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For people with moderate geodetic expertise, coordinates, consisting of long sequences of numbers and letters that indicate a unique point on the Earth, are not easy to understand.
This article is a crash course, explaining the calculation methods and their history.
“Universal Transverse Mercator“ (UTM) goes back to the scientific genius Gerhard Kremer, alias Gerardus Mercator.
In the middle of the 16th Century, Mercator found a method to picture the globe, including all sorts of then existing information, on a mere piece of paper.
Later, after the Second World War, the UTM Coordinate System has been further developed for Military purposes by the United States.
In the meantime, due to general globalization, national coordinate systems are constantly being replaced by internationally standardized UTM coordinates.
For those, there are different notations, depending on the usage.
This paper explains the most common display formats and reference to conversion software available from the German company C. Killet Software Engineering.
According to the UTM coordinate system, the globe is divided into vertical UTM zones of 6 longitudes each.
These zones are arranged round the equator, to be compared with orange peels.
Starting eastwards at 177 degrees West, they are numbered from 1 to 60.
Each UTM zone is regarded as an individual Cartesian coordinate system.
The origin for each UTM zone is the intersection of the equator with the corresponding central meridian.
The easting of the central meridian is shifted by 500.000 meters, in order to obtain exclusively positive values.
For the same reason, when being displayed on the southern hemisphere, the northing is shifted by 10.000.000 meters.
The Prime Meridian Greenwich is the exact border between the UTM zones 30 and 31.
Germany, for example, is mostly located in the UTM zones 32 and 33.
There are various options to represent UTM coordinates.
By way of example, we are going to list the UTM coordinates of the beacon “Red Sand” at the mouth of the river Weser (53° 51´ 18 N / 8° 4´ 54 E) using different notations.
All notations, however, describe the same point in the coordinate system.
The examples show the multiple possibilities of UTM coordinates.
The user may chose, which display mode is most suitable for the purpose in question.
Here, we are going to explain the exact meaning of the individual numerals and letters, appearing within the coordinate.
In the following, we are going to show ways to convert UTM coordinates from one display mode to another.
UTM Zone Coordinates
The most common representation is the one of UTM coordinates with an easting and a northing.
The coordinates within a UTM zone are metrical and perpendicular to each other.
The easting is preceded by the number of the UTM zone.
Our example, as a complete UTM zone coordinate, is represented as follows:
The point is located in the UTM zone 32, which is based at the central meridian, 9 degrees eastern longitude.
Because the value 439596 is below 500000, the point is located exactly 60404 meters west of the central meridian (500000 m - 439596 m = 60404 m).
To the North, the point is exactly at a distance of 5967780 meters from the equator.
TRANSDAT allows the conversion of coordinates between hundreds of coordinate and reference systems.
UTM zone coordinates may be directly entered into the input fields of the program or imported from data files, respectively.
This requires the selection of parameters from the list boxes shown here.
The entry of decimal places is optional.
The program is formatting the coordinates entered and to be calculated according to your requirements in the field “Decimals" (number of decimal places).
In the bottom list box, you can either select the natural UTM zone (indicated by its geographical longitude) or enforce the calculation into a defined zone.
Thereby, the UTM zone will be enlarged over its extension of 6 longitudes.
The denomination “UTM zone” is equal to “meridian strip”.
The enforcement of a certain UTM zone is therefore called "zone swap" or "meridian swap".
A zone swap is required, whenever a number of coordinates from different UTM zones are to be displayed together in one single zone – or they are subject of linear calculation.
There is the example of the representation of Germany (see picture), that extends over both zones 32 and 33.
If a zone swap to the UTM zone 33 is enforced for our example coordinate of the beacon “Red Sand”, we get the following result:
The point is now located in the UTM zone 33, which is based at the central meridian, 15 degrees eastern longitude.
Because the value 045270 is below 500000, the point is located exactly 454730 meters west of the central meridian (500000 m - 045270 m = 454730 m).
To the North, the point is exactly at a distance of 5989604 meters from the equator.
You will have noticed that the northing in zone 33 appears to be further away from the equator than the one in zone 32.
The distortion is due to the fact, that in the rectangular UTM system, the distance to the equator is measured on a parallel translation of the central meridian.
Because each UTM zone is represented as an individual Cartesian coordinate system, the differing northing in both zones are correct.
MGRS / UTMref / UTM Reference System
For military purposes, UTM coordinates are represented in the "Military Grid Reference System" (MGRS) or “UTM Reference System” (UTMref).
To indicate the geographical latitude, the meridians are subdivided into UTM bands of 8 degrees along the parallels that are denominated with letters.
The UTM zones, in turn, independent of the UTM bands, are divided into squares with a lateral length of 100 km each, positioned parallel to the central meridian.
The UTM squares are denominated with letter pairs.
A point, exact to the meter, is notated with 5 digits of the east and of the north position, respectively, within the UTM square.
Again, we take the coordinates of the beacon “Red Sand”:
The point is located in the UTM zone 32. It is the meridian with the central meridian at 9 degrees eastern longitude. Also, the point is located in the UTM band U, which extends between 48 and 56 degrees northern latitude. It is located as well within the UTM square ME, 100 km west of the central meridian and 5900 km north of the equator. The position exact to the meter is 39596 meters east of the south western corner of the UTM square and 67780 meters north of the same. The accuracy of a UTMREF coordinate can be varied by the (even) number of digits, in order to describe this way a larger or smaller area. These are some examples with differing accuracy:
The conversion program TRANSDAT can calculate UTMref coordinates in different accuracy levels.
The picture shows the necessary settings.
Because UTMref coordinates are not described as usual with a northing and an easting, but only by way of a combination of characters, the second entry field remains empty.
UTM Grid Coordinates
UTM Grid Coordinates are represented in a slightly different way.
The UTM grid coordinate of the bea-con “Red Sand” looks as follows:
The point is located in the UTM zone 32 and in the UTM band U.
The exact position is 60404 meters west of the central meridian (500000 m - 439596 m = 60404 m).
To the north, the point is at an exact distance of 5967780
It is quite simple to complete the UTM zone number 32 and the distance to the central meridian 439596 by hand to an easting 32439596 and use it together with the northing 5967780 as a UTM zone coordinate.
By having a closer look at the whole, you will notice, that the UTM square has been simply left out in this representation form.
Without nominating the UTM square, the UTM band seems to be superfluous.
However, it is used for immediate identification of the hemisphere.
The author favors the use of UTM Zone Coordinates or the UTM Reference System instead of UTM Grid Coordinates.
To date, TRANSDAT is not yet supporting this display format.
Future program versions will provide the conversion from and into UTM Grid Coordinates.
Reduced UTM Coordinates
Unfortunately, the zone number is not always included in UTM zone coordinates.
This kind of coordinate display is often used, presuming the knowledge of the UTM zone.
When showing the easting, the zone number is then simply left out.
In fact, this is not an official notation but a result of certain laziness.
Originally, reduced coordinates where due to technical reasons.
To reduce the effort, the number of digits has been cut.
From the side of the Army, additional criteria were brought in.
In their systems, an extra entry field had been added for the zone notation (e.g. 32 or also 32U).
In the Civil Environment, others copied the idea.
Our test coordinate might look as follows:
Sometimes, also the first digit of the northing (1000 km digit) is blanked, which for Germany is always a 5, apart from a small area in the north of the country:
In these cases, the UTM zone and sometimes the 1000 km digit of the northing, has to be guessed, calculated or at least taken as a constant value.
The author of this paper do not doubt in the necessity of indicating the full UTM coordinate.
Given the fact, that only coordinates from the same zone may be calculated, incomplete UTM coordinates can be compared to street numbers without indicating the street.
For these special cases, the TRANSDAT program provides the option to complete the coordinate with addends.
In the example, the addend for the easting is 32000000.
Thus, the value 439596 is complemented to 32439596.
The same applies for the northing, which is complemented to 5967780 by the addend 5000000.
From time to time, also multipliers are needed.
This applies for example, when using other measures then meters (like feet, yards or miles).
Behind the button “?!", there is a list box that includes the most common conversions.
With just one mouse click, you may convert the output of the Prussian Cadastre Coordinates from meters to “Prussian feet”.
For more recent use: Also the American NAD27 coordinates can be directly converted into US Survey feet.
By entering the same coordinate and reference system for the source coordinates and for the target coordinates, the described reduced coordinates can be comfortably completed by means of addends.
The TRANSDAT Program
TRANSDAT was developed by the German company C. Killet Software Engineering.
The program is in productive use in Europe, the United States and other countries worldwide for the professional conversion between international and national coordinate systems, with and without datum transformation – fast and with highest quality results.
For more detailed information, please go to our website http://www.killetsoft.de/p_trda_e.htm.
Developers of geodetic programs and applications may also access the Dynamic Link Library GeoDLL that contains precise functions for topics like 2D and 3D coordinate conversions, change between datum or reference systems, meridian swaps, geodetic tasks, distance calculations, Digital Elevation Models as well as support of NTv2.
For more detailed information, please go to our website http://www.killetsoft.de/p_gdla_e.htm.
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