The thing is, all projections are wrong in some sense. That's an unavoidable fact when transposing between flat surfaces where the angles in triangles always add up to 180 degrees, and triangles on curved surfaces where they don't.
For instance, on a flat plane, given a straight line with two lines perpendicular (i.e. both at 90 degrees), those two lines will be parallel, and will not form a triangle with the base. But on a globe, two lines of longitude that are both at 90 degrees to the equatorial line will nevertheless converge at the pole. Depending on how far apart they are, the sum of the angles in a triangle on a curved surface can approach 360 degrees.
What this means is that it's mathematically impossible to express triangles that work on a curved surface using triangles that work on a flat plane, because the latter is limited in ways that the former is not. In other words, in going from curved figures to flat ones, you're going to have to distort something.
Your three choices are shape, distance, and direction. The more a projection preserves one, the more it's going to have to distort another. Some projections try to strike a balance, others focus on one aspect at the expense of another.
The Mercator - which was originally designed for mariners - opted to preserve direction, and did so at the expense of shape, and, to a lesser degree, distance. So instead of a map where the distance between degrees varies at different points on the map, Mercator provides uniform measures of degree at every point. That means you can pick a location on the map, draw a straight line to your desired destination, note the angle formed by that line and magnetic and / or polar north, then set a course along that bearing with full confidence that you'll arrive where you want to. As far as direction goes, Mercator is absolutely correct.
To visualize how this works, see this Wikipedia article showing Tissot's Indicatrix on a sphere, then see this Esri writeup and note that on a Mercator, all the indices are perfect circles.
For instance, on a flat plane, given a straight line with two lines perpendicular (i.e. both at 90 degrees), those two lines will be parallel, and will not form a triangle with the base. But on a globe, two lines of longitude that are both at 90 degrees to the equatorial line will nevertheless converge at the pole. Depending on how far apart they are, the sum of the angles in a triangle on a curved surface can approach 360 degrees.
What this means is that it's mathematically impossible to express triangles that work on a curved surface using triangles that work on a flat plane, because the latter is limited in ways that the former is not. In other words, in going from curved figures to flat ones, you're going to have to distort something.
Your three choices are shape, distance, and direction. The more a projection preserves one, the more it's going to have to distort another. Some projections try to strike a balance, others focus on one aspect at the expense of another.
The Mercator - which was originally designed for mariners - opted to preserve direction, and did so at the expense of shape, and, to a lesser degree, distance. So instead of a map where the distance between degrees varies at different points on the map, Mercator provides uniform measures of degree at every point. That means you can pick a location on the map, draw a straight line to your desired destination, note the angle formed by that line and magnetic and / or polar north, then set a course along that bearing with full confidence that you'll arrive where you want to. As far as direction goes, Mercator is absolutely correct.
To visualize how this works, see this Wikipedia article showing Tissot's Indicatrix on a sphere, then see this Esri writeup and note that on a Mercator, all the indices are perfect circles.
http://en.wikipedia.org/wiki/Tissot%27s_indicatrix
http://blogs.esri.com/esri/arcgis/2011/03/24/tissot-s-indica...