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Sources of Error in Plane-Table Work
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Transverse Mercator Projection

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MAP PROJECTION

Now let’s discuss map and chart projection. This discussion includes the characteristics and development of various types of projections. A paper cylinder (without ends) and a paper cone can be cut along the side and flattened out without distortion. For this reason, the two most common basic projection methods are the Mercator, in which the earth’s surface is projected onto a cylinder, and the conic, in which the surface is projected onto a cone. A third method is the gnomonic method, in which the earth’s surface is projected onto a plane placed tangent to a particular point. For a polar gnomonic chart, this point is one of the earth’s geographical poles.

MERCATOR PROJECTION

To grasp the concept of Mercator projection, imagine the earth to be a glass sphere with a strong light at the center. Imagine, also, that the geographical meridians and parallels are inscribed as lines on the sphere at a given interval (for example, every 15 degrees). Now imagine a paper cylinder placed around the sphere, tangent to the equator, as shown in figure 9-11. The shadow images of the meridians will appear on the paper as equally spaced, parallel, vertical lines. The shadow images of the parallels will likewise appear as straight lines running perpendicular to the shadow images of the meridians. The parallels are not actually equally spaced, however; instead, the distance between adjacent parallels will progressively increase as latitude (distance north or south of the equator, the line of tangency) increases.

Figure 9-11l.—Mercator projection.

You can see that there are two elements of distortion here, each of which progressively increases with latitude. One is the fact that the meridians, which on the earth itself converge at each of the poles, are parallel (and therefore equidistant) for their entire length on the cylinder. The other is the fact that the parallels, which are actually equidistant on the sphere itself, become progressively farther apart as latitude increases.

These two elements produce the familiar distortion that is characteristic of a Mercator map of the world. On such a map the island of Greenland, which has an area of only about 46,740 square miles, is considerably larger in outline than the continental United States, which has an area (excluding Alaska) of about 2,973,776 square miles.

Figure 9-12 shows the meridians and parallels at 15-degree intervals of the earth’s surface on a Merca-tor projection. Note that the parallels extend only to 80 degrees north and south. Because the cylinder has no ends, Mercator projection of regions in latitudes higher than about 80 degrees is impossible. Note, too, that although the distance along a meridian between (for example) 15°N and 30°N and between 60°N and 75°N is the same on the ground, these distances are much different on a Mercator projection. Still another characteristic to note is the fact that a meridian is perpendicular to all parallels it intersects and that all the meridians are parallel to each other.

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