Download Notes: Map Projections and Great Circles

Map Projections
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 large-scale (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 east-west extent, and some are better for
mapping areas with a large north-south 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.
Geradus Mercator invented his famous projection in 1569 as an aid to navigators. On his map,
lines of latitude and longitude intersect at right angles and thus the direction of travel - the rhumb
line - is consistent. The distortion of the Mercator Map increases as you move north and south
from the equator. On Mercator's map Antarctica appears to be a huge continent that wraps
around the earth and Greenland appears to be just as large as South America although Greenland
is merely one-eighth the size of South America. Mercator never intended his map to be used for
purposes other than navigation although it became one of the most popular world map
projections.
Mercator Projection
Map Projections – continued
During the 20th century, the National Geographic Society, various atlases, and classroom wall
cartographers switched to the rounded Robinson Projection. The Robinson Projection is a
projection that purposely makes various aspects of the map slightly distorted to produce an
attractive world map. Indeed, in 1989, seven North American professional geographic
organizations (including the American Cartographic Association, National Council for Geographic
Education, Association of American Geographers, and the National Geographic Society) adopted a
resolution that called for a ban on all rectangular coordinate maps due to their distortion of the
planet.
Robinson Projection
The Lambert azimuthal equal-area projection is a particular mapping from a sphere to a disk
(that is, a region bounded by a circle). It accurately represents area in all regions of the sphere,
but it does not accurately represent angles. It is named for the Swiss mathematician Johann
Heinrich Lambert, who announced it in 1772.
Lambert's Azimuthal Equal-area Projection
Great Circles
Definition: great circle n. 1. A circle described by the intersection of the surface of a sphere with a
plane passing through the center of the sphere. 2. A segment of such a circle representing the
shortest distance between two terrestrial points.
A great circle is the largest possible circle that can be drawn around a sphere. All spheres have
great circles. If you cut a sphere at one of its great circles, you'd cut it exactly in half. A great
circle has the same circumference, or outer boundary, and the same center point as its sphere.
The geometry of spheres is useful for mapping the Earth and other planets. The Earth is not a
perfect sphere, but it maintains the general shape. All the meridians on Earth are great circles.
Meridians, including the prime meridian, are the north-south lines we use to help describe exactly
where we are on the Earth. All these lines of longitude meet at the poles, cutting the Earth neatly
in half. The Equator is another of the Earth's great circles. If you were to cut into the Earth right
on its Equator, you'd have two equal halves: the Northern and Southern Hemispheres. The
Equator is the only east-west line that is a great circle. All other parallels (lines of latitude) get
smaller as you get near the poles. Great circles can be found on spheres as big as planets and as
small as oranges.
The shortest path between two points on the surface of a sphere is always a segment of a great
circle. Plotting great circles comes in very handy for airplane pilots trying to fly the shortest
distance between two points. For example, if you flew from Atlanta, Georgia, to Athens, Greece,
you could fly roughly along the path of one of Earth's great circles, which would be the shortest
distance between those two points. When planning routes, however, pilots have to take other
factors into account, such as air currents and weather. Great circles are just general paths to
follow.
Examples of Great Circles
Equator
The only parallel of latitude
that is a Great Circle.
Prime Meridian and the International
Date Line, along with ALL other
meridians of longitude are Great Circles.