Geographic coordinates determine the position of a point on the earth's surface. Geographic coordinates are based on the spherical principle and consist of latitude and longitude.
Latitude- the angle between the local zenith direction and the equatorial plane, measured from 0° to 90° on both sides of the equator. The geographic latitude of points located in the northern hemisphere (northern latitude) is usually considered positive, the latitude of points in the southern hemisphere is considered negative. It is customary to speak of latitudes close to the poles as high, and about those close to the equator - as about low.
Longitude- the angle between the plane of the meridian passing through a given point and the plane of the initial prime meridian, from which longitude is measured. Longitudes from 0° to 180° east of the prime meridian are called eastern, and to the west - western. Eastern longitudes are considered positive, western longitudes negative.
Geographic coordinates recording format
Geographic coordinates of a single point can be expressed in different formats. Depending on whether minutes and seconds are represented as values from 0 to 60 or from 0 to 100 (decimals).
The coordinate format is usually written as follows: DD- degrees, MM- minutes, SS- seconds, if minutes and seconds are presented as decimals, then they are written simply DD.DDDD. For example:
- DD MM SS: 50° 40" 45"" E, 40 50" 30"" N - degrees, minutes, seconds
- DDMM.MM: 50° 40.75" E, 40 50.5" N - degrees, decimal minutes
- DD.DDDDD: 50.67916 E, 40.841666 N - decimal degrees
Why do you need to know the coordinates of your home?
Often, houses in holiday villages and many villages do not have clear navigation consisting of signs with street names and house numbers, or even houses with signs with numbers can be scattered throughout the village in a random order (historically established as the village was developed). There are times when everything is fine with navigation in a populated area, but not all car GPS navigators contain such a house or street. Residents of such houses have to explain for a long time and, as a rule, confusingly how to get to them using different landmarks. In this case, it is easier to give the coordinates of the house, because any car navigator can plot the route using the coordinates.
To work out the technical feasibility of connecting to the Internet in a country house, we also ask our customers to provide the coordinates of the house, especially if it is not located at the address on any of the online mapping services.
Determining coordinates using online mapping services
Currently, the most famous online mapping services with a search function are Google and Yandex maps. Let's look at how you can determine geographic coordinates from a map or satellite image in the service Google Maps:
2. Find the exact location on the map. For this card can be moved mouse, zoom in and out by scrolling the mouse wheel. You can also find the desired location using search by name using a locality, street and house. To find the location of your home as accurately as possible, switch between display modes: Map, Hybrid or Satellite.
3. Click right click on the desired location on the map and select from the menu that opens paragraph “What's in here?” . A marker in the form of a green arrow will appear on the map. Repeat the operation if the marker is not positioned accurately.
4. When you hover your mouse over the green arrow, the geographic coordinates of the location will appear, and they will also appear in the search bar from where they can be copied to the clipboard.
Rice. 1. Determining the coordinates of a place using a pointer on a Google map
Now let's look at how you can determine geographic coordinates from a map or satellite image in the service Yandex.Maps:
To find a place, we use the same algorithm as for searching on Google maps. Open Yandex.Maps: http://maps.yandex.ru. To obtain coordinates on a Yandex map, use tool"Get information"(button with an arrow and a question mark, in the upper left part of the map). When you click on the map with this tool, a marker appears on the map and coordinates are displayed in the search bar.
Rice. 2. Determining the coordinates of a place using a sign on the Yandex map
Search engine maps by default show coordinates in degrees and decimals, with "-" signs for negative longitude. On Google maps and Yandex maps, latitude comes first, then longitude (until October 2012, the reverse order was adopted on Yandex maps: first longitude, then latitude).
Modern technologies greatly facilitate our lives, making it easier, simpler and more convenient. Among the variety of such innovations, an important place is occupied by tools that allow you to easily navigate the terrain, build a convenient route to a particular geographic point, and find toponyms and other topographical objects on the map. One of the options for finding the desired object on the map is to search for it using geographic coordinates. And in this material I will tell you how to search by coordinates on Yandex Map, and what are the features of this search.
As you know, in the modern digital market for mapping services there are several competing companies that offer the user the ability to search for a point by coordinates. The list of such services includes the popular “Google Maps”, “Yandex.Maps”, “2GIS” (specializing in detailing cities), “Bing Maps”, “HERE WeGo”, “OpenStreetMap” and the previously existing “Yahoo! Maps" (now closed).
The main competitors in the Russian market are “ Google.Maps" And " Yandex.Maps" If using maps from Google is preferable on a global scale, then in the vastness of Russia we would recommend using the Yandex company’s service. The latter provides better coverage of Russia, has a high level of detail, boasts a special tool for editing maps by users called “People's Map”, displays traffic jams in domestic cities, works well with “Geocoder”, and has other useful features.
To determine your location in the Russian Federation, it is better to use Yandex.Maps At the same time, you can use the Yandex.Maps functionality either using a regular desktop browser on a PC or by installing the mobile application of the same name on your phone (for example, from the Play Market).
Search by latitude and longitude
If you are faced with the question of searching for any geographical place on the map, or there is a need to point out some place on the map to another person, then you should use the method of determining the location of a geographical object by its coordinates, including latitude or longitude.
Let me remind the reader that latitude coordinates show the location of the desired object in relation to the North and South Pole (i.e. it is a point between north and south), and longitude coordinates determine the location of the object between east and west.
The usual zero latitude is the equator, therefore the south pole is at 90 degrees south latitude, and the north pole is at 90 degrees north latitude.
In this case, northern latitude is designated by the letter “N” (Nord), South – by the letter “S” (South), western longitude by the letter “W” (West), and eastern longitude by the letter “E” (East). ).
Find a place by coordinates on the Yandex Map
To determine the latitude and longitude coordinates of an object, just open “Yandex.Maps”, find the object we need on the map, and click on it with the cursor. A small window will immediately open next to the cursor, informing about the selected object and indicating its latitude and longitude coordinates.
Now, to find this object on the map, it will be enough to write down these numerical values, and then simply enter them separated by commas in the “Yandex.Maps” search bar and press enter. The map will immediately move to the given location and point you to the object specified by the entered coordinates.
It is most convenient to share such coordinates while somewhere in nature; the other party will easily find your location simply by entering your coordinates into the Yandex.Maps search bar.
In addition to finding the desired point by latitude and longitude, the Yandex.Maps functionality makes it possible to build a pedestrian, car, or bus route to it. To do this, just enter the numbers of latitude and longitude of the object you need into the search bar, click on enter, and after it is displayed on the screen, click on the button on the left “Build a route”.
Click on “Build a route” to build various route options to the desired geographical point You will need to enter the coordinates of the starting point of your journey (or type its address), and the service will automatically plot the most optimal route to it, and also indicate the approximate travel time and mileage.
Conclusion
If you need to search by your coordinates on Yandex Map, then it will be enough to enter the coordinates of the desired object by latitude and longitude in the search bar, and then press enter. If you just need to get the coordinates of the object you need, it will be enough to find it on Yandex.Map, click on it, and the required latitude and longitude coordinates will immediately be displayed in the sign that appears on the left.
The position of each point on the earth’s surface is determined by its coordinates: latitude and longitude (Fig. 3).Latitude is the angle formed by a plumb line passing through a given point on the Earth's surface and the plane of the equator (in Fig. 3 for point M angle MOC).
No matter where the observer is on the globe, his force of gravity will always be directed towards the center of the Earth. This direction is called plumb or vertical.
Latitude is measured by the arc of the meridian from the equator to the parallel of a given point in the range from 0 to 90° and is designated by the letter f. Thus, the geographic parallel eabq is the locus of points having the same latitude.
Depending on which hemisphere the point is located in, the latitude is given the name northern (N) or southern (S).
Longitude is called the dihedral angle between the planes of the initial meridian and the meridian of a given point (in Fig. 3 for point M angle AOS). Longitude is measured by the smaller of the arcs of the equator between the prime meridian and the meridian of a given point in the range from 0 to 180° and is designated by the letter l. Thus, the geographic meridian PN MCPs is the locus of points having the same longitude.
Depending on which hemisphere the point is located in, the longitude is called eastern (O st) or western (W).
Latitude difference and longitude difference
While sailing, the ship continuously changes its place on the surface of the Earth, therefore, its coordinates also change. The magnitude of the change in latitude Af, resulting from the passage of a ship from the departure point MI to the arrival point C1, is called difference in latitude(RS). RS is measured by the meridian arc between the parallels of departure and arrival points M1C1 (Fig. 4).
Rice. 4
The name of the RS depends on the location of the parallel of the arrival point relative to the parallel of the departure point. If the parallel of the arrival point is located north of the parallel of the departure point, then the RS is considered to be made to N, and if it is to the south, then to S.
The amount of change in longitude Al resulting from the passage of a ship from the departure point M1 to the arrival point C2 is called longitude difference(RD). The taxiway is measured by the smaller arc of the equator between the meridians of the point of departure and the point of arrival MCN (see Fig. 4). If, during the passage of the vessel, the eastern longitude increases or the western one decreases, then the taxiway is considered to be made to O st, and if the eastern longitude decreases or the western longitude increases, then to W. To determine the taxiway and taxiway, the formulas are used:
РШ = φ1 - φ2; (1)
RD = λ1 - λ2 (2)
Where φ1 is the latitude of the departure point;
φ2 - latitude of arrival point;
λ1 - longitude of departure point;
λ2 - longitude of the point of arrival.
In this case, northern latitudes and eastern longitudes are considered positive and are assigned a plus sign, while southern latitudes and western longitudes are considered negative and are assigned a minus sign. When solving problems using formulas (1) and (2), in the case of positive RS results, it will be done to N, and RD - to O st (see example 1), and in the case of negative RS results, it will be made to S, and RD - to W (see example 2). If a RD result is more than 180° with a negative sign, you need to add 360° (see example 3), and if the RD result is more than 180° with a positive sign, you need to subtract 360° (see example 4).
Example 1. Known: φ1 = 62°49" N; λ1 = 34°49" O st ; φ2 = 72°50"N; λ2 = 80°56" O st .
Find RS and RD.
Solution.
Example 2. Known: φ1 = 72°50" N; λ1 = :80°56"O st: φ2 = 62 O st 49"N;
Find RS and RD.
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6. SOLVING PROBLEMS ON A TOPOGRAPHIC MAP
6.I. DEFINITION OF MAP SHEET NOMENCLATURE
When solving a number of design and survey problems, the need arises to find the required map sheet of a given scale for a certain area of the area, i.e. in determining the nomenclature of a given map sheet. The nomenclature of a map sheet can be determined by the geographic coordinates of terrain points in a given area. In this case, you can also use flat rectangular coordinates of points, since there are formulas and special tables for converting them into the corresponding geographic coordinates.
EXAMPLE: Determine the nomenclature of a map sheet at a scale of 1: 10,000 based on the geographic coordinates of point M:
latitude = 52 0 48 ' 37 '' ; longitude L = 100°I8′ 4I".
First you need to determine the nomenclature of the scale map sheet
I: I 000 000, on which point M is located with given coordinates. As is known, the earth's surface is divided by parallels drawn through 4° into rows designated by capital letters of the Latin alphabet. Point N with latitude 52°48’37” is located in the 14th row from the equator, located between parallels 52° and 56°. This row corresponds to the I4th letter of the Latin alphabet -N. It is also known that the earth's surface is divided by meridians, drawn through 6°, into 60 columns. The columns are numbered in Arabic numerals from west to east, starting from the meridian with longitude I80°. The numbers of the columns differ from the numbers of the corresponding 6-degree zones of the Gauss projection by 30 units. Point M with longitude 100°18′ 4I" is located in the 17th zone, located between the meridians 96° and 102°. This zone corresponds to column number 47. The nomenclature of a map sheet of scale I: 1,000,000 is made up of the letter designating this row and the column number. Consequently, the nomenclature of the map sheet at a scale of 1: 1,000,000, on which point M is located, will be N-47.
Next, you need to determine the nomenclature of the map sheet, scale I: 100,000, on which point M falls. Sheets of a map of scale 1: 100,000 are obtained by dividing a sheet of sledge of scale 1: I,000,000 into 144 parts (Fig. 8). We divide each side of sheet N-47 into 12 equal parts and connect the corresponding points with segments of parallels and meridians. The resulting map sheets of scale 1 : 100,000 are numbered in Arabic numerals and have dimensions: 20' - in latitude and 30' - in longitude. From Fig. 8 it can be seen that point M with the given coordinates falls on a map sheet of scale I: 100,000 e number 117. The nomenclature of this sheet will be N-47-117.
Sheets of a map of scale I: 50,000 are obtained by dividing a sheet of map of scale I: 100,000 into 4 parts and are designated in capital letters of the Russian alphabet (Fig. 9). The nomenclature of the sheet of this map, on which the exact M falls, will be N- 47- 117. In turn, map sheets of scale I: 25,000 are obtained by dividing a sheet of map of scale I: 50,000 into 4 parts and are designated with lowercase letters of the Russian alphabet (Fig. 9). Point M with the given coordinates falls on a map sheet of scale I: 25,000, having the nomenclature N-47-117 – G-A.
Finally, the 1:10,000 scale map sheets are obtained by dividing the 1:25,000 scale map sheet into 4 parts and are designated with Arabic numerals. From Fig. 9 it can be seen that point M is located on a map sheet of this scale, which has the nomenclature N-47-117-G-A-1.
The answer to the solution to this problem is placed on the drawing.
6.2. DETERMINING COORDINATES OF POINTS ON THE MAP
For each current on a topographic map, you can determine its geographic coordinates (latitude and longitude) and rectangular Gaussian coordinates x, y.
To determine these coordinates, the map's degree and kilometer grids are used. to determine the geographic coordinates of point P, draw the southern parallel and western meridian closest to this point, connecting the minute divisions of the degree frame of the same name (Fig. 10).
The latitude B o and longitude L o of point A o are determined by the intersection of the drawn meridian and parallel. Through a given point P, draw lines parallel to the drawn meridian and parallel, and measure the distances B = A 1 P and L = A 2 P using a millimeter ruler, as well as the sizes of minute divisions of latitude C and longitude on maps. Geographic coordinates of point P are determined using the formulas C l
— latitude: B p = B o + *60 ’’
— longitude: L p = L o + *60’’ , measured to tenths of a millimeter.
Distances b, l, Cb, C l measured to tenths of a millimeter.
To determine the rectangular coordinates of a point R use a kilometer grid map. By digitizing this grid, coordinates are found on the map X o And U o the southwestern corner of the grid square in which point P is located (Fig. 11). Then from the point R lower the perpendiculars S 1 L And C 2 L on the sides of this square. The lengths of these perpendiculars are measured with an accuracy of tenths of a millimeter. ∆Х And ∆У and taking into account the scale of the map, their actual values on the ground are determined. For example, the measured distance S 1 R equals 12.8 we, and the map scale is 1: 10,000. According to the scale, I mm on the map corresponds to 10 m of terrain, which means
∆Х= 12.8 x 10 m = 128 m.
After defining the values ∆Х And ∆У find the rectangular coordinates of point P using the formulas
Xp= Xo+∆ X
Yp= Y o+∆ Y
The accuracy of determining the rectangular coordinates of a point depends on the map scale and can be found using the formula
t=0.1* M, mm,
where M is the map scale denominator.
For example, for a map of scale I: 25,000, the accuracy of determining the coordinates X And U amounts to t= 0.1 x 25,000 = 2500 mm = 2.5 m.
6.3. DETERMINING LINE ORIENTATION ANGLES
Line orientation angles include directional angle, true and magnetic azimuths.
To determine the true azimuth of a certain aircraft line from the map (Fig. 12), the degree frame of the map is used. Through the starting point B of this line, parallel to the vertical line of the degree frame, the line of the true meridian is drawn (dashed line NS), and then the value of the true azimuth A is measured with a geodetic protractor.
To determine the directional angle of a certain line DE from the map (Fig. I2), a kilometer map grid is used. Through the starting point D, draw parallel to the vertical line of the kilometer grid (dashed line KL). The drawn line will be parallel to the x-axis of the Gaussian projection, i.e., the axial meridian of the given zone. The directional angle α de is measured by geodetic transport relative to the drawn line KL. It should be noted that both the directional angle and the true azimuth are counted, and therefore measured, clockwise relative to the initial direction to the oriented line.
In addition to directly measuring the directional angle of a line on a map using a protractor, you can determine the value of this angle in another way. For this definition, the rectangular coordinates of the starting and ending points of the line (X d, Y d, X e, Y e). The directional angle of a given line can be found using the formula
When performing calculations using this formula using a microcalculator, you should remember that the angle t=arctg(∆y/∆x) is not a directional angle, but a table angle. The value of the directional angle in this case must be determined taking into account the signs ∆Х and ∆У using the known reduction formulas:
Angle α lies in the first quarter: ∆Х>0; ∆Y>0; α=t;
Angle α lies in the II quarter: ∆Х<0; ∆Y>0; α=180 o -t;
Angle α lies in the III quarter: ∆Х<0; ∆Y<0; α=180 o +t;
Angle α lies in the IV quarter: ∆Х>0; ∆Y<0; α=360 o -t;
In practice, when determining the reference angles of a line, they usually first find its directional angle, and then, knowing the declination of the magnetic needle δ and the convergence of the meridians γ (Fig. 13), proceed to the true magnetic azimuth, using the following formulas:
A=α+γ;
A m =A-δ=α+γ-δ=α-P,
Where P=δ-γ — the total correction for the declination of the magnetic needle and the convergence of the meridians.
The quantities δ and γ are taken with their signs. Angle γ is measured from the true meridian to the magnetic one and can be positive (eastern) and negative (western). Angle γ is measured from the degree frame (true meridian) to the vertical line of the kilometer grid and can also be positive (eastern) and negative (western). In the diagram shown in Fig. 13, the declination of the magnetic needle δ is eastern, and the convergence of the meridians is western (negative).
The average value of δ and γ for a given map sheet is given in the southwestern corner of the map below the design frame. The date of determination of the declination of the magnetic needle, the magnitude of its annual change and the direction of this change are also indicated here. Using this information, it is necessary to calculate the declination of the magnetic needle δ on the date of its determination.
EXAMPLE. Declension for 1971 Eastern 8 o 06’. The annual change is western declination 0 o 03’.
The declination value of the magnetic needle in 1989 will be equal to: δ=8 o 06’-0 o 03’*18=7 o 12’.
6.4 DETERMINATION BY HORIZONTAL HEIGHTS OF POINTS
The elevation of a point located on the horizontal is equal to the elevation of this horizontal. If the horizontal is not digitized, then its elevation is found by digitizing adjacent contours, taking into account the height of the relief section. It should be remembered that every fifth horizontal line on the map is digitized, and for the convenience of determining marks, the digitized horizontal lines are drawn with thick lines (Fig. 14, a). Horizontal marks are signed in line breaks so that the base of the numbers is directed towards the slope.
A more general case is when the point is between two horizontal lines. Let point P (Fig. 14, b), the elevation of which needs to be determined, be located between the horizontal lines with marks of 125 and 130 m. A straight line AB is drawn through point P as the shortest distance between the horizontal lines and the location d = AB and the segment l = AP are measured on the plan . As can be seen from the vertical section along line AB (Fig. 14, c), the value ∆h represents the excess of point P above the minor horizontal (125 m) and can be calculated using the formula
∆ h= * h ,
where h is the height of the relief section.
Then the elevation of point P will be equal to
H r = H A + ∆h.
If the point is located between horizontal lines with identical marks (point M in Fig. 14, a) or inside a closed horizontal (point K in Fig. 14, a), then the mark can only be determined approximately. In this case, it is considered that the elevation of the point is less or greater than the height of this horizon and half the height of the relief section, i.e. 0.5h (for example, N m = 142.5 m, H k = 157.5 m). Therefore, marks of characteristic points of the relief (top of a hill, bottom of a basin, etc.), obtained from measurements on the ground, are written out on plans and maps.
6.5 DETERMINING THE STEPLESS OF THE SLOPE BY THE LAYING SCHEDULE
The slope of the slope is the angle of inclination of the slope to the horizontal plane. The larger the angle, the steeper the slope. The slope angle v is calculated using the formula
V=arctg(h/ d),
where h is the height of the relief section, m;
d-laying, m;
Layout is the distance on the map between two adjacent contour lines; The steeper the slope, the smaller the laying.
To avoid calculations when determining the slopes and steepness of slopes from a plan or map, in practice, special graphs are used, called plotting graphs. A plotting graph is a graph of a function d= n* ctgν, the abscissas of which are the values of inclination angles, starting from 0°30´, and the ordinates are the values of locations corresponding to these inclination angles and expressed on the map scale (Fig. 15, a).
To determine the steepness of the slope using a compass solution, take the corresponding location from the map (for example, AB in Fig. 15, b) and transfer it to the location graph (Fig. 15, a) so that the segment AB is parallel to the vertical lines of the graph, and one leg of the compass was located on the horizontal line of the graph, the other leg was on the deposit curve.
The values of the slope steepness are determined using the digitization of the horizontal scale of the graph. In the example under consideration (Fig. 15), the slope slope is ν= 2°10´.
6.6. DESIGNING A GRADE LINE
When designing roads and railways, canals, and various utilities, the task arises of constructing the route of a future structure with a given slope on a map.
Suppose that on a map of scale 1:10000 it is required to outline the route of the highway between points A and B (Fig. 16). So that its slope along its entire length does not exceed i=0,05 . Height of the relief section on the map h= 5 m.
To solve the problem, calculate the amount of foundation corresponding to a given slope and section height h:
Then express the location on the map scale
where M is the denominator of the numerical scale of the map.
The magnitude of the laying d´ can also be determined from the laying graph, for which it is necessary to determine the angle of inclination ν corresponding to a given slope i, and use a compass to measure the laying for this angle of inclination.
The construction of a route between points A and B is carried out as follows. Using a compass solution equal to d´ = 10 mm, the adjacent horizontal line is marked from point A and point 1 is obtained (Fig. 16). From point 1, the next horizontal line is marked with the same compass solution, obtaining point 2, etc. By connecting the resulting points, draw a line with a given slope.
In many cases, the terrain makes it possible to outline not one, but several route options (for example, Options 1 and 2 in Fig. 16), from which the most acceptable for technical and economic reasons is selected. So, for example, of two route options, carried out approximately under the same conditions, the option with a shorter length of the designed route will be selected.
When constructing a route line on a map, it may turn out that from some point on the route the compass opening does not reach the next horizontal line, i.e. the calculated location d´ is less than the actual distance between two adjacent horizontal lines. This means that on this section of the route the slope of the slope is less than the specified one, and during design it is expensively regarded as a positive factor. In this case, this section of the route should be drawn along the shortest distance between the horizontal lines towards the end point.
6.7. DETERMINATION OF THE BOUNDARY OF THE WATER COLLECTION AREA
Drainage area, or by the pool. This is a section of the earth's surface from which, according to relief conditions, water should flow into a given drain (hollow, stream, river, etc.). The delineation of the catchment area is carried out taking into account the horizontal topography. The boundaries of the drainage area are watershed lines that intersect horizontal lines at right angles.
Figure 17 shows a ravine through which stream PQ flows. The basin boundary is shown by the dotted line HCDEFG and drawn along the watershed lines. It should be remembered that watershed lines are the same as drainage lines (thalwegs). The horizontal lines intersect in places of their greatest curvature (with a smaller radius of curvature).
When designing hydraulic structures (dams, sluices, embankments, dams, etc.), the boundaries of the drainage area may slightly change their position. For example, let it be planned to build a hydraulic structure (AB-axis of this structure) on the site under consideration (Fig. 17).
From the end points A and B of the designed structure, straight lines AF and BC are drawn to the watersheds, perpendicular to the horizontal lines. In this case, the BCDEFA line will become the watershed boundary. Indeed, if we take points m 1 and m 2 inside the pool, and points n 1 and n 2 outside it, then it is difficult to notice that the direction of the slope from points m 1 and m 2 goes to the planned structure, and from points n 1 and n 2 passes him.
Knowing the drainage area, average annual precipitation, evaporation conditions and moisture absorption by the soil, it is possible to calculate the power of water flow to calculate hydraulic structures.
6.8. Construction of a terrain profile in a given direction
A line profile is a vertical section along a given direction. The need to construct a terrain profile in a given direction arises when designing engineering structures, as well as when determining visibility between terrain points.
To construct a profile along line AB (Fig. 18,a), by connecting points A and B with a straight line, we obtain the points of intersection of straight AB with the horizontal lines (points 1, 2, 3, 4, 5, 6, 7). These points, as well as points A and B, are transferred to a strip of paper, attaching it to line AB, and the marks are signed, defining them horizontally. If straight line AB intersects a watershed or drainage line, then the marks of the points of intersection of the straight line with these lines will be determined approximately by interpolating along these lines.
It is most convenient to construct a profile on graph paper. The construction of the profile begins by drawing a horizontal line MN, onto which the distances between the intersection points A, 1, 2, 3, 4, 5, 6, 7, B are transferred from a strip of paper.
Select a conventional horizon so that the profile line does not intersect anywhere with the conventional horizon line. To do this, the elevation of the conventional horizon is taken 20-20 m less than the minimum elevation in the considered row of points A, 1, 2, ..., B. Then a vertical scale is selected (usually for greater clarity, 10 times larger than the horizontal scale, i.e. map scale) . At each of the points A, 1, 2. ..., B, perpendiculars are restored on the line MN (Fig. 18, b) and the marks of these points are laid on them in the accepted vertical scale. By connecting the resulting points A´, 1´, 2´, ..., B´ with a smooth curve, a terrain profile is obtained along line AB.
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Lesson questions:
1. Coordinate systems used in topography: geographic, flat rectangular, polar and bipolar coordinates, their essence and use.
Coordinates are called angular and linear quantities (numbers) that determine the position of a point on any surface or in space.
In topography, coordinate systems are used that make it possible to most simply and unambiguously determine the position of points on the earth's surface, both from the results of direct measurements on the ground and using maps. Such systems include geographic, flat rectangular, polar and bipolar coordinates.
Geographic coordinates(Fig. 1) – angular values: latitude (j) and longitude (L), which determine the position of an object on the earth’s surface relative to the origin of coordinates – the point of intersection of the prime (Greenwich) meridian with the equator. On a map, the geographic grid is indicated by a scale on all sides of the map frame. The western and eastern sides of the frame are meridians, and the northern and southern sides are parallels. In the corners of the map sheet the geographical coordinates of the points of intersection of the sides of the frame are written.
Rice. 1. System of geographical coordinates on the earth's surface |
In the geographic coordinate system, the position of any point on the earth's surface relative to the origin of coordinates is determined in angular measure. In our country and in most other countries, the point of intersection of the prime (Greenwich) meridian with the equator is taken as the beginning. Being thus uniform for our entire planet, the system of geographic coordinates is convenient for solving problems of determining the relative position of objects located at significant distances from each other. Therefore, in military affairs, this system is used mainly for conducting calculations related to the use of long-range combat weapons, for example, ballistic missiles, aviation, etc.
Plane rectangular coordinates(Fig. 2) - linear quantities that determine the position of an object on a plane relative to the accepted origin of coordinates - the intersection of two mutually perpendicular lines (coordinate axes X and Y).
In topography, each 6-degree zone has its own system of rectangular coordinates. The X axis is the axial meridian of the zone, the Y axis is the equator, and the point of intersection of the axial meridian with the equator is the origin of coordinates.
The plane rectangular coordinate system is zonal; it is established for each six-degree zone into which the Earth’s surface is divided when depicting it on maps in the Gaussian projection, and is intended to indicate the position of images of points of the earth’s surface on a plane (map) in this projection.
The origin of coordinates in a zone is the point of intersection of the axial meridian with the equator, relative to which the position of all other points in the zone is determined in a linear measure. The origin of the zone and its coordinate axes occupy a strictly defined position on the earth's surface. Therefore, the system of flat rectangular coordinates of each zone is connected both with the coordinate systems of all other zones and with the system of geographical coordinates.
The use of linear quantities to determine the position of points makes the system of flat rectangular coordinates very convenient for carrying out calculations both when working on the ground and on a map. Therefore, this system is most widely used among the troops. Rectangular coordinates indicate the position of terrain points, their battle formations and targets, and with their help determine the relative position of objects within one coordinate zone or in adjacent areas of two zones.
Polar and bipolar coordinate systems are local systems. In military practice, they are used to determine the position of some points relative to others in relatively small areas of the terrain, for example, when designating targets, marking landmarks and targets, drawing up terrain diagrams, etc. These systems can be associated with systems of rectangular and geographic coordinates.
2. Determining geographic coordinates and plotting objects on a map using known coordinates.
The geographic coordinates of a point located on the map are determined from the nearest parallel and meridian, the latitude and longitude of which are known.
The topographic map frame is divided into minutes, which are separated by dots into divisions of 10 seconds each. Latitudes are indicated on the sides of the frame, and longitudes are indicated on the northern and southern sides.
Using the minute frame of the map you can:
1
. Determine the geographic coordinates of any point on the map.
For example, the coordinates of point A (Fig. 3). To do this, you need to use a measuring compass to measure the shortest distance from point A to the southern frame of the map, then attach the meter to the western frame and determine the number of minutes and seconds in the measured segment, add the resulting (measured) value of minutes and seconds (0"27") with the latitude of the southwest corner of the frame - 54°30".
Latitude points on the map will be equal to: 54°30"+0"27" = 54°30"27".
Longitude is defined similarly.
Using a measuring compass, measure the shortest distance from point A to the western frame of the map, apply the measuring compass to the southern frame, determine the number of minutes and seconds in the measured segment (2"35"), add the resulting (measured) value to the longitude of the southwestern corner frames - 45°00".
Longitude points on the map will be equal to: 45°00"+2"35" = 45°02"35"
2. Plot any point on the map according to the given geographical coordinates.
For example, point B latitude: 54°31 "08", longitude 45°01 "41".
To plot a point in longitude on a map, it is necessary to draw the true meridian through this point, for which you connect the same number of minutes along the northern and southern frames; To plot a point in latitude on a map, it is necessary to draw a parallel through this point, for which you connect the same number of minutes along the western and eastern frames. The intersection of two lines will determine the location of point B.
3. Rectangular coordinate grid on topographic maps and its digitization. Additional grid at the junction of coordinate zones.
The coordinate grid on the map is a grid of squares formed by lines parallel to the coordinate axes of the zone. Grid lines are drawn through an integer number of kilometers. Therefore, the coordinate grid is also called the kilometer grid, and its lines are kilometer.
On a 1:25000 map, the lines forming the coordinate grid are drawn through 4 cm, that is, through 1 km on the ground, and on maps 1:50000-1:200000 through 2 cm (1.2 and 4 km on the ground, respectively). On a 1:500000 map, only the outputs of the coordinate grid lines are plotted on the inner frame of each sheet every 2 cm (10 km on the ground). If necessary, coordinate lines can be drawn on the map along these outputs.
On topographic maps, the values of the abscissa and ordinate of coordinate lines (Fig. 2) are signed at the exits of the lines outside the inner frame of the sheet and in nine places on each sheet of the map. The full values of the abscissa and ordinate in kilometers are written near the coordinate lines closest to the corners of the map frame and near the intersection of the coordinate lines closest to the northwestern corner. The remaining coordinate lines are abbreviated with two numbers (tens and units of kilometers). The labels near the horizontal grid lines correspond to the distances from the ordinate axis in kilometers.
Labels near the vertical lines indicate the zone number (one or two first digits) and the distance in kilometers (always three digits) from the origin, conventionally moved west of the zone’s axial meridian by 500 km. For example, the signature 6740 means: 6 - zone number, 740 - distance from the conventional origin in kilometers.
On the outer frame there are outputs of coordinate lines ( additional mesh) coordinate system of the adjacent zone.
4. Determination of rectangular coordinates of points. Drawing points on a map according to their coordinates.
Using a coordinate grid using a compass (ruler), you can:
1.
Determine the rectangular coordinates of a point on the map.
For example, points B (Fig. 2).
To do this you need:
- write X - digitization of the bottom kilometer line of the square in which point B is located, i.e. 6657 km;
- measure the perpendicular distance from the bottom kilometer line of the square to point B and, using the linear scale of the map, determine the size of this segment in meters;
- add the measured value of 575 m with the digitization value of the lower kilometer line of the square: X=6657000+575=6657575 m.
The Y ordinate is determined in the same way:
- write down the Y value - digitization of the left vertical line of the square, i.e. 7363;
- measure the perpendicular distance from this line to point B, i.e. 335 m;
- add the measured distance to the Y digitization value of the left vertical line of the square: Y=7363000+335=7363335 m.
2.
Place the target on the map at the given coordinates.
For example, point G at coordinates: X=6658725 Y=7362360.
To do this you need:
- find the square in which point G is located according to the value of whole kilometers, i.e. 5862;
- set aside from the lower left corner of the square a segment on the map scale equal to the difference between the abscissa of the target and the bottom side of the square - 725 m;
- - from the obtained point, along the perpendicular to the right, plot a segment equal to the difference between the ordinates of the target and the left side of the square, i.e. 360 m.
The accuracy of determining geographic coordinates using 1:25000-1:200000 maps is about 2 and 10"" respectively.
The accuracy of determining the rectangular coordinates of points from a map is limited not only by its scale, but also by the magnitude of errors allowed when shooting or drawing up a map and plotting various points and terrain objects on it
Most accurately (with an error not exceeding 0.2 mm) geodetic points and are plotted on the map. objects that stand out most sharply in the area and are visible from a distance, having the significance of landmarks (individual bell towers, factory chimneys, tower-type buildings). Therefore, the coordinates of such points can be determined with approximately the same accuracy with which they are plotted on the map, i.e. for a map of scale 1:25000 - with an accuracy of 5-7 m, for a map of scale 1:50000 - with an accuracy of 10-15 m, for a map of scale 1:100000 - with an accuracy of 20-30 m.
The remaining landmarks and contour points are plotted on the map, and, therefore, determined from it with an error of up to 0.5 mm, and points related to contours that are not clearly defined on the ground (for example, the contour of a swamp), with an error of up to 1 mm.
6. Determining the position of objects (points) in polar and bipolar coordinate systems, plotting objects on a map by direction and distance, by two angles or by two distances.
System flat polar coordinates(Fig. 3, a) consists of point O - the origin, or poles, and the initial direction of the OR, called polar axis.
System flat bipolar (two-pole) coordinates(Fig. 3, b) consists of two poles A and B and a common axis AB, called the basis or base of the notch. The position of any point M relative to two data on the map (terrain) of points A and B is determined by the coordinates that are measured on the map or on the terrain.
These coordinates can be either two position angles that determine the directions from points A and B to the desired point M, or the distances D1=AM and D2=BM to it. The position angles in this case, as shown in Fig. 1, b, are measured at points A and B or from the direction of the basis (i.e. angle A = BAM and angle B = ABM) or from any other directions passing through points A and B and taken as the initial ones. For example, in the second case, the location of point M is determined by the position angles θ1 and θ2, measured from the direction of the magnetic meridians.
Drawing a detected object on a map
This is one of the most important points in detecting an object. The accuracy of determining its coordinates depends on how accurately the object (target) is plotted on the map.
Having discovered an object (target), you must first accurately determine by various signs what has been detected. Then, without stopping observing the object and without detecting yourself, put the object on the map. There are several ways to plot an object on a map.
Visually: A feature is plotted on the map if it is near a known landmark.
By direction and distance: to do this, you need to orient the map, find the point of your standing on it, indicate on the map the direction to the detected object and draw a line to the object from the point of your standing, then determine the distance to the object by measuring this distance on the map and comparing it with the scale of the map.
 Rice. 4. Drawing the target on the map using a straight line |
If it is graphically impossible to solve the problem in this way (the enemy is in the way, poor visibility, etc.), then you need to accurately measure the azimuth to the object, then translate it into a directional angle and draw on the map from the standing point the direction at which to plot the distance to the object. |
7. Methods of target designation on the map: in graphic coordinates, flat rectangular coordinates (full and abbreviated), by kilometer grid squares (up to a whole square, up to 1/4, up to 1/9 square), from a landmark, from a conventional line, in azimuth and target range, in a bipolar coordinate system.
The ability to quickly and correctly indicate targets, landmarks and other objects on the ground is important for controlling units and fire in battle or for organizing battle.
Targeting in geographical coordinates used very rarely and only in cases where targets are located at a considerable distance from a given point on the map, expressed in tens or hundreds of kilometers. In this case, geographic coordinates are determined from the map, as described in question No. 2 of this lesson.
The location of the target (object) is indicated by latitude and longitude, for example, height 245.2 (40° 8" 40" N, 65° 31" 00" E). On the eastern (western), northern (southern) sides of the topographic frame, marks of the target position in latitude and longitude are applied with a compass. From these marks, perpendiculars are lowered into the depth of the topographic map sheet until they intersect (commander’s rulers and standard sheets of paper are applied). The point of intersection of the perpendiculars is the position of the target on the map.
For approximate target designation by rectangular coordinates It is enough to indicate on the map the grid square in which the object is located. The square is always indicated by the numbers of the kilometer lines, the intersection of which forms the southwest (lower left) corner. When indicating the square of the map, the following rule is followed: first they call two numbers signed at the horizontal line (on the western side), that is, the “X” coordinate, and then two numbers at the vertical line (the southern side of the sheet), that is, the “Y” coordinate. In this case, “X” and “Y” are not said. For example, enemy tanks were detected. When transmitting a report by radiotelephone, the square number is pronounced: "eighty eight zero two."
If the position of a point (object) needs to be determined more accurately, then full or abbreviated coordinates are used.
Working with full coordinates. For example, you need to determine the coordinates of a road sign in square 8803 on a map at a scale of 1:50000. First, determine the distance from the bottom horizontal side of the square to the road sign (for example, 600 m on the ground). In the same way, measure the distance from the left vertical side of the square (for example, 500 m). Now, by digitizing kilometer lines, we determine the full coordinates of the object. The horizontal line has the signature 5988 (X), adding the distance from this line to the road sign, we get: X = 5988600. We determine the vertical line in the same way and get 2403500. The full coordinates of the road sign are as follows: X = 5988600 m, Y = 2403500 m.
Abbreviated coordinates respectively will be equal: X=88600 m, Y=03500 m.
If it is necessary to clarify the position of a target in a square, then target designation is used in an alphabetic or digital way inside the square of a kilometer grid.
During target designation literal way inside the square of the kilometer grid, the square is conditionally divided into 4 parts, each part is assigned a capital letter of the Russian alphabet.
Second way - digital way target designation inside the square kilometer grid (target designation by snail
). This method got its name from the arrangement of conventional digital squares inside the square of the kilometer grid. They are arranged as if in a spiral, with the square divided into 9 parts.
When designating targets in these cases, they name the square in which the target is located, and add a letter or number that specifies the position of the target inside the square. For example, height 51.8 (5863-A) or high-voltage support (5762-2) (see Fig. 2).
Target designation from a landmark is the simplest and most common method of target designation. With this method of target designation, the landmark closest to the target is first named, then the angle between the direction to the landmark and the direction to the target in protractor divisions (measured with binoculars) and the distance to the target in meters. For example: “Landmark two, forty to the right, further two hundred, near a separate bush there is a machine gun.”
Target designation from the conditional line usually used in motion on combat vehicles. With this method, two points are selected on the map in the direction of action and connected by a straight line, relative to which target designation will be carried out. This line is denoted by letters, divided into centimeter divisions and numbered starting from zero. This construction is done on the maps of both transmitting and receiving target designation.
Target designation from a conventional line is usually used in movement on combat vehicles. With this method, two points are selected on the map in the direction of action and connected by a straight line (Fig. 5), relative to which target designation will be carried out. This line is denoted by letters, divided into centimeter divisions and numbered starting from zero.
 Rice. 5. Target designation from the conditional line |
This construction is done on the maps of both transmitting and receiving target designation. |
Target designation from a conventional line can be given by indicating the direction to the target at an angle from the conventional line and the distance to the target, for example: “Straight AC, right 3-40, one thousand two hundred – machine gun.”
Target designation in azimuth and range to the target. The azimuth of the direction to the target is determined using a compass in degrees, and the distance to it is determined using an observation device or by eye in meters. For example: “Azimuth thirty-five, range six hundred—a tank in a trench.”
This method is most often used in areas where there are few landmarks.
8. Problem solving.
Determining the coordinates of terrain points (objects) and target designation on the map is practiced practically on training maps using previously prepared points (marked objects).
Each student determines geographic and rectangular coordinates (maps objects according to known coordinates).
Methods of target designation on the map are worked out: in flat rectangular coordinates (full and abbreviated), by squares of a kilometer grid (up to a whole square, up to 1/4, up to 1/9 of a square), from a landmark, along the azimuth and range of the target.
Notes
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