Air Fronts: FM 21-26, Advanced Map and Aerial Photograph Reading - Appendix.

APPENDIX: PROJECTIONS

1. GENERAL. a. The geographic system of parallels and meridians can be easily drawn on a globe, but the surface of the globe cannot be stripped and flattened into a map without distortion. A perfect map representation, therefore, is impossible although there are many ways of getting approximate representations on a flat sheet. The simplest of these is to envelop the globe with a cylinder or cone or to lay a tangent plane against it, and to project upon the cylinder, cone, or plane a part of the geographic coordinate system of the globe. The cylinder or cone is then cut open and laid out flat. The system of parallels and meridians on the flattened paper is then the framework, or projection, upon which the map is constructed. A projection, then, is any orderly system of parallels and meridians on which a map is drawn.

b. Many kinds of projections have been devised. Some are particularly good for one purpose and some for another; no one projection is best suited for all shaped areas. Military maps of the United States are based on a series of seven polyconic projections; each one being 9° in width. This system has been extended to cover the earth between latitudes 72° N to 72° S and is known as the World Polyconic. It is used for all those areas not covered by the British grid system.

c. The British employ three systems of grid projection: Lambert Conical Orthomorphic, Transverse Mercator, and the Cassini projections. The type used depends upon the shape of the area to be mapped. Although British grids are based on these three map projections, practically all quadrangle projections for large-scale operational maps are plotted from polyconic tables. Ease of construction and existing tables dictate this practice. This is possible, since for small areas, differences between the polyconic projection and any of the other grid projections is unplottable. The grid of the area is then superimposed on the quadrangle.

d. Following are brief explanations of these projections. For more detailed information see TM 5-230 or any textbook on cartography.

2. MERCATOR PROJECTION. a. This is a cylindrical projection in which parallels and meridians are projected onto a cylinder tangent to the earth at the equator (fig. 84). When the cylinder is laid out flat the meridians appear as vertical straight lines, evenly spaced, and true to scale on the equator (fig. 85), but true scale may be established at any latitude. The parallels are horizontal straight lines spaced so that for and small area the relation of scale along the meridians and along the parallels is the same as on the globe. For example, at latitude 60° the parallels are twice as far apart as at the equator. Therefore, since the meridians on the map are the same distance from each other at every latitude, the scale of the map is doubly exaggerated at 60°. At 80° the exaggeration is sixfold. It is obvious that the poles cannot be shown in this projection, because the expansion would be infinite. Therefore, maps on Mercator projections seldom are extended much beyond 80° of latitude.

b. The advantages of the Mercator projection are ease of plotting or reading geographic coordinates because the parallels and meridians form a rectangular grid; and, ease of plotting and reading navigation courses of-ships or aircraft. A compass course between

Figure 84. Cylindrical projection explains Mercator projection.

any two points (such as Capetown and Bombay in fig. 85) can be shown by a straight line connecting them.

Thus, the path of a ship or plane following a constant

Figure 85. Mercator projection.

compass bearing appears as a straight line. Because the Mercator projection is used in instrumental navigation of ships and planes it is the standard projection for hydrographic charts (U. S. Navy), Navy air-navigation charts, and Army long-distance air-navigation charts of small scale.

c. One disadvantage of the Mercator projection is the increasing exaggeration toward the poles. On a Mercator map Greenland shows larger than South America though, in reality, South America is nine times larger than Greenland (fig. 86). Small-scale Mercator maps have the additional disadvantage that because of polar distortion usual type scales cannot be used to measure distance. However, this limitation does not apply to large-scale maps of small areas. It is important to know these characteristics to make proper use of Mercator maps and to guard against their false appearance.

3. TRANSVERSE MERCATOR PROJECTION. This projection is made on a cylinder tangent to a meridian. When laid out flat, the control meridian is a straight line; all other meridians and all parallels are curved lines similar in appearance to those of the polyconic projection described in paragraph 4. It is used for many British military maps of land areas, divided into belts that are long in the north-south direction and narrow in the east-west direction. Distortion in a grid on a map falling in a transverse Mercator Belt is a minimum because of the limited east-west area covered by the grid system.

4. POLYCONIC PROJECTION. a. The polyconic projection is used for U. S. military maps. The central meridian of the area to be mapped is represented by a

Figure 86. Example of distortion in Mercator projection.

Figure 87. Development of polyconic projection.

straight line, and the parallels are represented by arcs of circles that are not concentric but the centers of which all lie in the extension of the central meridian (fig. 87). The distances between the parallels along the central meridian are proportional to the true distances between the parallels of the earth. The radius of each parallel is determined by an element of the cone tangent to the earth along the given parallel. Distances between meridians are laid off on the parallels proportional to the true distances between meridians. Smooth curves drawn through the points thus determined give the respective meridians. Figure 87 shows the nature of the exaggeration introduced by this method of projection. The north-south distortion increases rapidly on polyconic maps of areas with large east-west dimension. Because of this, it is customary to limit the width of projection and to use the central meridian of the area to  be mapped as the central meridian of the projection.

b. The characteristics of the polyconic projection are true distance along its parallels of latitude, true distance along its central meridian, and exaggerated distance along all other longitude lines, with the greatest exaggeration at the east and west edges. Within a projection the width of the United States the distortion along the Pacific Coast would be around 7 percent in a north-south direction. The width of projection used for U. S. military maps is limited to 9° of longitude, and the maximum scale error in this width is only about one-fifth of 1 percent and therefore is negligible.

5. LAMBERT CONICAL ORTHOMORPHIC PROJECTION. a. The Lambert conical orthomorphic projection (Lambert conformal conic) employs a simple cone tangent to the earth along a single parallel or intersecting the earth at two parallels known as the standard parallels for the area to be mapped (fig. 88). All meridians are converging straight lines that meet in a common point beyond the limits of the map. All parallels are concentric circles whose center is at the point of intersection of the meridians. Parallels and meridians intersect at right angles, and the angles formed by any two lines on the earth's surface are correctly represented on this projection.

b. To distribute scale error when two standard parallels are used, the standard parallels are chosen at one-sixth and five-sixths of the length of the central meridian to be represented. Between these parallels the scale will be too small, and beyond them too large. On military rnaps maximum scale error ordinarily does not exceed one-half of 1 percent.

Figure 88. Lambert conformal conic projection.

c. This projection is specially suited for maps having a predominating east-west dimension. It was widely used in World War I and is used currently for many British maps. Because of its correct azimuth, it is also used for the Sectional Airway Maps of the United States.

6. CASSINI PROJECTION. On the Cassini projection the central meridian is a straight line. All other meridians and all parallels are curved lines similar in appearance to those on a polyconic projection. The Cassini projection is the basis of important maps of the United Kingdom and France. Its principal defect is that the north-south scale is exaggerated on each side of the central meridian. Beyond 220 miles from the central meridian this exaggeration is excessive for military purposes.

* U.S. GOVERNMENT PRINTING OFFICE: 1945--621814