![]() UTM Projection - Universal Transverse MercatorThe systematic mapping of Brazil is performed using the UTM Projection (1:250.000. 1:100.000, 1:50.000). Below we can see its main characteristic:
DatumTo characterize a datum a surface of reference that is positioned relative to the real Earth is used. It is, therefore, a mathematical model that replaces the real Earth in the cartographic applications. A planimetric or horizontal datum
is established from the latitude and longitude of an initial point,
from the azimuth of line that starts at this point, and from two
constants needed to define the reference ellipsoid. Thus is formed the
basis for the calculations of the horizontal position survey.
Latitude: 19o 45' 41.34" S
Latitude: 19o 45' 41.6527" S Ellipsoid Models
|
Ellipsoid |
Equatorial Radius R(m) |
Polar Radius r(m) |
Flatness |
International
Astronomical Union (GRS-67) |
6.378.160,00 |
6.356.776,00 |
1/298.25 |
Hayford |
6.378.388,00 |
6.366.991,95 |
1/297 |
Is the one where the deformations are null, that is, the scale is
true. From this parallel the deformations increase progressively on the
parallels and on the meridians, with different values.
We use the standard parallel as a control line in the calculations
of a cartographic projection.
The standard parallel can be unique, like in the conic projections
that use a cone tangent to the Earth. If the cone is secant then there
will be two standard parallels, like in the Albers conic projection.
Any cartographic projection system has an origin and a pair of
cartesian axes, (X,Y) or (E,N), that are used to represent the plane
coordinates of the projection. The origin is defined at the
intersection of a parallel and a meridian. The tangent to the meridian
at the origin defines the Y or N axis, while the tangent to the
parallel at the origin defines the X or E axis.
The definition of longitude of origin depends on the projection used
by the user.
The figure below presents
the distribution of the 1:1.000.000 maps of Brazil.
To know the longitude of origin, the user must locate the area of
interest in the figure and verify to which zone it belongs. The central
meridian will correspond to the longitude of origin.
The city of Leme, for example,
located at 22o S and 47o W is in the 42o
to 48o W zone. Thus, its longitude of origin is 45o
W.
Another possibility is the use of equation MC = -183 + 6Z, where MC is
the central meridian and Z is an integer that represents
the UTM zone.
In the Gauss projection, the longitude of origin for Brazil is
equivalent to the limits of the one millionth maps. To verify these
values please see the figure above.
The origin latitude usually refers to the parallel which is closer the the region of interest.
In the polyconic projection, for example, it is common to use the
Equator as the latitude of origin, but we can also use a parallel that
is closer to the region of interest.
Cartographic
Concepts
Is the relationship between the dimensions of the
elements represented on a map and the real dimensions on the
surface of the Earth.
The scale is a mandatory information on any map and will generally
be presented in numerical form.
The numeric or fraction scales are expressed by fractions whose
denominators represent the natural dimensions while the numerators
represent the dimensions on the map. We indicate them with the
following form: 1:50 000 or 1/50 000.
The scale of 1:50 000, for example, indicates that one unit of
measure on the map is the equivalent to 50 000 units of the same unit
on the terrain. Thus, 1 cm on the map corresponds to 50 000 cm
(or 500 m) on the terrain.
The following table presents the available projections in SPRING and
their characteristics:
Projection |
Classification |
Applications |
Characteristics |
Albers |
Equal-area Conical |
Thematic Mapping. Used to map areas with predominantly east-west areas. |
Preserves areas. |
Bipolar |
Conic |
Designed for low-error mapping of the North and South America. |
Preserves angles. |
Cylindrical Equidistant |
Cylindrical Equidistant |
World Maps. |
Distorts areas. |
Gauss |
Cylindrical |
Old topographic maps. |
Distorts areas (but the distortion does not
exceed 0,5%). |
Polar |
Plane Conformal |
Mapping of polar regions. |
Preserves angles. Presents scale distortions. |
Lambert |
Conic Conformal |
Geographic maps and maps in general. |
Preserves angles. |
Lambert Million |
Conic Conformal |
Millionth maps. |
Preserves angles. |
Mercator |
Cylindrical Conformal |
Nautical charts. |
Preserves angles. |
Miller |
Cylindrical |
World Maps. |
Distorts angles. |
No_Projection |
Plane |
Archiving of data that are not linked to any specific traditional projection system (drawings, construction drawings, raw images, non-georeferenced images, etc.). |
Local System of plane coordinates. |
Polyconic |
Conic |
Thematic mapping in small scales. |
Distorts areas and angles. Replaced by the Lambert Conic Conformal in the most recent maps. |
Latlong |
- |
Archiving of raster data with spatial resolution in decimal degrees. |
Geometry identical to the cylindrical equidistant projection. |
Sinusoidal |
Pseudo-cylindrical Equivalent |
Thematic mapping in intermediate and small scales. |
Preserves areas. |
UTM |
Cylindrical Conformal |
Basic mapping in medium and big scales. |
Preserves angles. |