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Laboratory work 1 Topic: Topographic maps and plans. Scale. Conventional signs. Linear measurements on topographic maps and plans Purpose: To become familiar 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. Conventional signs 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 calculation and graphic work)

1. Topographic plan and topographic map A topographic plan is a reduced and similar image on paper in conventional symbols of horizontal projections of the contours of objects and the relief of a small area of the terrain without taking into account the sphericity of the Earth. In terms of content, plans are of two types: contour (situational) - they depict only local objects; topographical – 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 the earth’s surface is shown in all its diversity; special for various purposes (soil map, map of peat deposits, vegetation map, etc.), on which individual elements are depicted with particular completeness - soils, peat deposits, vegetation, etc. Based on the scale, maps are conventionally divided into three types: small-scale (smaller than 1:); medium-scale (1: – 1:); large-scale (scale from 1: to 1:10,000); Scale of plans - larger 1: Topographic map - a reduced generalized image in 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 indicate various terrain objects on plans and maps are the same for all of Russia and, based on the nature of the image, are divided into 2 groups. Scale (area) symbols are used to depict objects that occupy a significant area and are expressed on the scale of a map or plan. An area symbol consists of a sign of the boundary of an object and icons or symbols that fill it. At the same time, local objects are depicted in accordance with 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. Out-of-scale are those conventional signs that depict local objects without observing the scale of a map or plan, which indicates only the nature and position of the object in space at its center (wells, geodetic signs, springs, pillars, etc.). These signs do not allow one to judge the size of the local objects depicted. For example, on a large-scale map the city of Tomsk is represented as an outline (to scale); on the map of Russia in the form of a point (not to scale).

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

3. Scales, accuracy of scale Horizontal projections of segments when drawing up maps and plans are depicted on paper in a reduced form, i.e. to scale. Map (plan) scale - 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 can be numerical or 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: 1 cm 20 m, 1 cm 10 m Using scales, you can solve the following problems. 1. Using the length of a segment on a plan of a given scale, determine the length of the line on the ground. 2. Using 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 increase the accuracy of measurements on maps and plans, graphic scales are used: linear (Fig. 1.2) and transverse (Fig.). Linear scale is a graphic representation of a numerical scale in the form of a straight line. To construct a linear scale, a number of segments of equal length are laid out on a straight line. The original segment is called the base of the scale (O.M.). The scale base is the conventionally accepted length of segments plotted along 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 estimate a segment with an accuracy of 0.1 fraction of the base accurately and up to 0.01 fraction of the base by eye (for a given scale) m 200 base

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

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

3. Scales, scale accuracy Accuracy of scale makes it possible to determine which terrain objects can be depicted on the plan and which cannot because of their small size. The opposite question is also being resolved: on what scale should a plan be drawn up so that objects measuring, for example, 5 m in size are depicted on the plan. In order to make a certain decision in a particular case, the concept of scale accuracy is introduced. In this case, they proceed from the physiological capabilities of the human eye. It is accepted that it is impossible to measure the distance using a compass and a scale ruler more accurately than 0.1 mm on this scale (this is the diameter of a circle from a sharpened needle). Therefore, the maximum scale accuracy is understood as the length of a segment on the ground corresponding to 0.1 mm on a plan of a given 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 at a given scale to 0.2 mm on the plan, is called the graphic scale accuracy. Therefore, at this scale (1:2000), the smallest differences that can be identified graphically are 0.4 m. The accuracy of the transverse scale is the same as the accuracy of the graphical scale.

4. Linear measurements on topographic maps and plans Segments, the length of which is determined from a map or plan, can be rectilinear or 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 assessing the accuracy of linear measurements, it should be taken into account that with a ruler you can measure a segment with a length of at least 0.5 mm - this is the magnitude of the error in linear measurements using a ruler 2. measuring compass and linear scale; 3. measuring compass and transverse scale.

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

4. Linear measurements on topographic maps and compass and transverse scale plans digitize the transverse scale (normal) at the map scale (in this case 1:10000): Fig. Measuring a segment using a transverse scale We record in the following form 974.2 m 0 .0 7 o. m. 0.001 o.m. 0.8 o.m o.m.

5. Constructing segments of a given length using a transverse scale Let you need to plot on a map of a scale of 1:5000 a segment whose length is 173.3 m. 1. Make a painting in accordance with the map scale (1:5000): 2. Calculate the number of integers, tenths, hundredths and thousandths of a base scale. 3. Using a transverse scale, type on the measuring compass the calculated number of whole, tenths, hundredths and thousandths of the bases of the scale. 4.Draw a segment on paper - pierce a sheet of paper and circle the resulting two points. The diameter of the circles is 2-3 mm. Length of the segment Fig. 6. Drawing up a segment of a given length on paper

6. Measuring the length of broken and curved segments Measuring broken segments is carried out in parts or by increasing the method (Fig. 7): install the legs of the meter at points a and b, lay the ruler in the direction b-c, move the leg of the meter from point a to point a1, add a segment b-c, etc. a a1a1 a3a3 c d d b a2a2 Fig. 7. Measuring the length of broken segments using the extension method Measuring curved segments is possible in several ways:. 1.using a curvimeter (approximate); 2.extension method; 3.meter with a constant solution.

7. Solving problems 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 maximum and graphic accuracy of a scale of 1:1000; 1: Using a measuring compass and a normal transverse scale, mark a segment of 74.4 m on a sheet of paper on a scale of 1:2000. (1415 m on a scale of 1:25000) 6. Using a transverse scale, determine the distance between the absolute marks of the points - 129.2 and 122.1 (the square of the training map). (141.4 and 146.4 (square 67-12). 7. Measure the length of the stream (to the Golubaya River) (square 64-11) using a curvimeter and a measuring compass with a solution of 1 mm. Compare the results. 8. Horizontal the distance between two points on the M 1:1000 plan is 2 cm. Determine the distance between these points on the ground.

List of references 1. Methodological instructions for performing laboratory work in the discipline “Geodesy and Topography” for full-time students in the areas of “Geophysical methods of prospecting and exploration of mineral deposits” and “Geophysical methods of well exploration”. – Tomsk: ed. TPU, 2006 – 82 p. 2. Fundamentals of geodesy and topography: textbook / V.M. Perederin, N.V. Chukhareva, N.A. Antropova. – Tomsk: Publishing house of Tomsk Polytechnic University, p. 3. Conventional signs 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.

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

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

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

What is a topographical plan of a land plot?

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

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

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

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

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

All materials and measurements are processed using specialized licensed software.

Why is a topographic plan needed?

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

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

Documents required for ordering a topographic plan

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

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

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

What does a topographic plan look like?

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

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

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

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

Accuracy of topographic plans

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

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

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

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

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

Based on content and purpose, geographic maps are divided into special and general geographic.

Special maps show contours and special loads (mineral map, physical world map, political map, flora and fauna map, economic map).

General geographic maps show the situation and relief.

General geographic maps smaller than 1: 1,000,000 are called overview maps.

General geographic maps at a scale of 1: 1,000,000 and larger are called topographic maps.

Topographic maps, plans and differences between them

Topographic maps are created in the zonal equiangular transverse cylindrical projection of K.F. Gauss-Kruger, calculated on the reference ellipsoid F.N. Krasovsky in the state coordinate system of 1942 in the 6° zone. And the plans are on a scale of 1: 5,000 and larger in the 3° zone. The heights of the points are determined in the absolute Baltic system of heights from the zero of the Kronstadt footstock.

MAP - a reduced and generalized image constructed in a cartographic projection on the plane of the entire Earth or part of it, taking into account the curvature of the Earth.

Mapping begins with the construction of a cartographic grid, within which the situation and relief are depicted with conventional symbols.

The cartographic grid is a network of parallels and meridians.

PLAN - a reduced and similar image of the projection of a small area of terrain on a plane without taking into account the curvature of the Earth.

Drawing up a plan begins with the construction of a coordinate grid, within which, based on the results of field surveys, the situation and relief are depicted using conventional signs.

Coordinate grid - mutually perpendicular lines on the map, forming squares, the sides of which are parallel to the X and Y axes (i.e. the central meridian and the equator.)

Plans are divided into contour (situational) and topographical.

Contour plans are plans that show only the contours of the terrain without depicting the relief.

Topographical - plans that depict both the situation of the area and the relief.

Differences between a map and a plan:

1. The plan is based on a coordinate grid.

Map - based on a cartographic grid.

2. Plan - an image of a small area of the Earth without taking into account the curvature of the Earth.

A map is a depiction of the entire Earth or a large area of the Earth, taking into account the curvature of the Earth.

3. The plan shows only a rectangular coordinate system.

There are two coordinate systems on the map: rectangular and geographic.

Presentation on the topic: Topographic maps and plans. Scale. Conventional signs. Linear measurements on topographic maps and plans

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Presentation on the topic: Topographic maps and plans. Scale. Conventional signs. Linear measurements on topographic maps and plans

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Laboratory work No. 1 Topic: Topographic maps and plans. Scale. Conventional signs. Linear measurements on topographic maps and plans Purpose: To become familiar with topographic maps and plans, scales, types of symbols. Master the measurement and construction of segments using graphic scales Work plan: Topographic plan and topographic map Conventional signs Scales, scale accuracy Linear measurements on topographic plans and maps Construction of segments of a given length using a transverse scale Measuring the length of broken and curved segments Homework (Individual calculation and graphic work)

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1. Topographic plan and topographic map A topographic plan is a reduced and similar image on paper in conventional symbols of horizontal projections of the contours of objects and the relief of a small area of the terrain 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; topographical - local objects and relief are depicted.

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1. Topographic plan and topographic map A topographic map is a reduced generalized image in 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. According to the content of the map, there are the following types: general geographical - they show the earth’s surface in all its diversity; special ones for various purposes (soil map, peat deposit map, vegetation map, etc.), on which individual elements are depicted with particular completeness - soils, peat deposits, vegetation, etc. Maps are conventionally divided by scale into three types: small-scale (smaller than 1:1,000,000); medium-scale (1:1,000,000 - 1:200,000); large-scale (scale from 1:100,000 to 1:10,000); Plan scales - larger than 1:10,000 .

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2. Conventional signs Conventional signs that are used to designate various terrain objects on plans and maps are the same for the whole of Russia and, according to the nature of the image, are divided into 2 groups. Scale (area) conventional signs are used to depict objects that occupy a significant area and are expressed on a scale map or plan. An area symbol consists of a sign of the boundary of an object and icons or symbols that fill it. In this case, terrain objects are depicted in accordance 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. Non-scale symbols are those conventional signs by which terrain objects are depicted without observing the scale of the map or plan, which only indicates the nature and position of the object in space along its center (wells, geodetic signs, springs, pillars, etc.). These signs do not allow one to judge the size of the local objects depicted. For example, on a large-scale map the city of Tomsk is represented as an outline (to scale); on the map of Russia in the form of a point (not to scale).

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

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3. Scales, accuracy of scale Horizontal projections of segments when drawing up maps and plans are depicted on paper in a reduced form, i.e. to scale. The scale of the map (plan) is 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 can be numerical or 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: 1 cm 20 m, 1 cm 10 m Using scales you can solve the following problems.1. Using the length of a segment on a plan of a given scale, determine the length of the line on the ground. 2. Using the length of the horizontal projection of the line, determine the length of the corresponding segment on the scale plan.

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3. Scales, scale accuracy In order to avoid calculations and speed up work, as well as increase the accuracy of measurements on maps and plans, graphic scales are used: linear (Fig. 1.2) and transverse (Fig.). Linear scale is a graphic representation of a numerical scale in the form straight line. To construct a linear scale, a number of segments of the same length are laid out on a straight line. The original segment is called the base of the scale (O.M.). The scale base is the conventionally accepted length of segments plotted along 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 estimate a segment with an accuracy of 0.1 fraction of a base accurately and up to 0.01 fraction of a base by eye (for a given scale).

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3. Scales, scale accuracy For more accurate measurements, use a transverse scale, which has an additional vertical construction on a linear scale. Transverse scaleAfter laying down the required number of scale bases (usually 2 cm long, and then the scale is called normal), perpendiculars to the original line are restored and divided into equal segments (m parts). If the base is divided into n equal parts and the division points of the upper and lower base are connected by inclined lines as shown in the figure, then a segment. The transverse scale allows you to estimate the segment exactly 0.01 fractions of the base, and up to 0.001 fractions of the base - by eye.

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

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

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

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4. Linear measurements on topographic maps and compass and transverse scale plans digitize the transverse scale (normal) at the map scale (in this case 1:10000):Fig. 1.4. Measuring a segment using a transverse scale We record it in the following form

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5. Constructing segments of a given length using a transverse scale Let it be necessary to plot on a map of a scale of 1:5000 a segment whose length is 173.3 m. Make a painting in accordance with the map scale (1:5000): 2. Calculate the number of whole, tenths, hundredths and thousandths of bases of scale. Using a measuring compass, use a transverse scale to dial the calculated number of whole, tenths, hundredths and thousandths of bases of scale. Draw a segment on paper - pierce a sheet of paper and circle the resulting two points. The diameter of the circles is 2-3 mm.

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6. Measuring the length of broken and curved segments Measuring broken segments is carried out in parts or by increasing the method (Fig. 7): install the legs of the meter at points a and b, lay the ruler in the direction b-c, move the leg of the meter from point a to point a1, add a segment b-c, etc. Measuring curved segments is possible in several ways:. using a curvimeter (approximate); extension method; meter with a constant solution.

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7. Solving problems 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) Write a named scale corresponding to the numerical scale 1:500, 1:25000. (1:2000, 1:10000)On a 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. Determine the maximum and graphic accuracy of a scale of 1:1000; 1:5000.Using a measuring compass and a normal transverse scale, mark a segment of 74.4 m on a sheet of paper on a scale of 1:2000. (1415 m on a scale of 1:25000) Using a transverse scale, determine the distances between the absolute marks of points - 129.2 and 122.1 (square 67-12 of the training map). (141.4 and 146.4 (square 67-12). Measure the length of the stream (to the Golubaya River) (square 64-11) using a curvimeter and a measuring compass with a solution of 1 mm. Compare the results. Horizontal distance between two points on the plan M 1:1000 is 2 cm. Determine the distance between these points on the ground.

Slide description:

List of references Guidelines for performing laboratory work in the discipline “Geodesy and Topography” for full-time students in the areas 130201 “Geophysical methods of prospecting and exploration of mineral deposits” and 130202 “Geophysical methods of well exploration.” – Tomsk: ed. TPU, 2006 – 82 pp. Fundamentals of geodesy and topography: textbook / V.M. Perederin, N.V. Chukhareva, N.A. Antropova. – Tomsk: Tomsk Polytechnic University Publishing House, 2008. -123 pp. Conventional signs 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, 1989. -286 p.

Transcript

1 Ministry of Education and Science of the Russian Federation Federal State Budgetary Educational Institution of Higher Professional Education Altai State Technical University named after. I.I. Polzunova I.V. Karelina, L.I. Khleborodova Topographic maps and plans. Solving problems on topographic maps and plans Guidelines for conducting laboratory work, practical classes and for self-help students studying in the areas of “Construction” and “Architecture” Barnaul, 2013

2 UDC Karelina I.V., Khleborodova L.I. Topographic maps and plans. Solving problems using topographic maps and plans. Methodological instructions for conducting laboratory work, practical classes and for self-help students studying in the areas of “Construction” and “Architecture” / Alt. state tech. University named after I.I. Polzunov. - Barnaul: AltSTU, p. The guidelines discuss solutions to a number of engineering problems performed using maps: determining geographic and rectangular coordinates, reference angles, constructing a profile along a given line, determining slopes. The procedure for performing laboratory work (practical tasks) 1, 2 and assignments for SRS is described in detail. Samples of their design are provided. Methodological guidelines were discussed at a meeting of the department “Foundations, foundations, engineering geology and geodesy” of the Altai State Technical University named after. I.I. Polzunov. Protocol 2 from

3 Introduction Maps and plans serve as the topographic basis necessary for a civil engineer to solve problems related to industrial and civil housing construction, the construction of agricultural, hydraulic, thermal power, road and other types of construction. A number of engineering problems are solved using topographic maps and plans: determining distances, elevations, rectangular and geographical coordinates of points, reference angles, constructing a line profile in a given direction, etc. Having studied the symbols, you can determine the nature of the terrain, the characteristics of the forest, the number of settlements, etc. .d. The purpose of the guidelines is to teach students to solve problems using topographic maps and plans that are necessary in engineering practice for builders. 1. Topographic plans and maps When depicting a small area of the earth's surface with a radius of up to 10 km, it is projected onto a horizontal plane. The resulting horizontal spaces are reduced and applied to paper, i.e. they receive a topographical plan, a scaled-down and similar image of a small area of terrain, built without taking into account the curvature of the Earth. Topographic plans are created at large scales of 1:500, 1:1,000, 1:2,000, 1:5,000 and are used for master plans, technical designs and construction drawings. Plans are limited to cm or cm square frames oriented north. When depicting significant territories on a plane, they are projected onto a spherical surface, which is then expanded into a plane using image construction methods called cartographic projections. In this way, a topographic map is obtained - a reduced, generalized and constructed according to certain mathematical laws image on the plane of a significant area of the earth's surface, taking into account the curvature of the earth. The boundaries of the map are true meridians and parallels. A grid of geographic coordinates of lines of meridians and parallels, called a cartographic grid, and a grid of rectangular coordinates, called a coordinate grid, are applied to the map. Cards are conventionally divided into: 3

4 - large-scale - 1:10,000, 1:25,000, 1:50,000, 1: , - medium-scale - 1: , 1: , 1: , - small-scale - smaller 1: According to the content, maps are divided into geographical, topographical and special . 2. Scales Scale is the ratio of the length of a line on a plan or map to the horizontal location of the corresponding line on the ground. In other words, scale is the degree to which the horizontal distances of the corresponding segments on the ground are reduced when depicting them on plans and maps. Scales can be expressed in either numerical or linear forms. The numerical scale is expressed as a fraction, the numerator of which is one, and the denominator is a number showing how many times the horizontal lines on the ground are reduced when they are transferred to a plan or map. In general, 1:M, where M is the denominator of the scale d M d where d m is the horizontal location of the line on the ground; d k(p) - the length of this line on the map or plan. For example, scales of 1:100 and 1:1,000 indicate that the image on the plans is reduced in comparison with reality by 100 and 1000 times, respectively. If on a plan of scale 1:5000 the line ab = 5.3 cm (d p), then on the ground the corresponding segment AB (d m) will be equal to 4 m k(p), d m = M d p, AB = .3 cm = cm = 265 m. Numerical scales can be expressed in named form. So scale 1: in the named form it will be written: 1 cm of the plan corresponds to 100 m on the ground or 1 cm 100 m. Simpler, not requiring calculations, are graphic scales: linear and transverse (Figure 1).

5 Figure 1 Scales: a linear, b - transverse The linear scale is a graphical representation of the numerical scale. A linear scale is a scale in the form of a straight line segment divided into equal parts - the base of the scale. As a rule, the scale base is taken 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 minor divisions. Minor division is equal to 0.1 part of the base, i.e. 0.1 cm. The base of the scale will correspond to 10 m on the ground, the small one will be 1 m. The distance taken from the map with a solution of a compass-measuring device is transferred to a linear scale so that one needle of the compass-measuring device coincides with any whole stroke to the right of the zero stroke, and on the other, the number of small divisions of the left base is counted. In Figure 1-a, the distances measured on a 1:1,000 scale plan are 22 m and 15 m. In order to avoid estimating the fractions of small divisions by eye and thereby increase the accuracy of working with a plan or map, a transverse scale is used. It is built as follows. On a straight line, a scale base equal to, as a rule, 2 cm is laid several times. The leftmost base is divided into 10 equal parts, i.e. 5

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

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

8 the corresponding segment on the plan at a scale of 1:2000, using a transverse scale. Solution: On this scale, the base corresponds to 40 m, the minor division is 4 m, the smallest division is 0.4 m. In the length of the line CD, there are 6 integer bases, 2 integer small divisions, and 7 smallest divisions. Let’s check 6 40 m m + 7 0.4 m = 240 m + 8 m + 2.8 m = 250.8 m. 3. Layout and nomenclature of maps The division of topographic maps into sheets is called layout. For ease of use of maps, each sheet of the map receives a specific designation. The designation system for individual sheets of topographic maps and plans is called nomenclature. The layout and nomenclature of maps and plans is based on a map of scale 1: To obtain a sheet of such a map, the globe is divided by meridians through 6 in longitude into columns and parallels through 4 in latitude into rows (Figure 2-a). The dimensions of map sheet 1 are assumed to be the same for all countries. The columns are numbered in Arabic numerals from 1 to 60 from west to east, starting from the meridian with longitude 180. The rows are designated by capital letters of the Latin alphabet from A to V, starting from the equator to the north and south poles (Figure 2-b). FOR THE NORTHERN HEMISPHERE OF THE EARTH Figure 2-a - Scheme of layout and nomenclature of sheets of scale 1 maps:

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

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

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

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

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

14 A mountain has its own peak, slopes and base. The top of a mountain is its highest part. The top is called a plateau if it is flat, and a peak or hill if it is pointed. The side surface of a mountain is called a slope or ramp. Mountain slopes are gentle, sloping and steep, up to 5, 20 and 45, respectively. A very steep slope is called a cliff. The foot or sole of a mountain is the line separating the slopes and the plain. A basin is a bowl-shaped concave part of the earth's surface. The basin has a bottom, its lowest part, slopes directed from the bottom in all directions, and an edge - the line where the slopes transition into the plain. A small basin is called a depression. A ridge is a hill extending in one direction. The main elements of the ridge are the watershed line, slopes and soles. The watershed line runs along the ridge, connecting its highest points. A hollow, in contrast to a ridge, is a depression extended in one direction. It has a drainage line, slopes and an edge. The types of hollow are valley, gorge, ravine and ravine. A saddle is a bend in a ridge between two peaks. Some relief details (mounds, pits, quarries, screes, etc.) cannot be depicted as horizontal lines. Such objects are shown on maps and plans with special symbols. In addition to contour lines and symbols, the heights of characteristic points are indicated on the map (Figure 8-a): on the tops of hills, on the bends of watersheds, on saddles. 6. Conventional signs The content of maps and plans consists of graphic symbols - conventional signs. These symbols superficially resemble the shape of the corresponding elements of the situation. The clarity of conventional signs reveals the semantic content of the depicted objects and allows you to read a map or plan. Conventional signs are divided into areal (scale), non-scale, linear and explanatory (Figure 9). Scale or contour conventional signs are such conventional signs with the help of which elements of the situation, i.e. terrain objects are depicted on a plan scale in compliance with their actual sizes. For example: the outline of meadows, forests, gardens, vegetable gardens, etc. The boundary of the contour is shown as a dotted line, and inside the contour there is a symbol. Conventional off-scale signs are used to depict terrain objects that are not expressed on the scale of a map or plan. For example: a monument, a spring, a separate tree, etc. 14

15 Large-scale Fruit and berry garden Linear Communication line Wasteland Meadow Power line Main gas pipeline Shrub Clearings Birch forest Vegetable garden Non-large-scale Kilometer pillar Windmill Free-standing broad-leaved tree Figure 9 Conventional signs Linear symbols are used to depict linear objects, the length of which is expressed on the scale of a plan or map. For example: road network, trails, power and communication lines, streams, etc. Explanatory symbols supplement the above-mentioned symbols with digital data, icons, and inscriptions. They allow you to read the map more completely. For example: depth, river flow speed, bridge width, forest type, road width, etc. Symbols of topographic maps and plans of various scales are published in the form of special tables. 7. Design of a topographic map sheet Let's consider a schematic representation of a topographic map sheet on a scale of 1: (Figure 10). The sides of the map sheet are segments of meridians and parallels and form the inner frame of this sheet, which has the shape of a trapezoid. In each corner of the frame its latitude and longitude are indicated: the latitude and longitude of the southwestern corner are, respectively, 54 15" and 38 18"45", the northwestern "30 and 38 18"45", the southeastern "and 38 22 "30, northeast "30 and 38 22"30. 15

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

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

18 Latitude is the angle formed by a plumb line and the plane of the equator (Figure 11). Latitude is measured north and south of the equator and is called north and south latitude, respectively. Longitude is the dihedral angle formed by the plane of the prime meridian passing through the Greenwich (prime) meridian and the plane of the meridian of a given point. Longitude is measured east or west from the prime meridian and is called eastern and western longitude accordingly. On each sheet of the map the longitude and latitude of the corners of the sheet frames are labeled (see paragraph 7). Figure 11 Geographic coordinates The latitude of the 1:10,000 map sheet shown in Figure 12 varies from 54 45" (south frame) to 54 47" 30 (north frame), i.e. the difference in latitude is 2"30. Longitude varies from 18 07"30" (western frame) to 18 11"15 (eastern frame), i.e. the difference in longitude is 3"45". To determine the geographic coordinates of point A, true meridians and parallels are drawn: i.e. lines drawn at the same minute intervals on opposite sides of the frame, and from these lines the values of geographic coordinates are determined. Fractions of minutes or seconds are estimated graphically. In Figure 12, for point A, a parallel with latitude = 54 45"20 and a meridian with longitude = are drawn. The increments of geographic coordinates from these parallels and the meridian are evaluated graphically: = 9", = 8". As a result, A = 54 45"20 + = 54 45 "29, A = = The latitude and longitude of a point can be determined in another way. It is necessary to draw a true meridian and parallel through point B. To determine longitude, minutes and seconds are counted along the northern or southern minute frames of the map from the western corner and add it to the longitude of the western corner of the frame: B =

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

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

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

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

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

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Orientation of lines. Direct and inverse geodetic problems on the plane. To orient a line on the ground means to determine its position relative to another direction, taken as the original one. As

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PRACTICAL WORK 1 Determination of directions, distances, areas, geographic and rectangular coordinates, heights of points on a topographic map Work goal: to develop the ability to use topographic

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Laboratory work 6 Topic: Office processing of theodolite survey results and drawing a situational plan Purpose: Plan: Master the processing of the theodolite survey log. Learn to build a situational

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Relief of the earth's surface and its image on topographic maps Relief is the totality of all the irregularities of the earth's surface, different in shape and size. Relief is the main component

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Assignment 1 Topic: “Topographic maps” (4 hours of classroom + 4 hours of independent work) Topic: “Layout and nomenclature of topographic maps.” Goal: To master the technique of obtaining and designating topographic

Federal Agency for Railway Transport Ural State Transport University Department of Bridges and Transport Tunnels B. G. Chernyavsky SOLUTION OF GEODETIC AND ENGINEERING PROBLEMS

Purpose: To become familiar with the method of depicting relief on topographic maps and plans. Study the basic elementary forms of relief, their mutual transition into each other. Master the definition of excesses and absolute

Federal Agency for Education Tomsk State University of Architecture and Civil Engineering SCALE Guidelines for laboratory work Compiled by V.I. Kolupaev Tomsk 2009 Scale: methodological

MINISTRY OF EDUCATION AND SCIENCE OF THE RUSSIAN Federal State Budgetary Educational Institution of Higher Professional Education "Ukhta State Technical University" (USTU) SOLVING PROBLEMS ON TOPOGRAPHIC

Test 1 “Scale + Working with a topographic map” 1. What is scale? 2. List the types of scales. 3. What is precision and extreme precision of scale? 4. Given: on the ground, the length of the line is 250 m.

Ministry of Education and Science of the Russian Federation Moscow State University of Geodesy and Cartography S.V. Shvets, V.V. Taran Geodesy. Topographic maps Recommended by educational and methodological

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The work program of the academic discipline was developed on the basis of the Federal State Educational Standard for Specialties of Secondary Vocational Education (hereinafter referred to as SPO) 10701.51 “Land Management”

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