Geography: how to find coordinates. Geographic latitude and geographic longitude
Let us remind you that geographic coordinates (latitude and longitude) – these are angular quantities that determine the position of objects on the earth’s surface and on the map. In this case, the latitude of a point is the angle formed by the equatorial plane and the normal to the surface of the earth's ellipsoid passing through this point. Latitudes are counted along the meridian arc from the equator to the poles from 0 to 90°; In the northern hemisphere, latitudes are called northern (positive), in the southern hemisphere - southern (negative).
The longitude of a point is the dihedral angle between the plane of the Greenwich meridian and the meridian plane of the given point. Longitude is calculated along the arc of the equator or parallel in both directions from the prime meridian, from 0 to 180°. The longitude of points located east of Greenwich to 180° is called eastern (positive), to the west - western (negative).
Geographical (cartographic, degree) grid - image on the map of lines of parallels and meridians; used to determine geographic (geodesic) coordinates of points (objects) and target designation. On topographic maps, the lines of parallels and meridians are the inner frames of the sheets; their latitude and longitude are signed on the corners of each sheet. The geographic grid is fully shown only on topographic maps of scale 1:500000 (parallels are drawn through 30", and meridians - through 20") and 1:1000000 (parallels are drawn through 1°, and meridians - through 40"). Inside each sheet of the map there is The lines of parallels and meridians are marked with their latitude and longitude, which make it possible to determine geographic coordinates on a large map.
On maps of scales 1:25000, 1:50000, 1:100000 and 1:200000, the sides of the frames are divided into segments equal in degrees to 1". Minute segments are shaded every other and separated by dots (except for maps of scale 1:200000) into parts 10". In addition, inside each sheet of maps of scales 1:50000 and 1:100000 the intersection of the average parallel and meridian is shown and their digitization in degrees and minutes is given, and along the inner frame there are outputs of minute divisions with strokes 2-3 mm long, along which parallels can be drawn and meridians on a map glued together from several sheets.
If the territory for which the map was created is located in the Western Hemisphere, then the inscription “West of Greenwich” is placed in the northwestern corner of the sheet frame to the right of the meridian longitude signature.
Determining the geographic coordinates of a point on a map is carried out using the nearest parallel and meridian, the latitude and longitude of which are known. To do this, on maps of scales 1:25000 - 1:200000, you should first draw a parallel to the south of the point and a meridian to the west, connecting the corresponding strokes on the sides of the sheet frame with lines (Fig. 2.6). Then segments are taken from the drawn lines to the point being determined (Ah 1 Ahh 2 ), apply them to the degree scales on the sides of the frame and make readings. In the example in Fig. 1.2.6, the point A has coordinates B = 54°35"40" north latitude, L= 37°41"30" east longitude.
Plotting a point on a map using geographic coordinates . On the western and eastern sides of the frame of the map sheet, marks corresponding to the latitude of the point are marked with dashes. The latitude count starts from the digitization of the southern side of the frame and continues at minute and second intervals. Then a line is drawn through these lines - parallel to the point.
The meridian of a point passing through a point is constructed in the same way, only its longitude is measured along the southern and northern sides of the frame. The intersection of the parallel and the meridian will indicate the position of this point on the map. Figure 2.6 shows an example of plotting a point on a map M by coordinates B = 54°38.4"N, L= 37°34.4"E
Rice. 2.6 Determining geographic coordinates on a map and plotting points on a map using geographic coordinates
Video lesson “Geographical latitude and geographic longitude. Geographic Coordinates" will help you get an idea of geographic latitude and geographic longitude. The teacher will tell you how to correctly determine geographic coordinates.
Geographic latitude- arc length in degrees from the equator to a given point.
To determine the latitude of an object, you need to find the parallel on which this object is located.
For example, the latitude of Moscow is 55 degrees and 45 minutes north latitude, it is written like this: Moscow 55°45" N; latitude of New York - 40°43" N; Sydney - 33°52" S
Geographic longitude is determined by meridians. Longitude can be western (from the 0 meridian to the west to the 180 meridian) and eastern (from the 0 meridian to the east to the 180 meridian). Longitude values are measured in degrees and minutes. Geographic longitude can have values from 0 to 180 degrees.
Geographic longitude- length of the equatorial arc in degrees from the prime meridian (0 degrees) to the meridian of a given point.
The prime meridian is considered to be the Greenwich meridian (0 degrees).
Rice. 2. Determination of longitudes ()
To determine longitude, you need to find the meridian on which a given object is located.
For example, the longitude of Moscow is 37 degrees and 37 minutes east longitude, it is written like this: 37°37" east; the longitude of Mexico City is 99°08" west.
Rice. 3. Geographical latitude and geographic longitude
To accurately determine the location of an object on the surface of the Earth, you need to know its geographic latitude and geographic longitude.
Geographical coordinates- quantities that determine the position of a point on the earth’s surface using latitudes and longitudes.
For example, Moscow has the following geographic coordinates: 55°45"N and 37°37"E. The city of Beijing has the following coordinates: 39°56′ N. 116°24′ E First the latitude value is recorded.
Sometimes you need to find an object at already given coordinates; to do this, you must first guess in which hemispheres the object is located.
Homework
Paragraphs 12, 13.
1. What are geographic latitude and longitude?
Bibliography
Main
1. Basic course in geography: Textbook. for 6th grade. general education institutions / T.P. Gerasimova, N.P. Neklyukova. - 10th ed., stereotype. - M.: Bustard, 2010. - 176 p.
2. Geography. 6th grade: atlas. - 3rd ed., stereotype. - M.: Bustard, DIK, 2011. - 32 p.
3. Geography. 6th grade: atlas. - 4th ed., stereotype. - M.: Bustard, DIK, 2013. - 32 p.
4. Geography. 6th grade: cont. cards. - M.: DIK, Bustard, 2012. - 16 p.
Encyclopedias, dictionaries, reference books and statistical collections
1. Geography. Modern illustrated encyclopedia / A.P. Gorkin. - M.: Rosman-Press, 2006. - 624 p.
Literature for preparing for the State Exam and the Unified State Exam
1. Geography: initial course. Tests. Textbook manual for 6th grade students. - M.: Humanite. ed. VLADOS center, 2011. - 144 p.
2. Tests. Geography. 6-10 grades: Educational and methodological manual / A.A. Letyagin. - M.: LLC "Agency "KRPA "Olympus": "Astrel", "AST", 2001. - 284 p.
Materials on the Internet
1. Federal Institute of Pedagogical Measurements ().
2. Russian Geographical Society ().
Section 2. Map measurements
§ 1.2.1. Determining rectangular coordinates from a map
Rectangular coordinates (flat) - linear quantities (abscissa X and ordinate U), defining the position of a point on a plane (map) relative to two mutually perpendicular axes X And U. Abscissa X and ordinate U points A- 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 as the axis U- horizontal).
Rectangular (Gaussian) coordinates 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. Coordinate zones are parts of the earth's surface bounded by meridians with longitude divisible by 6°. 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. (for example, the territory of the USSR was located in 29 zones: from the 4th to the 32nd inclusive). The length of each zone from north to south is approximately 20,000 km. The width of the zone at the equator is approximately 670 km, at latitude 40° - 510 km, at latitude 50° - 430 km, 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. 2.1), the average meridian of the zone corresponds to the abscissa axis (X), and the equator is the ordinate axis (Y).
Rice. 2.1 Rectangular coordinate system on topographic maps:
a – one zone;
b – parts of the zone
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 ease of use of coordinates on topographic maps, a conditional ordinate count is adopted, excluding negative coordinate values U. This is due to the fact that the ordinates are counted not from zero, but from a value of 500 km, i.e. the origin of coordinates in each zone is, as it were, moved 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= 3,620,840, this means that it is located in the third zone at a distance of 120 km 840 m (620,840 - 500,000) east of the middle meridian of the zone and at a distance of 5,650 km 450 m north of the equator.
Full coordinates - rectangular coordinates, indicated in full, without any abbreviations. In the example above, the full coordinates of the point are given.
Abbreviated coordinates are used to speed up target designation on a topographic map. In this case, only tens and units of kilometers and meters are indicated, for example, X= 50 450; at= 20,840. Abbreviated coordinates cannot be used if the area of operation covers an area of more than 100 km in latitude or longitude.
Coordinate (kilometer) grid (Fig. 2.2) - a grid of squares on topographic maps, formed by horizontal and vertical lines drawn parallel to the axes of rectangular coordinates at certain intervals: on a map of scale 1:25000 - after 4 cm, on maps of scales 1:50000, 1:100000 and 1 :200000 - after 2 cm. These lines are called kilometer lines.
Rice. 2.2 Coordinate (kilometer) grid on topographic maps of various scales
On a map of scale 1:500000, the coordinate grid is not completely shown; only the outputs of kilometer lines are plotted on the sides of the frame (every 2 cm). If necessary, a coordinate grid can be drawn on the map along these outputs.
The coordinate grid is used to determine rectangular coordinates and plot points, objects, targets on the map according to their coordinates, for target designation and search for various objects (points) on the map, for orienting the map on the ground, measuring directional angles, approximate determination of distances and areas.
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. 2.3) shows that this line is located 6,082 km from the equator.
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 of coordinates, conventionally moved west of the middle meridian by 500 km. For example, the signature 4308 in the upper left corner means: 4 - zone number, 308 - distance from the conditional origin in kilometers.
Rice. 2.3 Additional 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 1:25000, 1:50000, 1:100000 and 1:200000 along the exits of kilometer lines in the adjacent western or eastern zone. Outputs of kilometer lines in the form of dashes with corresponding signatures are given on maps located 2° east and west of the boundary meridians of the zone.
In Fig. 2.3, the dashes on the outer side of the western frame with signatures 81 6082 and on the northern side of the frame with signatures 3693 94 95 indicate the exits of kilometer lines in the coordinate system of the adjacent (third) zone. If necessary, an additional coordinate grid is drawn on 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 in Fig. 2.4: X= 5 877 100; at= 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.
Rice. 2.4 Determination of rectangular coordinates of points on the map
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 of which there are 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. 2.4, 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- a value corresponding to a reading on a horizontal scale, only the summation is carried out with digitization of the left side of the square.
Figure 2.4 shows an example of determining the rectangular coordinates of point C: X= 5 873 300; at= 3 300 800.
Drawing points on 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 1:50000, 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 every 2 km and are 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 map of scale 1:200000, kilometer lines are drawn through 4 km and are labeled with numbers that are multiples of 4. They can be 1, 2 or 3 km less than the corresponding coordinate of the point. For example, if the coordinates of a point are given (in kilometers) x = 6755 and y = 4613, then the sides of the square will have digitizations 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.
Figure 2.5 shows an example of plotting a point on a map A by coordinates x = 3 768 850, at= 29 457 500.
Rice. 2.5 Plotting points on a map using rectangular coordinates
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.
Figure 2.5 shows an example of mapping point B, located in an incomplete square, according to coordinates x = 3 765 500; at= 29 457 650.
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 (29,457 km 650 m - 29,456 km = 1 km 650 m). The count corresponding to the difference between the digitization of the north side of the square and the coordinates X(3766 km - 3765 km 500 m), laid down on a vertical scale. Point location IN will be opposite the line at the 500 m mark.
§ 1.2.2. Determining geographic coordinates from a map
Let us remind you that geographical coordinates (latitude and longitude) – these are angular quantities that determine the position of objects on the earth’s surface and on the map. In this case, the latitude of a point is the angle formed by the equatorial plane and the normal to the surface of the earth's ellipsoid passing through this point. Latitudes are counted along the meridian arc from the equator to the poles from 0 to 90°; In the northern hemisphere, latitudes are called northern (positive), in the southern hemisphere - southern (negative).
The longitude of a point is the dihedral angle between the plane of the Greenwich meridian and the meridian plane of the given point. Longitude is calculated along the arc of the equator or parallel in both directions from the prime meridian, from 0 to 180°. The longitude of points located east of Greenwich to 180° is called eastern (positive), to the west - western (negative).
Geographical (cartographic, degree) grid - image on the map of lines of parallels and meridians; used to determine geographic (geodesic) coordinates of points (objects) and target designation. On topographic maps, the lines of parallels and meridians are the inner frames of the sheets; their latitude and longitude are signed on the corners of each sheet. The geographic grid is fully shown only on topographic maps of scale 1:500000 (parallels are drawn through 30", and meridians - through 20") and 1:1000000 (parallels are drawn through 1°, and meridians - through 40"). Inside each sheet of the map there is The lines of parallels and meridians are marked with their latitude and longitude, which make it possible to determine geographic coordinates on a large map.
On maps of scales 1:25000, 1:50000, 1:100000 and 1:200000, the sides of the frames are divided into segments equal in degrees to 1". Minute segments are shaded every other and separated by dots (except for maps of scale 1:200000) into parts 10". In addition, inside each sheet of maps of scales 1:50000 and 1:100000 the intersection of the average parallel and meridian is shown and their digitization in degrees and minutes is given, and along the inner frame there are outputs of minute divisions with strokes 2-3 mm long, along which parallels can be drawn and meridians on a map glued together from several sheets.
If the territory for which the map was created is located in the Western Hemisphere, then the inscription “West of Greenwich” is placed in the northwestern corner of the sheet frame to the right of the meridian longitude signature.
Determining the geographic coordinates of a point on a map is carried out using the nearest parallel and meridian, the latitude and longitude of which are known. To do this, on maps of scales 1:25000 - 1:200000, you should first draw a parallel to the south of the point and a meridian to the west, connecting the corresponding strokes on the sides of the sheet frame with lines (Fig. 2.6). Then segments are taken from the drawn lines to the point being determined (Aa 1 Aa 2), apply them to the degree scales on the sides of the frame and make readings. In the example in Fig. 1.2.6, the point A has coordinates B = 54°35"40" north latitude, L= 37°41"30" east longitude.
Plotting a point on a map using geographic coordinates . On the western and eastern sides of the frame of the map sheet, marks corresponding to the latitude of the point are marked with dashes. The latitude count starts from the digitization of the southern side of the frame and continues at minute and second intervals. Then a line is drawn through these lines - parallel to the point.
The meridian of a point passing through a point is constructed in the same way, only its longitude is measured along the southern and northern sides of the frame. The intersection of the parallel and the meridian will indicate the position of this point on the map. Figure 2.6 shows an example of plotting a point on a map M by coordinates B = 54°38.4"N, L = 37°34.4"E
Rice. 2.6 Determining geographic coordinates on a map and plotting points on a map using geographic coordinates
§ 1.2.3. Determination of azimuths and directional angles
As mentioned above, due to the peculiarities of its shape, internal structure and movement in space, the earth's ellipsoid has true (geographic) and magnetic poles that do not coincide with each other.
The North and South geographic poles are the points through which the axis of rotation of the globe passes, and the North and South magnetic poles are the poles of a giant magnet, which, in fact, is the Earth, with the North magnetic pole (≈ 74°N, 100 °W) and the South Magnetic Pole (≈ 69°S, 144°E) gradually drift and, accordingly, do not have constant coordinates. In this regard, it is important to understand that the magnetic needle of the compass points precisely to the magnetic, and not to the true (geographic) pole.
Thus, there are true and magnetic poles that do not coincide with each other, accordingly there are true (geographic) And magnetic meridians . From both of these, the direction to the desired object can be measured: in one case, the observer will deal with the true azimuth, in the other, with the magnetic one.
Rice. 2.7 True azimuth A, directional angle α, and convergence of meridians γ
True azimuth - this is the angle A (Fig. 2.7), measured clockwise from 0 to 360° between the northern direction of the true (geographical) meridian and the direction to the designated point.
Magnetic azimuth - this is the angle A m, measured clockwise from 0 to 360° between a given (selected) direction and the direction to North on the ground .
Back azimuth - azimuth (true, magnetic) of the direction opposite to the determined one (direct). It differs from the straight line by 180°, and can be measured using a compass against the pointer at the slot.
It is clear that the true and magnetic azimuths differ by at least the same amount by which the magnetic meridian differs from the true one. This value is called magnetic declination. In other words, magnetic declination - corner δ (delta) between the true and magnetic meridians.
The magnitude of the magnetic declination is influenced by various magnetic anomalies (ore deposits, underground flows, etc.), daily, annual and secular fluctuations, as well as temporary disturbances under the influence of magnetic storms. The magnitude of the magnetic declination and its annual changes are indicated on each sheet of the topographic map. The daily fluctuation of magnetic declination reaches 0.3° and, with accurate measurements of magnetic azimuth, is taken into account according to the correction schedule drawn up depending on the time of day. On maps of scales 1:500000 and 1:1000000, areas of magnetic anomalies are shown, and in each of them the amplitude of magnetic declination fluctuations is indicated. If the compass needle deviates from the true meridian to the east, the magnetic declination is called eastern (positive); if the compass needle deviates to the west, the declination is called western (negative). Accordingly, the eastern declination is often indicated by the sign “ + ", Western - sign " - ».
Directional angle - this is the angle α (alpha), measured on the map clockwise from 0 to 360° between the north direction of the vertical grid line and the direction to the designated point. In other words, the directional angle is the angle between the given (selected) direction and the direction to North on the map (Fig. 2.7). Directional angles are measured from a map and are also determined from magnetic or true azimuths measured on the ground.
Rice. 2.8 Measuring directional angle with a protractor
Measuring and plotting directional angles on the map is done using a protractor (Fig. 2.8).
To measure directional angle on a map some direction, you need to place a protractor on it so that the middle of its ruler, marked with a stroke, coincides with the point of intersection of the determined direction with the vertical kilometer grid line, and the edge of the ruler (i.e., divisions 0 and 180° on the protractor) aligns with this line. Then you should count the angle clockwise from the north direction of the kilometer line to the determined direction on the protractor scale.
To plot on a map in any point directional angle, a straight line is drawn through this point, parallel to the vertical lines of the kilometer grid, and from this straight line a given directional angle is constructed.
It should be taken into account that the average error in measuring the angle with the protractor available on the officer’s ruler is 0.5°.
The values of true azimuth and directional angle differ from each other by the amount of convergence of the meridians. Meridian convergence - corner ? (gamma) between the northern direction of the true meridian of a given point and the vertical line of the coordinate grid (Fig. 2.7). Meridian convergence is measured from the north direction of the true meridian to the north direction of the vertical grid line. For points located east of the middle meridian of the zone, the convergence value is positive, and for points located to the west it is negative. The amount of convergence of meridians on the axial meridian of the zone is zero and increases with distance from the middle meridian of the zone and from the equator, while its maximum value does not exceed 3°.
The convergence of meridians indicated on topographic maps refers to the midpoint (central) point of the sheet; its value within a sheet of a map of scale 1:100000 at middle latitudes near the western or eastern frame may differ by 10-15" from the value labeled on the map.
Transition from directional angle to magnetic azimuth and back can be done in various ways: according to a formula, taking into account the annual change in magnetic declination, according to a graphical diagram. Convenient transition through direction correction. The necessary data for this is available on each sheet of the map at scales 1:25000-1:200000 in a special text help and graphic diagram placed in the margins of the sheet in the lower left corner (Fig. 2.9).
Rice. 2.9 Directional correction amount data
At the same time, in the special text help, the key phrase is: “ Correction to directional angle when transitioning to magnetic azimuth plus (minus)...”, the angle between the “arrow” and the “fork” is also important:
- if the fork is on the left and the arrow is on the right (Fig. 2.10-A), then the declination is eastern and when moving from the directional angle to the azimuth, the correction is (2°15" + 6°15" = 8°30") on the value of the measured directional angle is taken away is added );
- if the “fork” is on the right and the “arrow” is on the left (Fig. 2.10-B), then the declination is western and when moving from the directional angle to the azimuth, the correction is (3°01" + 1°48" = 4°49") to the value of the measured directional angle is added (accordingly, when moving from azimuth to directional angle, the correction is taken away ).
Rice. 2.10 Amendment
Attention! Failure to correct the directional angle or magnetic azimuth, especially at large distances and large map scales, leads to significant errors in determining the coordinates, intermediate and final points of the route.
The ability to determine where latitude or longitude is on a map is important for a person. Especially when an accident occurs and you need to quickly make a decision and transfer coordinates to the police. She is recognized in different ways. They mean the angle that is the plumb line and the 0 parallel at a predetermined point. The value is only up to 90 degrees.
Don't forget that the equator divides the earth into the northern and southern hemispheres. Therefore, the latitude of points on earth that are higher than the longest parallel is northern, and if they are located lower, then southern.
How to find out the latitude of any object?
You can determine latitude and longitude on a map. Look at which parallel the object is indicated. If it is not indicated, then independently calculate the distance between neighboring lines. Then find the degree of parallel you are looking for.
At the equator, geographic latitude is 0°. Points that on the same parallel will have the same latitude. If you take a map, you will see it on the frames; if it is a globe, then where the parallels with the 0° and 180° meridians intersect. Geographic latitudes range from 0° and only up to 90° (at the poles).
5 main latitudes
Take a map, you will see the main parallels there. Thanks to them, coordinates are easier to recognize. From the latitudinal line to the line, the territories are located. They belong to one of the regions: temperate or equatorial, polar or tropical.
The equator is the longest parallel. Lines that are lower or higher decrease towards the poles. The latitude of the equator is 0°. This is the point from which parallels are calculated towards the south or north. The area that starts from the equator and extends to the tropics is the equatorial region. The northern tropic is the main parallel. It is always marked on world maps.
The exact coordinates of 23° 26 min can be detected. and 16 sec. north of the equator. This parallel is also called the Tropic of Cancer. The Tropic of the South is a parallel located at 23° 26 min. and 16 sec. south of the equator. It is called the Tropic of Capricorn. The area that is located in the middle of the line and towards the equator is tropical regions.
At 66° 33 min. and 44 sec. The Arctic Circle is located just above the equator. This is the border, beyond which the length of the night increases. Near the pole it is 40 calendar days.
Latitude of the southern polar circle -66° 33 min. and 44 sec. And this is the border, and beyond it there are polar days and nights. The regions between the tropics and the described lines are temperate, and those beyond them are called polar.
Instructions
Step #1
Everyone knows that the equator divides the earth into the southern and northern hemispheres. There are parallels beyond the equator. These are circles that are parallel to the equator itself. Meridians are conventional lines that are perpendicular to the equator.
The Prime Meridian passes through the observatory, it is called Greenwich and is located in London. That’s why they say: “Greenwich Meridian”. The system, which includes parallels with meridians, creates a coordinate grid. It is used when they want to determine where an object is located.
Step #2
Does geographic latitude indicate that a given point is south or north of the equator? It defines an angle of 0° and 90°. The angle begins to be calculated from the equator and towards the south or north pole. This way you can determine the coordinates; they say that the latitude is southern or northern.
Step #3
Geographic coordinates are measured in minutes and seconds, and most importantly - in degrees. A degree of a certain latitude is 1/180 from any of the meridians. The average length of 1 degree is 111.12 km. A minute in length is 1852 m. The diameter of Mother Earth is 12713 km. This is the distance from pole to pole.
Step #4
To find out latitude using the described method, you need a plumb line with a protractor. You can make a protractor yourself. Take several rectangular planks. Clamp them together like a compass so that they change the angle between them.
Step #5
Take the thread. Hang a weight (plumb) on it. Secure the string to the center of your protractor. Point the base of the protractor at the Polaris star. Do some geometric calculations. Specifically, from the angle between the plumb line and the base of your protractor, immediately subtract 90°. This result is the angle that passes between the polar star and the horizon. This angle is the geographic latitude where you are.
Another way
There is another option for finding the coordinates. It's not like the first one. Wake up before sunrise and time its beginning, and then sunset. Take a monogram in your hands to find latitude. On the left side of the monogram, write down how long the daylight hours lasted, and on the right side, write the date.
Back in the middle of the 18th century. similar coordinates could be determined on the basis of astronomical observations. In the 20s In the 20th century, it was already possible to communicate by radio and determine coordinates with special instruments.
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Lesson questions:
1. Coordinate systems used in topography: geographic, flat rectangular, polar and bipolar coordinates, their essence and use.
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.
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.
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.
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, 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 according to 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 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.
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.
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.
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.
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 using a straight line |
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. |
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 a 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. |
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.
Notes
Military topography
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