Topographic maps and plans. Solving problems on topographic maps and plans. What does a topographic plan look like? Question about topographic plans and 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 a situation, terrain and other objects with their metric and technical specifications, 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 it won't 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 topographic works, 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 regulatory 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.

2.1. Topographic map elements

Topographic map - a detailed large-scale general geographic map that reflects 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 occur 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 data.

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 the 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 objects environment and their flat cartographic representation. This connection is transmitted using 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 ensure a high degree of measurability, the map must have sufficient geometric accuracy for specific purposes, which means the correspondence of the location, shape and size 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. The Swiss, German and Russian mathematician Leonhard 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 well-known Russian geodesist, Professor Nikolai Georgievich Kell, was the first in the USSR to use 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 side 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 a brief description of each 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?
    

Topographic maps and plans

topographic map plan relief

1. General information about topographic materials

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

A topographic plan is a reduced 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 set of terrain objects, a relief is a set 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 segments of the terrain (building structures, roads, hydrographic elements, etc.).

In the form of a plan, a number of construction drawings are drawn up, which are included in the design and technical documentation necessary for the construction of buildings and structures. Such drawings make it possible, as it were, to view reduced images of building structures from above.

The image of large areas of the earth's surface on a plane cannot be obtained without distortion, i.e., with the preservation of complete similarity. Such sections 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), they are transferred to the plane. The reduced image on the plane obtained in this way is called a map.

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

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 allocation of typical features of the area that determine its distinctive features, by means of generalizations - generalization, as well as the use of topographic conventional signs - a system of conventional symbols for depicting the earth's surface.

Maps and plans must be reliable, that is, the information that makes up their content on a certain date must be correct, corresponding to the state of the objects depicted on them. An important element of reliability is the completeness of the content, including the necessary amount of information and their versatility.

By purpose, topographic maps and plans are divided into basic and specialized. The main ones include maps and plans for nationwide 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. So, road maps contain a more detailed description of the road network. Specialized survey 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 required for the construction of underground and surface pipelines, roads and other communications.

2. Scale

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

The numerical scale is a fraction, the numerator of which is one, and the denominator is a number showing how many times the lines and objects are reduced when they are depicted 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 - a graphical expression of a numerical scale (Fig. 9). For building linear scale draw a straight line and on it several times lay the same distance in centimeters, 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 in the course of its growth, 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 scale bases.

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

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

Fig.9. Linear and numerical scales on topographic maps

parts, and also lay 10 equal parts on perpendiculars and draw lines parallel to the base through the points of deposition, as shown in Fig. 10. From the similarity of triangles BDE and Bde it follows 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. e. The smallest division of the transverse scale is equal to a hundredth of the base. On a scale with a base of 10 mm, you can determine the length of the 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 distance of normal vision (25 cm), one can estimate on the plan a size that does not exceed 0.1 mm (details of terrain objects less than 0.1 mm 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 0.05, 0.1, 0.2m, respectively. Scale accuracy determines the degree of generalization (generalization) of details that can be depicted on a plan (map) of one or another scale.

3.Uwords on plans and maps

Topographic maps and plans depict various objects of the area: the contours of settlements, orchards, orchards, lakes, rivers, road lines, power lines. The totality of these objects is called a situation. The situation is depicted by conventional signs.

Conventional signs, mandatory for all institutions and organizations compiling topographic maps and plans, are established by the Federal Service for Geodesy and Cartography of Russia (Roskartografiya) 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 outwardly resemble the appearance and nature of the objects depicted.

Conventional signs are divided into five groups: areal, linear, off-scale, explanatory, special.

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

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

Off-scale conventional signs are used to depict objects whose dimensions are not displayed on a given map or plan scale (bridges, kilometer posts, wells, geodetic points).

As a rule, off-scale signs determine the location of objects, but they cannot be used to judge their size. Various characteristics are given on the signs, for example: length 17 and width 3 m of a wooden bridge 12, mark 393,500 points of the geodetic network 16.

Explanatory symbols are digital and alphabetic inscriptions that characterize objects, for example: the depth and speed of the flow of rivers, the carrying capacity and width of bridges, the type of forest, the average height and thickness of trees, the width of highways. They are put down on the main areal, linear, off-scale signs.

Special conventional signs (Fig. 11, d) are established by the relevant departments of the sectors of the national economy; they are used to compile specialized maps and plans for this industry, for example, signs for mine surveying plans for oil and gas fields - oilfield facilities and installations, wells, field pipelines.

To make the map or plan more visual, 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 utilities (pipelines, cables) are colored.

4.Rterrain relief and ways of its representation. The steepness of the slopes

Terrain is a collection of irregularities in the earth's surface.

Depending on the nature of the relief, the terrain is divided into flat, hilly and mountainous. The flat terrain has mild forms or almost no irregularities at all; hilly is characterized by alternation of relatively small elevations and depressions; mountainous is an alternation of elevations over 500 m above sea level, separated by valleys.

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

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

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

A hollow or depression is a depression in the form of a bowl. The lowest point of the basin is the bottom. Its lateral surface consists of slopes, the line of their confluence with the surrounding area is called the edge.

Ridge 2 is a hill, gradually decreasing in one direction and having 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 lowering in one direction. The axis of the hollow between two slopes is called a spillway or thalweg 6. The varieties of the hollow are: a valley is a wide hollow with gentle slopes, and a ravine is a narrow hollow with almost steep slopes (cliffs 10). The initial stage of a ravine is a ravine. A ravine overgrown with grass and shrubs is called a beam. Sites sometimes located along the slopes of hollows, having the form of a ledge or steps 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 the characteristic lines of the relief. The characteristic points and lines of the relief facilitate the recognition of its individual forms on the ground and their depiction on the map and plan.

The method of depicting the relief on maps and plans should make it possible to judge the direction and steepness of the slopes, as well as determine the marks of points in the terrain. However, it must be visible. known various ways relief images: perspective, shading with lines of different thicknesses, color washout (mountains - brown, hollows - green), contour lines. From an engineering point of view, the most advanced methods of depicting a relief are horizontals in combination with signatures of characteristic points marks (Fig. 13) and digital.

A contour line is a line on a map that connects points of equal elevation. If we imagine a section of the Earth's surface by a horizontal (level) surface P 0, 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 a horizontal line. If the surface P 0 is located at a height H from the level surface, taken as the origin absolute heights, then any point on this horizontal will have an absolute elevation equal to H. The image in the contours of the relief of the entire area of ​​​​the terrain can be obtained as a result of cutting the surface of this area by a number of horizontal planes P 1, P 2, ... P n located at the same distance from each other . As a result, contour lines are obtained on the map with marks H + h, H + 2h, etc.

The distance h between the secant horizontal planes is called the height of the relief section. Its value is indicated on a map or plan under a 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 the location. The greater the laying, the less the steepness of the slope on the ground, and vice versa.

Rice. 13. Image of the terrain with contour lines

Property of contour lines: contour lines never intersect, with the exception of an overhanging cliff, natural and artificial funnels, narrow ravines, steep cliffs, which are not displayed by contour lines, 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 thicker the horizontal, the steeper the terrain depicted, and vice versa.

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

Images of a mountain and a basin (see Fig. 14, a, b), as well as a ridge and a 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, marks of characteristic points are signed, and so that the top of the numbers is directed towards the rise of 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 semi- and quarter horizontal lines are drawn, respectively, through half or a quarter of the accepted height of the relief section. Additional horizontals are shown with dotted lines.

To make it easier to read the contour lines on the map, 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 magnitude of the deposits on the map. The smaller the laying (distance between horizontals), the steeper the slope. To characterize the steepness of the slope on the ground, the angle of inclination 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 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 excess to the horizontal distance = h / d = tgν.

It follows from the formula that the slope is a dimensionless quantity. It is expressed as a percentage% (hundredths) or in ppm ‰ (thousandths).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.

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

:200, 1:100 and 1:50.

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

Rice. 15. Division of the map scale: 1:100000 into sheets of maps with scales 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 4º in latitude and 6º in longitude. Each sheet occupies only its own place, being indicated by a capital Latin letter, which determines the horizontal belt, and an Arabic numeral, which determines the number of the vertical column. For example, a map sheet 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 successively dividing a sheet of a map at a scale of 1: 1000000. One sheet of a map at a scale of 1:1,000,000 corresponds to: four sheets of a scale of 1:500,000, denoted by the letters A, B, C, D (the nomenclature of these sheets looks like, for example, N-37-A); nine sheets of scale 1:300000, denoted by Roman numerals I, II, ..., IX (for example, IX -N-37); 36 sheets of scale 1:200000, also indicated by Roman numerals (for example, N-37-I); 144 sheets at a scale of 1:100000, denoted by Arabic numerals from 1 to 144 (for example, N-37-144).

One sheet of the map 1:100000 corresponds to four sheets of the map at a scale of 1:50,000, denoted 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 the map 1:50000 corresponds to four sheets of the map at a scale of 1:25000, denoted by the letters a, b, c, d, for example N-37-144-A-a. One sheet of the map 1:25000 corresponds to four sheets of the map 1:10000, denoted by the numbers 1, 2, 3, 4, for example N-37-144-A-a-l.

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

The layout of sheets of large-scale plans is carried out in two ways. For surveying and drawing up plans over an area of ​​\u200b\u200bmore than 20 km 2, a sheet of a scale map is taken as the basis for the layout

:100000, which is divided into 256 parts for a scale of 1:5000, and each sheet of a scale of 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 at a scale of 1:2000 - N-37-144(256-I).

For site plans with an area of ​​​​less than 20 km 2, a rectangular layout is used (Fig. 16) for a scale of 1:5000 with a sheet frame of 40x40 cm, and for scales of 1:2000 ... 1:500 - 50x50 cm. A scale sheet is taken as the basis for a rectangular layout 1:5000 denoted by Arabic numerals (for example, 1). A sheet of a plan on a scale of 1:5000 corresponds to four sheets on a scale of 1:2000, denoted by the letters A, B, C, D. A sheet of a plan on a scale of 1:2000 corresponds to four sheets on a scale of 1:1000, denoted by Roman numerals, and 16 sheets in scale 1:500, denoted by Arabic numerals.

Rice. 16. Rectangular layout of the plan sheet

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

6. Solving problems on plans and maps

The geographical 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 the latitude through point A, draw a line parallel to the frames of the trapezium and take readings at the points of intersection with the scale of the western or eastern frame.

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

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

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

Rectangular coordinates X A and Y A of point A are determined relative to kilometer grid lines.

To do this, measure the distance ∆X and ∆Y along the 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.

The distances between points on plans and maps are determined using a linear or transverse scale, curvilinear segments - with a curvimeter device.

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

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 the meridian is difficult to draw, you can first determine the directional angle of the line, and then calculate the true and magnetic azimuths using the above formulas.

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

tg ν = h/a, (15.1)

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

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

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

i=tanv. (15.2)

The slope of the line is measured as a percentage 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 the slope of the slope is determined using the graphs (Fig. 19) of the scale of the foundations.

Rice. 19. Graphs of foundations to the plan on a scale of 1:1000 with a height of the relief section h = 1.0 m a - for slope angles; b - slopes.

To do this, they take the laying between two horizontals along a given slope from the plan, then, according to the schedule, they find the place where the distance between the curve and the horizontal line is equal to this laying. For the ordinate found in this way, the value of ν or i is read along a horizontal straight line (marked with asterisks in the graphs: ν \u003d 2.5º; i \u003d 0.05 \u003d 5% \u003d 50 ‰).

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

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

Interpolation consists in determining the coefficient of proportionality of the distance d from the determined point to the smaller horizontal H MG. ratio d/a, and multiplying it by the height of the relief section h.

Example 2. The mark of the point K, located between the contour lines with marks 150 and 152.5 m (Fig. 20, a),

H K \u003d H M. G + (d / a) h \u003d 150 + 0.4 ∙ 2.5 \u003d 151m.

Rice. 20. Determining the elevations of points along the horizontals: a ... d - schemes with a section height h = 2.5 m

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

Drawing a line of a given limit slope on the map (Fig. 21). Between the points A and B specified 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 limit slope on the map

The easiest way to solve the problem is to use the scale for the slopes. Taking on it with a solution of a compass the laying a pr corresponding to the slope, points 1 ... 7 are successively marked all the 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 limit slope is obtained. If there is no scale of foundations, then the foundation a pr can be calculated by the formula a pr \u003d 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 on the map; b - profile in the direction

Building a terrain profile along the direction specified on the map. Consider the construction of a profile on a specific example (Fig. 22). Let it be required to build a terrain profile along the line AB. To do this, the line AB is transferred to the scale of the map on paper and points 1, 2, 4, 5, 7, 9 are marked on it, in which it crosses the horizontal lines, as well as the characteristic points of the relief (3, 6, 8). Line AB serves as the base of the profile. Point marks taken from the map are laid 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 conditional horizon UG (in Fig. 22, a height equal to 100 m is taken as a conditional horizon).

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

Calculation of volumes (Fig. 23). Using a map with contour lines, one can calculate the volumes of a mountain and a basin, represented by a system of contour lines, closed within a small area. For this, the landforms are divided into parts bounded by two adjacent horizontals. Each such part can be approximately taken as a truncated cone, the volume of which is V \u003d (1/2) (Si + Si + I) h c , where Si and Si + I are the areas bounded on the map by the lower and upper horizontals, 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).

Approximately, the area of ​​a site can be determined by dividing it into a set of regular mathematical figures (trapezoids, triangles, etc.) and summing up by area. The volume V in the uppermost part is calculated as the volume of a cone, the area of ​​​​the base of which is S B and the height h is the difference between the marks of the upper point t and the horizontal bounding the base of the cone:

Rice. 23. Scheme for determining the volume

V B = (S B / 3)∙h

If the mark of the point t on the map is not signed, 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.

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

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

The graphical method includes a method of dividing the measured area into simple geometric shapes and a method based on the use of a palette.

In the first case, the area to be measured is divided into the simplest geometric figures (Fig. 24.1), the area of ​​\u200b\u200beach of which is calculated using simple geometric formulas, and the total area of ​​\u200b\u200bthe figure is determined as the sum of the areas of geometric partial figures:

Rice. 24. Graphical methods for measuring the area of ​​\u200b\u200ba 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. The areas of incomplete figures are taken into account by eye. The palette is made of transparent materials.

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

The mechanical method consists in 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 counting mechanism

At the end of the pole lever there is a weight with a needle - pole 2, the bypass lever has a counting mechanism 5 at one end, and a bypass index 3 at the other. 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 rotation of the counting drum. The drum is divided into 100 divisions. Tenths of the small division of the drum are evaluated according to 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. On fig. 25, b, the counting by the counting mechanism is 3682.

Rice. 26. Analytical method for measuring area

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

S = P(b - a)

To determine the division value of the planimeter, a figure is measured, the area of ​​\u200b\u200bwhich is known or which can be determined with great accuracy. Such a figure on topographic plans and maps is a square formed by grid lines. The division value of the planimeter P is calculated by the formula

P \u003d S izv / (b - a),

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

The analytical method consists in calculating the area from the results of measurements of angles and lines on the ground. Based on the measurement results, the coordinates of the X,Y vertices are calculated. The area P of the polygon 1-2-3-4 (Fig. 26) can be expressed in terms of 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 transformations, we obtain two equivalent formulas for determining the doubled area of ​​a polygon

2P \u003d 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 \u003d 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 are easily performed on any calculator.

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 instruments (plotters) led to the creation of automated systems for solving various engineering problems related to the design and construction of structures. Some of these tasks are solved using topographic plans and maps. In this regard, it became necessary to present and store information about the topography of the area in 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 given by the x and y coordinates of the points that determine the position of objects and terrain contours. The digital elevation model characterizes the topographic surface of the area. It is determined by some set of points with coordinates x, y, h, selected on the earth's surface so as to adequately reflect the nature of the relief.

Rice. Fig. 27. Scheme of location of points of the digital model in characteristic places of the relief and on contour 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 can look like a table of x, y, and H coordinate values ​​at the vertices of some grid of squares or regular triangles evenly spaced over the entire area of ​​the terrain. The distance between the vertices is chosen 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 (bends) of the relief (watersheds, thalwegs, etc.) or on contour lines (Fig. 27). Using the values ​​of the coordinates of the points of the digital terrain model for a more detailed description of it on a computer using a special program, the height of any point of the terrain is determined.

Literature

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

Budenkov N.A., Nekhoroshkov P.A. Course of engineering geodesy. - M.: Publishing house of MGUL, 2008.

Budenkov N.A., Shchekova O.G. The engineering geodesy. - Yoshkar-Ola, MarGTU, 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. Razumova. - M.: Higher school, 2008.

The engineering geodesy. / Ed. prof. D.Sh.Mikheleva. - 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, Mordovian State University, 2008.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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