Determination of longitude and latitude on the map. How to determine geographic coordinates

Coordinates called angular and linear quantities (numbers) that determine the position of a point on a surface or in space.

In topography, such coordinate systems are used that allow the most simple and unambiguous determination of the position of points on the earth's surface, both from the results of direct measurements on the ground and using maps. These systems include geographic, flat rectangular, polar and bipolar coordinates.

Geographical coordinates(Fig.1) - angular values: latitude (j) and longitude (L), which determine the position of the object on the earth's surface relative to the origin of coordinates - the point of intersection of the initial (Greenwich) meridian with the equator. On the map, the geographic grid is indicated by a scale on all sides of the map frame. The western and eastern sides of the frame are meridians, while the northern and southern sides are parallels. Signed in the corners of the sheet geographical coordinates points of intersection of the sides of the frame.

Rice. 1. The system of geographical coordinates on the earth's surface

In the geographic coordinate system, the position of any point on the earth's surface relative to the origin of coordinates is determined in angular measure. For the beginning, in our country and in most other states, the point of intersection of the initial (Greenwich) meridian with the equator is accepted. Being, therefore, the same for our entire planet, the system of geographical coordinates is convenient for solving problems of determining the relative position of objects located at considerable distances from each other. Therefore, in military affairs, this system is used mainly for conducting calculations related to the use of long-range combat weapons, such as ballistic missiles, aviation, etc.

Planar rectangular coordinates(Fig. 2) - linear quantities that determine the position of the object on the plane relative to the accepted origin of coordinates - the intersection of two mutually perpendicular lines (coordinate axes X and Y).

In topography, each 6-degree zone has its own system of rectangular coordinates. The X-axis is the axial meridian of the zone, the Y-axis is the equator, and the point of intersection of the axial meridian with the equator is the origin of coordinates.

Rice. 2. System of flat rectangular coordinates on maps

The system of flat rectangular coordinates is zonal; it is set for each six-degree zone into which the Earth's surface is divided when depicted on maps in the Gaussian projection, and is intended to indicate the position of images of points on the earth's surface on a plane (map) in this projection.

The origin of coordinates in the zone is the point of intersection of the axial meridian with the equator, relative to which the position of all other points of the zone is determined in a linear measure. The origin of the zone coordinates and its coordinate axes occupy a strictly defined position on the earth's surface. Therefore, the system of flat rectangular coordinates of each zone is connected both with the coordinate systems of all other zones, and with the system of geographical coordinates.

The use of linear quantities to determine the position of points makes the system of flat rectangular coordinates very convenient for making calculations both when working on the ground and on the map. Therefore, in the troops, this system finds the most wide application. Rectangular coordinates indicate the position of terrain points, their battle formations and targets, with their help they determine the relative position of objects within one coordinate zone or in adjacent sections of two zones.

Polar and bipolar coordinate systems are local systems. In military practice, they are used to determine the position of some points relative to others on a comparatively small areas terrain, for example, when targeting, marking landmarks and targets, drawing up terrain diagrams, etc. These systems can be associated with systems of rectangular and geographical coordinates.

2. Determination of geographical coordinates and mapping of objects by known coordinates

The geographical coordinates of a point located on the map are determined from the parallels and meridians closest to it, the latitude and longitude of which are known.

The frame of the topographic map is divided into minutes, which are separated by dots into divisions of 10 seconds each. Latitudes are indicated on the sides of the frame, and longitudes are indicated on the northern and southern sides.

Rice. 3. Determination of the geographical coordinates of a point on the map (point A) and drawing a point on the map by geographical coordinates (point B)

Using the minute frame of the map, you can:

1 . Determine the geographic coordinates of any point on the map.

For example, the coordinates of point A (Fig. 3). To do this, use a measuring compass to measure the shortest distance from point A to the southern frame of the map, then attach the meter to the western frame and determine the number of minutes and seconds in the measured segment, add the obtained (measured) value of minutes and seconds (0 "27") with the latitude of the southwestern corner of the frame - 54 ° 30 ".

Latitude points on the map will be equal to: 54°30"+0"27" = 54°30"27".

Longitude defined in a similar way.

Using a measuring compass, measure the shortest distance from point A to the western frame of the map, apply the measuring compass to the southern frame, determine the number of minutes and seconds in the measured segment (2 "35"), add the obtained (measured) value to the longitude of the southwestern corner frames - 45°00".

Longitude points on the map will be equal to: 45°00"+2"35" = 45°02"35"

2. Put any point on the map according to the given geographical coordinates.

For example, point B latitude: 54°31 "08", longitude 45°01 "41".

To map a point in longitude, it is necessary to draw a true meridian through a given point, for which connect the same number of minutes along the northern and southern frames; to plot a point in latitude on a map, it is necessary to draw a parallel through this point, for which connect the same number of minutes along the western and eastern frames. The intersection of two lines will determine the location of point B.

3. Rectangular coordinate grid on topographic maps and its digitization. Additional grid at the junction of coordinate zones

The coordinate grid on the map is a grid of squares formed by lines parallel to the coordinate axes of the zone. The grid lines are drawn through an integer number of kilometers. Therefore, the coordinate grid is also called the kilometer grid, and its lines are kilometer.

On the 1:25000 map, the lines forming the coordinate grid are drawn through 4 cm, that is, through 1 km on the ground, and on maps 1:50000-1:200000 through 2 cm (1.2 and 4 km on the ground, respectively). On the 1:500000 map, only line exits are plotted grid on the inner frame of each sheet after 2 cm (10 km on the ground). If necessary, coordinate lines can be drawn on the map along these exits.

On topographic maps, the values ​​of the abscissas and ordinates of the coordinate lines (Fig. 2) are signed at the exits of the lines outside the inner frame of the sheet and nine places on each sheet of the map. Full values abscissas and ordinates in kilometers are signed near the coordinate lines closest to the corners of the map frame and near the intersection of the coordinate lines closest to the northwestern corner. The rest of the coordinate lines are signed in abbreviated form with two digits (tens and units of kilometers). Signatures near the horizontal lines of the coordinate grid correspond to distances from the y-axis in kilometers.

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 to the west of the zone's central meridian by 500 km. For example, the signature 6740 means: 6 - zone number, 740 - distance from the conditional origin in kilometers.

The outputs of the coordinate lines are given on the outer frame ( additional mesh) coordinate systems of the adjacent zone.

4. Determination of rectangular coordinates of points. Drawing points on the map by their coordinates

On the coordinate grid using a compass (ruler) you can:

1. Determine the rectangular coordinates of a point on the map.

For example, points B (Fig. 2).

For this you need:

• write X - digitization of the lower kilometer line of the square in which point B is located, i.e. 6657 km;
• measure along the perpendicular the distance from the lower kilometer line of the square to point B and, using the linear scale of the map, determine the value of this segment in meters;
• add the measured value of 575 m with the digitization value of the lower kilometer line of the square: X=6657000+575=6657575 m.

The Y ordinate is determined in the same way:

• write the Y value - the digitization of the left vertical line of the square, i.e. 7363;
• measure the perpendicular distance from this line to point B, i.e. 335 m;
• add the measured distance to the Y digitization value of the left vertical line of the square: Y=7363000+335=7363335 m.

2. Put the target on the map according to the given coordinates.

For example, point G by coordinates: X=6658725 Y=7362360.

For this you need:

• find the square in which the point G is located by the value of whole kilometers, i.e. 5862;
• set aside from the lower left corner of the square a segment on the scale of the map, equal to the difference between the abscissa of the target and the lower side of the square - 725 m;
• from the obtained point along the perpendicular to the right, set aside a segment equal to the difference in the ordinates of the target and the left side of the square, i.e. 360 m.

Rice. 2. Determining the rectangular coordinates of a point on the map (point B) and plotting a point on the map using rectangular coordinates (point D)

5. Accuracy of determining coordinates on maps of various scales

The accuracy of determining geographical coordinates on maps 1:25000-1:200000 is about 2 and 10 "" respectively.

The accuracy of determining the rectangular coordinates of points on a map is limited not only by its scale, but also by the magnitude of the errors allowed when shooting or compiling a map and plotting various points and terrain objects on it

Geodetic points and are plotted most accurately (with an error not exceeding 0.2 mm) on the map. objects that stand out most sharply on the ground and are visible from afar, having the value of landmarks (individual bell towers, factory chimneys, tower-type buildings). Therefore, the coordinates of such points can be determined with approximately the same accuracy with which they are plotted on the map, i.e. for a map of a scale of 1:25000 - with an accuracy of 5-7 m, for a map of a scale of 1:50000 - with an accuracy of -10- 15 m, for a map at a scale of 1:100000 - with an accuracy of 20-30 m.

The remaining landmarks and contour points are plotted on the map, and, therefore, are determined from it with an error of up to 0.5 mm, and points related to contours that are not clearly expressed on the ground (for example, the contour of a swamp), with an error of up to 1 mm.

6. Determining the position of objects (points) in systems of polar and bipolar coordinates, mapping objects in direction and distance, in two angles or in two distances

System flat polar coordinates(Fig. 3, a) consists of a point O - the origin, or poles, and the initial direction of the OR, called polar axis.

Rice. 3. a – polar coordinates; b – bipolar coordinates

The position of the point M on the ground or on the map in this system is determined by two coordinates: the position angle θ, which is measured clockwise from the polar axis to the direction to the determined point M (from 0 to 360 °), and the distance OM = D.

Depending on the task being solved, an observation post, a firing position, a starting point for movement, etc. are taken as a pole, and a geographic (true) meridian, a magnetic meridian (the direction of a magnetic compass needle) or a direction to some landmark is taken as a polar axis .

These coordinates can be either two position angles that determine directions from points A and B to the desired point M, or distances D1=AM and D2=BM to it. The position angles, as shown in Fig. 1, b, are measured at points A and B or from the direction of the basis (i.e., angle A=BAM and angle B=ABM) or from any other directions passing through points A and B and taken as initial ones. For example, in the second case, the location of the point M is determined by the position angles θ1 and θ2, measured from the direction of the magnetic meridians. System flat bipolar (two-pole) coordinates(Fig. 3, b) consists of two poles A and B and a common axis AB, called the basis or base of the serif. The position of any point M relative to the two data on the map (terrain) points A and B is determined by the coordinates that are measured on the map or on the terrain.

Drawing the detected object on the map

This is one of highlights in object detection. The accuracy of determining its coordinates depends on how accurately the object (target) will be mapped.

Having found an object (target), you must first accurately determine by various features, which is found. Then, without stopping the observation of the object and without revealing yourself, put the object on the map. There are several ways to plot an object on a map.

visually: Places a feature on the map when it is close to a known landmark.

By direction and distance: to do this, you need to orient the map, find your point of standing on it, sight the direction to the detected object on the map and draw a line to the object from the point of your standing, then determine the distance to the object by measuring this distance on the map and commensurate it with the scale of the map.

Rice. 4. Drawing a target on the map with a straight cut from two points.

If in this way it is graphically impossible to solve the problem (the enemy interferes, poor visibility, etc.), then you need to accurately measure the azimuth to the object, then translate it into a directional angle and draw a direction on the map from the standing point, on which to plot the distance to the object.

To get the directional angle, you need to add the magnetic declination of this map (direction correction) to the magnetic azimuth.

straight serif. In this way, an object is put on a map of 2-3 points from which it is possible to observe it. To do this, from each selected point, the direction to the object is drawn on the oriented map, then the intersection of straight lines determines the location of the object.

7. Ways of target designation on the map: in graphical coordinates, flat rectangular coordinates (full and abbreviated), by squares of a kilometer grid (up to a whole square, up to 1/4, up to 1/9 of a square), from a landmark, from a conditional line, by azimuth and target range, in the bipolar coordinate system

The ability to quickly and correctly indicate targets, landmarks and other objects on the ground is important for controlling subunits and fire in combat or for organizing combat.

Target designation in geographic coordinates It is used very rarely and only in those cases when the targets are removed from a given point on the map at a considerable distance, expressed in tens or hundreds of kilometers. In this case, geographical coordinates are determined from the map, as described in question No. 2 of this lesson.

The location of the target (object) is indicated by latitude and longitude, for example, height 245.2 (40 ° 8 "40" N, 65 ° 31 "00" E). On the eastern (western), northern (southern) sides of the topographic frame, mark the position of the target in latitude and longitude with a prick of a compass. From these marks, perpendiculars are lowered into the depth of the sheet of the topographic map until they intersect (commander lines are applied, standard sheets paper). The point of intersection of the perpendiculars is the position of the target on the map.

For approximate target designation rectangular coordinates it is enough to indicate on the map the square of the grid in which the object is located. The square is always indicated by the numbers of kilometer lines, the intersection of which forms the southwestern (lower left) corner. When indicating the square, the cards follow the rule: first they name two numbers signed at the horizontal line (at the western side), that is, the “X” coordinate, and then two numbers at the vertical line (south side of the sheet), that is, the “Y” coordinate. In this case, "X" and "Y" are not spoken. For example, enemy tanks are spotted. When transmitting a report by radiotelephone, the square number is pronounced: eighty-eight zero two.

If the position of a point (object) needs to be determined more accurately, then full or abbreviated coordinates are used.

Work with the full coordinates. For example, it is required to determine the coordinates of a road sign in square 8803 on a map at a scale of 1:50000. First, determine what is the distance from the lower horizontal side of the square to the road sign (for example, 600 m on the ground). In the same way, measure the distance from the left vertical side of the square (for example, 500 m). Now, by digitizing kilometer lines, we determine the full coordinates of the object. The horizontal line has the signature 5988 (X), adding the distance from this line to the road sign, we get: X=5988600. In the same way, we determine the vertical line and get 2403500. The full coordinates of the road sign are as follows: X=5988600 m, Y=2403500 m.

Abbreviated coordinates respectively will be equal: X=88600 m, Y=03500 m.

If it is required to clarify the position of the target in a square, then target designation is used in alphabetical or digital way inside the square of the kilometer grid.

When targeting in a literal way inside the square of the kilometer grid, the square is conditionally divided into 4 parts, each part is assigned a capital letter of the Russian alphabet.

The second way - digital way target designation inside the kilometer grid square (target designation by snail ). This method got its name from the arrangement of conditional digital squares inside the square of the kilometer grid. They are arranged as if in a spiral, while the square is divided into 9 parts.

When targeting in these cases, they name the square in which the target is located, and add a letter or number that specifies the position of the target inside the square. For example, a height of 51.8 (5863-A) or a high-voltage support (5762-2) (see Fig. 2).

Target designation from a landmark is the simplest and most common method of target designation. With this method of target designation, the nearest landmark to the target is first called, then the angle between the direction to the landmark and the direction to the target in goniometer divisions (measured with binoculars) and the distance to the target in meters. For example: "Landmark two, forty to the right, further two hundred, at a separate bush - a machine gun."

target designation from the conditional line usually used in combat vehicles. With this method, two points are selected on the map in the direction of action and connected by a straight line, relative to which target designation will be carried out. This line is indicated by letters, divided into centimeter divisions and numbered starting from zero. Such a construction is done on the maps of both the transmitting and receiving target designation.

Target designation from a conditional line is usually used in combat vehicles. With this method, two points are selected on the map in the direction of action and connected by a straight line (Fig. 5), relative to which target designation will be carried out. This line is indicated by letters, divided into centimeter divisions and numbered starting from zero.

Rice. 5. Target designation from a conditional line

Such a construction is done on the maps of both the transmitting and receiving target designation.

The position of the target relative to the conditional line is determined by two coordinates: a segment from the starting point to the base of the perpendicular, lowered from the target location point to the conditional line, and a segment of the perpendicular from the conditional line to the target.

When targeting, the conditional name of the line is called, then the number of centimeters and millimeters contained in the first segment, and, finally, the direction (left or right) and the length of the second segment. For example: “Direct AC, five, seven; zero to the right, six - NP.

Target designation from a conditional line can be issued by indicating the direction to the target at an angle from the conditional line and the distance to the target, for example: "Direct AC, right 3-40, one thousand two hundred - machine gun."

target designation in azimuth and range to the target. The azimuth of the direction to the target is determined using a compass in degrees, and the distance to it is determined using an observation device or by eye in meters. For example: "Azimuth thirty-five, range six hundred - a tank in a trench." This method is most often used in areas where there are few landmarks.

8. Problem solving

Determining the coordinates of terrain points (objects) and target designation on the map is practiced practically on training maps using pre-prepared points (marked objects).

Each student determines geographic and rectangular coordinates (maps objects at known coordinates).

Target designation methods on the map are practiced: in flat rectangular coordinates (full and abbreviated), by squares of a kilometer grid (up to a whole square, up to 1/4, up to 1/9 of a square), from a landmark, in azimuth and range of the target.

The ability to determine where the latitude or longitude is on the map is important for a person. Especially when there was an accident and you need to quickly make a decision and transfer the coordinates to the police. She will be recognized different methods. They mean the angle that is a vertical line and 0 parallel at a predetermined point. The value is only up to 90 degrees.

Do not forget that the equator divides the earth into northern and southern hemispheres. Therefore, the latitude of earthly points that are higher than the longest parallel are northern, and if they are located below, then southern.

How to find out the latitude of any object?

You can determine the latitude and longitude on the map. Look at which parallel the object is marked. If it is not specified, then independently calculate the distance between neighboring lines. Then find the degree of parallel you are looking for.

At the equator, geographic latitude is 0°. Points that are on the same parallel will have the same latitude. If you take a map, you will see it on the frames, if a globe, then where the parallels intersect with 0° and 180° meridians. Geographic latitudes range from 0° and only up to 90° (near the poles).

5 major latitudes

Take a map, there you will see the main parallels. Thanks to them, the coordinates are easier to recognize. From the latitudinal line to the line, territories are located. They belong to one of the areas: temperate or equatorial, arctic or tropics.

The equator is the longest parallel. Lines that are lower or higher decrease towards the poles. The latitude of the equator is 0°. This is the point from which the parallels are counted towards the south or north. The area that starts from the equator and stretches to the tropics is the equatorial region. Tropic north - the main parallel. It is always marked on the maps of the world.

You can find the exact coordinates of 23° 26 min. and 16 sec. north of the equator. This parallel is also called the Tropic of Cancer. Tropic South is a parallel located at 23° 26 min. and 16 sec. south of the equator. It is called the Tropic of Capricorn. The area that is located in the middle of the line and to the equator are tropical regions.

At 66° 33 min. and 44 sec. Just above the equator is the Arctic Circle. This is the border, beyond it the duration of the night increases. Near the Pole it is 40 calendar days.

Latitude of the Antarctic Circle -66° 33 min. and 44 sec. And this is the border, and beyond it there are polar days and nights. The regions between the tropics and the described lines are temperate, and those beyond them are called polar.

Instruction

Step #1

Everyone knows that the equator divided the earth into southern and northern hemispheres. In addition to the equator, there are parallels. These are circles that are parallel to the equator itself. Meridians are conditional lines that are perpendicular to the equator.

The zero meridian passes through the observatory, it is called the Greenwich observatory and it is located in London. That's why they say so: "Greenwich Meridian". The system, which includes parallels with meridians, creates a grid of coordinates. It is used when they want to determine where an object is located.

Step #2

Does the geographic latitude show this point to the south or north of the equator? It defines the angle 0° and to 90°. The angle begins to count from the equator and to the south or north pole. So you can determine the coordinates, they say that the latitude is southern or northern.

Step #3

Geographic coordinates are measured in minutes with seconds, and most importantly - in degrees. A degree of a certain latitude is 1/180 of any of the meridians. The average length of 1 degree is 111.12 km. A minute in length is 1852 m. The diameter of Mother Earth is 12713 km. This is the distance from pole to pole.

Step #4

To find out latitude 1 in the described way, you need a plumb line with a protractor. You can make a protractor yourself. Take a few rectangular planks. Fasten them like compasses so that they change the angle between them.

Step #5

Take the thread. Hang a load (plumb) on it. Anchor the thread in the center of your protractor. Point the base of the protractor at the polar star. Do some geometric calculations. Specifically, from the angle that is between the plumb line and the base of your protractor, immediately subtract 90 °. This result is the angle that passes between the polar star and the horizon. This angle is the geographic latitude where you are.

Another way

There is another option, how you can find the coordinates. It doesn't look like the first one. Wake up before sunrise and spot its beginning, and then the sunset. Pick up a monogram to find the latitude. On the left of the monogram, set aside how long the daylight hours lasted, and write the date on the right.

Even in the middle of the XVIII century. such coordinates could be learned on the basis of astronomical observations. In the 20s. The 20th century can already be contacted by radio and determine the coordinates with special tools.

For determining latitude it is necessary, using a triangle, to lower the perpendicular from point A to the degree frame to the line of latitude and read to the right or left on the latitude scale, the corresponding degrees, minutes, seconds. φА= φ0+ Δφ

φА=54 0 36 / 00 // +0 0 01 / 40 //= 54 0 37 / 40 //

For determining longitude it is necessary, using a triangle, to lower the perpendicular from point A to the degree frame of the line of longitude and read the corresponding degrees, minutes, seconds from above or below.

Determination of rectangular coordinates of a point on the map

The rectangular coordinates of the point (X, Y) on the map are determined in the square of the kilometer grid as follows:

1. Using a triangle, perpendiculars are lowered from point A to the kilometer grid line X and Y, values ​​are taken XA=X0+Δ X; UA=U0+Δ At

For example, the coordinates of point A are: XA \u003d 6065 km + 0.55 km \u003d 6065.55 km;

UA \u003d 4311 km + 0.535 km \u003d 4311.535 km. (coordinate is reduced);

Point A is located in the 4th zone, as indicated by the first digit of the coordinate at given.

9. Measurement of line lengths, directional angles and azimuths on the map, determination of the angle of inclination of the line specified on the map.

Length measurement

To determine the distance between points of the terrain (objects, objects) on the map, using a numerical scale, it is necessary to measure the distance between these points in centimeters on the map and multiply the resulting number by the scale value.

A small distance is easier to determine using a linear scale. To do this, it is enough to apply a compass-meter, the solution of which is equal to the distance between given points on the map, to a linear scale and take a reading in meters or kilometers.

To measure the curves, the “step” solution of the measuring compass is set so that it corresponds to an integer number of kilometers, and an integer number of “steps” is set aside on the segment measured on the map. The distance that does not fit into an integer number of “steps” of the measuring compass is determined using a linear scale and added to the resulting number of kilometers.

Measurement of directional angles and azimuths on the map

.

We connect point 1 and 2. We measure the angle. The measurement takes place with the help of a protractor, it is located parallel to the median, then the angle of inclination is reported clockwise.

Determining the slope angle of a line defined on the map.

The definition occurs exactly according to the same principle as finding the directional angle.

10. Direct and inverse geodesic problem on the plane. In the computational processing of measurements made on the ground, as well as in the design of engineering structures and calculations for transferring projects to nature, it becomes necessary to solve direct and inverse geodetic problems. Direct geodetic problem . Known coordinates X 1 and at 1 point 1, directional angle 1-2 and distance d 1-2 to point 2 you need to calculate its coordinates X 2 ,at 2 .

The coordinates of point 2 are calculated by the formulas (Fig. 3.5): (3.4) where X,atincrements of coordinates equal to

(3.5)

Inverse geodesic problem . Known coordinates X 1 ,at 1 point 1 and X 2 ,at 2 points 2 need to calculate the distance between them d 1-2 and directional angle  1-2 . From formulas (3.5) and fig. 3.5 shows that. (3.6) To determine the directional angle  1-2, we use the function of the arc tangent. At the same time, we take into account that computer programs and microcalculators give the main value of the arc tangent  = , lying in the range 90+90, while the desired directional angle  can have any value in the range 0360.

The formula for the transition from  to  depends on the coordinate quarter in which the given direction is located or, in other words, on the signs of the differences y=y 2 y 1 and  x=X 2 X 1 (see table 3.1 and fig. 3.6). Table 3.1

Rice. 3.6. Directional angles and main values ​​of the arc tangent in I, II, III and IV quarters

The distance between points is calculated by the formula

(3.6) or in another way - according to the formulas (3.7)

In particular, electronic tacheometers are equipped with programs for solving direct and inverse geodetic problems, which makes it possible to determine the coordinates of observed points directly in the course of field measurements, calculate angles and distances for marking work.

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 one zone have common system 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 on the left is assigned the zone number (unambiguous 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 captions 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 framework. 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 IN, 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 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 applied to 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 IN 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 geographic north and south poles are the points through which the axis of rotation passes the globe, and the North and South magnetic poles are the poles of a giant magnet, which, in fact, is the Earth, with the North magnetic pole (≈ 74°N, 100°W) and the South magnetic pole (≈ 69°S. latitude, 144°E) gradually drift 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 counted 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 the map sheet 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 produced different ways: according to the formula, taking into account the annual change in magnetic declination, according to the graphic 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 for directional angle or magnetic azimuth, especially at long distances and large scale maps, leads to significant errors in determining the coordinates, intermediate and final points of the route.

And to find the exact location of objects on the earth's surface allows degree network- a system of parallels and meridians. It serves to determine the geographical coordinates of points on the earth's surface - their longitude and latitude.

Parallels(from Greek. parallelos- walking nearby) - these are lines conditionally drawn on the earth's surface parallel to the equator; equator - a line of section of the earth's surface depicted by a plane passing through the center of the earth perpendicular to the axis of its rotation. The longest parallel is the equator; the length of the parallels from the equator to the poles decreases.

meridians(from lat. meridianus- midday) - lines conventionally drawn on the earth's surface from one pole to another along the shortest path. All meridians are equal in length. All points of a given meridian have the same longitude, and all points of a given parallel have the same latitude.

Rice. 1. Elements of a degree network

Geographic latitude and longitude

Geographic latitude of the point is the value of the meridian arc in degrees from the equator to the given point. It varies from 0° (equator) to 90° (pole). Distinguish between northern and southern latitudes, abbreviated n. and y.sh. (Fig. 2).

Any point south of the equator will have a south latitude, and any point north of the equator will have a north latitude. To determine the geographical latitude of any point means to determine the latitude of the parallel on which it is located. On maps, the latitude of parallels is signed on the right and left frames.

Rice. 2. Latitude

Geographic longitude of a point is the magnitude of the parallel arc in degrees from the prime meridian to the given point. The initial (zero, or Greenwich) meridian passes through the Greenwich Observatory, located near London. To the east of this meridian, the longitude of all points is east; to the west, it is west (Fig. 3). Longitude varies from 0 to 180°.

Rice. 3. Geographic longitude

To determine the geographical longitude of any point means to determine the longitude of the meridian on which it is located.

On the maps, the longitude of the meridians is signed on the upper and lower frames, and on the map of the hemispheres - on the equator.

The latitude and longitude of any point on Earth make up its geographical coordinates. Thus, the geographic coordinates of Moscow are 56°N. and 38°E

Geographic coordinates of cities in Russia and CIS countries