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Before we cover any other aspects of navigation, it's important to have a discussion about maps. The earth is round: it's more or less spherical, though not perfectly so. And it's certainly not flat. However, maps and nautical charts are usually flat. This alone presents a challenge: how do we use a flat map to represent something that isn't? It turns out that there are many different projections used to create maps of the world. But there's one that is by far the most useful to navigators, and that's the Mercator projection.
The following map uses the Mercator projection. The vertical lines are lines of longitude and are equally spaced. The horizontal lines are lines of latitude, and they are not equally spaced: the further away from the equator we move, the further apart the lines of latitude are. The downside of this is that it causes areas in the polar regions to appear much larger than they are. For example, Greenland appears to be larger than South America, when it is less than half the size of Brazil. Also, Antarctica looks like it's the size of Europe, Asia, and Africa combined, when it is less than half the size of Africa. This may be problematic for some uses, but it's necessary to make this map good for navigators.
File obtained from https://commons.wikimedia.org/wiki/File:Mercator_projection_Square.JPG with attribution/license:
The important thing that the Mercator projection does is preserving angles and directions. So if you were on a ship and you were traveling at a bearing of 60° (this means you're traveling at a 60° east of due north), you could simply draw a line segment from your location at a bearing of 60°, and that would correspond to your ship's course. It may seem like a small thing, but the Mercator map was the first one to satisfy this requirement on a global scale!
The way that the Mercator map preserves angles is by spacing the lines of latitude in a nonuniform way: as we move closer toward the poles, the latitude lines are spaced farther apart. This is how the map accounts for the fact that in the real world, the longitude lines get closer together as they near the poles. There are other projections that instead choose to bend the longitude lines to achieve this, but this creates a map that's not rectangular, which then causes all sorts of other issues. The solution of spacing the latitude lines farther apart near the poles kept the map rectangular and allowed for angles and directions to be preserved. To see how this affects distances on maps, take a look at the following two images. The first one came from the top-left corner of a chart, and the second one came from the bottom-left corner of the same chart:
You can see in the first image that the distance from 55°S to 57°S, which is two degrees of latitude, is roughly equal to the distance between 74°S and 75°S in the second image, which is one degree of latitude. On the actual earth, each degree of latitude is the same distance. So this is a distortion on the map, which is put there to make sure that angles and directions are preserved.
The only situation where this affects calculations in navigation is when trying to measure distances. In this case, it's important to use the vertical scales to measure. And because the vertical scales change as they move up and down, it's important to use the portion of the scale that's roughly at the same latitude as the area you're trying to measure. But this is a bit beyond our needs for now.
Sample Problems
Sample Problems
1. Take a look at the Wikipedia article on Map Projections and explore the various examples of projections listed there.
2. While the Mercator projection is excellent for navigation purposes, it fails in giving an accurate representation of the shape of Antarctica as a continent. Find a projection that gives a better representation of the shape of Antarctica.
3. Compare the Mercator projection with the projection you chose in problem 2. What do they have in common? What are some of their differences? What are the advantages and limitations of each projection?
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