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Military Grid Reference System
An MGRS grid reference is a point reference system. When the term 'grid square'
is used, it can refer to a square with a side length of 10 km, 1 km, 100 m, 10 m or
1 m, depending on the precision of the coordinates provided. (In some cases,
squares adjacent to a Grid Zone Junction (GZJ) are clipped, so polygon is a better
descriptor of these areas.) The number of digits in the numerical location must be
even: 0, 2, 4, 6, 8 or 10, depending on the desired precision. When changing
precision levels, it is important to truncate rather than round the easting and
northing values to ensure the more precise polygon will remain within the
boundaries of the less precise polygon. Related to this is the primacy of the
southwest corner of the polygon being the labeling point for an entire polygon. In
instances where the polygon is not a square and has been clipped by a grid zone
junction, the polygon keeps the label of the southwest corner as if it had not been
clipped.
An example of an MGRS coordinate, or grid reference, would be 4QFJ12345678, which consists of three parts:
4Q (grid zone designator, GZD),
FJ (the 100,000-meter square identifier), and
12345678 (numerical location; easting is 1234 and northing is 5678,
in this case specifying a location with 10m resolution).
SOURCE: http://en.wikipedia.org/wiki/Military_grid_reference_system#100.2C000-meter_square_identification
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MGRS Zipper Effect
The Universal Transverse Mercator (UTM) projection is a planer projection used
to project the curved surface of the earth on a two-dimensional plane. In the U.S,
excluding Alaska, there are approximately 12 UTM zones. Irregular grid cells with
areas less than 1-kilometer square occur along the edges of each zone junction.
These Zipper Cells occur because mapping the three-dimensional spherical earth
on a two-dimensional plane creates distortions which may appear as sliver polygons.
SOURCE: http://www.fws.gov/southwest/AboutUs/LCC/docs/GP_LCC_ReportFinalDraft_Hanni.pdf
Additionally there is also a small North and South MGRS zipper effect where
seams with slivers are also a by-product of the transformation of the earth from a
round object to a flat one, however, this by-product is more easily observed in the
East and West MGRS seams.
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Transverse Mercator Projection
The familiar Mercator map is based on the great circle of the equator. Any great
circle can be taken as the basis, in particular a meridian. When this is done, the
projection is called the Transverse Mercator. The coordinate transformation from
latitude and longitude with respect to the equator to latitude and longitude with
respect to the chosen meridian (they all are the same) is shown at the right.
Solution of the shaded right-angled spherical triangle gives the desired relations,
which are shown on the diagram. The Mercator projection is then carried out on
the new coordinates ?' and f' in the usual way.
A Transverse Mercator coordinate net showing meridians and parallels appears at
the left. The orthogonal intersections show that it is conformal. Neither meridians
nor parallels are straight lines, or any simple curve. At the center of the map,
meridians and parallels are almost a rectangular net. The map is used only in this
area, centered on a certain longitude and latitude. The basic map has unity scale
on the standard meridian, but the scale can be changed slightly to make it smaller
than unity on the meridian, and unity a certain distance east and west of the
meridian, so that the scale is closer to unity over a wider band of the map.
IMAGE: http://mysite.du.edu/~jcalvert/math/trmerc.gif
The Transverse Mercator projection is used as a basis for the Universal
Transverse Mercator (UTM) grid system for military maps. It is easy to cover any
relatively small area anywhere on the globe with this system, though not maps
showing a large area, when the great changes in scale would be objectionable. A
grid system overlays a rectangular grid on the map, to which points are referred
instead of using longitude and latitude. The earth between 80S and 80N is
divided into quadrilateral zones 8 N-S and 6 E-W, numbered 1-60 eastward
beginning at 180 and C-X (I and O omitted) south to north. These are divided into
100 000-m squares designated by two letters. The principle of stating a UTM grid
reference is shown at the right. The zone designation, 12S, is added if references
cover a wide area. This reference locates point P, the village of Red Rock on the
New Mexico-Arizona border in the Navajo Reservation, to within 1000 meters.
More precise grid coordinates, XR735526, locates Red Rock to 100 meters. A
special L-shaped ruler facilitates accurate reading of the grid coordinates. One
used by the Army had scales of 1:25000 and 1:50000, with meters on one side
and yards on the other. In order to make a grid reference, a map is required, of
course, such as the one in the References. I have not investigated in detail how
these grids and squares are made to fit together, and what approximations are
involved. An arbitrary square grid could easily be superimposed on any map, but
making it correspond to distance with any accuracy is a more difficult question.
SOURCE: http://mysite.du.edu/~jcalvert/math/mercator.htm
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UTM - Universal Transverse Mercator Geographic Coordinate System
The idea of the transverse mercator projection has its roots in the 18th century,
but it did not come into common usage until after World War II. It has become the
most used because it allows precise measurements in meters to within 1 meter.
A mercator projection is a 'pseudocylindrical' conformal projection (it preserves
shape). What you often see on poster-size maps of the world is an equatorial
mercator projection that has relatively little distortion along the equator, but quite a
bit of distortion toward the poles.
What a transverse mercator projection does, in effect, is orient the 'equator'
north-south (through the poles), thus providing a north-south oriented swath of little
distortion. By changing slightly the orientation of the cylinder onto which the map is
projected, successive swaths of relatively undistorted regions can be created.
This is exactly what the UTM system does. Each of these swaths is called a UTM
zone and is six degrees of longitude wide. The first zone begins at the
International Date Line (180, using the geographic coordinate system). The
zones are numbered from west to east, so zone 2 begins at 174W and extends to
168W. The last zone (zone 60) begins at 174E and extends to the International
Date Line.
IMAGE: http://geology.isu.edu/geostac/Field_Exercise/topomaps/images/zones.gif
The zones are then further subdivided into an eastern and western half by
drawing a line, representing a transverse mercator projection, down the middle of
the zone. This line is known as the 'central meridian' and is the only line within the
zone that can be drawn between the poles and be perpendicular to the equator
(in other words, it is the new 'equator' for the projection and suffers the least
amount of distortion). For this reason, vertical grid lines in the UTM system are
oriented parallel to the central meridian. The central meridian is also used in setting
up the origin for the grid system.
Any point can then be described by its distance east of the origin (its 'easting'
value). By definition the Central Meridian is assigned a false easting of 500,000
meters. Any easting value greater than 500,000 meters indicates a point east of
the central meridian. Any easting value less than 500,000 meters indicates a point
west of the central meridian. Distances (and locations) in the UTM system are
measured in meters, and each UTM zone has its own origin for east-west
measurements.
To eliminate the necessity for using negative numbers to describe a location, the
east-west origin is placed 500,000 meters west of the central meridian. This is
referred to as the zone's 'false origin'. The zone doesn't extend all the way to the
false origin.
The origin for north-south values depends on whether you are in the northern or
southern hemisphere. In the northern hemisphere, the origin is the equator and all
distances north (or 'northings') are measured from the equator. In the southern
hemisphere the origin is the south pole and all northings are measured from there.
Once again, having separate origins for the northern and southern hemispheres
eliminates the need for any negative values. The average circumference of the
earth is 40,030,173 meters, meaning that there are 10,007,543 meters of northing
in each hemisphere.
IMAGE: http://geology.isu.edu/geostac/Field_Exercise/topomaps/images/utm2.gif
UTM coordinates are typically given with the zone first, then the easting, then the
northing. So, in UTM coordinates, Red Hill is located in zone twelve at 328204 E
(easting), 4746040 N (northing). Based on this, you know that you are west of the
central meridian in zone twelve and just under halfway between the equator and
the north pole. The UTM system may seem a bit confusing at first, mostly because
many people have never heard of it, let alone used it. Once you've used it for a
little while, however, it becomes an extremely fast and efficient means of finding
exact locations and approximating locations on a map.
Many topographic maps published in recent years use the UTM coordinate system
as the primary grids on the map. On older topographic maps published in the United
States, UTM grids are shown along the edges of the map as small blue ticks.
SOURCE: http://geology.isu.edu/geostac/Field_Exercise/topomaps/utm.htm
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