Antipodal Flight

Priyadi

Member
The antipode of a point on Earth is the point opposite to it. Any flights between the two points should cover approximately the same distance, no matter the direction it travels. These flights cannot be explained by the flat-Earth model and can be used to rule out a flat Earth.

For this purpose, we need two large airports, with the position of one airport as close as possible to the antipodal point of the second airport. To determine these ideal antipodal pairs, I used the data from Top 1000 busiest airports in the world and OpenFlights for the coordinates. First, I merged multiple airports for a single city. Then, for every possible combination, I filtered only the pairs that have more than 5000000 passengers in a year, then sorted them by their antipodal distance. These are the top 20 of the pairs:

  1. Auckland - New Zealand // Malaga - Spain // 18628876 // 0.6579251440332874
  2. Auckland - New Zealand // Sevilla - Spain // 5108807 // 0.682434752892215
  3. Xi'an - China // Santiago - Chile // 22316093 // 1.1217059425879221
  4. Madrid - Spain // Wellington - New Zealand // 6049194 // 1.501238991685529
  5. Jakarta - Indonesia // Bogota - Colombia // 30989932 // 1.7529934795927706
  6. Qingdao - China // Buenos Aires - Argentina // 23210530 // 1.832839477995116
  7. Bogota - Colombia // Palembang - Indonesia // 5677234 // 2.1390957517972455
  8. Auckland - New Zealand // Faro - Portugal // 8727000 // 2.2021768129792982
  9. Porto - Portugal // Christchurch - New Zealand // 6566598 // 2.4138603271843246
  10. Porto Alegre - Brazil // Kagoshima - Japan // 5220710 // 2.4296432539059474
  11. Porto - Portugal // Wellington - New Zealand // 6049194 // 2.620707352522477
  12. Buenos Aires - Argentina // Yantai - China // 6503015 // 2.7137816843231928
  13. Bangkok - Thailand // Lima - Peru // 22046042 // 2.790110528558645
  14. Okinawa - Japan // Curitiba - Brazil // 6722058 // 2.936611946865315
  15. Buenos Aires - Argentina // Wuxi - China // 6683380 // 3.3253744953604043
  16. Shanghai - China // Buenos Aires - Argentina // 24124913 // 3.5200649177134395
  17. Lisbon - Portugal // Auckland - New Zealand // 19020573 // 3.5705363309106013
  18. Madrid - Spain // Auckland - New Zealand // 19020573 // 3.6937256985747178
  19. Nanjing - China // Buenos Aires - Argentina // 24124913 // 3.6950470028545666
  20. Fukuoka - Japan // Porto Alegre - Brazil // 8012114 // 3.8469693566003396
(the third field is the passenger traffic for the lesser city; the last field is the antipodal distance, in degrees)

Some of the interesting pairs:

Xi'an – Santiago
xiy-scl.gif xiy-scl.png
Selected flight durations:

  • XIY-PVG-ATL-SCL: 2h 15m + 15h 1m + 9h 29m = 26.75h
  • XIY-HKG-AKL-SCL: 3h 10m + 11h 5m + 11h 0m = 25.25h
  • XIY-CAN-SYD-SCL: 2h 40m + 9h 25m + 12h 30m = 24.58h
On a supposed flat Earth, if we take a 'detour' to locations far from the Xi'an-Santiago route —like Sydney or Auckland—, it will actually save our time. Or maybe the Earth is not flat.

Jakarta – Bogota

cgk-bog.gif
cgk-bog.png
  • BOG-SCL-AKL-SYD-CGK: 5h 40m + 12h 25m + 3h 35m + 7h 40m = 29.3h
  • BOG-JFK-HKG-CGK: 5h 50m + 16h 15m + 4h 45m = 28.83h
Taking a three-legged flight, all the way to Santiago, Auckland, and Sydney near the edge of the world apparently will only lengthen the total time of the trip by less than half an hour compared to the direct flight path. Or maybe the Earth is not flat after all.

Shanghai – Buenos Aires

pvg-eze.gif
pvg-eze.png


This is possibly the best example from the list, with plenty of one-stop flights between the two locations every day.

  • PVG-LAX-EZE: 11h 35m + 11h 58m = 23.55 h
  • PVG-AKL-EZE: 11h 20m + 11h 45m = 22.78 h
  • PVG-ADD-GRU-EZE: 11h 30m + 12h 5m + 3h 15m = 26.83 h
  • PVG-JFK-EZE: 14h 55m + 10h 55m = 25.83 h
The dashed line is Sydney–Buenos Aires, the most southerly route once operational, but no longer in service. As a side note, the route Buenos Aires – Perth is currently under negotiation. When it is operational, the diagrams for the flat earth model here will be much weirder.
 

JohnP

New Member
The antipode of a point on Earth is the point opposite to it. Any flights between the two points should cover approximately the same distance, no matter the direction it travels. These flights cannot be explained by the flat-Earth model and can be used to rule out a flat Earth.

For this purpose, we need two large airports, with the position of one airport as close as possible to the antipodal point of the second airport. To determine these ideal antipodal pairs, I used the data from Top 1000 busiest airports in the world and OpenFlights for the coordinates. First, I merged multiple airports for a single city. Then, for every possible combination, I filtered only the pairs that have more than 5000000 passengers in a year, then sorted them by their antipodal distance. These are the top 20 of the pairs:

  1. Auckland - New Zealand // Malaga - Spain // 18628876 // 0.6579251440332874
  2. Auckland - New Zealand // Sevilla - Spain // 5108807 // 0.68243475289221
  3. [...]
(the third field is the passenger traffic for the lesser city; the last field is the antipodal distance, in degrees)
Very interesting, but can you clarify a bit: How do you define "the antipodal distance, in degrees"? I would naively(?) have expected values near 180.

In terms of a challenge to Flat-Earth models, I suspect the flight times you've found might be more effective. [Edit: or was that what you intended all along?] A determined FE-er would probably claim you'd just built the globe model into your antipodal distance calculation (and I doubt that spelling out the spherical trig would be an effective riposte).
 
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Spectrar Ghost

Senior Member.
I think that the antipodal distance is measured in variance from 180deg. What I’d like to know is why they’re using 16 digits after the decimal. That’s literally angstrom-level precision, which is obviously unnecessary for cities that cover several minutes of latitude in diameter.
 

Priyadi

Member
Very interesting, but can you clarify a bit: How do you define "the antipodal distance, in degrees"? I would naively(?) have expected values near 180.
I should have been clearer. It is the distance from one location to the antipodal point of the other.

In terms of a challenge to Flat-Earth models, I suspect the flight times you've found might be more effective. [Edit: or was that what you intended all along?] A determined FE-er would probably claim you'd just built the globe model into your antipodal distance calculation (and I doubt that spelling out the spherical trig would be an effective riposte).
Flight times are good proxy data for distances, especially with long haul flights where there are few differences in the speed between different aircraft. Obviously, flat-Earthers will invent something like "they adjust the speed of the planes to conform with the globe model".

I think that the antipodal distance is measured in variance from 180deg. What I’d like to know is why they’re using 16 digits after the decimal. That’s literally angstrom-level precision, which is obviously unnecessary for cities that cover several minutes of latitude in diameter.
The number is what the calculation gave me. It is a one-off, quick and dirty script & I didn't bother to reformat for displaying purposes.
 

Rory

Senior Member.
How would you use this in a discussion? Like, let's say a flat earther says to you, "have you got any proof that the world isn't flat?" and you say, "yes, because there are flights that..."

And then fill in the blank.
 
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Priyadi

Member
How would you use this in a discussion? Like, let's say a flat earther says to you, "have you got any proof that the world isn't flat?" and you say, "yes, because there are flights that..."
... because on a spherical earth, in an ideal situation, it should be possible to depart the original location in any direction, and eventually, we will reach the antipodal position in roughly the same duration. On a flat earth, there's only a single correct direction to reach another point on earth.

For example, Buenos Aires and Shanghai are a close enough antipodal pair. from Buenos Aires, we can choose any flights to Shanghai with a stopover in the US, Europe, Africa, Middle East or Australia & New Zealand, and they all will take us to Shanghai in roughly the same duration.

On a flat Earth, Buenos Aires–Auckland–Shanghai should take a much longer duration than Buenos Aires–New York–Shanghai. Indeed, Buenos Aires–Auckland is farther than Buenos Aires–Shanghai, and there should be no point going from Buenos Aires to Shanghai with a stopover in Auckland. In reality, both trips take roughly the same duration and can be easily explained by the spherical Earth model.
 

deirdre

Senior Member.
On a flat earth, there's only a single correct direction to reach another point on earth.
you probably need to show this.
and I would suggest simplifying your round earth flight presentation because I cant follow your OP at all, too many moving gifs and acronymns

i would pick ONE example
then show it on a nonmoving round earth map. and then what those flights would like like on a flat earth map.
 

Priyadi

Member
you probably need to show this.
and I would suggest simplifying your round earth flight presentation because I cant follow your OP at all, too many moving gifs and acronymns

i would pick ONE example
then show it on a nonmoving round earth map. and then what those flights would like like on a flat earth map.
The "acronyms" are airport codes. Yes, I should have taken the time to convert them to city names.

I gave three examples. In each, there is a rotating globe with flight paths on the spherical Earth model. the other is on the flat earth model. Unfortunately, this is the best way to visualize the paths. the rotating motion is not from Earth's rotation. I rotate the globe along the 'antipodal axis' to show every flight between the two locations to have practically the same distance. With any flat projection, it is not possible to draw the routes and have all of them to have the same length due to distortions inherent in any map projection.

If this is not clear enough, I think the best way to visualize it is to take a globe and locate both Shanghai and Buenos Aires on the globe. You will understand that we should be able to fly from Shanghai in any direction and reach Buenos Aires at roughly the same distance, irrespective of the direction we are flying from Shanghai.

These are the airport codes converted to city names:

  • Xi'an-Shanghai-Atlanta-Santiago: 2h 15m + 15h 1m + 9h 29m = 26.75h
  • Xi'an-Hong Kong-Auckland-Santiago: 3h 10m + 11h 5m + 11h 0m = 25.25h
  • Xi'an-Guangzhou-Sydney-Santiago: 2h 40m + 9h 25m + 12h 30m = 24.58h
  • Bogota-Santiago-Auckland-Sydney-Jakarta: 5h 40m + 12h 25m + 3h 35m + 7h 40m = 29.3h
  • Bogota-New York-Hong Kong-Jakarta: 5h 50m + 16h 15m + 4h 45m = 28.83h
  • Shanghai-Los Angeles-Buenos Aires: 11h 35m + 11h 58m = 23.55 h
  • Shanghai-Auckland-Buenos Aires: 11h 20m + 11h 45m = 22.78 h
  • Shanghai-Addis Ababa-São Paulo-Buenos Aires: 11h 30m + 12h 5m + 3h 15m = 26.83 h
  • Shanghai-New York-Buenos Aires: 14h 55m + 10h 55m = 25.83 h
 
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Rory

Senior Member.
As above, I think picking one pair of cities - the best pair - would work well (with the addendum that this will work for any pair of antipodal cities).

The gif could work well if it 'rotated' a little slower.

Counterarguments I would expect from flat earthers would include: there is no flat earth map; we don't know if the flights are real; we don't know how fast the aeroplanes go; and "have you measured all this for yourself?"

Plus, of course, the existence of any long distance direct flight in the Southern Hemisphere automatically debunks flat earth.
 
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Priyadi

Member
oh ok. that last still pic is a flat earth map? I was wondering what the heck that was showing me. :)
yes, the second picture is the so-called "flat earth map". with the same cities and routes from the globe model laid out on the map. on a flat model, these different routes should have far different durations.
 

Priyadi

Member
As above, I think picking one pair of cities - the best pair - would work well (with the addendum that this will work for any pair of antipodal cities).

The gif could work well if it 'rotated' a little slower.

Counterarguments I would expect from flat earthers would include: there is no flat earth map; we don't know if the flights are real; we don't know how fast the aeroplanes go; and "have you measured all this for yourself?"
Yes, I think the best pair is easily Shanghai-Buenos Aires.

The GIFs are tricky. they are generated from video files. But using a smoother frame rate will give me huge 30MB+ files, and it doesn't appear it is possible to upload & embed videos here.

Flat Earthers' counter-arguments are predictable. They can be classified into 3 broad categories: 1. invent "explanations", 2. "they are lying or deceptive", 3. "LOL! sheeple!". With the facts presented here, I think most of them will use 3, but some will use 2.
 

Rory

Senior Member.
The GIFs are tricky. they are generated from video files. But using a smoother frame rate will give me huge 30MB+ files.
Could you take a few screenshots from the video and then make a gif using ezgif.com (or similar)? You can vary the frame rate.
 

Chris Rippel

New Member
This demonstration is interesting.
My comprehension is slowed when the list of destinations starts with city names and then switches to the three-letter airport codes for flight paths. And city names are also on the rotating globe and map. Before I can understand your point, I have to translate the three-letter airport codes back into city names. Sticking with city names for flight paths would have made your point more quickly.

Thanks for reading.
 
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Chris Rippel

New Member
Here's a handy tool I wrote for showing a flat route and a globe route on three different maps (Equirectangular, Globe, and AEP/Flat)
https://www.metabunk.org/flat/
Five minutes ago requested this exact demonstration on a posting.
I had to go back and edit my request out of that posting because here is what I asked for.

One problem with this tool is that I can't scroll down in either Firefox or Chrome to read the instructions.

One question. Is there anyway to add additional flight paths? This may be in the instructions I can't read.

Chris Rippel
 

Mick West

Administrator
Staff member
One problem with this tool is that I can't scroll down in either Firefox or Chrome to read the instructions.
Must have fairly low resolution. It says:
 
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