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Charts and Projections (Part One)

in Maps and Charts

There are several basic terms and ideas relative to charts and projections that the reader should be familiar with before discussing the various projections used in the creation of aeronautical charts.


  1. A map or chart is a small scale representation on a plane of the surface of the earth or some portion of it.
  2. The chart projection forms the basic structure on which a chart is built and determines the fundamental characteristics of the finished chart.
  3. There are many difficulties that must be resolved when representing a portion of the surface of a sphere upon a plane. Two of these are distortion and perspective.
    • Distortion cannot be entirely avoided, but it can be controlled and systematized to some extent in the drawing of a chart. If a chart is drawn for a particular purpose, it can be drawn in such a way as to minimize the type of distortion that is most detrimental to the purpose. Surfaces that can be spread out in a plane without stretching or tearing, such as a cone or cylinder, are called developable surfaces, and those like the sphere or spheroid that cannot be formed into a plane without distortion are called non-developable. [Figure 1-19] The problem of creating a projection lies in developing a method for transferring the meridians and parallels to the chart in a manner that preserves certain desired characteristics as nearly as possible. The methods of projection are either mathematical or perspective.
    • The perspective or geometric projection consists of projecting a coordinate system based on the earth-sphere from a given point directly onto a developable surface. The properties and appearance of the resultant map depends upon two factors: the type of developable surface and the position of the point of projection.
  4. The mathematical projection is derived analytically to provide certain properties or characteristics that cannot be arrived at geometrically. Consider some of the choices available for selecting projections that best accommodate these properties and characteristics.
Figure 1-19. Developable and nondevelopable surfaces.

Figure 1-19. Developable and nondevelopable surfaces.

Choice of Projection

The ideal chart projection would portray the features of the earth in their true relationship to each other; that is, directions would be true and distances would be represented at a constant scale over the entire chart. This would result in equality of area and true shape throughout the chart. Such a relationship can only be represented on a globe. On a flat chart, it is impossible to preserve constant scale and true direction in all directions at all points, nor can both relative size and shape of the geographic features be accurately portrayed throughout the chart. The characteristics most commonly desired in a chart projection are conformality, constant scale, great circles as straight lines, rhumb lines as straight lines, true azimuth, and geographic position easily located.

Conformality

Conformality is very important for air navigation charts. For any projection to be conformal, the scale at any point must be independent of azimuth. This does not imply, however, that the scales at two points at different latitudes are equal. It means the scale at any given point is, for a short distance, equal in all directions. For conformality, the outline of areas on the chart must conform in shape to the feature being portrayed. This condition applies only to small and relatively small areas; large land masses must necessarily reflect any distortion inherent in the projection. Finally, since the meridians and parallels of earth intersect at right angles, the longitude and latitude lines on all conformal projections must exhibit this same perpendicularity. This characteristic facilitates the plotting of points by geographic coordinates.

Constant Scale

The property of constant scale throughout the entire chart is highly desirable, but impossible to obtain as it would require the scale to be the same at all points and in all directions throughout the chart.

Straight Line

The rhumb line and the great circle are the two curves that a navigator might wish to have represented on a map as straight lines. The only projection that shows all rhumb lines as straight lines is the Mercator. The only projection that shows all great circles as straight lines is the gnomonic projection. However, this is not a conformal projection and cannot be used directly for obtaining direction or distance. No conformal chart represents all great circles as straight lines.

True Azimuth

It would be extremely desirable to have a projection that showed directions or azimuths as true throughout the chart. This would be particularly important to the navigator, who must determine from the chart the heading to be flown. There is no chart projection representing true great circle direction along a straight line from all points to all other points.

Coordinates Easy to Locate

The geographic latitudes and longitudes of places should be easily found or plotted on the map when the latitudes and longitudes are known.

Chart Projections

Chart projections may be classified in many ways. In this book, the various projections are divided into three classes according to the type of developable surface to which the projections are related. These classes are azimuthal, cylindrical, and conical.

Azimuthal Projections

An azimuthal, or zenithal projection, is one in which points on the earth are transferred directly to a plane tangent to the earth. According to the positioning of the plane and the point of projection, various geometric projections may be derived. If the origin of the projecting rays (point of projection) is the center of the sphere, a gnomonic projection results. If it is located on the surface of the earth opposite the point of the tangent plane, the projection is a stereographic, and if it is at infinity, an orthographic projection results. Figure 1-20 shows these various points of projection.

Figure 1-20. Azimuthal projections.

Figure 1-20. Azimuthal projections. [click image to enlarge]

 

 

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