Robinofloxley:
Thanks for the detailed flight info, but I'll clarify my question. What is the straight line distance between Buenos Aires and Cape Town? On a globe it would roughly be the same distance as Chicago to Barcelona. But on a flat map it would be 2.5x further. Also, if I read a flat map correctly, taking a straight line trip from Buenos Aires to Cape Town would require flying northeast essentially along the entire east coast of South America, where on a globe it would be over open ocean the entire trip. So which is it? This seems a fairly easy question to prove. I'm less interested in what commercial flights actually do and more interested in how to prove globe vs flat. Skipping the great circle routes, it seems a simple test would be taking off from two cities mentioned, and flying due east along each latitude at same speed toward each destination. Globe model says they'll reach their destinations, FE theory says they won't.
I'm including a graphic to show that a globe trip would require travel due east, over open ocean, while FE model indicates northeast travel over land - the east coast of South America. Again, seems like a simple way to prove which is correct. I also marked the distance on a flat map of Chicago to Barcelona, which is quite shorter than Buenos Aires to Cape Town on a flat map.