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1.25.5. The transverse or inverse Mercator is a conformal map designed for areas not covered by the
equatorial Mercator. With the transverse Mercator, the property of straight meridians and parallels is
lost, and the rhumb line is no longer represented by a straight line. The parallels and meridians become
complex curves and, with geographic reference, the transverse Mercator is difficult to use as a plotting
42 AFPAM11-216 1 MARCH 2001
chart. The transverse Mercator, though often considered analogous to a projection onto a cylinder, is in
reality a nonperspective projection, constructed mathematically. This analogy (illustrated in Figure 1.24),
however, does permit the reader to visualize that the transverse Mercator will show scale correctly along
the central meridian which forms the great circle of tangency. In effect, the cylinder has been turned 90o
from its position for the ordinary Mercator, and a meridian, called the central meridian, becomes the
tangential great circle. One series of NIMA charts using this type of projection places the cylinder
tangent to the 90o E–90o W longitude.
Figure 1.24. Transverse Cylindrical Projection— Cylinder Tangent at the Poles.
1.25.5.1. These projections use a fictitious graticule similar to, but offset from, the familiar network of
meridians and parallels. The tangent great circle is the fictitious equator. Ninety degrees from it are two
fictitious poles. A group of great circles through these poles and perpendicular to the tangent constitutes
the fictitious meridians, while a series of lines parallel to the plane of the tangent great circle forms the
fictitious parallels.
1.25.5.2. On these projections, the fictitious graticule appears as the geographical one ordinarily
appearing on the equatorial Mercator. That is, the fictitious meridians and parallels are straight lines
perpendicular to each other. The actual meridians and parallels appear as curved lines, except the line of
tangency. Geographical coordinates are usually expressed in terms of the conventional graticule. A
straight line on the transverse Mercator projection makes the same angle with all fictitious meridians, but
not with the terrestrial meridians. It is, therefore, a fictitious rhumb line.
1.25.5.3. The appearance of a transverse Mercator using the 90o E–90o W meridian as a reference or
fictitious equator is shown in Figure 1.24. The dotted lines are the lines of the fictitious projection. The
N–S meridian through the center is the fictitious equator, and all other original meridians are now curves
concave on the N–S meridian with the original parallels now being curves concave to the nearer pole.To
straighten the meridians, use the graph in Figure 1.25 to extract a correction factor that will
mathematically straighten the longitudes.
AFPAM11-216 1 MARCH 2001 43
Figure 1.25. Transverse Mercator Convergence Graph.
44 AFPAM11-216 1 MARCH 2001
1.26. Conic Projections. There are two classes of conic projections. The first is a simple conic
projection constructed by placing the apex of the cone over some part of the earth (usually the pole) with
the cone tangent to a parallel called the standard parallel and projecting the graticule of the reduced earth
onto the cone as shown in Figure 1.26. The chart is obtained by cutting the cone along some meridian
and unrolling it to form a flat surface. Notice, in Figure 1.27, the characteristic gap appears when the
cone is unrolled. The second is a secant cone, cutting through the earth and actually contacting the
surface at two standard parallels as shown in Figure 1.28.
Figure 1.26. Simple Conic Projection.
Figure 1.27. Simple Conic Projection of Northern Hemisphere.
AFPAM11-216 1 MARCH 2001 45
Figure 1.28. Conic Projection Using Secant Cone.
1.26.1. Lambert Conformal (Secant Cone). The Lambert conformal conic projection is of the conical
type in which the meridians are straight lines that meet at a common point beyond the limits of the chart
and parallels are concentric circles, the center of each being the point of intersection of the meridians.
Meridians and parallels intersect at right angles. Angles formed by any two lines or curves on the earth's
surface are correctly represented. The projection may be developed by either the graphic or mathematical
method. It employs a secant cone intersecting the spheroid at two parallels of latitude, called the standard
parallels, of the area to be represented. The standard parallels are represented at exact scale. Between
these parallels, the scale factor is less than unity and, beyond them, greater than unity. For equal
distribution of scale error (within and beyond the standard parallels), the standard parallels are selected
at one-sixth and five-sixths of the total length of the segment of the central meridian represented. The
　
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