[robinofloxley]

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



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 "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 "Attributes: Unit: metre".

So you see, NAD83 uses degrees, a UTM projection from NAD83 to a 2D map can then use metres.

[robinofloxley]

Based upon the evidence presented in this thread, it seems that the conclusion is:

At the risk of a slap for a low content post - brilliant! love it!

[edby]

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.

[inquisitive]

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.

[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.

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.

[inquisitive]

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?

[robinofloxley]

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.

[RonJ]

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.     

[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.

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.

[inquisitive]

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?

[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.

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.