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are the azimuths of lines true. At this point, the projection is said to be azimuthal. Gnomonic projections
are classified according to the point of tangency of the plane of projection. A gnomonic projection is
AFPAM11-216 1 MARCH 2001 39
polar gnomonic when the point of tangency is one of the poles, equatorial gnomonic when the point of
tangency is at the equator and any selected meridian (Figure 1.21).
Figure 1.21. Polar Gnomonic and Stereographic Projections.
1.24.2. Stereographic Projection. The stereographic projection is a perspective conformal projection of
the sphere.
1.24.2.1. The term oblique stereographic is applied to any stereographic projection where the center of
the projection is positioned at any point other than the geographic poles or the equator.
1.24.2.2. If the center is coincident with one of the poles of the reference surface, the projection is called
polar stereographic. The illustration in Figure 1.21 shows both gnomonic and stereographic projections.
1.24.2.3. If the center lies on the equator, the primitive circle is a meridian, which gives the name
meridian stereographic or equatorial stereographic.
1.25. Cylindrical Projections. The only cylindrical projection used for navigation is the Mercator,
named after its originator, Gerhard Mercator (Kramer), who first devised this type of chart in the year
1569. The Mercator is the only projection ever constructed that is conformal and at the same time
displays the rhumb line as a straight line. It is used for navigation, for nearly all atlases (a word coined
by Mercator), and for many wall maps.
1.25.1. Imagine a cylinder tangent to the equator, with the source of projection at the center of the earth.
It would appear much like the illustration in Figure 1.22, with the meridians being straight lines and the
parallels being unequally spaced circles around the cylinder. It is obvious from the illustration that those
parts of the terrestrial surface close to the poles could not be projected unless the cylinder was
tremendously long, and the poles could not be projected at all.
40 AFPAM11-216 1 MARCH 2001
Figure 1.22. Cylindrical Projection.
1.25.2. On the earth, the parallels of latitude are perpendicular to the meridians, forming circles of
progressively smaller diameters as the latitude increases. On the cylinder, the parallels of latitude are
shown perpendicular to the projected meridians but, since the diameter of a cylinder is the same at any
point along the longitudinal axis, the projected parallels are all the same length. If the cylinder is cut
along a vertical line (a meridian) and spread flat, the meridians appear as equal-spaced, vertical lines,
and the parallels as horizontal lines, with distance between the horizontal lines increasing with distance
away from the false (arbitrary) meridian.
1.25.3. The cylinder may be tangent at some great circle other than the equator, forming other types of
cylindrical projections. If the cylinder is tangent at some meridian, it is a transverse cylindrical
projection; if it is tangent at any point other than the equator or a meridian, it is called an oblique
cylindrical projection. The patterns of latitude and longitude appear quite different on these projections
because the line of tangency and the equator no longer coincide.
AFPAM11-216 1 MARCH 2001 41
1.25.4. The Mercator projection is a conformal, nonperspective projection; it is constructed by means of
a mathematical transformation and cannot be obtained directly by graphical means. The distinguishing
feature of the Mercator projection among cylindrical projections is: At any latitude the ratio of expansion
of both meridians and parallels is the same, thus, preserving the relationship existing on the earth. This
expansion is equal to the secant of the latitude, with a small correction for the ellipticity of the earth.
Since expansion is the same in all directions and since all directions and all angles are correctly
represented, the projection is conformal. Rhumb lines appear as straight lines and their directions can be
measured directly on the chart. Distance can also be measured directly, but not by a single distance scale
on the entire chart, unless the spread of latitude is small. Great circles appear as curved lines, concave to
the equator or convex to the nearest pole. The shapes of small areas are very nearly correct, but are of
increased size unless they are near the equator as shown in Figure 1.23. The Mercator projection has the
following disadvantages:
1.25.4.1. Measuring large distances accurately is difficult.
1.25.4.2. Must apply conversion angle to great circle bearing before plotting.
1.25.4.3. Is useless above 80o N or below 80o S since the poles cannot be shown.
Figure 1.23. Mercator Is Conformal but Not Equal Area.
　
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