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Here is a quick lesson in great circle usefulness.

Ok, so they can project a global map based on a flat earth map or vise versa means earth is a globe? Or that what was once known as plane sailing is now called circle sailing, so that means earth is a globe? These don't prove earth is not flat. So why use these examples? Unless you don't have proof that earth is a globe. Sorry, just being reasonable.

Why give us a map lesson on an object that does not exist? What is your point?

The point is, the rhumb line is easy to follow because the bearing is kept constant and the navigator doesn't have to constantly adjust bearing to follow the great circle route in order to achieve the shortest distance. 

Near the end of this video it shows two points in the northern hemisphere, something like a city in Canada and a city in Scandinavia (or thereabouts) where the rhumb line distance (nearly constant latitude) is much greater than the great circle distance, the latter of which takes the course through the arctic. If viewed on a "flat" earth map with the north pole in the center, both courses are curved. The great circle course will appear to be longer than a route following an apparently straight line on the flat map, but if you actually plot those courses and measure the distance, the apparently straight line course is actually longer than the apparently curved great circle route!! 

But more tellingly, the rhumb line course takes the transit far afield in the other direction, which seems to be absurdly out of the way. It appears to be nearly twice as far as the apparently straight line route. (The rhumb line course is indeed longer but the video's drawing exaggerates it a lot.)

In the end, rhumb line courses are easy to follow because you don't have to adjust your course heading, you just keep it the same the whole way. But you end up traveling further, that is, unless your are traveling over the equator or along a meridian. By understanding how rhumb lines work, one is better able to comprehend the significance of great circle routes, which do not have any relation to a projection of the spherical earth on a flat map. In order to find the great circle route you need to consider the distance to the center of the earth from any given point on the route. This is often approximated by an average distance to the earth's center, and the results are close enough to allow for corrections near the end of the flight or course (air or water).