How to determine the geographic coordinates of an object on a map. What is the geographic latitude and longitude of an object: explanation and determination of geographic coordinates of latitude and longitude on the world map, Yandex and Google map online

Geographical coordinates -angular values: latitude (p and longitude TO, determining the position of objects on the earth’s surface and on the map (Fig. 20).

Latitude is the angle (p between the plumb line at a given point and the plane of the equator. Latitudes vary from 0 to 90°; in the northern hemisphere they are called northern, in the southern - southern.

Longitude - dihedral angle TO between the plane of the prime meridian and the plane of the meridian of a given point on the earth's surface. The prime meridian is taken to be the meridian passing through the center of the Greenwich Observatory (London area). The prime meridian is called Greenwich. Longitudes vary from 0 to 180°. Longitudes measured east of the Greenwich meridian are called eastern, and longitudes,. counted to the west - western.

Geographic coordinates obtained from astronomical observations are called astronomical, and coordinates obtained by geodetic methods and determined from topographic maps are called geodetic. The values ​​of astronomical and geodetic coordinates of the same points differ slightly - in linear measures by an average of 60-90 m.

Geographic (cartographic) grid formed on the map by lines of parallels and meridians. It is used for targeting and determining the geographic coordinates of objects.

On topographic maps, the lines of parallels and meridians serve as the internal frames of the sheets; their latitudes and longitudes are signed on the corners of each sheet. On sheets of maps of the western hemisphere, the inscription “West of Greenwich” is placed in the northwestern corner of the frame.

Rice. 20.Geographic coordinates: f-latitude of point L; TO- longitude of the point A

On sheets of maps of scale 1:50000, 1:100000 and 1:200000 the intersections of average parallels and meridians are shown and their digitization in degrees and minutes is given. Using these data, the signatures of the latitudes and longitudes of the sides of the frames of the sheets cut off when gluing the map are reconstructed. In addition, along the sides of the frames inside the sheet there are small ones (2-3 mm) strokes after one minute, along which you can draw parallels and meridians on a map glued together from many sheets.

On maps of scale 1:25,000, 1:50,000 and 1:200,000, the sides of the frames are divided into segments equal to one minute in degrees. Minute segments are shaded every other and separated by dots (with the exception of the 1:200000 scale map) into parts of 10".

On map sheets at a scale of 1:500,000, parallels are drawn through 30", and meridians through 20"; on maps at scale 1:1000000

parallels are drawn through 1°, meridians - through 40". Inside each sheet of the map, their latitudes and longitudes are signed on the lines of parallels and meridians, which make it possible to determine geographic coordinates on a large map glued together.

Definition geographic coordinates of the object on the map is carried out according to the parallels and meridians closest to it, the latitude and longitude of which are known. On maps of scale 1:25000-

1:200,000 for this it is necessary, as a rule, to first draw a parallel to the south of the object and a meridian to the west, connecting with lines the corresponding strokes along the frame of the map sheet. The latitude of the parallel and the longitude of the meridian are calculated and signed on the map (V degrees and minutes). Then the segments from the object to the parallel and the meridian are estimated in angular measure (in seconds or fractions of a minute) ( Ami And Amiin Fig. 21), comparing their linear dimensions with minute (second) intervals on the sides of the frame. Size of the segment At\ is added to the latitude of the parallel, and the segmentAmi-to the longitude of the meridian and obtain the desired geographic coordinates of the object - latitude and longitude.

In Fig. Figure 21 shows an example of determining the geographic coordinates of an object A, its coordinates: north latitude 54°35"40", east longitude 37°41"30".

Drawing an object on a map using geographic coordinates. On the western and eastern sides of the frame of the map sheet, marks corresponding to the latitude of the object are marked with dashes. The latitude count starts from the digitization of the southern side of the frame and continues at minute and second intervals. Then a parallel line to the object is drawn through these lines.

The meridian of an object is constructed in the same way, only its longitude is measured along the southern and northern sides of the frame. The intersection point of the parallel and the meridian will indicate the position of the object on the map.

In Fig. 21 provides an example of mapping an object IN at coordinates: 54°38",3 and 37°34",7.

Geographic longitude and latitude are used to accurately determine the physical location of any object on the globe. The easiest way to find geographic coordinates is to use a geographic map. This method requires some theoretical knowledge to implement it. How to determine longitude and latitude is described in the article.

Geographical coordinates

Coordinates in geography are a system in which each point on the surface of our planet is assigned a set of numbers and symbols that allows the precise location of that point to be determined. Geographic coordinates are expressed in three numbers - latitude, longitude and altitude above sea level. The first two coordinates, that is, latitude and longitude, are most often used in various geographical problems. The origin of the report in the geographic coordinate system is at the center of the Earth. To represent latitude and longitude, spherical coordinates are used, which are expressed in degrees.

Before considering the question of how to determine longitude and latitude by geography, you should understand these concepts in more detail.

The concept of latitude

The latitude of a specific point on the Earth's surface is understood as the angle between the equatorial plane and the line connecting this point with the center of the Earth. Through all points of the same latitude, you can draw a plane that will be parallel to the plane of the equator.

The equatorial plane is the zero parallel, that is, its latitude is 0°, and it divides the entire globe into the southern and northern hemispheres. Accordingly, the north pole lies at the parallel of 90° north latitude, and the south pole lies at the parallel of 90° south latitude. The distance that corresponds to 1° when moving along a particular parallel depends on what kind of parallel it is. As latitude increases, moving north or south, this distance decreases. Therefore, is 0°. Knowing that the circumference of the Earth at the latitude of the equator has a length of 40075.017 km, we obtain the length of 1° along this parallel equal to 111.319 km.

Latitude shows how far north or south a given point on the Earth's surface lies from the equator.

The concept of longitude

The longitude of a specific point on the Earth's surface is understood as the angle between the plane passing through this point and the Earth's axis of rotation, and the plane of the prime meridian. According to the settlement agreement, the zero meridian is the one that passes through the Royal Observatory at Greenwich, located in the southeast of England. The Greenwich meridian divides the globe into eastern and

Thus, each line of longitude passes through the north and south poles. The lengths of all meridians are equal and amount to 40007.161 km. If we compare this figure with the length of the zero parallel, we can say that the geometric shape of planet Earth is a ball flattened at the poles.

Longitude shows how far west or east of the prime (Greenwich) meridian a specific point on Earth lies. If latitude has a maximum value of 90° (the latitude of the poles), then the maximum value of longitude is 180° west or east of the prime meridian. The 180° meridian is known as the International Date Line.

An interesting question to ask is which points cannot have their longitude determined. Based on the definition of a meridian, we find that all 360 meridians pass through two points on the surface of our planet; these points are the south and north poles.

Geographical degree

From the above figures it is clear that 1° on the Earth’s surface corresponds to a distance of more than 100 km, either along a parallel or along a meridian. For more accurate coordinates of an object, the degree is divided into tenths and hundredths, for example, they say 35.79 north latitude. This type of information is provided by satellite navigation systems such as GPS.

Conventional geographic and topographic maps represent fractions of degrees in minutes and seconds. Thus, each degree is divided into 60 minutes (denoted by 60"), and each minute is divided into 60 seconds (denoted by 60"). An analogy can be drawn here with the idea of ​​measuring time.

Getting to know the geographic map

To understand how to determine geographic latitude and longitude on a map, you must first become familiar with it. In particular, you need to understand how longitude and latitude coordinates are represented on it. Firstly, the top part of the map shows the northern hemisphere, the bottom part shows the southern hemisphere. The numbers on the left and right sides of the map indicate latitude, and the numbers on the top and bottom of the map indicate longitude coordinates.

Before determining the latitude and longitude coordinates, you need to remember that they are presented on the map in degrees, minutes and seconds. This system of units should not be confused with decimal degrees. For example, 15" = 0.25°, 30" = 0.5°, 45"" = 0.75".

Using a geographic map to determine longitude and latitude

We will explain in detail how to determine longitude and latitude by geography using a map. To do this, you first need to purchase a standard geographic map. This map can be a map of a small area, a region, a country, a continent, or the entire world. To understand which card you are dealing with, you should read its name. At the bottom, under the name, the limits of latitude and longitude that are presented on the map can be given.

After this, you need to select a certain point on the map, some object that needs to be marked in some way, for example, with a pencil. How to determine the longitude of an object located at a selected point, and how to determine its latitude? The first step is to find the vertical and horizontal lines that lie closest to the selected point. These lines are latitude and longitude, the numerical values ​​of which can be seen at the edges of the map. Let's assume that the selected point lies between 10° and 11° north latitude and 67° and 68° west longitude.

Thus, we know how to determine the geographic latitude and longitude of the object selected on the map with the accuracy that the map provides. In this case, the accuracy is 0.5°, both in latitude and longitude.

Determining the exact value of geographic coordinates

How to determine the longitude and latitude of a point more accurately than 0.5°? First you need to find out what scale the map you are working with is on. Typically, a scale bar is indicated in one of the corners of the map, showing the correspondence of distances on the map to distances in geographic coordinates and in kilometers on the ground.

After you have found a scale ruler, you need to take a simple ruler with millimeter divisions and measure the distance on the scale ruler. Let, in the example under consideration, 50 mm correspond to 1° latitude and 40 mm correspond to 1° longitude.

Now we position the ruler so that it is parallel to the lines of longitude drawn on the map, and measure the distance from the point in question to one of the nearest parallels, for example, the distance to the 11° parallel is 35 mm. We make a simple proportion and find that this distance corresponds to 0.3° from the 10° parallel. Thus, the latitude of the point in question is +10.3° (the plus sign means north latitude).

Similar steps should be done for longitude. To do this, place the ruler parallel to the lines of latitude and measure the distance to the nearest meridian from the selected point on the map, let’s say this distance is 10 mm to the meridian 67° west longitude. According to the rules of proportion, we find that the longitude of the object in question is -67.25° (the minus sign means western longitude).

Converting the received degrees into minutes and seconds

As stated above, 1° = 60" = 3600". Using this information and the rule of proportion, we find that 10.3° corresponds to 10°18"0". For the longitude value we get: 67.25° = 67°15"0". In this case, the proportion was used for conversion once for longitude and latitude. However, in the general case, when after using the proportion once fractional values ​​of minutes are obtained, it should be use the proportion a second time to get the value of incremental seconds. Note that the accuracy of determining coordinates up to 1" corresponds to an accuracy on the surface of the globe equal to 30 meters.

Recording received coordinates

After the question of how to determine the longitude of an object and its latitude has been answered, and the coordinates of the selected point have been determined, they should be written down correctly. The standard form of notation is to indicate longitude after latitude. Both values ​​must be specified with as many decimal places as possible, since this determines the accuracy of the object's location.

Defined coordinates can be represented in two different formats:

1. Using only the degree icon, for example +10.3°, -67.25°.
2. Using minutes and seconds, for example 10°18"0""N, 67°15"0""W.

It should be noted that in the case of representing geographic coordinates only using degrees, the words “north (south) latitude” and “east (west) longitude” are replaced by the corresponding plus or minus sign.

Geographic latitude and longitude are plotted on a world map. With their help, it is easy to determine the location of an object.

A geographical map of the world is a reduced projection of the earth's surface on a plane. It shows continents, islands, oceans, seas, rivers, as well as countries, large cities and other objects.

• The geographical map has a coordinate grid.
• On it you can clearly see information about the continents, seas and oceans, and the map allows you to create an image of the relief of the world.
• Using a geographic map, you can calculate the distance between cities and countries. It is also convenient to search for the location of land and ocean objects.

The shape of the Earth is like a sphere. If you need to determine a point on the surface of this sphere, then you can use a globe, which is our planet in miniature. But there is the most common way to find a point on Earth - these are geographical coordinates - latitude and longitude. These parallels are measured in degrees.

Geographic map of the world with latitude and longitude - photo:

The parallels that are drawn along and across the entire map are latitude and longitude. With their help you can quickly and easily find anywhere in the world.

The geographical map of the hemispheres is easy to understand. On one hemisphere (eastern) Africa, Eurasia and Australia are depicted. On the other, the western hemisphere, are North and South America.

Our ancestors studied latitude and longitude. Even then there were world maps that were not similar to modern ones, but with their help you can also determine where an object is located and what. A simple explanation of what the geographic latitude and longitude of an object on a map are:

Latitude is a coordinate value in the system of spherical numbers, which defines a point on the surface of our planet relative to the equator.

• If objects are located in the northern hemisphere, then the geographic latitude is called positive, if in the southern hemisphere - negative.
• South latitude - the object moves from the equator towards the North Pole.
• North latitude - the object is moving towards the South Pole from the equator.
• On a map, latitudes are lines parallel to each other. The distance between these lines is measured in degrees, minutes, seconds. One degree is 60 minutes, and one minute is 60 seconds.
• The equator is zero latitude.

Longitude is a coordinate quantity that determines the location of an object relative to the prime meridian.

• This coordinate allows you to find out the location of the object relative to the west and east.
• Lines of longitude are meridians. They are located perpendicular to the equator.
• The zero reference point for longitude in geography is the Greenwich Laboratory, which is located in east London. This line of longitude is commonly called the Greenwich Meridian.
• Objects that are located to the east of the Greenwich meridian are the eastern longitude region, and to the west are the western longitude region.
• Indicators of eastern longitude are considered positive, and indicators of western longitude are considered negative.

Using the meridian, a direction such as north-south is determined, and vice versa.

Latitude on a geographic map is measured from the equator—zero degrees. At the poles there are 90 degrees of latitude.

From what points, what meridian is geographic longitude measured?

Longitude on a geographic map is measured from Greenwich. The prime meridian is 0°. The farther an object is from Greenwich, the greater its longitude.

To determine the location of an object, you need to know its geographic latitude and longitude. As mentioned above, latitude shows the distance from the equator to a given object, and longitude shows the distance from Greenwich to the desired object or point.

How to measure, find out geographic latitude and longitude on a world map? Each parallel of latitude is designated by a specific number - a degree.

Meridians are also designated by degrees.

Any point will be located either at the intersection of the meridian and the parallel, or at the intersection of intermediate indicators. Therefore, its coordinates are indicated by specific indicators of latitude and longitude. For example, St. Petersburg is located at the following coordinates: 60° north latitude and 30° east longitude.

As stated above, latitude is parallels. To determine it, you need to draw a line parallel to the equator or a nearby parallel.

• If the object is located on the parallel itself, then it is easy to determine its location (as described above).
• If an object is between parallels, then its latitude is determined by the nearest parallel from the equator.
• For example, Moscow is located north of the 50th parallel. The distance to this object is measured along the meridian and it is equal to 6°, which means that Moscow’s geographic latitude is 56°.

A clear example of determining geographic latitude coordinates on a world map can be found in the following video:

Video: Geographic latitude and geographic longitude. Geographical coordinates

To determine geographic longitude, you need to determine the meridian on which the point is located, or its intermediate value.

• For example, St. Petersburg is located on a meridian whose value is 30°.
• But what if the object is located between the meridians? How to determine its longitude?
• For example, Moscow is located east of 30° east longitude.
• Now add the number of degrees along the parallel to this meridian. It turns out 8° - which means the geographic longitude of Moscow is equal to 38° east longitude.

Another example of determining the geographic coordinates of longitude and latitude on a world map in the video:

Video: Determining latitude and longitude

Any map shows all the parallels and meridians. What is the maximum value of geographic latitude and longitude? The greatest value of geographic latitude is 90°, and longitude is 180°. The smallest latitude value is 0° (equator), and the smallest longitude value is also 0° (Greenwich).

Geographic latitude and longitude of the poles and the equator: what is it equal to?

The geographic latitude of the points of the earth's equator is 0°, the North Pole +90°, and the South Pole -90°. The longitude of the poles is not determined, since these objects are located on all meridians at once.

Students may need to determine geographic coordinates from maps in real time when taking a test or exam.

• It's convenient, fast and simple. Determining the geographic coordinates of latitude and longitude on Yandex and Google maps online can be done on various services on the Internet.
• For example, you just need to enter the name of an object, city or country and click on it on the map. The geographic coordinates of this object will instantly appear.
• In addition, the resource will show the address of the identified point.

The online mode is convenient because you can find out the necessary information here and now.

If you do not know the exact address of an object, but you know its geographical coordinates, then its location can be easily found on Google or Yandex maps. How to find a place by coordinates on Yandex and Google map? Follow these steps:

• For example, go to Google map.
• Enter the geographic coordinates in the search box. You can enter degrees, minutes and seconds (for example 41°24’12.2″N 2°10’26.5″E), degrees and decimal minutes (41 24.2028, 2 10.4418), decimal degrees: (41.40338, 2.17403).
• Click “Search” and the desired object on the map will appear in front of you.

The result will appear instantly, and the object itself will be marked on the map with a “red drop”.

Finding satellite maps with latitude and longitude coordinates is easy. You only need to enter keywords into the Yandex or Google search window, and the service will instantly return what you need.

For example, “Satellite maps with latitude and longitude coordinates.” Many sites will open providing such a service. Choose any one, click on the desired object and determine the coordinates.

The Internet gives us great opportunities. If previously you only had to use a paper map to determine longitude and latitude, now it is enough to have a gadget with a network connection.

Video: Geographic coordinates and coordinate determination

Download from Depositfiles

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 the 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 given coordinates falls on a map sheet of scale I: 25,000, which has the nomenclature N-47-117 – G-A.

Finally, 1:10,000 scale map sheets are obtained by dividing a 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. DETERMINATION OF 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 this 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 true azimuths 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 tabular angle. The value of the directional angle in this case must be determined taking into account the signs of ∆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 LINE OF A SPECIFIED SLOPE

When designing roads and railways, canals, and various utilities, the task arises of constructing on a map the route of a future structure with a given slope.

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, using the same compass solution, mark the next horizontal line, 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 end points A and B of the structure being designed, 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.

Geographic coordinates and their determination on the map

Geographical coordinates– angular values ​​(latitude and longitude) that determine the position of objects on the earth’s surface and on the map. They are divided into astronomical, obtained from astronomical observations, and geodetic, obtained from geodetic measurements on the earth's surface.

Astronomical coordinates determine the position of points of the earth's surface on the surface of the geoid, where they are projected by plumb lines; geodetic coordinates determine the position of points on the surface of the earth's ellipsoid, where they are projected by normals to this surface.

Discrepancies between astronomical and geodetic coordinates are due to the deviation of the plumb line from the normal to the surface of the earth's ellipsoid. For most of the globe, they do not exceed 3-4" or linearly 100 m. The maximum deviation of the plumb line reaches 40".

On topographic maps they are used geodetic coordinates. In practice, when working with maps, they are usually called geographic.

The geographic coordinates of a point M are its latitude B and longitude L.

Point latitude- the angle formed by the equatorial plane and the normal to the surface of the earth's ellipsoid passing through a given point. Latitudes are counted along the meridian arc from the equator to the poles from 0 to 90°; In the northern hemisphere, latitudes are called northern (positive), in the southern hemisphere - southern (negative).

Longitude of the point- dihedral angle between the plane of the initial (Greenwich) meridian and the plane of the meridian of a given point. Longitude is calculated along the arc of the equator or parallel in both directions from the prime meridian, from 0 to 180°. The longitude of points located east of Greenwich to 180o is called eastern (positive), to the west - western (negative).

Geographical (cartographic, degree) grid - image on the map of lines of parallels and meridians; used to determine geographic (geodesic) coordinates of points (objects) and target designation. On topographic maps, the lines of parallels and meridians are the inner frames of the sheets; their latitude and longitude are signed on the corners of each sheet.

The geographic grid is fully shown only on topographic maps of scale 1:500,000 (parallels are drawn through 30", and meridians - through 20") and 1:1,000,000 (parallels are drawn through 1o, and meridians through - 40"). Inside each sheet maps on the lines of parallels and meridians are labeled with their latitude and longitude, which make it possible to determine geographic coordinates on a large gluing of maps.

On maps of scales 1: 25,000, 1: 50,000, 1: 100,000 and 1: 200,000, the sides of the frames are divided into segments equal in degrees to 1". Minute segments are shaded every other and separated by dots (with the exception of a scale 1 map: 200,000) into parts of 10 "". In addition, inside each sheet of maps of scales 1:50,000 and 1:100,000 the intersection of the middle parallel and meridian is shown and is given from the digitization in degrees and minutes, and along the inner frame the outputs of the minute divisions are given strokes 2-3mm long, along which you can draw parallels and meridians on a map glued together from several sheets.

If the territory for which the map was created is located in the Western Hemisphere, then the inscription “West of Greenwich” is placed in the northwestern corner of the sheet frame to the right of the meridian longitude signature.

Determining the geographic coordinates of a point on a map is carried out using the nearest parallel and meridian, the latitude and longitude of which are known. To do this, on maps of scales 1: 25,000 - 1: 200,000, you should first draw a parallel to the south of the point and west of the 0 meridian, connecting the corresponding strokes on the sides of the sheet frame with lines (Fig. 2). Then, from the drawn lines, they take segments to the determined point (Aa1, Aa2)10, apply them to the degree scales on the sides of the frame and produce reports. In the example in Fig. 2 point A has coordinates B = 54o35"40"" north latitude, L = 37o41"30"" east longitude.

Drawing a point on a map using geographic coordinates. On the western and eastern sides of the frame of the map sheet, marks corresponding to the latitude of the point are marked with dashes. The latitude count starts from the digitization of the southern side of the frame and continues at minute and second intervals. Then a line is drawn through these lines - parallel to the point.

The meridian of a point passing through a point is constructed in the same way, only its longitude is measured along the southern and northern sides of the frame. The intersection of the parallel and the meridian will indicate the position of this point on the map.

In Fig. 2 shows an example of plotting point M on the map at coordinates B = 54о38.4" N, L = 37о34.4" E.