As an example, here is North America.

I traced it from a known round-earth model and gathered flight times from LA to New York to Miami to LA.

When I plotted the lines, I had to move Florida a little to make the flight times work. You can see my original Miami dot on there.

As I expand the map, I will redraw the continent lines to make them match my flight time data. With the flight time data, the map of the continents should reveal themselves.

If my 1st premise is true and a flat earth on a flat paper is easy, then I'll get this done.

I predict that when you add a fourth city at some large-ish distance from the current three choices - and presuming you measure the length of both diagonals consistently - then the resulting figure will not be able to be drawn on a 2D map because one of the diagonals will be "too small".

I've already demonstrated that this definitely happens using published airline flight distances. I compared the airline's claimed long distance flight times (verified independently from 3rd party "On-Time flight" records) - and the distances they publish are a perfect fit for the published cruise speeds of the aircraft.

So the chain of reasoning is thus:

1) We know the flight times from examining the airline's schedules.

2) We know that they fly "on time" for the vast proportion of flights because multiple consumer watchdogs and government offices monitor them...so the published schedules are DEFINITELY CORRECT.

3) We can obtain the cruising speed of the airplanes from multiple sources - including both airlines and manufacturers.

4) We can infer the distances travelled from that.

5) We can compare that with the airlines published distances - and THEY AGREE.

6) We can find distances for four widely spaced cities laid out in a quadrilateral and construct two flat, 2D triangles using one of the two diagonals.

7) We can then calculate what the other diagonal distance should be if the world is flat.

We compare the calculated second diagonal distance with the airline route distances - and they DO NOT AGREE!!!

So one of these steps is broken...I contend it's that the world ISN'T flat - and when you work it out, the data we have is 100% consistent with a round earth.

The only FE "get out" is that Tom claims that the published cruise speeds of modern airliners is incorrect (assumption (3), above) and is therefore claiming that neither airlines nor airliner manufacturers are aware of the speeds that their planes actually fly(!!) - he seems to believe that they determine the practical cruise speeds of their planes by flying some long route with a stopwatch...which is...beyond crazy!

Since you're gathering flight TIMES (not actual distances) in the same basic way we did - your map will fall foul of the exact same critiques that our efforts did.

HOWEVER: There is a second part to this.

9) If (as Tom claims) the airliner cruise speeds that we have are (say) 20% too low - then all of the distances that the airlines are stating in their route maps are 20% larger than the airlines believe them to be.

10) This scales up my "quadrilateral of cities" diagram by 20% - but the diagonal calculations are still incompatible with the flat earth hypothesis.

So even if Tom is right - my disproof of the flat earth still works.

The ONLY way to escape my trap is to claim that the airlines deliberately vary the speeds that they fly in order to make it APPEAR as though the world is round, even though it's clearly not.

Since airliners fly most efficiently only at one particular speed - this would be costing them a TON of money every year. It seems highly unlikely that every airline around the entire world would keep the conspiracy silent.

Tom then deflected the conversation into arguments about GPS's and such.

Hence, it's largely a waste of time to try to create your map because it just leads down the exact same rabbit hole.

If the FE'ers adamantly refuse to accept any form of distance measurement whatever, they cannot make a good map.

But here's the thing:

**They don't WANT a good map!**Having no map is actually their defense against a whole slew of arguments. They know that the very moment they come up with an "official" map, I 100% guarantee that I can instantly debunk it - because their compass readings and positions of the Pole Star and Southern Cross cannot POSSIBLY agree with reality as observed by ship's captains and navigators for the past 1000 years or so...airliners will have to fly at Mach 2 on some routes and at 200mph on others.

The laws of topology are on the side of the RE'ers here. Mathematics doesn't tell lies and it doesn't take sides. Math says, clearly and unambigously that you can't make a flat earth map that reproduces the important features of a round earth map. It's called "The Hairy Ball Theorem" (or "The Hedgehog Theorem" in situations where "hairy balls" have an entirely unfortunate connotation!). You can look it up on Wikipedia.

According to hairy ball, you can't make a spherical map (a globe) without creating two points on the sphere that are "special" (for stellar cartography, the north and south geographic poles - for magnetic cartography, the north and south magnetic poles). Flat surfaces do not have this property - which means that 100% of all flat earth maps are doomed.

Basically - you're screwed.