Geographical, flat rectangular and polar coordinates

There are many different coordinate systems. All of them are used to determine the position of points on the Earth's surface. Here are mainly geographical, flat rectangular and polar coordinates. In general, the coordinates are called angular and linear values, which determine the position of points on a surface or in space.

Geographical coordinates — this angle values — latitude and longitude coordinates, defining a point position on the globe. Latitude is the angle formed by the plane of the equator and the plumb line at a given point in the Earth's surface (Figure 25). This value indicates the angle of how this or that point on earth north or south of the equator. If the point is located in the Northern Hemisphere, it will be called the latitude north, and if in the Southern Hemisphere — South latitude. Latitude points located on the equator, is zero (0 °), and at the poles (North and South) — 90 °.

Geographical longitude as a corner, but the plane formed by the meridian taken as the initial (zero), and the plane of the meridian passing through the point.

Geographical, flat rectangular and polar coordinates

To determine the uniformity of the initial meridian of longitude agreed to consider the meridian passing through the astronomical observatory in Greenwich (near London), and call it Greenwich. All points are located to the east of it, will have east longitude (to the meridian of 180 °), and to the west of the initial — west longitude.

Figure 25 shows how to determine the position of the point A on the ground, if you know the geographic coordinates (latitude — longitude and f — X). Note that the difference in longitude of the two points on the Earth shows not only their relative position with respect to the zero meridian, but the difference in time at these points in the same time. The fact is that every 15 ° (24th part of a circle) of longitude equals one hour of time. On this basis, it is possible to determine the longitude difference in time at these two points.

Example. Moscow has a longitude of 37 ° 37'' (east), and Khabarovsk — 135 ° 05'', that is, lies east of 97 ° 28''. What time are the cities in the same time?

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

How is the geographical coordinates on the map?

In Figure 42 shows the design of frame sheet of any topographic map. As can be seen in the corners of the map signed longitude meridians and parallels of latitude, which form the frame of the map sheet.

On all sides the frame has a scale divided into minutes (and for the latitude and longitude). Moreover, every minute of points is divided into 6 equal parts, which — correspond to 10 seconds of longitude and latitude. Thus, in order to determine the latitude of a point M on the map (Figure 42), it is necessary through this point draw a line parallel to the bottom or top of the box card, and read to the right or to the left on the scale of latitude corresponding to degrees, minutes, second. In our example, the point M has latitude 45o31'' f = 30. "Similarly, spending vertical through M parallel to the side (closest to the given point) of the meridian border

Geographical, flat rectangular and polar coordinates

map sheet, read the longitude (east) X = 43 ° 31/18 / /. Mapping points on a given geographical coordinates in reverse order. Is initially on the scales of the geographical coordinates, and then after they had a parallel and perpendicular lines. The intersection will show them on the map point with geographic coordinates.

Lines of latitude and longitude, which serve as a frame for the map sheet, are curved lines, although their curvature in a single sheet, and almost imperceptible. But within each zone there are two Gaussian lines, which are represented by straight lines on the map — is the zone meridian and the equator (Fig. 26). These two lines are taken as the axis of the plane rectangular coordinates. Central meridian line said x-axis and x denote, the equator — the y-axis and y represent. As the origin take the intersection of the central meridian to the equator. Thus, in each zone has its own grid Gauss plane rectangular coordinates. Coordinates x (abscissa) is measured north and south of the equator, that is, from 0 (at the equator) to 10,000 km (the pole). To the north of the equator coordinate have to be positive, to the south — negative. Xy coordinates (ordinates) are measured from the central meridian to the right (east) and the left (west). In order not to have to deal with negative values for these coordinates, have agreed to the ordinate value at the central meridian of 500 km take. Thus, the x-axis as it moved west for 500 km and all the values of the ordinates within this zone will always have a positive sign. In addition, the value of the ordinate at the front is always attributed to its number of Gauss zone in order to avoid a repetition of coordinates, located in different areas.

To determine the plane rectangular coordinates of the points in each zone of the Gauss maps applied to a rectangular grid (Fig. 26), that is, held the line parallel to the axial meridian and the equator.

These straight line, of course, will not coincide with the lines depicting the meridians and parallels (except for the central meridian and the equator, along which they prorodyatsya). This grid is called kilometer, as its lines are drawn through the kilometer (to scale 1: 10,000, 1: 25 000, 1: 50,000).

On each map sheet along the inner frame gives the coordinates kilometer grid from the central meridian of the zone and the equator. As seen in Figure 42, the total value of the coordinates are signed only on the end (top and bottom) line grid coordinates. All the same intermediate lines signed abbreviation, that is, only the last two digits (tens and units of kilometers). For example, the bottom line kilometer grid (Fig. 42) is designated as 5042, and the next one over it line net figures only 43 km, and not 5043. Figures kilometer grid for southern Shay and over the northern edge of the sheet map represents the ordinate (y) of the lines. The end line is also indicated full coordinates. But unlike the horizontal lines, the first digit indicates the number of ordinates in the zone. For example, the ordinate y = 8384 km. This means that the list of the card is in the eighth zone shestigradusnoy Gauss, that is limited 42 and 48 ° east longitude meridians and points on the line y = 384, to the left of the central meridian at a distance of 500 — 384 = 116 km.

With kilometer grid coordinates can, without additional measurements, to determine the coordinates of any point on the map (up to a kilometer). It suffices to find in which grid cell is determined by the point M (Fig. 42), and read the digits of the given square. First, usually called a (recorded) value of the coordinate x = 5044, then y = 8384.

To specify an object on the map usually say: point M is in the box 50448384, that is called the coordinates of her contract, not dividing them, but are more likely to indicate abbreviated name only two subsequent figures of the rectangular coordinates of the point — a square 4484. Calling this square on the map, we specify the coordinates of the lower left corner it, that is the south-western corner of the square, which is the point M. If you want to specify a more precise location of the point inside the square, then further define its distance from the boundary lines of the square. Using the scale, translate the distance in meters, and attribute them to the numbers indicated by the square. For example, the point M has the following coordinates: x = 44 500 m and y = 84 500 m This will be reduced to the coordinates of the point M, and full coordinates for it are written as: x = 5,044,500 m, y = 384 500 m .

Plotted points on the map by the known flat rectangular coordinates in the reverse order. First rejected the last three digits in the coordinates are line kilometer grid, that is, the square in which the point is located. Then, using a ruler, scale and compass, applied the exact coordinates of the points in this square.

On some maps you can vetretit two flat rectangular grid coordinates, one applied fully as it is shown in Figure 42, and the second is designated just outside the border of the map. Why is that? We have already established that the vertical kilometer lines parallel to the axial meridian of the zone (Figure 26) and the meridian between adjacent zones are not parallel. Consequently, during the docking kilometer grids of the two neighboring zones line of one of them at an angle to the lines of the other. As a result, at the junction of two ^ swarms may have difficulty in determining the origin, since they relate to different axes. To eliminate this disadvantage, in each zone, all shestigradusnoy a map, located within 2 ° to 2 ° east and west boundaries of the zone are to: LIMS its grid more and more, which is a continuation of the grid of the neighboring area. And in order not to obscure the second grid data sheets card, its figures represent only the outer edge of the sheet. These figures are a continuation of the numbering of the grid lines adjacent zones. We have discussed how to define the geographic and plane rectangular coordinates of individual points on a topographic map.

With the advent of radar and radio direction-finding was necessary to determine, on the map and on the ground the individual points by the angle with respect to a direction and distance from a selected point, called the pole.

If we take the place of two mutually perpendicular axes x and y in the system of plane rectangular coordinates of only one x-axis and the starting point for her 0 (pole) and from it we define angle a (alpha) (Fig. 27), which is called the angle position, and the distance D (from the pole to a point), these two values are the name of the "polar coordinates." In polar coordinates, the x-axis is called the polar axis, and the angle of the individual point has three designations and accordingly three items: the directional angle a true azimuth A and magnetic azimuth Am.

Such a large number of angular position and a different name due to the fact that it is we take the polar axis in a polar coordinate

Geographical, flat rectangular and polar coordinates

from which direction we measure the angular position.

If we take the polar axis direction of the vertical grid lines (Fig. 28), then this angle will be called the directional angle and denoted as, if the polar axis we take the direction of the true meridian (and he has a map), this angle will be called the true azimuth and designated A. Finally, if we take the polar axis magnetic meridian (The direction of the magnetic compass), this is called the angle of the magnetic bearing and will be denoted by Am.

In all these cases, the position angle varies from about 360 ° and always measured clockwise.

If you set the ratio of the polar axis with each other, then it will be determined by the ratio between directional angle a true and magnetic bearings A and Am.

We have already established that the vertical lines of the rectangular grid coordinates are certain angle with the meridians, that is, the side of the frame map (Fig. 29). The reason for this is that all the meridians converge at the poles, and vertical grid lines remain parallel to its axial meridian zone.

The angle between the true meridian in the

Geographical, flat rectangular and polar coordinates

point and vertical grid line passing through the same point, called the convergence of meridians and represent the Greek letter 7 (gamma).

Convergence of meridians is East (with a +), when the grid is tilted relative to the frame to the right card, and west (with the sign -), when the grid is tilted to the left. If theta angle reaches 1 ° or more, it must be taken into account in the transition from the azimuth (a) to the true azimuth (A). Its value at the band edges up to 3 °.

The true meridian, in turn, coincides with the magnetic (which features a compass). This angle between them is called magnetic declination, and is denoted by the Greek letter B (delta). Magnetic declination is east (with a +), when the northern end of the magnetic needle compass deviates to the east of the true meridian, and west (with a -) for evasion to the west. Taking into account the complexity of the magnetic declination in the transition from the direction angle to the magnetic azimuth is that because of the magnetic properties of the earth it at various points the earth's surface varies. Moreover, at the same place as it is not constant, and from year to year changes.

Thus, from this it is clear that the vertical grid lines and magnetic meridians form an angle, which is the amount of convergence of the meridians and the magnetic variation in (b). This angle is called the angle of deflection of the needle, or the amendment of direction and represent a capital letter — P = a + 6.

Geographical, flat rectangular and polar coordinates

If we know the y-a, and it will need to determine the magnetic azimuth, the equation becomes:

Geographical, flat rectangular and polar coordinates

Amendment P is measured from the direction of the northern direction of the vertical grid lines and is considered positive (+ sign), if the north end of the needle is deflected to the east of that line, and negative (with a -) at the western deviation of the magnetic needle. The data on the direction of correction (P) and its constituent variables: convergence of the meridians (a), the magnetic variation (b), is placed in a scheme under the lower edge of the sheet with an explanation card (Fig. 29). These data are necessary in order to move quickly from a directional angles, measured on a map to their corresponding magnetic azimuth (Am) in the locality. For this scheme the relation between the angle and position of the amendment would look like;

All this is valid only for the eastern magnetic declination (+ b), and the western convergence of meridians (-y). For others, the direction of the correction schemes can not be equal to the sum of these angles, and the difference, or, in fact, she may become negative. Then the transition from the azimuth (a) the magnetic azimuth of the {1) it must be deducted, and the formula (2), on the contrary, to add.

This fact makes everyone working with the card carefully consider the layout of the vertical lines of the grid, true and magnetic meridians and the data on the amount of correction to be placed at each topographical map.

Mistakes made in the correction direction (R) and more so in its sign when defining data on the map to move the azimuth on the terrain, are dangerous because when the value of 5 ° and in motion at a distance of 1 km at the end of the path deviation may be about 100 m If in the open, the benchmark can still be detected. But in a closed area (in the forest) find it almost impossible.

We have discussed the issues relating to the methods and ways to create topographic maps (map projection Gauss) and their possible scale, razgrafki and range maps, as well as showing how the framework is designed maps (geographic meridians and parallels net plane rectangular coordinates). We now know how to determine the directional angles, true and magnetic bearings, the correction direction and make the transition from one corner to the other. It is time to fill the frame of the image map areas and learn to read it, that is to study the alphabet cards.

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