Why does distortion occur on a map

See the problem coming? Instead of comparing a big orange to a little orange, we're comparing a big orange to a little wafer. This map also has a scale of ,,, but because the map and the earth are differently shaped, this scale cannot be true for every line on the map. The stated scale of a map is true for certain lines only. Which lines these are depends on the projection and even on particular settings within a projection. We'll come back to this subject in Module 4, Understanding and Controlling Distortion.

Not all of the earth's curves can be represented as straight lines at the same fixed scale. Some lines must be shortened and others lengthened. Expressing map scale There are three common ways to express map scale:. Linear scales Linear scales are lines or bars drawn on a map with real-world distances marked on them. To determine the real-world size of a map feature, you measure it on the map with a ruler or a piece of string.

Then you compare the feature's length on the string to the scale bar. A typical scale bar. Verbal scales Verbal scales are statements of equivalent distances. For example, if a 4. Representative fractions Representative fractions express scale as a fraction or ratio of map distance to ground distance.

Since the scale is a ratio, it doesn't matter what the units are. Small scale and large scale maps It's easy to mix these terms up. Here's one way to keep them straight: on a large-scale map, the earth is large so not very much of it fits on the map. On a small-scale map, the earth is small so all or most of it fits on the map. A map of your town, or your property, is going to be a large-scale map. A continental or world map is a small-scale map. Another way to think of the difference in terms of representative fractions.

The larger the fraction, the larger the map's scale. So a , map is larger scale than a ,, map. Measuring distortion using Tissot's Indicatrix. In the nineteenth century, Nicolas Auguste Tissot developed a method to analyze map projection distortion. An infinitely small circle on the earth's surface will be projected as an infinitely small ellipse on any given map projection.

The resulting ellipse of distortion, or indicatrix , shows the amount and type of distortion at the location of the ellipse. For example, if an indicatrix is elongated from north to south, shape is correspondingly distorted at that location on the map.

The same goes for east—west stretching or oblique stretching. On a conformal map, the indicatrices are all circles, but they vary in size. The Stereographic projection is one of these. Now the straight line is the great circle, and the curved one is the loxodrome. These lines are the same as in the Mercator above, but the projection changes their appearance. When a projection preserves great circle routes as straight lines, we call it an azimuthal projection.

Unfortunately, much like the equidistant projections, it only works for one point at a time. In the Stereographic above, the projection is centered on New York.

Only straight lines coming into or going out of New York will be great circles. If you skim through the example images above, you may notice that, as a general trend, distortions tend to get worse and worse as you get near the edges of the map.

As a general rule, the larger the area your map shows, the worse distortions will be, especially as you move away from the center. What all this means is that we are most worried about distortions when we are doing things like mapping the world, and less when we are mapping smaller areas like cities or states. To solve the problem of world maps having such severe distortions at the edges, people have come up with compromise projections.

These special projections represent trade offs: while most projections have minimal distortion in one area but distort heavily as you move away from that area, compromise projections distort a moderate amount everywhere. The Robinson projection is one example of a compromise projection:. Compromise projections spread the distortion around somewhat evenly. The plus side of this is that no place gets ridiculously distorted.

This is what makes compromise projections good for world maps. Since there are so very many projections, the question becomes: which one should you use?

Each has advantages and disadvantages and is better suited to certain situations. Here are some questions to ask yourself when choosing a projection:. Is there any specific property that you need to preserve?

Remember that some projections will keep areas, forms, distances, or directions free of distortion. Sometimes, the subject your mapping is better served by preserving one of these properties. Here are some examples:. There are plenty of other reasons to preserve each of these properties; the above are simply examples to get you thinking.

Some other considerations:. As we discussed above, each projection has places where distortion is worse, and places where it is not too bad. So-called equal-area projections maintain correct proportions in the sizes of areas on the globe and corresponding areas on the projected grid allowing for differences in scale, of course. Notice that the shapes of the ellipses in the Cylindrical Equal Area projection above Figure 2.

Equal-area projections are preferred for small-scale thematic mapping, especially when map viewers are expected to compare sizes of area features like countries and continents. The distortion ellipses plotted on the conformal projection shown above in Figure 2. The consistent shapes indicate that conformal projections like this Mercator projection of the world preserve the fidelity of angle measurements from the globe to the plane.

In other words, an angle measured by a land surveyor anywhere on the Earth's surface can be plotted on at its corresponding location on a conformal projection without distortion. This useful property accounts for the fact that conformal projections are almost always used as the basis for large scale surveying and mapping. Conformality and equivalence are mutually exclusive properties. Whereas equal-area projections distort shapes while preserving fidelity of sizes, conformal projections distort sizes in the process of preserving shapes.

Equidistant map projections allow distances to be measured accurately along straight lines radiating from one or two points only.