Topographic maps of the terrain and plans. Presentation on the topic: Topographic maps and plans

2.1. Topographic map elements

Topographic map - a detailed large-scale general geographical map reflecting the location and properties of the main natural and socio-economic objects, making it possible to determine their planned and altitude position.

Topographic maps are created mainly on the basis of:

• processing of aerial photographs of the territory;
• by direct measurements and surveys of terrain objects;
• cartographic methods with already available plans and maps of large scales.

Like any other geographical map, a topographic map is a reduced, generalized and figurative-sign image of the area. It is created according to certain mathematical laws. These laws minimize the distortions that inevitably arise when the surface of the earth's ellipsoid is transferred to a plane, and, at the same time, ensure its maximum accuracy. The study and compilation of maps require an analytical approach, the division of maps into its constituent elements, the ability to understand the meaning, meaning and function of each element, and to see the connection between them.

Map elements (components) include:

• cartographic image;
• mathematical basis;
• legend
• auxiliary equipment;
• Additional information.

The main element of any geographical map is a cartographic image - a set of information about natural or socio-economic objects and phenomena, their location, properties, connections, development, etc. Topographic maps depict water bodies, relief, vegetation, soils, settlements, communication routes and means of communication, some objects of industry, agriculture, culture, etc.
Mathematical basis topographic map - a set of elements that determine the mathematical relationship between the real surface of the Earth and a flat cartographic image. It reflects the geometric laws of map construction and the geometric properties of the image, provides the ability to measure coordinates, plot objects by coordinates, fairly accurate cartometric determinations of lengths, areas, volumes, angles, etc. Due to this, a map is sometimes called a graph-mathematical model of the world.

The mathematical basis is:

• map projection;
• coordinate grids (geographical, rectangular and others);
• scale;
• geodetic substantiation (strong points);
• layout, i.e. placement of all elements of the map within its frame.

kata scale can have three types: numerical, graphic (linear) and explanatory label (named scale). The scale of the map determines the degree of detail with which a cartographic image can be plotted. Map scales will be discussed in more detail in Topic 5.
Map grid represents the image of the degree grid of the Earth on the map. The type of grid depends on the projection in which the map is drawn. On topographic maps of scales 1:1,000,000 and 1:500,000, meridians look like straight lines converging at a certain point, and parallels look like arcs of eccentric circles. On topographic maps of a larger scale, only two parallels and two meridians (frame) are applied, limiting the cartographic image. Instead of a cartographic grid, a coordinate (kilometer) grid is applied to large-scale topographic maps, which has a mathematical relationship with the degree grid of the Earth.
card frame name one or more lines bounding the map.
To strong points include: astronomical points, triangulation points, polygonometry points and leveling marks. Control points serve as a geodetic basis for surveying and compiling topographic maps.

2.2. Topographic map properties

Topographic maps have the following properties: visibility, measurability, reliability, modernity, geographical correspondence, geometric accuracy, content completeness.
Among the properties of a topographic map, one should highlight visibility and measurability . The visibility of the map provides a visual perception of the image of the earth's surface or its individual sections, their characteristic features and features. Measurability allows you to use the map to obtain quantitative characteristics of the objects depicted on it by measurements.

Visibility and measurability are provided by:

a mathematically defined relationship between multidimensional environmental objects and their flat cartographic image. This connection is conveyed using a map projection;

the degree of reduction in the size of the depicted objects, which depends on the scale;

highlighting typical terrain features by means of cartographic generalization;

the use of cartographic (topographic) conventional signs to depict the earth's surface.

To provide a high degree measurability, the map must have a geometric accuracy sufficient for specific purposes, which means the correspondence of the location, outlines and sizes of objects on the map and in reality. The smaller the depicted area of ​​the earth's surface while maintaining the size of the map, the higher its geometric accuracy.
The card must be credible, i.e., the information that makes up its content on a certain date must be correct, must also be contemporary, correspond to the current state of the objects depicted on it.
An important property of a topographic map is completeness content, which includes the volume of information contained in it, their versatility.

2.3. Classification of topographic maps by scale

All domestic topographic maps, depending on their scale, are conditionally divided into three groups:

• small scale maps (scales from 1:200,000 to 1:1,000,000), as a rule, are used for general study of the area in the development of projects and plans for the development of the national economy; for preliminary design of large engineering structures; as well as for taking into account the natural resources of the surface of the earth and water spaces.
• Medium scale maps (1:25,000, 1:50,000 and 1:100,000) are intermediate between small-scale and large-scale. The high accuracy with which all terrain objects are depicted on maps of a given scale makes it possible to widely use them for various purposes: in the national economy in the construction of various structures; for making calculations; for geological prospecting, land management, etc.
• large scale cards (1:5,000 and 1:10,000) are widely used in industry and public utilities; when conducting detailed geological exploration of mineral deposits; when designing transport hubs and structures. Large-scale maps play an important role in military affairs.

2.4. Topographic plan

Topographic plan - a large-scale drawing depicting in conventional symbols on a plane (on a scale of 1:10,000 and larger) a small area of ​​the earth's surface, built without taking into account the curvature of the level surface and maintaining a constant scale at any point and in all directions. A topographic plan has all the properties of a topographic map and is its special case.

2.5. Topographic map projections

When depicting large areas of the earth's surface, the projection is made on the level surface of the Earth, in relation to which the plumb lines are normals.

map projection - method of depicting the surface of the globe on a plane when making maps.

It is impossible to develop a spherical surface on a plane without folds and breaks. For this reason, distortions of lengths, angles and areas are inevitable on maps. Only in some projections the equality of angles is preserved, but because of this, the lengths and areas are significantly distorted, or the equality of areas is preserved, but the angles and lengths are significantly distorted.

Projections of topographic maps at a scale of 1:500,000 and larger

Most countries of the world, including Ukraine, use conformal (conformal) projections to compile topographic maps, preserving the equality of angles between the directions on the map and on the ground. Swiss, German and Russian mathematician Leonard Euler in 1777 developed the theory of conformal image of a ball on a plane, and the famous German mathematician Johann Carl Friedrich Gauss in 1822 substantiated the general theory of conformal image and used conformal flat rectangular coordinates when processing triangulation (method of creating a network of reference geodetic points). Gauss applied a double transition: from an ellipsoid to a ball, and then from a ball to a plane. The German geodesist Johannes Heinrich Louis Krüger developed a method for solving conditional equations arising in triangulation and a mathematical apparatus for the conformal projection of an ellipsoid onto a plane, called the Gauss-Krüger projection.
In 1927, the famous Russian geodesist, Professor Nikolai Georgievich Kell, was the first in the USSR to apply the Gaussian coordinate system in Kuzbass, and on his initiative, since 1928, this system was adopted as a single system for the USSR. To calculate the coordinates of Gauss in the USSR, the formulas of Professor Feodosy Nikolaevich Krasovsky were used, which are more accurate and more convenient than Kruger's formulas. Therefore, in the USSR there was no reason to give the Gaussian projection the name "Gauss-Kruger".
Geometric entity This projection can be represented as follows. The entire terrestrial ellipsoid is divided into zones and maps are made for each zone separately. At the same time, the dimensions of the zones are set so that each of them can be deployed into a plane, that is, depicted on a map, with virtually no noticeable distortion.
To obtain a cartographic grid and draw up a map in the Gaussian projection, the surface of the earth's ellipsoid is divided along the meridians into 60 zones of 6 ° each (Fig. 2.1).

Rice. 2.1. The division of the Earth's surface into six-degree zones

To imagine how the image of zones is obtained on a plane, imagine a cylinder that touches the axial meridian of one of the zones of the globe (Fig. 2.2).

Rice. 2.2. Zone projection onto a cylinder tangent to the Earth's ellipsoid along the axial meridian

According to the laws of mathematics, we project the zone onto the lateral surface of the cylinder so that the property of the equiangularity of the image is preserved (the equality of all angles on the surface of the cylinder to their magnitude on the globe). Then we project all other zones, one next to the other, onto the side surface of the cylinder.

Rice. 2.3. Image of zones of the earth's ellipsoid

Further cutting the cylinder along the generatrix AA1 or BB1 and turning its lateral surface into a plane, we obtain an image of the earth's surface on a plane in the form of separate zones (Fig. 2.3).
The axial meridian and the equator of each zone are depicted as straight lines perpendicular to each other. All axial meridians of the zones are depicted without length distortion and maintain the scale throughout their entire length. The remaining meridians in each zone are depicted in the projection by curved lines, therefore they are longer than the axial meridian, i.e. distorted. All parallels are also shown as curved lines with some distortion. Line length distortions increase with distance from the central meridian to the east or west and become greatest at the edges of the zone, reaching a value of the order of 1/1000 of the line length measured on the map. For example, if along the axial meridian, where there is no distortion, the scale is 500 m in 1 cm, then at the edge of the zone it will be 499.5 m in 1 cm.
It follows that topographic maps are distorted and have a variable scale. However, these distortions when measured on a map are very small, and therefore it is believed that the scale of any topographic map for all its sections is constant.
For surveys at a scale of 1:25,000 and larger, the use of 3 degree and even narrower zones is allowed. The overlap of zones is taken 30" to the east and 7", 5 to the west of the axial meridian.

The main properties of the Gaussian projection:

the axial meridian is depicted without distortion;

the projection of the axial meridian and the projection of the equator are straight lines perpendicular to each other;

the remaining meridians and parallels are depicted by complex curved lines;

in the projection, the similarity of small figures is preserved;

in projection, horizontal angles and directions are preserved in the image and terrain.

Projection of a topographic map at a scale of 1:1,000,000

Projection of a topographic map at a scale of 1:1,000,000 - modified polyconic projection, accepted as international. Its main characteristics are: the projection of the earth's surface covered by a map sheet is carried out on a separate plane; parallels are represented by arcs of circles, and meridians by straight lines.
To create topographic maps of the USA and the countries of the North Atlantic Alliance, Universal Transverse Mercator, or UTM. In its final form, the UTM system uses 60 zones, each 6 degrees longitude. Each zone is located from 80º S. up to 84º N The reason for the asymmetry is that 80º S. passes very well in the southern ocean, southern South America, Africa and Australia, but it is necessary to climb to 84º N to reach the north of Greenland. Zones are counted starting from 180º, with increasing numbers to the west. Together, these zones cover almost the entire planet, excluding only the Arctic Ocean and North and Central Antarctica in the south.
The UTM system does not use a "standard" based on the transverse Mercator projection - the tangent. Instead, it is used secant, which has two section lines located approximately 180 kilometers on either side of the central meridian. Map zones in the UTM projection differ from each other not only in the positions of their central meridians and distortion lines, but also in the earth model they use. The official definition of the UTM system defines five other spheroids for use in various zones. All UTM zones in the United States are based on the Clarke 1866 spheroid.

Questions and tasks for self-control

1. Give definitions: "Topography", "Geodesy", "Topographic map".
2. What are the sciences of topography? Explain this relationship with examples.
3. How are topographic maps created?
4. What is the purpose of topographic maps?
5. What is the difference between a topographic plan and a topographic map?
6. What are the elements of a map?
7. Give a description of each element of the topographic map.
8. What are the parallels and meridians on topographic maps?
9. What elements determine the mathematical basis of a topographic map? Give brief description every element.
10. What are the properties of topographic maps? Give a brief description of each property.
11. On what surface are images of large areas of the Earth projected?
12. Define a map projection.
13. What distortions can be formed when a spherical surface is deployed on a plane?
14. What projections are used by most countries of the world to compile topographic maps?
15. What is the geometric essence of the construction of the Gaussian projection?
16. Show on the drawing how a six-degree zone is projected from the earth's ellipsoid to a cylinder.
17. How are the meridians, parallels, and equator drawn in the six-degree Gaussian zone?
18. How does the nature of distortion change in the six-degree Gaussian zone?
19. Can the scale of a topographic map be considered constant?
20. In what projection is the topographic map made at a scale of 1:1,000,000?
21. What map projection is used to create topographic maps in the United States, and how is it different from the Gaussian projection?
    

1. Topographic maps and plans

1.1. Topographic maps and plans. General information.

Topographic maps depict significant areas of the Earth.

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

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

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

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

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

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

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

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

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

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

1.2. Scales of topographic plans and maps

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

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

Scale serves two main purposes:

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

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

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

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

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

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

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

Rice. 1.1. Linear scale chart

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

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

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

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

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

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

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

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

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

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

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Rice. 1.2. Cross-Scale Plot

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

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

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

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

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

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

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

Test questions:

1. What is called scale?

2. What are the scales?

3. What is a numerical scale?

4. What are the graphic scales?

5. What is the base of the scale chart?

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

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

8. How to determine the accuracy of the scale?

1.3. Conventional signs of plans and maps

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

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

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

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

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

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

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

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

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

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

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

Test questions:

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

2. What types of conventional signs exist?

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

1.4. Nomenclature of topographic maps

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

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

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

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

Table 1

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

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

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

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

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

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Nomenclature

Number of sheets

Sheet dimensions

(last

map sheet)

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

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

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

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

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

An example of a nomenclature definition:

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

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

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

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

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

Rice. 1.5. Map 1:1

Rice. 1.6. Map 1:

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

Test questions:

1. What is the nomenclature of maps?

2. What map scales are accepted in Russia?

3. What are the boundaries of the map sheet?

The second language of geography is the cartographic image. Maps were used even by ancient navigators. When planning the expedition, the researchers collected all available cartographic materials for the required area. Upon completion, the results were transferred to paper. So the plan of the area was created. This was the basis for creating new maps. What is a plan of the area and what are its fundamental differences from a geographical map?

terrain?

The very first maps in human history were plans. Now they are used in almost all branches of science and technology: they are indispensable in construction, agriculture, engineering surveys, etc.

A terrain plan is a large-scale image of a section of the earth's surface, which is created using conventional signs. As a rule, these cartographic images are compiled for small areas with areas up to several square kilometers. In this case, the curvature does not affect the image in any way.

How is a plan different from a map?

Often in life we ​​meet both a map and a plan of the area. Geography as a science relies on these cartographic images. But it's not the same.

When creating a geographical map, a smaller scale is used (that is, a larger area is covered), the nature of the earth's surface is taken into account, that is, the mathematical law of image construction is used - projection. Essential element geographical maps- degree grid: it is necessary to determine the cardinal points. Parallels and meridians are often shown as arcs rather than straight lines. Only significant large objects are subject to mapping. A variety of materials are used to compile them, including maps of a larger scale, satellite images.

A terrain plan is a more detailed image of a small one. It is built without taking into account the projection, since, due to the size of the site, the surface is considered to be flat. The cardinal directions are determined by the directions of the plan frames. Absolutely all elements of the terrain are subject to display. They are compiled on the basis of large-scale aerial photography or on the ground.

How is the plan made?

To begin with, a point is selected on the site, from which the entire area to be mapped is clearly visible. After that, you need to choose the scale of the future plan. The next step is to determine the direction to the north. This can be done using a tablet board and a hand compass. On paper, you need to designate the point from which the terrain will be surveyed, and then draw all the main landmarks (corners of buildings, large trees, poles).

Then, using special high-precision instruments, azimuths are measured to each point that needs to be reflected on the plan. Each time, the azimuths are plotted from the main point, and an auxiliary line is drawn from it, the angle is marked on the plan. The distance from the main to the desired points of the terrain is also measured and transferred to paper.

Then, the objects of the site are displayed in conventional signs, the necessary signatures are made.

Over the entire area of ​​the cartographic image of the plan, its scale remains unchanged. There are three types of scale:

• Numerical.
• Named.
• Linear.

Numerical is expressed as a fraction, the numerator of which is 1, and the denominator is M. This number M shows the degree of reduction in the size of the image on the plan. Topographic plans have scales of 1:500, 1:1000, 1:2000, 1:5000. Smaller scale plans are also used for land management works - 1:10,000, 1:25,000, 1:50,000. The scale with the larger M number is considered smaller, and vice versa.

With a named scale it is easier - here the length of the lines is expressed verbally. For example, there are 50 meters in 1 cm. This means that 1 cm of distance on the map corresponds to 50 m on the ground.

Linear scale - a graph depicted as a straight line segment, which is divided into equal parts. Each such part is signed by a numerical value of the proportionate length of the terrain.

Conventional signs of the terrain plan

In order to display any objects or processes on a topographic plan, to indicate their important qualitative or quantitative values, it is necessary to use conventional signs or designations. They give a complete picture of the spatial arrangement of objects, as well as their characteristics and appearance.

There are four types of symbols:

• Large-scale - linear and areal (for example, the squares of states, roads, bridges).
• Off-scale (well, spring, pillar, tower, etc.).
• Explanatory (signatures of the characteristics of objects, for example, the width of the highway, the names of subjects).

All of them are reflected in the legend of the plan. Based on the legend, a primary idea of ​​the site is compiled.

So, the plan of the area is an image of a small area of ​​the earth's surface on a large scale. It is used in almost all spheres of human activity. Without it, it would be impossible to create topographic maps.

Carries out a complex of works on the preparation of engineering and topographic plans of all scales. The area of ​​work is Moscow and all the Moscow region. Contact us - and you will not regret!

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

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

What is a topographic plan of a land plot?

We will not load you with the official definition, which is more needed for professionals (although they already know the essence). The main thing is to understand the essence of this plan and its difference from others (for example, a floor plan, etc.). To compose it, you need to spend. So, a topoplan is a drawing of the elements of the situation, the terrain and other objects with their metric and technical characteristics, made in approved conventional signs. The main feature is its height component. That is, in any place of the topographic plan, you can determine the height of the object depicted there. In addition to the height, it is possible to measure the coordinates and linear dimensions of objects on the topoplan, taking into account, of course. All these data can be obtained both from a paper copy and from a digital one. Usually both options are prepared. Therefore, the topographic plan, in addition to a visual representation of the terrain, is the starting point for design and modeling.

Another topoplan is often called geo-underlying and vice versa . In fact, these are two identical concepts with minor reservations. A geo-underlay can contain several topographic plans. That is, this is a collective concept for the entire territory of the object under study. Underground utilities must be indicated on the geo-base, in contrast to the topographic plan (the subway is indicated there if necessary). But despite the subtleties, these concepts can still be equated.

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

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

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

Processing of all materials and measurements is carried out on specialized licensed software.

Why do you need a topographic plan?

Why is a topographic plan needed by an ordinary owner of a land plot, or a large construction organization? In fact, this document is a pre-design 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.

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. For legal entities, this will not be enough. Still, interaction by a legal entity implies the mandatory drawing up of an agreement, an act of acceptance and receipt of the following documents from the Customer:

Terms of reference for the production of topographic and geodetic works
-Situational plan of the object
-Available data on previously produced topos graphic works ah, 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 in the development of technologies and interactions, a paper version is still needed.

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

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

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

Topographic plan accuracy

The above regulatory documents detail the tolerances for determining the planned and height coordinates of the position of objects on topographic maps. 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 ones).

Topoplan accuracy is not a single and indestructible value. One cannot simply say that the angle of the fence is determined with an accuracy of, for example, 0.2m. You need to specify what. And here are the following values.

- the average error of the planned position of clear contours of objects should not exceed 0.25 m (undeveloped area) and 0.35 m (built-up area) from the nearest points of the geodetic base (GGS). That is, this is not an absolute value - it consists of errors in the shooting process and errors in the starting points. But in fact it is an absolute error in determining the point of the terrain. After all, the 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 of the planned position of underground utilities (detected by a pipe-cable detector) should not exceed 0.35 m from the GGS points.

Federal Agency for Railway Transport Ural State University of Railway Transport Department "Bridges and Transport Tunnels"

B. G. Chernyavsky

SOLUTION OF GEODETIC AND ENGINEERING PROBLEMS

ON TOPOGRAPHIC MAPS AND PLANS

Methodical instructions on engineering geodesy for students of construction specialties

Yekaterinburg Publishing House UrGUPS

Chernyavsky, B. G.

Ch-49 Solution of geodetic and engineering problems on topographic maps and plans: method. instructions / B. G. Chernyavsky. - Yekaterinburg: Publishing House of UrGUPS, 2011. - 44 p.

The guidelines are intended for 1st year students of all forms of education in the direction of preparation 270800 - "Construction". Compiled in accordance with the curriculum and the program for the discipline "Engineering Geodesy", they can be used both in the classroom and in the independent work of students.

Examples of calculation and graphic design of works are given, the scope of the task is indicated, control questions are given.

Reviewer: F.E. Reznitsky, Associate Professor, Ph.D. tech. Sciences

Educational edition

Editor S.I. Semukhin

Signed for publication on November 22, 2011. Format 60x84/16 Offset paper. Conv. oven l. 2.6.

Circulation 300 copies. Order No. 165.

Publishing house UrGUPS 620034, Yekaterinburg, st. Kolmogorova, 66

© Ural State Transport University (UrGUPS), 2011

Introduction ………………………………………………………………….. 4

1. Scales of topographic maps and plans, measurement of line lengths on maps and plans. Symbols for topographic maps and plans ………………………………………………………………………...5

2. Determination of geodetic and rectangular coordinates of points,

orientation angles of lines according to topographic maps and plans ……………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………

3. The study of the terrain on the topographic map and plan. Drawing contour lines on a digital elevation model. Determining point elevations ……………………………………………….19

4. Solving engineering problems using topographic maps

and plans ……………………………………………........................... ..25

5. Geodetic preparation of the project of a building, structure for transferring it from a topographic plan to the area……….……32

6. Measurement of the areas of the earth's surface using maps

and plans using a polar planimeter………………...….……...40

Bibliographic list……………………………………………...44

Introduction

Topographic maps and plans are the basis for drafting various linear structures (railways and roads, power lines, heating mains, etc.), industrial and civil buildings, engineering structures (bridges, overpasses, tunnels), as well as for the land cadastre.

As a result of the work on six topics, students should be able to solve geodetic and engineering problems according to maps and plans, perform geodetic preparation of the project, including drawing up a layout drawing to perform work on determining the design of a building, structure on the ground, and also determine the areas of the earth's surface.

1. Scales of topographic maps and plans. Measurement of line lengths on maps and plans.

Symbols for topographic maps and plans

1. Familiarize yourself with topographic maps and plans, their scales and symbols.

2. Using a measuring compass and a linear scale, measure the lengths of lines on a map at a scale of 1:10,000.

3. Paste in the notebook the given graph of a transverse scale with a base of 2 cm and digitize it for a scale of 1: 2000. Set aside several lines of a given length on the graph.

4. Draw with a base of 5 cm a graph of the transverse scale for the plan at a scale of 1:2000. Plot several lines of a given length on the graph.

5. Draw a table of symbols.

6. Prepare a report on the work performed.

1.1. General information about maps and plans, their scales

A map is a reduced image on a plane of significant areas of the earth's surface, taking into account the curvature of the Earth. The map is inherently distorted, since the ellipsoidal surface onto which the earth's surface is projected cannot be turned into a plane without distortion. Map projections are used to reduce and account for these distortions.

Maps of scales 1:100,000, 1:50,000, 1:25,000 and 1:10,000 are called

topographic. In Russia, topographic maps are compiled in the Gaussian projection. On maps of certain scales, elements of the terrain are depicted with approximately the same accuracy and detail.

A plan is a reduced and similar image on a plane of small areas of terrain (up to 320 km2), within which the curvature of the Earth can be neglected. Topographic plans are created to scale

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

The points of the earth's surface are projected onto a mathematical surface - an ellipsoid or a plane along the normals, i.e. orthogonally (Fig. 1).

Rice. 1. Projection of points on the earth's surface onto a plane:

D is the slope distance; ν is the angle of inclination of the line; d is the horizontal distance; P - horizontal plane

The scale of the map, plan is the degree of reduction of horizontal projections - the laying of terrain lines (10 - 20) when depicted on a plane or, in other words, the ratio of the depicted line (1 ′ -2 ′) on the map or plan to its horizontal laying on the ground:

where M is the scale denominator.

For example, a scale of 1: 2000 means: one centimeter of the length of the line on the plan corresponds to 2000 centimeters on the ground in horizontal alignment. Recording the scale as a fraction with a numerator equal to one is called a numerical scale.

On topographic maps, for example, at a scale of 1:10,000, there is also an entry in the form of a phrase: “100 meters in 1 centimeter” - a named scale.

On maps and plans under the south side of the sheet indicate the numerical and named scales. In addition, the map shows a linear scale in the form of a scale, the divisions of which are signed (digitized) in accordance with the numerical scale.

The accuracy of the scale of the plan, map is the horizontal distance on the ground, corresponding to 0.1 mm on the plan, map.

1.2. Guidelines for the implementation of the work “Scales of topographic maps and plans. Measurement of line lengths on maps and plans"

Graphic constructions on paper when creating plans or maps are carried out with an accuracy of 0.1 mm. To obtain such accuracy in laying or measuring line lengths, transverse scale graphs are used, engraved on a special metal scale ruler or on the ruler of a geodetic protractor.

To build such a graph on a straight line, the segment AB is laid several times, called the base of the scale (Fig. 2). Usually, the segment AB \u003d 2 cm. Then, from this line, 10 more lines parallel to the base are drawn upwards at the same distance.

Rice. 2. Graph of the cross scale

From the ends of the segments of the base, perpendiculars are restored. Then the lower and upper bases of the AB scale are divided into 10 equal parts and oblique lines are drawn through the division points as shown in Fig. 2.

Depending on the scale of the plan or map, a special digitization of the graph is performed (see Fig. 2, digitization for a scale of 1:2000), but in any case, “zero” is set at point B. The resulting plot is called a cross-scale plot.

The AC line is a linear scale used to measure lines on maps. The smallest division ef of the transverse scale plot is 0.01 AB bases. A graph with a base AB \u003d 2 cm is called normal, since the segment ef is 0.2 mm (ef \u003d 0.01 AB \u003d 0.01 2 cm \u003d 0.2 mm) and it can be divided in half. Therefore, the accuracy of graphic constructions on paper is assumed to be 0.1 mm.

The accuracy of measuring or laying down the lengths of lines on maps, plans is determined by the formula:

t = 0.1 mm M, where M is the denominator of the map or plan scale.

To determine the horizontal position of the line on the plan (map), take this line into the solution of the measuring compass and transfer it to the bottom line of the graph so that the right needle of the meter is aligned with one of the perpendiculars, and the left one hits the base of the scale AB. Moving the gauge up so that the right needle remains perpendicular, note the position when the left needle touches the inclined line. In this case, both needles should be on the same horizontal line. The desired length will be obtained by summing the whole bases of the scale that fit between the needles, their tenths and hundredths.

On fig. 2 line length d mn, taken from the scale plan 1: 2000, has a length

d mn \u003d 80 m + 5 x 4 m + 7 x 0.4 m \u003d 102.8 m.

Measurement accuracy 0.2 m.

The graph of the transverse scale with a base of 2 cm is plotted on the ruler of a geodetic protractor and digitized for a scale of 1:500. On a special scale ruler, four graphs of a transverse scale with a base of 1, 2, 4 and 5 cm are plotted. Using such a ruler, the measurement or laying down of line lengths is performed without calculations, since all divisions of the graphs are multiples of 0.1 m; 1m; 10 m; 100 m line length on the ground for all standard scales.

1.3. Guidelines for the implementation of the work "Conventional signs for topographic plans." General information

Objects of the situation and terrain are depicted on topographic plans by conventional symbols, which are given in special tables of the book "Conventional symbols for topographic scale plans

1:5000, 1:2000, 1:1000 and 1:500". - M. Nedra, 1989.

Conventional signs are divided into areal (contour), linear and off-scale.

Areal (contour) conventional signs depict terrain objects that have contour dimensions, the area of ​​\u200b\u200bwhich is expressed on the scale of this plan. A conventional sign or an explanatory inscription is placed inside the contour, revealing the content of the object. The boundary (contour) of terrain objects can be a dotted line or a solid line.

Linear symbols are used to represent linear objects. In the scale of the plan for such objects, only the length is expressed. These are roads, power lines and communications, pipelines, etc.

Out-of-scale conventional signs depict terrain objects that are not expressed on the scale of the plan. This is how geodetic points, structures at railways and roads, poles of power lines and communications, wells, etc. are depicted. Extra-scale include explanatory conventional signs: inscriptions, numbers, signs of vegetation types. Most of the inscriptions on the plans are placed horizontally - parallel to the south side of the frame.

Paints are used to finish the plans. The black color is used to show the elements of the situation and the inscriptions. Pink and yellow (orange) colors are used to show paved surfaces (surfaces of roads, sidewalks, etc.). Areas occupied by forests and shrubs are painted in green, hydrography is shown in blue, relief is shown in brown.

Task for performing graphic work

Having got acquainted in the reading room of the university with the book "Conventional signs for topographic plans of scales 1:5000, 1:2000, 1:1000 and 1:500", students study and draw in pencil or, if desired, in color (ink, gel) on on an A4 sheet, the following symbols for plans at a scale of 1:2000, which will be used when performing graphic work on compiling a topographic plan (signs 5.1; 12; 13.2; 16.1; 115.5; 136; 155; 174.1; 193.1; 310; 314.2; 330.1; 366.1; 367.2; 368; 395.1; 401; 417; 475). Symbols are drawn according to size. The dimensions themselves are also indicated on the drawing.

The sizes of letters and numbers in conventional signs are taken according to Table. 116-118 of the book (signs 493, 494, 495). The rules for drawing conventional signs are given in the explanations on p. 121 - 254.

For the correct placement of the signature of the work, students study the sample design of plans according to Table. 87 book inserts. The height of lowercase letters in the signature of this and all subsequent graphic works is taken equal to 2 mm, capital letters and numbers - 3 mm.

1.4. The work report is:

– drawn cross-scale graph with a base of 5 cm for a scale of 1:2000;

– table of symbols;

– answers to control questions.

test questions

1. What is the scale of a map and plan?

2. How is the scale shown on maps and plans?

3. What is called the accuracy of the scale of the map, plan?

4. How to determine the accuracy of measuring the lengths of lines on a map or plan?

5. What is the sequence of work when measuring the length of a line on a map using measuring compass and linear scale?

6. How is a cross-sectional graph plotted?

7. What is the sequence of work when measuring the length of a line on a map (plan) using a meter and a scale bar?

8. What is the sequence of work when postponing the length of a line on paper using compass and scale ruler?

9. What are the features of transverse scale plots with a base of 2 cm and 5 cm?

10. Give examples of areal, linear and off-scale symbols.