How to determine coordinates on a topographic map. Military topography. Plane rectangular coordinates. Measuring line lengths, directional angles and azimuths on the map, determining the angle of inclination of a line specified on the map
When determining the full coordinates of a point by digitizing the coordinate line forming the southern side of the square in which the point is located, the full value of the abscissa X in kilometers is found and recorded. Then, using a measuring compass (ruler, coordinate meter), measure the perpendicular distance from this point to this coordinate line in meters and add it to the abscissa X.
Rice. 92. Determination of rectangular coordinates on the map using an officer’s ruler (coordinatometer)
After this, the Y ordinate value of this point is determined by finding the Y ordinate value along the northern or southern frame of the map and recording the Y ordinate value of the vertical coordinate line forming the western side of the square in which the point is located. To the resulting ordinate Y, add the distance in meters, measured perpendicularly with a measuring compass (ruler, coordinate meter) from the point to the western coordinate line.
Figures 92 and 94 show examples of defining rectangular coordinate points in various ways.
Rice. 93. Coordinate grid on topographic maps of various scales
When working with topographic maps, it is necessary to take into account that grid lines are drawn on maps of scales 1:10,000, 1:25,000, 1:50,000 after 1 kilometer, on a scale of 1:100,000 - after 2 kilometers, and on maps of scale 1: 200,000 - after 4 kilometers (Fig. 93), so the values of the X and Y coordinates may be more than 1 km in absolute value. In this case, the whole number of kilometers is summed with the values of the X and Y coordinates, and the remaining meters are added to them on the right (always three digits) (Fig. 94, points A and C).
Coordinates of point A:
X = (5,876 km + 1,100 m) = 5,877,100,
X = (5,872 km + 1,300 m) = 5,873,300,
If the point is located near the western side of the map frame in an incomplete square (Fig. 94 point B), then the distance in the square is measured along the Y axis from the point to the vertical coordinate line forming the eastern side of the square in which the point is located. The resulting distance in meters is subtracted from the values of the Y ordinate, for example the coordinates of point B:
U = 3,300 km – 1,200 m = 3,298,800
Rice. 94. Determination of rectangular coordinates of points on a map of scale 1:100,000: points A - with a compass and measuring device; points B – in an incomplete square; point C - officer's ruler
Accuracy of determining rectangular coordinates from a map. The accuracy of determining coordinates depends on the scale of the map, the magnitude of errors allowed when shooting the map, and does not exceed ± 0.5 mm using a millimeter ruler and coordinate meter.
Most accurately - with an error not exceeding 0.2 mm - geodetic points and the most prominent objects on the ground and visible from afar, which have the value of landmarks and are defined as geodetic points (churches, factory chimneys, tower-type buildings), are plotted on the map. Therefore, the coordinates of such points can be determined from the map with approximately the same accuracy with which they are plotted on it (i.e. with an error of 10-15 meters for a map at a scale of 1:50,000 and 20-30 meters for a map at a scale of 1:100,000) .
Drawing objects on a map using rectangular coordinates. First of all, using the coordinates of the object in kilometers and the digitization of kilometer lines, a square is found on the map in which the object should be located. The square in which the object is located, on maps of scales 1:10,000 - 1:50,000, where kilometer lines are drawn through 1 km, is found directly from the digitization of coordinate lines.
Rice. 95. The procedure for drawing an object P on a map at a scale of 1:50,000 along rectangular coordinates: X = 6176,600; Y = 6,329,350
On a map of scale 1:100,000, kilometer lines are drawn through 2 km and labeled with even numbers, so if one or two coordinates of an object 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 map of scale 1:200,000, kilometer lines are drawn through 4 km, so the sides of the desired square will be labeled with numbers that are multiples of four, smaller than the corresponding coordinate of the object in kilometers by one, two or three kilometers. For example, if the coordinates of an object are given: X = 6755 and Y = 4613, then the sides of the square will have numbers: 6752 and 4612.
After finding the square in which the object is located, calculate the distance of the object from the southern (bottom) side of the square and plot it on the map scale from the lower corners of the square upward. The points obtained on the vertical kilometer lines are connected by a straight line (Fig. 95). In the same way, the values of the Y ordinate are plotted from the western side of the square along its northern and southern sides, and the resulting points are also connected by a straight line. The position of the object will be at the intersection of these lines.
Rice. 96. Drawing objects on a map at a scale of 1:100,000 using rectangular coordinates: points A in the full square of the coordinate grid X = 3768,850; Y = 29,457,500; points B in an incomplete square X = 3765 500; Y = 29,457,650
Figures 95 and 96 show examples of plotting objects at different scales according to their coordinates.
In this case, the officer’s ruler 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 between the Y coordinate of the object and the digitization of this side (29,457 km 650 m – 29,456 km = 1 km 650 m) . The reading corresponding to the difference between the digitization of the northern side of the square and the Y coordinate of the object (3766 km - 3765 km 500 m) is plotted down on a vertical scale. The dot opposite the dash at the 500 m reference point will indicate the position of the object on the map.
Full and abbreviated rectangular coordinates – 30 min.
Plane rectangular coordinate system is zonal. In each six-degree zone into which the entire surface of the Earth is divided when it is depicted on a map in the Gaussian projection, a system of flat rectangular coordinates is established (Fig. 3.2.1).
Fig.3.2.1 Plane rectangular coordinate system
The coordinate axes are the axial meridian of the zone and the equator. Each zone is taken as a plane. Thus, the planned position of a point on the earth's surface in a six-degree zone is determined by two linear quantities relative to the axial meridian of this zone and the equator.
Coordinate zones have serial numbers from 1 to 60, increasing from west to east. The western meridian of the first zone coincides with the Greenwich meridian. Consequently, the coordinate axes of each zone occupy a strictly defined position on the earth's surface. Therefore, the system of flat rectangular coordinates of any zone is connected with the coordinate system of other zones and with the system of geographical coordinates of points on the Earth’s surface.
Rectangular coordinates are most widely used in solving practical problems on the ground and on a map. They are more convenient than geographic coordinates, since it is easier to operate with linear quantities than with angular ones.
Flat rectangular coordinates in topography are linear quantities - abscissa X and ordinate at, defining the position of a point on a plane (map) on which the surface of the earth’s ellipsoid is displayed according to a certain mathematical law (in the Gaussian projection). These coordinates are somewhat different from the Cartesian coordinates on a plane accepted in mathematics. The positive direction of the coordinate axes is taken to be north for the abscissa axis (axial meridian of the zone), and east for the ordinate axis (ellipsoid equator).
The coordinate axes divide the six-degree zone into four quarters, which are counted clockwise from the positive direction of the x-axis X. The position of any point in each zone relative to the origin of coordinates, for example point M, is determined by the shortest distances to the coordinate axes, that is, along perpendiculars.
Thus, for the same absolute values X And at Point M, depending on the signs of the coordinates, can occupy four different positions in the coordinate zone.
The width of any coordinate zone is approximately 670 km at the equator, at latitude 40° - 510 km, at latitude 50° - 430 km. In the Northern Hemisphere of the Earth (I and IV quarter zones) the abscissa signs are positive. The ordinate sign in the fourth quarter is negative. In order not to have negative ordinate values when working with topographic maps, at the origin of coordinates of each zone, the ordinate value is taken equal to 500 km. Thus the axis X as if transferred to the west of the axial meridian by 500 km (Fig. 3.2.2). In this case, the ordinate of any point located to the west of the axial meridian of the zone will always be positive and in absolute value less than 500 km, and the ordinate of a point located to the east of the axial meridian will always be more than 500 km.
Fig.3.2.2 Plane rectangular coordinates
To connect ordinates between zones, to the left of the ordinate record of a point, the number of the zone in which this point is located is assigned. The coordinates of a point obtained in this way are called complete. For example, the full rectangular coordinates of a point X=2 567 845, at = 36 376 450.
This means that the point is located 2567 km 845 m north of the equator, in the 36th zone and 123 km 550 m west of the axial meridian of this zone (500000-376450 = 123550).
Rectangular coordinate grid on topographic maps. A coordinate grid is constructed in each coordinate zone. It 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 called kilometer grids.
If the image of one zone with a grid of squares printed on it is divided into separate sheets of the map, then each sheet will be covered with a coordinate grid, forming part of a layout common to the entire zone.
On a map of scale 1:25,000, the lines forming the coordinate grid are drawn every 4 cm, that is, every 1 km on the ground, and on maps of scale 1:50,000 - 1:200,000 - every 2 cm (1, 2 and 4 km on locality respectively). On a map at a scale of 1:500,000, only the exits 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.
Plane rectangular coordinates are linear quantities, the abscissa X and the ordinate Y, that determine the position of points on the plane.
Let us recall that the entire globe for depiction on topographic maps is divided into six-degree zones (1...60).
In the cartographic equiangular transverse cylindrical Gauss–Kruger projection (see 1.2.2), the axial meridian and the equator of any of these zones are depicted on a plane by mutually perpendicular lines (see Figure 1.7).
If the axial meridian in each zone is taken as the x-axis X, the equator as the ordinate axis Y, and their intersection as the origin of coordinates, then we obtain a system of flat rectangular coordinates in this zone (Figure 2.12). Plane rectangular coordinates are somewhat different from the Cartesian coordinates accepted in mathematics, because the coordinate axes are named backwards.
Each zone has its own axial meridian, and the equator intersects all zones, therefore, each of the 60 zones has its own axes and origin, that is, its own coordinate system. Therefore, the system of flat rectangular coordinates is zonal.
The abscissa of point X in the system of flat rectangular coordinates is the distance from the equator, and the ordinate Y is the distance from the axial meridian of the zone. Such coordinates are usually called real.
As can be seen from Figure 2.12, the X abscissas of all points located in the northern half of the zone have a positive value, and in the southern part - a negative value. Negative abscissa values for the Southern Hemisphere do not cause any inconvenience in work. As a rule, the abscissa sign is not used. After all, it simply shows the distance of a point from the equator.
The ordinates Y also has different signs: to the east of the axial meridian there is a plus sign (the ordinate of point A in the figure is positive), to the west there is a minus sign (the ordinate of point B is negative). This makes work difficult, including when solving geodetic problems, since two terrain points, when located in the same hemisphere at slightly greater distances, may have different signs of their ordinates.
To avoid having negative ordinates, use this technique. The abscissa axis seems to move to the west (to the left) from the axial meridian by 500,000 m (500 km) (Figure 2.13) and is located parallel to it. The abscissa of point X will remain the distance from the equator, and the ordinate Y will be the distance from the conventionally designated axial meridian of the zone. Such coordinates of a point are called conditional.
As a result of this movement, all ordinate values within the entire zone will have only positive values and will increase from west to east. To the east of the axial meridian they will be more than 500 km, and to the west less. Considering that distances in rectangular coordinates are indicated in meters, the point of intersection of the equator with the axial meridian of the zone will have the coordinates: X = 000000, Y = 500000. The maximum value of the abscissa X in the zone is the distance from the equator to the pole, it is equal to 10002130 m. Maximum the ordinate value in the zone is at the equator, it is approximately 833000 m.
In each zone, the numerical values of the X and Y coordinates will be repeated. In order to be able to unambiguously determine which zone a point with the specified coordinates belongs to, and thereby find its position on the globe, a number (or two) indicating the zone number is assigned to the value of the Y ordinate on the left.
So, the X coordinate is the distance in m from the ordinate axis (equator) to the point whose coordinates are determined. In the Northern Hemisphere, the abscissa values increase from south to north, and in the Southern Hemisphere, from north to south. Coordinate X = 5743837 means that the point is 5743837 m away from the equator or 5743 km and 837 m.
The Y coordinate is a conventional ordinate indicating the zone number (one or two digits, since there are only 60 zones) and the distance of the point from the conditionally designated axial meridian of the zone. The removal of a point is expressed as a six-digit number, because the maximum ordinate value in the zone does not exceed 833000 m. For example, coordinate Y = 7345135 means that the point is located in the seventh zone at a distance of 345135 m (345 km and 135 m) from the conventional axial meridian of this zone . Such point coordinates (X = 5743837, Y = 7345135) are called complete. The abscissa of a point contains seven digits, and the ordinate contains seven or eight.
In practice, when carrying out various calculations, orienting on a map, and plotting the situation, it is inconvenient to use such large numbers. Therefore, we move on to abbreviated coordinates. Abbreviated coordinates of a point are linear values that characterize its distance from the nearest map grid lines located to the south and west, the distance from the equator corresponds to integer values of hundreds of kilometers. In practice, abbreviated coordinates are the last five digits of the full coordinates.
In the example above, the abbreviated coordinates of the point would be: X = 43837; Y = 45135.
On topographic maps (see Appendix B), at the exits of the coordinate grid lines, the values of the abscissa and ordinate of the coordinate lines in kilometers are written behind the inner frame of the sheet. 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 lines distant from the equator and the conditionally extended axial meridian of the zone at a distance multiple of one hundred kilometers. The remaining coordinate lines are abbreviated with two numbers (tens and units of kilometers). In this case, thousands and hundreds of kilometers for the abscissa, number and hundreds of kilometers for the ordinate are written in smaller font. In the appendix, these are the values 60 and 43, respectively. For the convenience of determining coordinates on a folded or glued map, the abscissa and ordinate values of coordinate lines in kilometers are also signed in nine places on the map sheet itself. So in Appendix B, for example, the coordinate line is signed along the abscissa 69 and along the ordinate 11.
When determining the full coordinates of a point (Figure 2.14) by digitizing the coordinate line forming the southern side of the square in which the point is located, the full value of the abscissa X in kilometers is found and recorded. Then, using a measuring compass (ruler), measure the perpendicular distance from the point to this coordinate line in meters (increment ΔХ in meters) and add it to the abscissa X.
After this, the value of the Y ordinate of this point is determined, for which, by digitizing the coordinate line forming the western side of the square in which the point is located, the full value of the Y ordinate in kilometers is found and recorded. The distance in meters measured along the perpendicular from the point to the western coordinate line is added to the learned ordinate Y (increment ΔУ in meters).
When determining abbreviated coordinates of a point, the digital designation of kilometer lines is not written down in full, but only with the last two digits (tens and units of kilometers).
When working with topographic maps, it is necessary to take into account that grid lines are drawn every kilometer only on maps of scale 1:25000 and 1:50000. On a map of scale 1:100000 these lines are drawn every 2 km, and on a map of scale 1:200000 - after 4 km. Therefore, the values of coordinate increments ΔХ and ΔУ may be more than 1 km. In this case, the whole number of kilometers is summed with the values of the digitization of the coordinate lines that form the southern and western sides of the square, respectively, and the remaining meters are added to them on the right (always three digits).
The point whose coordinates need to be determined may be located in an incomplete square when there is no coordinate line on the map forming the south or west side of the square. For example, on the map in Appendix B, when determining the coordinates of a road fork in square 6506 (the first two digits when indicating the position of a point in this way indicate the digitization of the coordinate line located to the south of the point, and the last two - the line located to the west), there is no way to measure the distance from the coordinate line, forming the western side of the square. In this case, to determine the increment ΔУ in meters, measure the distance from the line forming the eastern side of the square and subtract it from the distance in meters between adjacent coordinate lines for a map of a given scale.
If it is not possible to measure the distance from the coordinate line forming the southern side of the square, then to determine the value of the increment ΔХ in meters, do the same, measuring the distance from the line forming the northern side of the square.
Rectangular coordinates of points on the map can also be determined using the coordinate measures of the AK-3 (AK-4) artillery circle in the following sequence:
apply the hole of the measurement corresponding to the scale of the map when working with AK-3 or the hole of the center of the circle when working with AK-4 on a given point;
Without moving the hole from the point, turn the circle so that the lines marked on the circle and on the measure are parallel to the corresponding lines of the map grid;
at the intersection of the X scale, the measurements with the horizontal grid line of the map read the number of meters of the X coordinate (increment ΔХ in meters), and at the intersection of the Y scale with the vertical grid line - the number of meters of the Y coordinate (increment ΔУ in meters);
by adding the corresponding values obtained to the values of kilometers indicating the square of the map in which the given point is located, the coordinates of the point are obtained.
To plot points on a map using rectangular coordinates, primarily using coordinates in kilometers and digitization of coordinate lines on the map, find the square in which the point is located. On maps of scales 1:25000 and 1:50000, where coordinate lines are drawn every 1 km, the southwestern (lower left) corner of the square is found by digitizing the coordinate lines. On maps of scales 1:100000 and 1:200000, where coordinate lines are drawn through several kilometers, the values in the X and Y coordinates of the southwestern corner of the square should always be less than the coordinates of the point in kilometers.
The position of a point in a square is determined as follows. On the western and eastern sides of the square from its southern side on the map scale, the value of the increment of the abscissa ΔХ in meters is plotted, which is equal to the difference between the abscissa of the point and the abscissa of the southern kilometer line of the square. The points obtained on vertical kilometer lines are connected by a straight line. In the same way, the value of the ordinate increment ΔУ in meters is plotted from the western side of the square along its northern and southern sides, and the resulting points are also connected by a straight line. The location of the point will be at the intersection of these lines.
The values of coordinate increments are plotted using a ruler or measuring compass and a transverse scale.
The procedure for working with a measuring compass and a transverse scale (Figure 1.18) in this case is as follows. Having placed the right leg of the compass on the base of the vertical scale line marked with the number 0, make such a solution of the compass so that its left leg is on the base of the inclined line marked with the number corresponding to hundreds of meters of the distance being set aside. Then the right and left legs are simultaneously moved up along a vertical and inclined line, respectively, until they are on a horizontal line corresponding to tens and units of meters. Subsequently, without changing the solution of the measuring compass, the required distance is plotted on the map.
Plotting points on the map according to known rectangular coordinates using an AK-3 (AK-4) artillery circle is carried out in the following order.
Coordinates are called angular and linear quantities (numbers) that determine the position of a point on any surface or in space.
In topography, coordinate systems are used that make it possible to most simply and unambiguously determine the position of points on the earth's surface, both from the results of direct measurements on the ground and using maps. Such systems include geographic, flat rectangular, polar and bipolar coordinates.
Geographic coordinates(Fig. 1) – angular values: latitude (j) and longitude (L), which determine the position of an object on the earth’s surface relative to the origin of coordinates – the point of intersection of the prime (Greenwich) meridian with the equator. On a map, the geographic grid is indicated by a scale on all sides of the map frame. The western and eastern sides of the frame are meridians, and the northern and southern sides are parallels. In the corners of the map sheet the geographical coordinates of the points of intersection of the sides of the frame are written.
Rice. 1. System of geographical coordinates on the earth's surface
In the geographic coordinate system, the position of any point on the earth's surface relative to the origin of coordinates is determined in angular measure. In our country and in most other countries, the point of intersection of the prime (Greenwich) meridian with the equator is taken as the beginning. Being thus uniform for our entire planet, the system of geographic coordinates is convenient for solving problems of determining the relative position of objects located at significant distances from each other. Therefore, in military affairs, this system is used mainly for conducting calculations related to the use of long-range combat weapons, for example, ballistic missiles, aviation, etc.
Plane rectangular coordinates(Fig. 2) - linear quantities that determine the position of an object on a plane relative to the accepted origin of coordinates - the intersection of two mutually perpendicular lines (coordinate axes X and Y).
In topography, each 6-degree zone has its own system of rectangular coordinates. The X axis is the axial meridian of the zone, the Y axis is the equator, and the point of intersection of the axial meridian with the equator is the origin of coordinates.
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 every 4 cm, that is, every 1 km on the ground, and on maps 1:50000-1:200000 every 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). Labels near the horizontal grid lines correspond to distances from the ordinate axis in kilometers.
Labels near the vertical lines indicate the zone number (one or two first digits) and the distance in kilometers (always three digits) from the origin, conventionally moved west of the zone’s axial meridian by 500 km. For example, the signature 6740 means: 6 - zone number, 740 - distance from the conventional origin in kilometers.
On the outer frame there are outputs of coordinate lines ( additional mesh) coordinate system of the adjacent zone.
4. Determination of rectangular coordinates of points. Drawing points on a map 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 points in detecting an object. The accuracy of determining its coordinates depends on how accurately the object (target) is plotted on the map.
Having discovered an object (target), you must first accurately determine by various signs what has been detected. Then, without stopping observing the object and without detecting yourself, put the object on the map. There are several ways to plot an object on a map.
Visually: A feature is plotted on the map if it is near a known landmark.
By direction and distance: to do this, you need to orient the map, find the point of your standing on it, indicate on the map the direction to the detected object and draw a line to the object from the point of your standing, then determine the distance to the object by measuring this distance on the map and comparing it with the scale of the map.
Rice. 4. Drawing the target on the map 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.
Working with full coordinates. For example, you need to determine the coordinates of a road sign in square 8803 on a map at a scale of 1:50000. First, determine the distance from the bottom horizontal side of the square to the road sign (for example, 600 m on the ground). In the same way, measure the distance from the left vertical side of the square (for example, 500 m). Now, by digitizing kilometer lines, we determine the full coordinates of the object. The horizontal line has the signature 5988 (X), adding the distance from this line to the road sign, we get: X = 5988600. We determine the vertical line in the same way and get 2403500. The full coordinates of the road sign are as follows: X = 5988600 m, Y = 2403500 m.
Abbreviated coordinates respectively will be equal: X=88600 m, Y=03500 m.
If it is necessary to clarify the position of a target in a square, then target designation is used in an alphabetic or digital way inside the square of a kilometer grid.
During target designation literal way inside the square of the kilometer grid, the square is conditionally divided into 4 parts, each part is assigned a capital letter of the Russian alphabet.
Second way - digital way target designation inside the square kilometer grid (target designation by snail ). This method got its name from the arrangement of conventional digital squares inside the square of the kilometer grid. They are arranged as if in a spiral, with the square divided into 9 parts.
When designating targets in these cases, they name the square in which the target is located, and add a letter or number that specifies the position of the target inside the square. For example, height 51.8 (5863-A) or high-voltage support (5762-2) (see Fig. 2).
Target designation from a landmark is the simplest and most common method of target designation. With this method of target designation, the landmark closest to the target is first named, then the angle between the direction to the landmark and the direction to the target in protractor divisions (measured with binoculars) and the distance to the target in meters. For example: “Landmark two, forty to the right, further two hundred, near a separate bush there is a machine gun.”
Target designation from the conditional line usually used in motion on combat vehicles. With this method, two points are selected on the map in the direction of action and connected by a straight line, relative to which target designation will be carried out. This line is denoted by letters, divided into centimeter divisions and numbered starting from zero. This construction is done on the maps of both transmitting and receiving target designation.
Target designation from a conventional line is usually used in movement on combat vehicles. With this method, two points are selected on the map in the direction of action and connected by a straight line (Fig. 5), relative to which target designation will be carried out. This line is denoted by letters, divided into centimeter divisions and numbered starting from zero.
Rice. 5. Target designation from the conditional line
This construction is done on the maps of both transmitting and receiving target designation.
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 practiced practically on training maps using previously prepared points (marked objects).
Each student determines geographic and rectangular coordinates (maps objects according to known coordinates).
Methods of target designation on the map are worked out: in flat rectangular coordinates (full and abbreviated), by squares of a kilometer grid (up to a whole square, up to 1/4, up to 1/9 of a square), from a landmark, along the azimuth and range of the target.
These coordinates can be either two position angles that determine the directions from the points A And IN to the desired point M, or distances D 1 =A M and D 2 = B.M. before her. The position angles in this case, as shown in Fig. 17, measured in points A and B or from the direction of the basis (i.e. Ð A=YOU And Ð B=A.B.M.) or from any other directions passing through points A and IN and accepted as initial ones. For example, in Fig. 17th place point M determined by position angles Q 1 n Q 2, measured from the directions of the magnetic meridians.
The above coordinate systems determine the planned position of points on the surface of the earth's ellipsoid. To determine the position of a point on the physical surface of the Earth, in addition to the planned position, indicate its height (elevation) above sea level. In the USSR, heights are calculated from the average level of the Baltic Sea, from the zero point of the Kronstadt water gauge. The heights of points on the earth's surface above sea level are called absolute, and their elevations above any other point are called relative.
2. Determination of geographical coordinates
There are geographical coordinates obtained from observations of celestial bodies, called astronomical, and from geodetic measurements of the earth's surface, called geodetic.
Astronomical coordinates determine the position of terrain points on the geoid surface (Fig. 1 and 2), onto which these points are projected by plumb lines from the physical surface of the Earth.
Geodetic coordinates indicate the position of points on the surface of the earth's ellipsoid, where they are projected by normals to this surface.
When creating topographic maps, geodetic coordinates are used primarily. Therefore, when speaking about geographic coordinates, in the future we will only mean geodetic coordinates.
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Geographic coordinates of a point, for example M(Fig. 18), are its latitude IN and longitude L.
The latitude of a point is the angle formed by the equatorial plane and the normal to the surface of the earth's ellipsoid passing through a given point. Latitudes are counted along the arc of the meridian in both directions from the equator, from 0 to 90°. The latitudes of points in the northern hemisphere are called northern, and those in the southern hemisphere are called southern.
The longitude of a point is the dihedral angle between the plane of the prime (Greenwich) meridian and the plane of the meridian of a given point. Longitudes are counted along the arc of the equator or parallel in both directions from the prime meridian, from 0 to 180°. The longitudes of points located east of Greenwich to 180° are called eastern, and those to the west are called western.
Based on topographic maps of scales 1:25000 - 1:200000, geographic coordinates are determined using the scales available on the frame of each sheet (Fig. 19). The scale division price on maps of scales 1:25000 - 1:100000 is 10", and on a map of scale 1: 200000 - G. To determine geographical coordinates from a glued map, short lines are placed inside the frame of each sheet, showing the exits of meridians and parallels inside the sheet with at intervals V.
On maps of scales 1:500000 (Fig. 20) and 1:1000000, in addition to the scales on the frames, there are also the lines of meridians and parallels themselves, forming a grid of geographic coordinates (geographic grid).
Digitization of scales and grid lines of geographic coordinates is shown in Fig. 19 and 20.
To determine the latitude of a point, such as M, on a map of scales 1: 25,000 - 1: 200,000 (Fig. 19), you need to attach a ruler to this point so that it passes through the divisions of the same name (or their shares) on the scales of the western and eastern sides of the frame, and along one of these scales make a count. Similarly, using the scales of the northern and southern sides of the frame, the longitude of the point is determined.
When determining geographic coordinates using a map of scale 1:500000 or 1:1000000, instead of scales on the map frame, a ruler is applied to the divisions of the same name (or their shares) located on the meridians (parallels) closest to the point being determined (Fig. 20).
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3. Determination of rectangular coordinates
Features of the system of flat rectangular coordinates used in topography. The coordinate axes (Fig. 21) in this system are taken to be the image of the axial meridian of the coordinate zone - the abscissa axis X and the image of the equator is the ordinate axis Y.
The coordinate axes divide the zone into quarters, which are counted clockwise from the positive direction of the axis X. The positive direction of the axes is taken to be: for the abscissa axis - the direction to the north, for the ordinate axis - to the east.
The position of a point, for example M, indicated by its distance from the coordinate axes: abscissa X and ordinate u.
In order not to deal with negative ordinates, we agreed on the value of the ordinate at The axial meridian of each zone is taken equal to 500 km. This is the axis X as if transferred to the west of the axial meridian by 500 km.
Since in each zone the numerical values of the ordinates are repeated, in order to be able to determine from the coordinates of a point which zone it belongs to, the zone number is assigned to the ordinate value on the left.
Rectangular coordinate grid on topographic maps. All map sheets (except for the 1:1000000 scale map) have a grid of squares (Fig. 19), which is called a rectangular coordinate grid.
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Grid lines (Fig. 22) are drawn parallel to the coordinate axes after 2 cm on maps of scales 1: 50,000 - 1: 500,000 and after 4 cm on a map of scale 1: 25,000, which corresponds to an integer number of kilometers on the ground. Therefore, a rectangular coordinate grid is also called a kilometer grid, and its lines are called kilometer grids.
The coordinate grid is used to determine the rectangular coordinates of points, find the location of various objects on the map during reports, setting tasks, drawing up reports, for quick visual assessment of distances, areas, determining directions and orienting the map.
Kilometer lines closest to the corners of the map sheet frame are signed with the full number of kilometers, the rest - abbreviated with the last two digits. Thus, the signature 5588 (Fig. 19) at the bottommost horizontal line means that this line runs 5588 km north of the equator. The signature 6394 at the leftmost vertical kilometer line means that it is in the sixth zone and runs 394 km from the beginning of ordinate counting, i.e. 106 km west of the axial meridian of the zone.
In the case when you have to use the map in folded form, you can determine the numerical value of the kilometer lines by the labels located inside the sheet at the intersections of horizontal lines with vertical ones (Fig. 19).
Additional grid at the junction of coordinate zones. Since the vertical kilometer lines are parallel to the axial meridian of their zone, and the axial meridians of neighboring zones are not parallel to each other, when the grids of two zones are closed, the lines of one of them will be located at an angle to the lines of the other. As a result, when working at the junction of zones, difficulties may arise with the use of coordinate grids, since they will refer to different coordinate axes.
To eliminate this inconvenience, in each zone, on all sheets of maps located within 2° east and west of the zone boundary, the coordinate grid of the adjacent zone is indicated. In order not to obscure such map sheets, this grid is shown on the map only as it extends beyond the sheet frame (Fig. 23). Its digitization is a continuation of the numbering of kilometer lines of the adjacent zone.
The kilometer grid of an adjacent zone is used when work is carried out with map sheets at the junction of two zones and it is necessary to use a single coordinate system on all these sheets. This grid is drawn in pencil on sheets of maps of one of these zones, connecting along a ruler the opposite ends of the same kilometer (vertical and horizontal) grid lines of the adjacent zone.
Using a kilometer grid to determine the rectangular coordinates of points and plot points on a map using their coordinates. To indicate the approximate location of a point on the map, it is enough to name the grid square in which it is located. To do this, first read (call) the digitization of the horizontal kilometer line forming the southern side of the square, and then the vertical line forming its western side, i.e. first the abscissa and then the ordinate of the southwestern corner of the square.
For example, when indicating the position of height 347.1 (Fig. 23), you should say: “Square ten, fourteen: height 347.1.” In written form it will look like this: “Height 347, 1 (1014).”
To more accurately indicate the position of a point, its coordinates are determined. To do this, to the coordinates of the southern and western lines of the square in which it is located, add the distance to the determined point from these lines, writing the abscissa separately X and ordinate at points.
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When determining, for example, the coordinates of point A (Fig. 24), first write down the abscissa of the lower kilometer line of the square in which this point is located (i.e. 78). Then measure by scale (distance (perpendicular) from the point A to this kilometer line, i.e. the segment T, and the resulting value (1.225 km) is added to the abscissa of the line. This is how the abscissa turns out X points A.
To obtain an ordinate at points write down the ordinate of the left (vertical) side of the same square (i.e. 14) and then add to it the distance measured along the perpendicular from the determined point to this line, i.e. the segment n(in our example 1,365 km).
Thus, the coordinates of point A will be
x=79225 m; y =15,365 m.
Since in this case, when determining the coordinates of a point, the digital designation of kilometer lines was not written down in full, but only with the last two digits (78 and 14), such coordinates are called abbreviated coordinates of point L.
If we record the digitization of kilometer lines in full, we will get complete coordinates. For point L:
x=6179225 m; y=8315365 m.
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If the abbreviated signatures of kilometer lines on a given section of the map are not repeated, and therefore the position of objects on it is determined unambiguously, then abbreviated coordinates are used. Otherwise, the full coordinates are applied.
When determining the coordinates of points on a map and plotting points on a map according to coordinates, measurements are made with a compass or a ruler with millimeter divisions. For this purpose, special coordinateometers can also be used, which somewhat simplify the work by replacing a compass and a scale ruler.
Coordinators (separately for a map of scale 1:25000 and a map of scale 1:50000) are available, for example, on the AK-3 celluloid artillery circle (Fig. 27). Each of them represents a square of a kilometer grid on a map of the appropriate scale, divided into smaller squares with sides of 200 m on the map scale. The smallest division on a coordinateometer made on a scale of 1: 25,000 corresponds to 20 m, on a scale of 1: 50,000 - 50 m.
The officer’s ruler also serves as a coordinator, on two mutually perpendicular edges of which, divided into millimeter divisions, there are signatures "X" And "y". Using an officer's ruler to mark a point on a map C its coordinates are shown in Fig. 24.
The accuracy of measuring (counting) rectangular coordinates on a map along a transverse scale is approximately ±0.2 mm, using a millimeter ruler and coordinate meter ±0.5 mm.
