#### Mock

• • 43 ##### (Dis-)proving a FE without using RE distances - here we go
« on: August 12, 2017, 10:44:38 AM »
So, TFES' counter-argument for the Quadrilateral Proof is that we don't know if the distances are correct. All right.
What if we prove that for any FE map configuration that does get the angles right by using other distances, therefore avoiding the proof, those other distances will still not match up with the flight times and speeds?

If the Earth is flat, there MUST be a constellation where BOTH

1.   The Quadrilateral Proof gives identical angles
2.   The times that it would take planes to fly the distances matches those given by airlines like Qantas, calculatable by dividing the distances by the cruise speed of the planes used / Alternatively: The cruising speed the plane would need to have in order to complete its journey in the given time matches the one that is given for each plane type and flight
3.   (optional) The angles between the cities would have to remain roughly the same (not sure, since FET seems to question those angles anyway)

If there is no such constellation, then the Earth cannot be flat. Shouldn't be too hard.

I will be using http://www.calculator.net/triangle-calculator.html for the angles.
Flight distances will be taken from WorldAtlas (all in km). The corner points are New York (NY), Paris (PA), Buenos Aires (BA) and Cape Town (CT).

NY - PA 5919
NY - BA 8383
NY - CT 12472
CT - PA 9148
CT - BA 6938
BA - PA 10930

Result for angle at NY calculated directly: 98.201°
Result for angle at NY calculated by adding: 31.814° + 43.611° = 76° => Difference of ~22°

Okay, so as we all can see, with the data we get from WorldAtlas, Earth cannot be flat. So let’s just change those numbers up a bit. At this point I’m not sure yet, but I think in order for the second angle to get closer to the first one, we’ll have to make NY – CT and BA – PA a bit shorter. Shall we? Let's say NY – CT 10000; BA – PA 8000, the other distance figures stay the same.
Result for angle at NY calculated directly: 65.401°
Result for angle at NY calculated by adding:  43.24° + 64.294° = 108° => Difference of ~43° in the other direction

Okay, seems like I went a little bit overboard, but the angles did go into the direction I wanted them to. We can change the relevant angles by changing those two distances. Let’s try NY – CT 11000 and BA – PA 9500. The rest stays the same.
Result for angle at NY calculated directly: 81.272°
Result for angle at NY calculated by adding: 56.248 + 39.092° = 95°

We’re getting closer to distances that would work on a FE, but NY – CT and PA – BA still seem to be a little too short. Considering the huge effect it had before, let’s just add 500 km to each figure. NY – CT 11500 and BA – PA 10000.
Result for angle at NY calculated directly: 86.993°
Result for angle at NY calculated by adding: 36.8° + 52.115° = 88.915°

We’re getting really close now – so close that the digits after the dot will soon get important, so I stopped rounding the sums out of laziness. Our added angle is two degrees greater than the first one. I’m going to add a smaller bit of length: NY – CT 11550 and BA – PA 10050.
Result for angle at NY calculated directly: 87.513°
Result for angle at NY calculated by adding: 36.561° +  51.695° = 88.256°

The two angles are now less than a degree apart – a mere 0.743°. I’ll try adding just 30 km more to both distances. NY – CT 11580 and BA – PA 10080.
Result for angle at NY calculated directly: 87.862°
Result for angle at NY calculated directly: 36.417° +  51.442° = 87.859°

(I have proof for those angles and distances - 87.862°, 36.417° and 51.442°)

As you can see, the difference between the angle calculated from NY – PA, NY – BA and BA – PA is now only 0.003 degrees smaller than the one added up using the other distances. If the distances were like this in the real world, then mathematically the world could be flat.

Summing the first part up, our distances could be:

NY - PA 5919
NY - BA 8383
NY - CT 11580 – now 892 km less than before
CT - PA 9148
CT - BA 6938
BA - PA 10080 – now 850 km less than before

Note that we could also have done this by increasing the other distances, instead of decreasing those two – or a combination of both, which would probably give more accurate results, but I don’t think it matters. If anyone wants to put in the extra work (I’m looking at you, Flat Earthers – this might actually be a method to create a more or less accurate flat map!), you’re very much welcome to do that. I'll edit my post accordingly.

Now, before I start calculating with the flight times and velocities of the planes, does anyone have objections to how I'm doing this? Because I don’t want to do all that work without making sure it doesn’t get discredited again.
« Last Edit: August 12, 2017, 09:41:31 PM by Mock » #### Curious Squirrel

• • 1338 ##### Re: (Dis-)proving a FE without using RE distances - here we go
« Reply #1 on: August 12, 2017, 03:31:24 PM »
Actually, you're now at the easy part. You've got all of the angles of one corner down, and have two sides. From here you can use variations of the SSA methods to find out the distances and angles of every side and corner. Then you have a known distance and a known time for the length of the flights, and you can use that to test how fast a plane has to go for each trip. I suspect at least some of them will have pretty wild answers for speed, as well as being quite varied. The second part if why you can't change the ratio between lengths too much. You'll end up with vastly different speeds the plane has to be moving to cover each distance in the time provided. But take what you've got, use SSA and it's variations to find everything else as it's pretty easy, and then take your new distances and divide them by how long those flights take. That'll give you the average speed the plane must maintain for each leg. Anything too large: FE can't work. Too large of differences: FE can't work.

#### Mock

• • 43 ##### Re: (Dis-)proving a FE without using RE distances - here we go
« Reply #2 on: August 12, 2017, 08:42:04 PM »
Thanks for answering. I get why calculating the angles is a good idea, but what do you mean when you say I should calculate the other distances? This is one possible FE layout of many. In this specific one, all the distances are known already. I could make another one (either by tweaking other distances than NY-CT and BA-PA, or by calculating the angle in another corner), but I don't understand how that would help disprove FE theory.

We're having house guests from tomorrow until next weekend, but I'll see if I can find the time to do all the math. If anyone else wants to do it in the meantime, you're welcome to post it here.