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Geographic coordinates, latitude and longitude, how to determine geographical coordinates from a topographic map. How to find a point by latitude and longitude coordinates

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 for its implementation. How to determine the 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 you to accurately determine the position of this point. Geographical coordinates are expressed in three numbers - this is latitude, longitude and height above sea level. The first two coordinates, that is, latitude and longitude, are most often used in various geographical tasks. The origin of the report in the geographic coordinate system is at the center of the Earth. Spherical coordinates are used to represent latitude and longitude, 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 particular point on the surface of the Earth is understood as the angle between the equatorial plane and the line connecting this point with the center of the Earth. Through all points on having the same latitude, you can draw a plane that will be parallel to the plane of the equator.

The plane of the equator 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 on parallel 90° north latitude and the south pole lies on parallel 90° south latitude. The distance that corresponds to 1° when moving along a particular parallel depends on which parallel it is. With increasing latitude when moving north or south, this distance decreases. Thus is 0°. Knowing that the circumference of the Earth at the latitude of the equator has a length of 40075.017 km, we obtain a length of 1 ° along this parallel equal to 111.319 km.

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

The concept of longitude

The longitude of a particular point on the surface of the Earth is understood as the angle between the plane passing through this point and the axis of rotation of the Earth, and the plane of the prime meridian. According to the settlement agreement, the meridian is supposed to be zero, which passes through the Royal Observatory in Greenwich, located in the southeast in England. The Greenwich meridian divides the globe into east 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, then we can say that the geometric shape of the planet Earth is a ball flattened from the poles.

Longitude shows how far west or east of the zero (Greenwich) meridian lies a specific point on Earth. If latitude has a maximum value of 90° (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.

One can ask an interesting question, the longitude of which points cannot be determined. Based on the definition of the meridian, we get that all 360 meridians pass through two points on the surface of our planet, these points are the south and north poles.

Geographic degree

From the above figures it can be seen that 1 ° on the Earth's surface corresponds to a distance of more than 100 km, both along the parallel and along the meridian. For more accurate coordinates of the object, the degree is divided into tenths and hundredths, for example, they talk about 35.79 north latitude. In this form, information is provided by satellite navigation systems such as GPS.

Ordinary geographical and topographic maps represent fractions of a degree in the form of minutes and seconds. So, each degree is divided into 60 minutes (denoted by 60"), and each minute is divided into 60 seconds (denoted by 60""). Here you can draw an analogy with the representation of the measurement of time.

Getting to know the map

To understand how to determine the geographical latitude and longitude on the map, you must first familiarize yourself with it. In particular, you need to figure out how the coordinates of longitude and latitude are represented on it. First, the top of the map shows the northern hemisphere, the bottom shows the southern. The numbers on the left and right of the edge of the map indicate latitude, and the numbers at the top and bottom of the map are longitude coordinates.

Before you determine the coordinates of latitude and longitude, you must remember that they are presented on the map in degrees, minutes and seconds. Do not confuse this system of units with decimal degrees. For example, 15" = 0.25°, 30" = 0.5°, 45"" = 0.75".

Using a geographic map to determine longitude and latitude

Let us 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, region, country, continent, or the whole world. To understand which card to deal with, you should read its name. At the bottom, under the name, the limits of latitudes and longitudes, which are presented on the map, can be given.

After that, you need to select some 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 the latitude and longitude, the numerical values of which can be viewed at the edges of the map. Assume that the chosen 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.

Determination of the exact value of geographical coordinates

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

After the scale bar is found, it is necessary to take a simple ruler with millimeter divisions and measure the distance on the scale bar. Let in this example, 50 mm corresponds to 1 ° latitude and 40 mm - 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 up a simple proportion and find that this distance corresponds to 0.3 ° from the 10 ° parallel. Thus, the latitude of the point under consideration is +10.3° (the plus sign means north latitude).

Similar actions 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, for example, this distance is 10 mm to the meridian of 67 ° west longitude. According to the rules of proportion, we obtain that the longitude of the object in question is -67.25 ° (the minus sign means west longitude).

Convert received degrees to 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 once for the longitude and latitude for the conversion. However, in the general case, when fractional minutes are obtained after using the proportion once, it follows use the proportion a second time to get the value of incremental seconds. Note that the accuracy of determining the coordinates 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 resolved, and the coordinates of the selected point have been determined, they should be written down correctly. The standard notation is to indicate the longitude after the latitude. Both values must be specified with as many decimal places as possible, since the accuracy of the object location depends on this.

Certain coordinates can be represented in two different formats:

Using only the degree icon, e.g. +10.3°, -67.25°.
Using minutes and seconds, for example, 10°18"0"" North, 67°15"0"" West.

It should be noted that when representing geographic coordinates in degrees only, the words "North (South) latitude" and "East (West) longitude" are replaced by the appropriate plus or minus sign.

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6. SOLUTION OF PROBLEMS ON A TOPOGRAPHIC MAP

6.I. DEFINITION OF THE NOMENCLATURE OF THE MAP SHEET

When solving a number of design and survey tasks, it becomes necessary to search for the desired map sheet of a given scale for a certain area of the area, i.e. in determining the nomenclature of a given map sheet. It is possible to determine the nomenclature of a map sheet by the geographical coordinates of the 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 to the corresponding geographical coordinates.

EXAMPLE. Determine the nomenclature of a map sheet at a scale of 1: 10,000 according to the geographical 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 you know, the earth's surface is divided by parallels, drawn through 4 °, into rows, denoted by capital letters of the Latin alphabet. Point N with a latitude of 52 ° 48'37 "is located in the I4th row from the equator, located between the parallels 52 ° and 56 °. This series 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 meridians 96° and 102°. This zone corresponds to column number 47. The nomenclature of a sheet of a map of scale I: 1,000,000 is composed of the letter denoting this row and the number of the column. Therefore, 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 a sledge of scale 1: I 000,000 into 144 parts (Fig. 8). Let's 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. Figure 8 shows 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 a 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, the sheets of the map of scale I: 25,000 are obtained by dividing the sheet of the map of scale I: 50,000 into 4 parts and denoted by lowercase letters of the Russian alphabet (Fig. nine). 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, map sheets at a scale of 1: 10,000 are obtained by dividing a map sheet at a scale of 1: 25,000 into 4 parts and denoted by 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 of this problem is placed on the drawing.

6.2. DETERMINING THE COORDINATES OF POINTS ON THE MAP

For each toka on a topographic map, you can determine its geographical coordinates (latitude and longitude) and Gaussian rectangular coordinates x, y.

To determine these coordinates, the degree and kilometer grids of the map are used. to determine the geographical coordinates of the point P, the southern parallel and the western meridian closest to this point are drawn, connecting the same minute divisions of the degree frame (Fig. 10).

The latitude B o and longitude L o of the point A o of the intersection of the drawn meridian and parallel are determined. Draw lines parallel to the drawn meridian and parallel through a given point P, and measure the distances B \u003d A 1 P and L \u003d A 2 P using a millimeter ruler, as well as the sizes of minute divisions of latitude C and longitude on the maps. The geographical coordinates of the point P are determined by 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, Cl measured to tenths of a millimetre.

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 o the southwest corner of the grid square where point P is located (Fig. 11). Then from the point R drop perpendiculars C 1 L and C 2 L on the sides of this square. With an accuracy of tenths of a millimeter, measure the lengths of these perpendiculars ∆X and ∆U and, taking into account the scale of the map, their actual values on the ground are determined. For example, measured distance C 1 R is equal to 12.8 us, and the scale of the map is 1: 10,000. According to the scale, I mm on the map corresponds to 10 m of terrain, which means that

∆Х= 12.8 x 10 m = 128 m.

After determining the values ∆X and ∆U find the rectangular coordinates of the point P by the formulas

Xp= X o+∆ X

Yp= Y o+∆ Y

The accuracy of determining the rectangular coordinates of a point depends on the scale of the map and can be found by 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 At is 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 line of the aircraft on the map (Fig. 12), the degree frame of the map is used. Through the starting point In this line, a line of the true meridian (dashed line NS) is drawn parallel to the vertical line of the degree frame, and then the value of the true azimuth A sun is measured with a geodetic protractor.

To determine the directional angle of a certain line DE from the map (Fig. I2), a kilometer grid of the map is used. Through the starting point D is drawn parallel to the vertical line of the kilometer grid (dashed line KL). The drawn line will be parallel to the abscissa axis of the Gaussian projection, i.e., to 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 azimuths are counted, and therefore measured clockwise relative to the initial direction to the line being oriented.

In addition to directly measuring the directional angle of a line on the map using a protractor, you can determine the value of this angle in another way. For this definition, the rectangular coordinates of the start and end points of the line are (X d, Y d, X e, Y e). The directional angle of a given line can be found by the formula

When performing calculations using this formula using a microcalculator, it should be remembered 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 ∆Х and ∆У according to the known reduction formulas:

Angle α lies in the first quarter: ∆Х>0; ∆Y>0; α=t;

Angle α lies in the II quarter: ∆X<0; ∆Y>0; α=180o-t;

Angle α lies in the III quarter: ∆X<0; ∆Y<0; α=180 o +t;

The 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, one usually first finds its directional angle, and then, knowing the declination of the magnetic needle δ and the convergence of the meridians γ (Fig. 13), they pass to the true to the magnetic azimuths using the following formulas:

A=α+γ;

A m \u003d A-δ \u003d α + γ-δ \u003d 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. The angle γ is measured from the true meridian to the magnetic one and can be positive (east) and negative (west). The angle γ is measured from the degree frame (true meridian) to the vertical line of the kilometer grid and can also be positive (east) and negative (west). In the diagram shown in fig. 13, the declination of the magnetic needle δ is east, and the convergence of the meridians is west (negative).

The average value of δ and γ for a given map sheet is given in the southwest corner of the map below the design frame. The date of determining the declination of the magnetic needle, the magnitude of its annual change and the direction of this change are also indicated here. Using the indicated information, it is necessary to calculate the magnitude of the declination of the magnetic needle δ on the date of its determination.

EXAMPLE. Declension for 1971 east 8 about 06 '. Annual change declination west 0 o 03 '.

The value of the declination of the magnetic needle in 1989 will be: δ=8 o 06'-0 o 03'*18=7 o 12'.

6.4 DETERMINATION OF POINT HEIGHTS FROM HORIZONTALS

The elevation of a point located on a horizontal line is equal to the elevation of this horizontal line. If the horizontal line is not digitized, then its elevation is found by digitizing neighboring contour lines, taking into account the height of the relief section. It should be remembered that every fifth contour line has a digitization on the map, and for the convenience of determining the marks, the digitized contour lines are drawn with thickened lines (Fig. 14, a). Horizontal marks are signed at line breaks so that the base of the numbers is directed towards the slope.

More general is the case when the point is between two contours. Let the point P (Fig. 14, b), the mark of which is required to be determined, is located between the contour lines with marks of 125 and 130 m. . As can be seen from the vertical section along the line AB (Fig. 14, c), the value of ∆h is the excess of the point P above the minor horizontal (125 m) and can be calculated by the formula

∆ h= * h ,

where h is the height of the relief section.

Then the mark of the point P will be equal to

H R = H a + ∆h.

If the point is located between contours with the same 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 mark of the point is less than 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, the marks of the characteristic points of the relief (the top of the hill, the bottom of the basin, etc.), obtained from measurements on the ground, are written out on plans and maps.

6.5 DETERMINATION OF THE SLOPE BY THE SCHEDULE OF LAYING

The steepness of the slope is the angle of inclination of the slope to the horizontal plane. The larger the angle, the steeper the slope. The value of the angle of inclination of the slope v is calculated by the formula

V=arctg(h/ d),

where h is the height of the relief section, m;

d-layout, m;

The laying is the distance on the map between two adjacent horizontals; the steeper the slope, the less the laying.

To avoid calculations when determining the slopes and steepness of slopes according to a plan or map, in practice they use special graphs called laying graphs. The laying graph is a function graph d= n* ctgν, whose abscissas are the values of the inclination angles, starting from 0°30´, and the ordinates are the values of the elevations corresponding to these inclination angles and expressed on the map scale (Fig. 15,a).

To determine the steepness of the slope with a compass solution, take the corresponding position from the map (for example, AB in Fig. 15, b) and transfer it to the laying chart (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 - on the curve of occurrences.

The slope slope values 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 GIVEN SLOPE

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

Let on a map of scale 1:10000 it is required to outline the road route between points A and B (Fig. 16). To ensure that its slope throughout its entire length does not exceed i=0,05 . The height of the relief section on the map h= 5 m.

To solve the problem, the amount of laying is calculated corresponding to the given slope and section height h:

Then express the location on the scale of the map

where M is the denominator of the numerical scale of the map.

The value of the laying d´ can also be determined from the laying schedule, for which it is necessary to determine the angle of inclination ν corresponding to the given slope i, and measure the laying for this angle of inclination with a compass solution.

The construction of the route between points A and B is carried out as follows. With a compass solution equal to the laying d´ \u003d 10 mm, an adjacent horizontal is detected from point A and point 1 is obtained (Fig. 16). From point 1, the next horizontal line is marked with the same compass solution, getting point 2, and so on. By connecting the obtained points, draw a line with a given slope.

In many cases, the terrain allows you to outline not one, but several options for the route (for example, Options 1 and 2 in Fig. 16), from which the most appropriate one is selected for technical and economic reasons. So, for example, from two options for a route drawn approximately in under the same conditions, the option with a shorter length of the designed route will be selected.

When constructing a route line on the 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 laying d´ is less than the actual distance between two adjacent horizontals. This means that in this section of the route, the slope of the slope is less than the specified one, and the design is expensively regarded as a positive factor. In this case, this section of the route should be drawn along the shortest distance between contour lines towards the end point.

6.7. DETERMINATION OF THE BOUNDARY OF THE DRAINAGE AREA

catchment area, or a swimming pool. A section of the earth's surface is called, from which, according to the conditions of the relief, water must flow into a given drain (hollow, stream, river, etc.). The contouring of the catchment area is carried out taking into account the contours of the terrain. The boundaries of the catchment area are watershed lines that intersect horizontal lines at right angles.

Figure 17 shows a hollow through which the 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 water collection lines (thalwegs). Cross horizontals in places of their greatest curvature (smaller radius of curvature).

When designing hydraulic structures (dams, locks, embankments, dams, etc.), the boundaries of the catchment area may change their position somewhat. 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 horizontals. 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 intended structure, and from points n 1 and n 2 bypasses him.

Knowing the catchment area, the average annual rainfall, the conditions of evaporation and the absorption of moisture by the soil, it is possible to calculate the power of the water flow for the calculation of hydraulic structures.

6.8. Building a terrain profile in a given direction

A line profile is a vertical section along a given direction. The need to build a terrain profile in a given direction arises in the design of engineering structures, as well as in determining the visibility between terrain points.

To build a profile along the line AB (Fig. 18, a), by connecting points A and B with a straight line, we get the points of intersection of the straight line AB with horizontals (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 the line AB, and sign the marks, defining them horizontally. If the line AB intersects a watershed or catchment line, then the marks of the points of intersection of the line with these lines will be determined approximately by interpolation along these lines.

It is most convenient to build a profile on graph paper. The construction of the profile begins with the fact that a horizontal line MN is drawn, onto which the distances between the intersection points A, 1, 2, 3, 4, 5, 6, 7, B are transferred from a strip of paper.

The conditional horizon is chosen so that the profile line does not intersect anywhere with the conditional horizon line. To do this, the conditional horizon mark is taken 20-20 m less than the minimum mark in the considered series of points A, 1, 2, ..., B. Then a vertical scale is chosen (usually, for greater clarity, 10 times larger than the horizontal scale, i.e. map scale) . At each of the points A, 1, 2. ..., B on the MN line, the perpendiculars are restored (Fig. 18, b) and the marks of these points are laid on them in the accepted vertical scale. By connecting the obtained points A´, 1´, 2´, ..., B´ with a smooth curve, a terrain profile along the line AB is obtained.

Good day!

Almost every one of us has found ourselves in a situation where you wander into an unfamiliar part of the city and try to find the right address. Now, of course, technology has stepped forward and a regular smartphone allows you to navigate the terrain great...

However, far from everywhere and not everything is drawn on Google and Yandex maps. Not so long ago, I was in a new part of my city, and, as it turned out, some streets of this area are simply not shown on the map. How can you tell another person where you are and how to find you?

Actually, this short note is devoted to coordinates and finding a specific point on the map using map services from Yandex and Google. So...

How to determine your coordinates and how to find an address by coordinates

I'll start with Google maps, the official site :

To accurately determine your coordinates - click on the "Location determination" button, usually a small window immediately pops up in the browser asking whether to allow access (select "Allow").

Important! By the way, in some cases, different services can show you in "different places". Therefore, double-check your coordinates on 2 maps at once.

If the street is long, and there are no house numbers (or, in Google maps, houses in this territory are not indicated at all) - then left-click on the point next to the one determined by Google - a small tab should pop up below, in which your coordinates!

Coordinates represent out of two numbers. For example, on the screen below, these are: 54.989192 and 73.319559

Knowing these numbers, you can transfer your location to anyone (even if he does not use Google maps, which is very convenient).

To find the desired point in Google by coordinates, just open the maps and enter these two numbers in the search box (upper left): after 1-2 seconds. a red flag will light up on the maps, indicating the desired point.

Note:

coordinates must be specified through a dot, not a comma (correct: 54.989192 73.319559; incorrect: 54.989192 and 73.319559);
indicate the coordinates in the order in which their map gives you: i.e. first latitude, then longitude (if you violate the order, you will get the wrong point at all, perhaps even 1000 km further than the desired one ...);
coordinates can be specified in degrees and minutes (example: 51°54" 73°31").

Yandex maps

By and large, with Yandex-maps, the principle of operation is similar. It is worth noting that if one service does not determine the address, try using another one. Sometimes, if a street or area is not drawn in Google maps, then in Yandex, on the contrary, it is displayed quite fully, all streets are signed, and you can easily find out where to go and what to do.

Yandex Maps also has a special. a tool that allows you to find out your location online (on the right, click on the arrow in the white circle, see the screen below).

To determine the coordinates - just click on the necessary points on the map - a small window will pop up with addresses and two numbers - that's what they are.

You can insert both a specific address and coordinates into the search string (do not forget that they must be set correctly: do not confuse the sequence, specify through a dot, not a comma!).

Addition!

I have another article of a similar nature on my blog - about determining distances between cities, choosing the best road and estimating travel time. It will be useful to everyone who is going to go to another city, I recommend:

Additions are welcome...

Section 2 Map measurements

§ 1.2.1. Determination of rectangular coordinates on the map

Rectangular coordinates (flat) - linear quantities (abscissa X and ordinate At), defining the position of a point on a plane (map) relative to two mutually perpendicular axes X and At. Abscissa X and ordinate At points BUT- distances from the origin of coordinates to the bases of the perpendiculars dropped from the point BUT on the corresponding axes, indicating the sign.

In topography and geodesy, orientation is carried out along the north, counting the angles in a clockwise direction. Therefore, to preserve the signs of trigonometric functions, the position of the coordinate axes, adopted in mathematics, is rotated by 90 ° (beyond the axis X a vertical line is taken, for the axis At- horizontal).

Rectangular coordinates (Gauss) on topographic maps are applied according to the coordinate zones into which the Earth's surface is divided when depicted on maps in the Gaussian projection. Coordinate zones - parts of the earth's surface, limited by meridians with a longitude that is a multiple of 6 °. The zones are counted from the Greenwich meridian from west to east. The first zone is limited by meridians 0 and 6°, the second - 6° and 12°, the third -12° and 18°, etc. (for example, the territory of the USSR was located in 29 zones: from the 4th to the 32nd inclusive). The length of each zone from north to south is approximately 20,000 km. The width of the zone at the equator is approximately 670 km, at a latitude of 40° - 510 km, at a latitude of 50° - 430 km, at a latitude of 60° - 340 km.

All topographic maps within the same zone have a common system of rectangular coordinates. The origin of coordinates in each zone is the point of intersection of the middle (axial) meridian of the zone with the equator (Fig. 2.1), the middle meridian of the zone corresponds to the abscissa axis (X), and the equator is the y-axis (Y).

Rice. 2.1 Rectangular coordinate system on topographic maps:
a - one zone;
b - parts of the zone

With such an arrangement of the coordinate axes, the abscissas of points located south of the equator and the ordinates of points located west of the middle meridian will have negative values. For the convenience of using coordinates on topographic maps, a conditional account of ordinates is adopted, excluding negative values of the coordinate At. This is due to the fact that the ordinates are not counted from zero, but from a value of 500 km, i.e. the origin of coordinates in each zone is, as it were, shifted 500 km to the left along the axis At.

In addition, to unambiguously determine the position of a point in rectangular coordinates on the globe to the value of the coordinate at the zone number is assigned to the left (one-digit or two-digit number). If, for example, the point has coordinates X= 5 650 450; at= 3 620 840, this means that it is located in the third zone at a distance of 120 km 840 m (620 840 - 500 000) east of the middle meridian of the zone and at a distance of 5,650 km 450 m north of the equator.

Full coordinates - rectangular coordinates indicated in full, without any abbreviations. In the example above, the full coordinates of the point are given.

Abbreviated coordinates are used to speed up target designation on a topographic map. In this case, only tens and units of kilometers and meters are indicated, for example, X= 50 450; at= 20 840. Abbreviated coordinates cannot be used if the area of operations covers an area of more than 100 km in latitude or longitude.

Coordinate (kilometer) grid (Fig.2.2) - a grid of squares on topographic maps, formed by horizontal and vertical lines drawn parallel to the axes of rectangular coordinates at certain intervals: on a map at a scale of 1:25000 - every 4 cm, on maps at scales 1:50000, 1:100000 and 1 :200000 - after 2 cm. These lines are called kilometer lines.

Rice. 2.2 Coordinate (kilometer) grid on topographic maps of various scales

On a map with a scale of 1:500000, the coordinate grid is not shown completely, only the exits of kilometer lines are plotted on the sides of the frame (every 2 cm). If necessary, a coordinate grid can be drawn on the map using these outputs.

The coordinate grid is used to determine rectangular coordinates and plot points, objects, targets on the map by their coordinates, for target designation and finding various objects (points) on the map, for orienting the map on the ground, measuring directional angles, and approximate determination of distances and areas.

Kilometer lines on the maps are signed at their exits outside the sheet frame and in nine places inside the map sheet. The kilometer lines closest to the corners of the frame, as well as the intersection of lines closest to the northwestern corner, are signed in full, the rest are abbreviated, in two figures (only tens and units of kilometers are indicated). Signatures near horizontal lines correspond to distances from the y-axis (from the equator) in kilometers. For example, the signature 6082 in the upper right corner (Fig. 2.3) shows that this line is 6,082 km away from the equator.

Signatures near the vertical lines indicate the zone number (one or two first digits) and the distance in kilometers (always three digits) from the origin of coordinates, conditionally moved west of the middle meridian by 500 km. For example, the signature 4308 in the upper left corner means: 4 - zone number, 308 - distance from the conditional origin in kilometers.

Rice. 2.3 Additional coordinate grid

Additional coordinate (kilometer) grid is designed to convert the coordinates of one zone into the coordinate system of another, neighboring zone. It can be plotted on topographic maps at scales of 1:25,000, 1:50,000, 1:100,000 and 1:200,000 at the exits of kilometer lines in the adjacent western or eastern zone. The exits of kilometer lines in the form of dashes with the corresponding signatures are given on maps located over a distance of 2 ° to the east and west of the boundary meridians of the zone.

In Fig. 2.3, dashes on the outer side of the western frame with captions 81 6082 and on the northern side of the frame with captions 3693 94 95 indicate the exits of kilometer lines in the coordinate system of the adjacent (third) zone. If necessary, an additional coordinate grid is drawn on the map sheet by connecting dashes of the same name on opposite sides of the frame. The newly constructed grid is a continuation of the kilometer grid of the map sheet of the adjacent zone and must completely coincide (merge) with it when gluing the map.

Determination of rectangular coordinates of points on the map . First, the distance from the point to the lower kilometer line is measured along the perpendicular, its actual value in meters is determined by the scale and attributed to the right of the kilometer line signature. If the length of the segment is more than a kilometer, the kilometers are first summed up, and then the number of meters on the right is also attributed. This will be the coordinate X(abscissa). The coordinate is determined in the same way. at(ordinate), only the distance from the point is measured to the left side of the square.

An example of determining the coordinates of a point BUT shown in Figure 2.4: X= 5 877 100; at= 3 302 700. Here is an example of determining the coordinates of a point AT, located at the frame of the map sheet in an incomplete square: x = 5 874 850; at= 3 298 800.

Rice. 2.4 Determination of rectangular coordinates of points on the map

Measurements are performed with a compass, ruler or coordinator. The simplest coordinator is an officer's ruler, on two mutually perpendicular edges of which there are millimeter divisions and inscriptions X and y.

When determining the coordinates, the coordinate meter is placed on the square in which the point is located, and, having aligned the vertical scale with its left side, and the horizontal one with the point, as shown in Fig. 2.4, readings are taken.

Readings in millimeters (tenths of a millimeter are counted by eye) in accordance with the scale of the map are converted into real values \u200b\u200b- kilometers and meters, and then the value obtained on the vertical scale is summed (if it is more than a kilometer) with the digitization of the lower side of the square or attributed to it on the right (if the value is less than a kilometer). This will be the coordinate X points.

In the same way, get the coordinate at- the value corresponding to the reading on the horizontal scale, only the summation is carried out with the digitization of the left side of the square.

Figure 2.4 shows an example of determining the rectangular coordinates of point C: X= 5 873 300; at= 3 300 800.

Drawing points on the map by rectangular coordinates. First of all, according to the coordinates in kilometers and the digitization of kilometer lines, a square is found on the map in which the point should be located.

The square of the location of a point on a map at a scale of 1:50000, where kilometer lines are drawn through 1 km, is found directly by the coordinates of the object in kilometers. On a 1:100,000 scale map, kilometer lines are drawn every 2 km and signed with even numbers, so if one or two point coordinates are in. kilometers are odd numbers, then you need to find a square whose sides are signed by numbers one less than the corresponding coordinate in kilometers.

On a 1:200,000 scale map, kilometer lines are drawn through 4 km and signed with multiples of 4. They can be less than the corresponding point coordinate by 1, 2, or 3 km. For example, if given the coordinates of a point (in kilometers) x = 6755 and y = 4613, then the sides of the square will have digits 6752 and 4612.

After finding the square in which the point is located, its distance from the lower side of the square is calculated and the resulting distance is plotted on the map scale from the lower corners of the square upwards. A ruler is applied to the obtained points, and from the left side of the square, also on a map scale, a distance equal to the distance of the object from this side is laid.

Figure 2.5 shows an example of mapping a point BUT by coordinates x = 3 768 850, at= 29 457 500.

Rice. 2.5 Drawing points on the map by rectangular coordinates

When working with a coordinate meter, they also first find the square in which the point is located. A coordinate meter is placed on this square, its vertical scale is aligned with the western side of the square so that against the lower side of the square there is a reading corresponding to the coordinate X. Then, without changing the position of the coordinate meter, they find on the horizontal scale the reading corresponding to the coordinate y. The counterpoint point will show its location corresponding to the given coordinates.

Figure 2.5 shows an example of mapping point B, located in an incomplete square, by coordinates x = 3 765 500; at= 29 457 650.

In this case, the coordinate meter is superimposed so that its horizontal scale is aligned with the northern side of the square, and the reading against its western side corresponds to the difference in the coordinate at points and digitization of this side (29 457 km 650 m - 29 456 km = 1 km 650 m). Count corresponding to the difference between the digitization of the north side of the square and the coordinate X(3766 km - 3765 km 500 m), laid down on the vertical scale. Point location AT will be against the stroke at the reading of 500 m.

§ 1.2.2. Determination of geographical coordinates on the map

Recall that geographical coordinates (latitude and longitude) - these are angular quantities that determine the position of objects on the earth's surface and on the map. In this case, the latitude of a point is the angle formed by the plane of the equator and the normal to the surface of the earth's ellipsoid passing through the 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 - southern (negative).

The longitude of a point is the dihedral angle between the plane of the Greenwich meridian and the plane of the meridian of the 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 up to 180 ° is called eastern (positive), to the west - western (negative).

Geographic (cartographic, degree) grid - the image on the map of the lines of parallels and meridians; used to determine the geographical (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 at the corners of each sheet. The geographic grid is fully displayed only on topographic maps at a scale of 1: 500000 (parallels are drawn through 30 "and meridians through 20") and 1: 1000000 (parallels are drawn through 1 °, and meridians through 40 "). Inside each sheet of the map on lines of parallels and meridians are signed by their latitude and longitude, which allow you to determine the geographical coordinates on a large gluing of maps.

On maps of scales 1:25000, 1:50000, 1:100000 and 1:200000, the sides of the frames are divided into segments equal in degrees to 1". by 10". In addition, inside each sheet of maps at a scale of 1:50000 and 1:100000, the intersection of the middle parallels and the meridian is shown and their digitization in degrees and minutes is given, and along the inner frame the outputs of minute divisions are given with strokes 2-3 mm long, along which parallels can be drawn 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 in the northwestern corner of the sheet frame, to the right of the meridian longitude signature, the inscription "West of Greenwich" is placed.

The determination of the geographical coordinates of a point on the map is carried out according to the parallels and meridians closest to it, the latitude and longitude of which are known. To do this, on maps with a scale of 1:25000 - 1:200000, you should first draw a parallel to the south of the point and a meridian to the west, connecting the corresponding strokes on the sides of the sheet frame with lines (Fig. 2.6). Then, segments are taken from the drawn lines to the determined point (Aa 1 Aa 2) apply them to the degree scales on the sides of the frame and take readings. In the example in Fig. 1.2.6, the point BUT has coordinates B \u003d 54 ° 35 "40" north latitude, L= 37°41"30" East longitude.

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

In the same way, the meridian of the point passing through the point is built, only its longitude is counted 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. Figure 2.6 shows an example of drawing a point on a map M by coordinates B = 54°38.4"N, L = 37°34.4"E

Rice. 2.6 Determination of geographic coordinates on the map and plotting points on the map by geographic coordinates

§ 1.2.3. Determination of azimuths and directional angles

As mentioned above, due to the peculiarities of the shape, internal structure and movement in space, the earth's ellipsoid has true (geographic) and magnetic poles that do not coincide with each other.

The North and South geographic poles are the points through which the axis of rotation of the globe passes, and the North and South magnetic poles are the poles of a giant magnet, which, in fact, is the Earth, and the North magnetic pole (≈ 74 ° N, 100 °W) and the South Magnetic Pole (≈ 69°S, 144°E) drift gradually and, accordingly, do not have constant coordinates. In this regard, it is important to understand that the magnetic needle of the compass points precisely to the magnetic, and not to the true (geographical) pole.

Thus, there are true and magnetic poles that do not coincide with each other; accordingly, there are true (geographic) and magnetic meridians . And from one and the other, you can count the direction to the desired object: in one case, the observer will deal with the true azimuth, in the other - with the magnetic one.

Rice. 2.7 True azimuth A, directional angle α, and convergence of meridians γ

true azimuth is the angle BUT (Fig. 2.7), measured clockwise from 0 to 360 ° between the north direction of the true (geographic) meridian and the direction to the point being determined.

Magnetic azimuth is the angle A m, measured clockwise from 0 to 360° between the given (selected) direction and the direction to the North on the ground .

Back azimuth - azimuth (true, magnetic) of the direction opposite to the determined (direct). It differs from the straight line by 180°, and it can be read by compass against the pointer at the slot.

It is clear that the true and magnetic azimuths differ by at least the same amount by which the magnetic meridian differs from the true one. This value is called the magnetic declination. In other words, magnetic declination - injection δ (delta) between the true and magnetic meridians.

The magnitude of the magnetic declination is influenced by various magnetic anomalies (ore deposits, underground flows, etc.), daily, annual and secular fluctuations, as well as temporary disturbances under the influence of magnetic storms. The magnitude of the magnetic declination and its annual changes are indicated on each sheet of the topographic map. The daily fluctuation of the magnetic declination reaches 0.3° and, with accurate measurements of the magnetic azimuth, it is taken into account according to the correction schedule drawn up depending on the time of day. On maps of scales 1:500000 and 1:1000000, areas of magnetic anomalies are shown, and in each of them the value of the amplitude of the magnetic declination fluctuation is signed. If the compass needle deviates from the true meridian to the east, the magnetic declination is called east (positive), if the compass needle deviates to the west, the declination is called western (negative). Accordingly, the eastern declination is often indicated by the sign " + ", Western - sign" - ».

Directional angle is the angle α (alpha), measured on the map in a clockwise direction from 0 to 360 ° between the north direction of the vertical grid line and the direction to the point being determined. In other words, the directional angle is the angle between the given (chosen) direction and the direction to the North on the map (Fig.2.7). Directional angles are measured on the map, and are also determined by magnetic or true azimuths measured on the ground.

Rice. 2.8 Measuring the directional angle with a protractor

Measurement and construction of directional angles on the map is carried out using a protractor (Fig. 2.8).

To measure the directional angle on the map any direction, it is necessary to impose a protractor on it so that the middle of its ruler, marked with a stroke, coincides with the intersection point of the determined direction with the vertical kilometer grid line, and the edge of the ruler (i.e. divisions 0 and 180 ° on the protractor) is aligned with this line. Then, on the scale of the protractor, the angle should be counted clockwise from the north direction of the kilometer line to the direction being determined.

To plot on a map any point directional angle, a straight line is drawn through this point, parallel to the vertical lines of the kilometer grid, and a given directional angle is built from this straight line.

It should be borne in mind that the average error in measuring the angle with the protractor available on the officer's ruler is 0.5 °.

The values of the true azimuth and directional angle differ from each other by the amount of convergence of the meridians. convergence of meridians - injection ? (gamma) between the north direction of the true meridian of a given point and the vertical line of the coordinate grid (Fig. 2.7). The convergence of the meridians is measured from the north direction of the true meridian to the north direction of the vertical grid line. For points located to the east of the middle meridian of the zone, the convergence value is positive, and for points located to the west, it is negative. The value of convergence of meridians on the axial meridian of the zone is equal to zero and increases with the distance from the middle meridian of the zone and from the equator, while its maximum value does not exceed 3°.

The convergence of meridians, indicated on topographic maps, refers to the middle (central) point of the sheet; its value within a sheet of a map at a scale of 1:100000 at middle latitudes near the western or eastern frame may differ by 10-15 "from the value signed on the map.

Transition from directional angle to magnetic azimuth and vice versa can be done in various ways: according to the formula, taking into account the annual change in magnetic declination, according to the graphical scheme. Convenient transition through the direction correction. The necessary data for this is available on each sheet of the map at a scale of 1:25000-1:200000 in a special text reference and a graphical diagram placed in the margins of the sheet in the lower left corner (Fig. 2.9).

Rice. 2.9 Heading correction amount data

At the same time, in the special text help, the key phrase is: “ Correction in directional angle when switching to magnetic azimuth plus (minus)...”, the angle between the “arrow” and the “fork” is also important:

if the "fork" is on the left, and the "arrow" is on the right (Fig. 2.10-A), then the declination is east and when moving from the directional angle to the azimuth, the correction (2 ° 15 "+ 6 ° 15" = 8°30") on the value of the measured directional angle taken away added );
if the "fork" is on the right, and the "arrow" is on the left (Fig. 2.10-B), then the declination is western and when moving from the directional angle to the azimuth, the correction (3 ° 01 "+ 1 ° 48" = 4°49") to the measured directional angle added (respectively, when moving from azimuth to directional angle, the correction taken away ).

Rice. 2.10 Amendment

Attention! Failure to correct the directional angle or magnetic azimuth, especially at large distances and large map scales, leads to significant errors in determining the coordinates, intermediate and final points of the route.

Recall that geographic coordinates (latitude and longitude) - these are angular quantities that determine the position of objects on the earth's surface and on the map. In this case, the latitude of a point is the angle formed by the plane of the equator and the normal to the surface of the earth's ellipsoid passing through the 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 - southern (negative).

Geographic (cartographic, degree) grid - the image on the map of the lines of parallels and meridians; used to determine the geographical (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 at the corners of each sheet. The geographic grid is fully displayed only on topographic maps at a scale of 1: 500000 (parallels are drawn through 30 "and meridians through 20") and 1: 1000000 (parallels are drawn through 1 °, and meridians through 40 "). Inside each sheet of the map on lines of parallels and meridians are signed by their latitude and longitude, which allow you to determine the geographical coordinates on a large gluing of maps.

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

The determination of the geographical coordinates of a point on the map is carried out according to the parallels and meridians closest to it, the latitude and longitude of which are known. To do this, on maps with a scale of 1:25000 - 1:200000, you should first draw a parallel to the south of the point and a meridian to the west, connecting the corresponding strokes on the sides of the sheet frame with lines (Fig. 2.6). Then, segments are taken from the drawn lines to the determined point (ah 1 Ah 2 ), apply them to the degree scales on the sides of the frame and take readings. In the example in Fig. 1.2.6, the point BUT has coordinates B \u003d 54 ° 35 "40" north latitude, L= 37°41"30" East longitude.

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