The Flat Earth Society
Flat Earth Discussion Boards => Flat Earth Investigations => Topic started by: robinofloxley on November 01, 2018, 03:14:31 PM
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One of the problems with flat earth discussions is that there is no consensus behind any particular flat map, however the one thing I assume everyone does agree on is that whatever it looks like, it will be flat.
On any flat surface, there can only be one shortest route between any two points - a straight line - and therefore only ever one sensible direction of travel if you want to get to your destination via the shortest route.
On a sphere, the shortest route between two points is a great circle arc and in general there is only one great circle passing through both points and hence one shortest route. The exception occurs when the two points are antipodal (directly opposite each other). In this case many great circle routes are possible so there is no longer a single shortest route, there are many.
So for example, on a globe earth, the UK and New Zealand are almost antipodal, therefore you can head off in any direction you like from the UK, follow a great circle route for about 12500 miles and you will be more or less in New Zealand. On a globe travelling in opposite directions yet ending up in the same place makes perfect sense, on a flat earth it doesn't.
In reality, from the UK, I can fly west via Los Angeles to New Zealand or I can fly east via Tokyo and there are plenty of other routes to choose from such as via Hong Kong, Dubai, Manilla etc. These routes all have similar flight durations and cost similar amounts of money.
Anyone care to try and explain?
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There is a chapter on Great Circle Sailing (http://www.sacred-texts.com/earth/za/za47.htm) in Earth Not a Globe.
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There is a chapter on Great Circle Sailing (http://www.sacred-texts.com/earth/za/za47.htm) in Earth Not a Globe.
The problem with Rowbotham's chapter is that his presumption is that pretty much all forms of transport are and have been navigating incorrectly for centuries. As in Great Circles versus Rhumb Lines. A flight from JFK to Heathrow follows a great circle, not a rhumb line. And I highly suspect shipping and airliners of the world would prefer the shortest route for myriad reasons, most notably cost versus profit.
Here's what a simplistic view of a typical flight path looks like on a great circle versus a rhumb line, seems counter-intuitive if the world was flat:
(http://www.geo.upm.es/postgrado/CarlosLopez/materiales/cursos/www.ncgia.ucsb.edu/education/curricula/giscc/units/u014/figures/figure06.gif)
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Paint the red route on the AE map.
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There is a chapter on Great Circle Sailing (http://www.sacred-texts.com/earth/za/za47.htm) in Earth Not a Globe.
OK thanks for the link, I read through that and a lot of it seems more to do with the practicalities of 19th C sailing, so I'm not really clear whether Rowbotham is actually claiming that there is a shorter distance on a sphere (not talking about the Earth here, just a plain old sphere) than a great circle distance. If he is claiming that, then it begs the question - what is this shorter route?
Put plainly, on a sphere, is the shortest distance between any two points a great circle distance or not?
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Paint the red route on the AE map.
Which AE map?
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Paint the red route on the AE map.
Which AE map?
I am gauging from your response that you have seen your error. We need not discuss the matter further.
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Paint the red route on the AE map.
Which AE map?
I am gauging from your response that you have seen your error. We need not discuss the matter further.
I think the matter is best served by discussing it further. In classic zetetic fashion, one should sail these routes, and bring the resulting data to this forum. Until you do so, you are simply appealing to an authority without personal evidence. That is not zetetic, but instead is exactly what FEers accuse REers of doing: believing some source without personal verification.
Hence, Rowbotham citations are no more valid than any other RE citation. True zetetic methods insist that one discards Rowbotham claims (or any other claims), until personally verified.
We do adhere to zetetic methods, yes? That is the whole point, yes?
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Paint the red route on the AE map.
Which AE map?
I am gauging from your response that you have seen your error. We need not discuss the matter further.
I think the matter is best served by discussing it further.
Feel free to draw the route on the AE map and I will discuss it with you.
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Paint the red route on the AE map.
Which AE map?
I am gauging from your response that you have seen your error. We need not discuss the matter further.
A few things:
1) As you know, an AE map is a globe projection that can be centered on any point on earth.
2) You have previously stated, you don't subscribe to the FE mono-pole "model", but to the bi-polar "model". Hence my question. But I presume you mean one centered on the north pole. As in the FE mono-pole model.
3) Since all AE maps are globe projections, there is no such thing as an FE map as you have stated yourself many times. So using an FE earth map is moot, b/c one doesn't exist.
Moving on.
Comparing rhumb line to great circle navigation, using JFK to Heathrow, rhumb line is 219km more than a great circle.
Comparing rhumb line to great circle navigation, using Cape Town to Sydney, rhumb line is 1240km more than a great circle.
(https://i.imgur.com/Kf9wvdG.jpg)
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Paint the red route on the AE map.
Which AE map?
I am gauging from your response that you have seen your error. We need not discuss the matter further.
I think the matter is best served by discussing it further.
Feel free to draw the route on the AE map and I will discuss it with you.
Do you ever NOT pass the buck? Or is your position always one of retreat? That is not a response of strength.
Anyway, see above. The lines have been drawn (as it were).
So go ahead and discuss it. If you have the nerve.
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Maybe you should submit your queries to a repeating-Mercator Flat Earth group. We use none of those models.
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Do you ever NOT pass the buck? Or is your position always one of retreat? That is not a response of strength.
Anyway, see above. The lines have been drawn (as it were).
So go ahead and discuss it. If you have the nerve.
If you have nothing to add to the thread beyond asking other people to do your homework for you, then I will kindly ask that you refrain from posting in the upper fora. You are teetering on the edge of a permanent ban; you may want to stop being your normal charming self for a while.
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Maybe you should submit your queries to a repeating-Mercator Flat Earth group. We use none of those models.
I guess a couple of more things:
- I wasn't aware this was the Azimuthal Equidistant Flat Earth Society.
- You yourself have stated many times that there is no Flat Earth map.
- And FE really doesn't have a "model". The two main contenders are the mono-pole and the bipolar. But as you stated the other day, in FET, the layout of the continents is unknown.
Given the above, why do you have an issue with one projection over the other? FE doesn't have a map, AE, Mercator or otherwise and all the maps we do have are Globe projections. The mercator projection is especially well suited for Rhumb Line plotting for short distances. As well the mercator projection is the most widely used map for the bulk of all sea, air, and land transport and has been for a couple 100 years. And seems to do quite a good job.
So I don't think you really have a point to make. Regardless of map projection or model, you just simply have a problem arguing against widely used great circle navigation versus Rowbotham's "all the world's navigation is wrong as everyone should actually be using rhumb lines" notion.
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Paint the red route on the AE map.
Or. Construct a flat earth map using known distances. The global transport industry is reliable enough to have confidence in their data.
Two possibilities:
1) You succeed and become the first flat earther to successfully construct an accurate flat earth map
2) You can't and realise that the earth can't be flat.
Obviously the 3rd option is to claim that a global industry which reliably gets people and goods around the world don't know how far places are apart of how fast their vessels move. Although quite how they run their businesses without that information is a mystery.
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I'm still keen to get an answer to the original point which is that if I'm travelling between say UK and New Zealand, on a globe I believe I can head off in any direction I like, following a great circle route for 12500 miles and I will arrive at my desired destination. Does anyone disagree that if we are on a globe, that assertion would hold true?
The only assumption being made is that a great circle distance is the shortest distance between any two points on a sphere and that flights on a globe would presumably follow such routes where practicable (and with minor adjustments for weather) for efficiency. Is there agreement on this or not?
I've read Tom's ENAG link and I'm not clear at all whether Rowbottom is disputing that a great circle distance is always the shortest on a sphere or if he's simply saying sailors in the 19th C and earlier aren't sailing great circle routes so that means we're not on a globe.
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VBA code for anyone interested. Calculates distance between two points using different assumptions about the shape of the earth
See also this thread where the code was used to plot flight times against predicted distance.
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'enter latitude and longitude for the two points, in degrees (not radians)
'Calculates the distance between the two points on the assumption that the earth is spherical
Function haversine(lat1 As Double, long1 As Double, lat2 As Double, long2 As Double)
Dim x As Double, r As Double
r = 6371#
'convert to radians
lat1 = lat1 * WorksheetFunction.Pi() / 180
long1 = long1 * WorksheetFunction.Pi() / 180
lat2 = lat2 * WorksheetFunction.Pi() / 180
long2 = long2 * WorksheetFunction.Pi() / 180
haversine = 2 * r * WorksheetFunction.Asin(Sqr((1 - Cos(lat2 - lat1)) / 2# + Cos(lat1) * Cos(lat2) * (1 - Cos(long2 - long1)) / 2#))
End Function
'enter latitude and longitude for the two points, in degrees (not radians)
'Calculates the distance between the two points on the AE map
Function FEdistance(lat1 As Double, long1 As Double, lat2 As Double, long2 As Double)
Dim l1 As Double, l2 As Double, l3 As Double, a1 As Double, l4 As Double, h1 As Double
l1 = (90 - WorksheetFunction.Max(lat1, lat2)) * 111.19
a1 = (long2 - long1) * WorksheetFunction.Pi() / 180
h1 = Sin(a1) * l1
l2 = Cos(a1) * l1
l3 = (90 - WorksheetFunction.Min(lat1, lat2)) * 111.19
l4 = l3 - l2
FEdistance = Sqr(l4 ^ 2 + h1 ^ 2)
End Function
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I'm still keen to get an answer to the original point which is that if I'm travelling between say UK and New Zealand, on a globe I believe I can head off in any direction I like
I don't think you can head in any direction you like. Only one great circle passes through any two points, and the haversine formula above gives you the distance along that great circle.
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I'm still keen to get an answer to the original point which is that if I'm travelling between say UK and New Zealand, on a globe I believe I can head off in any direction I like
I don't think you can head in any direction you like. Only one great circle passes through any two points, and the haversine formula above gives you the distance along that great circle.
Hmm. But if those points are antipodal then you pretty much can, can't you? Imagine the two poles, if you're standing at the North Pole you can follow any line of Longitude you like and you'll end up at the South Pole.
Obviously when it comes to flights there are practical considerations like where there is a conveniently placed airport part of the way and when you take a flight with a stop over that stop over is unlikely to be exactly on the great circle between the two places.
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I'm still keen to get an answer to the original point which is that if I'm travelling between say UK and New Zealand, on a globe I believe I can head off in any direction I like
I don't think you can head in any direction you like. Only one great circle passes through any two points, and the haversine formula above gives you the distance along that great circle.
Hmm. But if those points are antipodal then you pretty much can, can't you? Imagine the two poles, if you're standing at the North Pole you can follow any line of Longitude you like and you'll end up at the South Pole.
Obviously when it comes to flights there are practical considerations like where there is a conveniently placed airport part of the way and when you take a flight with a stop over that stop over is unlikely to be exactly on the great circle between the two places.
Ah yes, and that's exactly what I'm trying to get at. UK to New Zealand flights do in fact offer a very wide choice of conveniently placed airports serving as stopovers in very different locations across the globe, from North America (e.g. Los Angeles) through the Middle East (e.g Dubai) and the far east (e.g. Tokyo).
I don't agree that...
when you take a flight with a stop over that stop over is unlikely to be exactly on the great circle between the two places.
On the contrary, because the two endpoints are antipodal then there must always exist one great circle route which passes through both the endpoints and the stopover. Only one great circle passes through the departure and stopover and only one through the stopover and destination, so they must be one and the same great circle.
Put it another way. Pick any two non-antipodal points A and B and there is one great circle route between them. Extend that route all the way round and you must necessarily pass through the antipodal points of both A and B.
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On the contrary, because the two endpoints are antipodal then there must always exist one great circle route which passes through both the endpoints and the stopover. Only one great circle passes through the departure and stopover and only one through the stopover and destination, so they must be one and the same great circle.
Still don't follow. Suppose I travel down the meridian (0 longitude) from London A to some point on the equator B. Then suppose I travel along the equator (which is another great circle) to somewhere else C. It clearly doesn't follow that ABC is 'one and the same great circle'. Clearly there is a third great circle AC, but B does not lie on it.
Perhaps I misunderstand.
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Maybe you should submit your queries to a repeating-Mercator Flat Earth group. We use none of those models.
Perhaps.
Perhaps maybe you should just try to answer a question honestly.
Mercator methods are un-zetetic, because they forfeit basic calculus to find their answers. Perhaps that is why you do not like them.
So rather than shine the lampshade-Sun onto models you don't believe in, would it not be more productive to emphasize the models you do champion?
I invite you.
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On the contrary, because the two endpoints are antipodal then there must always exist one great circle route which passes through both the endpoints and the stopover. Only one great circle passes through the departure and stopover and only one through the stopover and destination, so they must be one and the same great circle.
Still don't follow. Suppose I travel down the meridian (0 longitude) from London A to some point on the equator B. Then suppose I travel along the equator (which is another great circle) to somewhere else C. It clearly doesn't follow that ABC is 'one and the same great circle'. Clearly there is a third great circle AC, but B does not lie on it.
Perhaps I misunderstand.
I think it's more likely that I'm not explaining this very well. I'll have another go.
In your example you have points A, B and C, but you don't have two antipodal points and that difference is crucial. So let's fix that and make A and C antipodal.
Travel down the meridian (0 longitude) as you did before to get to B (on the equator). Now you need to head for C, but C is constrained to be directly opposite A, which means it must also be on the 0 longitude line somewhere, so basically you just carry on in the same direction until you get to C.
Hope that helps.
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On the contrary, because the two endpoints are antipodal then there must always exist one great circle route which passes through both the endpoints and the stopover. Only one great circle passes through the departure and stopover and only one through the stopover and destination, so they must be one and the same great circle.
Still don't follow. Suppose I travel down the meridian (0 longitude) from London A to some point on the equator B. Then suppose I travel along the equator (which is another great circle) to somewhere else C. It clearly doesn't follow that ABC is 'one and the same great circle'. Clearly there is a third great circle AC, but B does not lie on it.
Perhaps I misunderstand.
I think it's more likely that I'm not explaining this very well. I'll have another go.
In your example you have points A, B and C, but you don't have two antipodal points and that difference is crucial. So let's fix that and make A and C antipodal.
Travel down the meridian (0 longitude) as you did before to get to B (on the equator). Now you need to head for C, but C is constrained to be directly opposite A, which means it must also be on the 0 longitude line somewhere, so basically you just carry on in the same direction until you get to C.
Hope that helps.
Yes it does. I was reading 'antipodal' as meaning 'in the antipodes'. You see my mistake.
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Maybe you should submit your queries to a repeating-Mercator Flat Earth group. We use none of those models.
Perhaps.
Perhaps maybe you should just try to answer a question honestly.
Mercator methods are un-zetetic, because they forfeit basic calculus to find their answers. Perhaps that is why you do not like them.
So rather than shine the lampshade-Sun onto models you don't believe in, would it not be more productive to emphasize the models you do champion?
I invite you.
Draw the lines of the images presented in this thread on any of the maps or models we present and you will see your error.
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Maybe you should submit your queries to a repeating-Mercator Flat Earth group. We use none of those models.
Perhaps.
Perhaps maybe you should just try to answer a question honestly.
Mercator methods are un-zetetic, because they forfeit basic calculus to find their answers. Perhaps that is why you do not like them.
So rather than shine the lampshade-Sun onto models you don't believe in, would it not be more productive to emphasize the models you do champion?
I invite you.
Draw the lines of the images presented in this thread on any of the maps or models we present and you will see your error.
Please give links to some of your maps.
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Please give links to some of your maps.
You have been registered on this website for almost 5 years. Why are you guys resorting to delay tactics?
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Maybe you should submit your queries to a repeating-Mercator Flat Earth group. We use none of those models.
Perhaps.
Perhaps maybe you should just try to answer a question honestly.
Mercator methods are un-zetetic, because they forfeit basic calculus to find their answers. Perhaps that is why you do not like them.
So rather than shine the lampshade-Sun onto models you don't believe in, would it not be more productive to emphasize the models you do champion?
I invite you.
Draw the lines of the images presented in this thread on any of the maps or models we present and you will see your error.
Continue to dodge the question, if you must. But if you wish to be honest; if the truth matters to you, then you will draw the lines as shown above, compare them to data, and will immediately see your error.
But you probably won't do this. Such an act is too zetetic for you to swallow. But others reading this post might do it. When they do, they will see a result that I have transparently offered, but which you have tried to hide.
Ouch!
True zetetic process leads to one conclusion: modern scientific thought.
The extent to which you deny this is the extend to which you depart from true zetetic practice.
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On the contrary, because the two endpoints are antipodal then there must always exist one great circle route which passes through both the endpoints and the stopover. Only one great circle passes through the departure and stopover and only one through the stopover and destination, so they must be one and the same great circle.
Still don't follow. Suppose I travel down the meridian (0 longitude) from London A to some point on the equator B. Then suppose I travel along the equator (which is another great circle) to somewhere else C. It clearly doesn't follow that ABC is 'one and the same great circle'. Clearly there is a third great circle AC, but B does not lie on it.
Perhaps I misunderstand.
I think it's more likely that I'm not explaining this very well. I'll have another go.
In your example you have points A, B and C, but you don't have two antipodal points and that difference is crucial. So let's fix that and make A and C antipodal.
Travel down the meridian (0 longitude) as you did before to get to B (on the equator). Now you need to head for C, but C is constrained to be directly opposite A, which means it must also be on the 0 longitude line somewhere, so basically you just carry on in the same direction until you get to C.
Hope that helps.
Yes it does. I was reading 'antipodal' as meaning 'in the antipodes'. You see my mistake.
Yes indeed, sorry - I could probably have explained better.
Now we're on the same page, do you see why I think this is an interesting challenge for the flat earth?
On a flat earth it makes no sense to me that flying from London, one route could start out heading north-west, another due east, with stopovers thousands of miles apart and yet they meet up at the same place and take the same amount of time. These routes exist.
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Draw the lines of the images presented in this thread on any of the maps or models we present and you will see your error.
Try and construct a map on a flat plane using known distances between places and you will see yours :)
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Maybe you should submit your queries to a repeating-Mercator Flat Earth group. We use none of those models.
Perhaps.
Perhaps maybe you should just try to answer a question honestly.
Mercator methods are un-zetetic, because they forfeit basic calculus to find their answers. Perhaps that is why you do not like them.
So rather than shine the lampshade-Sun onto models you don't believe in, would it not be more productive to emphasize the models you do champion?
I invite you.
Draw the lines of the images presented in this thread on any of the maps or models we present and you will see your error.
The two main FE "models" use as a placeholder AE Globe Projection maps as FET does not have a map, as we all know. The mono-pole, AE Globe Projection centered on the North Pole and the bi-polar, AE Lambert Globe Projection centered on 0° N 0° E.
The Mercator Globe Projection, is probably the more widely used version when it comes all forms of goods and people transport because of it's simplicity; all verticals point N & S, all horizontals point E & W.
Rhumb Line navigation is fine for short haul navigation.
Great Circle is what is used for long haul navigation, e.g. an ocean passage.
Both can be plotted on either an AE or Mercator map. The routes and distances are the same.
B/c Tom prefers the AE Globe Projection view, here's an example of a Rhumb Line vs a Great Circle on a North Pole centered one (same as the FE mono-pole model). You'll notice the Great Circle route, even that far north, is better than the Rhumb Line route and that's why airlines fly the Great Circle path.
(https://i.imgur.com/SwgimZd.jpg)
Fast forward 150 years from Rowbotham's contention in ENAG regarding the superiority of Rhumb Line navigation, it just doesn't apply to modern, even less than modern, long haul transport.
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I don't agree that...
when you take a flight with a stop over that stop over is unlikely to be exactly on the great circle between the two places.
On the contrary, because the two endpoints are antipodal then there must always exist one great circle route which passes through both the endpoints and the stopover. Only one great circle passes through the departure and stopover and only one through the stopover and destination, so they must be one and the same great circle.
Put it another way. Pick any two non-antipodal points A and B and there is one great circle route between them. Extend that route all the way round and you must necessarily pass through the antipodal points of both A and B.
Right. Yes, you are correct. Again, taking my example because it's easier to think about. If you're at the North Pole then you can, as I said above, go down any line of Longitude to get to the South Pole. And since you must go through every point of Latitude as you do so you can go to any place of Longitude and Latitude on earth on your way between the poles.
That remains true for any antipodal points on earth. The way to think about it is imagine a ring around the earth going through the two points A and B which are antipodal. That ring is a great circle. You can pivot that ring around points A and B so it goes through any point on earth.
Note to certain people. This is how grown ups discuss things, actually conceding points and admitting error when shown to be incorrect. It's not that difficult...
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I don't agree that...
when you take a flight with a stop over that stop over is unlikely to be exactly on the great circle between the two places.
On the contrary, because the two endpoints are antipodal then there must always exist one great circle route which passes through both the endpoints and the stopover. Only one great circle passes through the departure and stopover and only one through the stopover and destination, so they must be one and the same great circle.
Put it another way. Pick any two non-antipodal points A and B and there is one great circle route between them. Extend that route all the way round and you must necessarily pass through the antipodal points of both A and B.
Right. Yes, you are correct. Again, taking my example because it's easier to think about. If you're at the North Pole then you can, as I said above, go down any line of Longitude to get to the South Pole. And since you must go through every point of Latitude as you do so you can go to any place of Longitude and Latitude on earth on your way between the poles.
That remains true for any antipodal points on earth. The way to think about it is imagine a ring around the earth going through the two points A and B which are antipodal. That ring is a great circle. You can pivot that ring around points A and B so it goes through any point on earth.
Note to certain people. This is how grown ups discuss things, actually conceding points and admitting error when shown to be incorrect. It's not that difficult...
I like the pivoting ring analogy and I love the "grown ups" comment, but in the spirit of this forum, perhaps we should really have thrown at least a few insults at each other along the way ;-)
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Please give links to some of your maps.
You have been registered on this website for almost 5 years. Why are you guys resorting to delay tactics?
Surely you have been delaying in drawing a map using measured distances?
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Please give links to some of your maps.
This question is valid. Where are the flat earth maps?
So far I've seen none. I've seen some maps which clearly are projections of a globe, so these are globe earth maps.
You cannot navigate without maps. So if you want to debate about navigation, Great Circles, Rhumb Lines etc. you need a map.
How should we discuss issues of flat earth navigation, when there's no map?
We could discuss about globe earth navigation, there are plenty of maps in all resolutions, with multiple projections.
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After pondering the title of this thread for a bit, I can't help but to wonder if the concept of antipodes even applies in the context of a flat earth map. What exactly does it mean to have opposite points on a flat earth?
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After pondering the title of this thread for a bit, I can't help but to wonder if the concept of antipodes even applies in the context of a flat earth map. What exactly does it mean to have opposite points on a flat earth?
Well, quite. It would be a pretty meaningless concept. But the fact that you can get flights from London to New Zealand via multiple routes is pretty much the point. On a flat earth there is only one shortest line between points A and B. On a globe if the points are antipodal then there are multiple shortest lines and you can put those lines through any point C on the globe.
When I've got more time I'll have a look at flight times between antipodal points via different "C" points and do some comparisons.
In theory they should be reasonably consistent and that wouldn't make any sense on a flat earth.
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After pondering the title of this thread for a bit, I can't help but to wonder if the concept of antipodes even applies in the context of a flat earth map. What exactly does it mean to have opposite points on a flat earth?
Well, quite. It would be a pretty meaningless concept. But the fact that you can get flights from London to New Zealand via multiple routes is pretty much the point. On a flat earth there is only one shortest line between points A and B. On a globe if the points are antipodal then there are multiple shortest lines and you can put those lines through any point C on the globe.
When I've got more time I'll have a look at flight times between antipodal points via different "C" points and do some comparisons.
In theory they should be reasonably consistent and that wouldn't make any sense on a flat earth.
Yep, that's exactly the point I was trying to make, thank you. And it doesn't matter what the actual map looks like either, so hopefully we avoid arguments about whether we should be looking at unipolar, bipolar etc. or the "we're working on it" map. So long as it's flat then these flights make no sense. If it's a globe, then they do.
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After pondering the title of this thread for a bit, I can't help but to wonder if the concept of antipodes even applies in the context of a flat earth map. What exactly does it mean to have opposite points on a flat earth?
Well, quite. It would be a pretty meaningless concept. But the fact that you can get flights from London to New Zealand via multiple routes is pretty much the point. On a flat earth there is only one shortest line between points A and B. On a globe if the points are antipodal then there are multiple shortest lines and you can put those lines through any point C on the globe.
When I've got more time I'll have a look at flight times between antipodal points via different "C" points and do some comparisons.
In theory they should be reasonably consistent and that wouldn't make any sense on a flat earth.
Yep, that's exactly the point I was trying to make, thank you. And it doesn't matter what the actual map looks like either, so hopefully we avoid arguments about whether we should be looking at unipolar, bipolar etc. or the "we're working on it" map. So long as it's flat then these flights make no sense. If it's a globe, then they do.
Agreed. I would say at this point, FET doesn't have an explanation as to how travel as described and happens everyday can occur.
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After pondering the title of this thread for a bit, I can't help but to wonder if the concept of antipodes even applies in the context of a flat earth map. What exactly does it mean to have opposite points on a flat earth?
Well, quite. It would be a pretty meaningless concept. But the fact that you can get flights from London to New Zealand via multiple routes is pretty much the point. On a flat earth there is only one shortest line between points A and B. On a globe if the points are antipodal then there are multiple shortest lines and you can put those lines through any point C on the globe.
When I've got more time I'll have a look at flight times between antipodal points via different "C" points and do some comparisons.
In theory they should be reasonably consistent and that wouldn't make any sense on a flat earth.
Just to kick things off then, looking at bookable options, I picked a few extreme examples, all on the same day, starting from London Heathrow (LHR), one via Los Angeles (LAX), the other via Tokyo (NRT). The ultimate destination in both cases is Auckland NZ (AKL).
LHR and AKL are not ideal because the antipode of LHR is actually about 1600km (1000mi) S of AKL. There are other pairs of locations in the UK and New Zealand which are a better match, but we need major international airports with lots of flight options and these two are the main ones. What this means is there will naturally be some variation in distance (and hence flight time) depending on route and prevailing winds, but when we're talking of flights approaching 24h and 12500 miles, the differences aren't that great as we shall see.
Having done a bit more research, I think Madrid (MAD) in Spain and Auckland (AKL) are actually a closer match as the antipode of Madrid is only 400km (245mi) from Auckland and Madrid is an international airport, so although there are fewer flight options compared to London Heathrow, I've also included a couple of flights between the two, one via Beijing (PEK) and the other via LAX.
I looked them all up on flightradar24 to find actual route and flight times. Distances given are great circle distances from the flightradar24 pages:
A) 31st Oct BA269 LHR -> LAX flight time 10h 4m, distance: 8780km, followed by AA83 LAX -> AKL flight time 12h 11m distance 10467km (total flight time 22h 15m, total distance 19247km)
B) 31st Oct BA5 LHR-> NRT flight time 10h 46m, distance 9615km, followed by NZ90 NRT -> AKL flight time 10h 2m, distance 8806km (total flight time 20h 48m, total distance 18421km)
C) 31st Oct DY7743 MAD->LAX flight time 11h 25m, distance 9406km, followed by NZ1 LAX->AKL flight time 12h 1m, distance 10467km (total flight time 23h 26m, total distance 19873km)
D) 31st Oct CA908 MAD->PEK flight time 10h 30m, distance 9266km, followed by CA783 PEK->AKL flight time 11h 58m, distance 10402km (total flight time 22h 38m total distance 19668km)
The London flight via LAX is longer than the flight via Tokyo. The difference between the two is 1h 27m in the air and 826km (513mi). This is a relatively small discrepancy, explained by the fact that they are not exactly antipodal, but they are close enough for the two routes to make economic sense.
As expected, the two Madrid options are closer still, 48mins and 5km.
On different days with different winds and routing, timings and distances will vary somewhat, but not substantially. Bear in mind that these are also extreme examples of routes spread a long way apart.
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Agreed. I would say at this point, FET doesn't have an explanation as to how travel as described and happens everyday can occur.
What about jet streams?
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To add to that, can someone answer this travel question: What's the distance from Chicago to Barcelona? and what's the distance from Buenos Aires to Cape Town, South Africa?
Here's why:
Traveling by airplane from Chicago to Barcelona on a globe is measured at about 4,400 miles. Traveling from Buenos Aires to Capetown is about the same distance (4,200 miles). Flying from Chicago to Barcelona would stay entirely along the 42° n latitude (exactly straight ahead; never turning the airplane), and Buenos Air/Capetown trip would remain entirely along the 34° south latitude (also never turning). If 2 planes take off at the same time, they should both arrive at their destinations at the same time. However, I haven't seen detailed flat earth maps, but it looks like the Buenos Aires trip should be 2.5x longer distance. Also, you would have to keep the airplane turning along a curve, rather than straight ahead. Have either of these been measured and proven? Seems like an easy way to prove the flat map once and for all.
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Agreed. I would say at this point, FET doesn't have an explanation as to how travel as described and happens everyday can occur.
Since these discussions have become been quite detailed, I think maybe a picture would be in order.
Three routes shown here, all between London Heathrow (LHR) and Auckland NZ (AKL). Going via Los Angeles (LAX), Tokyo (HND) and Dubai (DXB).
On a globe these would be very straightforward great circle routes and it wouldn't matter which one you took, they'd all be more or less the same distance and take the same time.
On a flat earth, the yellow dotted straight lines would be the shortest, but it's clearly a lot further going via Dubai (DXB) than Tokyo (HND) and all of these routes are longer than the direct path between LHR and AKL (blue dashed line).
The red lines are the three great circle routes, but these are clearly different lengths as well and going via Dubai makes no logical sense, even though in the real world it is a popular route to take.
(https://i.imgur.com/8wxMXK3.jpg)
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To add to that, can someone answer this travel question: What's the distance from Chicago to Barcelona? and what's the distance from Buenos Aires to Cape Town, South Africa?
Here's why:
Traveling by airplane from Chicago to Barcelona on a globe is measured at about 4,400 miles. Traveling from Buenos Aires to Capetown is about the same distance (4,200 miles). Flying from Chicago to Barcelona would stay entirely along the 42° n latitude (exactly straight ahead; never turning the airplane), and Buenos Air/Capetown trip would remain entirely along the 34° south latitude (also never turning). If 2 planes take off at the same time, they should both arrive at their destinations at the same time. However, I haven't seen detailed flat earth maps, but it looks like the Buenos Aires trip should be 2.5x longer distance. Also, you would have to keep the airplane turning along a curve, rather than straight ahead. Have either of these been measured and proven? Seems like an easy way to prove the flat map once and for all.
Regarding the distance from Chicago to Barcelona, note that the shortest route (approximately 4400 miles as you say) will not follow the 42 deg latitude line, that would be a rhumb line and would be longer (4644 miles). The shortest route is always a great circle route and in this case, you're saving a couple of hundred miles compared with following the 42 degree latitude route. The great circle route would arc northwards in a curve up to about 52N and then arc back down again.
Commercial flights generally follow great circle routes. I say generally because it often makes sense to take a slightly longer route to pick up favourable winds or avoid unfavourable ones - longer, but faster. Modern aircraft autopilots have no problems making constant course corrections to follow a carefully pre-planned route. The actual route may then vary from the pre-planned one, depending on the weather conditions encountered. So in reality we'd expect to see a planned flight being slightly further than the ideal direct great circle distance and the actual probably a little different from the planned.
Taking the American AA40 flight between Chicago (ORD) and Barcelona (BCN) on 27th Oct as an example, this flight had a planned route of 4487 miles, that ended up being 4511 miles (source https://uk.flightaware.com/live/flight/AAL40 (https://uk.flightaware.com/live/flight/AAL40)). Pretty much exactly what you'd expect.
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Robinofloxley:
Thanks for the detailed flight info, but I'll clarify my question. What is the straight line distance between Buenos Aires and Cape Town? On a globe it would roughly be the same distance as Chicago to Barcelona. But on a flat map it would be 2.5x further. Also, if I read a flat map correctly, taking a straight line trip from Buenos Aires to Cape Town would require flying northeast essentially along the entire east coast of South America, where on a globe it would be over open ocean the entire trip. So which is it? This seems a fairly easy question to prove. I'm less interested in what commercial flights actually do and more interested in how to prove globe vs flat. Skipping the great circle routes, it seems a simple test would be taking off from two cities mentioned, and flying due east along each latitude at same speed toward each destination. Globe model says they'll reach their destinations, FE theory says they won't.
I'm including a graphic to show that a globe trip would require travel due east, over open ocean, while FE model indicates northeast travel over land - the east coast of South America. Again, seems like a simple way to prove which is correct. I also marked the distance on a flat map of Chicago to Barcelona, which is quite shorter than Buenos Aires to Cape Town on a flat map.
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Robinofloxley:
Thanks for the detailed flight info, but I'll clarify my question. What is the straight line distance between Buenos Aires and Cape Town? On a globe it would roughly be the same distance as Chicago to Barcelona. But on a flat map it would be 2.5x further. Also, if I read a flat map correctly, taking a straight line trip from Buenos Aires to Cape Town would require flying northeast essentially along the entire east coast of South America, where on a globe it would be over open ocean the entire trip. So which is it? This seems a fairly easy question to prove. I'm less interested in what commercial flights actually do and more interested in how to prove globe vs flat. Skipping the great circle routes, it seems a simple test would be taking off from two cities mentioned, and flying due east along each latitude at same speed toward each destination. Globe model says they'll reach their destinations, FE theory says they won't.
I'm including a graphic to show that a globe trip would require travel due east, over open ocean, while FE model indicates northeast travel over land - the east coast of South America. Again, seems like a simple way to prove which is correct. I also marked the distance on a flat map of Chicago to Barcelona, which is quite shorter than Buenos Aires to Cape Town on a flat map.
Well I suppose it depends which flat map you are using. The one most people are going to agree on is the "we're working on it" map which nobody has ever seen. The moment you pick a map, someone is going to come along and ask why you picked that one and tell you we all know it's wrong.
However, I'll go ahead and pick the commonly referenced azimuthal equidistant map (AE). If I draw a straight line between Buenos Aires airport (EZE) and Capetown airport (CPT), I find that's about 1.73 times the distance from the north pole to the equator, so if we take that to be 10,000km, that makes the straight-line distance between the two airports to be 17300km or 10,750 miles. Same method gives me Chicago to Barcelona as 7700km (4,785 miles).
I agree, on a globe, very similar distance, flat earth - well who knows really, but you have my workings for what they are worth.