Five Frequently Encountered Map Projections
Mercator Projection
The Mercator Projection is formed by imagining a cylinder wrapped
around the earth and tangent at the equator. The point of projection is
from the center of the earth. This is a mathematically derived projection in
which parallels and meridians are projected onto a cylinder tangent to the earth at
the equator. When the cylinder is laid out flat, the meridians appear as vertical
straight lines. Meridians are evenly spaced and true to scale at the equator or at
the selected standard parallel of latitude. Lines of latitude are also straight and
parallel, but they do not fall at their normally projected positions; instead, they
are mathematically spaced to produce the property of conformality or true shape.
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For small areas (e.g. a 1 square) the relationship of scale along meridians and parallels is the same as on
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the globe. Scale changes are slight in the mid latitudes, amounting to only about 3 percent at 30 north or
south from the equator. However, since the meridians do not converge, areas in the higher latitudes are
greatly enlarged when the equator is used as the standard parallel. An outstanding feature of the Mercator
is that all straight lines are loxodromes or rhumb lines. On a sphere, a rhumb line (or loxodrome) is a line
crossing all meridians of longitude at the same angle. Great circle lines are curved except at the equator
and meridians, but can be approximated by a series of straight rhumb lines. Distortion of shapes and areas
increases away from the equator.
Transverse Mercator Projection
The Transverse Mercator Projection is formed by imagining a cylinder
wrapped around the earth and tangent at one of the lines of longitude. The
point of projection is from the center of the earth. This projection is
geometrically equivalent to a cylinder wrapped around the earth and tangent to
it along a meridian with the origin of projection at the center of the earth. The
cylinder is cut lengthwise, opened, and laid flat to produce the map. The
projected longitude lines are nearly straight and evenly spaced near the tangent
meridian but become greatly distorted farther out. With the transverse
Mercator projection, most lines of latitude and longitude are curved lines. The
quadrangles formed by the intersection of these curved parallels and meridians are of different sizes and
shapes, complicating location of points and the measurement of directions. To solve this problem, a
rectangular grid system may be superimposed upon the projection. Such a grid (a series of straight lines
intersecting at right angles furnishes map readers with a system of squares similar to the block system of
most city streets. The dimensions and orientation of different types of grids vary, but these three
properties are common to most grid systems, particularly those adopted by mapping and military agencies:
1. They are true rectangular grids
2. They are superimposed on the geographic projection
3. They permit linear and angular measurement.
Both great circle lines and rhumb lines are curved lines. The scale factor is nearly constant throughout the
map. Distortion of shapes and areas increases away from the meridian of true scale although near the
meridian of true scale, the projection is nearly conformal.
From Avery, T. E. 1977. Interpretation of Aerial Photographs. Burgess Publishing Company. 3 rd Edition. 392 pp.
Polar Gnomonic Projection
The Polar Gnomonic Projection is formed by imagining a flat plane tangent
to the earth only at one of the poles. The point of projection is from the
center of the earth. The Polar Gnomonic projection is tangent to the earth’s
surface at either the north or south pole. Projections of parallels and
meridians originate from the center of the earth resulting in concentric,
unequally spaced circles for parallels of latitude and straight lines radiating
from the point of tangency for lines of longitude. Because of the source of
the projection, only the polar regions can be mapped. Theoretically, any line
of latitude except the equator could be shown with a large enough map sheet.
In reality, much smaller polar regions usually define the extent of this
projection. Because great circles are shown as straight lines on this projection, it is frequently used for
great circle navigation. Rhumb lines are approximated by straight lines. The scale factor for this
projection is everywhere variable, and distortion of shapes and areas increases away from the pole.
Lambert Conformal Conic
The Lambert Conformal Conic projection is formed by imagining a cone
wrapped around the earth and secant at two lines of latitude, both on the same
side of the equator. The point of projection is from the center of the earth.
This projection is formed by imagining a cone wrapped around the earth and
secant at two lines of latitude, both on the same side of the equator. The point
of projection is from the center of the earth. This projection, developed by a
German mathematician, is derived by the projection of lines from the center
of the globe onto a simple cone. The cone intersects the earth along two
standard parallels of latitude, both of which are on the same side of the
equator. All meridians are converging straight lines that meet at a common
point beyond the limits of the map. Parallels are concentric circles whose center is at the intersection point
of the meridians. Parallels and meridians cross at right angles, an essential of conformality. To minimize
and distribute scale errors, the two standard parallels are chosen to enclose two-thirds of the north-south
map area. Between these parallels, the scale factor will be less than 1. Beyond them, it will be greater
than 1. However, maximum scale errors rarely exceed 1 percent. Area exaggeration between and near the
standard parallels is relatively slight; thus the projection provides good directional and shape relationships
for areas having their long axes running in the east-west belt. The Lambert conformal conic is the most
commonly used projection for sectional aeronautical charts in the United States.
Great Circle routes are approximated by straight lines while rhumb lines are curved. Scale factor is nearly
constant with the constraints described above. There is very little distortion of shapes and areas with this
projection.
Polyconic Projection
Because of its suitability for large-scale maps of relatively small areas, the
polyconic projection is ordinarily of great interest to photo interpreters. It is
derived by projecting lines from the center of the earth onto a series of
cones, each of which is tangent to a parallel of latitude. The central
meridian of the area to be mapped is a straight line along which the linear
scale is correct. Parallels are represented by arcs of circles that are not
concentric, but the centers of which all lie on the extension of the central
meridian. Distances between parallels along the central meridian are
proportional to true distances on the earth’s surface. Spacing between
meridians are similarly proportioned. The projection is neither conformal
nor equivalent, but for small areas, both qualities are closely approximated.
From Avery, T. E. 1977. Interpretation of Aerial Photographs. Burgess Publishing Company. 3 rd Edition. 392 pp.