How to determine the rectangular coordinates of a point on the map. Solving problems using a topographic map. Determining the nomenclature of a map sheet. Determining the coordinates of points on the map. Determination of orientation angles. Relationship between flat rectangular and polar coo systems

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

In topography, coordinate systems are used that make it possible to most simply and unambiguously determine the position of points earth's surface both from the results of direct measurements on the ground and using maps. Such systems include geographic, flat rectangular, polar and bipolar coordinates.

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

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

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

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

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

Rice. 2. System of flat rectangular coordinates on maps

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

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

The use of linear quantities to determine the position of points makes the system of flat rectangular coordinates very convenient for carrying out calculations both when working on the ground and on a map. Therefore, this system is most widely used among the troops. Rectangular coordinates indicate the position of terrain points, their battle formations and targets, and with their help determine the relative position of objects within one coordinate zone or in adjacent areas of two zones.

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

2. Determining geographic coordinates and plotting objects on a map using known coordinates

The geographic coordinates of a point located on the map are determined from the nearest parallel and meridian, the latitude and longitude of which are known.

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

Rice. 3. Determining the geographic coordinates of a point on the map (point A) and plotting the point on the map according to geographic 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, you need to use a measuring compass to measure the shortest distance from point A to the southern frame of the map, then attach the meter to the western frame and determine the number of minutes and seconds in the measured segment, add the resulting (measured) value of minutes and seconds (0"27") with the latitude of the southwest corner of the frame - 54°30".

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

Longitude is defined similarly.

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

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

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

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

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

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

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

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

On topographic maps, the values ​​of the abscissa and ordinate of coordinate lines (Fig. 2) are signed at the exits of the lines outside the inner frame of the sheet and in nine places on each sheet of the map. The full values ​​of the abscissa and ordinate in kilometers are written near the coordinate lines closest to the corners of the map frame and near the intersection of the coordinate lines closest to the northwestern corner. The remaining coordinate lines are abbreviated with two numbers (tens and units of kilometers). The labels near the horizontal grid lines correspond to the distances from the ordinate axis in kilometers.

Labels near the vertical lines indicate the zone number (one or two first digits) and the distance in kilometers (always three digits) from the origin of coordinates, conventionally moved west of the zone’s axial meridian by 500 km. For example, the signature 6740 means: 6 - zone number, 740 - distance from the conventional origin in kilometers.

On the outer frame there are outputs of coordinate lines ( additional mesh) coordinate system of the adjacent zone.

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

Using a coordinate grid using a compass (ruler), you can:

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

For example, points B (Fig. 2).

To do this you need:

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

The Y ordinate is determined in the same way:

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

2. Place the target on the map at the given coordinates.

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

To do this you need:

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

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

5. Accuracy of determining coordinates on maps of various scales

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

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

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

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

6. Determining the position of objects (points) in polar and bipolar coordinate systems, plotting objects on a map by direction and distance, by two angles or by two distances

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

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

The position of 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 problem being solved, the pole is taken to be an observation point, firing position, starting point of movement, etc., and the polar axis is the geographic (true) meridian, magnetic meridian (direction of the magnetic compass needle), or the direction to some landmark .

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

Drawing a detected object on a map

This is one of the most important moments in object detection. The accuracy of determining its coordinates depends on how accurately the object (target) is plotted on the map.

Having discovered an object (target), you must first accurately determine by various signs what has been detected. Then, without stopping observing the object and without detecting yourself, put the object on the map. There are several ways to plot an object on a map.

Visually: A feature is plotted on the map if it is near a known landmark.

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

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

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

To obtain a directional angle, you need to add the magnetic declination of a given map to the magnetic azimuth (direction correction).

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

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

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

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

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

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

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

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

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

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

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

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

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

Target designation from a landmark is the simplest and most common method of target designation. With this method of target designation, the landmark closest to the target is first named, then the angle between the direction to the landmark and the direction to the target in protractor divisions (measured with binoculars) and the distance to the target in meters. For example: “Landmark two, forty to the right, further two hundred, near a separate bush there is a machine gun.”

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

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

Rice. 5. Target designation from the conditional line

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

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 perpendicular segment from the conditional line to the target.

When designating targets, the conventional 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: “Straight AC, five, seven; to the right zero, six - NP.”

Target designation from a conventional line can be given by indicating the direction to the target at an angle from the conventional line and the distance to the target, for example: “Straight AC, right 3-40, one thousand two hundred – machine gun.”

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

8. Problem solving

Determining the coordinates of terrain points (objects) and target designation on the map is practically practiced educational maps at previously prepared points (marked objects).

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

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

Topic #2:Preparing the map for work, measuring using the map. Determination of coordinates and target designation.

Lesson No. 2Measurements on the map.

Question 1: Flat rectangular coordinates on maps, determining rectangular coordinates on a map, plotting objects on a map.

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

In topography and geodesy, orientation is carried out according to the north, counting angles clockwise. Therefore, to preserve the signs of trigonometric functions, the position of the coordinate axes, accepted in mathematics, is rotated by 90° (as the axis X the vertical line is taken, the horizontal axis is taken as the Y axis).

Rectangular coordinates (Gaussian) on topographic maps are used according to the coordinate zones into which the Earth’s surface is divided when depicting it on maps in the Gaussian Projection (see section 1.4). Coordinate zones are parts of the earth's surface bounded by meridians with longitude divisible by 6°.

Rice. 4. Rectangular coordinate system on topographic maps:

a - one zone; b - parts of the zone

The zones are counted from the Greenwich meridian from west to east. The first zone is limited by the meridians 0 and 6°, the second - 6 and 12°, the third -12 and 18°, etc. The territory of the USSR is 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 latitude 40° - 510, at latitude 50° - 430, at latitude 60° - 340 km.

All topographic maps within one zone have a common system of rectangular coordinates. The origin of coordinates in each zone is the point of intersection of the average (axial) meridian of the zone with the equator (Fig. 15), the average meridian of the zone corresponds to the x-axis (X), and the equator is the ordinate axis (U). With this arrangement of coordinate axes, the abscissa of points located south of the equator and the ordinate of points located west of the middle meridian will have negative values. For the convenience of using coordinates on topographic maps, a conditional counting of ordinates has been adopted, excluding negative values ​​of the Y coordinate. This is due to the fact that the counting of ordinates does not start from zero, but from a value of 500 km, i.e. the origin of coordinates in each zone is, as it were, moved to 500 km to the left along the axis "U". In addition, to unambiguously determine the position of a point using rectangular coordinates on the globe, to the coordinate value at The zone number (single or double digit number) is assigned to the left. If, for example, a point has coordinates X =5 650 450; at=3620840, this means that it is located in the third zone at a distance of 120 km 840 m (620840-500000) east of the middle meridian of the zone and at a distance of 5650 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 topographic map. In this case, only tens and units of kilometers and meters are indicated, for example, X = 50450; y = 20840.

Abbreviated coordinates cannot be used if the area of ​​operation covers an area of ​​more than 100 km in latitude or longitude.

Coordinate (kilometer) grid(Fig. 16) - 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 of scale 1: 25,000 - every 4 cm, on maps of scales 1: 50,000, 1: 100,000 and 1: 200,000 - every 2 cm. These lines are called kilometer lines.

On a map at a scale of 1:500,000, the coordinate grid is not completely shown; only the outputs of the 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 according to their coordinates on the map, for target designation and search on the map various objects(points), for orienting the map on the ground, measuring directional angles, approximate determination of distances and areas.

Rice. 16. Coordinate (kilometer) grid on topographic

maps of various scales

Kilometer lines on 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, with two numbers (only tens and units of kilometers are indicated). The labels on the horizontal lines correspond to the distances from the ordinate axis (from the equator) in kilometers. For example, the signature - 6082 in the upper right corner (Fig. 17) shows that this line of distance from the equator is at a distance of 6082 km

The labels on the vertical lines indicate the zone number (one or two first digits) and the distance in kilometers (always three digits) from the origin, conventionally moved west of the middle meridian by 500 km. For example, signature 4308 in top left corner means: 4 - zone number, 308 - distance from conventional origin in kilometers.

Fig. 17. Additional grid

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

In Fig. 17 lines on the outer side of the western frame with signatures 816082 and on the northern side of the frame with signatures 369394, etc. indicate the exits of kilometer lines in the coordinate system of the adjacent (third) zone. If necessary, an additional coordinate grid is drawn on a sheet of map by connecting lines 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 (close) with it when gluing the map.

Determination of rectangular coordinates of points on the map.

First, the distance from the point to the bottom kilometer line is measured along the perpendicular, its actual value in meters is determined by scale and added to the right to the signature of the kilometer line. If the length of the segment is more than a kilometer, the kilometers are first summed up, and then the number of meters is also added to the right. This will be the coordinate X(abscissa).

The coordinates are 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 A shown on Figure 18- X = 5 877 100. y = 3 302 700

Here is an example of determining the coordinates of a point IN, located near the frame of the map sheet in an incomplete square - X == 5 874 850, at = 3 298 800

Measurements are performed with a measuring compass, ruler or coordinate meter. The simplest coordinate meter is an officer's ruler, on two mutually perpendicular edges, which has millimeter divisions and inscriptions X And u.

When determining coordinates, the coordinate meter is placed on the square in which the point is located, and, aligning the vertical scale with its left side, and the horizontal scale with the point, as shown in Fig. 18, readings are taken.

Counts - in millimeters (tenths of a millimeter are counted by eye) in accordance with the scale of the map are converted into real values ​​- 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 bottom side of the square or assigned to it on the right (if the value is less than a kilometer). This will be the coordinate X points.

In the same way we 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.

In Fig. Figure 18 shows an example of determining the rectangular coordinates of point C: x = 5 873 300; at "3300 800.

Drawing points on a map using rectangular coordinates. First of all, using coordinates in kilometers and 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 of scale 1:50,000, where kilometer lines are drawn through 1 km, is found directly by the coordinates of the object in kilometers. On a map of scale 1:100000, kilometer lines are drawn through 2 km and labeled with even numbers, so if one or two coordinates of a point in kilometers are odd numbers, then you need to find a square whose sides are labeled with numbers one less than the corresponding coordinate in kilometers.

On a 1:200,000 scale map, kilometer lines are drawn every 4 km and are labeled with numbers divisible by 4. They can be 1.2 or 3 km less than the corresponding point coordinate. For example, if the coordinates of a point are given (in kilometers) x= 6755 and at= 4613, then the sides of the square will have numbers 6752 and 4612.

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

In Fig. Figure 19 shows an example of plotting point L by coordinates X == 3 768 850, at = 29 457 500.

When working with a coordinateometer, first they also 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 bottom side of the square there is a reading corresponding to the coordinate X. Then, without changing the position of the coordinate meter, find a reading on the horizontal scale corresponding to the coordinate u. The point against the reference will show its location corresponding to the given coordinates.

In Fig. Figure 19 shows an example of plotting a point on a map IN, located in an incomplete square, at coordinates w = 3,765,500; y =29 457 650.

Fig.19

In this case, the coordinate meter is applied 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 coordinate at points and digitization of this side (29457 km 650 m-29456 km==1 km 650 m). The count corresponding to the difference (encryption of the northern side of the square and coordinates X(E766 km - 3765 km 500 m), laid down on a vertical scale. Point location IN will be opposite the line at the 500 m mark.

Geographical coordinates. The Earth has the shape of a spheroid, that is, an oblate ball. Since the earth's spheroid differs very little from a sphere, this spheroid is usually called the globe.

The earth rotates around an imaginary axis and makes a complete revolution in 24 hours. The ends of the imaginary axis are called poles; one of them is called northern, and the other - southern.

Let us mentally cut the globe with a plane passing through the axis of rotation of the Earth. This imaginary plane is called the meridian plane. The line of intersection of this plane with the earth's surface is called the geographic or true meridian. You can draw as many meridians as you like, and they will all intersect at the poles.

The plane perpendicular to the earth's axis and passing through the center of the globe is called the equatorial plane, and the line of intersection of this plane with the earth's surface is called the equator.

If you mentally cross the globe with planes parallel to the equator, then on the surface of the Earth you will get circles called parallels.

The parallels and meridians marked on globes and maps form a degree grid (Fig. 63). The degree grid makes it possible to determine the position of any point on the earth's surface.

Rice. 63. Degree grid

When compiling maps in metric measures, the Greenwich meridian, passing through the Greenwich Observatory (near London), is taken as the prime meridian.

The position of any point on the earth's surface, for example a point A(Fig. 64), can be determined as follows: the angle φ between the equatorial plane and the plumb line from the point is determined A(a plumb line is a line along which bodies without support fall).

This angle φ is called the geographic latitude of the point A.

Latitudes are measured along the arc of the meridian from the equator to the north and south from 0 to 90°. In the Northern Hemisphere, latitudes are positive, in the Southern Hemisphere they are negative.

Rice. 64. Determining the latitude of a point A

Corner TO, enclosed between the planes of the prime meridian and the meridian passing through the point A, is called the geographic longitude of point L (Fig. 65).

Rice. 65. Determining the longitude of a point A

Longitudes are measured along the arc of the equator or parallel in both directions from the prime meridian from 0 to 180°, to the east with a plus sign, to the west with a minus sign.

The geographic latitude and longitude of a point are called its geographic coordinates.

To completely determine the position of a point on the earth's surface, it is necessary to know its third coordinate - the height measured from sea level.

Rectangular coordinates. In topography, the most widely used are the so-called rectangular coordinates. Let's take two mutually perpendicular lines on the plane - OH And OU(Fig. 66). These lines are called coordinate axes, and the point of their intersection ABOUT called the origin.

Rice. 66. The concept of rectangular coordinates

The position of any point on the plane can be easily determined by specifying the shortest distances from the coordinate axes to the given point. The shortest distances are perpendiculars. The perpendicular distances from the coordinate axes to a given point are called the coordinates of this point.

Lines parallel to the axis X, are called coordinates X, and parallel axes U- coordinates u.

For example, you need to determine the coordinates of points A and B. From Fig. 66 it is clear that the point A has coordinates: x = 7 cm, = 5 cm, and point B: x= - 7 cm, y =-5 cm.

Rectangular coordinate system. The rectangular coordinates discussed are applied on a plane. Hence they are called flat rectangular coordinates. This coordinate system is successfully used in small areas of terrain taken as a plane.

In order to apply a system of flat rectangular coordinates to the spherical surface of the globe, we have to make some conventions.

Rice. 67. Sixty degree zone

Since it is impossible to unfold the ball on a plane without breaks, the entire globe is conventionally divided by the lines of the earth’s meridians into 60 zones (Fig. 67).

In order to obtain a zone on a plane, it is projected onto a cylinder, and then this cylinder is deployed.

Strictly speaking, the area projected onto the cylinder will be somewhat distorted, especially at the edges, but this distortion is so slight that it can practically be ignored.

Having thus obtained a zone on a plane, a system of plane rectangular coordinates can be applied to it. Axis X is the middle (axial) meridian of the zone, and the Y axis is the equator. The intersection of the axial meridian with the equator is called the origin. Each zone has its own origin. The zones are counted from the Greenwich meridian, which is western for the 1st zone.

This coordinate system is called a rectangular coordinate system.

Counting coordinates X is carried out in meters from the equator to the poles. Everything north of the equator X are positive (have a plus sign), to the south are negative (have a minus sign). Obviously, throughout the USSR, as well as Europe and the Asian mainland, the coordinates X are positive.

Counting coordinates at is carried out from the axial meridian. East of the central meridian coordinates at have a plus sign, to the west there is a minus sign. The entire territory of the USSR occupies 29 zones (from the 4th to the 33rd inclusive), and in each zone there are coordinates at positive and negative. It's connected With a number of inconveniences, since when writing down the coordinates, each time you need to remember to put the appropriate sign. To get rid of the signs, or rather, to have only one sign, we agreed to count the coordinate for the axial meridian not as zero, but as 500 km (500,000 m). As a result of this, the coordinates at within the entire zone have a plus sign, which can be discarded when recording without fear of confusion.

Obviously, all coordinates y, those going east from the axial meridian will be more than 500 km, and those going west will be less than 500 km.

6. Kilometer grid and its use

Each sheet of the map occupies a small part of the zone, and therefore the origin of coordinates does not appear on the map. In order to be able to use coordinates, maps of scale 1:10000, 1:25000 and 1:50000 are marked with coordinate grids, i.e. squares with a side of 1 km (they are also called kilometer grids). On maps at a scale of 1:100,000, squares with a side of 2 km are plotted.

The vertical grid lines are parallel to the central meridian, and the horizontal lines are parallel to the equator. Horizontal kilometer lines are counted from bottom to top, and vertical ones - from left to right.

The tilt of the grid is explained by the fact that the western and eastern lines of the frame, which are geographical meridians, are not parallel to the axial meridian and form a certain angle with it, called the convergence of the meridians. But since all the vertical lines of the coordinate grid are parallel to the axial meridian, the entire grid will be inclined relative to the vertical lines of the frame at the same angle.

Let's look at the use of a coordinate grid using an example.

It is required to determine from the map the coordinates of the trigonometric point at an altitude of 141.5 (Fig. 68).

First you need to determine the distance in meters from the equator to a given point. This will be the coordinate X; coordinate at this point will be the distance in meters from the central meridian (considering the central meridian to be 500,000 m). Whole kilometers are determined by the numbers outside the frame, and fractions of a kilometer (meters) are measured inside the square on the map scale, so the coordinates of the trigonometric point will be x = 5 880 700, at= 5 297 300.

At practical work within one or two sheets of the map, to shorten the record, the first two digits are discarded because they are repeated.

Rice. 68. Grid on the map

Therefore, the coordinates of the trigonometric point will be x = 80,700, at= 97 300.

Determining the coordinates of points on the map and, conversely, plotting points on the map by coordinates is necessary when indicating targets and the entire location, linking firing positions and observation points to map points, orienting on the map, setting tasks, reports and reports.

To determine and indicate abbreviated coordinates of a point on a map (for example, to determine the position of a target or your standing point with coordinates), you need to name the square in which this point is located. A square is always indicated by the coordinates of its southwest corner (lower left corner). In order to find out these coordinates, you need to read the digital designations of the kilometer lines forming this angle outside the map frame. In this case, the following rule must be observed: first read the numbers related to the horizontal line (at the right or left frame of the map), i.e. the coordinate x, a then - related to the vertical line (at the upper or lower frame), i.e. the coordinate u. These readings, always consisting of four digits, are called abbreviated coordinates. They are written and read without dividing them into X And at, for example, the abbreviated coordinates of the bridge (Fig. 69) will be 1552 (read “fifteen fifty-two, bridge”). In other words, the abbreviated coordinates of a point are the number of the map square in which this point is located.

Rice. 69. Determining the coordinates of a point

If the position of a point within a square needs to be indicated more accurately, first measure in meters on a scale map the distance (along the perpendicular) from a given point to the nearest horizontal kilometer line below, and then also measure the distance to the vertical line closest to the left. The resulting readings are added to the abbreviated coordinates X And u. In this case, the resulting refined coordinates x and y recorded and transmitted (by telephone, radio) separately. For example, the updated coordinates of the intersection of the above roads will be x = 15650 m, y-= 52,530m.

Often you have to decide inverse problem. Let us assume that the target (enemy machine gun) is located on the ground at a point that is not marked on the map, but its precise coordinates are known. For example, x = 15175 m, y = 52420 m. You need to put this target on the map.

The problem is solved like this (see Fig. 69):

determine the square in which the target is located (its abbreviated coordinates); To do this, separate y coordinates X And at the first two digits each - in our example, 15 (horizontal kilometer line) and 52 (vertical line);

in square 1552, scale up along the vertical grid lines of 175 m and the resulting points are connected by a straight line; there must be a target on it;

laid along the drawn line 420 m to the right of the vertical grid line (52); the resulting point will be the location of the target.

Projection of topographic maps of the USSR. To reduce the inevitable distortions that arise when depicting large territories on a plane, they resort to mapping the territories in parts. When creating topographic maps (except for maps on a scale of 1:1,000,000) in the USSR and a number of other countries, a conformal transverse cylindrical projection Gauss-Kruger, in which the surface of the ellipsoid is divided into spherical bigons (zones) and then each of them is depicted separately on the plane (Fig. 18). In this case, the middle (axial) meridian of the zone and the equator will be depicted as mutually perpendicular straight lines without distortion.

Rice. 18. Image of geodetic zones on a plane

Distortions gradually increase with distance from the axial meridian. To reduce them to a minimum, the sizes of zones in longitude are limited to six degrees, and six-degree zones are used to construct maps at a scale of 1:10,000 and smaller.

For maps at a scale of 1:5000 and larger, three-degree zones are used. The entire earth's ellipsoid is covered by 60 six-degree zones. They are numbered in Arabic numerals, starting from the Greenwich meridian to the east. The first zone is between 0° and 6° E, the second - between 6° and 12°, etc. The boundaries of the Gauss-Kruger zones coincide with the boundaries of the columns (when plotting a map at a scale of 1:1,000,000), but their the numbering differs by 30 units, so column N° = zone N° +30.

Rice. 19. Schematic representation of the Gauss-Kruger zone on a plane

The zone is depicted on a plane according to a certain mathematical law and takes the form as schematically shown in Figure 19. In reality, it is a very narrow strip, the width of which at the equator is 30 times less than its length between the poles. Meridians (except the axial one) and parallels are depicted on a plane by lines with curvature. The axial meridian has a true length on the map scale, the length of the remaining meridians increases with distance from the axial meridian, however greatest distortion lengths within the zone (at the extreme meridian at the equator point) do not exceed 0.0014. Distortions of areas and angles are also small. Within the territory of the USSR they are even smaller. Thus, errors in areas and in the position of contours on the map are significantly less than the accuracy of reproduction of maps in print, deviations due to paper deformation, etc. Therefore, we can assume that the image of the zone in the Gauss-Kruger map projection has practically no distortions and allows for various measurements.

When creating maps, the zone is divided into separate sheets, each of which has the form of an equilateral trapezoid, limited by segments of parallels and meridians.

Rectangular coordinates. On a plane in the Gauss-Kruger zone, a rectangular coordinate system is used, in which the axial meridian of the zone is taken as the x-axis X, and the image of the equator is taken as the y-axis (Fig. 20). In topography and geodesy, orientation is carried out according to the north, counting angles clockwise. Therefore, to preserve the signs of trigonometric functions, the position of the coordinate axes in the Gauss-Kruger zone is rotated 90° relative to the axes adopted in the Cartesian system of rectangular coordinates. The positive direction of the axes is taken to be: for the X axis - the direction to the north, for the Y axis - to the east. The position of point A in the coordinate zone is determined by its distance XA and YA from the coordinate axes. On the territory of the USSR, all abscissas (distances from the equator) are positive. As for the ordinates, they could be either positive or negative in each zone. For the convenience of working with maps, it was agreed that the Y ordinate value of the axial meridian of each zone should be equal to 500 km, i.e. the origin of coordinates seemed to be moved to the west outside the zone. The number 500 was chosen because the distance along the equator from the axial meridian to the extreme western meridian is 3° or 333 km, and it would be inconvenient to count ordinates from an axis with such an ordinate. Rectangular coordinates of objects on the map are expressed in kilometers and their parts.

Rice. 20. Axes of rectangular coordinates of the zone and coordinates of points A and B located in zone 7

Since the same coordinates of points can be repeated in each of the 60 zones, the number of the zone in which a given point is located is indicated in front of the Y ordinate. For example, the coordinates of point A, located in the 7th zone, are written as follows: XA = 6230.200; YA = 7400.150 (Fig. 20).

To plot points using rectangular coordinates and determine the coordinates of points on topographic maps (except for maps at a scale of 1:1,000,000), there is a rectangular coordinate grid in the form of a system of squares formed by lines parallel to the X and Y axes (Fig. 21). Grid lines are drawn depending on the map scale at distances of 1 or 2 km (taken at map scale), and are therefore often called kilometer lines, and the grid of rectangular coordinates is kilometer grid.

Rice. 21. Layout of the map sheet (shaded) and rectangular grid lines within the zone

The kilometer grid lines are not parallel to the map frames because the straight coordinate axes are not parallel to the meridians and parallels, which have curvature. Grid lines parallel to the equator have a constant abscissa, and zones parallel to the axial meridian have a constant ordinate. The first ones on the map are approximately horizontal, the second ones are perpendicular to them.

The coordinates of the grid lines, expressed in km, are signed at the map frames (between the inner and minute frames): the abscissas of horizontal lines are at the side frames, the ordinates of vertical lines are at the upper and lower frames (see Fig. 22). Near the corners of the map, the rectangular coordinates of the lines are signed in full, with the first two digits in a smaller font than the last two. For intermediate lines, only the last two digits are indicated large to avoid repetition. So, for example, near the eastern frame of the map sheet, schematically shown in Figure 16, the abscissas of the horizontal kilometer lines from south to north are as follows: 6015, 16, 17 and 6018; near the northern frame the ordinates of the vertical kilometer lines 7456, 57, 58 and 7459 km are signed, they read as the 7th zone 456 km, etc.

Rice. 22. Position and digitization of rectangular coordinate grid lines on a sheet of map of scale 1:100,000 (fragment) and determination of rectangular coordinates of points

The ordinate labels on topographic maps are consistent with the nomenclature of the map sheet, taking into account that the zone number is 30 less than the column number indicated in the nomenclature. When connecting map sheets within one zone, the kilometer lines of adjacent sheets exactly coincide, and at the border of the zones they are located at a certain angle to each other. To ensure the possibility of working on adjacent map sheets included in different zones, the outputs of the coordinate lines of the adjacent zone are applied to them. The coordinates of these lines are signed outside the outer frame of the sheet (see Fig. 22).

Using a kilometer grid, you can quickly find the coordinates of objects, plot points by coordinates, and indicate the location of objects on the map. The rectangular coordinates of the point through which the kilometer grid lines pass on the map (such as point A in Fig. 22) are obtained immediately by reading the digitization of the coordinate lines on the map frames.

The coordinates of the points lying inside the grid cells are determined by the coordinates of the grid lines closest to the point and the increment of the coordinates of the points relative to these lines. Thus, the coordinates of point B (Fig. 22) are as follows: X B = 6132 + ΔX; Y B = 7312 + ΔY. Coordinate increments ΔX and ΔY are measured using a compass and linear scale maps, summarized with the coordinates of kilometer lines. As a result, X B = 6,133.280; Y B = 7,313.450.

Coordinate increments can be measured using coordinateometer- a small square with two perpendicular sides. Along the internal edges of the rulers are scales, the lengths of which are equal to the length of the side of the coordinate cells of the map of a given scale. The horizontal scale is aligned with the bottom line of the square (in which the point is located), and the vertical scale must pass through this point. The distances from the point to the kilometer lines are determined using the scales (Fig. 23).

Rice. 23. Measuring rectangular coordinates of points using a coordinate meter

To quickly indicate the location of an object on a given map sheet, abbreviated coordinates of the southwestern corner of the corresponding square of the kilometer grid are used. From the designations of both kilometer lines, take the last two digits, printed in large font, and write them so that the first two digits refer to the south side, and the last two to the west side of the square. For example, in Figure 22, point B is located in square 3212, and in Figure 16, point B is in square 1656.

An important area of ​​application of the rectangular grid - for orientation purposes - is discussed in §15.

There are many different coordinate systems. All of them serve to determine the position of points on the earth's surface. This includes mainly geographic, plane rectangular and polar coordinates. In general, coordinates are usually called angular and linear quantities that determine the position of points on any surface or in space.

Geographic coordinates are angular values—latitude and longitude—that determine the position of a point on the globe. Geographic latitude is the angle formed by the equatorial plane and the plumb line at a given point on the earth's surface (Fig. 25). This angle value shows how far a particular point on the globe is north or south of the equator. If a point is located in the Northern Hemisphere, then its geographic latitude will be called northern, and if in the Southern Hemisphere - southern latitude. The latitude of points located at the equator is zero (0°), and at the poles (North and South) - 90°.

Geographic longitude is also an angle, but formed by the plane of the meridian, taken as the initial (zero), and the plane of the meridian passing through a given point.

For uniformity in determining longitudes, we agreed to consider the prime meridian to be the meridian passing through the astronomical observatory in Greenwich (near London) and call it Greenwich. All points located to the east of it will have eastern longitude (up to the 180° meridian), and to the west of the initial one will have western longitude.

Figure 25 shows how to determine the position of point A on the earth’s surface if its geographic coordinates (latitude - φ and longitude - X) are known. Note that the difference in longitude of two points on Earth shows not only their relative position with respect to the prime meridian, but also the difference in time at these points at the same moment. The fact is that every 15° (24th part of the circle) in longitude is equal to one hour of time. Based on this, it is possible to determine the time difference at these two points using geographic longitude.

Example. Moscow has a longitude of 37°37′ (east), and Khabarovsk - 135°05′, that is, lies east of 97°28′. What time do these cities have at the same moment?

Simple calculations show that if it is 13 hours in Moscow, then in Khabarovsk it is 19 hours 30 minutes.

How are geographic coordinates determined on a map?

Figure 42 shows the design of the sheet frame of any topographic map. As can be seen from the figure, in the corners of this map the longitude of the meridians and the latitude of the parallels that form the frame of the sheet of this map are written.

On all sides the frame has scales divided into minutes (for both latitude and longitude). Moreover, each minute is divided into 6 equal sections by dots, which correspond to 10 seconds of longitude or latitude. Thus, in order to determine the latitude of any point M on the map (Fig. 42), it is necessary to draw a line through this point, parallel to the lower or upper frame of the map, and read on the right or left on the latitude scale, the corresponding degrees, minutes, seconds. In our example, point M has a latitude φ = 45о31’30". Similarly, drawing a vertical line through point M parallel to the lateral (closest to the given point) meridian of the boundary of this

sheet of map, read longitude (eastern) X = 43°31/18//. Drawing a point on a map at specified geographic coordinates is done in the reverse order. First, the indicated geographic coordinates are found on the scales, and then parallel and perpendicular lines are drawn through them. Their intersection on the map will show a point with the given geographic coordinates.

The lines of parallels and meridians, which serve as a frame for a given sheet of the map, are curved lines, although their curvature within the limits of one sheet is practically imperceptible. But within each Gaussian zone there are two lines that are depicted on the map as straight lines - this is the axial meridian of the zone and the equator (Fig. 26). These two lines are taken as the axes of flat rectangular coordinates. The line of the axial meridian is considered the abscissa axis and is designated x, the equator line is considered the ordinate axis and is designated y. The origin of coordinates is taken to be the point of intersection of the axial meridian with the equator. Thus, each Gaussian zone has its own grid of flat rectangular coordinates. The x coordinates (abscissa) are measured north and south of the equator, that is, from 0 (at the equator) to 10,000 km (at the pole). North of the equator coordinate y is considered positive, south is considered negative. The xy coordinates (ordinates) are measured from the axial meridian to the right (east) and left (west). In order not to deal with negative values ​​for these coordinates, it was agreed that the value of the y ordinate for the axial meridian should be taken equal to 500 km. Thus, the x-axis seems to be shifted to the west by 500 km and all ordinate values ​​within this zone will always have a positive sign. In addition, a figure corresponding to the number of the Gaussian zone is always assigned to the front ordinate value in order to avoid repetition of coordinates located in different zones.

To determine the flat rectangular coordinates of points in each Gaussian zone, a rectangular coordinate grid is plotted on topographic maps (Fig. 26), that is, lines are drawn parallel to the axial meridian and the equator.

These straight lines, naturally, will not coincide with the lines depicting meridians and parallels (with the exception of the axial meridian and the equator, parallel to which they will appear). This coordinate grid is called a kilometer grid, since its lines are drawn through a kilometer (for scales 1: 10000, 1: 25 000, 1: 50000).

On each sheet of the map, along the inner frame, the coordinate values ​​of the kilometer grid are given from the axial meridian of the given zone and from the equator. As can be seen from Figure 42, the values ​​of the full coordinates are signed only at the extreme (top and bottom) lines of the coordinate grid. All intermediate lines have abbreviated designations, that is, only the last two digits (tens and units of kilometers). For example, the bottom line of the kilometer grid (Fig. 42) is designated 5042, and the next one above it line The grid is indicated only by the number 43 km, and not 5043. The numbers of the kilometer grid under the south-neck and above the northern frame of the map sheet indicate the ordinates (y) of these lines. The extreme lines are also indicated by full coordinates. But unlike horizontal lines, the first digit of the ordinate indicates the zone number. For example, ordinate y = 8384 km. This means that the sheet of this map is located in the eighth six-degree zone of Gauss, that is, limited by the 42 and 48 ° meridians of eastern longitude, and the points lying on the line y = 384 are located to the left of the axial meridian at a distance of 500 - 384 = 116 km.

Using a kilometer coordinate grid, you can, without resorting to additional measurements, determine the coordinates of any point on the map (with an accuracy of a kilometer). To do this, it is enough to find in which grid square the determined point M is located (Fig. 42), and read the numbers indicating this square. First, the coordinate value x = 5044 is usually called (written), and then y = 8384.

To indicate an object on a map they usually say this: dot M is in the square 50,448,384, that is, they name its coordinates in a row, without separating them, but more often they give instructions in abbreviated form, they name only the next two digits from the rectangular coordinates of a given point - square 4484. When naming this square on the map, we indicate the coordinates of the lower left its corner, that is, the southwestern corner of the square in which point M is located. If it is necessary to indicate a more precise position of the point inside this square, then its distance from the boundary lines of this square is additionally determined. Using a scale, convert these distances into meters and assign them to the numbers of the designated square. For example, point M has the following coordinates: x = 44,500 m, and y = 84,500 m. These will be abbreviated coordinates for point M, and the full coordinates for it will be written as follows: x = 5,044,500 m, y = 384,500 m .

Plotting points on the map using known flat rectangular coordinates is done in the reverse order. First, the last three digits in the coordinates are discarded and the lines of the kilometer grid are found, that is, the square in which the point is located. Then, using a ruler, scale and compass, the exact coordinates of a given point in this square are plotted.

On some topographic maps, you can display two grids of flat rectangular coordinates, one plotted completely as shown in Figure 42, and the second indicated only outside the frame of this map. What's the matter? We have already established that vertical kilometer lines are parallel to the axial meridian of their zone (Fig. 26), and the axial meridians of neighboring zones are not parallel to each other. Consequently, when the kilometer grids of two adjacent zones are joined, the lines of one of them are located at an angle to the lines of the other. As a result, at the junction of two swarms, difficulties may arise in determining the coordinates, since they will relate to different coordinate axes. To eliminate this inconvenience, in each six-degree zone, all map sheets located within 2° to the east and 2° to the west of the zone boundary also have an additional coordinate grid, which is a continuation of the coordinate grid of the neighboring zone. And in order not to darken these map sheets with the second grid, it is indicated only by numbers on the outer frame of the sheet. These numbers are a continuation of the numbering of the coordinate grid lines of the adjacent zone. So, we looked at how the geographic and flat rectangular coordinates of individual points on a topographic map are determined.

With the advent of radar and radio direction finding, it became necessary to determine the position of individual points on the map and on the ground using the angle relative to any direction and the distance to them from some selected point, which is called a pole.

If we take, instead of two mutually perpendicular axes x and y in the system of flat rectangular coordinates, only one axis x and the starting point on it 0 (pole) and from it we determine corner a (alpha) (Fig. 27), which is called the position angle, as well as the distance D (from pole to point), then these two quantities are called “polar coordinates”. In polar coordinates, the x axis is called the polar axis, and the position angle of an individual point can have three designations and, accordingly, three names: directional angle a, true azimuth A and magnetic Azimuth Am.

Such a large number of position angles and their different names are explained by the fact that exactly we take the polar axis in the polar coordinate system,

from which direction we will measure the angle of position.

If we take the direction of the vertical line of the coordinate grid (Fig. 28) as the polar axis, then this angle will be called the directional angle and will be denoted a; if we take the direction of the true meridian as the polar axis (and it is on the map), then this angle will be called true azimuth and denoted A. And, finally, if we take the magnetic meridian(direction of the magnetic needle of the compass), then this position angle is called magnetic azimuth will be designated Am.

In all these cases, the position angle varies from 0 to 360° and is necessarily measured clockwise.

If we establish the relationship between the polar axes, then the relationship between the directional angle a and the true and magnetic azimuths A and Am will also be determined.

We have already established above that the vertical lines of the rectangular coordinate grid make a certain angle with the meridians, that is, the sides of the map frame (Fig. 29). The reason for this is that all meridians converge at the poles, and the vertical grid lines remain parallel to their zone meridian.

The angle formed by the true meridian at a given

point and a vertical grid line passing through the same point is called the convergence of meridians and is denoted by the Greek letter 7 (gamma).

The convergence of meridians is eastern (with a + sign), when the coordinate grid is inclined to the right relative to the map frame, and western (with a - sign), when the coordinate grid is inclined to the left. If the angle of convergence of the meridians reaches 1° or more, it must be taken into account when transitioning from the directional angle (a) to the true azimuth (A). Its value at the edges of the zone reaches 3°.

The true meridian, in turn, does not coincide with the magnetic one (which is shown by the compass needle). This angle between them is called magnetic declination and is denoted by the Greek letter b (delta). Magnetic declination is considered eastern (with a + sign) if the northern end of the magnetic compass needle deviates east of the true meridian, and western (with a - sign) if it deviates to the west. The difficulty in taking into account the magnetic declination when transitioning from the directional angle to the magnetic azimuth is that, due to the magnetic properties of the Earth, it is not the same at different points on the earth’s surface. Moreover, it also does not remain constant in the same place, but changes from year to year.

Thus, from the above it is clear that the vertical lines of the coordinate grid and the magnetic meridians form an angle between themselves, representing the sum of the convergence of the y meridians and the magnetic declination (b). This angle is called the magnetic needle deflection angle, or direction correction, and is designated capital letter- P = y + 6.

The P direction correction is measured from the north direction of the vertical grid line and is considered positive (with a + sign) if the northern end of the magnetic needle deviates east of this line, and negative (with a - sign) if the magnetic needle deviates to the west. Data on the magnitude of the direction correction (P) and its component quantities: the convergence of the meridians (y), magnetic declination (b), is placed in the form of a diagram under the bottom frame of the map sheet with explanations (Fig. 29). This data is necessary in order to quickly move from directional angles a, measured on the map, to the corresponding magnetic azimuths (Am) on the ground. For this scheme, the relationship between the position angle and the correction will look like this:

All this is true only with the eastern magnetic declination (+ b) and the western convergence of the meridians (-y). For other schemes, the direction correction may not be equal to the sum of these angles, but to the difference, or, moreover, it itself may become negative. Then, when moving from the directional angle (a) to the magnetic azimuth in formula (1), it must be subtracted, and in formula (2), on the contrary, added.

This circumstance forces everyone working with the map to carefully study the layout of the vertical grid line; true and magnetic meridians and data on the magnitude of the correction placed on each topographic map.

Errors made in determining the direction correction (P), and even more so in its sign when determining data from a map for moving along azimuths across the terrain, are dangerous because with their value of 5° and when moving at a distance of up to 1 km, the deviation at the end of the path may be about 100 m. If it is in an open area, then the landmark can still be detected. But in closed areas (in the forest) it is almost impossible to find it.

So, we have considered questions regarding methods and methods for creating topographic maps (Gaussian map projection) and their possible scales, layout and nomenclature of maps, as well as questions showing how the map framework is structured (geographic meridians and parallels, net flat rectangular coordinates). We are now able to determine directional angles, true and magnetic azimuths, direction correction and make the transition from one angle to another. It's time to fill the frame of the map with an image of the area and learn to read it, that is, learn the alphabet of the map.