UTM Projection - Universal Transverse Mercator

The 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:

  • the surface of projection is a transverse cylinder and the projection is conformal;
  • the central meridian of the region of interest, the equator and the meridians placed 90o or more above the central meridian are represented by straight lines;
  • the other meridians and the parallels are  complex curves;
  • the central meridian can be represented in true size;
  • the scale increases with the distance in relation to the central meridian. At 90o from it the scale becomes infinite;
  • The Earth is divided in 60 zones of 6o longitude. The transverse cylinder adopted as the surface of projection can take up to 60 different positions, since its axis always remains perpendicular to the central meridian of each zone;
  • a scale reduction factor equal to 0.9996 is applied to the central meridian of each zone in order to minimize the variations in scale within a zone. As a consequence, there are two approximately straight lines, one to the East and the other to the West, distant about 1o 37' from the central meridian, that are represented in true size;
  • despite the "universal" characteristics of the projection, it must be emphasized that the reference ellipsoid varies as a function of the region on the surface of the Earth.


OBSERVATION (for the generation of maps): SPRING allows the user to define, for the UTM projection, the orientation of the data relative to the geographic North or to the north of the quadricule. The meridians (geographic north) coincide with the vertical lines of the quadricules (north of the quadricule) of the UTM projection only on the central meridians. With the increase in longitude and latitude an increase in the angle between meridians and the vertical lines on the quadricule is observed (convergence of meridians).

Cartographic Concepts


Datum

To 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.
There is also the concept of a vertical datum, that refers to the elevations measured on the surface of the Earth.

The ancient maps of Brazil used the planimetric datum Corrego Alegre. More recently, the SAD-69 planimetric datum has been used as the reference. Nowadays, with the wide application of GPS technology, it is becoming increasingly more common the use of the planimetric global datum WGS-84.

  • Corrego Alegre

Latitude: 19o 45' 41.34" S
Longitude: 48o 06' 07.08" W

  • SAD-69

Latitude: 19o 45' 41.6527" S
Longitude: 48o 06' 04.0639" W
Azimuth of Uberaba: 271o 30' 04.05"



Cartographic Concepts


Ellipsoid Models

For practical applications, we model the Earth with a ellipsoid of revolution. An ellipsoid of revolution is a solid generated by the rotation of an ellipse around the axis of the poles (minor axis).

Geodetic studies present slightly different values for the elements of this ellipsoid, as measured on  various points of the Earth. Thus, each region should adopt the best ellipsoid.

In Brazil, we adopted the Hayford ellipsoid, whose dimensions were considered the most convenient for South America. Currently, though, the International Astronomical Union ellipsoid has been used ever more frequently. This ellipsoid was adopted in 1967 by the International Association of Geodesy and Geophysics as the standard and called it the Geodetic Reference System 1967 (GRS-67).

The Hayford ellipsoid is used by the datum Corrego Alegre while the 1967 reference ellipsoid, the International Astronomical Association's one, is used by the SAD-69 datum.


The following table illustrates the parameters of both ellipsoids.

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

 

Cartographic Concepts


Standard Parallel or Reduced Latitude

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.


Cartographic Concepts


Longitude and Latitude of Origin

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.

  • In the UTM projection the longitude of origin corresponds to the central meridian of a zone (at each 6o we have a new zone), that is, to the central meridian of a millionth map.

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


Scale

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.



Cartographic Concepts


Illustrative Table

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.
Substitutes with advantages all the others equal-area conical.

Bipolar

Conic
Conformal

Designed for low-error mapping of the North and South America.

Preserves angles.
Is an adaptation of the Lambert Conical.

Cylindrical Equidistant

Cylindrical Equidistant

World Maps.
Maps in small scales.
Computational works.

Distorts areas.
Distorts angles.

Gauss

Cylindrical
Conformal

Old topographic maps.
Basic Mapping in medium and big scales.

Distorts areas (but the distortion does not exceed 0,5%).
Preserves angles.
Similar to the UTM with a difference of 3o longitude between the central meridians.

Polar
Stereographic

Plane Conformal

Mapping of polar regions.
Mapping of the Moon, Mars, and Mercury.

Preserves angles.

Presents scale distortions.

Lambert

Conic Conformal

Geographic maps and maps in general.
Military maps.
Aeronautical maps of the world.

Preserves angles.

Lambert Million

Conic Conformal

Millionth maps.

Preserves angles.

Mercator

Cylindrical Conformal

Nautical charts.
Geological e magnetic maps.
World Maps.

Preserves angles.

Miller

Cylindrical 

World Maps.
Small scale maps.

Distorts angles.
Distorts areas.

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.
Topographic maps.

Preserves angles.
Distorts areas (but distortion does not exceed 0,5%).



Cartographic Concepts