[inquisitive]

Really, you must have a rough idea.  How do ships and planes work out journey times?

There is a theoretical model based on latitudes and longitudes on a Round Earth which supposedly tells us how far away point A should be from point B, and planes use this value in its calculations when guessing its own cruising speed (which may be inaccurate since it is using Round Earth assumptions).

My GPS tells me speed and distance accurately.

And how do you know that the speed and distance is accurate? Even at the scale of a car, the GPS speed is inaccurate when compared to the car's speedometer.

GPS speed is more accurate that a speedometer.  Please give us your method of measurements.

[Tom Bishop]

My GPS tells me speed and distance accurately.

And how do you know that the speed and distance is accurate? Even at the scale of a car, the GPS speed is inaccurate when compared to the car's speedometer.

Really? Because mine is pretty spot on within 1 MPH usually. As long as I'm not changing speeds faster than it's refresh rate. It also does a pretty damn good job at giving arrival times, which means it needs to be fairly accurate for speed, distance, and current location.

The internet is littered with complaints asking why GPS speed differs so drastically from their speedometer.

https://www.reddit.com/r/cars/comments/2sjy8x/which_is_more_accurate_my_factory_speedometer_or/

Which is more accurate? My factory speedometer or my garmin GPS? (self.cars)

I notice a difference in my GPS speed from my factory speedo. At 100kph there is almost a 15kph difference. The vehicle speedo always reads a bit higher. I use the GPS speedo usually because its hard to read the kilo's on my US Spec speedo. Just trying to avoid a possible ticket!

https://en.discussions.tomtom.com/tomtom-traffic-live-and-other-services-47/why-is-my-speed-always-4-5-mph-out-of-sync-272539

WHY IS MY SPEED ALWAYS 4-5 MPH OUT OF SYNC ?

all my TT devices eg: XXL IQ  and recently GO 1005 World`s speed info is always 4-5 MPH out and other people I have met say on a motorway service station are spot on?

Is there a reason for this ... I have tried many positions on my windscreen and its the same and I only have a mondeo and not some strangely obscuring windscreen type of car or truck?

[Tom Bishop]

Really, you must have a rough idea.  How do ships and planes work out journey times?

There is a theoretical model based on latitudes and longitudes on a Round Earth which supposedly tells us how far away point A should be from point B, and planes use this value in its calculations when guessing its own cruising speed (which may be inaccurate since it is using Round Earth assumptions).

My GPS tells me speed and distance accurately.

And how do you know that the speed and distance is accurate? Even at the scale of a car, the GPS speed is inaccurate when compared to the car's speedometer.

GPS speed is more accurate that a speedometer.  Please give us your method of measurements.

That is what is claimed as an explanation for the difference. But all we really know is that the speeds are different and there are a few explanation floating around to try and explain why. We will need some kind of test independent of looking at your car's speedometer to tell us the accuracy of GPS if a speedometer cannot be relied on at all.

Since the speeds often differ, for whatever reason, the "speed accuracy" argument that GPS is spot-on cannot be used as an argument to say that GPS is correct.

[Jura-Glenlivet]

I know you lot don’t get out much, but lame excuses like we can’t be totally sure the maps and GPS aren’t lying to us, so we can’t make a map, sorry, it just wouldn’t be zetetic enough. Really!

There may be some reddit whingers where discrepancies in speeds are the only excitement they will ever get, but I’m pretty sure there aren’t any saying, I drove to Edinburgh/(anywhere) using my Michelin map/Garmin but it wasn’t there, and the old guy sitting there reckons it’s 20miles north.





(Then again, my wife had an appointment at Birmingham Uni’ at 9.30 am, didn’t get back to just past Leicester (50 miles) until 8.00 at night, I just thought she was shagging someone else, I guess I’d better dig her up and apologise, the flat earth made me do it officer.)

[inquisitive]

Really, you must have a rough idea.  How do ships and planes work out journey times?

There is a theoretical model based on latitudes and longitudes on a Round Earth which supposedly tells us how far away point A should be from point B, and planes use this value in its calculations when guessing its own cruising speed (which may be inaccurate since it is using Round Earth assumptions).

My GPS tells me speed and distance accurately.

And how do you know that the speed and distance is accurate? Even at the scale of a car, the GPS speed is inaccurate when compared to the car's speedometer.

GPS speed is more accurate that a speedometer.  Please give us your method of measurements.

That is what is claimed as an explanation for the difference. But all we really know is that the speeds are different and there are a few explanation floating around to try and explain why. We will need some kind of test independent of looking at your car's speedometer to tell us the accuracy of GPS if a speedometer cannot be relied on at all.

Since the speeds often differ, for whatever reason, the "speed accuracy" argument that GPS is spot-on cannot be used as an argument to say that GPS is correct.

You agree about the location accuracy and repeatibility of GPS?  Used by surveyors across the world.

[Curious Squirrel]

My GPS tells me speed and distance accurately.

And how do you know that the speed and distance is accurate? Even at the scale of a car, the GPS speed is inaccurate when compared to the car's speedometer.

Really? Because mine is pretty spot on within 1 MPH usually. As long as I'm not changing speeds faster than it's refresh rate. It also does a pretty damn good job at giving arrival times, which means it needs to be fairly accurate for speed, distance, and current location.

The internet is littered with complaints asking why GPS speed differs so drastically from their speedometer.

https://www.reddit.com/r/cars/comments/2sjy8x/which_is_more_accurate_my_factory_speedometer_or/

Which is more accurate? My factory speedometer or my garmin GPS? (self.cars)

I notice a difference in my GPS speed from my factory speedo. At 100kph there is almost a 15kph difference. The vehicle speedo always reads a bit higher. I use the GPS speedo usually because its hard to read the kilo's on my US Spec speedo. Just trying to avoid a possible ticket!

https://en.discussions.tomtom.com/tomtom-traffic-live-and-other-services-47/why-is-my-speed-always-4-5-mph-out-of-sync-272539

WHY IS MY SPEED ALWAYS 4-5 MPH OUT OF SYNC ?

all my TT devices eg: XXL IQ  and recently GO 1005 World`s speed info is always 4-5 MPH out and other people I have met say on a motorway service station are spot on?

Is there a reason for this ... I have tried many positions on my windscreen and its the same and I only have a mondeo and not some strangely obscuring windscreen type of car or truck?

These are both at least 2 years old, which with the speed of technological advancement is a bigger issue than one would normally think. They also appear to be one case each, for two different GPS brands/devices. Not to completely steal a page out of your book, but how do we know both A) They aren't lying and B) They aren't isolated incidents? Even the best manufactured products, when made in bulk, are going to get defects and issues with some percentage of them. As I recall from the Xbox 360 fiasco, the 'standard'/accepted rate is somewhere in the 1.5-2% ballpark.

You also aren't going to find hosts of people going "My GPS gives my speed perfectly all the time, thank you!" because that's not the nature of the internet, or humanity. I would argue that, logically, if it was a huge issue and not accurate often enough, GPS devices wouldn't have the feature anymore. Because if a feature is shown to be bad over and over again, with enough frequency of occurrence among multiple batches, you remove it so it doesn't hurt your brand.

[3DGeek]

I certainly wouldn't rely on any speed display in a car.   Car speedometers are not 100% precise.  Because car manufacturers don't want to be sued in the event that their speedometer reads a little too low and someone gets a speeding ticket when their speedometer said that they were within the speed limit.  For this reason almost all cars have speedometers that are DELIBERATELY made to read higher speeds than the car is actually moving...the precise amount varies between cars.  BMW say that their speedometers are designed to read "high" by 5mph or 2.5% whichever is less.  The same thing happens with GPS units built into cars and those roadside displays that show your speed when you approach them.  Cars also go up and down hills - which means that the distance on the odometer doesn't match the distance as drawn on a map.  The four wheels of the car rotate at different rates as you go around curves - and if the speedometer takes the speed from just one of them - then it'll either read faster or slower than the true speed of the car itself.   So, yeah - car speedometers suck.  People don't believe it - so there is a ton of Internet debate on the subject.   GPS is remarkably accurate though...within 10 feet if the receiver can pick up 3 satellites - better than that if it can 'see' 4 of them.

But speed isn't the issue here...and neither are cars.

This is about distances between cities...as measured by airlines.  Please - let us not let Mr Bishop deflect the conversation away from areas of discomfort and back into his comfort zone.

So forget cars...they are not important to this calculation.

Tom:

In STEP 1 I established that distances quoted by Qantas airline are 100% credible.  They match the performance of the aircraft and their stated flight times.  Their "on time" record is good enough that their times and distances are 100% trustworthy.

In STEP 2 I demonstrated that the distances produced by the "WorldAtlas" site produces distances that are within 1% of Qantas' distances - and therefore whatever internal math it's using is a very good match for airline distance statements in general.

You used those numbers (without a word of complaint) when you (incorrectly) believed that they supported your Flat Earth Theory and triumphantly quoted them when you THOUGHT they disproved the Round Earth.  As it turns out, this is a clever trap that you fell into.   I wish I was smart enough to have planned it that way...but I'm not.

In STEP 3 I pointed out that simple Euclidean geometry allows us to calculate the internal angles of a PLANAR quadrilateral in two different ways if you know the length of the sides and the diagonals.   If the Earth is flat then those angles will be the same for both calculation methods.

In STEP 4, User "Inquisitive" kindly did the calculations for us - presumably using the (trustworthy) WorldAtlas data for those distances...and discovered that for at least one internal angle of the quadrilateral between New York, Paris, Cape Town & Buenos Aries, there is a HUGE discrepancy...123 degrees versus 162 degrees.

Those four steps are a CLEAR disproof that no possible FLAT Earth map can possibly make the distances between those four cities come out correctly.   It is IMPOSSIBLE to make a planar quadrilateral where those four distances come out right.

Now you're flim-flamming about STEP 2...(which you seemed to trust so long as you thought it proved your theory).   STEP 2 is that we demonstrate that WorldAtlas's software does indeed come out with the correct distances for every route we tested.   I invite you to test it for as many other routes and as many other airlines as you like...the answer will always be the same.

So - what you resort to is the rather pathetic complaint that there are no direct flights between some of those four cities with which we could back up the WorldAtlas distances between them.   I would also point out that if you go to Google Maps - and enter those same cities and ask for an route BY AIRPLANE - it comes out with very similar numbers...within 1%.

What that means is that you must either believe that:

1) WorldAtlas, and Google are a part of the global conspiracy and that their software produces distances that match those of Qantas flights - but are deliberately incorrect for the four cities that Inquisitive just happened to pick...OR...

2) WorldAtlas produces incorrect distances by accident but just happens to produce very good distances for all of the Qantas routes.

OK - well, we can test your two theories with some more experiments.

FIRSTLY:  We can find a bunch more "quadrilaterals of widespread cities"...and demonstrate that NONE of the distances between them work in FET.  This would be good evidence that Inquisitive didn't "cherry pick" four cities that didn't include a route for which WorldAtlas' data is incorrect.

SECONDLY: We can find a "quadrilateral of widespread cities" for which we CAN find direct airline flight distances to confirm the WorldAtlas distances.

These two approaches would inevitably prove that there is no possible Flat Earth map that can match what the airlines tell us are their flight distances.  And we already demonstrated in STEP 1 that those distances are a very accurate match for their "On time" flight times and for the range and capabilities of real aircraft.

Do you really believe that this data cannot be found?   That WorldAtlas just happens selectively correct for one airline and wildly incorrect for others?

WorldAtlas are not some secret society - there is a list of all of their staff: http://www.worldatlas.com/about.htm

   "We're a group of publishers who delight hundreds of thousands of people every day
    by providing them with access to information at their fingertips. Our flagship web property
    is WorldAtlas.com, the world's oldest and most authoritative geography website."

...don't you think that if their flight distances were HORRIBLY inaccurate for non-Qantas airlines that nobody would have noticed this?

Tom - you ARE going to be boxed in a corner here.

Surely you know that I'll find published airline flight distances that produce the same "quadrilateral problem" that Inquisitive's data produces?   Do you really doubt that this information can be found?

You are 100% certain to come out of this knowing in your heart that you're wrong...that the Earth is not flat...you may continue to flim-flam and deflect - but YOU know that you're doing this rather than honestly facing the facts and following a clear line of evidence to a conclusions which you may not like, but you must know is the truth.   At that point, you'd be a dishonest man...and I don't think you are.

Intellectual honesty must eventually lead you to believe that you've been wrong all this time.

[Curious Squirrel]

Really, you must have a rough idea.  How do ships and planes work out journey times?

There is a theoretical model based on latitudes and longitudes on a Round Earth which supposedly tells us how far away point A should be from point B, and planes use this value in its calculations when guessing its own cruising speed (which may be inaccurate since it is using Round Earth assumptions).

My GPS tells me speed and distance accurately.

And how do you know that the speed and distance is accurate? Even at the scale of a car, the GPS speed is inaccurate when compared to the car's speedometer.

GPS speed is more accurate that a speedometer.  Please give us your method of measurements.

That is what is claimed as an explanation for the difference. But all we really know is that the speeds are different and there are a few explanation floating around to try and explain why. We will need some kind of test independent of looking at your car's speedometer to tell us the accuracy of GPS if a speedometer cannot be relied on at all.

Since the speeds often differ, for whatever reason, the "speed accuracy" argument that GPS is spot-on cannot be used as an argument to say that GPS is correct.

I certainly wouldn't rely on any speed display in a car.   Car speedometers are not 100% precise and because car manufacturers don't want to be sued in the event that their speedometer reads a little too low and someone gets a speeding ticket when their speedometer said that they were within the speed limit.  For this reason almost all cars have speedometers that are DELIBERATELY made to read higher speeds than the car is actually moving.   The same thing happens with GPS units inside cars and those roadside displays that show your speed when you approach them.

But speed isn't the issue here...and neither are cars.

This is about distances between cities...as measured by airlines.  Please - let us not let Mr Bishop deflect the conversation away from areas of discomfort and back into his comfort zone.

So forget cars...they are not important to this calculation.

Tom:

In STEP 1 I established that distances quoted by Qantas airline are 100% credible.  They match the performance of the aircraft and their stated flight times.  Their "on time" record is good enough that their times and distances are 100% trustworthy.

In STEP 2 I demonstrated that the distances produced by the "WorldAtlas" site produces distances that are within 1% of Qantas' distances - and therefore whatever internal math it's using is a very good match for airline distance statements in general.

You used those numbers (without a word of complaint) when you (incorrectly) believed that they supported your Flat Earth Theory and triumphantly quoted them when you THOUGHT they disproved the Round Earth.  As it turns out, this is a clever trap that you fell into.   I wish I was smart enough to have planned it that way...but I'm not.

In STEP 3 I pointed out that simple Euclidean geometry allows us to calculate the internal angles of a PLANAR quadrilateral in two different ways if you know the length of the sides and the diagonals.   If the Earth is flat then those angles will be the same for both calculation methods.

In STEP 4, User "Inquisitive" kindly did the calculations for us - presumably using the (trustworthy) WorldAtlas data for those distances...and discovered that for at least one internal angle of the quadrilateral between New York, Paris, Cape Town & Buenos Aries, there is a HUGE discrepancy...123 degrees versus 162 degrees.

Those four steps are a CLEAR disproof that no possible FLAT Earth map can possibly make the distances between those four cities come out correctly.   It is IMPOSSIBLE to make a planar quadrilateral where those four distances come out right.

Now you're flim-flamming about STEP 2...(which you seemed to trust so long as you thought it proved your theory).   STEP 2 is that we demonstrate that WorldAtlas's software does indeed come out with the correct distances for every route we tested.   I invite you to test it for as many other routes and as many other airlines as you like...the answer will always be the same.

So - what you resort to is the rather pathetic complaint that there are no direct flights between some of those four cities with which we could back up the WorldAtlas distances between them.   I would also point out that if you go to Google Maps - and enter those same cities and ask for an route BY AIRPLANE - it comes out with very similar numbers...within 1%.

What that means is that you must either believe that:

1) WorldAtlas, and Google are a part of the global conspiracy and that their software produces distances that match those of Qantas flights - but are deliberately incorrect for the four cities that Inquisitive just happened to pick...OR...

2) WorldAtlas produces incorrect distances by accident but just happens to produce very good distances for all of the Qantas routes.

OK - well, we can test your two theories with some more experiments.

FIRSTLY:  We can find a bunch more "quadrilaterals of widespread cities"...and demonstrate that NONE of the distances between them work in FET.  This would be good evidence that Inquisitive didn't "cherry pick" four cities that didn't include a route for which WorldAtlas' data is incorrect.

SECONDLY: We can find a "quadrilateral of widespread cities" for which we CAN find direct airline flight distances to confirm the WorldAtlas distances.

These two approaches would inevitably prove that there is no possible Flat Earth map that can match what the airlines tell us are their flight distances.  And we already demonstrated in STEP 1 that those distances are a very accurate match for their "On time" flight times and for the range and capabilities of real aircraft.

Do you really believe that this data cannot be found?   That WorldAtlas just happens selectively correct for one airline and wildly incorrect for others?

WorldAtlas are not some secret society - there is a list of all of their staff: http://www.worldatlas.com/about.htm

   "We're a group of publishers who delight hundreds of thousands of people every day
    by providing them with access to information at their fingertips. Our flagship web property
    is WorldAtlas.com, the world's oldest and most authoritative geography website."

...don't you think that if their flight distances were HORRIBLY inaccurate for non-Qantas airlines that nobody would have noticed this?

Tom - you ARE going to be boxed in a corner here.

Surely you know that I'll find published airline flight distances that produce the same "quadrilateral problem" that Inquisitive's data produces?   Do you really doubt that this information can be found?

You are 100% certain to come out of this knowing in your heart that you're wrong...that the Earth is not flat...you may continue to flim-flam and deflect - but YOU know that you're doing this rather than honestly facing the facts and following a clear line of evidence to a conclusions which you may not like, but you must know is the truth.   At that point, you'd be a dishonest man...and I don't think you are.

Intellectual honesty must eventually lead you to believe that you've been wrong all this time.

Damn, I had managed to completely miss the implications between step 1 & 2 somehow. Now I feel like a dunce. Thanks for the great summation 3DGeek, I knew you were going somewhere great with all of this and I wish I had 100% grasped to where and from where that the first go round. XD

Also thank you for getting us fully back on track with a very useful post. Now back to Tom.

[3DGeek]

Damn, I had managed to completely miss the implications between step 1 & 2 somehow. Now I feel like a dunce. Thanks for the great summation 3DGeek, I knew you were going somewhere great with all of this and I wish I had 100% grasped to where and from where that the first go round. XD

Also thank you for getting us fully back on track with a very useful post. Now back to Tom.

Indeed.  The thing here is to produce a "chain of evidence".   If someone wishes to dispute some weak step in the chain - then we can re-visit that step and strengthen it with more evidence.   Unfortunately, describing each step does tend to get a little "wordy".   So the idea is to provide a short summary of the steps (there are only four) - and if anyone wishes to dispute any of those steps, then there will be a longer post that elaborates and provides references for it.

* Find an authoritative list of distances between known points on the Earth (Steps 1 & 2).
* Use Euclidean geometry to show that those distances are (or are not) consistent with a flat plane over widespread places (Steps 3 and 4).

The second part is easy - It's impossible deny Euclids proofs for geometry on a plane or dispute the veracity of the cosine theorem.

If the Earth's surface does not obey Euclidean geometry, it cannot be flat.

[3DGeek]

I can't find any New York to Paris flights, or New York to Buenos Airies flights, or New York to Cape Town flights on https://www.qantas.com/travel/airlines/route-maps/global/en. Please provide your sources.

http://onw.innosked.com/(S(mizq3vf4cnmfklzngbi0u5kt))/default.aspx?show=MAP

(You have to be sure to click the "Sort By" button and select "Number of Stops" and only use the "Non-stop" results!)

So, for example - if you click on Paris - it shows flight distances to three different NY airports as 5,840km, 5,861lm and 5,829km...all pretty close to the 5,834km number that Inquisitive used.

Sorry - I don't have more time to work on this today - but I will certainly produce a "city quadrilateral" using data that can be backed up directly from the airlines when I have free time available.

(You already know how this is going to turn out...right?)

[BigFatRoundEarther]

I pulled FE map from this site and attached an example of why the FE map simply doesn't work.  Basically a flight to JNB to NBO is 4 hours and a flight from JNB to SYD is 12 hours (3x).  Yet the distance from JNB to SYD is at least 7x as long per the FE map.  The flight route to Sydney would actually be much longer as we know flights from South Africa to Sydney go over the ocean (not Asia).  Sorry about image quality (limited by Forum). 

[TomInAustin]

I certainly wouldn't rely on any speed display in a car.   Car speedometers are not 100% precise.  Because car manufacturers don't want to be sued in the event that their speedometer reads a little too low and someone gets a speeding ticket when their speedometer said that they were within the speed limit.  For this reason almost all cars have speedometers that are DELIBERATELY made to read higher speeds than the car is actually moving...the precise amount varies between cars.  BMW say that their speedometers are designed to read "high" by 5mph or 2.5% whichever is less.  The same thing happens with GPS units built into cars and those roadside displays that show your speed when you approach them.  Cars also go up and down hills - which means that the distance on the odometer doesn't match the distance as drawn on a map.  The four wheels of the car rotate at different rates as you go around curves - and if the speedometer takes the speed from just one of them - then it'll either read faster or slower than the true speed of the car itself.   So, yeah - car speedometers suck.  People don't believe it - so there is a ton of Internet debate on the subject.   GPS is remarkably accurate though...within 10 feet if the receiver can pick up 3 satellites - better than that if it can 'see' 4 of them.

But speed isn't the issue here...and neither are cars.

This is about distances between cities...as measured by airlines.  Please - let us not let Mr Bishop deflect the conversation away from areas of discomfort and back into his comfort zone.

So forget cars...they are not important to this calculation.

Tom:

In STEP 1 I established that distances quoted by Qantas airline are 100% credible.  They match the performance of the aircraft and their stated flight times.  Their "on time" record is good enough that their times and distances are 100% trustworthy.

In STEP 2 I demonstrated that the distances produced by the "WorldAtlas" site produces distances that are within 1% of Qantas' distances - and therefore whatever internal math it's using is a very good match for airline distance statements in general.

You used those numbers (without a word of complaint) when you (incorrectly) believed that they supported your Flat Earth Theory and triumphantly quoted them when you THOUGHT they disproved the Round Earth.  As it turns out, this is a clever trap that you fell into.   I wish I was smart enough to have planned it that way...but I'm not.

In STEP 3 I pointed out that simple Euclidean geometry allows us to calculate the internal angles of a PLANAR quadrilateral in two different ways if you know the length of the sides and the diagonals.   If the Earth is flat then those angles will be the same for both calculation methods.

In STEP 4, User "Inquisitive" kindly did the calculations for us - presumably using the (trustworthy) WorldAtlas data for those distances...and discovered that for at least one internal angle of the quadrilateral between New York, Paris, Cape Town & Buenos Aries, there is a HUGE discrepancy...123 degrees versus 162 degrees.

Those four steps are a CLEAR disproof that no possible FLAT Earth map can possibly make the distances between those four cities come out correctly.   It is IMPOSSIBLE to make a planar quadrilateral where those four distances come out right.

Now you're flim-flamming about STEP 2...(which you seemed to trust so long as you thought it proved your theory).   STEP 2 is that we demonstrate that WorldAtlas's software does indeed come out with the correct distances for every route we tested.   I invite you to test it for as many other routes and as many other airlines as you like...the answer will always be the same.

So - what you resort to is the rather pathetic complaint that there are no direct flights between some of those four cities with which we could back up the WorldAtlas distances between them.   I would also point out that if you go to Google Maps - and enter those same cities and ask for an route BY AIRPLANE - it comes out with very similar numbers...within 1%.

What that means is that you must either believe that:

1) WorldAtlas, and Google are a part of the global conspiracy and that their software produces distances that match those of Qantas flights - but are deliberately incorrect for the four cities that Inquisitive just happened to pick...OR...

2) WorldAtlas produces incorrect distances by accident but just happens to produce very good distances for all of the Qantas routes.

OK - well, we can test your two theories with some more experiments.

FIRSTLY:  We can find a bunch more "quadrilaterals of widespread cities"...and demonstrate that NONE of the distances between them work in FET.  This would be good evidence that Inquisitive didn't "cherry pick" four cities that didn't include a route for which WorldAtlas' data is incorrect.

SECONDLY: We can find a "quadrilateral of widespread cities" for which we CAN find direct airline flight distances to confirm the WorldAtlas distances.

These two approaches would inevitably prove that there is no possible Flat Earth map that can match what the airlines tell us are their flight distances.  And we already demonstrated in STEP 1 that those distances are a very accurate match for their "On time" flight times and for the range and capabilities of real aircraft.

Do you really believe that this data cannot be found?   That WorldAtlas just happens selectively correct for one airline and wildly incorrect for others?

WorldAtlas are not some secret society - there is a list of all of their staff: http://www.worldatlas.com/about.htm

   "We're a group of publishers who delight hundreds of thousands of people every day
    by providing them with access to information at their fingertips. Our flagship web property
    is WorldAtlas.com, the world's oldest and most authoritative geography website."

...don't you think that if their flight distances were HORRIBLY inaccurate for non-Qantas airlines that nobody would have noticed this?

Tom - you ARE going to be boxed in a corner here.

Surely you know that I'll find published airline flight distances that produce the same "quadrilateral problem" that Inquisitive's data produces?   Do you really doubt that this information can be found?

You are 100% certain to come out of this knowing in your heart that you're wrong...that the Earth is not flat...you may continue to flim-flam and deflect - but YOU know that you're doing this rather than honestly facing the facts and following a clear line of evidence to a conclusions which you may not like, but you must know is the truth.   At that point, you'd be a dishonest man...and I don't think you are.

Intellectual honesty must eventually lead you to believe that you've been wrong all this time.

This exercise should be iron clad proof to anyone with an ability to comprehend math and geometry.   Knowing the size and shape of each continent, it would be simple to arrange the pieces in such a way to create a flat map using known distances if one were possible.   

But, I would bet this will fall on deaf ears becuse... reasons.

[TomInAustin]

Damn, I had managed to completely miss the implications between step 1 & 2 somehow. Now I feel like a dunce. Thanks for the great summation 3DGeek, I knew you were going somewhere great with all of this and I wish I had 100% grasped to where and from where that the first go round. XD

Also thank you for getting us fully back on track with a very useful post. Now back to Tom.

Indeed.  The thing here is to produce a "chain of evidence".   If someone wishes to dispute some weak step in the chain - then we can re-visit that step and strengthen it with more evidence.   Unfortunately, describing each step does tend to get a little "wordy".   So the idea is to provide a short summary of the steps (there are only four) - and if anyone wishes to dispute any of those steps, then there will be a longer post that elaborates and provides references for it.

* Find an authoritative list of distances between known points on the Earth (Steps 1 & 2).
* Use Euclidean geometry to show that those distances are (or are not) consistent with a flat plane over widespread places (Steps 3 and 4).

The second part is easy - It's impossible deny Euclids proofs for geometry on a plane or dispute the veracity of the cosine theorem.

If the Earth's surface does not obey Euclidean geometry, it cannot be flat.

Linking to this thread will be very useful for newcomers to the site.  They are always asking for proof and this is well... proof.   

I will try and get some time free to provide an example or 2 myself. 

[TomInAustin]

Really, you must have a rough idea.  How do ships and planes work out journey times?

There is a theoretical model based on latitudes and longitudes on a Round Earth which supposedly tells us how far away point A should be from point B, and planes use this value in its calculations when guessing its own cruising speed (which may be inaccurate since it is using Round Earth assumptions).

My GPS tells me speed and distance accurately.

And how do you know that the speed and distance is accurate? Even at the scale of a car, the GPS speed is inaccurate when compared to the car's speedometer.

GPS speed is more accurate that a speedometer.  Please give us your method of measurements.

That is what is claimed as an explanation for the difference. But all we really know is that the speeds are different and there are a few explanation floating around to try and explain why. We will need some kind of test independent of looking at your car's speedometer to tell us the accuracy of GPS if a speedometer cannot be relied on at all.

Since the speeds often differ, for whatever reason, the "speed accuracy" argument that GPS is spot-on cannot be used as an argument to say that GPS is correct.

Consumer GPS is not 100% accurate.  But over thousands of miles, it is close enough.  Rounding error will not get you out of the corner you painted yourself into.  You displayed rounding error in you flawed attempt with math.  I bet you didn't see this coming.

The United States government currently claims 4 meter RMS (7.8 meter 95% Confidence Interval) horizontal accuracy for civilian (SPS) GPS. Vertical accuracy is worse. Mind you, that's the minimum. Some devices/locations reliably (95% of the time or better) can get 3 meter accuracy.Dec 10, 2012

[inquisitive]

Really, you must have a rough idea.  How do ships and planes work out journey times?

There is a theoretical model based on latitudes and longitudes on a Round Earth which supposedly tells us how far away point A should be from point B, and planes use this value in its calculations when guessing its own cruising speed (which may be inaccurate since it is using Round Earth assumptions).

My GPS tells me speed and distance accurately.

And how do you know that the speed and distance is accurate? Even at the scale of a car, the GPS speed is inaccurate when compared to the car's speedometer.

GPS speed is more accurate that a speedometer.  Please give us your method of measurements.

That is what is claimed as an explanation for the difference. But all we really know is that the speeds are different and there are a few explanation floating around to try and explain why. We will need some kind of test independent of looking at your car's speedometer to tell us the accuracy of GPS if a speedometer cannot be relied on at all.

Since the speeds often differ, for whatever reason, the "speed accuracy" argument that GPS is spot-on cannot be used as an argument to say that GPS is correct.

Consumer GPS is not 100% accurate.  But over thousands of miles, it is close enough.  Rounding error will not get you out of the corner you painted yourself into.  You displayed rounding error in you flawed attempt with math.  I bet you didn't see this coming.

The United States government currently claims 4 meter RMS (7.8 meter 95% Confidence Interval) horizontal accuracy for civilian (SPS) GPS. Vertical accuracy is worse. Mind you, that's the minimum. Some devices/locations reliably (95% of the time or better) can get 3 meter accuracy.Dec 10, 2012

WRONG.  GPS is not a case of percent accurate.  It is about the accuracy of a particular location.

[TomInAustin]

Really, you must have a rough idea.  How do ships and planes work out journey times?

There is a theoretical model based on latitudes and longitudes on a Round Earth which supposedly tells us how far away point A should be from point B, and planes use this value in its calculations when guessing its own cruising speed (which may be inaccurate since it is using Round Earth assumptions).

My GPS tells me speed and distance accurately.

And how do you know that the speed and distance is accurate? Even at the scale of a car, the GPS speed is inaccurate when compared to the car's speedometer.

GPS speed is more accurate that a speedometer.  Please give us your method of measurements.

That is what is claimed as an explanation for the difference. But all we really know is that the speeds are different and there are a few explanation floating around to try and explain why. We will need some kind of test independent of looking at your car's speedometer to tell us the accuracy of GPS if a speedometer cannot be relied on at all.

Since the speeds often differ, for whatever reason, the "speed accuracy" argument that GPS is spot-on cannot be used as an argument to say that GPS is correct.

Consumer GPS is not 100% accurate.  But over thousands of miles, it is close enough.  Rounding error will not get you out of the corner you painted yourself into.  You displayed rounding error in you flawed attempt with math.  I bet you didn't see this coming.

The United States government currently claims 4 meter RMS (7.8 meter 95% Confidence Interval) horizontal accuracy for civilian (SPS) GPS. Vertical accuracy is worse. Mind you, that's the minimum. Some devices/locations reliably (95% of the time or better) can get 3 meter accuracy.Dec 10, 2012

WRONG.  GPS is not a case of percent accurate.  It is about the accuracy of a particular location.

That's what my quote said, it can be off by a few meters and that can skew speed readouts.  Hence the "not 100% accurate" statement.

[inquisitive]

Really, you must have a rough idea.  How do ships and planes work out journey times?

There is a theoretical model based on latitudes and longitudes on a Round Earth which supposedly tells us how far away point A should be from point B, and planes use this value in its calculations when guessing its own cruising speed (which may be inaccurate since it is using Round Earth assumptions).

My GPS tells me speed and distance accurately.

And how do you know that the speed and distance is accurate? Even at the scale of a car, the GPS speed is inaccurate when compared to the car's speedometer.

GPS speed is more accurate that a speedometer.  Please give us your method of measurements.

That is what is claimed as an explanation for the difference. But all we really know is that the speeds are different and there are a few explanation floating around to try and explain why. We will need some kind of test independent of looking at your car's speedometer to tell us the accuracy of GPS if a speedometer cannot be relied on at all.

Since the speeds often differ, for whatever reason, the "speed accuracy" argument that GPS is spot-on cannot be used as an argument to say that GPS is correct.

'We' know how to measure speeds and distances with known accuracy.  You and yours have not shown any interest in providing anything to disprove that.

[3DGeek]

I pulled FE map from this site and attached an example of why the FE map simply doesn't work.  Basically a flight to JNB to NBO is 4 hours and a flight from JNB to SYD is 12 hours (3x).  Yet the distance from JNB to SYD is at least 7x as long per the FE map.  The flight route to Sydney would actually be much longer as we know flights from South Africa to Sydney go over the ocean (not Asia).  Sorry about image quality (limited by Forum).

Yes - I think it's very clear that THIS flat earth map doesn't work.  But you're missing the importance of this thread.

Some FE'ers (notably Tom) have put up alternative maps...and when challenged about these new maps, Tom (and others) has frequently responded that these maps are all tentative and that the FE'ers admit that they don't know for sure how the REAL Flat Earth continents are laid out.

I presume that they hope that this will deflect all problems of the kind you just gave under a layer of uncertainty...."Well, we know THIS map isn't perfect - but we're not finished with drawing the perfect FE map."...they fondly imagine that this is a sneaky way to avoid answering these "flight distance" problems.

HOWEVER

I'm not letting them get away with that.

The significance of THIS thread is that it proves that no possible flat earth map can EVER reconcile all of the distances given to us by airlines for their route distances.

So not just the map on the Wiki - not just Tom's new map - this thread clearly demonstrates that there is NO POSSIBLE flat map that can get the distances between four widely-separated cities right.

It constitutes definite proof that Flat Earth theory is wrong...AND that it can't possibly be fixed by redrawing their maps because this proof doesn't rely on their maps...instead it says that you can't resolve these distances between cities no matter how you juggle them around.

Cool or what?!   :-)

[geckothegeek]

A few observations.

Flat Earth Maps :
Amongst the only things I have read and seen from flat eathers on the subject of "A Flat Earth Maps" are :
(1) There is no flat earth map.
(2) We haven't had time to develop a flat earth map, but we're working on it.
(3) The Unipolar Azimuthal Equidistant Projection (of the globe)(with the ice ring) is the flat earth map.
(4) The Bipolar Map (according to Tom Bishop)                                                           "   "      "       "         "

Mileage and Speed Readings on cars  :
I have checked the mileage readings on the car's trip odometer against Mile Markers and the results were the same.
I have checked the speed on a level road at 60 MPH between Mile Markers by using a stop watch with the same results.

If a flat earther asks the usual question "Did you do this yourself and observe it yourself ? "
The answer is  "Yes ! I have done it many times on I-40 in Texas, New Mexico, Arizona and California."

Both checks proved they were reasonably acccurate.

[geckothegeek]

I pulled FE map from this site and attached an example of why the FE map simply doesn't work.  Basically a flight to JNB to NBO is 4 hours and a flight from JNB to SYD is 12 hours (3x).  Yet the distance from JNB to SYD is at least 7x as long per the FE map.  The flight route to Sydney would actually be much longer as we know flights from South Africa to Sydney go over the ocean (not Asia).  Sorry about image quality (limited by Forum).

Yes - I think it's very clear that THIS flat earth map doesn't work.  But you're missing the importance of this thread.

Some FE'ers (notably Tom) have put up alternative maps...and when challenged about these new maps, Tom (and others) has frequently responded that these maps are all tentative and that the FE'ers admit that they don't know for sure how the REAL Flat Earth continents are laid out.

I presume that they hope that this will deflect all problems of the kind you just gave under a layer of uncertainty...."Well, we know THIS map isn't perfect - but we're not finished with drawing the perfect FE map."...they fondly imagine that this is a sneaky way to avoid answering these "flight distance" problems.

HOWEVER

I'm not letting them get away with that.

The significance of THIS thread is that it proves that no possible flat earth map can EVER reconcile all of the distances given to us by airlines for their route distances.

So not just the map on the Wiki - not just Tom's new map - this thread clearly demonstrates that there is NO POSSIBLE flat map that can get the distances between four widely-separated cities right.

It constitutes definite proof that Flat Earth theory is wrong...AND that it can't possibly be fixed by redrawing their maps because this proof doesn't rely on their maps...instead it says that you can't resolve these distances between cities no matter how you juggle them around.

Cool or what?!   :-)

Cool enough  ! :-)  They jist ain't no flat earth map cuz the earth ain't flat ! :-)