Define topographic map and plan. Technological map of the lesson on the topic “how to make topographic plans and maps.” Topographic maps, plans and differences between them

GENERAL INFORMATION

REAL ESTATE

MAPS AND PLANS USED IN THE CREATION OF CADASTRE DOCUMENTATION

The Federal Law of the Russian Federation “On State Registration of Rights to Real Estate and Transactions with It” (Article 12, paragraph 6) identifies the following as real estate objects: land plots, buildings, structures, premises, apartments, as well as other real estate objects, firmly connected to the land plot; other objects included in buildings and structures. Geodetic, cartographic and other data are necessary in order to reliably determine the location of the border of a property, its area, as well as the qualitative characteristics of soils, vegetation, bearing capacity of soils, etc.

When creating cadastre documentation for a real estate property, 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 cards(plans).

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

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

Topographic maps and plans display all objects and areas of the terrain provided for specific scales by current symbols, which are a kind of language for maps (plans).

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

Each conventional sign always corresponds to a specific object or phenomenon earth's surface;

the symbol must be unique;

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

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

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

1:2000, compiled on settlement lands (built-up areas), is shown in Figure 5.1.

Conventional signs distributed 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 a given map, and non-scale, used to depict objects on a map (plan) that are not expressed on the scale of the map (plan).

Out-of-scale symbols are also used to depict linear objects (roads, small rivers, etc.), the width of which is not expressed on scale. In this case, the geometric axis of the symbol must correspond to the position of the geometric axis of the terrain object, presented in the corresponding map projection. Inscriptions and explanatory captions, which, as a rule, are conveyed in the form of generally accepted abbreviations, supplement 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 utility facilities 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 when drawing up the relevant real estate cadastre documents.

Topographic maps Large territories, for ease of use, are published in separate sheets of a limited format, combined into a common multi-sheet map using a single layout system. For topographic maps, a trapezoidal (degree) layout 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 general earth's ellipsoid by meridians at 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 notation for individual sheets. The starting cell (6° longitude and 4° latitude) represents the leaf International card scale 1:1000000.

Sheets of a map of scale 1:1000000, enclosed between adjacent parallels, form belts that indicate in capital letters Latin alphabet A, B,..., V, Z. In the northern hemisphere there are 22 complete belts and one incomplete. 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 indicating the corresponding belt, and a number - the column number, for example, N-37 (Fig. 5.2).

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

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

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

The number of sheets of larger scale topographic maps in a sheet of a smaller scale topographic map, as well as the corresponding dimensions and nomenclature of the last sheet of the 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, drawn up in the Gaussian projection in the local system of flat rectangular coordinates, differs from those presented 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 1:5000 scale plan with the dimensions of its frame 40 by 40 cm (2 by 2 km on the ground). Dimensions of the frames sheets of plans of other scales are 50 by 50 cm. Within one coordinate zone, the numbers of belts and columns for sheets of scale 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 adjacent sheets

The nomenclature of a 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 frames of the sheets of plans at a scale of 1:5000 are the even lines of the kilometer grid of the local coordinate system.

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

The nomenclature of a 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 a plan sheet at a scale of 1:5000 (Fig. 5.4). The nomenclature of a 1:1000 scale plan sheet is made up of the nomenclature of a 1:2000 scale plan sheet 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 plan sheet at a scale of 1:500, a sheet of a plan at a scale of 1:2000 is divided into 16 parts, which are designated in Arabic numerals from 1 to 16. Taking into account the above, the nomenclature of the last sheet of a plan at a scale of 1:500 is written as follows:

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 buildings, structures, public utilities and communications facilities expressed on a large scale in particular detail. These objects are usually plotted on plans by coordinates. For plans at a scale of 1:2000 inclusive, objects such as sheds on poles, basement hatches, electric lights on power poles, telephone booths, etc. are depicted.

A significant feature of the content of plans at scales 1:500-1:5000 is an almost identical graphic representation of natural objects using conventional signs; hydrography, relief, vegetation, etc. For example, when displaying a forest, they show on the plan the type of forest, the average height of the trees, their thickness at chest height, and also highlight the contours of clearings, clearings located among the forest, etc. The smallest area of ​​​​the contours depicted on the plans for economically valuable areas, it is equal to 20mm 2, and for areas of no 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 line lengths, areas and angles, and these distortions depend on the corresponding mathematical transition algorithm. In some projections, distortion of land areas can be avoided, in others - distortion of horizontal angles, but the lengths of terrain lines will be distorted in all map projections, except for their locations at individual points or lines, for example, the axial meridian of the zone. Let's look at this issue in more detail.

When presenting the results of transforming the surface of the general earth's ellipsoid (sphere) onto a plane, for example, in the form of topographic and special maps, as a rule, a reduced mathematical (or graphic) model of the surface of the ellipsoid (sphere) is obtained. The degree of reduction of the entire mapped surface shows the main scale, which is labeled on the map. Due to the presence of inevitable distortions in line lengths during corresponding transformations, the main scale, in the general case, is preserved 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 equal to 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 a line (segment) in a map projection will be expressed more accurately, the smaller the value S. In this case, the scale of the image, 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 line lengths. Calculations show that greatest distortion receive those of them that are on the edge of the six-degree zone at the latitude of the equator. On the territory of Russia, the relative distortion of line lengths in the six-degree zone reaches 0.00083, which has no practical significance for small-scale mapping. However, when creating large-scale maps, such as 1:5000 scale, 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 distortions in the areas of displayed figures (land plots). Amendment Δ P in area R land plot for the transition from the surface of a ball to a plane in the Gauss-Kruger projection can be calculated using the following approximate formula:

Where Ym- converted ordinate of the midpoint of the land plot, R= 6371 km.

Calculations show that with a distance of 100 km from the axial meridian of the zone and a land area of ​​1000 hectares, the correction Δ P= 0.25 hectares, and when removed by 200 km, the same amendment will be equal to 0.98 hectares.

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 geographic 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. Of no small importance in this case is the nature of the distortions and the possibility of taking them into account when solving practical land cadastral problems.

To depict the spatial position of land plots and other real estate located in small areas, orthogonal cartographic projections are often used - an image of a spatial terrain object (part of the earth's surface) on a plane using projecting rays perpendicular to the design plane. As a rule, they are plumb lines. In this case, the level surface within the mapped territory is taken as a plane, and the plumb lines are 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 a line (segment) of the terrain onto a horizontal plane is called a horizontal layout, and the corresponding cartographic product is called a topographic plan of the area.

The terrain plan is characterized by the following basic properties:

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

horizontal angles with a vertex at any point on 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 a plot of land, 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 IN(Fig. 5.5). Let us draw a tangent to the surface of the ball at the point A and at the same time perpendicular to the direction of the radius of the ball at this point. Let us denote the arc connecting the points A And IN as AB and the projection of this arc onto the plane is through S AB Then the difference Δ S, equal to Δ S = S AB -AB there will be nothing more than a distortion of the length of the arc when it is displayed on the plane.

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

For arcs of different lengths, absolute Δ S and relative Δ S/AB The discrepancies are as follows.

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

When solving the overwhelming number of land cadastral problems 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 map projection can be chosen as a map projection when displaying a section of the earth's surface less than 10 km 2 in size, and in conditions of flat terrain less than 20 km 2. In other words, the necessary cartographic information for solving the relevant land cadastral problems in this case can be obtained based on the use of a topographic plan.

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

As a numerical characteristic of the accuracy of maps (plans), the mean square error m of the position of the contour point is used, which for clear contours is taken equal to approximately 0.04 cm on the plan.

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

Numerical characteristics of the mean square errors of the position of contour points t, on the plan for various objects the following:

Name of object t t, cm. on the plan

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

and points of other permanent, clearly identifiable
objects on the ground

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

rural settlements, ditches and other

similar constant points of objects

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

forest clearings and other slightly variable identifiable

objects

Border points of forests, bushes, meadow vegetation, 0.11...0D5

edges of ravines, water edges of rivers, streams, and other

variable, unclearly identifiable terrain objects

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

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

One of the possible criteria for choosing a plan scale is the criterion of information redundancy, which involves representing information about the area in the form of a corresponding information model of contours and writing it as a function of two arguments. First - characteristic rq information content of a topographic map or plan (inf. units/ha), which is understood as a sufficient amount of information for the consumer to calculate a specific land cadastral task. The second is the characteristic of scale-forming information capacity R m of topographic map or plan (information 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 problems, since many 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 1:500, 1:1000, 1:2000, 1:5000 and 1:10000, respectively, are 500, 330, 110, 30 and 10 inf. units/ha.

Characteristics of information content R 0, inf.unit/ha, can be calculated using the formula:

Where TO- number of information units depending on the minimum area of ​​the land plot R(m2), which needs 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.units. respectively for land areas of 1,5,10,20 and 100m2; n And P - the average number of areas and terrain objects that need to be respectively displayed with scale and non-scale symbols to solve 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 the map (plan). This criterion is essential for justifying the choice of scales of maps (plans) created for the purpose of using them to provide the cadastre of real estate with spatial data on land plots.

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

Where R- land area, hectares.

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 of 1: M topographic plan for calculating the area of ​​a land plot can be taken equal to 1: 1000.

1. Topographic maps and plans

1.1. Topographic maps and plans. General information.

Topographic maps depict significant surface 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 a conformal transverse - cylindrical projection Gauss-Kruger. 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 enough to calculate the projection of only one zone onto the plane. The zone is first projected onto the surface of the cylinder, and then the latter is expanded 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.

Distortions of line lengths 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

where DIV_ADBLOCK226">

When tracing railways near the edge of the line zone, corrections should be introduced, calculated using formula (1.1), and 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 smaller, 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 a point with these coordinates belongs, the zone number is added to the ordinate value on the left. The numbering of the zones starts from the Greenwich meridian to the east, that is, the first zone will be limited by the meridians with latitudes 0 and 6. In order not to have negative ordinates, the points of the axial meridian are conventionally assigned 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 areas of the Earth’s surface on a plane. There are overview maps compiled on a small scale. To solve engineering problems they use large scale maps, having scales of 1:100,000, 1:50,000, 1:25,000, 1:10,000. Note that maps at a scale of 1:25,000 have been compiled for the entire territory of the Russian Federation. Maps of larger scales have been compiled for individual areas of the area, for example, on the territory of large cities, on mineral deposits and other objects.

A topographic plan is a reduced and similar image on the plane of horizontal projections of the contours and shapes of the terrain without taking into account the sphericity of the Earth. Objects and terrain contours are depicted conventional icons, relief with horizontal lines. The ratio of the length of a line segment on the plan to its horizontal location on the ground is called scale..gif" width="48" height="48 src=">. On the plan, the scale is constant, and the image of the contours remains similar to their location on the ground, throughout plan area Sometimes plans are made without depicting the terrain, such plans are called situational or contour.

The area of ​​terrain for which plans can be drawn up, that is, without taking into account the curvature of the Earth, is 22 km https://pandia.ru/text/77/489/images/image006_81.gif" width="15" height="12"> 500 km2.

Plans are usually drawn up in scales of 1:500, 1:1000, 1:2000, 1:5000.

1.2. Scales of topographic plans and maps

Purpose of the task: learn to construct and apply graphs of various scales to solve problems related to scale.

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

Using scale, two main problems are solved:

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

2) the lengths of lines on the ground are determined from 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, the numerator of which is set to one, and the denominator is the number m, showing how many times the images of the lines are reduced, i.e., their horizontal locations on the map:

Numerical scale– a relative quantity, independent of the system of linear measures, therefore, if the numerical scale of the map is known, then measurements on it can be made in any linear measures. For example, if a 1 cm segment 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 make calculations every time, which makes using the scale difficult. To avoid calculations, graphic scales are used.

Graphic scales are a graphic 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 construct a linear scale, a segment of a certain length, called basis of scale. If, for example, the base of the scale is 2 cm, and the numerical scale is 1:2000, then the base of the scale on the ground will correspond to a segment of 40 m (Fig. 1.1). We put it at the end of the second segment - 40 m, at the end of the third - 80 m, at the end of the fourth - 120 m. We divide the first base into ten equal parts and shade it after one division for ease of use of the linear scale graph. Obviously, one tenth of the base will correspond to 4 m on the ground.

Rice. 1.1. Linear scale graph

In order to determine from a linear scale what length of a line on the ground corresponds to a certain length of a line taken on the plan, take a line from the plan with a meter solution, install one leg of the meter 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 was necessarily located within the first base, which was divided into n=10 equal parts.

If the leg of the meter falls between the strokes of a fine 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 known values ​​of the horizontal locations 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.

Transverse scale is a system of horizontal parallel lines drawn every 2–3 mm and divided by vertical lines into equal segments, the size of which is equal to the base of the scale. This scale is engraved on rulers called scales, as well as on the rulers of some geodetic instruments. Let us consider the construction of the so-called normal transverse scale, suitable for any numerical scale.

On a horizontal line we will lay out several segments (scale bases), 2 cm each. From the end points of the postponed segments, we restore perpendiculars to the line. On the two outer perpendiculars we will put 10 equal parts (2 mm each) and connect the ends of these parts by straight lines parallel to the base of the scale (Fig. 1.2). We divide the leftmost base (its upper segment SD and lower segment 0B) into 10 equal parts and draw inclined lines (transversals) in the following order:

Point 0 (zero) on segment 0B is connected to point 1 on segment SD;

We connect point 1 on segment 0B to point 2 on segment SD, etc., as shown in Fig. 1.2, a.

Consider a triangle OS1, which is shown in 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"> 0B scale bases.

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

https://pandia.ru/text/77/489/images/image012_54.gif" width="59" height="222">

Rice. 1.2. Cross-scale plot

This property of the transverse scale allows you to measure and plot segments up to 0.01 base of the scale without judging by eye.

Thus, the value of the smallest segment on the transverse (linear) scale graph 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 the normal centennial 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 a 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 of scale 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 examples given, on a graph of a normal transverse scale for a numerical scale of 1:5000, you can measure the smallest segments up to 1 m, and for a numerical scale of 1:50,000 - up to 10 m, i.e., the accuracy is 10 times lower. Consequently, the accuracy of a transverse (linear) scale graph is the price of the smallest division of the graph on the scale of a plan or map. In addition, the human eye cannot distinguish very small divisions without the use of optical devices, and a compass, no matter how thin the points of its needles, does not make it possible to completely accurately set the opening of the legs. As a result, the accuracy of plotting and measuring segments to scale is limited to a limit, which in topography is taken equal to 0.1 mm and is called the maximum 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 a map can be much greater (due to errors in scale measurements, errors in the map itself, deformation of the paper, and other reasons). In practice, we can assume that the error in measuring distances on a map is approximately 5–7 times greater than the maximum values.

Let us consider the methods of using 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 dividing its bases. In this case, the left leg of the meter should be on the bottom line of the leftmost base. Now, simultaneously, the legs of the meter are raised up until the left one is on some transversal. In this case, both legs of the meter should lie on the same horizontal line. The required distance is obtained by summing whole bases of scale, tenths and hundredths of 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 a scale graph?

6. What is the accuracy of a cross-scale plot?

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

8. How to determine scale accuracy?

1.3. Symbols 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 during surveys, the methodology for carrying out the work and the experience of the work contractor.

The expressiveness of a map and plan depends on the clear and distinct image of terrain objects on them. For such an image of local objects in geodesy, special cartographic symbols 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 the symbols makes them easy to memorize, which, in turn, makes it easier to read plans and maps.

Cartographic symbols (GOST 21667-76) are usually divided into areal, non-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.

Using a plan or map, you can determine with the help of such a sign not only the location of an object, object, but also its size.

If an object on a given scale cannot be expressed by an area symbol due to its smallness, then an out-of-scale conventional symbol is used. Objects indicated by such symbols take up more space on the plan than they should in scale. Off-scale symbols are widely used on maps.

To depict linear objects on maps and plans, the lengths of which are expressed to 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 appears somewhat exaggerated. Most of the captions on a topographic plan or map are placed parallel to the lower and upper frames. Inscriptions of rivers, streams, and mountain ranges are made along their directions.

The visibility of topographic maps, together with accuracy, is their most important indicator. It is achieved by using 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 character (quality) of the object. Therefore, inscriptions on maps and plans are used to indicate proper names geographical objects, designations of the type of object and as explanatory inscriptions.

The choice of a particular 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 point of establishing common symbols?

2. What types of symbols exist?

3. How can you use symbol tables to read plans and maps?

1.4. Nomenclature of topographic maps

Nomenclature is a system of layout and designation of sheets of topographic maps and plans.

Rice. 1.3. Nomenclature of map sheets at scale 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 map of scale 1:1,000,000 is an image on a plane of a spherical trapezoid formed by meridians and parallels. It measures 6° in longitude and 4° in latitude. To obtain the indicated 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° 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 designated by capital letters of the Latin alphabet A, B, C, D, ..., starting from the equator in directions north and south (Table 1).

Table 1

Row designation	Series boundaries by latitude	Row designation	Series boundaries by latitude	Row designation	Series boundaries by latitude

The columns are numbered in Arabic numerals 1, 2, ..., 60, starting from the 180° meridian in the direction from west to east. Each sheet of a 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 sheet of a map at a scale of 1:1,000,000, on which Moscow is located (Fig. 1.3), has the nomenclature N-37.

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

For maps of scale 1:200000, a sheet of scale 1:1000000 is divided into 36 sheets, numbered with Roman numerals I, II, ..., XXXVI.

For maps of scale 1: dividing a sheet of scale 1:1000000 by latitude and longitude into 12 parts, we get the boundaries of 144 sheets (Fig. 1.4, a), which are numbered 1, 2, ..., 144. The nomenclature of each sheet consists 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 sizes

(last

map sheet)

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

With trapezoidal layout, the boundaries of sheets of plans at a scale of 1:5000 are obtained by dividing a sheet of scale 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 of scale 1:2000 is obtained by dividing a sheet of scale 1:5000 into 9 parts (3´3) and is designated by letters of the Russian alphabet, for example, M-37-87 (70-i).

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

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

Example of nomenclature definition:

Task. Find the nomenclature of a map sheet at a scale of 1:50,000 and the geographic coordinates of the corners of the trapezoid frames, if it is known that 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 given in Fig. 1.4 by latitude and longitude of point K, the map sheet within which it is located is found and its nomenclature is written out. For our case, K is located on a sheet of a map at a scale of 1:1,000,000 with the nomenclature N - 44. Knowing that within this sheet of the map there are 144 sheets of a map at a scale of 1:100,000 (Fig. 1.5) and taking into account the size of the frames, we search by geographic coordinates of point K, its location within a sheet of a map 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 a sheet of a map of scale 1:50,000. To do this, we need to draw a diagram of sheet N - Fig. 1.6), showing on it the location and designation of sheets of a map of scale 1:50,000.

Rice. 1.5. Map 1:1

Rice. 1.6. Card 1:

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

Control questions:

1. What is the nomenclature of cards?

2. What map scales are accepted in Russia?

3. What are the boundaries of a map sheet?

Topographic maps and plans

topographic map plan relief

1. General information about topographic materials

Topographic materials, which are a reduced-scale projected image of sections of the earth's surface onto a plane, are divided into maps and plans.

A topographic plan is a reduced-scale and similar image on paper of the situation and terrain. A similar image is obtained by orthogonally projecting sections of the earth's surface with a size not exceeding 20 x 20 km onto a horizontal plane. In a reduced form, such an image represents a plan of the area. A situation is a collection of terrain objects, a relief is a collection of various forms of unevenness of the earth's surface. A terrain plan drawn up without a relief image is called situational (contour).

Thus, a plan is a drawing consisting of horizontal positions-segments obtained by orthogonal design of the corresponding sections of the terrain (building structures, roads, hydrographic elements, etc.).

In the form of a plan, a series of construction drawings are compiled that are included in the design and technical documentation necessary for the construction of buildings and structures. Such drawings allow one to view, as it were, reduced-scale images of building structures from above.

An image of large areas of the earth's surface on a plane cannot be obtained without distortion, that is, while maintaining complete similarity. Such areas are orthogonally projected onto the surface of the ellipsoid, and then from the surface of the ellipsoid according to certain mathematical laws called cartographic projections (Gauss-Kruger projection) are transferred to the plane. The resulting reduced image on a plane is called a map.

A topographic map is a reduced, generalized image of significant areas of the Earth's surface constructed according to certain mathematical laws.

Visual perception of the image of the earth's surface, its characteristic features and features is associated with the clarity of plans and maps. Visibility is determined by the identification of typical features of the area that determine its distinctive features, through generalizations - generalization, as well as the use of topographical symbols - a system of symbols - to depict the earth's surface.

Maps and plans must be reliable, that is, the information that constitutes their content as of a certain date must be correct and correspond to the state of the objects depicted on them. An important element of reliability is the completeness of the content, including the required amount of information and its versatility.

According to their purpose, topographic maps and plans are divided into basic and specialized. The main ones include maps and plans for national mapping. These materials are multi-purpose, so they display all the elements of the situation and terrain.

Specialized maps and plans are created to solve specific problems of a particular industry. Thus, road maps contain a more detailed description of the road network. Specialized plans also include survey plans used only during the design and construction of buildings and structures. In addition to plans and maps, topographic materials include terrain profiles, which are a reduced image of a vertical section of the earth's surface along a selected direction. Terrain profiles are the topographic basis for the preparation of design and technical documentation necessary for the construction of underground and above-ground pipelines, roads and other communications.

2.Scale

The degree of reduction of the image on the plan of the contours of the terrain, otherwise the ratio of the length of the line segment on the plan (map) to the corresponding horizontal position of this segment on the terrain is called scale. Scales are divided into numerical and linear.

A numerical scale is a fraction, the numerator of which is one, and the denominator is a number showing how many times lines and objects are reduced when depicting them on a plan (map).

On each sheet of a map or plan, its numerical scale is signed in the form: 1:1000; 1:5000; 1:10,000; 1:25000, etc.

Linear scale is a graphic expression of a numerical scale (Fig. 9). To construct a linear scale, draw a straight line and mark the same distance in centimeters on it several times, called the base of the scale. The base is usually taken two centimeters long. The length of the line on the ground, corresponding to the base of the linear scale, is signed from left to right as it grows, and the first left base is divided into 10 more parts. The practical accuracy of the linear scale is ±0.5 mm, which corresponds to 0.02-0.03 bases of the scale.

For more accurate graphic works On the plan, a transverse scale is used, which allows you to measure segments with an accuracy of 0.01 of its base.

The transverse scale is a graph based on proportional division (Fig. 10); to construct a scale on a straight line, the bases of the scale are laid off several times; perpendiculars are drawn from the division points; The first left base is divided by 10

Fig.9. Linear and numerical scales on topographic maps

parts, and 10 equal parts are also laid on perpendiculars and lines parallel to the base are drawn through the points of deposition, as shown in Fig. 10. From the similarity of triangles BDE and Bde it follows that de/DE = Bd/BD or de= Bd∙DE/BO, but DE = AB/10, Bd= BD/10. Substituting the values ​​of DE and Bd, we get de= AB/100, i.e. that is, the smallest division of the transverse scale is equal to a hundredth of the base. Using a scale with a base of 10 mm, you can determine the lengths of segments with an accuracy of 0.1 mm. The use of any scale, even transverse, cannot provide accuracy above a certain limit, depending on the properties of the human eye. With the naked eye, from a normal vision distance (25cm), you can estimate a size on the plan that does not exceed 0.1mm (details of terrain objects smaller than 0.1mm cannot be depicted on the plan). Scale accuracy is characterized by a horizontal distance on the ground corresponding to 0.1 mm on the plan. For example, for plans drawn on a scale of 1:500, 1:1000, 1:2000, the scale accuracy is respectively 0.05, 0.1, 0.2 m. The accuracy of the scale determines the degree of generalization (generalization) of details that can be depicted on a plan (map) of a particular scale.

3.Uword marks on plans and maps

Topographic maps and plans depict various terrain objects: the outlines of settlements, gardens, vegetable gardens, lakes, rivers, road lines, power transmission lines. The collection of these objects is called a situation. The situation is depicted using conventional signs.

Conventional signs, mandatory for all institutions and organizations that compile topographic maps and plans, are established by the Federal Service of Geodesy and Cartography of Russia (Roscartography) and are published either separately for each scale or for a group of scales. Although the number of conventional signs is large (about 400), they are easy to remember, since they superficially resemble the appearance and character of the depicted objects.

Conventional signs are divided into five groups: area, linear, non-scale, explanatory, special.

Area symbols (Fig. 11, a) are used to fill the areas of objects (for example: arable lands, forests, lakes, meadows); they consist of a sign of the boundary of an object (a dotted line or a thin solid line) and images or conventional coloring that fill it; for example, symbol 1 shows a birch forest; the numbers (20/0.18)∙4 characterize the tree stand: the numerator is the average height, the denominator is the average trunk thickness, 4 is the average distance between trees.

Linear symbols are objects of a linear nature (roads, rivers, communication lines, power transmission lines), the length of which is expressed on a given scale. On conventional images various characteristics of objects are given; for example, on highway 7 it is shown, m: the width of the roadway is 8, the width of the entire road is 12; on railway 8, m: +1.8 - embankment height, -2.9 - excavation depth.

Out-of-scale symbols are used to depict objects whose dimensions are not displayed at a given scale of a map or plan (bridges, kilometer posts, wells, geodetic points).

As a rule, off-scale signs determine the location of objects, but their size cannot be judged from them. The signs give various characteristics, for example: length 17 and width 3 m of wooden bridge 12, mark 393.500 points of geodetic network 16.

Explanatory symbols are digital and alphabetic inscriptions that characterize objects, for example: the depth and speed of river flows, load capacity and width of bridges, forest species, average height and thickness of trees, width of highways. They are placed on the main areal, linear, and non-scale signs.

Special symbols (Fig. 11, d) are established by the relevant departments of the national economy; they are used to draw up specialized maps and plans of this industry, for example, signs for survey plans of oil and gas fields - oil field structures and installations, wells, field pipelines.

To give a map or plan greater clarity, colors are used to depict various elements: for rivers, lakes, canals, wetlands - blue; forests and gardens - green; highways - red; improved dirt roads - orange.

Everything else is given in black. On survey plans, underground communications (pipelines, cables) are colored.

4.Pterrain and methods of depicting it. Steepness of slopes

The terrain is a collection of irregularities on the earth's surface.

Depending on the nature of the relief, the terrain is divided into flat, hilly and mountainous. Flat terrain has weakly defined forms or almost no unevenness; hilly is characterized by alternating relatively small elevations and decreases; mountainous is an alternation of elevations more than 500m above sea level, separated by valleys.

Of the variety of landforms, the most characteristic ones can be identified (Fig. 12).

A mountain (hill, height, hill) is a cone-shaped relief form rising above the surrounding area, the highest point of which is called the peak (3, 7, 12). The top in the form of a platform is called a plateau, the top of a pointed shape is called a peak. The side surface of the mountain consists of slopes, the line where they merge with the surrounding terrain is the sole, or base, of the mountain.

Rice. 12. Characteristic forms of relief: 1 - hollow; 2 - ridge; 3,7,12 - vertices; 4 - watershed; 5.9 - saddles; 6 - thalweg; 8 - river; 10 - break; 11 - terrace

A basin or depression is a bowl-shaped depression. The lowest point of the basin is the bottom. Its lateral surface consists of slopes, the line where they merge with the surrounding area is called the edge.

Ridge2 is a hill that gradually decreases in one direction and has two steep slopes called slopes. The axis of the ridge between the two slopes is called the watershed line or watershed 4.

Hollow 1 is an elongated depression in the terrain, gradually descending in one direction. The axis of the hollow between two slopes is called the drainage line or thalweg 6. The varieties of the hollow are: valley - a wide hollow with gentle slopes, and also a ravine - a narrow hollow with almost vertical slopes (cliffs 10). The initial stage of a ravine is a ravine. A ravine overgrown with grass and bushes is called a gully. Sites sometimes located along the slopes of hollows, looking like a ledge or step with an almost horizontal surface, are called terraces 11.

Saddles 5, 9 are low parts of the terrain between two peaks. Roads often pass through saddles in the mountains; in this case the saddle is called a pass.

The top of the mountain, the bottom of the basin and the lowest point of the saddle are characteristic points of the relief. The watershed and thalweg are characteristic lines of the relief. Characteristic points and lines of relief make it easier to recognize its individual forms on the ground and depict them on a map and plan.

The method of depicting the relief on maps and plans should make it possible to judge the direction and steepness of slopes, as well as determine the marks of terrain points. At the same time, it must be visual. Various methods of depicting the relief are known: perspective, shading with lines of different thicknesses, colored washing (mountains - brown, hollows - green), horizontal lines. The most advanced methods from an engineering point of view for depicting the relief are horizontal lines in combination with a signature of the marks of characteristic points (Fig. 13) and digital.

A horizontal line is a line on a map connecting points of equal heights. If we imagine a section of the Earth's surface by a horizontal (level) surface P0, then the line of intersection of these surfaces, orthogonally projected onto a plane and reduced to a size on the scale of a map or plan, will be horizontal. If the surface P 0 is located at a height H from the leveled surface, taken as the origin of absolute heights, then any point on this horizontal line will have an absolute elevation equal to H. An image in the contour lines of the relief of the entire area of ​​the terrain can be obtained by cutting the surface of this area with a series of horizontal planes Р 1, Р 2,… Р n, located at the same distance from each other. As a result, contour lines with marks H + h, H + 2h, etc. are obtained on the map.

The distance h between cutting horizontal planes is called the height of the relief section. Its value is indicated on the map or plan under the linear scale. Depending on the scale of the map and the nature of the depicted relief, the height of the section is different.

The distance between contour lines on a map or plan is called elevation. The greater the laying, the less steep the slope on the ground, and vice versa.

Rice. 13.Image of the terrain with contours

Property of contours: contours never intersect, with the exception of an overhanging cliff, natural and artificial craters, narrow ravines, steep cliffs, which are not displayed by contours, but are indicated by conventional signs; horizontal lines are continuous closed lines that can only end at the border of a plan or map; the denser the horizontal lines, the steeper the relief of the depicted area, and vice versa.

The main forms of relief are depicted by horizontal lines as follows (Fig. 14).

The images of the mountain and the basin (see Fig. 14, a, b), as well as the ridge and hollow (see Fig. 14, c, d), are similar to each other. To distinguish them from each other, the direction of the slope is indicated at the horizontal. On some horizontal lines, markings of characteristic points are signed, and so that the top of the numbers is directed in the direction of increasing the slope.

Rice. 14. Depiction of characteristic relief forms by horizontal lines: a - mountain; b - basin; c - ridge; g - hollow; d - saddle; 1 - top; 2 - bottom; 3 - watershed; 4 - thalweg

If, at a given height of the relief section, some of its characteristic features cannot be expressed, then additional half and a quarter horizontal lines are drawn, respectively, through half or a quarter of the accepted height of the relief section. Additional horizontal lines are shown with dotted lines.

To make contour lines on the map easier to read, some of them are thickened. With a section height of 1, 5, 10, and 20 m, every fifth horizontal line is thickened with marks that are multiples of 5, 10, 25, 50 m, respectively. With a section height of 2.5 m, every fourth horizontal line is thickened with marks that are multiples of 10 m.

The steepness of the slopes. The steepness of the slope can be judged by the size of the deposits on the map. The lower the position (the distance between the horizontal lines), the steeper the slope. To characterize the steepness of the slope on the ground, the inclination angle ν is used. The vertical angle of inclination is the angle between the terrain line and its horizontal position. The angle ν can vary from 0º for horizontal lines and up to ± 90º for vertical lines. The greater the angle of inclination, the steeper the slope.

Another characteristic of steepness is slope. The slope of the terrain line is the ratio of the elevation to the horizontal distance = h/d = tgν.

From the formula it follows that the slope is a dimensionless quantity. It is expressed as a percentage % (hundredths) or in ppm ‰ (thousands).Back<../Октябрь/Бесплатные/геодезия/новые%20методички/Учебное%20пособие%20по%20инженерной%20геодезии.wbk>

5. Classification and nomenclature of plans and maps

Maps and plans are classified mainly by scale and purpose.

By scale, maps are divided into small-, medium- and large-scale. Small-scale maps smaller than 1:1000000 are overview maps and are practically not used in geodesy; medium-scale (survey-topographic) maps at scales 1:1000000, 1:500000, 1:300000 and 1:200000; large-scale (topographic) - scales 1:100000, 1:50000, 1:25000, 1:10000. The scale series adopted in the Russian Federation ends with topographic plans of scales 1:5000, 1:2000, 1:1000, 1:500. In construction, plans are sometimes drawn up to scale

:200, 1:100 and 1:50.

According to their purpose, topographic maps and plans are divided into basic and specialized. The main ones include maps and plans for national mapping. These are multi-purpose maps, so they display all the elements of the terrain.

Rice. 15. Dividing a map of scale: 1:100000 into sheets of maps with scales of 1:50000, 1:25000 and 1:10000

The nomenclature is based on the international layout of map sheets at a scale of 1:1000000. Map sheets of this scale are limited by meridians and parallels in latitude 4º, longitude 6º. Each sheet occupies only its own place, being designated by a capital Latin letter, which defines the horizontal belt, and an Arabic numeral, which defines the number of the vertical column. For example, a sheet of a map at a scale of 1:1000000, on which Moscow is located, has the nomenclature N-37.

The layout of maps of larger scales is obtained by sequentially dividing a sheet of a map at a scale of 1:1000000. One sheet of a map of scale 1:1,000,000 corresponds to: four sheets of scale 1:500,000, designated by the letters A, B, C, D (the nomenclature of these sheets is, for example, N-37-A); nine sheets of scale 1:300000, designated by Roman numerals I, II, ..., IX (for example, IX -N-37); 36 sheets of scale 1:200000, also designated by Roman numerals (for example, N-37-I); 144 sheets of scale 1:100000, designated by Arabic numerals from 1 to 144 (for example, N-37-144).

One sheet of a 1:100,000 map corresponds to four sheets of a map of scale 1: 50,000, designated by the letters A, B, C, D; the nomenclature of sheets of this map looks like, for example, N-37-144-A. One sheet of a 1:50000 map corresponds to four sheets of a map of scale 1:25000, designated by the letters a, b, c, d, for example N-37-144-A-a. One sheet of a 1:25000 map corresponds to four sheets of a 1:10000 map, designated by the numbers 1, 2, 3, 4, for example N-37-144-A-a-l.

Figure 15 shows the numbering of sheets of maps of scales 1:50000 ... 1:10000, making up a sheet of map of scale 1:100000.

Layout of sheets of large-scale plans is done in two ways. For surveying and drawing up plans over an area of ​​more than 20 km 2, a scale map sheet is used as the basis for the layout

:100000, which is divided into 256 parts for a scale of 1:5000, and each sheet of scale 1:5000 is divided into nine parts for plans of a scale of 1:2000. In this case, the nomenclature of a sheet at a scale of 1:5000 looks like, for example, N-37-144(256), and for a scale of 1:2000 - N-37-144(256-I).

For site plans with an area of ​​less than 20 km2, a rectangular layout is used (Fig. 16) for a scale of 1:5000 with sheet frames of 40x40 cm, and for scales 1:2000...1:500 - 50x50 cm. The scale sheet is taken as the basis for the rectangular layout 1:5000, denoted by Arabic numerals (for example, 1). A plan sheet on a scale of 1:5000 corresponds to four sheets on a scale of 1:2000, designated by the letters A, B, C, D. A plan sheet on a scale of 1:2000 corresponds to four sheets on a scale of 1:1000, designated by Roman numerals, and 16 sheets in scale 1:500, indicated by Arabic numerals.

Rice. 16. Rectangular layout of the plan sheet

The plans of scales 1:2000, 1:1000, 1:500 shown in the figure have the nomenclature 2-G, 3-B-IV, 4-B-16, respectively.

6. Solving problems on plans and maps

The geographic coordinates of point A (Fig. 17), latitude φ and longitude λ are determined on a plan or map, using the minute scales of the trapezoid frames.

To determine latitude, a line is drawn through point A parallel to the trapezoid frames and readings are taken at the intersections with the scale of the western or eastern frame.

Similarly, to determine longitude, a meridian is drawn through point A and readings are taken on the scales of the northern or southern frame.

Rice. 17. Determination of the coordinates of a point on a topographic plan: 1 - vertical kilometer line; 2 - digital designation of horizontal grid lines; 3 - digital designations of vertical grid lines; 4 - internal frame; 5 - frame with minutes; 6 - horizontal kilometer line

In the example given, latitude φ = 54º58.6′ s. latitude, longitude λ = 37º31.0′ E. d.

The rectangular coordinates X A and Y A of point A are determined relative to the kilometer grid lines.

To do this, measure the distance ∆X and ∆Y along perpendiculars to the nearest kilometer lines with coordinates X 0 and Y 0 and find

X A = X 0 + ∆X

Y A = Y 0 + ∆Y.

Distances between points on plans and maps are determined using a linear or transverse scale, curved segments are determined using a curvimeter device.

To measure the directional angle of a line, a line is drawn through its starting point parallel to the abscissa axis, and the directional angle is measured directly at this point. You can also extend the line until it intersects the nearest grid ordinate line and measure the directional angle at the intersection point.

To directly measure the true azimuth of a line, a meridian is drawn through its starting point (parallel to the eastern or western frame of the trapezoid) and the azimuth is measured relative to it.

Since it is difficult to draw the meridian, you can first determine the directional angle of the line, and then use the given formulas to calculate the true and magnetic azimuths.

Determining the steepness of the slope. The steepness of the slope is characterized by the angle of inclination ν, which is formed by a terrain line, for example AB, with a horizontal plane P (Fig. 18).

tan ν = h/a, (15.1)

where h is the height of the relief section; a - mortgage.

Knowing the tangent, use tables of values ​​of trigonometric functions or use a microcalculator to find the value of the angle of inclination.

The steepness of the slope is also characterized by the slope of the line

i= tanν. (15.2)

The slope of the line is measured in percent or ppm (‰), i.e. thousandths of a unit.

Rice. 18. Scheme for determining the steepness of the slope

As a rule, when working with a map or plan, the angle of inclination or slope of the slope is determined using graphs (Fig. 19) with the scale of the locations.

Rice. 19. Layout graphs for the plan at a scale of 1:1000 with a relief section height of h = 1.0 m a - for inclination angles; b - slopes.

To do this, take the position between two horizontal lines along a given slope from the plan, then use the graph to find the place where the distance between the curve and the horizontal line is equal to this position. For the ordinate found in this way, read the value ν or i along a horizontal straight line (marked with asterisks on the graphs above: ν = 2.5º; i = 0.05 = 5% = 50‰).

Example 1. Determine the angle of inclination and slope of the terrain between horizontal lines on a scale plan of 1:1000, if the elevation is 20 mm, the height of the relief section is h = 1.0 m. On the ground, the laying will correspond to a segment length of 20mm ∙ 1000 = 20000mm = 20m. According to formulas (15.1) and (15.2) tanν = i = 1:20 = 0.05. Therefore, i = 5% = 50‰, and ν = 2.9º.

Determination of elevations of terrain points. If a point is located on the horizontal, its elevation is equal to the horizontal elevation. When point K (Fig. 20) is located between horizontal lines with different heights, its mark H K is determined by interpolation (finding intermediate values) “by eye” between the marks of these horizontal lines.

Interpolation consists in determining the coefficient of proportionality of the distance d from the determined point to the smaller horizontal line N MG. To the value of the location a, i.e. ratio d/a, and multiplying it by the value of the height of the relief section h.

Example 2. Marking of point K, located between horizontal lines with marks of 150 and 152.5 m (Fig. 20, a),

H K = H M. G + (d/a)h = 150 + 0.4 ∙ 2.5 = 151m.

Rice. 20. Determination of horizontal elevations of points: a...d - diagrams with a section height h = 2.5 m

If the point being determined is located between horizontal lines of the same name - on a saddle (Fig. 20, b) or inside a closed horizontal line - on a hill or basin (Fig. 20, c, d), then its mark can only be determined approximately, assuming that it is greater than or less than the height of this horizontal line by 0.5h. For example, in the figure for the saddle the elevation of the Kravna point is 138.8 m, for the hill - 128.8 m, for the basin - 126.2 m.

Drawing a line of a given maximum slope on the map (Fig. 21). Between points A and B given on the map, it is required to draw the shortest line so that not a single segment has a slope greater than the specified limit i pr.

Rice. 21. Scheme of drawing a line of a given maximum slope on the map

The easiest way to solve the problem is by using the scale for slopes. Having taken along it with a compass solution the position apr, corresponding to the slope, sequentially mark points 1...7 all horizontals from point A to point B. If the compass solution is less than the distance between the horizontals, then the line is drawn in the shortest direction. By connecting all the points, a line with a given maximum slope is obtained. If there is no scale of locations, then the location of a pr can be calculated using the formula a pr = h/(i pr M), where M is the denominator of the numerical scale of the map.

Rice. 22. Scheme for constructing a profile in a given direction: a - direction according to the map; b - profile in direction

Construction of a terrain profile in the direction specified on the map. Let's look at building a profile using a specific example (Fig. 22). Let it be necessary to construct a terrain profile along line AB. To do this, line AB is transferred on the map scale to paper and points 1, 2, 4, 5, 7, 9 are marked on it, at which it intersects the horizontal lines, as well as characteristic relief points (3, 6, 8). Line AB serves as the base of the profile. Point marks taken from the map are plotted on perpendiculars (ordinates) to the base of the profile on a scale 10 times greater than the horizontal scale. The resulting points are connected by a smooth line. Usually, the profile ordinates are reduced by the same amount, i.e., the profile is built not from zero heights, but from the conventional horizon UG (in Fig. 22, a height of 100 m is taken as the conventional horizon).

Using a profile, you can set the mutual visibility between two points, for which you need to connect them with a straight line. If you build profiles from one point in several directions, you can plot on a map or plan areas of the terrain that are not visible from this point. Such areas are called visibility fields.

Calculation of volumes (Fig. 23). Using a map with contour lines, you can calculate the volumes of a mountain and a basin, depicted by a system of contour lines enclosed within a small area. To do this, landforms are divided into parts bounded by two adjacent horizontal lines. Each such part can be approximately taken as a truncated cone, the volume of which is V = (1/2)(Si+ Si+I)h c , where Si and Si+I are the areas limited on the map by the lower and upper horizontal lines, which are the bases of the truncated cone; h c - height of the relief section; i = 1, 2, ..., k - current number of the truncated cone.

Areas S are measured with a planimeter (mechanical or electronic).

The approximate area of ​​a plot can be determined by dividing it into many regular mathematical figures (trapezoids, triangles, etc.) and summing it by area. The volume V in the uppermost part is calculated as the volume of a cone, the base area of ​​which is equal to S B and the height h is the difference between the elevations of the top point t and the horizontal line limiting the base of the cone:

Rice. 23. Scheme for determining volume

V B = (S B / 3)∙h

If the mark of point t on the map is not marked, then take h = h c /2. The total volume is calculated as the sum of the volumes of the individual parts:

V 1 + V 2 + ... + V k + V B,

where k is the number of parts.

Measuring areas on maps and plans is required to solve various engineering and economic problems.

There are three known ways to measure areas on maps: graphical, mechanical and analytical.

The graphical method includes the method of dividing the measured area into the simplest geometric figures and a method based on using a palette.

In the first case, the area to be measured is divided into simple geometric figures (Fig. 24.1), the area of ​​each of which is calculated using simple geometric formulas and the total area of ​​the figure is determined as the sum of the areas of geometric partial figures:

Rice. 24. Graphic methods for measuring the area of ​​a figure on a map or plan

In the second case, the area is covered with a palette consisting of squares (see Fig. 24.2), each of which is a unit of area measurement. The areas of incomplete figures are calculated by eye. The palette is made of transparent materials.

If the area is limited by broken lines, then its area is determined by dividing it into geometric shapes. With curved boundaries, it is easier to determine the area using a palette.

The mechanical method involves calculating areas on maps and plans using a polar planimeter.

The polar planimeter consists of two levers, pole 1 and bypass 4, pivotally connected to each other (Fig. 25a).

Rice. 25. Polar planimeter: a - appearance; b - counting by the counting mechanism

At the end of the pole lever there is a weight with a needle - pole 2, the bypass lever at one end has a counting mechanism 5, at the other - bypass index 3. The bypass lever has a variable length. The counting mechanism (Fig. 25, b) consists of a dial 6, a counting drum 7 and a vernier 8. One division on the dial corresponds to the revolution of the counting drum. The drum is divided into 100 divisions. Tenths of the small division of the drum are estimated by the vernier. The full reading on the planimeter is expressed as a four-digit number: the first digit is counted on the dial, the second and third - on the counting drum, the fourth - on the vernier. In Fig. 25, b the counting on the counting mechanism is equal to 3682.

Rice. 26. Analytical method for measuring area

Having set the bypass index at the starting point of the contour of the measured figure, take count a using the counting mechanism, then use the bypass index to move clockwise along the contour to the starting point and take count b. The difference in readings b - a represents the area of ​​the figure in planimeter divisions. Each planimeter division corresponds to an area on the ground or plan, called the planimeter division value P. Then the area of ​​the outlined figure is determined by the formula

S = P(b - a)

To determine the division price of a planimeter, measure a figure whose area is known or which can be determined with great accuracy. Such a figure on topographic plans and maps is a square formed by the lines of a coordinate grid. The division price of the planimeter P is calculated using the formula

P = S out / (b - a),

where S is the known area of ​​the figure; (b - a) - difference of samples c. starting point when tracing a figure with a known area.

The analytical method consists of calculating the area from the results of measurements of angles and lines on the ground. Based on the measurement results, the X, Y coordinates of the vertices are calculated. The area P of polygon 1-2-3-4 (Fig. 26) can be expressed through the areas of trapezoids

P = P 1′-1-2-2′ + P 2′-2-3-3′ - P 1′-1-4-4′ - P 4′-4-3-3′ = 0.5( (x 1 + x 2)(y 2 - y 1) + (x 2 + x 3)(y 3 - y 2) -(x 1 + x 4)(y 4 - y 1) - (x 4 + x 3)(y 3 - y 4)).

Having made the transformations, we obtain two equivalent formulas for determining the double area of ​​a polygon

2P = x 1 (y 2 - y 4) + x 2 (y 3 - y 1) + x 3 (y 4 - y 2) + x 4 (y 1 - y 3);

P = y 1 (x 4 - x 2) + y 2 (x 1 - x 3) + y 3 (x 2 - x 4) + y 4 (x 3 - x 1).

Calculations can be easily performed on any microcalculator.

The accuracy of determining areas analytically depends on the accuracy of the measured values.

7.Idigital image of the earth's surface

The development of computer technology and the emergence of automatic drawing devices (plotters) led to the creation of automated systems for solving various engineering problems related to the design and construction of structures. Some of these problems are solved using topographic plans and maps. In this regard, there is a need to present and store information about the topography of the area in a digital form convenient for the use of computers.

In computer memory, digital terrain data can best be represented in the form of x, y, H coordinates of a certain set of points on the earth's surface. Such a set of points with their coordinates forms a digital terrain model (DTM).

All elements of the situation are specified by the x and y coordinates of the points that determine the position of objects and terrain contours. A digital elevation model characterizes the topographic surface of the area. It is determined by a certain set of points with coordinates x, y, H, selected on the earth's surface so as to sufficiently reflect the nature of the relief.

Rice. 27. Diagram of the location of points of the digital model in characteristic places of the relief and on horizontal lines

Due to the variety of relief forms, it is quite difficult to describe it in detail in digital form, therefore, depending on the problem being solved and the nature of the relief, various methods of compiling digital models are used. For example, a DEM may take the form of a table of coordinate values ​​x, y, H at the vertices of a grid of squares or regular triangles, evenly distributed over the entire area of ​​the terrain. The distance between the peaks is selected depending on the shape of the relief and the problem being solved. The model can also be specified in the form of a table of coordinates of points located in characteristic places (inflections) of the relief (watersheds, thalwegs, etc.) or on horizontal lines (Fig. 27). Using the coordinate values ​​of the points of the digital relief model for a more detailed description on a computer using a special program, the height of any point on the terrain is determined.

Literature

Basova I.A., Razumov O.S. Satellite methods in cadastral and land management works. - Tula, Tula State University Publishing House, 2007.

Budenkov N.A., Nekhoroshkov P.A. Engineering geodesy course. - M.: Publishing house MGUL, 2008.

Budenkov N.A., Shchekova O.G. The engineering geodesy. - Yoshkar-Ola, MarSTU, 2007.

Bulgakov N.P., Ryvina E.M., Fedotov G.A. Applied geodesy. - M.: Nedra, 2007.

GOST 22268-76 Geodesy. Terms and Definitions

Engineering geodesy in construction./Ed. O.S. Razumov. - M.: Higher School, 2008.

The engineering geodesy. / Ed. prof. D.Sh.Mikhelev. - M.: Higher School, 2009.

Kuleshov D.A., Strelnikov G.E. Engineering geodesy for builders. - M.: Nedra, 2007.

Manukhov V.F., Tyuryakhin A.S. Engineering geodesy - Saransk, Mordovia State University, 2008.

Manukhov V.F., Tyuryakhin A.S. Glossary of satellite geodesy terms - Saransk, Mordovian State University, 2008.

Conducts a range of works to prepare engineering and topographical plans of all scales. Work area: Moscow and the entire Moscow region. Contact us - and you will not regret it!

Drawing up a topographic plan is an integral part of any construction or improvement on a land plot. Of course, you can put a shed on your property without it. Lay out paths and plant trees too. However, starting more complex and voluminous work without a topographic plan is undesirable and often impossible. In this article we will talk specifically about the document itself, as such - why it is needed, what it looks like, etc.

After reading it, you need to understand for yourself whether you really need a topographic plan, and if so, what it is.

What is a topographical plan of a land plot?

We won’t burden you with the official definition, which is needed more for professionals (although they already know the essence). The main thing is to understand the essence of this plan and how it differs from others (for example, a floor plan, etc.). To compile it, you need to carry out. So, a topoplan is a drawing of the elements of the situation, terrain and other objects with their metric and technical characteristics, made in approved symbols. The main feature is its high-altitude component. That is, anywhere on the topographic plan you can determine the height of the object depicted there. In addition to height, on a topoplan you can measure the coordinates and linear dimensions of objects, taking into account, of course. All this data can be obtained either from a paper copy or from a digital copy. Usually both options are prepared. Therefore, the topographic plan, in addition to a visual representation of the area, is the starting point for design and modeling.

Topoplan is also often called geological basis and vice versa . Essentially these are two identical concepts with minor reservations. The geobase may contain several topographic plans. That is, this is a collective concept for the entire territory of the object under study. Underground communications must be indicated on the geobasis, in contrast to the topoplan (where the underground is indicated if necessary). But despite the subtleties, these concepts can still be equated.

Who draws up and what is used to make a topographic plan?

Topographical plans are drawn up by surveying engineers. However, now you can’t just graduate from university, get a diploma, buy equipment and start doing topographic surveys. It is also necessary to work as part of an organization that has membership in the relevant SRO (self-regulated organization). This has become mandatory since 2009 and is intended to increase the responsibility and preparedness of surveying engineers. Our company has all the necessary permits for engineering survey activities.

We use advanced equipment () to successfully work in any conditions and areas of geodetic surveys. In particular, electronic roulettes, etc. All devices have been certified and have.

All materials and measurements are processed using specialized licensed software.

Why is a topographic plan needed?

Why does an ordinary land owner or a large construction organization need a topoplan? In essence, this document is a pre-design document for any construction. A topographic plan of a land plot is needed in the following cases:

We have written a full article on this topic - if you are interested, click here.

Documents required for ordering a topographic plan

If the Customer is an individual, it is enough to simply indicate the location of the object (address or cadastral number of the site) and verbally explain the purpose of the work. This will not be enough for legal entities. Still, interaction with a legal entity implies the mandatory drawing up of an agreement, an acceptance certificate and receipt of the following documents from the Customer:

Terms of reference for topographic and geodetic works
-Situation plan of the object
-Available data on previously completed topographic work, or other documents containing cartographic data about the object

After receiving all the data, our specialists will immediately begin work.

What does a topographic plan look like?

A topographic plan can be either a paper document or a DTM (digital terrain model). At this stage of development of technologies and interactions, a mostly paper version is still needed.

An example of a topographic plan for an ordinary private plot of land presented on the right⇒.

As for the regulatory documents on the methods of conducting topographic surveys and drawing up topographic plans, quite “ancient” SNIPs and GOSTs are also used:

All these documents can be downloaded by clicking on the links.

Accuracy of topographic plans

The above regulatory documents specify in detail the tolerances for determining the horizontal and altitude coordinates of the position of objects on topoplans. But in order not to delve into a large amount of technical and often unnecessary information, we will present the main accuracy parameters for topographic plans at a scale of 1:500 (as the most popular).

The accuracy of a topoplan is not a single and inviolable quantity. You cannot simply say that the angle of the fence is determined with an accuracy of, for example, 0.2 m. It is necessary to indicate regarding what. And here the following quantities appear.

— the average error in the planned position of clear contours of objects should not exceed 0.25 m (undeveloped territory) and 0.35 m (built-up territory) from the nearest points of the geodetic basis (GGS). That is, this is not an absolute value; it consists of errors in the shooting process and errors in starting points. But in essence it is an absolute error in determining a terrain point. After all, starting points are considered infallible when leveling topographic moves.

— the maximum error in the relative position of points of clear contours spaced from each other at a distance of up to 50 meters should not exceed 0.2 m. This is a control of the relative error in the location of terrain points.

— the average error in the planned position of underground communications (identified by a pipe-cable detector) should not exceed 0.35 m from the GGS points.

Transcript

1 Ministry of Education and Science of the Russian Federation Federal State Budgetary Educational Institution of Higher Professional Education Altai State Technical University named after. 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 classes and for self-help 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 using topographic maps and plans. Methodological instructions for conducting laboratory work, practical classes and for self-help students studying in the areas of “Construction” and “Architecture” / Alt. state tech. University named after I.I. Polzunov. - Barnaul: AltSTU, p. The guidelines discuss solutions to a number of engineering problems performed using maps: determining geographic and rectangular coordinates, reference angles, constructing a profile along a given line, determining slopes. The procedure for performing laboratory work is described in detail ( practical tasks) 1, 2 and tasks for SRS. Samples of their design are provided. Methodological guidelines were discussed 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 from

3 Introduction Maps and plans serve as the topographic basis necessary for a civil engineer to solve problems related to industrial and civil housing construction, the construction of agricultural, hydraulic, thermal power, road and other types of construction. Using topographic maps and plans, a number of engineering problems are solved: determining distances, elevations, rectangular and geographic coordinates of points, reference angles, constructing a line profile in a given direction, etc. Having studied the symbols, 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 using topographic maps and plans that 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 spaces are reduced and applied to paper, i.e. they receive a topographical plan, a scaled-down and similar image of a small area of ​​terrain, built without taking into account the curvature of the Earth. Topographic plans are created on large scales 1:500, 1:1 000, 1:2 000, 1:5 000 and are used to compile master plans, technical designs and drawings to support construction. Plans are limited to cm or cm square frames oriented north. When depicting significant territories on a plane, they are projected onto a spherical surface, which is then expanded into a plane using image construction methods called cartographic projections. In this way, a topographic map is obtained - a reduced, generalized and constructed according to certain mathematical laws image on the plane of a significant area of ​​the earth's surface, taking into account the curvature of the earth. The boundaries of the map are true meridians and parallels. A grid of geographic coordinates of lines 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 conventionally 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, topographical 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, scale is the degree to which the horizontal distances of the corresponding segments on the ground are reduced when depicting them on plans and maps. Scales can be expressed in either numerical or 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, 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 1:1,000 indicate that the image on the plans is reduced in comparison with reality by 100 and 1000 times, respectively. If on a plan of scale 1:5000 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 = cm = 265 m. Numerical scales can be expressed in named form. So scale 1: in the named form it will be written: 1 cm of the plan corresponds to 100 m on the ground or 1 cm 100 m. Simpler, not requiring calculations, are graphic scales: linear and transverse (Figure 1).

5 Figure 1 Scales: a linear, b - transverse The linear scale is a graphical representation of the numerical scale. A 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 scale base is taken to be 1 cm. The ends of the bases are signed with numbers corresponding to distances on the ground. Figure 1-a shows linear scale with a base of 1 cm for numerical scale 1: The left base is divided into 10 equal parts, called minor divisions. Minor division is equal to 0.1 part of the base, i.e. 0.1 cm. The base of the scale will correspond on the ground to 10 m, the small one to 1 m. The distance taken from the map with a solution of a compass-measuring device is transferred to a linear scale so that one needle of the compass-measuring device 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. In order to avoid estimating the fractions of small divisions by eye and thereby increase the accuracy of working with a plan or map, a transverse scale is used. It is built as follows. On a straight line, a scale base equal to, as a rule, 2 cm is laid several times. 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 constructing a linear scale. Perpendiculars with a length of mm are restored from the ends of the bases. The outermost ones are divided into 10 parts and passed through these points parallel lines. The leftmost upper 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 rules. In Figure 1-b, a transverse scale with a base of 2 cm has inscriptions corresponding to a numerical scale of 1:500. The segment ab is called the least 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; VO = 1 part; bo = 0.1 part. Let's 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 KB (Figure 1-b). This scale is called normal or centimeters. Basic 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 line length of 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 measuring compass solution will correspond to 12.35 m. 6

7 The same line on a scale of 1:1000 will correspond to 24.70 m, because on a scale of 1:1,000 (1 cm of plan corresponds to 1000 cm or 10 m on the ground) a base of 2 cm corresponds to 20 m on the ground, a 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 the lengths of lines can be determined using a transverse scale is taken to be equal to 0.01 cm - the smallest distance that can be distinguished by the “naked” eye. The distance on the ground corresponding at a given scale to 0.01 cm on a plan or map is called the graphic accuracy of the scale t or simply the accuracy of the scale t cm = 0.01 cm M, where M is the denominator of the scale. So, for a scale of 1:1000, the accuracy is t cm = 0.01 cm 1000 = 10 cm, for a scale of 1:500 5 cm, 1: cm, etc. This means that segments smaller than those indicated will no longer be depicted on a plan or map of a given scale. The maximum accuracy t pr is equal to triple the accuracy of the scale t pr = 3 t. Using the scale, two problems are solved: 1) using measured segments on a plan or map, the corresponding segments on the ground are determined; 2) using the measured distances on the ground, the corresponding segments are found on the plan or map. Let's consider the solution to 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 1:2000, 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 whole small divisions, and 7 smallest divisions. Let’s check 6 40 m m + 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 nomenclature. The layout and nomenclature of maps and plans is 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 designated 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 Figure 2-a - Scheme of layout and nomenclature of sheets of scale 1 maps:

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

10 The nomenclature of such a sheet will consist of a letter indicating 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:, designated by capital letters of the Russian alphabet, which are assigned to the nomenclature of the millionth sheet (Figure 3). Nomenclature of the last sheet N-44-G. 56 N A B B D N-44-G Figure 3 Layout and nomenclature of scale 1 map sheets: Barnaul N Figure 4 Layout and nomenclature of scale 1 map sheets:

11 N A B a c B G b Figure 5 Layout and nomenclature of map sheets at scale 1:50,000, 1: 25,00, 1: One map sheet 1: corresponds to 144 map sheets at scale 1:, which are designated by Arabic numerals from 1 to 144 and follow the nomenclature of the millionth sheet (Figure 4). Nomenclature of the last sheet N One sheet of a map of scale 1: corresponds to 4 sheets of a map of scale 1:50,000, which are designated by capital letters of the Russian alphabet A, B, C, D. Nomenclature of the last sheet N G (Figure 5). One sheet of a map of scale 1: corresponds to 4 sheets of a map of scale 1:25,000, which are designated by lowercase letters of the Russian alphabet a, b, c, d (Figure 5). For example: N G-b. One sheet of a map of scale 1: corresponds to 4 sheets of a map of scale 1:10,000, which are designated by Arabic numerals 1, 2, 3, 4 (Figure 5). For example: N G-d Nomenclature of plans Map sheet of scale 1: corresponds to 256 sheets of plan of scale 1:5,000, which are designated by Arabic numerals from 1 to 256. These numbers are assigned in parentheses to the nomenclature of sheet 1: For example, N (256). One sheet of a plan at a scale of 1:5,000 corresponds to 9 sheets of a plan at a scale of 1:2,000, which are designated by lowercase letters of the Russian alphabet a, b, c, d, d, f, g, h, i. For example: N (256). When creating topographic plans for areas up to 20 km2, a rectangular layout (conditional) can be used. In this case, it is recommended to use a tablet as a basis for the layout - a sheet of map plan - 11

12 headquarters 1:5 000 with frame dimensions cm or m and designate it in Arabic numerals, for example 4. One sheet of plan of scale 1:5 000 corresponds to 4 sheets of plan of scale 1:2 000, which are designated by capital letters of the Russian alphabet. Nomenclature of the last sheet of the scale 1 plan: G (Figure 6). One sheet of a plan of scale 1:2,000 corresponds to 4 sheets of scale 1:1,000, which are designated by Roman numerals I, II, III, IV. For example: 4-B-II. To determine the nomenclature of a 1:500 scale plan sheet, divide the 1:2,000 scale plan sheet into 16 sheets and designate them with Arabic numerals from 1 to 16. For example: 4-B Figure 6 Rectangular layout and nomenclature of 1:5,000 scale plan sheets, 1 :1,000 and 1:500 The numbering order for tablets at a scale of 1:5,000 is established by organizations that issue permits for topographic and geodetic work. 5. Relief The totality of irregularities in the physical surface of the Earth is called relief. To depict the relief on plans and maps, shading, dotted lines, colors (coloring), and shading are used, but most often the method of contour lines is used (Figure 7). The essence of this method is as follows. The surface of a section of the Earth at equal intervals h is mentally dissected by horizontal planes A, B, C, D, etc. The intersections of these planes with the surface of the Earth form curved lines called horizontals. In other words, a horizontal line is a closed curved line connecting 4 Figure 7 Image of the terrain with horizontal lines

13th point on the earth's surface same heights. The resulting contours are projected onto the horizontal plane P, and then plotted on a plan or map at the appropriate scale. The distance between the cutting planes h is called the height of the relief section. The smaller the height of the relief section, the more detailed the relief will be depicted. The height of the section, depending on the scale and relief, is taken equal to 0.25 m; 0.5 m; 1.0 m; 2.5 m; 5 m, etc. If, at a given section height, changes in relief are not captured by the horizontals, then additional horizontals with half the section height are used, called semi-horizontals, which are drawn by dotted lines. For ease of reading a map or plan, every fifth horizontal line is thickened (Figure 8-a). The distance between adjacent horizontal lines in terms of ab = d (Figure 7) is called the location of the horizontals. The greater the laying, the less steep the slope and vice versa. Some horizontal lines in the direction of the slope are marked with dashes called berg strokes. If the bergstroke is located on the inside of a closed horizontal line, 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 increase in relief (Figure 8-a). The relief of the Earth's surface is very diverse (Figure 8-a). Its main forms are distinguished: plain, mountain, basin, ridge, hollow and saddle (Figure 8-b). Each landform has its own characteristics and corresponding names. a) b) Figure 8 Basic landforms of the earth's surface 13

14 A mountain has its own peak, slopes and base. The top of a mountain is its highest part. The top 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 ramp. Mountain slopes are gentle, sloping and steep, up to 5, 20 and 45, respectively. A very steep slope is called a cliff. The foot or sole of a mountain is the line separating the slopes and the plain. A basin 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 an edge - the line where the slopes transition into the plain. A small basin is called a depression. A ridge is a hill extending 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 extended in one direction. It has a drainage line, slopes and an edge. The types of hollow are valley, gorge, ravine and ravine. A saddle is a bend in a ridge between two peaks. Some relief details (mounds, pits, quarries, screes, etc.) cannot be depicted as horizontal lines. Such objects are shown on maps and plans with special symbols. In addition to contour lines and symbols, the heights of characteristic points are indicated 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 consists of graphic symbols - conventional signs. These symbols superficially resemble the shape of the corresponding elements of the situation. The clarity of conventional signs reveals the semantic content of the depicted objects and allows you to read a map or plan. Conventional signs are divided into areal (scale), non-scale, linear and explanatory (Figure 9). Scale or contour conventional signs are such conventional signs with the help of which elements of the situation, i.e. terrain objects are depicted on a plan scale in compliance with their actual sizes. For example: the outline of meadows, forests, gardens, vegetable gardens, etc. The boundary of the contour is shown as a dotted line, and inside the contour there is a symbol. Conventional off-scale signs are used to depict terrain objects 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 garden Linear Communication line Wasteland Meadow Power line Main gas pipeline Shrub Clearings Birch forest Vegetable garden Non-large-scale Kilometer pillar Windmill Free-standing broad-leaved tree Figure 9 Conventional signs Linear symbols are used to depict linear objects, the length of which is expressed on the scale of a plan or map. For example: road network, trails, power and communication lines, streams, etc. Explanatory symbols supplement the above-mentioned symbols with digital data, icons, and inscriptions. They allow you to read the map more completely. For example: depth, river flow 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 topographic map sheet Let's consider a schematic representation of a topographic map sheet on a scale of 1: (Figure 10). The sides of the map sheet 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 southwestern corner are, respectively, 54 15" and 38 18"45", the northwestern "30 and 38 18"45", the southeastern "and 38 22 "30, northeast "30 and 38 22"30. 15

16 Figure 10 - Schematic representation of a sheet of topographic map Next to the inner one there is a minute frame of the map, the divisions of which correspond to 1 latitude and longitude. They are shown in shading 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 abscissa 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 indicate that the ordinates of the corresponding kilometer lines are 456, 457, 458, 459 km; The number 7 is the zone number of system 16

17 Gauss-Kruger coordinates in which this sheet is located. The ordinate values ​​do not exceed 500 km, therefore, the sheet is located 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. Digitization of kilometer lines is used to approximately determine the position of points specified on the map. To do this, indicate the last two digits of the coordinate values ​​of the kilometer lines (abbreviated coordinates) of the southwestern corner of the square in which the point being determined is located. In this case, the abscissa is indicated first (for example, instead of 6015 they indicate 15), and then the abbreviated ordinate (for example, instead of 456 they indicate 56). The map sheet nomenclature is signed in a larger font above the north side of the outer frame. Next to it in parentheses is the name of the largest within the sheet settlement. Under the middle of the southern side of the frame, the numerical scale, the corresponding named scale and the drawn linear scale of the map are indicated. Below are the accepted heights of the relief section and the height system. The explanatory inscription under the southwestern corner of the frame contains data on the declination of the magnetic needle, the convergence of the meridians, the angle between the northern direction of the “vertical” kilometer lines and the magnetic meridian, etc. In addition to this, the relative positions of the true, axial and magnetic meridians are presented on a special graph to the left of the scale. Under the southeast corner of the frame, a plot of locations for the angles of inclination is plotted. 8. Problems solved using topographic maps and plans When developing design and technical documentation, the construction engineer has to solve a number of different problems using topographic maps and plans. Let's consider the most common of them. Determination of geographic coordinates Geographic coordinates: latitude and longitude - angular values. 17

18 Latitude is the angle formed by a 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 (prime) meridian and the plane of the meridian of a given point. Longitude is measured east or west from the prime meridian and is called eastern and western longitude accordingly. On each sheet of the map the longitude and latitude of the corners of the sheet frames are labeled (see paragraph 7). Figure 11 Geographic coordinates The latitude of the 1:10,000 map sheet shown in Figure 12 varies from 54 45" (south frame) to 54 47" 30 (north frame), i.e. 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 geographic coordinates of point A, true meridians and parallels are drawn: i.e. lines drawn at minute intervals of the same name on opposite sides frames, and from these lines the values ​​of geographic coordinates are determined. Fractions of minutes or seconds are estimated graphically. In Figure 12, for point A, a parallel with latitude = 54 45"20 and a meridian with longitude = are drawn. The increments of geographic coordinates from these parallels and the meridian are evaluated graphically: = 9", = 8". As a result, A = 54 45"20 + = 54 45 "29, A = = The latitude and longitude of a point can be determined in another way. It is necessary to draw a true meridian and parallel through point B. To determine longitude, minutes and seconds are counted along the northern or southern minute frames of the map from the western corner and add it to the longitude of the western corner of the frame: B =

19 Figure 12 - Determination of geographical coordinates To determine latitude, minutes and seconds are counted along the eastern or western frames from the southern corner and add it to the latitude of the southern corner of the frame: B = 54 45" Determination of rectangular coordinates Topographic maps of Russia are compiled in a Gaussian conformal map projection - Kruger. This projection serves as the basis for creating a zonal nationwide system of flat rectangular coordinates. To reduce distortions, the ellipsoid is projected onto the plane in parts (zones) limited by meridians spaced 3 or 6 from each other. The average meridian of each zone is called the axial meridian. The zones are counted from the Greenwich meridian to the east (Figure 13).When constructing an image of each zone on a 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 as a straight line perpendicular to the axial meridian; - other meridians and parallels are depicted by curved lines; - in each zone a zonal system of flat rectangular coordinates is created: the origin of coordinates is the point of intersection of the axial meridian and the equator. The axial meridian is taken as the abscissa axis, and the equator as the ordinate axis. Lines parallel to the central meridian and the equator form a rectangular coordinate grid that is printed on topographic maps. At the exits of the coordinate grid beyond the map frame, the x and y values ​​are indicated 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 the rectangular coordinates of a point from a plan or map, a coordinate grid is used. On plans of scale 1:5,000, the coordinate grid is drawn every 0.5 km; on maps of scales 1:10,000, 1:25,000, 1: every 1 km (kilometer grid). At the northern and southern frames of the map, the outputs of the kilometer grid of ordinates are written out, and the eastern and western frames - the outputs of the kilometer grid of abscissas (see paragraph 7). For example (Figure 15): for point A, the entry on the abscissa 6066 means that X A = 6066 km - shows the distance from the equator; the entry on 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 axis 20

21 Rectangular coordinates of point C lying inside the grid square (Figure 15) are calculated using the formulas X C = X ml. + X, Y C = Y ml. + Y, or X C = X art. - X 1, Y C = Y art. - 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 using a topographic map of scale 1: the minor kilometer line along the abscissa axis X ml. = 6067 km, along the ordinate axis 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 highest kilometer lines X st. =6068 km and Y station. = 308 km: X C = m 538 m = m = 6067.462 km, Y C = m 385 m = m = 307.615 km Measuring true azimuth and directional angle of a line, calculating magnetic azimuth and bearing True azimuth is the angle measured from the northern end of the true meridian clockwise to the given direction of the line. To determine the true azimuth of line AB (Figure 16) through the beginning of the line - point A, you need to draw the true meridian or continue 21

22 line until it intersects with the western or eastern frame of the map (remember that the boundaries of the map are true meridians and parallels). Then you should measure with a protractor the true azimuth of the line AB: A source. AB = 65. D C A B Figure 16 Measuring true azimuths If you draw one of the true meridians that intersects the CD line in a given direction (Figure 16), you can easily measure the true azimuth by attaching a protractor to it and counting clockwise the angle from the north direction true meridian to a given direction A ist. CD = = 275. Directional angle is the angle measured 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 construction - you need to attach a protractor to any of the lines intersecting this direction kilometer grid. 22

23 Figure 17 Measuring directional angles The angle between the northern direction of the kilometer grid and the given direction (counting clockwise) will be the directional angle of the given direction: in the figure = = 256. Figure 18 Diagram of the frames and kilometer grid of a topographic map sheet showing true azimuths and directional ones angles of lines BC and EF 23

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