Symbols Linear conventional symbols are used to depict objects of a linear type, the length of which is expressed on the scale of a plan or map. For example: road network, trails, power lines and communications, streams, etc. Explanatory symbols supplement the above symbols with digital data, icons, inscriptions. They allow you to more fully read the map. For example: depth, river speed, bridge width, forest type, road width, etc. Symbols of topographic maps and plans of various scales are published in the form of special tables. 7. Design of a sheet of a topographic map Consider a schematic representation of a sheet of a topographic map on a scale of 1: (Figure 10). The sides of the sheet of the map are segments of meridians and parallels and form the inner frame of this sheet, which has the shape of a trapezoid. In each corner of the frame, its latitude and longitude are indicated: the latitude and longitude of the southwest corner are, respectively, 54 15 "and 38 18" 45", northwest "30 and 38 18" 45", southeast" and 38 22 "30, Northeast" 30 and 38 22 "30. 15

16 Figure 10 - Schematic representation of a sheet of a topographic map Next to the inside is a minute frame of the map, the divisions of which correspond to 1 latitude and longitude. They are shown as fills at minute intervals. Each minute division is divided by dots into 6 parts, i.e. at 10 second intervals. Between the inner and minute frames, the ordinates of the vertical and abscissas of the horizontal lines of the coordinate (kilometer) grid are written. The distance between adjacent lines of the same direction for maps of scales 1:50,000, 1:25,000, 1: is equal to 1 km. The inscriptions along the southern and northern sides of the inner frame 7456, 7457, 7458, 7459 mean that the ordinates of the corresponding kilometer lines are 456, 457, 458, 459 km; digit 7 is system zone number 16

17 Gauss-Kruger coordinates in which the sheet is located. The ordinate values do not exceed 500 km; therefore, the leaf is located to the west of the axial meridian, the longitude of which is 0 = 39. The abscissas of the horizontal lines of the kilometer grid are written along the western and eastern sides of the inner frame: 6015, 6016, 6017, 6018 km. The digitization of kilometer lines is used to approximate the position of points specified on the map. To do this, indicate the last two digits of the values of the coordinates of the kilometer lines (abbreviated coordinates) of the southwestern corner of the square in which the point to be determined is located. In this case, the abscissa is indicated first (for example, 15 is indicated instead of 6015), and then the abbreviated ordinate (for example, 56 is indicated instead of 456). The nomenclature of the map sheet is signed in larger type above the northern side of the outer frame. Nearby in brackets is the name of the largest settlement within the sheet. Under the middle of the southern side of the frame, the numerical scale is indicated, the corresponding named scale and the drawn linear scale of the map. Even lower are the accepted height of the relief section and the system of heights. The explanatory inscription under the southwestern corner of the frame contains data on the declination of the magnetic needle, the convergence of meridians, the angle between the northern direction of the "vertical" kilometer lines and the magnetic meridian, etc. In addition to this, the relative position of the true, axial and magnetic meridians is presented on a special graph to the left of the scale. Under the southeast corner of the frame, a chart of laying for the angles of inclination is plotted. 8. Tasks solved by topographic maps and plans When developing design and technical documentation, a civil engineer has to solve a number of different tasks using topographic maps and plans. Consider the most common of them Determination of geographical coordinates Geographic coordinates: latitude and longitude - angular values. 17

18 Latitude is the angle formed by the plumb line and the plane of the equator (Figure 11). Latitude is measured north and south of the equator and is called north and south latitude respectively. Longitude is the dihedral angle formed by the plane of the prime meridian passing through the Greenwich (primary) meridian and the plane of the meridian of a given point. Longitude is measured east or west of the prime meridian and is called east and west longitude, respectively. On each sheet of the map, the longitudes and latitudes of the corners of the sheet frames are signed (see paragraph 7). Figure 11 Geographical coordinates the difference in latitude is 2 "30. Longitude varies from 18 07" 30 "(western frame) to 18 11" 15 (eastern frame), i.e. the difference in longitude is 3"45". To determine the geographical coordinates of point A, true meridians and parallels are drawn: i.e. lines drawn through minute intervals of the same name on opposite sides of the frame, and from these lines determine the values of geographical coordinates. Fractions of minutes or seconds are evaluated graphically. In Figure 12, for point A, a parallel is drawn with latitude \u003d 54 45 "20 and a meridian with longitude = \u003d 54 45 "29, A \u003d \u003d The latitude and longitude of the point can be determined in another way. It is necessary to draw the true meridian and parallel through point B. To determine the longitude, minutes and seconds are counted along the northern or southern minute frame of the map from the western corner and added to it to the longitude of the western corner of the frame: B =

19 Figure 12 - Determination of geographical coordinates To determine the latitude, the minutes and seconds are counted along the eastern or western frames from the southern corner and added to the latitude of the southern corner of the frame: B \u003d 54 45 "Determination of rectangular coordinates Topographic maps of Russia are compiled in the conformal Gaussian map projection - Kruger. This projection serves as the basis for creating a zonal nationwide system of flat rectangular coordinates. To reduce distortion, the ellipsoid is projected onto a plane in parts (zones) bounded by meridians spaced 3 or 6 apart. The average meridian of each zone is called axial. The zones are counted from the Greenwich meridian to the east (Figure 13) When constructing the image of each zone on the plane, the following conditions are observed (Figure 14): - the axial meridian is transferred to the plane in the form of a straight line without 19

20 distortions: - the equator is depicted by a straight line perpendicular to the axial meridian; - other meridians and parallels are represented by curved lines; - in each zone, a zonal system of flat rectangular coordinates is created: the point of intersection of the axial meridian and the equator serves as the origin of coordinates. The axial meridian is taken as the abscissa axis, and the equator is taken as the ordinate axis. Lines parallel to the axial meridian and the equator form a grid of rectangular coordinates, which is printed on topographic maps. At the exits of the coordinate grid outside the map frame, the values of x and y are signed in whole kilometers. In order not to use negative coordinate values (in the western part of the zone), all Y values are increased by 500 km, i.e. point O (Figure 14) has coordinates X = 0, Y = 500 km. When determining rectangular coordinates, points according to a plan or map use a coordinate grid. On plans at a scale of 1:5,000, the coordinate grid is drawn through 0.5 km, on maps of scales 1:10,000, 1:25,000, 1: through 1 km (kilometer grid). At the northern and southern frames of the map, the exits of the kilometer grid of ordinates are written out, and the exits of the kilometer grid of abscissas are written out at the eastern and western frames (see paragraph 7). For example (Figure 15): for point A, the abscissa entry 6066 means that X A = 6066 km - shows the distance from the equator; the entry along the ordinate axis 309 means that Y A = 309 km - shows the distance from the axial meridian of the zone, and the number 4 indicates the number of the six-degree zone. Figure 13 Dividing the Earth's surface into six-degree zones Figure 14 - Image of the zone on the plane and coordinate axes 20

21 The rectangular coordinates of the point C, which lies inside the grid square (Figure 15), are calculated by the formulas X C = X ml. + X, Y С = Y ml. + Y, or X C \u003d X st. - X 1, Y C \u003d Y st. - Y 1, where X ml., Y ml., X st., Y st., junior and senior kilometer lines, respectively, along the x and y axes; X, Y, X 1, Y 1 - distances from the corresponding kilometer lines to point C along the abscissa and ordinate axes, measured using a measuring compass and a linear or transverse scale. For example: for point C Figure 15 - Determination of rectangular coordinates on a topographic map of scale 1: the minor kilometer line along the abscissa axis X ml. = 6067 km, Y ml. = 307 km; X = 462 m, Y = 615 m. The rectangular coordinates of point C will be X C = m m = m = 6067.462 km, Y C = m m = m = 307.615 km. For control, the same values of X C, Y C can be determined by measuring the increments of coordinates X 1, Y 1 from the senior kilometer lines X st. \u003d 6068 km and Y st. = 308 km: XC = m 538 m = m = 6067.462 km, YC = m 385 m = m = 307.615 km Measurement of the true azimuth and bearing angle of the line, calculation of magnetic azimuth and rhumb True azimuth is the angle measured from the north end of the true meridian clockwise to the given direction of the line. To determine the true azimuth of the line AB (Figure 16) through the beginning of the line - point A, you need to draw a true meridian or continue 21

22 line to the intersection with the western or eastern frame of the map (recall that the boundaries of the map are the true meridians and parallels). Then you should measure the true azimuth of the line AB with a protractor: A ist. AB \u003d 65. D C A B Figure 16 Measurement of true azimuths If you draw one of the true meridians that intersect the given direction line CD (Figure 16), you can easily measure the true azimuth by attaching a protractor to it and counting the angle from the north direction clockwise the true meridian to the given direction A ist. CD = = 275. The directional angle is the angle counted from the northern end of the axial meridian clockwise to the given direction of the line. The directional angle of any line on a map or plan can be measured from the north direction of the vertical grid line to a given direction (Figure 17), 1-2 = 117. The directional angle can be measured without additional constructions - you need to attach a protractor to any of the lines crossing this direction kilometer grid. 22

23 Figure 17 Measurement of directional angles The angle between the north direction of the kilometer grid and the given direction (counting clockwise) will be the directional angle of the given direction: in the figure = = 256. angles of lines BC and EF 23

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