There are some other threads on this, but those rely on flight times being inconsistent with existing ‘flat earth maps’. The objection to that of course is that there is no flat earth cartography, and no one is saying that existing FE maps are correct.
There was also a strange claim by Tom Bishop in this thread
https://forum.tfes.org/index.php?topic=6633.0 about the angles of a triangle.
Here is a challenge that doesn’t rely on angles or any existing map, but simply on observed distances between cities. FEers are absolutely welcome to challenge that asumption, but then the argument can move on. If I take the distances given here
https://www.distancecalculator.net, which should be absolutely consistent with flight times (please challenge if not).
London – Cape Town 5988m
London – Buenos Aires 6922m
Buenos Aires – Cape Town 4273m
London – New York 3465m
Buenos Aires – New York 5304m
Cape Town – New York 7816m
Note I am using four cities and six distances. I believe this is the absolute minimum needed for the challenge, though I haven’t proved it.
The challenge is to represent those distances on a flat piece of paper. For my part, I drew the lines in the order shown above, using the distance in miles divided by 1,000 in centimetres. Thus the distance London – Cape Town is 6.988 cm = about 7cm.
For the rest you will need a schooldays compass. Whatever the order you draw, you will find it possible to draw 5 of the six lines accurately on a piece of paper.
The challenge is the sixth line. I ended up with Cape Town – New York. Unfortunately I measured that at 6.7cm, whereas the ‘official’ distance corresponds to 7.8cm, i.e. more than a 1,000 miles out.
My challenge to flat earthers is to reproduce that experiment above, in a way that is consistent with the FE assumption. If you want to challenge the distances themselves, i.e. the data source, the argument can move on.
The simplest explanation, in accordance with Ockham’s razor, is that the paper could be folded, say on the hinge New York- Cape Town. Then you can travel the shorter distance under the paper. In real life, you could drill a huge tunnel under the Atlantic, and avoid flight sickness.
This whole thing is about the scientific method, which is about constructing a model of reality, and seeing whether it matches our observations of reality. The model here was a flat piece of paper with lines drawn between points. I found this did not match the observations.
I suppose you could argue there was a warp in space-time that explained the discrepancy. OK, but the very simplest explanation (going back to Ockham) is that the earth is roughly spherical. This is what science is about.