






Article 

Map Projections: From Spherical Earth to Flat Map 

What
is a Map Projection?
Classes
of Map Projections and Their Use
Commonly
Used Map Projection Terms
Related
Links


What is a Map Projection? 

A
map projection is a way to represent the curved surface of the Earth
on the flat surface of a map. A good globe can provide the most
accurate representation of the Earth. However, a globe isn't
practical for many of the functions for which we require maps. Map
projections allow us to represent some or all of the Earth's
surface, at a wide variety of scales, on a flat, easily transportable
surface, such as a sheet of paper. Map projections also apply to
digital map data, which can be presented on a computer screen.
There are hundreds of different map projections. The process of
transferring information from the Earth to a map causes every projection
to distort at least one aspect of the real world – either
shape, area, distance, or direction.
Each map projection has advantages and disadvantages; the appropriate
projection for a map depends on the scale of the map, and on the
purposes for which it will be used. For example, a projection may
have unacceptable distortions if used to map the entire country,
but may be an excellent choice for a largescale (detailed) map
of a county. The properties of a map projection may also influence
some of the design features of the map. Some projections are good
for small areas, some are good for mapping areas with a large eastwest
extent, and some are better for mapping areas with a large northsouth
extent.
Some projections have special properties. For example, a Mercator
projection has straight rhumb lines and is
therefore excellent for navigation, because compass courses are
easy to determine.


back
to top 

Classes of Map Projections and Their Use 

There are several ways
to classify the wide variety of map projections. One of the most common
classifications is by distortion characteristics: which properties
of the Earth does the projection maintain? Which does it distort?
Classification based on distortion characteristics
A projection that maintains accurate relative sizes is called an
equal area, or equivalent projection. These projections are used
for maps that show distributions or other phenomena where showing
area accurately is important. Examples are the Lambert Azimuthal
EqualArea projection and the Albers EqualArea
Conic projection.
The National Atlas of the United States uses a Lambert Azimuthal
EqualArea projection to display information in the online Map
Maker. In addition to its equalarea properties, this projection
also shows true directions from the center point of the map. This
means that the projection works well for mapping areas that extend
equally from the center point, such as North America.
Mercator projection
A projection that maintains angular relationships and accurate
shapes over small areas is called a conformal
projection. These projections are used where angular relationships
are important, such as for navigational or meteorological charts.
Examples are the Mercator projection and the Lambert Conformal Conic
projection. The U.S. Geological Survey uses a conformal projection
for many of its topographic maps.
A projection that maintains accurate distances from the center
of the projection or along given lines is called an equidistant
projection. These projections are used for radio and seismic mapping,
and for navigation. Examples are the Equidistant Conic projection
and the Equirectangular projection. The Azimuthal Equidistant projection
is the projection used for the emblem of the United Nations.
A projection that maintains accurate directions (and therefore
angular relationships) from a given central point is called an azimuthal
or zenithal projection. These projections
are used for aeronautical charts and other maps where directional
relationships are important. Examples are the Gnomonic projection
and the Lambert Azimuthal EqualArea projection.
A map projection may combine several of these characteristics,
or may be a compromise that distorts all the properties of shape,
area, distance, and direction, within some acceptable limit. Examples
of compromise projections are the Winkel Tripel projection and the
Robinson projection, often used for world maps.


Classification
based on developable surface
Map projections can also be classified based on the shape of the developable
surface to which the Earth's surface is projected. A developable
surface is a simple geometric form capable of being flattened without
stretching, such as a cylinder, cone, or plane.
Cylindrical projection
For example, a cylindrical projection
projects information from the spherical Earth to a cylinder. The
cylinder may be either tangent to the Earth along a selected line,
or may be secant (intersect the Earth) along two lines. Imagine
that once the Earth's surface is projected, the cylinder is unwrapped
to form a flat surface. The lines where the cylinder is tangent or
secant are the places with the least distortion.
A
Mercator projection is created using a cylinder tangent at the equator.
A Transverse Mercator projection is created using a cylinder that
is tangent at a selected meridian. An Oblique Mercator projection
is created using a cylinder that is tangent along a great circle
other than the equator or a meridian.


Polyconic projection
A conic projection projects information from
the spherical Earth to a cone that is either tangent to the Earth
at a single parallel, or that is secant at two standard parallels.
Once the projection is complete, the cone is unwrapped to form a
flat surface. The lines where the cone is tangent or secant are
the places with the least distortion. A polyconic projection uses
a series of cones to reduce distortion.
A planar projection projects information
to a plane. The plane may be either tangent or secant.


back
to top 

Commonly Used Map Projection Terms 

Azimuth—The
angle, measured in degrees, between a base line radiating from a center
point and another line radiating from the same point. Normally, the
base line points North, and degrees are measured clockwise from the
base line.
Azimuthal—A map
projection in which the direction from a given central point to
any other point is shown correctly. Also called a zenithal projection.
Aspect—The placement of a projection system
relative to the Earth's axis. A polar aspect is tangent at
the pole, an equatorial aspect is tangent at the Equator, and an
oblique aspect is tangent anywhere else. (The word "aspect"
has replaced the word "case" in the modern cartographic
literature.)
Cartesian coordinate system —A coordinate
system in which a point's location is described by its distances
from a set of perpendicular lines that intersect at an origin, either
two lines in a plane or three in space.
Conformal—A map
projection in which the angles at each point are preserved. This
means that the shapes of small areas are maintained accurately.
The size of most areas, however, is distorted.
Conic—A map projection
where the Earth's surface is projected onto a tangent or secant
cone, which is then cut from apex to base and laid flat.




Cylindrical—A
map projection where the Earth's surface is projected onto a tangent
or secant cylinder, which is then cut lengthwise and laid flat.
Datum—A reference for position on the surface
of the Earth. In surveying, a datum is a reference system for computing
or correlating the results of surveys. There are two principal
types of datums: vertical and horizontal. A vertical datum is a
level surface to which heights are referred. In the United States,
the generally adopted vertical datum for leveling operations is
the National Geodetic Vertical Datum of 1929. The horizontal datum
is used as a reference for position. The North American Datum of
1983 is based on the Geodetic Reference System 1980 (GRS80) spheroid;
it is an Earthcentered datum having no initial point or initial
direction. This is the horizontal datum used for National Atlas
map layers.
Developable surface—A developable surface
is a simple geometric form capable of being flattened without stretching.
Map projections can be grouped by the developable surface they
use: cylinder, cone, or plane.
Ellipsoid—A mathematical figure that approximates
the shape of the Earth in form and size, and which is used as a
reference surface for geodetic surveys. Used interchangeably with
Spheriod.
Equalarea—A map
projection where every part, as well as the whole, has the same
area as the corresponding part on the Earth, at the same reduced
scale.
Equator—The line which encircles the Earth
at an equal distance from the North and South Poles.
Equidistant—A
map projection that shows true distances from the center of the
projection or along a special set of lines. For example, an Azimuthal
Equidistant map centered at Washington, DC, shows the correct distance
between Washington, DC, and any other point on the projection.
It shows the correct distance between Washington, DC, and San Diego
and between Washington, DC, and Seattle, but it does not show the
correct distance between San Diego and Seattle.
Graticule—A network of lines representing
a selection of the Earth's parallels and meridians.
Great circle—A circle formed on the surface
of a sphere by a plane that passes through the center of the sphere.
The Equator, each meridian, and each other full circumference of
the Earth forms a great circle. The arc of a great circle shows
the shortest distance between points on the surface of the Earth.
Grid—Two sets of parallel lines intersecting
at right angles, forming a rectangular Cartesian coordinate system
superimposed on a map projection. Sometimes the term "grid" is
used loosely to mean the projection system itself rather than the
rectangular system superimposed on the projection.
Latitude—Angular distance, in degrees,
minutes, and seconds measured from the center of the Earth, of
a point north or south of the Equator. Latitude may also be measured
in decimal degrees.
Longitude—Angular distance, in degrees,
minutes, and seconds measured from the center of the Earth, of
a point east or west of the Prime Meridian. Longitude may also
be measured in decimal degrees.
Meridian—A great circle on the surface
of the Earth, passing through the geographical poles and some third
point on the Earth's surface. All points on a given meridian have
the same longitude.
Parallel—A circle or approximation of a
circle on the surface of the Earth, parallel to the Equator and
connecting points of equal latitude.
Planar—A map projection
resulting from the conceptual projection of the Earth onto a tangent
or secant plane. Usually, a planar projection is the same as an
azimuthal projection.




Prime Meridian—The meridian of longitude
0 degrees, used as the origin for the measurement of longitude.
The meridian of Greenwich, England, is the internationally accepted
prime meridian in most cases.
Projection parameters—A series of values
that define a particular projection, and that tell how the projection
is related to the Earth. Projection parameters may indicate the
point of tangency, or the lines where a secant surface intersects
the Earth. They also define the spheriod used to create the projection,
and any other information necessary to identify the projection.
Rhumb line—A rhumb
line is a line on the surface of the Earth cutting all meridians
at the same angle. A rhumb line shows true direction. Parallels
and meridians, which also maintain constant true directions, may
be considered special cases of the rhumb line. A rhumb line is
a straight line on a Mercator projection. A straight rhumb line
does not show the shortest distance between points unless the points
are on the Equator or on the same meridian. A navigator can proceed
between any two points along a rhumb line by maintaining a constant
bearing, or compass direction.
Scale—The relationship between a distance
on a map, chart, or photograph, and the corresponding distance
on the Earth. Scale is usually given as a fraction or ratio: 1:2,000,000,
or 1/2,000,000.
Secant—Cutting the sphere or spheroid along
a line or lines. A secant cone or cylinder intersects the sphere
or spheroid along two separate lines; these lines are parallels
of latitude if the axes of the geometric figures coincide. A secant
plane intersects the sphere or spheroid along a line that is a
parallel of latitude if the plane is at right angles to the axis.
Spherical – Approximating the shape of
a sphere.
Spheroid—A mathematical figure that approximates
the shape of the Earth in form and size, and which is used as a
reference surface for geodetic surveys. Used interchangeably with
Ellipsoid.
Tangent—Touching at a single point or along
a single line. A tangent cone or cylinder touches the sphere or
spheroid along a single line. This line is a parallel of latitude
if the axes of the geometric figures coincide.
Zenithal—A map projection
in which the direction from a given central point to any other
point is shown correctly. Also called an azimuthal projection.


back
to top 

Related Links 





References
Bugayevskiy, Lev M. and John P. Snyder; Map Projections –
A Reference Manual; Taylor and Francis Inc., Bristol, PA; 1995
Snyder, John P.; Map Projections – A Working Manual; U.S.
Geological Survey Professional Paper 1395; Washington, DC; 1987
Snyder, John P., and Philip M. Voxland; An Album of Map Projections;
U.S. Geological Survey Professional Paper 1453; Denver, CO; 1989
Thompson, Morris M.; Maps for America, Third Edition; U.S. Geological
Survey; Reston, VA; 1988
USGS,
Map Projections , January 13, 2003
Map
projections as essential tools of physical oceanography. , January
13, 2003
The
Atlas of Canada, Learning Resources, Map
Making, Map Projections.
February 11, 2003


back
to top 
