Great Circle
How to take a short cut on the Ocean.
Simply put a great circle is a straight line on the globe. A straight line on earth will form a circle all the way around the earth, with the centre point in the middle of the planet.
Nautical Charts
When traveling from point A to point B, following the line descript by a great circle intersecting both points will give you the shortest route. But this is not a route that is necesary easy to follow. No compass course will point directly along it.
Mercator
The Mercator projection is hated by those who don't understand it. But for navigoters it's one of the best maps to use. Because it shows course lines as striaght lines everywhere. Distances are distorted, but directions are not. So for plotting a rhumb line it is best.
But if you want to plot a great circle course, it will show as a curve on a map. So you have to do some mathematics to find out the courses along the way. Because it shows as a curve on a flat chart, it is a bit counter intuative, but a Great circle is a shorter route.
A rhumb line (blue) compared to a great circle (red) between Lisbon, Portugal and Havana, Cuba.
Top: Orthographic projection.
Bottom: Mercator projection.
The rhumb line (constant compass bearing; straight line on the Mercator projection) is longer in reality than the great circle (curve on the Mercator Projection).
Earth's grid system
The Equator is a great circle, but the parallels are not. They are, as the name suggest parallel to the Equator, and get smaller in diameter and circumference the further away from the equator and the closer to the poles they get. All longitudes are great circles. They all intersect at the north and south pole and share their centre with Earth's.
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