# Flat rectangular coordinates, how to determine flat rectangular coordinates from a topographic map.

The lines of parallels and meridians, which serve as the frame for this sheet of paper topographic map, are curved lines, although their curvature within one sheet is practically invisible. But within each Gaussian zone, there are two lines that are drawn on the map with straight lines. This is the axial meridian of the zone and the equator. These two lines are taken as the axes of plane rectangular coordinates and determine the plane rectangular coordinates themselves.

## Flat rectangular coordinates, how to determine flat rectangular coordinates from a topographic map.

The line of the axial meridian is considered the abscissa axis and denoted by x, the equator line by the ordinate axis and denoted by y. For the origin, the point of intersection of the axial meridian with the equator is taken. Thus, each Gaussian zone has its own grid of plane rectangular coordinates. The x coordinates (abscissas) are measured north and south of the equator, i.e. from 0 (at the equator) to 10,000 km (at the pole). To the north of the equator, the y coordinate is considered positive, to the south – negative. The xy coordinates (ordinates) are counted from the axial meridian to the right (east) and left (west). In order not to deal with negative values ​​for these coordinates, we agreed to take the ordinate y for the axial meridian equal to 500 km.

Thus, the x axis is as if transferred westward for 500 km and all ordinates within this zone will always have a positive sign. In addition, the figure corresponding to the Gaussian zone number is always assigned to the ordinate value at the front in order to avoid repeating coordinates located in different zones.

## How to determine flat rectangular coordinates from a topographic map.

In order to be able to determine the flat rectangular coordinates of the points in each Gaussian zone, a rectangular grid of coordinates is drawn on topographic maps, that is, lines are drawn parallel to the axial meridian and equator.

These straight lines, of course, will not coincide with the lines depicting the meridians and parallels. With the exception of the axial meridian and equator, in parallel to which they are held. This coordinate grid is called kilometer, because its lines are drawn through a kilometer for scales 1:10 000, 1:25 000, 1:50 000. On each sheet of the map along the inner frame, the coordinates of the kilometer grid from the axial meridian of this zone and from the equator are given. The values ​​of the full coordinates are signed only at the extreme (upper and lower) lines of the grid. At all intermediate lines, abbreviations are signed, that is, only the last two digits (tens and units of kilometers).

For example, the bottom line of the kilometer grid in the figure is designated 5042, and the next grid line above it is indicated only by the number 43 km, not 5043. The numbers of the kilometer grid under the south and above the northern frame of the map sheet indicate the ordinates (y) of these lines. The extreme lines are also indicated by full coordinates. But unlike horizontal lines, the first digit in ordinates indicates the zone number.

For example, the ordinate y = 8384 km. This means that the sheet of this map is located in the eighth six-degree zone of Gauss, that is, limited by 42 and 48 meridians of east longitude, and the points lying on the line y = 384 are located to the left of the axial meridian at a distance of 500-384 = 116 km.

Using the kilometer grid, you can, without resorting to additional measurements, determine the flat rectangular coordinates of any point on the map. Up to a kilometer. To do this, just find in which square of the grid the determined point M is located, and read the numbers denoting this square. First, the value of the coordinate x – 5044 is usually called (written), and then y = 8384.

## Indication of any object on a topographic map using plane rectangular coordinates.

To indicate any object on the map, they usually say this: point M is in the square 50 448 384, that is, they call its coordinates in a row without separating them, but more often they give instructions in abbreviated form, they call only the next two digits from the plane rectangular coordinates of this point – a square 4484.

Calling this square on the map, we indicate the coordinates of its lower left corner. That is, the southwestern corner of the square in which the point M is located. If you need to specify a more accurate position of the point inside this square, then its distance from the boundary lines of this square is additionally determined. Using scale, translate these distances into meters and attribute them to the numbers of the designated square.

For example, point M has the following coordinates: x = 44,500 meters, and y = 84,500 meters. These will be the abbreviated coordinates for point M, and the full flat rectangular coordinates for it will be written as follows: x = 5,044,500 m, y – 384,500 m.

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

## Two grids of flat rectangular coordinates on topographic maps.

On some topographic maps, you can find two grids of flat rectangular coordinates. One is applied completely as shown in the figure above. The second is indicated only outside the scope of this card. What is the matter here? We have previously established that 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.

Therefore, when connecting kilometer grids of two neighboring zones, the lines of one of them are located at an angle to the lines of the other. As a result of this, at the junction of the two zones, difficulties may arise in the determination of coordinates, since they will relate to different coordinate axes.

To eliminate this inconvenience, in each six-degree zone, all map sheets located within 2 degrees east and 2 degrees west of the zone border have, in addition to their coordinate grid, an extension that is a continuation of the coordinate grid of the neighboring zone.

And in order not to obscure the data on the map sheets with the second grid, it is indicated only by numbers on the outer frame of the sheet. These numbers are a continuation of the numbering of the lines of the coordinate grid of the adjacent zone..

Based on the book “Map and Compass My Friends”.
Klimenko A.I..