On the "usual FE map" I believe simple map scaling indicates that Sydney to Santiago is over 25,000 km.
Your belief is wrong.
There are exactly the same amount of lines of longitude depicted on the AE map as there are on the Mercator.
True, but that is not the main issue. The spacing between those longitude lines is also extremely important:- on the Globe, starts at zero (km/degree) at the North Pole, reaches a maximum (of 111 km/deg) on the Equator and drops to zero again at the South Pole,
- on the Mercator Projection, stays constant at all latitudes (but the scale of that projection is known to be correct only at the equator) and
- on the AE map starts from zero (km/deg) at the North Pole increases to about 175 km/deg at the Equator and finally to 349 km/deg around the "rim".[/li
If you want to check on my "Sydney to Santiago is over 25,000 km" just scale it off an AEP map, such as Gleason's..
The Wiki states that:Erathostenes on Diameter
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Therefore we can take the distance of 500 nautical miles, multiply by 25, and find that the radius of the flat earth is about 12,250 nautical miles. Doubling that figure for the diameter we get a figure of 25,000 miles.
The Wiki's 500 nautical miles" should be 500 statute miles - check it yourself if you like.
This 25,000 miles is almost the same as 40,000 km and this can be easily used to scale that map.
No great accuracy is needed because the difference the quote airline route distance and the AEP map distance is so great.
I'd like to point out some observations from this map.
Straight line flight from Santiago To Sydney puts you in the northern hemisphere directly across the USA.
San Diego to Tokyo you would fly northward up the coast and never lose sight of land. I guessing about 8,000 miles on that map. Reality is different. It's a little over 5,000 miles out across the pacific ocean.
Where's Hawaii on that map. On RE Hawaii is southwest of San Diego about 2,500 miles
Hawaii is southwest of San Diego. Tokyo northwest of Hawaii.
Hawaii to Tokyo is about 4,000 miles.
How far from San Diego to Hawaii then to Tokyo is it on that FE map?
Sydney to the edge of the world or ice wall on this map, really really close. That brings up a whole new set of questions.