[edby]

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.

[Tom Bishop]

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

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."

[stack]

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

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. 

[Tom Bishop]

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.

[stack]

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.

[stack]

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."

[Bobby Shafto]

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.

[Tom Bishop]

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?

[stack]

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

[Tom Bishop]

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!"

[Tom Bishop]

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!"

[stack]

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

[RonJ]

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.



 

[AATW]

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?

[Tom Bishop]

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:

[AATW]

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?

[inquisitive]

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.

[edby]

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?
Very well for the next experiment we must find two similar points connected by road.

[edby]

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.

[edby]

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.