I was just looking at the Mercator-projection World Map on my wall here at work, and something occurred to me: Why does the distance between the parallels get larger as you approach the poles? The map I have is marked out in 15-degree quadrants, with the meridians equidistant. Why not make the latitude lines equidistant, as well, so that you have nice, neat squares? Seems like it would take care of some of those freaky “Greenland is bigger than Africa” distortions, too.
In an attempt to be helpful, I Googled to this site but I doubt it will help you! I found the opening para to be one of the least comprehensible things I’ve ever read on the web.
Good link. A deeper link inside yielded this:
So, good when combined with a compass. Since almost no one who buys such maps actually uses them for navigation, I wish they’d change the default cylindrical projection to a square grid. I’ll have to call the American Map Corp. and complain.
One of the great benefits of the Mercator Projection is that a straight line on the map corresponds to a straight line on the earth. If the parallels were equidistant this would no longer be the case.
Strictly speaking there are no straight lines on the globe; the closest you can get is a great circle. And some straight lines on the projection, like lattitude lines, are not great circles (except the equator).
Strictly speaking there are no straight lines on the globe; the closest you can get is a great circle. And some straight lines on the projection, like latitude lines, are not great circles (except the equator).
Well lets say sailing without turn the ship. Which I believe would be a great circle. As has been pointed out only a small subset of lines on the Mercator Projection are great circles. So it looks like I was flat out wrong. And the real benefit is what toadspittle found in the provided link.
WRONG. Eccept for the equator and lines running exactly north/south, great circles are not straight lines on a Mercator Projection.
>> Why not make the latitude lines equidistant, as well, so that you have nice, neat squares?
The reason is that the world is round, like a sphere, yes, really, so the meridians get closer together as you move away from the equator. So, at the equator, one degree of latitude is about equal to one degree of longitude but as you move away from the equator one degree of latitude remains sensibkly the same (60 nautical miles) while one degree of longitude is less and less until it is zero at the poles. You do not have to care about the size of Greenland. Thake a local map of anywhere in the mid-latitudes and you will see what I mean. Mercator has nothing to do with it. If i own a plot of land in Washington DC which is rectangular and 1’of latitude wide by 1’of longitude wide, I do not have a square piece of land as it is longer in the N-S direction.
And that is why maps look funny to you.
just want to point out that there are other projections even though I don’t recal any of their names. The one I do recall is called the Peterson (Peters?) projection which actually streaches out vertically the land at the equator and shrinks it at the poles. The idea behind it is even if the map isn’t exactly to form the land mass area would be accurate. (Alaska, Greenland would be squashed while Africa would be much longer then it normally appears)
As pointed out earlier, on a globe one degree of latitude is the same distance everywhere. The distance of one degree of longitude is a function of latitude. The distance of a degree (or any nmber of degrees) of longitude at latitude L divided by the distance of a degree (or any nmber of degrees) of longitude at the equator is equal to cos(L). We’ll call this the Longitude Distortion. The Latitude Distortion is 1 because a degree (or any number of degrees) of latitude is the same distance all over the globe.
Longitude Distortion/Latitude Distortion = cos(L) for a globe.
Now for a Mercator Projection we want a map that is a cylindrical projection that will allow us to keep our bearings when we set sail. On any cylindrical projection a degree (or any number of degrees) on the map (not on the land the map represents) is always the same everywhere on the map. (This means longitude lines are equally spaced.) Therefore Longitude Distortion = 1. The Mercator Projection is a special cylindrical projection because it allows us to keep our bearings. Why is this? Because Longitude Distortion/Latitude Distortion = cos(L) just like on a globe. Therefore Latitude Distortion for the Mercator Projection = 1/cos(L) or sec(L).
How does knowing this help?
toadspittle, look at your map again. Measure the distance between two lines of longitude. Divide by the number of degrees between the two lines. Call this number X measured in whatever units suit you. A latitude line at L degrees should be X*L/cos(L) units from the equator.
For bonus points, figure out how far the North Pole should be from the equator to better understand why it is not on the map.