What are topographic maps and plans? What does a topographic plan look like? Questions and tasks for self-control
Transcript
1 Ministry of Education and Science of the Russian Federation Federal State Budgetary Educational Institution of Higher Professional Education Altai State Technical University them. 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 geographic coordinates of points, reference angles, constructing a line profile in a given direction, etc. Having studied the symbols, you can determine the nature of the terrain, characteristics of the forest, population settlements etc. 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 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 reduced version, and a similar image of a small area of terrain, constructed without taking into account the curvature of the Earth. Topographic plans are created on large scales 1:500, 1:1 000, 1:2 000, 1:5 000 and are used to compile master plans, technical projects and drawings to support construction. Plans are limited to cm or cm square frames oriented north. When depicting significant territories on a plane, they are projected onto a spherical surface, which is then expanded into a plane using image construction methods called cartographic projections. In this way, a topographic map is obtained - a reduced, generalized and constructed according to certain mathematical laws image on the plane of a significant area of the earth's surface, taking into account the curvature of the Earth. The boundaries of the map are true meridians and parallels. A grid of geographic coordinates of lines of meridians and parallels, called a cartographic grid, and a grid of rectangular coordinates, called a coordinate grid, are applied to the map. Cards are conventionally divided into: 3
4 - large-scale - 1:10,000, 1:25,000, 1:50,000, 1: , - medium-scale - 1: , 1: , 1: , - small-scale - smaller 1: According to the content, maps are divided into geographical, topographical and special . 2. Scales Scale is the ratio of the length of a line on a plan or map to the horizontal location of the corresponding line on the ground. In other words, scale is the degree to which the horizontal distances of the corresponding segments on the ground are reduced when depicting them on plans and maps. Scales can be expressed in either numerical or linear forms. The numerical scale is expressed as a fraction, the numerator of which is one, and the denominator is a number showing how many times the horizontal lines on the ground are reduced when they are transferred to a plan or map. In general, 1:M, where M is the denominator of the scale d M d where d m is the horizontal location of the line on the ground; d k(p) - the length of this line on the map or plan. For example, scales of 1:100 and 1:1,000 indicate that the image on the plans is reduced in comparison with reality by 100 and 1000 times, respectively. If on a plan of scale 1:5000 the line ab = 5.3 cm (d p), then on the ground the corresponding segment AB (d m) will be equal to 4 m k(p), d m = M d p, AB = .3 cm = cm = 265 m. Numerical scales can be expressed in named form. So scale 1: in the named form it will be written: 1 cm of the plan corresponds to 100 m on the ground or 1 cm 100 m. Simpler, not requiring calculations, are graphic scales: linear and transverse (Figure 1).
5 Figure 1 Scales: a linear, b - transverse The linear scale is a graphical representation of the numerical scale. A linear scale is a scale in the form of a straight line segment divided into equal parts - the base of the scale. As a rule, the scale base is taken to be 1 cm. The ends of the bases are signed with numbers corresponding to distances on the ground. Figure 1-a shows linear scale with a base of 1 cm for numerical scale 1: The left base is divided into 10 equal parts, called minor divisions. Minor division is equal to 0.1 part of the base, i.e. 0.1 cm. The base of the scale will correspond on the ground to 10 m, the small one to 1 m. The distance taken from the map with a solution of a compass-measuring device is transferred to a linear scale so that one needle of the compass-measuring device coincides with any whole stroke to the right of the zero stroke, and on the other, the number of small divisions of the left base is counted. In Figure 1-a, the distances measured on a 1:1,000 scale plan are 22 m and 15 m. In order to avoid estimating the fractions of small divisions by eye and thereby increase the accuracy of working with a plan or map, a transverse scale is used. It is built as follows. On a straight line, a scale base equal to, as a rule, 2 cm is laid several times. The leftmost base is divided into 10 equal parts, i.e. 5
6, the small division will be equal to 0.2 cm. The ends of the bases are signed in the same way as when constructing a linear scale. Perpendiculars with a length of mm are restored from the ends of the bases. The outermost ones are divided into 10 parts and 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 at a given scale to 0.01 cm on a plan or map is called the graphic accuracy of the scale t or simply the accuracy of the scale t cm = 0.01 cm M, where M is the denominator of the scale. So, for a scale of 1:1000, the accuracy is t cm = 0.01 cm 1000 = 10 cm, for a scale of 1:500 5 cm, 1: cm, etc. This means that segments smaller than those indicated will no longer be depicted on a plan or map of a given scale. The maximum accuracy t pr is equal to triple the accuracy of the scale t pr = 3 t. Using the scale, two problems are solved: 1) using measured segments on a plan or map, the corresponding segments on the ground are determined; 2) using the measured distances on the ground, the corresponding segments are found on the plan or map. Let's consider the solution to the second problem. The length of the line CD d CD = 250.8 m was measured on the ground. Determine 7
8 the corresponding segment on the plan at a scale of 1:2000, using a transverse scale. Solution: On this scale, the base corresponds to 40 m, the small division is 4 m, the smallest division is 0.4 m. In the length of the line CD, there are 6 whole bases, 2 whole small divisions, and 7 smallest divisions. Let’s check 6 40 m m + 7 0.4 m = 240 m + 8 m + 2.8 m = 250.8 m. 3. Layout and nomenclature of maps The division of topographic maps into sheets is called layout. For ease of use of maps, each sheet of the map receives a specific designation. The designation system for individual sheets of topographic maps and plans is called nomenclature. The layout and nomenclature of maps and plans is based on a scale 1 map: To obtain a sheet of such a map Earth is divided by meridians through 6 in longitude into columns and by 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 Mr. Nomenclature plans Sheet of map of scale 1: corresponds to 256 sheets of plan of scale 1:5,000, which are designated by Arabic numerals from 1 to 256. These numbers are assigned in parentheses to the nomenclature of sheet 1: For example, N (256). One sheet of a plan at a scale of 1:5,000 corresponds to 9 sheets of a plan at a scale of 1:2,000, which are designated by lowercase letters of the Russian alphabet a, b, c, d, d, f, g, h, i. For example: N (256). When creating topographic plans for areas up to 20 km2, a rectangular layout (conditional) can be used. In this case, it is recommended to use a tablet as a basis for the layout - a sheet of map plan - 11
12 headquarters 1:5 000 with frame dimensions cm or m and designate it in Arabic numerals, for example 4. One sheet of plan of scale 1:5 000 corresponds to 4 sheets of plan of scale 1:2 000, which are designated by capital letters of the Russian alphabet. Nomenclature of the last sheet of the scale 1 plan: G (Figure 6). One sheet of a plan of scale 1:2,000 corresponds to 4 sheets of scale 1:1,000, which are designated by Roman numerals I, II, III, IV. For example: 4-B-II. To determine the nomenclature of a 1:500 scale plan sheet, divide the 1:2,000 scale plan sheet into 16 sheets and designate them with Arabic numerals from 1 to 16. For example: 4-B Figure 6 Rectangular layout and nomenclature of 1:5,000 scale plan sheets, 1 :1,000 and 1:500 The numbering order for tablets at a scale of 1:5,000 is established by organizations that issue permits for topographic and geodetic work. 5. Relief The totality of irregularities in the physical surface of the Earth is called relief. To depict the relief on plans and maps, shading, dotted lines, colors (coloring), and shading are used, but most often the method of contour lines is used (Figure 7). The essence of this method is as follows. The surface of a section of the Earth at equal intervals h is mentally dissected by horizontal planes A, B, C, D, etc. The intersections of these planes with the surface of the Earth form curved lines called horizontals. In other words, a horizontal line is a closed curved line connecting 4 Figure 7 Image of the terrain with horizontal lines
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 minute intervals of the same name 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. Zones are counted from the Greenwich meridian to the east (Figure 13).When constructing an image of each zone on a plane, the following conditions are observed (Figure 14): - the axial meridian is transferred to the plane in the form of a straight line without 19
20 distortions: - the equator is depicted as a straight line perpendicular to the axial meridian; - other meridians and parallels are depicted by curved lines; - in each zone a zonal system of flat rectangular coordinates is created: the origin of coordinates is the point of intersection of the axial meridian and the equator. The axial meridian is taken as the abscissa axis, and the equator as the ordinate axis. Lines parallel to the axial meridian and the equator form a rectangular coordinate grid, which is printed on topographic maps. At the exits of the coordinate grid beyond the map frame, the x and y values are indicated in whole kilometers. In order not to use negative coordinate values (in the western part of the zone), all Y values are increased by 500 km, i.e. point O (Figure 14) has coordinates X = 0, Y = 500 km. When determining the rectangular coordinates of a point from a plan or map, a coordinate grid is used. On plans of scale 1:5,000, the coordinate grid is drawn every 0.5 km; on maps of scales 1:10,000, 1:25,000, 1: every 1 km (kilometer grid). At the northern and southern frames of the map, the outputs of the kilometer grid of ordinates are written out, and the eastern and western frames - the outputs of the kilometer grid of abscissas (see paragraph 7). For example (Figure 15): for point A, the entry on the abscissa 6066 means that X A = 6066 km - shows the distance from the equator; the entry on the ordinate axis 309 means that Y A = 309 km - shows the distance from the axial meridian of the zone, and the number 4 indicates the number of the six-degree zone. Figure 13 Dividing the Earth's surface into six-degree zones Figure 14 - Image of the zone on the plane and coordinate axis 20
21 Rectangular coordinates of point C lying inside the grid square (Figure 15) are calculated using the formulas X C = X ml. + X, Y C = Y ml. + Y, or X C = X art. - X 1, Y C = Y art. - Y 1, where X ml., Y ml., X st., Y st.., junior and senior kilometer lines, respectively, along the x and y axes; X, Y, X 1, Y 1 - distances from the corresponding kilometer lines to point C along the abscissa and ordinate axes, measured using a measuring compass and a linear or transverse scale. For example: for point C Figure 15 - Determination of rectangular coordinates using a topographic map of scale 1: the minor kilometer line along the abscissa axis X ml. = 6067 km, along the ordinate axis Y ml. = 307 km; X = 462 m, Y = 615 m. The rectangular coordinates of point C will be X C = m m = m = 6067.462 km, Y C = m m = m = 307.615 km. For control, the same values of X C, Y C can be determined by measuring the increments of coordinates X 1, Y 1 from the highest kilometer lines X st. =6068 km and Y station. = 308 km: X C = m 538 m = m = 6067.462 km, Y C = m 385 m = m = 307.615 km Measuring true azimuth and directional angle of a line, calculating magnetic azimuth and bearing True azimuth is the angle measured from the northern end of the true meridian clockwise to the given direction of the line. To determine the true azimuth of line AB (Figure 16) through the beginning of the line - point A, you need to draw the true meridian or continue 21
22 line until it intersects with the western or eastern frame of the map (remember that the boundaries of the map are true meridians and parallels). Then you should measure with a protractor the true azimuth of the line AB: A source. AB = 65. D C A B Figure 16 Measuring true azimuths If you draw one of the true meridians that intersects the CD line in a given direction (Figure 16), you can easily measure the true azimuth by attaching a protractor to it and counting clockwise the angle from the north direction true meridian to a given direction A ist. CD = = 275. Directional angle is the angle measured from the northern end of the axial meridian clockwise to the given direction of the line. The directional angle of any line on a map or plan can be measured from the north direction of the vertical grid line to a given direction (Figure 17), 1-2 = 117. The directional angle can be measured without additional construction - you need to attach a protractor to any of the lines intersecting this direction kilometer grid. 22
23 Figure 17 Measuring directional angles The angle between the northern direction of the kilometer grid and the given direction (counting clockwise) will be the directional angle of the given direction: in the figure = = 256. Figure 18 Diagram of the frames and kilometer grid of a topographic map sheet showing true azimuths and directional ones angles of lines BC and EF 23
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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 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. Based on the scale, maps are conventionally divided 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 are larger than 1:10,000.
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2. Conventional signs Conventional signs that are used for designation on plans and maps various items areas 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. 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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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 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 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.
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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 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 along direction b-c, move the measuring leg from point a to point a1, add 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 distance 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.
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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.
Topographic maps and plans
topographic map plan relief
1. General information about topographic materials
Topographic materials, which are a reduced-scale projected image of sections of the earth's surface onto a plane, are divided into maps and plans.
A topographic plan is a reduced-scale and similar image on paper of the situation and terrain. A similar image is obtained by orthogonally projecting sections of the earth's surface with a size not exceeding 20 x 20 km onto a horizontal plane. In a reduced form, such an image represents a plan of the area. A situation is a collection of terrain objects, a relief is a collection of various forms of unevenness of the earth's surface. A terrain plan drawn up without a relief image is called situational (contour).
Thus, a plan is a drawing consisting of horizontal positions-segments obtained by orthogonal design of the corresponding sections of the terrain (building structures, roads, hydrographic elements, etc.).
In the form of a plan, a series of construction drawings are compiled that are included in the design and technical documentation necessary for the construction of buildings and structures. Such drawings allow one to view, as it were, reduced-scale images of building structures from above.
An image of large areas of the earth's surface on a plane cannot be obtained without distortion, that is, while maintaining complete similarity. Such areas are orthogonally projected onto the surface of the ellipsoid, and then from the surface of the ellipsoid according to certain mathematical laws called cartographic projections (Gauss-Kruger projection) are transferred to the plane. The resulting reduced image on a plane is called a map.
A topographic map is a reduced, generalized image of significant areas of the Earth's surface constructed according to certain mathematical laws.
Visual perception of the image of the earth's surface, its characteristic features and features is associated with the clarity of plans and maps. Visibility is determined by the identification of typical features of the area that determine its distinctive features, through generalizations - generalization, as well as the use of topographical symbols - a system of symbols - to depict the earth's surface.
Maps and plans must be reliable, that is, the information that constitutes their content as of a certain date must be correct and correspond to the state of the objects depicted on them. An important element of reliability is the completeness of the content, including the required amount of information and its versatility.
According to their purpose, topographic maps and plans are divided into basic and specialized. The main ones include maps and plans for national mapping. These materials are multi-purpose, so they display all the elements of the situation and terrain.
Specialized maps and plans are created to solve specific problems of a particular industry. So, road maps contain a more detailed description of the road network. Specialized plans also include survey plans used only during the design and construction of buildings and structures. In addition to plans and maps, topographic materials include terrain profiles, which are a reduced image of a vertical section of the earth's surface along a selected direction. Terrain profiles are the topographic basis for the preparation of design and technical documentation necessary for the construction of underground and above-ground pipelines, roads and other communications.
2.Scale
The degree of reduction of the image on the plan of the contours of the terrain, otherwise the ratio of the length of the line segment on the plan (map) to the corresponding horizontal position of this segment on the terrain is called scale. Scales are divided into numerical and linear.
A numerical scale is a fraction, the numerator of which is one, and the denominator is a number showing how many times lines and objects are reduced when depicting them on a plan (map).
On each sheet of a map or plan, its numerical scale is signed in the form: 1:1000; 1:5000; 1:10,000; 1:25000, etc.
Linear scale is a graphic expression of a numerical scale (Fig. 9). To construct a linear scale, draw a straight line and mark the same distance in centimeters on it several times, called the base of the scale. The base is usually taken two centimeters long. The length of the line on the ground, corresponding to the base of the linear scale, is signed from left to right as it grows, and the first left base is divided into 10 more parts. The practical accuracy of the linear scale is ±0.5 mm, which corresponds to 0.02-0.03 bases of the scale.
For more accurate graphic work on the plan, use a transverse scale, which allows you to measure segments with an accuracy of 0.01 of its base.
The transverse scale is a graph based on proportional division (Fig. 10); to construct a scale on a straight line, the bases of the scale are laid off several times; perpendiculars are drawn from the division points; The first left base is divided by 10
Fig.9. Linear and numerical scales on topographic maps
parts, and 10 equal parts are also laid on perpendiculars and lines parallel to the base are drawn through the points of deposition, as shown in Fig. 10. From the similarity of triangles BDE and Bde it follows that de/DE = Bd/BD or de= Bd∙DE/BO, but DE = AB/10, Bd= BD/10. Substituting the values of DE and Bd, we get de= AB/100, i.e. that is, the smallest division of the transverse scale is equal to a hundredth of the base. Using a scale with a base of 10 mm, you can determine the lengths of segments with an accuracy of 0.1 mm. The use of any scale, even transverse, cannot provide accuracy above a certain limit, depending on the properties of the human eye. With the naked eye, from a normal vision distance (25cm), you can estimate a size on the plan that does not exceed 0.1mm (details of terrain objects smaller than 0.1mm cannot be depicted on the plan). Scale accuracy is characterized by a horizontal distance on the ground corresponding to 0.1 mm on the plan. For example, for plans drawn on a scale of 1:500, 1:1000, 1:2000, the scale accuracy is respectively 0.05, 0.1, 0.2 m. The accuracy of the scale determines the degree of generalization (generalization) of details that can be depicted on a plan (map) of a particular scale.
3.Uword marks on plans and maps
Topographic maps and plans depict various terrain objects: the outlines of settlements, gardens, vegetable gardens, lakes, rivers, road lines, power transmission lines. The collection of these objects is called a situation. The situation is depicted using conventional signs.
Conventional signs, mandatory for all institutions and organizations that compile topographic maps and plans, are established by the Federal Service of Geodesy and Cartography of Russia (Roscartography) and are published either separately for each scale or for a group of scales. Although the number of conventional signs is large (about 400), they are easy to remember, since they superficially resemble the appearance and character of the depicted objects.
Conventional signs are divided into five groups: area, linear, non-scale, explanatory, special.
Area symbols (Fig. 11, a) are used to fill the areas of objects (for example: arable lands, forests, lakes, meadows); they consist of a sign of the boundary of an object (a dotted line or a thin solid line) and images or conventional coloring that fill it; for example, symbol 1 shows a birch forest; the numbers (20/0.18)∙4 characterize the tree stand: the numerator is the average height, the denominator is the average trunk thickness, 4 is the average distance between trees.
Linear symbols are objects of a linear nature (roads, rivers, communication lines, power transmission lines), the length of which is expressed on a given scale. The conventional images show various characteristics of objects; for example, on highway 7 it is shown, m: the width of the roadway is 8, the width of the entire road is 12; on the railway 8, m: +1.8 - embankment height, -2.9 - excavation depth.
Out-of-scale symbols are used to depict objects whose dimensions are not displayed at a given scale of a map or plan (bridges, kilometer posts, wells, geodetic points).
As a rule, off-scale signs determine the location of objects, but their size cannot be judged from them. The signs give various characteristics, for example: length 17 and width 3 m of wooden bridge 12, mark 393.500 points of geodetic network 16.
Explanatory symbols are digital and alphabetic inscriptions that characterize objects, for example: the depth and speed of river flows, load capacity and width of bridges, forest species, average height and thickness of trees, width of highways. They are placed on the main areal, linear, and non-scale signs.
Special symbols (Fig. 11, d) are established by the relevant departments of the national economy; they are used to draw up specialized maps and plans of this industry, for example, signs for survey plans of oil and gas fields - oil field structures and installations, wells, field pipelines.
To give a map or plan greater clarity, colors are used to depict various elements: for rivers, lakes, canals, wetlands - blue; forests and gardens - green; highways - red; improved dirt roads - orange.
Everything else is given in black. On survey plans, underground communications (pipelines, cables) are colored.
4.Pterrain and methods of depicting it. Steepness of slopes
The terrain is a collection of irregularities on the earth's surface.
Depending on the nature of the relief, the terrain is divided into flat, hilly and mountainous. Flat terrain has weakly defined forms or almost no unevenness; hilly is characterized by alternating relatively small elevations and decreases; mountainous is an alternation of elevations more than 500m above sea level, separated by valleys.
Of the variety of landforms, the most characteristic ones can be identified (Fig. 12).
A mountain (hill, height, hill) is a cone-shaped relief form rising above the surrounding area, the highest point of which is called the summit (3, 7, 12). The top in the form of a platform is called a plateau, the top of a pointed shape is called a peak. The side surface of the mountain consists of slopes, the line where they merge with the surrounding terrain is the sole, or base, of the mountain.
Rice. 12. Characteristic forms of relief: 1 - hollow; 2 - ridge; 3,7,12 - vertices; 4 - watershed; 5.9 - saddles; 6 - thalweg; 8 - river; 10 - break; 11 - terrace
A basin or depression is a bowl-shaped depression. The lowest point of the basin is the bottom. Its lateral surface consists of slopes, the line where they merge with the surrounding area is called the edge.
Ridge2 is a hill that gradually decreases in one direction and has two steep slopes called slopes. The axis of the ridge between the two slopes is called the watershed line or watershed 4.
Hollow 1 is an elongated depression in the terrain, gradually descending in one direction. The axis of the hollow between two slopes is called the drainage line or thalweg 6. The varieties of the hollow are: valley - a wide hollow with gentle slopes, and also a ravine - a narrow hollow with almost vertical slopes (cliffs 10). The initial stage of a ravine is a ravine. A ravine overgrown with grass and bushes is called a ravine. Sites sometimes located on the slopes of hollows, looking like a ledge or step with an almost horizontal surface, are called terraces 11.
Saddles 5, 9 are low parts of the terrain between two peaks. Roads often pass through saddles in the mountains; in this case the saddle is called a pass.
The top of the mountain, the bottom of the basin and the lowest point of the saddle are characteristic points of the relief. The watershed and thalweg are characteristic lines of the relief. Characteristic points and lines of relief make it easier to recognize its individual forms on the ground and depict them on a map and plan.
The method of depicting the relief on maps and plans should make it possible to judge the direction and steepness of the slopes, as well as determine the marks of terrain points. At the same time, it must be visual. Various methods of depicting the relief are known: perspective, shading with lines of different thicknesses, colored washing (mountains - brown, hollows - green), horizontal lines. The most advanced methods from an engineering point of view for depicting the relief are horizontal lines in combination with a signature of the marks of characteristic points (Fig. 13) and digital.
A horizontal line is a line on a map connecting points of equal heights. If we imagine a section of the Earth's surface by a horizontal (level) surface P0, then the line of intersection of these surfaces, orthogonally projected onto a plane and reduced to a size on the scale of a map or plan, will be horizontal. If the surface P 0 is located at a height H from the leveled surface, taken as the origin of absolute heights, then any point on this horizontal line will have an absolute elevation equal to H. An image in the contour lines of the relief of the entire area of the terrain can be obtained by cutting the surface of this area with a series of horizontal planes Р 1, Р 2,… Р n, located at the same distance from each other. As a result, contour lines with marks H + h, H + 2h, etc. are obtained on the map.
The distance h between cutting horizontal planes is called the height of the relief section. Its value is indicated on the map or plan under the linear scale. Depending on the scale of the map and the nature of the depicted relief, the height of the section is different.
The distance between contour lines on a map or plan is called elevation. The greater the laying, the less steep the slope on the ground, and vice versa.
Rice. 13.Image of the terrain with contours
Property of contours: contours never intersect, with the exception of an overhanging cliff, natural and artificial craters, narrow ravines, steep cliffs, which are not displayed by contours, but are indicated by conventional signs; horizontal lines are continuous closed lines that can only end at the border of a plan or map; the denser the horizontal lines, the steeper the relief of the depicted area, and vice versa.
The main forms of relief are depicted by horizontal lines as follows (Fig. 14).
The images of the mountain and the basin (see Fig. 14, a, b), as well as the ridge and hollow (see Fig. 14, c, d), are similar to each other. To distinguish them from each other, the direction of the slope is indicated at the horizontal. On some horizontal lines, markings of characteristic points are signed, and so that the top of the numbers is directed in the direction of increasing the slope.
Rice. 14. Depiction of characteristic relief forms by horizontal lines: a - mountain; b - basin; c - ridge; g - hollow; d - saddle; 1 - top; 2 - bottom; 3 - watershed; 4 - thalweg
If, at a given height of the relief section, some of its characteristic features cannot be expressed, then additional half and a quarter horizontal lines are drawn, respectively, through half or a quarter of the accepted height of the relief section. Additional horizontal lines are shown with dotted lines.
To make contour lines on the map easier to read, some of them are thickened. With a section height of 1, 5, 10, and 20 m, every fifth horizontal line is thickened with marks that are multiples of 5, 10, 25, 50 m, respectively. With a section height of 2.5 m, every fourth horizontal line is thickened with marks that are multiples of 10 m.
The steepness of the slopes. The steepness of the slope can be judged by the size of the deposits on the map. The lower the position (the distance between the horizontal lines), the steeper the slope. To characterize the steepness of the slope on the ground, the inclination angle ν is used. The vertical angle of inclination is the angle between the terrain line and its horizontal position. The angle ν can vary from 0º for horizontal lines and up to ± 90º for vertical lines. The greater the angle of inclination, the steeper the slope.
Another characteristic of steepness is slope. The slope of the terrain line is the ratio of the elevation to the horizontal distance = h/d = tgν.
From the formula it follows that the slope is a dimensionless quantity. It is expressed as a percentage % (hundredths) or in ppm ‰ (thousands).Back<../Октябрь/Бесплатные/геодезия/новые%20методички/Учебное%20пособие%20по%20инженерной%20геодезии.wbk>
5. Classification and nomenclature of plans and maps
Maps and plans are classified mainly by scale and purpose.
By scale, maps are divided into small-, medium- and large-scale. Small-scale maps smaller than 1:1000000 are overview maps and are practically not used in geodesy; medium-scale (survey-topographic) maps at scales 1:1000000, 1:500000, 1:300000 and 1:200000; large-scale (topographic) - scales 1:100000, 1:50000, 1:25000, 1:10000. The scale series adopted in the Russian Federation ends with topographic plans of scales 1:5000, 1:2000, 1:1000, 1:500. In construction, plans are sometimes drawn up to scale
:200, 1:100 and 1:50.
According to their purpose, topographic maps and plans are divided into basic and specialized. The main ones include maps and plans for national mapping. These are multi-purpose maps, so they display all the elements of the terrain.
Rice. 15. Dividing a map of scale: 1:100000 into sheets of maps with scales of 1:50000, 1:25000 and 1:10000
The nomenclature is based on the international layout of map sheets at a scale of 1:1000000. Map sheets of this scale are limited by meridians and parallels in latitude 4º, longitude 6º. Each sheet occupies only its own place, being designated by a capital Latin letter, which defines the horizontal belt, and an Arabic numeral, which defines the number of the vertical column. For example, a sheet of a map at a scale of 1:1000000, on which Moscow is located, has the nomenclature N-37.
The layout of maps of larger scales is obtained by sequentially dividing a sheet of a map at a scale of 1:1000000. One sheet of a map of scale 1:1,000,000 corresponds to: four sheets of scale 1:500,000, designated by the letters A, B, C, D (the nomenclature of these sheets is, for example, N-37-A); nine sheets of scale 1:300000, designated by Roman numerals I, II, ..., IX (for example, IX -N-37); 36 sheets of scale 1:200000, also designated by Roman numerals (for example, N-37-I); 144 sheets of scale 1:100000, designated by Arabic numerals from 1 to 144 (for example, N-37-144).
One sheet of a 1:100,000 map corresponds to four sheets of a map of scale 1: 50,000, designated by the letters A, B, C, D; the nomenclature of sheets of this map looks like, for example, N-37-144-A. One sheet of a 1:50000 map corresponds to four sheets of a map of scale 1:25000, designated by the letters a, b, c, d, for example N-37-144-A-a. One sheet of a 1:25000 map corresponds to four sheets of a 1:10000 map, designated by the numbers 1, 2, 3, 4, for example N-37-144-A-a-l.
Figure 15 shows the numbering of sheets of maps of scales 1:50000 ... 1:10000, making up a sheet of map of scale 1:100000.
Layout of sheets of large-scale plans is done in two ways. For surveying and drawing up plans over an area of more than 20 km 2, a scale map sheet is used as the basis for the layout
:100000, which is divided into 256 parts for a scale of 1:5000, and each sheet of scale 1:5000 is divided into nine parts for plans of a scale of 1:2000. In this case, the nomenclature of a sheet at a scale of 1:5000 looks like, for example, N-37-144(256), and for a scale of 1:2000 - N-37-144(256-I).
For site plans with an area of less than 20 km2, a rectangular layout is used (Fig. 16) for a scale of 1:5000 with sheet frames of 40x40 cm, and for scales 1:2000...1:500 - 50x50 cm. The scale sheet is taken as the basis for the rectangular layout 1:5000, denoted by Arabic numerals (for example, 1). A plan sheet on a scale of 1:5000 corresponds to four sheets on a scale of 1:2000, designated by the letters A, B, C, D. A plan sheet on a scale of 1:2000 corresponds to four sheets on a scale of 1:1000, designated by Roman numerals, and 16 sheets in scale 1:500, indicated by Arabic numerals.
Rice. 16. Rectangular layout of the plan sheet
The plans of scales 1:2000, 1:1000, 1:500 shown in the figure have the nomenclature 2-G, 3-B-IV, 4-B-16, respectively.
6. Solving problems on plans and maps
The geographic coordinates of point A (Fig. 17), latitude φ and longitude λ are determined on a plan or map, using the minute scales of the trapezoid frames.
To determine latitude, a line is drawn through point A parallel to the trapezoid frames and readings are taken at the intersections with the scale of the western or eastern frame.
Similarly, to determine longitude, a meridian is drawn through point A and readings are taken on the scales of the northern or southern frame.
Rice. 17. Determination of the coordinates of a point on a topographic plan: 1 - vertical kilometer line; 2 - digital designation of horizontal grid lines; 3 - digital designations of vertical grid lines; 4 - internal frame; 5 - frame with minutes; 6 - horizontal kilometer line
In the example given, latitude φ = 54º58.6′ s. latitude, longitude λ = 37º31.0′ E. d.
The rectangular coordinates X A and Y A of point A are determined relative to the kilometer grid lines.
To do this, measure the distance ∆X and ∆Y along perpendiculars to the nearest kilometer lines with coordinates X 0 and Y 0 and find
X A = X 0 + ∆X
Y A = Y 0 + ∆Y.
Distances between points on plans and maps are determined using a linear or transverse scale, curved segments are determined using a curvimeter device.
To measure the directional angle of a line, a line is drawn through its starting point parallel to the abscissa axis, and the directional angle is measured directly at this point. You can also extend the line until it intersects the nearest grid ordinate line and measure the directional angle at the intersection point.
To directly measure the true azimuth of a line, a meridian is drawn through its starting point (parallel to the eastern or western frame of the trapezoid) and the azimuth is measured relative to it.
Since it is difficult to draw the meridian, you can first determine the directional angle of the line, and then use the given formulas to calculate the true and magnetic azimuths.
Determining the steepness of the slope. The steepness of the slope is characterized by the angle of inclination ν, which is formed by a terrain line, for example AB, with a horizontal plane P (Fig. 18).
tan ν = h/a, (15.1)
where h is the height of the relief section; a - mortgage.
Knowing the tangent, use tables of values of trigonometric functions or use a microcalculator to find the value of the angle of inclination.
The steepness of the slope is also characterized by the slope of the line
i= tanν. (15.2)
The slope of the line is measured in percent or ppm (‰), i.e. thousandths of a unit.
Rice. 18. Scheme for determining the steepness of the slope
As a rule, when working with a map or plan, the angle of inclination or slope of the slope is determined using graphs (Fig. 19) with the scale of the locations.
Rice. 19. Layout graphs for the plan at a scale of 1:1000 with a relief section height of h = 1.0 m a - for inclination angles; b - slopes.
To do this, take the position between two horizontal lines along a given slope from the plan, then use the graph to find the place where the distance between the curve and the horizontal line is equal to this position. For the ordinate found in this way, read the value ν or i along a horizontal straight line (marked with asterisks on the graphs above: ν = 2.5º; i = 0.05 = 5% = 50‰).
Example 1. Determine the angle of inclination and slope of the terrain between horizontal lines on a scale plan of 1:1000, if the elevation is 20 mm, the height of the relief section is h = 1.0 m. On the ground, the laying will correspond to a segment length of 20mm ∙ 1000 = 20000mm = 20m. According to formulas (15.1) and (15.2) tanν = i = 1:20 = 0.05. Therefore, i = 5% = 50‰, and ν = 2.9º.
Determination of elevations of terrain points. If a point is located on the horizontal, its elevation is equal to the horizontal elevation. When point K (Fig. 20) is located between horizontal lines with different heights, its mark H K is determined by interpolation (finding intermediate values) “by eye” between the marks of these horizontal lines.
Interpolation consists in determining the coefficient of proportionality of the distance d from the determined point to the smaller horizontal line N MG. To the value of the location a, i.e. ratio d/a, and multiplying it by the value of the height of the relief section h.
Example 2. Marking of point K, located between horizontal lines with marks of 150 and 152.5 m (Fig. 20, a),
H K = H M. G + (d/a)h = 150 + 0.4 ∙ 2.5 = 151m.
Rice. 20. Determination of horizontal elevations of points: a...d - diagrams with a section height h = 2.5 m
If the point being determined is located between horizontal lines of the same name - on a saddle (Fig. 20, b) or inside a closed horizontal line - on a hill or basin (Fig. 20, c, d), then its mark can only be determined approximately, assuming that it is greater than or less than the height of this horizontal line by 0.5h. For example, in the figure for the saddle the elevation of the Kravna point is 138.8 m, for the hill - 128.8 m, for the basin - 126.2 m.
Drawing a line of a given maximum slope on the map (Fig. 21). Between points A and B given on the map, it is required to draw the shortest line so that not a single segment has a slope greater than the specified limit i pr.
Rice. 21. Scheme of drawing a line of a given maximum slope on the map
The easiest way to solve the problem is by using the scale for slopes. Having taken along it with a compass solution the position apr, corresponding to the slope, sequentially mark points 1...7 all horizontals from point A to point B. If the compass solution is less than the distance between the horizontals, then the line is drawn in the shortest direction. By connecting all the points, a line with a given maximum slope is obtained. If there is no scale of locations, then the location of a pr can be calculated using the formula a pr = h/(i pr M), where M is the denominator of the numerical scale of the map.
Rice. 22. Scheme for constructing a profile in a given direction: a - direction according to the map; b - profile in direction
Construction of a terrain profile in the direction specified on the map. Let's look at building a profile using a specific example (Fig. 22). Let it be necessary to construct a terrain profile along line AB. To do this, line AB is transferred on the map scale to paper and points 1, 2, 4, 5, 7, 9 are marked on it, at which it intersects the horizontal lines, as well as characteristic relief points (3, 6, 8). Line AB serves as the base of the profile. Point marks taken from the map are plotted on perpendiculars (ordinates) to the base of the profile on a scale 10 times greater than the horizontal scale. The resulting points are connected by a smooth line. Usually, the profile ordinates are reduced by the same amount, i.e., the profile is built not from zero heights, but from the conventional horizon UG (in Fig. 22, a height of 100 m is taken as the conventional horizon).
Using a profile, you can set the mutual visibility between two points, for which you need to connect them with a straight line. If you build profiles from one point in several directions, you can plot on a map or plan areas of the terrain that are not visible from this point. Such areas are called visibility fields.
Calculation of volumes (Fig. 23). Using a map with contour lines, you can calculate the volumes of a mountain and a basin, depicted by a system of contour lines enclosed within a small area. To do this, landforms are divided into parts bounded by two adjacent horizontal lines. Each such part can be approximately taken as a truncated cone, the volume of which is V = (1/2)(Si+ Si+I)h c , where Si and Si+I are the areas limited on the map by the lower and upper horizontal lines, which are the bases of the truncated cone; h c - height of the relief section; i = 1, 2, ..., k - current number of the truncated cone.
Areas S are measured with a planimeter (mechanical or electronic).
The approximate area of a plot can be determined by dividing it into many regular mathematical figures(trapezoids, triangles, etc.) and summing by area. The volume V in the uppermost part is calculated as the volume of a cone, the base area of which is equal to S B and the height h is the difference between the elevations of the top point t and the horizontal line limiting the base of the cone:
Rice. 23. Scheme for determining volume
V B = (S B / 3)∙h
If the mark of point t on the map is not marked, then take h = h c /2. The total volume is calculated as the sum of the volumes of the individual parts:
V 1 + V 2 + ... + V k + V B,
where k is the number of parts.
Measuring areas on maps and plans is required to solve various engineering and economic problems.
There are three known ways to measure areas on maps: graphical, mechanical and analytical.
The graphical method includes the method of dividing the measured area into the simplest geometric figures and a method based on using a palette.
In the first case, the area to be measured is divided into simple geometric figures (Fig. 24.1), the area of each of which is calculated using simple geometric formulas and the total area of the figure is determined as the sum of the areas of geometric partial figures:
Rice. 24. Graphic methods for measuring the area of a figure on a map or plan
In the second case, the area is covered with a palette consisting of squares (see Fig. 24.2), each of which is a unit of area measurement. The areas of incomplete figures are calculated by eye. The palette is made of transparent materials.
If the area is limited by broken lines, then its area is determined by dividing it into geometric shapes. With curved boundaries, it is easier to determine the area using a palette.
The mechanical method involves calculating areas on maps and plans using a polar planimeter.
The polar planimeter consists of two levers, pole 1 and bypass 4, pivotally connected to each other (Fig. 25a).
Rice. 25. Polar planimeter: a - appearance; b - counting by the counting mechanism
At the end of the pole lever there is a weight with a needle - pole 2, the bypass lever at one end has a counting mechanism 5, at the other - bypass index 3. The bypass lever has a variable length. The counting mechanism (Fig. 25, b) consists of a dial 6, a counting drum 7 and a vernier 8. One division on the dial corresponds to the revolution of the counting drum. The drum is divided into 100 divisions. Tenths of the small division of the drum are estimated by the vernier. The full reading on the planimeter is expressed as a four-digit number: the first digit is counted on the dial, the second and third - on the counting drum, the fourth - on the vernier. In Fig. 25, b the counting on the counting mechanism is equal to 3682.
Rice. 26. Analytical method for measuring area
Having set the bypass index at the starting point of the contour of the measured figure, take count a using the counting mechanism, then use the bypass index to move clockwise along the contour to the starting point and take count b. The difference in readings b - a represents the area of the figure in planimeter divisions. Each planimeter division corresponds to an area on the ground or plan, called the planimeter division value P. Then the area of the outlined figure is determined by the formula
S = P(b - a)
To determine the division price of a planimeter, measure a figure whose area is known or which can be determined with great accuracy. Such a figure on topographic plans and maps is a square formed by the lines of a coordinate grid. The division price of the planimeter P is calculated using the formula
P = S out / (b - a),
where S is the known area of the figure; (b - a) - difference of samples c. starting point when tracing a figure with a known area.
The analytical method consists of calculating the area from the results of measurements of angles and lines on the ground. Based on the measurement results, the X, Y coordinates of the vertices are calculated. The area P of polygon 1-2-3-4 (Fig. 26) can be expressed through the areas of trapezoids
P = P 1′-1-2-2′ + P 2′-2-3-3′ - P 1′-1-4-4′ - P 4′-4-3-3′ = 0.5( (x 1 + x 2)(y 2 - y 1) + (x 2 + x 3)(y 3 - y 2) -(x 1 + x 4)(y 4 - y 1) - (x 4 + x 3)(y 3 - y 4)).
Having made the transformations, we obtain two equivalent formulas for determining the double area of a polygon
2P = x 1 (y 2 - y 4) + x 2 (y 3 - y 1) + x 3 (y 4 - y 2) + x 4 (y 1 - y 3);
P = y 1 (x 4 - x 2) + y 2 (x 1 - x 3) + y 3 (x 2 - x 4) + y 4 (x 3 - x 1).
Calculations can be easily performed on any microcalculator.
The accuracy of determining areas analytically depends on the accuracy of the measured values.
7.Idigital image of the earth's surface
The development of computer technology and the emergence of automatic drawing devices (plotters) led to the creation of automated systems for solving various engineering problems related to the design and construction of structures. Some of these problems are solved using topographic plans and maps. In this regard, there is a need to present and store information about the topography of the area in a digital form convenient for the use of computers.
In computer memory, digital terrain data can best be represented in the form of x, y, H coordinates of a certain set of points on the earth's surface. Such a set of points with their coordinates forms a digital terrain model (DTM).
All elements of the situation are specified by the x and y coordinates of the points that determine the position of objects and terrain contours. A digital elevation model characterizes the topographic surface of the area. It is determined by a certain set of points with coordinates x, y, H, selected on the earth's surface so as to sufficiently reflect the nature of the relief.
Rice. 27. Diagram of the location of points of the digital model in characteristic places of the relief and on horizontal lines
Due to the variety of relief forms, it is quite difficult to describe it in detail in digital form, therefore, depending on the problem being solved and the nature of the relief, various methods of compiling digital models are used. For example, a DEM may take the form of a table of coordinate values x, y, H at the vertices of a grid of squares or regular triangles, evenly distributed over the entire area of the terrain. The distance between the peaks is selected depending on the shape of the relief and the problem being solved. The model can also be specified in the form of a table of coordinates of points located in characteristic places (inflections) of the relief (watersheds, thalwegs, etc.) or on horizontal lines (Fig. 27). Using the coordinate values of the points of the digital relief model for a more detailed description on a computer using a special program, the height of any point on the terrain is determined.
Literature
Basova I.A., Razumov O.S. Satellite methods in cadastral and land management works. - Tula, Tula State University Publishing House, 2007.
Budenkov N.A., Nekhoroshkov P.A. Engineering geodesy course. - M.: Publishing house MGUL, 2008.
Budenkov N.A., Shchekova O.G. The engineering geodesy. - Yoshkar-Ola, MarSTU, 2007.
Bulgakov N.P., Ryvina E.M., Fedotov G.A. Applied geodesy. - M.: Nedra, 2007.
GOST 22268-76 Geodesy. Terms and Definitions
Engineering geodesy in construction./Ed. O.S. Razumov. - M.: Higher School, 2008.
The engineering geodesy. / Ed. prof. D.Sh.Mikhelev. - M.: graduate School, 2009.
Kuleshov D.A., Strelnikov G.E. Engineering geodesy for builders. - M.: Nedra, 2007.
Manukhov V.F., Tyuryakhin A.S. Engineering geodesy - Saransk, Mordovia State University, 2008.
Manukhov V.F., Tyuryakhin A.S. Glossary of satellite geodesy terms - Saransk, Mordovian State University, 2008.
TRAINING AND METHODOLOGICAL CENTER
METHODOLOGICAL DEVELOPMENT
To conduct classes on initial training of rescuers
(topography)
TOPIC No. 2 “Topographic maps, terrain diagrams and plans”
Chelyabinsk
LEARNING OBJECTIVES: Study with students the scales of topographic maps,
give basic concepts of map orientation and topography
graphic symbols used on the map.
M E S T O: Cool.
TIME: 2 hours.
M E T O D: Practical lesson.
STUDY QUESTIONS AND TIME RECORDING
Introductory part - 5 min
1st study question: Drawing up plans and diagrams.- 45 min
2nd educational question: Orientation on the map. - 30 min
Conclusion: - 10 min.
L I T E R A T U R A:
1. Textbook “Military topography” for cadets of educational units.
2. Officer's Handbook on Military Topography.
HOW TO DO:
Check the availability of listeners,
Announce the topic, purpose, educational questions.
INTRODUCTORY PART:
Rescuers' actions take place on the ground or are closely related to it. The knowledge, teachings and skills acquired during the study of topography are of great practical importance in the activities of rescuers.
Knowledge of ways to study terrain, skills in orientation and movement on it in various conditions, day, night, with limited visibility contribute correct use favorable terrain properties for achieving success, help to quickly and confidently navigate and maintain a given direction when moving and maneuvering. The ability to use a topographic map makes it possible to study and evaluate the terrain in advance, and prepare the necessary data for the march.
Using the map, it is easier to make the most appropriate decision and assign tasks to subordinates.
1st educational question: Classification of topographic maps, local maps
sti and plans. Conventional signs.
TOPOGRAPHIC MAP - the main graphic document about the area, containing an accurate, detailed and visual representation of local objects and relief. On topographic maps, local objects are depicted by generally accepted symbols, and the relief is depicted by contour lines.
Topographic maps are intended for the work of rescuers in preparing, organizing and conducting work. Using them, they study and evaluate the terrain, solve various calculation problems related to determining distances, angles and areas, heights, elevations and mutual visibility of terrain points, steepness and types of slopes, etc. They are planning a march and preparing
data for movement in azimuths.
The completeness, detail and accuracy of the depiction of the area on the map depend primarily on its scale.
Map scale shows how many times the length of a line on a map is less than its corresponding length on the ground. It is expressed as a ratio of two numbers. For example, a scale of 1:50,000 means that all terrain lines are depicted on the map with a reduction of 50,000 times, i.e. 1 cm on the map corresponds to 50,000 cm (or 50 m) on the ground.
The scale is indicated under the bottom side of the map frame in digital terms (numerical scale) and in the form of a straight line (linear scale), on the segments of which the corresponding distances on the ground are labeled. The scale value is also indicated here - the distance in meters (or kilometers) on the ground, corresponding to one centimeter on the map. It is useful to remember the rule: if you cross out the last two zeros on the right side of the ratio, then the remaining number will show how many meters on the ground correspond to 1 cm on the map, i.e. scale value.
When comparing several scales, the larger one will be the one with the smaller number on the right side of the ratio. Let us assume that for the same area of terrain there are maps of scales 1:25,000, 1:50,000 and 1:100,000. Of these, the scale of 1:25,000 will be the largest, and the scale of 1:100,000 will be the smallest.
A scale range has been established for topographic maps.
TOPOGRAPHICAL PLANS.
Topographic plans can be created for large settlements and other important objects. They are a type of topographic maps and differ from them in that they are published in separate sheets, the dimensions of which are determined by the boundaries of the depicted area of the area (settlement, object). The plans have some design features.
Most often, plans are drawn up at scales of 1:10,000 - 1:25,000, which make it possible to show in great detail the nature of the depicted object and provide detailed information about the qualitative and quantitative characteristics of local objects and relief details located both on the object itself and on the nearest approaches to him. According to the depicted area (object) of the area, the name of the plan is signed, for example, Plan of Zavodskaya Station, Plan of Camps, etc.
For ease of use and greater clarity, city plans highlight prominent buildings with special symbols and colors, and city transport lines (metro, tram) are shown. To facilitate the purpose of the indication, the plan provides a conventional numbering of blocks and some local items, and a brief legend, a list of prominent buildings and an alphabetical street index are placed in the margins or on the back of the plan. A sample part of the city plan is given in Appendix 4.
Area diagram – a drawing on which the most characteristic local objects, as well as individual relief elements, are depicted with approximate accuracy.
Local objects are depicted on the diagram by topographical symbols, hills and depressions (heights, basins) are represented by several closed horizontal lines, and ridges and hollows are represented by fragments of horizontal lines that outline the configuration of these relief forms. At the same time, in order to speed up the work, the symbols of some local objects are simplified.
Drawing up terrain maps using eye survey techniques. To carry out eye survey, you need to have a compass, a sight line, a pencil, an eraser and a blank sheet of paper mounted on a rigid base (a piece of cardboard, plywood, etc.) In some cases, when the survey needs to be carried out quickly and does not require special care , it can be done with only a pencil and paper.
Let's consider some eye survey techniques used in drawing up terrain diagrams.
Shooting from one standing point used when the drawing requires showing a small area of terrain located directly around the standing point or in a given sector. In this case, shooting is performed using the circular sighting method in the following sequence.
A standing point is placed on a sheet of paper so that the area to be removed fits on this sheet. For example, if we are standing in the center of the area being photographed, then the standing point should be marked in the center of the sheet of paper, if
If we stand in one of the corners or on the edge of the area, then a dot on the paper should be placed in the corresponding corner or on the edge of the sheet of paper. Then, having oriented the sheet of paper relative to the area being filmed, they fix it on some object (stump, bridge railing, trench parapet) and, without disturbing the position of the sheet, carry out the survey.
If you have to work while holding a sheet of paper in your hand, then first draw a north-south direction on it. To do this, orienting a sheet of paper relative to the area being photographed, place a compass on it, release the needle brake and, when the needle calms down, draw a line parallel to the compass needle.
In the future, make sure that the direction of the compass needle exactly coincides with the drawn north-south line. When it is necessary to orient the drawing again, for example after a break in work, a compass is placed on it so that the divisions are 0 degrees (O) and 180 degrees. (S) coincide with the drawn north-south direction, then turn the drawing until the northern end of the compass needle is opposite the 0 degree division (N). In this position, the drawing will be oriented and you can continue working on it.
In order to put this or that object on the drawing, after orienting the sheet, you need to attach a ruler (pencil) to the standing point indicated on it and turn it around the point until the direction of the ruler coincides with the direction of the object. With this position of the ruler, draw a straight line along it from the standing point, this line will be the direction in which the object being drawn on the diagram is located. So they sequentially point the ruler at all other objects and draw directions for each of them.
Then the distances to the objects are determined and they are laid out in the appropriate directions from the standing point on the scale of the drawing or approximately, maintaining the approximate ratio of these distances in the drawing and on
Localities. The points obtained in the directions will indicate the location of objects in the drawing. In the places of the points, conventional signs of the applied objects are drawn, in relation to which the remaining details of the terrain, located directly near the point of standing, as well as those located between the applied landmarks or near them, are visually applied. Individual trees, bushes near the road, a section of an improved dirt road, ruins, holes, etc. are marked in this way on the terrain map.
Shooting from multiple vantage points performed when it is necessary to show a relatively large area of terrain.
In this case, local objects are marked on the drawing with serifs, by measuring distances, along the alignment, by the method of circular sighting, by the method of perpendiculars.
When preparing for shooting, it is necessary to secure the sheet of paper on which the shooting will be carried out on a solid base (tablet). A compass is attached to the same base so that the north-south line on the compass scale is approximately parallel to one of the sides of the tablet or sheet of paper.
For the speed and convenience of plotting distances measured in steps, it is necessary to make a step scale. This scale is built on a separate strip of paper or on the margin of the sheet on which the shooting is being carried out.
The scale of steps is built like this. Let's assume that the shooting is being done on a scale
1:10,000, i.e. 1 cm in the drawing corresponds to 100 m on the ground. The value of one pair of steps of the surveyor is 1.5 m. Therefore, 100 pairs of steps are equal to 150 m on the ground or 1.5 cm on the drawing. A 1.5 cm segment is laid on a straight line three, four or larger number once. The number 0 is written against the second division on the left, and the numbers 100, 200, 300, etc. are written against subsequent divisions. Against the leftmost (first) division sign: 100 pairs of steps. In this way we obtain a scale of steps, each major division of which
Corresponds to 100 pairs of steps. In order for distances to be plotted with great accuracy, the leftmost segment is divided into 10 small divisions of 1.5 mm, each of which will be equal to 10 pairs of steps.
Having such a scale, there is no need to convert pairs of steps into meters each time; it is enough to plot the number of pairs of steps taken on a scale to get the distance on the shooting scale, which is plotted on the drawing.
The shooting is carried out by walking around the site along roads, the banks of a river, the edge of a forest, along a communication line, etc. The directions along which the survey is carried out are called running lines, and the points at which the directions of new running lines are determined and drawn are called stations.
IMAGE OF LOCAL OBJECTS ON
TOPOGRAPHIC MAPS
Types of symbols of topographic maps. Local objects on topographic maps are depicted by conventional symbols.
For ease of reading and memorization, many symbols have outlines that resemble the top or side view of the local objects they depict. For example, symbols of factories, oil rigs, free-standing trees, bridges are similar in shape to appearance listed local items.
Conventional signs depicting the same terrain elements on topographic maps of different scales are identical in their outline and differ only in size.
The relief on topographic maps is depicted by contour lines, and some of its details (cliffs, ravines, gullies, etc..) - by corresponding symbols.
Conventional signs are usually divided into three main groups: large-scale, non-scale and explanatory.
Large-scale Conventional signs depict those local objects and relief details that can be expressed in size on a map scale (lakes, forests, residential areas, large rivers, ravines, etc.).
The contours (external boundaries) of such objects (objects) are shown on the map as solid lines or dotted lines in exact accordance with their actual outlines. Solid lines show the contours of lakes, wide rivers, ravines, residential areas, dotted lines show the contours of forests, meadows, swamps. The area inside the outline of such symbols on the map is usually covered with paint of the appropriate color or filled with additional
Signs (Tables 1, 4, and 5 of Appendix 3).
Scale symbols allow you to determine from the map the actual length, width and area of depicted or objects. For example, if the width of a river on a 1:50,000 scale map is 2 mm, then its actual width on the ground is 100 m.
Off-scale Conventional signs are used to depict local objects and relief details that, due to the small size of the area they occupy, cannot be expressed on a map scale. Such local objects are mines, radio masts, wells, tower-type structures, mounds, etc.
The exact position on the map of an object depicted by a non-scale conventional sign is determined by the geometric center of the figure, the middle of the base of the sign, the vertex of the right angle at the base of the sign, and the geometric center of the lower figure.
An intermediate position between scale and non-scale symbols is occupied by symbols of roads, streams, gullies, water pipelines, power lines and other linear local objects, for which only the length is expressed on a scale. Such conventional signs are usually called linear. Their exact position on the map is determined by the longitudinal axis of the object.
Explanatory Conventional signs are used in combination with scale and non-scale; they serve to further characterize local objects and their varieties. For example, an image of a coniferous or deciduous tree in combination with a conventional sign of a forest shows the dominant tree species in it (see figure), an arrow on a river indicates the direction of its flow, transverse strokes on a symbol railway show the number of paths.
The maps contain signatures of the proper names of settlements, rivers, lakes, mountains, forests and other objects, as well as explanatory signatures in the form of alphabetic and numerical designations. They allow us to obtain additional information about the quantitative and qualitative characteristics of local objects and relief. Lettered explanatory signatures are most often given in abbreviated form according to the established list of conventional abbreviations (Appendix 5).
Technological lesson map
Teacher: Martynova Inna Vladimirovna Municipal Educational Institution Terengul Secondary School
Item: geography, 6th grade,
UMK: author's program A.A. Letyagin, I.V. Dushina, V.B. Pyatunin and others.
Textbook: Geography. Beginner course. 6th grade. A.A. Letyagin; edited by V.P. Dronova. M: Ventana-Graf, 2010.
Workbook No. 1 for the textbook by A. A. Letyain “Geography. Beginning course."
Toolkit. Geography. Beginner course. 6th grade: Approximate lesson planning. A.A. Letyagin. M: Ventana-Graf, 2008
Lesson topic: How to make topographic plans and maps
Place lesson in the topic: 6th lesson in the topic “Terrain plan”
Lesson type : combined
Lesson objectives:
Educational: contribute to the formationskills in working with topographic plan, map, scale; read a topographic plan using symbols; ability to draw up simple terrain plans.
Educational: create conditions for the development of cognitive activity, intellectual and creativity students; promote the development of skills to highlight, describe, explain the essential features of the main concepts of the topic; promote the development of skills in independent work with the text of a textbook, atlas, and multimedia presentation materials.
Educational: contribute to the education of geographical culture, the development of communication skills; develop interest in the subject being studied.
Planned results:
Personal: formationability to independently acquire new knowledge and practical skills using a terrain plan, fformation of moral behavior and moral consciousness.
Metasubject: formation and development through geographical knowledgecognitive interests, intellectual and creative abilities,Ability to independently search and select information.
Subject: read a topographic plan using symbols.Use the concepts of conducting visual surveys of the area to draw up a site plan. Use acquired knowledge and skills to navigate the terrain and conduct surveys of its areas.
Universal learning activities (UAL):
Personal: realize the need to study the topic.
Regulatory: plan your activities under the guidance of the teacher, evaluate the work of classmates, work in accordance with the assigned task.
Cognitive: extract, select and analyze information, obtain new knowledge, process information to obtain the desired result.
Communicative: be able to communicate and interact with each other, work in pairs, groups, and with teams.
Forms of student work: individual, in pairs, group, frontal.
Teacher equipment: laptop, multimedia projector, presentation.
MoldedUUD
1. Updating students’ knowledge
Fill in the blanks in the text: “A topographic plan is calleddetailed flat largelarge-scale image of a small area of terrain in which, usingconventional signs show geographical objects and theirlocation on the earth's surface"
Give answers
(2 minutes.)
Cognitive:
Regulatory:
Reasoned evaluation of answers
Communication: Express your opinion
2. Goal setting
Determination by students of the lesson topic, goals and objectives
Creating a problematic situation. Imagine that we were asked to draw a road from school to home, what do we need to know for this?
Let's determine the topic of the lesson
The purpose of our lesson?
Tasks?
Formulate the topic of the lesson “Howmake topographic plans and maps"
Formulate the purpose of the lesson: To learnmake topographic plans and maps.
They put forward the objectives of the lesson by analogy with the previous lesson.
Find solutions - use different sources of geographic information.
(3 min)
Regulatory:
Goal setting, planning
Cognitive:
Independent identification of a cognitive goal, selection of optimal ways to solve problems
Communication:
The ability to listen and engage in dialogue, participation in a collective discussion of a problem, the ability to express one’s thoughts
Personal:
Formation of personal worldview
3. Checking homework
Read the story (slide)
Read the plan and write down the text on pieces of paper. We exchange papers and check each other’s notes.
(7 min)
Cognitive:
Present information in different forms Regulatory: Work according to plan
Communication: Collaboration with peers.
Communication: Organize work.
4. Discovery of new knowledge
Organization of independent work of students
5 . Consolidation of knowledge and methods of action.
Sets educational objectives for students: To study types of terrain surveys
1 row Instrumental survey of the area
2 row Eye survey polar
3 row Plan of the area along the route
Physical education minute
So that my head doesn't hurt,We rotate it left and right.And now we roll our shoulders -And there will be a warm-up for them.Turns left and right.Step in place. We walk in formation.At least it's nice to warm up,It's time for us to get busy again. (1 min)
Working with a topographic plan.
Students in the group are given a plan of the area with a designated route. Exercise. Write a travel story about this area.
Instrumental survey of the area - use tools and equipment.
1. Polar terrain survey - a method of depicting a surface area from one point, within the visibility of objects.
2. The survey pole is selected in the middle of the site so that all objects of the surveyed territory are visible from it.
1. Route survey of the area - a method of depicting a surface area from one point to another.
2. Objects on both sides of the observer within visibility are plotted on the terrain plan
3. During route photography, objects are indicated by conventional topographic signs.
(8 min)
Students make up a story, then one of the students reads out what they came up with.
Group members conduct self-assessment (give marks to all group members)
(15 minutes)
Complete the task in the workbook (if there is time left)
Cognitive:
Find (in textbooks and other sources) reliable information
Present information in a form verbal response
Regulatory: Work according to the plan, checking the goal
Communication: Collaboration with teacher and peers.
Ability to listen and engage in dialogue.
Communication: Organize work in pairs or groups
6.Reflection
Summarizing
Flower of knowledge
I understood the lesson material, I was interested(red)
I didn't quite understand the lesson(yellow)
I didn't understand anything, I was bored(blue)
(1 min)
7. Homework
Everyone:
Paragraph 10, answer questions 2-4 p. 61 (orally), bring colored pencils.
Optionally:
Complete the task on p. 62
