The Flat Earth Society
Flat Earth Discussion Boards => Flat Earth Investigations => Topic started by: edby on December 12, 2018, 10:47:48 PM
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Rowbotham (in Earth not a globe):
The following is the true state of the question:--If the earth is a globe, it is certain that the degrees of longitude are less on both sides of the equator than upon it. If the degrees of longitude are less beyond, or to the south of the equator, than upon it, then it is equally certain that the earth is globular" (my emphasis)
This investigation is to test his statement by measuring the distance of 1 degree of longitude at different latitudes south of the Equator.
I assume that the distance of 1 degree of longitude at the equator is 111.14 km (but this can also be checked).
Experiment one: Hill Cove (51.51S 60.14W) and and Port San Carlos (51.51S 59W). The difference measured by Google maps is 78.43 km. Dividing by the difference in longitude (1.14 degrees) gives the implied distance of a degree of longitude there is 68.8km.
This is less than 111.14km. Rowbotham is incorrect in this case. I shall try some more later.
[edit] R's account https://www.sacred-texts.com/earth/za/za42.htm is well worth study.
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Longitude and Latitude isn't used by Google Maps/WebMercator to measure distances.
Have a read: The Earth is Not Round! Utah, NAD83 and WebMercator Projections (https://gis.utah.gov/nad83-and-webmercator-projections/)
Latitude and Longitude are useless for measuring distance and area because the unit of length, degrees, is not held constant for longitude, except along parallels -- individual perfectly east-west lines.
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Web Mercator's significant weakness is that measurements of distance and area in its native coordinates are completely unusable. Where accurate distance and area calculations are needed, web-mercator GIS data must be temporarily reprojected to a more suitable coordinate system (UTM NAD83).
It is admitted that the latitude and longitude coordinates of the spherical earth model is completely unusable, and that the data must be reprojected onto a local state plane coordinate system for accuracy.
You are trying to compare lat/long coordinates which are said to be "completely unusable."
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Longitude and Latitude isn't used by Google Maps/WebMercator to measure distances.
Have a read: The Earth is Not Round! Utah, NAD83 and WebMercator Projections (https://gis.utah.gov/nad83-and-webmercator-projections/)
Latitude and Longitude are useless for measuring distance and area because the unit of length, degrees, is not held constant for longitude, except along parallels -- individual perfectly east-west lines.
...
Web Mercator's significant weakness is that measurements of distance and area in its native coordinates are completely unusable. Where accurate distance and area calculations are needed, web-mercator GIS data must be temporarily reprojected to a more suitable coordinate system (UTM NAD83).
It is admitted that the latitude and longitude coordinates of the spherical earth model is completely unusable, and that the data must be reprojected onto a local state plane coordinate system for accuracy.
You are trying to compare lat/long coordinates which are said to be "completely unusable."
It's not "admitted that the latitude and longitude coordinates of the spherical earth model is completely unusable". It's stating that UTM NAD83 is better, as referenced in your quote. UTM stands for Universal Transverse Mercator, a Globe projection and NAD83 is the datum based upon a spherical ellipsoidal earth model.
Whether you like it or not, for the millionth time, all of these maps are derived from a spherical earth model. By you just saying they are not doesn't change the fact that they are Globe based.
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Look up what a datum is. It says that "The UTM NAD83 projection uses the GRS80 ellipsoid and a center-of-the-earth anchor point as its datum," likely to connect to the spherical earth models such as WebMercator, not that it's a spherical earth map. It's a flat map.
https://catalog.data.gov/dataset/united-states-stateplane-zones-nad83
United States Stateplane Zones - NAD83
Metadata Updated: August 11, 2016
U.S. State Plane Zones (NAD 1983) represents the State Plane Coordinate System (SPCS) Zones for the 1983 North American Datum within United States.
then
https://en.wikipedia.org/wiki/State_Plane_Coordinate_System
The State Plane Coordinate System (SPS or SPCS) is a set of 124 geographic zones or coordinate systems designed for specific regions of the United States. Each state contains one or more state plane zones, the boundaries of which usually follow county lines. There are 110 zones in the contiguous US, with 10 more in Alaska, 5 in Hawaii, and one for Puerto Rico and US Virgin Islands. The system is widely used for geographic data by state and local governments. Its popularity is due to at least two factors. First, it uses a simple Cartesian coordinate system to specify locations rather than a more complex spherical coordinate system (the geographic coordinate system of latitude and longitude). By using the Cartesian coordinate system's simple XY coordinates, "plane surveying" methods can be used, speeding up and simplifying calculations.
XY coordinates. Flat map. Plane surveying.
You are not demonstrating anything "for the millionth time." You are merely stating things rather than demonstrating.
These maps are "based on a globe," in your opinion, but they are flat planar maps with an XY coordinate system, and apparently are more accurate than a possible spherical earth map? This appears to be a pretty absurd claim.
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Look up what a datum is. It says that the "The UTM NAD83 projection uses the GRS80 ellipsoid and a center-of-the-earth anchor point as its datum," likely to connect to the spherical earth models such as WebMercator, not that it's a spherical earth map. It's a flat map.
https://catalog.data.gov/dataset/united-states-stateplane-zones-nad83
United States Stateplane Zones - NAD83
Metadata Updated: August 11, 2016
U.S. State Plane Zones (NAD 1983) represents the State Plane Coordinate System (SPCS) Zones for the 1983 North American Datum within United States.
then
https://en.wikipedia.org/wiki/State_Plane_Coordinate_System
The State Plane Coordinate System (SPS or SPCS) is a set of 124 geographic zones or coordinate systems designed for specific regions of the United States. Each state contains one or more state plane zones, the boundaries of which usually follow county lines. There are 110 zones in the contiguous US, with 10 more in Alaska, 5 in Hawaii, and one for Puerto Rico and US Virgin Islands. The system is widely used for geographic data by state and local governments. Its popularity is due to at least two factors. First, it uses a simple Cartesian coordinate system to specify locations rather than a more complex spherical coordinate system (the geographic coordinate system of latitude and longitude). By using the Cartesian coordinate system's simple XY coordinates, "plane surveying" methods can be used, speeding up and simplifying calculations.
XY coordinates. Flat map. Plane surveying.
You are not demonstrating anything "for the millionth time." You are merely stating things rather than demonstrating.
These maps are "based on a globe," in your opinion, but they are flat planar maps with an XY coordinate system, and apparently are more accurate than a possible spherical earth map? This appears to be a pretty absurd claim.
They are not more accurate than a "spherical earth map" because all of these maps are spherical earth maps. Seemingly no matter how many references to the explicit nature that these maps are based upon a spherical model, you're still not getting it. The XY coordinate system is a grid laid on top of a spherically derived map. Simple as that.
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See the title of the article: "The Earth is Not Round!"
They are clearly telling us that it is not round because they are using flat maps in these systems.
If that's what you think the article is saying, I don't know what to tell you.
The title is in reference to: "Geographic coordinates use latitude and longitude values to define positions on the 3D surface of the earth, which is of course, best modeled as an ellipsoid, not a sphere."
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Look up what a datum is. It says that the "The UTM NAD83 projection uses the GRS80 ellipsoid and a center-of-the-earth anchor point as its datum," likely to connect to the spherical earth models such as WebMercator, not that it's a spherical earth map. It's a flat map.
Not "likely to connect to a spherical earth." It's not a conspiracy or a trick. It's specifically and for the sole purpose of establishing reference coordinates to an ellipsoid shape. The GRS80 geodetic reference is based on an ellipsoid. NAD83 is thus based on an ellipsoid. It's not a flat map in any way other than it is projected onto a 2-D surface for presentation.
You can't weasel-word your way around that fact by interjection your own bias with unfounded speculation on the reason by GRS80 ellipsoid is used as a reference. "Like to connect to the spherical earth." Please!
The XY coordinate system is a grid laid on top of a spherically derived map. Simple as that.
Exactly.
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They are not more accurate than a "spherical earth map" because all of these maps are spherical earth maps. Seemingly no matter how many references to the explicit nature that these maps are based upon a spherical model, you're still not getting it. The XY coordinate system is a grid laid on top of a spherically derived map. Simple as that.
You have no sources. XY coordinates = Flat Map. Show where it is a "grid laid on top of a spherically derived map"
"Simple as that" is not evidence. The article above clearly says that traditional plane surveying is used in the State Plane maps. Spherical coordinates are NOT used. Yet you claim without evidence that the flat map is really depicting a sphere? Show your sources.
How do you make a flat map more accurate than a spherical map, exactly?
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They are not more accurate than a "spherical earth map" because all of these maps are spherical earth maps. Seemingly no matter how many references to the explicit nature that these maps are based upon a spherical model, you're still not getting it. The XY coordinate system is a grid laid on top of a spherically derived map. Simple as that.
You have no sources. XY coordinates = Flat Map. Show where it is a "grid laid on top of a spherically derived map"
"Simple as that" is not evidence. The article above clearly says that traditional plane surveying is used in the State Plane maps. Yet you claim without evidence that the flat map is really depicting a sphere? Show your sources.
How do you make a flat map more accurate than a spherical map, exactly?
Already have, but here it is again, among others:
https://www.ngs.noaa.gov/SPCS/index.shtml
Here are some tools to covert Lat/Long to SPC:
https://www.ngs.noaa.gov/TOOLS/spc.shtml
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They are not more accurate than a "spherical earth map" because all of these maps are spherical earth maps. Seemingly no matter how many references to the explicit nature that these maps are based upon a spherical model, you're still not getting it. The XY coordinate system is a grid laid on top of a spherically derived map. Simple as that.
You have no sources. XY coordinates = Flat Map. Show where it is a "grid laid on top of a spherically derived map"
"Simple as that" is not evidence. The article above clearly says that traditional plane surveying is used in the State Plane maps. Yet you claim without evidence that the flat map is really depicting a sphere? Show your sources.
How do you make a flat map more accurate than a spherical map, exactly?
Already have, but here it is again, among others:
https://www.ngs.noaa.gov/SPCS/index.shtml
Sorry, I don't see where your claim is substantiated at all.
"As a reminder, a map projection is a systematic transformation of the latitudes and longitudes of locations on the surface of a sphere or ellipsoid representing the Earth to grid coordinates (x, y or easting, northing values) on a plane."
This substantiates what you are trying to communicate? A definition of a map projection?
The maps are flat. The data is flat. The data comes from simple plane surveying. How do you make a flat earth map more accurate than a spherical earth map if the earth is round?
Refer to the title of the previous article: "The Earth is Not Round!"
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We read the following: https://www-group.slac.stanford.edu/met/Align/GPS/CCS83.pdf
The State Plane Coordinate System was established to provide a means for transferring the
geodetic positions of monumented points to plane coordinates that would permit the use of
these monuments in plane surveying over relatively large areas without introducing
significant error.
A plane-rectangular coordinate system is by definition a flat surface. Geodetic positions on
the curved surface of the earth must be “projected” to their corresponding plane coordinate
positions. Projecting the curved surface onto a plane requires some form of deformation.
Imagine the stretching and tearing necessary to flatten a piece of orange peel. In California
the Lambert Conformal map projection is used to transform the geodetic positions of
latitude and longitude into the y (Northing) and x (Easting) coordinates of the CCS83.
The spherical coordinates are projected to the plane coordinates. Not the other way around.
http://wvgis.wvu.edu/data/otherdocs/standardsandpubs/wv_coordinate_systems_jan02.html
Geographic Coordinate System (GCS): An unprojected coordinate system that uses latitude and longitude to define the locations of points on a sphere or spheroid. The use of longitude and latitude is encouraged for general reference and distribution of national framework data because it provides a seamless coordinate system for most of the United States. Geographic coordinates can be readily projected onto a planar coordinate system to display data properly or measure distances accurately. The Geographic Coordinate System is the recommended coordinate system for unprojected GIS data sets that cover the entire geographic extent of West Virginia.
We read that it is to measure distances accurately.
How can spherical coordinates projected onto a planar coordinate system display data and distances accurately if the earth is a globe? Why should these systems require that? Maps with spherical coordinates are not possible?
If the earth is a globe, the opposite should be true. Projecting spherical coordinates onto a plane should make data and distances more inaccurate. Not accurate.
What you are proposing is happening here does not make any sense at all. They have a spherical earth model and they are projecting its coordinates onto an XY plane which you think is somehow a spherical earth in disguise? Achieved through the process of regular plane surveying? And that these flat earth maps are more accurate than spherical earth maps? That does not make sense.
Again, I refer you to the title of the article: "The Earth is Not Round!" (https://gis.utah.gov/nad83-and-webmercator-projections/)
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How can spherical coordinates projected onto a planar coordinate system display data and distances accurately if the earth is a globe? Why should these systems require that? Maps with spherical coordinates are not possible?
"State Plane Coordinate System
By using the Cartesian coordinate system's simple XY coordinates, "plane surveying" methods can be used, speeding up and simplifying calculations. Second, the system is highly accurate within each zone (error less than 1:10,000). Outside a specific state plane zone accuracy rapidly declines, thus the system is not useful for regional or national mapping."
https://en.wikipedia.org/wiki/State_Plane_Coordinate_System
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I don't want to get into an argument regarding a coordinate system because it's irrelevant in this case. Rowbotham was pretty rough in his estimates of the distances involved. Furthermore he made an assumption that was a little 'loose' as well. In any even he can't be blamed too much because distance data may not have been the best in those days.
My modern day calculations revealed a distance between Botany Bay in Sidney to Nelson of about 1134 Nautical miles. The two ports aren't quite on the same latitude as Rowbotham assumed. One is about 34 degrees South and the other is about 41 degrees South latitude. The change in longitude I can agree with. If you do the calculation you will find that the earth should be about 18531 NM in diameter at that point yielding a 51.47 NM per degree longitude. That seems to be a reasonable number for the distance between a degree longitude, at 33 degrees South, even for Rowbotham given all the rough estimates that were used.
Rowbotham had the distance for a Nautical mile at 1.16 statute miles. Today the correct value is 1.15078 statue miles. With all the rough approximations of the distances, and the error in the latitudes assumed, I would say that Rowbotham just made a biased assumption that the world was flat. His small errors and erroneous assumptions, if corrected, should prove that his conclusions were just wrong.
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Look up what a datum is. It says that "The UTM NAD83 projection uses the GRS80 ellipsoid and a center-of-the-earth anchor point as its datum," likely to connect to the spherical earth models such as WebMercator, not that it's a spherical earth map. It's a flat map.
Why is projection needed if the earth is flat?
If the earth were flat we wouldn't need projections, we'd just need to scale the real world down to map size.
Why are they using projections from an ellipsoid to make maps? Are cartographers all in on the globe conspiracy too?
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Look up what a datum is. It says that the "The UTM NAD83 projection uses the GRS80 ellipsoid and a center-of-the-earth anchor point as its datum," likely to connect to the spherical earth models such as WebMercator, not that it's a spherical earth map. It's a flat map.
Not "likely to connect to a spherical earth." It's not a conspiracy or a trick. It's specifically and for the sole purpose of establishing reference coordinates to an ellipsoid shape. The GRS80 geodetic reference is based on an ellipsoid. NAD83 is thus based on an ellipsoid. It's not a flat map in any way other than it is projected onto a 2-D surface for presentation.
You can't weasel-word your way around that fact by interjection your own bias with unfounded speculation on the reason by GRS80 ellipsoid is used as a reference. "Like to connect to the spherical earth." Please!
It is used to connect to the spherical earth model. Lets read about it together:
https://gis.utah.gov/nad83-and-webmercator-projections/
First it talks about the spherical model:
Geographic coordinates use latitude and longitude values to define positions on the 3D surface of the earth, which is of course, best modeled as an ellipsoid, not a sphere. The ellipsoid and its accompanying anchor point that ties it in to the real world, are known collectively as the WGS84 datum.
Note "real world."
Then it talks about the flat model:
UTM NAD83 is a projected coordinate system that represents physical locations abstracted to a flat, cartesian coordinate system. The UTM NAD83 projection uses the GRS80 ellipsoid and a center-of-the-earth anchor point as its datum
It is talking about an anchor point to connect the two types of systems together.
The accompanying image is the flat map with anchor point:
(https://gis.utah.gov/images/projections-300x288.png)
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But again, Tom, why is any of that needed if the earth is flat?
If the earth is flat then a flat map can represent the flat earth, no projection is needed.
Why are they doing all this? What's the point?
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They are not more accurate than a "spherical earth map" because all of these maps are spherical earth maps. Seemingly no matter how many references to the explicit nature that these maps are based upon a spherical model, you're still not getting it. The XY coordinate system is a grid laid on top of a spherically derived map. Simple as that.
You have no sources. XY coordinates = Flat Map. Show where it is a "grid laid on top of a spherically derived map"
"Simple as that" is not evidence. The article above clearly says that traditional plane surveying is used in the State Plane maps. Spherical coordinates are NOT used. Yet you claim without evidence that the flat map is really depicting a sphere? Show your sources.
How do you make a flat map more accurate than a spherical map, exactly?
Look at the lat/long scales on a flat map. Not difficult.
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None of this is relevant to the question being investigated, which is a simple and verifiable one.
1. Take any two points on the same Southern latitude, one degree of longitude apart.
2. Find the distance between them.
3. If the distance is less than 111km (which is the distance of 1 degree at the equator) then the earth is not flat.
This is as close as we can get to Rowbotham's test, not mine.
Applying the test for two chosen points in the Falklands, we find the distance between them is much less than at the equator.
If Tom has an objection, then either (1) the positional coordinates are incorrect. But I have done extensive research on pre-satellite systems of measurement, and they seem to be correct. Or (2) the distance is wrong. But 50-100km is not a long distance, and it could easily be tested by driving.
In any case, please address the OP, and don't go off topic.
Longitude and Latitude isn't used by Google Maps/WebMercator to measure distances.
Are you disputing the distance between Hill Cove and Port San Carlos (https://forum.tfes.org/index.php?topic=11558.0)?
Very well for the next experiment we must find two similar points connected by road.
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Another test
Groblershoop SA -28.89 21.93
Kimberley SA -28.74 24.76
Difference in longitude 2.83 degrees.
Measured distance according to Google maps 275.46km
Implied distance of 1 degree = 275.46/2.83 = 97.34.
This is also less than 111km.
But it is claimed that the distance is wrong, those towns are connected by a straight road. I shall contact friends in SA and ask them to do the experiment.
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Of course the road is crooked, but in case of any dispute about that, I measured the crooked bits as well. See the chart below. This changes the crow-flies distance of 275.46 to 283.3km. Dividing by 2.83 gives 100.11km, which is still less than 111km.
So there is an easy test. If we drive from Groblershoop to Kimberley, do we get a distance of about 283km? If so, then Google maps is measuring the distance correctly. Otherwise not.
This is Zeteticism at its purest.
(http://www.logicmuseum.com/w/images/e/e7/Groblershoop.jpg)
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And here is a road sign just outside Groblershoop, showing the distance as 285km. So Google maps agrees with road signs.
(http://www.logicmuseum.com/w/images/d/d7/Groblershoop_road_sign.jpg)
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Longitude and Latitude isn't used by Google Maps/WebMercator to measure distances.
Have a read: The Earth is Not Round! Utah, NAD83 and WebMercator Projections (https://gis.utah.gov/nad83-and-webmercator-projections/)
Latitude and Longitude are useless for measuring distance and area because the unit of length, degrees, is not held constant for longitude, except along parallels -- individual perfectly east-west lines.
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Web Mercator's significant weakness is that measurements of distance and area in its native coordinates are completely unusable. Where accurate distance and area calculations are needed, web-mercator GIS data must be temporarily reprojected to a more suitable coordinate system (UTM NAD83).
It is admitted that the latitude and longitude coordinates of the spherical earth model is completely unusable, and that the data must be reprojected onto a local state plane coordinate system for accuracy.
You are trying to compare lat/long coordinates which are said to be "completely unusable."
OK Tom, the article you reference specifies UTM NAD83 zone 12 North, so just for you, here is a UTM NAD83 zone 12 North projection of the Falklands/Malvinas with a helpful scale and Hill Cove and Port San Carlos marked. The graticule lines are at 1 deg intervals so it's pretty easy to see how wide a degree of longitude is here I think.
(https://i.imgur.com/SVs4SV7.jpg)
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Longitude and Latitude isn't used by Google Maps/WebMercator to measure distances.
Irrelevant. Latitude and longitude coordinates can be, and often are, used as reference points for navigation and distances between those reference points can be accurately measured and/or calculated.
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Thank you Mr Hood but lest Tom object that these distances are the result of a conspiracy, below is a road sign from New Zealand, taken just outside Gore where Route 1 crosses the Waikaka River. It says 68km to Balclutha, via a winding route. The crow flies distance according to Google is 59km. Both distances give a longitude 1-degree length of well below 111km.
Where was Rowbotham getting his distances from??
(http://www.logicmuseum.com/w/images/b/bf/Balclutha.jpg)
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Rowbotham https://www.sacred-texts.com/earth/za/za42.htm
If, now, we take, from the same map, the distance between Melbourne and Bluff Harbour, South New Zealand--1400 nautical, or 1633 statute miles--and take the difference of longitude between the two places, allowing 50 statute miles for the angular or diagonal direction of the route to Bluff Harbour, we find the degrees of longitude fully 70 statute miles; whereas, at the average latitude of the two places, viz., 42° S., the degrees, if the earth is a globe, would be less than 54 statute miles; thus showing that in the south, where the length of a degree of longitude should be 54 miles, it is really 70 miles, or 16 miles longer than would be possible according to the theory of the earth's rotundity.
Google says the distance is actually 1331 miles, but let's allow Rowbotham his estimate. He is right that the theoretical GE distance of 1 degree is about 54 miles, and roughly right about the average latitude. However, he is comparing positions with completely different latitudes:
Bluff Harbour -46.60
Melbourne -37.88
This make the imputed distance longer than if between points with the same difference of longitude but on the same parallel.
[EDIT]
And let's check this with two cities that are nearly on a parallel. See the table below. Adelaide and Sydney are almost on the same latitude. The theoretical length of 1 degree of longitude (using the standard formula, same as Rowbotham was clearly using) is 92.34km.
The difference in longitude is 12.6 degrees, and the Google crow flies distance is 1,163.26 km. Dividing this by 12.6 gives 92.32 km per 1 degree, which is very close to the theoretical number of 92.34 km above.
Adelaide -34.94 138.60
Sydney -33.86 151.20
Degee of lat 92.34 12.60
Crow flies 1,163.26 92.32
It is interesting that Rowbotham was clearly aware of the standard cosine formula for determining length of longitude, so he had some mathematical understanding of trigonometry. But not enough to realise that a large difference in latitude would completely distort this result.
Was this an innocent mistake?
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Rowbotham actually goes a ways toward proving that the earth is a sphere. That proof is by his own numbers and calculations.
His first example in his book was to calculate the distance between Sydney and Nelson. By his own quote “the two places are nearly on the same latitude”. Rowbotham’s stated distance between the two ports was 1550 statue miles. These statements are the crux of the whole problem and seems to be his basis for determining that the earth is NOT as sphere, but flat. Now lets examine the statements for some discrepancies and apply proven and known modern day math to the statements.
1st……..Sidney is at 34deg, 00’, 00’’ South by 151deg 11’, 00’’ East
2nd…….Nelson is at 41deg, 16’, 00’’ South by 173deg ,17’,00’ East
The difference in longitude is correct and I agree with that. However, the difference in latitude is about 7 degrees. It is true that Rowbotham did say that the differences are ‘nearly’ the same. Now let’s apply “the whole matter now becomes a mere arithmetical question” quote from Rowbotham and calculate the distance 7 degrees of latitude makes. That distance going straight North or South is 483 statue miles. I agree that the route isn’t directly North or South so the whole 483 mile mistake won’t apply. A modern day measurement between the two ports would yield a distance of about 1305 statue miles. The difference between Rowbotham’s assumed distance and the corrected one is about 245 miles.
Split the difference between the two latitudes and do a calculation of the points 37.5deg S by 115deg, 11’E to 37.5deg S by 173deg, 17’E and that comes out to 1208.57 statue miles or 1050.21 Nautical miles. That’s about 47.7 Nautical Miles per degree longitude at the 37.5 degree South Latitude. According to Rowbotham’s own chart provided so the reader could make calculations for himself I come up with pretty good agreement with a spherical earth.
Now I agree that the calculations are a bit tricky. I didn’t use Google Earth for any distances but effectively did a dot multiplication of two vectors and got the distance between the two coordinates using standard spherical trigonometric methods that would work on any sphere. These methods are used each and every day by both the shipping companies and airlines so you know for sure that they are quite valid.
My only assumptions were of the exact locations alluded to by Rowbotham. I took an estimate and did the calculations with those figures. If someone wants to provide the ‘official’ Rowbotham approved port coordinates I can re-calculate.
Having said everything above it is hard to determine if the minor calculation error above was intentional to make a case for a flat earth or just a wrong assumption. The question now is can you trust anything in Rowbotham’s book and his assumptions that the earth is flat based upon a mistaken assumption?
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How can spherical coordinates projected onto a planar coordinate system display data and distances accurately if the earth is a globe? Why should these systems require that? Maps with spherical coordinates are not possible?
This is the first time I've seen you demonstrate the beginnings a modicum of reasoned thinking. Questions like these are the beginnings of knowledge. You're lucky in that others have already answered these questions a long time a go. You can, if you wish, just look up what's already been done, or re-do it if you doubt the veracity of those that came before you. However. that said, I believe your thinking may have gone off the rails several times just in this thread.
1) What they were saying over at gis.utah.org was not that the world is flat. It's that we use flat maps. It was a simple play on words and the technology used for convenience - trust you to take it the wrong way. But of course, if being obviously worng will support your position, by all means, don't let intellectual honesty stand in your way.
2) When they said lat. and long. were useless for calculating distances they meant when reading those from a map projection, and they meant long distances. I think you know that too, so don't go on playing the fool.
3) Lat. and long. are perfectly fine for measuring distances on a sphere. They have to be and if you had any mathematics knowledge at all you would know that. Of course, as a flat earther your use of spherical coordinates is probably minimal, but that's you fault, not the rest of the world's. You are free to learn this stuff you know, or are mathematicians considered in on the conspiracy too?
4) To your question "Maps with spherical coordinates are not possible?", not impossible but certainly impractical. You can get a flat projection map that gives a 10,000:1 magnification, but to accurately do that with spherical coordinates you'd need a globe about 1.3km in diameter. I'd hate to carry that thing around with me, if I could afford one.
5) BTW, the earth is only non-spherical by a small amount - about 1 part in 300, and this non-sphericality is very regular in nature so can easily be accounted for to get exact results using lat and long on our oblate little earth. The last official update to the earth's shape measurements was done in 1984 when the actual geodetic of the earth was measured (using some those non-existent satellites) to 12 digits of accuracy. Applying those corrections lat and long are good for precision in the mm range when applied to the earth's surface.
However, even without those corrections lat and long allowed people to navigate the earth for centuries with amazing and very practical success. How did they accomplish that supposing a flat earth? There must be an explanation, as they did actually do it. Or were James Cook, Ferdinand Magellan and Mr. Polo all shills on the NASA payroll? How they navigated is all a matter of history and you can read up about it. Their methods would not work on a flat earth - can you explain for us pleas? After all, in this thread here you are passing yourself off as a mapping expert. So expert as to debunk all of modern cartography.
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Rowbotham makes another minor error in calculations as outlined below.
The second example in his book was a route between Melbourne, AU and Bluff Harbor, NZ. I used the position for Melbourne as 37.8455 South -- 144.9425 East and the position for Bluff Harbor as 46.59833 South – 168.345 East. Using standard spherical trigonometry, I calculated the distance between the two ports at 1160 Nautical Miles. Due to the fact that there was a southerly component to the route of 8.75 degrees it makes sense that there would be about a 526 nautical miles ‘southing’ on the voyage and the 23.4 degree ‘easting’ would be 962 nautical miles. Rowbotham did say that he was allowing 50 statute miles for the angular or diagonal direction of the route. Probably he meant to say 500 Nautical Miles and just made a mistake. If you divide 962 NM by the 23.4 degree change in Longitude that comes out to a little over 41 nautical miles per degree longitude at 46 degrees South. The chart in the book would confirm that the expected distance between a degree of Longitude in the spherical earth model is quite close to the calculated distance of 41 nautical miles.
Rowbotham also said that the ‘latitude of Sydney would be 49.74 nautical miles or 58 statute miles’. If you do the calculation you find the figures above yield a 1.1666 conversion factor to convert Nautical Miles to Statute Miles. The modern-day figure currently is 1.15078. That’s just another small discrepancy that I noticed.
I’m sure that it was quite difficult for Rowbotham to bring together all the data that he did and attempt the calculations with his limited education. He didn’t have the nice computers and calculators that are available today. If you make the minor error corrections and redo all the calculations, you find that the spherical earth paradigm is nicely confirmed by Rowbotham’s data. Thank You Samuel Rowbotham.
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Longitude and Latitude isn't used by Google Maps/WebMercator to measure distances.
Have a read: The Earth is Not Round! Utah, NAD83 and WebMercator Projections (https://gis.utah.gov/nad83-and-webmercator-projections/)
Latitude and Longitude are useless for measuring distance and area because the unit of length, degrees, is not held constant for longitude, except along parallels -- individual perfectly east-west lines.
...
Web Mercator's significant weakness is that measurements of distance and area in its native coordinates are completely unusable. Where accurate distance and area calculations are needed, web-mercator GIS data must be temporarily reprojected to a more suitable coordinate system (UTM NAD83).
It is admitted that the latitude and longitude coordinates of the spherical earth model is completely unusable, and that the data must be reprojected onto a local state plane coordinate system for accuracy.
You are trying to compare lat/long coordinates which are said to be "completely unusable."
Indeed mapping a spherical surface on to flat paper is a tricky prospect with plenty of room to introduce errors. Interesting web site. How do you feel Tom that the link you provided is basing all its prime data on the earth being a sphere? If you accept all the information on this web site it follows you will have to ditch Rowbotham and all your flat earth beliefs.
Thanks for the link as it reinforces how ludicrous the idea of a flat earth map is. One true data set equals the possibility of onetrue map.
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Longitude and Latitude isn't used by Google Maps/WebMercator to measure distances.
Have a read: The Earth is Not Round! Utah, NAD83 and WebMercator Projections (https://gis.utah.gov/nad83-and-webmercator-projections/)
Latitude and Longitude are useless for measuring distance and area because the unit of length, degrees, is not held constant for longitude, except along parallels -- individual perfectly east-west lines.
...
Web Mercator's significant weakness is that measurements of distance and area in its native coordinates are completely unusable. Where accurate distance and area calculations are needed, web-mercator GIS data must be temporarily reprojected to a more suitable coordinate system (UTM NAD83).
It is admitted that the latitude and longitude coordinates of the spherical earth model is completely unusable, and that the data must be reprojected onto a local state plane coordinate system for accuracy.
You are trying to compare lat/long coordinates which are said to be "completely unusable."
Indeed mapping a spherical surface on to flat paper is a tricky prospect with plenty of room to introduce errors. Interesting web site. How do you feel Tom that the link you provided is basing all its prime data on the earth being a sphere? If you accept all the information on this web site it follows you will have to ditch Rowbotham and all your flat earth beliefs.
Thanks for the link as it reinforces how ludicrous the idea of a flat earth map is. One true data set equals the possibility of onetrue map.
Based on the article he quotes, Tom seems to be willing to trust a map generated from a UTM NAD83 projection, but he can't have it both ways. Earlier on I posted a map of the Falklands which is also generated via a UTM NAD83 (Zone 12N) projection (exactly the same one used in the article), so it should by Tom's reasoning be acceptably accurate. The problem is it shows a degree of longitude to be less than 70km wide, which means it's shorter than a degree of longitude on the equator, which means Rowbotham, by his own statements, faced with that evidence, would have had to admit that the earth was "globular" as he put it.
Whether Tom accepts or understands that a UTM NAD83 projection is entirely based on a globe earth or whether he does not, if he trusts that a map produced via this projection is accurate, then OK, here's just such a map and it shows the earth is at the very least "globular".
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Whether Tom accepts or understands that a UTM NAD83 projection is entirely based on a globe earth or whether he does not, if he trusts that a map produced via this projection is accurate, then OK, here's just such a map and it shows the earth is at the very least "globular".
A couple of times Tom has posted sources mentioning maps being a projection.
He seems to accept this but I’ve asked him why any projection necessary were the earth flat.
Maps on paper are obviously flat because pieces of paper are flat. Were the earth flat then it would be possible to represent the earth accurately on a map. Projection is necessary only because the earth is not flat.
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The OP starts from the premise of using google Earth.
If you go back to basics, with Norwood's method from the 1600s (summarised here by Bryson);
Starting with his back against the Tower of London, Norwood spent two devoted years marching 208 miles north to York, repeatedly stretching and measuring a length of chain as he went, all the while making the most meticulous adjustments for the rise and fall of the land and the meanderings of the road. The final step was to measure the angle of the sun at York at the same time of day and on the same day of the year as he had made his first measurement in London. From this, he reasoned he could determine the length of one degree of the Earth’s meridian and thus calculate the distance around the whole. It was an almost ludicrously ambitious undertaking—a mistake of the slightest fraction of a degree would throw the whole thing out by miles—but in fact, as Norwood proudly declaimed, he was accurate to “within a scantling”—or, more precisely, to within about six hundred yards. In metric terms, his figure worked out at 110.72 kilometres per degree of arc.
then ...
You surely must agree that the method hinges on the premise of the angle being drawn around a central point, and that can only be true of a globe. Where would you draw the central point on a flat earth?
The trigonometry hinges on the difference of two angles yielding the single angle drawn at the centre of an arc between the two points where the sightings were taken to the sun. Again, it has no meaning on anything other than a globe
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There are many points that use latitude and longitude on the earth. These points are accurately placed on a map and accurately depict how things are laid out on the earth. Now I can take those same latitude and longitude coordinates and calculate accurate distances between them using spherical trigonometry. That means either the earth is spherical because the results are accurate, or spherical trigonometry is an invalid mathematical procedure. These are two mutually exclusive things. It's a done deal. Sailors and pilots have for a long time used charts based upon a spherical earth. Navigational calculations are made every day based upon spherical trigonometry. Sailors don't get lost at sea. Planes don't get lost on long overseas flights and run out of fuel because they are lost. You just can't argue with success. You can discuss the fine points and debate getting the last little bits of accuracy from a chart, but the very basic, rock bottom, facts are that the earth is a sphere.
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We are missing the point of the OP. Rowbotham says:
The following is the true state of the question:--If the earth is a globe, it is certain that the degrees of longitude are less on both sides of the equator than upon it. If the degrees of longitude are less beyond, or to the south of the equator, than upon it, then it is equally certain that the earth is globular" (my emphasis)
So all that is needed to prove him wrong is to find any two positions of similar latitude and find whether the distance corresponding to 1 degree of longitude is less than the expected distance at the equator.
I have noticed (and Max Almond too) how GE tends to complicate the arguments unnecessarily. The argument is actually quite simple. See my posts above about road signs of the sort that say '100 miles to X'.
The OP starts from the premise of using google Earth.
If you go back to basics, with Norwood's method from the 1600s (summarised here by Bryson)
All true, but the question is the distance of 1 degree of longitude, not latitude.
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I illustrated the fact that the distance between 1 degree longitude lines South of the equator is less than 60 nautical miles in two of my posts above. Both of the examples were given by Rowbotham in his book where he just made a measurement or calculation error. After the errors were corrected the example clearly showed that the earth is a globe. It's a very simple concept to understand that the flat earth paradigm simply can't tolerate converging longitude lines South of the equator.
Google Earth was used and you could clearly observe and read road signs and distances. I tried a couple of examples doing that, but my results were inconclusive. You need a nice straight East-West road in Australia of about 100 to 200 miles. If you could read the road signs you could get a mileage figure and maybe match it up with the calculated mileage based upon the coordinates you also get from Google Earth. I have done that between a couple points and can confirm that my spherical trigonometric calculations match very closely to the mileage you get on Google Earth.
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Here's another sample of measuring longitude between two points. I got lucky. There are two airports in Australia. The first one is in Adelaide and the other is in Rowra.
Adelaide 34 degrees 56' -- 50'' South | 138 degrees 31' -- 59'' East Rowra 34 degrees 56' -- 30'' South | 150 degrees 32' -- 40" East
Notice how there's only a 20 second difference in Latitudes. That's about 1/2 mile difference at the most. The distance was checked several different ways. If you just went by the most verifiable way and drove the route you could expect a 715 Nautical mile trip. If you flew airport to airport you could expect the distance to be about 591 Nautical Miles. My spherical mileage calculations based upon the coordinates yielded the same 591 Nautical Miles. Now, as Rowbotham says, let's do the math: Difference in Longitudes is just a little over 12 degrees. That means the worst case driving mileage 715/12 = 59.58 Nautical Miles per degree. If you go the direct air route which is 124 Nautical Miles shorter you get: 591/12 = 49.25 Nautical Miles per degree. That is very close to Rowbotham's prediction for a spherical earth.
You can verify my figures yourself. Airports have verifiable locations so pilots can do their flight planning and not run out of gas. Maybe with a lot of work I could find some short cuts to reduce the driving mileage but this was just a simple example of what can be done. If you went by Rowbotham's figure of 25000 miles of flat earth circumference at the equator figure, that would mean at 34 degrees South Latitude the distance between 1 degree Longitude should be around 90 Nautical Miles by the flat earth paradigm. The worst case driving mileage calculations still comes out a whole lot closer to the globe earth rather than the flat earth paradigm. If you go by the direct air mileages you are within 1 percent of the spherical earth figures even by Rowbotham.
That's another one for Rowbotham ---- Round Earth: 3 Flat Earth: 0 (See the other examples in my posts above)
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Longitude and Latitude isn't used by Google Maps/WebMercator to measure distances.
Have a read: The Earth is Not Round! Utah, NAD83 and WebMercator Projections (https://gis.utah.gov/nad83-and-webmercator-projections/)
Latitude and Longitude are useless for measuring distance and area because the unit of length, degrees, is not held constant for longitude, except along parallels -- individual perfectly east-west lines.
...
Web Mercator's significant weakness is that measurements of distance and area in its native coordinates are completely unusable. Where accurate distance and area calculations are needed, web-mercator GIS data must be temporarily reprojected to a more suitable coordinate system (UTM NAD83).
It is admitted that the latitude and longitude coordinates of the spherical earth model is completely unusable, and that the data must be reprojected onto a local state plane coordinate system for accuracy.
You are trying to compare lat/long coordinates which are said to be "completely unusable."
Indeed mapping a spherical surface on to flat paper is a tricky prospect with plenty of room to introduce errors. Interesting web site. How do you feel Tom that the link you provided is basing all its prime data on the earth being a sphere? If you accept all the information on this web site it follows you will have to ditch Rowbotham and all your flat earth beliefs.
Thanks for the link as it reinforces how ludicrous the idea of a flat earth map is. One true data set equals the possibility of onetrue map.
Based on the article he quotes, Tom seems to be willing to trust a map generated from a UTM NAD83 projection, but he can't have it both ways. Earlier on I posted a map of the Falklands which is also generated via a UTM NAD83 (Zone 12N) projection (exactly the same one used in the article), so it should by Tom's reasoning be acceptably accurate. The problem is it shows a degree of longitude to be less than 70km wide, which means it's shorter than a degree of longitude on the equator, which means Rowbotham, by his own statements, faced with that evidence, would have had to admit that the earth was "globular" as he put it.
Whether Tom accepts or understands that a UTM NAD83 projection is entirely based on a globe earth or whether he does not, if he trusts that a map produced via this projection is accurate, then OK, here's just such a map and it shows the earth is at the very least "globular".
As I have mentioned previously, the production of accurate maps is much more complex than one would imagine. Here is quite a good guide from the OS in the UK that explains about how they use their GNSS data sets.
https://www.ordnancesurvey.co.uk/docs/support/guide-coordinate-systems-great-britain.pdf?awc=2495_1472758581_2be7907c343c32b09a8d5171103197d7 (https://www.ordnancesurvey.co.uk/docs/support/guide-coordinate-systems-great-britain.pdf?awc=2495_1472758581_2be7907c343c32b09a8d5171103197d7)
Once you have some inkling into the complexity of map production, it really makes you realise how ludicrous some flat earthers are when they claim to be working on producing a flat earth map!
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Based upon the evidence presented in this thread, it seems that the conclusion is:
(https://i.imgur.com/U6C23Av.jpg)
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Edby,
NAD doesn't use a Longitude or Latitude coordinate system.
The coordinates on the plane survey maps are simple integers.
Latitude and Longitude is a system for a globe in these models, and is not native to the planar maps. It is a spherical coordinate system.
If you are figuring out what the globe's Latitude and Longitude would be for the State Plane Coordinates you are interpreting a plane onto a globe, for the location of that plane on the globe model.
Here we see the State Plane Coordinates (SPC) and the associated Lat and Lon for the location on a sphere.
wvgis.wvu.edu/conference/2014/Wed_Track3/Iskic_NorthAmerican_Datums.pptx
(https://i.imgur.com/ZsaToHM.png)
The SPC coordinates look much different than the Latitude and Longitude's spherical coordinates.
This ad-hoc system they have is part sphere and part plane. You are arguing on basis of the spherical coordinate piece of it to justify your spherical earth.
I don't even hold that the longitude lines would widen, myself, as I have always been a proponent of the Bi-Polar model. I just see that the analysis on this matter appears to be flawed.
Rowbotham is actually referring to manual ways to find longitude, as was done in his time... The spherical geographical model that is associated with these planar maps is literally a sphere.
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We are missing the point of the OP. Rowbotham says:
The following is the true state of the question:--If the earth is a globe, it is certain that the degrees of longitude are less on both sides of the equator than upon it. If the degrees of longitude are less beyond, or to the south of the equator, than upon it, then it is equally certain that the earth is globular" (my emphasis)
So all that is needed to prove him wrong is to find any two positions of similar latitude and find whether the distance corresponding to 1 degree of longitude is less than the expected distance at the equator.
I have noticed (and Max Almond too) how GE tends to complicate the arguments unnecessarily. The argument is actually quite simple. See my posts above about road signs of the sort that say '100 miles to X'.
The OP starts from the premise of using google Earth.
If you go back to basics, with Norwood's method from the 1600s (summarised here by Bryson)
All true, but the question is the distance of 1 degree of longitude, not latitude.
Couldn't agree more. How wide is a degree of longitude south of the equator compared with on the equator? A really simple question to ask, very easy in the modern world to answer and if the answer is smaller to the south, then one of Rowbotham's central claims falls apart and by his own reasoning the earth is globular.
No need to complicate the discussion beyond the central question (and I admit I did get sidetracked myself trying to address Tom's spurious UTM NAD83 map arguments - sucked into that one!).
The New Zealand pic to me is great, it's so far south that the measurements are unambiguous and the road sign is there for all to see.
The fact that Tom seems to have withdrawn completely from further discussion and no other flat earthers seem willing to address the issue at all says nail on head, hit to me all day long.
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Edby,
NAD doesn't use a Longitude or Latitude coordinate system.
The coordinates on the plane survey maps are simple integers.
Latitude and Longitude is a system for a globe in these models, and is not native to the planar maps. It is a spherical coordinate system.
If you are figuring out what the globe's Latitude and Longitude would be for the State Plane Coordinates you are interpreting a plane onto a globe, for the location of that plane on the globe model.
Here we see the State Plane Coordinates (SPC) and the associated Lat and Lon for the location on a sphere.
wvgis.wvu.edu/conference/2014/Wed_Track3/Iskic_NorthAmerican_Datums.pptx
(https://i.imgur.com/ZsaToHM.png)
The SPC coordinates look much different than the Latitude and Longitude's spherical coordinates.
This ad-hoc system they have is part sphere and part plane. You are arguing on basis of the spherical coordinate piece of it to justify your spherical earth.
I don't even hold that the longitude lines would widen, myself, as I have always been a proponent of the Bi-Polar model. I just see that the analysis on this matter appears to be flawed.
Rowbotham is actually referring to manual ways to find longitude, as was done in his time... The spherical geographical model that is associated with these planar maps is literally a sphere.
I don't want to be picky but NAD83 (EPSG:4269) does use degrees for its units https://epsg.io/4269 (https://epsg.io/4269) "Attributes: Unit: degree (supplier to define representation)".
NAD83 itself is based on a reference ellipsoid (GRS80) which is locally a better approximation for the true shape of the earth (bumps, warts, and all) in North America than WGS84 which is on average a better approximation world wide. Other than that, NAD83 and WGS84 are based on exactly the same ideas, just different parameters. There are lots of other coordinate reference systems for different parts of the world which simply make for more accurate local maps, but they all work in basically the same way.
You start with WGS84 or NAD83 and then choose a projection to suit. The whole purpose of a projection is to give you a much more convenient 2D representation such as a paper map. Often these 2D representations switch to a more convenient cartesian coordinate system. An example would be NAD83 UTM Zone 12N (EPSG:2956) https://epsg.io/2956 (https://epsg.io/2956) "Attributes: Unit: metre".
So you see, NAD83 uses degrees, a UTM projection from NAD83 to a 2D map can then use metres.
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Based upon the evidence presented in this thread, it seems that the conclusion is:
(https://i.imgur.com/U6C23Av.jpg)
At the risk of a slap for a low content post - brilliant! love it!
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Latitude and Longitude is a system for a globe in these models, and is not native to the planar maps. It is a spherical coordinate system.
No, as stated many times above, measurements of latitude and longitude do not in themselves imply any shape of the earth.
(1) Longitude is defined by the (Greenwich) time at which the sun, circling round the flat earth, is at the highest position relative to the observer. All we need to know is Greenwich time, easy these days, a challenge for the early navigators.
(2) Latitude is defined by the height of the Sun above the flat earth horizon at midday.
The theoretical distance between two points of longitude and latitude depends on the shape of the earth, I don't disagree.
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The haversine formula determines the great-circle distance between two points on a sphere given their longitudes and latitudes. Important in navigation, it is a special case of a more general formula in spherical trigonometry, the law of haversines, that relates the sides and angles of spherical triangles.
Useful.
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I don't even hold that the longitude lines would widen, myself, as I have always been a proponent of the Bi-Polar model. I just see that the analysis on this matter appears to be flawed.
The problem with the Bi-Polar model is that it gets known latitude and longitude figures completely wrong. As I pointed out earlier, these are observable on a Flat Earth, and we have the observations.
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I don't even hold that the longitude lines would widen, myself, as I have always been a proponent of the Bi-Polar model. I just see that the analysis on this matter appears to be flawed.
The problem with the Bi-Polar model is that it gets known latitude and longitude figures completely wrong. As I pointed out earlier, these are observable on a Flat Earth, and we have the observations.
What observations do you (plural?) have?
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Edby,
I don't even hold that the longitude lines would widen, myself, as I have always been a proponent of the Bi-Polar model. I just see that the analysis on this matter appears to be flawed.
Rowbotham is actually referring to manual ways to find longitude, as was done in his time... The spherical geographical model that is associated with these planar maps is literally a sphere.
I'm not clear what the problem is TBH. Let's say we could pick somewhere suitably far south (and I think New Zealand is a good example).
We then identify a couple of places as far south as possible, a reasonable distance apart with a fairly straight road between them running approximately E-W. Pick two endpoints on this road. Can we find the distance between the two points? Well what would you trust? We can ask Google maps for a route, would you trust the result? Personally I find distances Google maps give me are accurate enough and correspond with reality, you may disagree, I don't know. We could look for road signs along the route with distances (exactly as edby has done in his examples). Would you (within reason) trust them? Again, personally I would tend to. Or perhaps you could suggest another way to determine the distance between the endpoints? Maybe we can find a map you would agree is accurate and estimate distances directly from the map?
Next, can we find the longitude and latitude of the two end points.
Do you agree that in principle we could go anywhere on earth and find through some means or other our latitude and longitude, with or without a suitable map?
A simple way to do this would be to get them from Google maps. A question again of trust. Personally I'd expect to be able to visit a random spot on earth, use "manual methods" (e.g. accurate clocks, a nautical almanac and a sextant) or a GPS device or otherwise to determine position and then find this in close agreement with Google Maps. I'd be very surprised to find a discrepancy of more than a few hundred meters for example.
Do you agree that we can trust Google Maps to give us accurate values for these positions? If not, is there some method you would accept?
If (hypothetically) we get past this point, we have two places a known distance apart then surely it's a simple calculation to determine distance divided by difference in longitude to find the width of a degree of longitude at that particular location.
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The problem I had was determining two known locations in New Zealand and then determining the distances between them. That's why I picked two airports. If you ever take flying lessons after you learn to control the aircraft you must learn navigation. Any flight you make between two points must start with knowing the distances and the known speed of your aircraft. Then you must know what your expected fuel consumption will be. Airport locations have been accurately surveyed and if there were any significant errors in that regard you can be sure that would soon be discovered and corrected. Sure, you can have plenty of variables while flying between two points. The wind can vary and you might have to fly at a different altitude that you originally planned, but the locations of the airports on your map can't be a variable. It must be known exactly. The next problem I had was determining an accurate way to measure the distances between two known locations. Here's where math comes into play. You can obtain a standard aeronautical sectional chart and simply measure the distance that way. There might be a discussion about the accuracy of the chart, or how it was made, or all the other kinds of straw man questions that come up on here. To short circuit all that I simply used spherical trigonometry and dot multiplied the two vectors representing the coordinates of the airports. That procedure will accurately give you the distance on a sphere between the two points in question. After having said all that, will the actual distances between my two airport locations on earth match my calculations? The answer was a definite yes. Errors were less than 1%. What can be learned from this exercise? You can very accurately determine the distance between two lines of longitude. There can be little doubt as to the accuracy of those calculations and that they accurately depict the shape of the earth as it is. My calculations also produced a result that showed that the earth is a sphere in the Southern hemisphere. I actually used Rowbotham's own distance figures between longitude lines to show that.
If there is any criticism of my methodology please let me know. There's no sense in bringing up any of the common straw man arguments. I could easily concede a 5% error and it wouldn't change the overall conclusion.
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I don't even hold that the longitude lines would widen, myself, as I have always been a proponent of the Bi-Polar model. I just see that the analysis on this matter appears to be flawed.
The problem with the Bi-Polar model is that it gets known latitude and longitude figures completely wrong. As I pointed out earlier, these are observable on a Flat Earth, and we have the observations.
What observations do you (plural?) have?
Observations of the position of the sun at various times and places.
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I don't even hold that the longitude lines would widen, myself, as I have always been a proponent of the Bi-Polar model. I just see that the analysis on this matter appears to be flawed.
The problem with the Bi-Polar model is that it gets known latitude and longitude figures completely wrong. As I pointed out earlier, these are observable on a Flat Earth, and we have the observations.
What observations do you (plural?) have?
Observations of the position of the sun at various times and places.
What distance to the sun do you calculate?
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I don't even hold that the longitude lines would widen, myself, as I have always been a proponent of the Bi-Polar model. I just see that the analysis on this matter appears to be flawed.
The problem with the Bi-Polar model is that it gets known latitude and longitude figures completely wrong. As I pointed out earlier, these are observable on a Flat Earth, and we have the observations.
What observations do you (plural?) have?
Observations of the position of the sun at various times and places.
What distance to the sun do you calculate?
No need to calculate distance. Time of highest point and angle is all that is needed.