Thread: Math Question.
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Old 04-26-09, 01:18 AM   #7
Etienne
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Quote:
Originally Posted by UnderseaLcpl View Post
It sounds to me like you might be talking about a great circle.
http://en.wikipedia.org/wiki/Great_circle
Since the Earth is curved, the shortest distance from point A to B is not neccesarily a straight heading, but one that circumscribes the curvature as much as possible.
Great circles in a nut shell: Take a piece of string, stretch it between two points on a globe. That's a great circle - the shortest route between the two points.

The thing is, most of the maps we use are Mercator projections - maps where things are stretched out as the lattitude increase, so that angles stay constant - If you draw a line on a Mercator map and it meets meridian 0 at 30 degrees, it will cross meridian 15 at 30 degrees. Parallels and meridians also meet at a convenient right angle. (Mercator maps are also the reason many people are confused as to the relative size of Greenland and Africa.)

Anyway, if you draw a straight line between the same two points you used earlier on a Mercator chart, you get a straight line - What we call a rhumb line. Obviously. Now, if you take the coordinates of the line every five miles, then plot that on the globe, you'll get a line that curves toward the equator.

If you do the same, but copying the line you traced on the globe with the string to the chart, you'll get a line that arches away from the equator.

The great circle is shorter (Since the Earth, SHIV nonwithstanding, isn't actually flat), but it takes you closer to the poles and it's a pain in the rear... And for it to really make a difference, you have to have about 600 nautical miles to go. Otherwise, you're saving pennies.

...yeah, my explanation isn't that great. But in my defense, I had to do 45 hours of spherical trig in nautical school, which is essentially "Great Circle 101" - It's surprisingly easy to explain when you have a blackboard...
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