Mapping the Earth

Hello johannes,
Please see my comments below.

johannes.wallenfang wrote:bdhfe,

The speedometers in our cars are also adjusted to these erroneous values; it would quickly become apparent if the distance to the neighboring town was indicated by the speedometer as 4 miles, but on traffic signs and on the web as 6 miles.

Nobody will bother to measure the distance with a folding ruler...

I do not believe we have to go to such a small increment based on standards that have been used for hundreds of years.....  namely for example, the definition of a SECTION of land.
From Wikipedia:
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In U.S. land surveying under the Public Land Survey System (PLSS), a section is an area nominally one square mile (2.6 square kilometers), containing 640 acres (260 hectares), with 36 sections making up one survey township on a rectangular grid.
...
The existence of section lines made property descriptions far more straightforward than the old metes and bounds system. The establishment of standard east-west and north-south lines ("township" and "range lines") meant that deeds could be written without regard to temporary terrain features such as trees, piles of rocks, fences, and the like, and be worded in the style such as "Lying and being in Township 4 North; Range 7 West; and being the northwest quadrant of the southwest quadrant of said section," an exact description in this case of 40 acres, as there are 640 acres (260 ha) in a square mile.

The importance of "sections" was greatly enhanced by the passage of "An Ordinance for ascertaining the mode of disposing of lands in the Western Territory" of 1785 by the U.S. Congress (see Land Ordinance of 1785).
>>

Now, taking the one square mile area into account, each side being one mile, we see there are 6 sections between the township of Farmer and Withrow.  See the illustration below:

....................

...................

Hence, I am comfortable using the definition of the size of the SECTION for accuracy in measuring distances.  

Now, what you are saying about the manipulation of distance with regard to speedometers is well taken, and it is likely some manipulation is going on.

bdh

Hi johannes,
There are some more comments I would like to make to hopefully clarify my position on Gleason's map and Greenwich coordinates.  See below:

johannes.wallenfang wrote:bdhfe,

The Greenwich data for latitude and longitude are not wrong. But you can't transfer them to a globe if you don't want to get lost.
In addition, the entire measurement of time is based on their data.
All this is so precise that the course of the stars in the firmament can also be calculated exactly.
I would therefore leave the 12:00 UTC time and the longitude 0 as they are...

Two things:
1.  I would like to confirm the Greenwich data for latitude and longitude to show the validity of the flat surface of the Earth as depicted by Gleason.  
2.  As well, I have not suggested replacing Greenwich as the Prime Meridian with any other.

johannes.wallenfang wrote:

There are some things I don't quite understand.
On the one hand, you want to be independent of Greenwich data; on the other hand, you use distance data from Google Maps, which are not necessarily known as friends of the flat earth...

If the Greenwich data is incorrect, then yes, I would not use it.  At no time do I use Google Map distance as the true arbiter of  distance.  I will use it if it jives with  personal experience and valid assumptions.  All Google Map distances are not incorrect.

johannes.wallenfang wrote:

If you make adjustments to get the same results as in Google Maps, you might as well throw the calculator in the garbage can.
Every official version calculates distances using a non-existent curvature of a ridiculous sphere.

I never intended to have the same numbers as everyone else as a result.
That's why I made the DC exactly as it is.

Your DC calculator is an invaluable tool and I use it constantly.
By making any adjustment, essentially making it jive with the distance on Google maps between Farmer WA and Withrow WA, I am not using Google maps as the baseline, but in fact applying my experience with Township, Range, Acre, Hectare, and Sections.  I live on 5 acres....  660 feet by 330 feet.  I  measure 660 walking from one end of the property to the other, and I measure 330 walking from one side to the other.  I know what a Section size is as we have most of our streets in this area running along Section borders in ONE mile increments.  I know it is 6 miles between Farmer WA and Withrow WA based on the size of a Section.  Again, it is not  Google maps as the reference point just because I took a screen shot of the Farmer/Withrow area.

johannes.wallenfang wrote:

The conversion factor would be:
1 ÷ radius of the equator × quarter circle north pole - equator.
(1 ÷ 6366.707 km ×10000.80 km = 1.570796332)

Question:  This is the conversion factor for what exactly?

johannes.wallenfang wrote:

What do we do now with the nautical mile and its siblings mile & kilometer?
Redefine them if the equator now has a much larger circumference?
Was it not just me but also Alexander Gleason who was completely wrong because we use 60 nautical miles at the equator and 120 at 90 degrees south?
If so, we must also add to the hall of fame those people who defined the nautical mile as a minute of arc or 1/60th of a degree... (Hall of fame of big errors)

(Sorry; I'm blonde on the outside but deep down there's a lot of dark humor...)

Dark humor aside, I am not planning to redefine what a nautical mile is.  I am questioning the conversion between a nautical mile and statute mile as given to us in textbooks.
Why do I question it?  
Because, and please correct my math if I am wrong, the radius of the circle between the North Pole and the Equator necessitates a circumference that is larger than the value provided by the globe.  It is 60 nautical miles per degree on Longitude......... yes...... correct......indeed.  But, what is the value in Statute miles?  You say leave the conversions between nautical mile, statute mile, kilometer alone.  If I did, we would be caving to the values given by the globe.

You choose to question speedometers (or odometers) with its mileage calcs, but is it not easier to fiddle with a conversion factor between nautical mile and statute?

You disagree when I state that the distance between degrees of LATITUDE are approximately 69 STATUTE miles,  Yet on Globe or Flat plane, anywhere on the Earth, the distance between degrees of Latitude are a constant, unless it can be shown that there is a widening or shortening in distance, to a large degree, somewhere on Earth.

bdh

I would point to the trigonometric surveys carried out real scientists during the 17th and early 18th centuries . The fact is that latitude shortens towards the N pole. The work of Giovanni Cassini for the French Royal Academy of Sciences .

Also the distance between Paris and Brest , when triangulated by Cassini and Picard ( I think) resulted in shortening the expected size of France according to the globe model by around 20%. The distance between longitudes was not consistent with the globe model .

We do not live on a globe and the equator being at 0 degrees N is imaginary nonsense . You can't mix coordinate systems and expect to form a true map. You either map everything from the N pole using the celestial dome or you could possibly triangulate from the equinoctial circle but that would far more complicated to do.

I extrapolated Cassinis figures for the meridian across France north to the pole . At 89N a degree of latitude would be around 65 mls. Very time consuming work ,checking & rechecking .

I tried to find the distances between flights along the equator but there are no direct flights along the equinoctial circle from which we could approximate its true distance.

Using the given distance between the N pole and Equator and removing the globe arc i.e. measure the length of the chord may give a means of calculating a length for the circumference around the equinoctial circle . Might try that when I get more time .

Hope this makes sense and I hope you see this just as constructive criticism and my own thoughts - but they are based on real scientific measure.

P.S. the Greenwich and Paris Meridians have been moved and altered over the years .

johannes.wallenfang wrote:bdhfe,

During my research into determining longitude, I came across a PDF which, although it adores the spherical theory, describes a special method of sextant measurement for measuring the position of the sun.
This avoids the problem that the sun is at this angle for almost four minutes at its highest position.

johannes, I did not know that.  Excellent find!!  This shall be incorporated into the next version of Finding Longitude.  Interesting thing about the 4 minutes.....  On the testing I was  performing, I was getting about a 3.5 minute discrepancy each time....

johannes.wallenfang wrote:
If you measure a certain angle to the sun, e.g. 30 degrees at 11:30 a.m., then you have to observe at what time the sun has the same angle in the afternoon.
The average of the time measurements gives the exact time of the sun's highest point and thus the longitude at which you are located.







https://docplayer.org/18769750-Zeitbestimmung-auf-see.html
>>>Page 38 and 39.

It was a mystery to me how to determine the maximum position of the sun on a ship without a fixed reference point, apart from the horizon...

bdh

TyrannicalSawdustRex wrote:I would point to the trigonometric surveys carried out real scientists during the 17th and early 18th centuries . The fact is that latitude shortens towards the N pole. The work of Giovanni Cassini for the French Royal Academy of Sciences .

Also the distance between Paris and Brest , when triangulated by Cassini and Picard ( I think) resulted in shortening the expected size of France according to the globe model by around 20%. The distance between longitudes was not consistent with the globe model .

Tyrannical,
If what you are saying is correct as regards the shortening of distance between Latitudes as one goes North, then Gleason's map is no  longer valid as he is using Greenwich data for it.  One can see on Gleason's a constant difference in distance between Latitudes.  
Even his table on Longitude widening with each 15 degrees of Latitude will not be accurate.

So, while I cogitate on this data, and I am not dismissing it, but based on Gleason's, I am not ready to abandon Gleason as yet.

TyrannicalSawdustRex wrote:
We do not live on a globe and the equator being at 0 degrees N is imaginary nonsense . You can't mix coordinate systems and expect to form a true map. You either map everything from the N pole using the celestial dome or you could possibly triangulate from the equinoctial circle but that would far more complicated to do.

We do not live on a globe as we live on a flat plane that is circular in nature (visibly circular that is) with a Sun that rotates in a full circle above us every 24 hours.
As such,  history and experience have shown that one can use this Sun to arrive at one's  location on the flat  plane.  That is what my project here is all about..... putting  the correct numbers to locations  so that we overcome the Greece Ball nonsensical fantasy that has been imposed upon us.

TyrannicalSawdustRex wrote:
Hope this makes sense and I hope you see this just as constructive criticism and my own thoughts - but they are based on real scientific measure.

P.S. the Greenwich and Paris Meridians have been moved and altered over the years .

I take it very constructively and am in no  position or inclination to dismiss this information.

bdh

Let's smash the Greece Ball!

Ok, here is the Greece Ball with  Diameter X....  at the equator:



Here is the Flat Earth with Diameter X for the Equatorial Circle:



Putting the Flat Earth on top of the Greece Ball by matching the center of the Greece Ball with the NP  point on the Flat Earth, and wrapping the Flat Earth on top of the Greece Ball, results in the Equator of the Flat Earth unable to reach the equator of the Greece Ball.
I have to draw a new Equator on the Flat Earth to match the equator on the Greece Ball when wrapping the Flat Earth over the Greece Ball.  See the new Equatorial Circle on the Flat Earth:



This new Diameter on the Flat Earth is 1.5X... that is One and Half times larger than the original Equatorial Circle's diameter on the Flat Earth.

This is the basis for my adjustment of johannes' DC, and this new Circle on the Flat Earth represents the true Equatorial Circumference of the Flat Earth.
This assumes a constant value for difference in Latitudinal degrees.

bdh

Nautical Mile definitions

From Seemeile (Deutsch) aus Wikipedia:
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A full circle contains 360 degrees, with 60 minutes per degree, i.e. a total of 21600 minutes. The nautical mile was therefore the 21600th part of the Earth's circumference at the equator.
>>

From  aerocorner.com:
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So a nautical mile is derived from latitude. One minute of latitude is equal to one nautical mile. How long is a nautical mile? A nautical mile contains 6,076 feet or 1,852 meters. There was a period when different systems defined the nautical miles differently, but this has been standardized now so that everyone uses the same measurement.
>>

From simpleflying.com:
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Developing the nautical mile
The nautical mile came about as a practical navigational development. The concept of parallels of latitude and meridians of longitude developed during the 16th Century. Navigation this way was sought as an alternative to visual methods.

The nautical mile is based on latitude and longitude. As we know, the sphere of the earth is broken up into 360 degrees. Dividing this further, each degree is split into 60 minutes. A nautical mile represents the distance of one of these minutes of latitude. This is essentially one-sixtieth of a degree.
>>

From these definitions, it is given that the nautical mile is based on both Latitude and Longitude on the Spherical Earth.... and the definitions indicate that One minute of Latitude EQUALS One minute of Longitude.

Is this true though?
Does one (1) minute of Latitude EQUAL one (1) minute of Longitude on the Flat Earth?

The answer is NO!

There is only one Latitude where One minute of Longitude  equals One minute of Latitude.  And where would that be?

Somewhere between the 30th and 45th Northern Latitudes.  See Gleason:



The virtual square formed between the 30th and 45th N  Latitudes and Longitudes provides us this fact as the Longitude and Latitude are virtually the same length.
So that magic Latitude Longitude matchup lies somewhere in that virtual square.

What  does this say about the definition of the Nautical Mile?  It cannot be based on Latitude, except for one spot on Earth where the Nautical Mile, based on Longitude at the Equator, resides.  Every where else on Earth, Latitude cannot be used to define the nautical mile.
Only the definition provided by the Seemeile (Deutsch) aus Wikipedia can be used for Flat Earth calculations going forward.

To be continued

bdh

Continuing with Nautical versus Statute Miles,

One can, after further study and testing, definitively say that One (1) NAUTICAL MILE =  21600th part of the Earth's circumference at the equator.  The Circumference of the Equatorial Circle therefore Equals 21600 Nautical Miles.  This is consistent with Gleason's map and johannes' Distance Calculator.

As for STATUTE Miles, the prevailing doctrine states that 1 Nautical Mile Equals 1.15 Statute Miles.
As this doctrine is applicable to the Globe  and not to a Flat Plane, consequently, I dispute that number.

Instead, On the Flat Plane, I have found by testing and study that 1 Nautical Mile Equals approximately 1.8 Statute Miles.  **

** Testing is still under way.

NB: This value is  based on the ASSUMPTION that the Latitudes and Longitudes  provided by Greenwich England and found on Google Earth are accurate.

Of further note, the Globe definition of Nautical Mile being based on Latitude cannot be used on the Flat  Plane, as I earlier stated, and this is due to the fact that distances between degrees of Longitude constantly increase as one moves South.  

bdh

Regarding LATITUDE, this can be arrived at by Definition.

Two things:
1.  It is a constant anywhere on Earth and it does not vary in the way that distance between degrees of Longitude vary.

2.  Its value is based on the defined 21600 Nautical Miles around the Equatorial Circle.
The formula 2*PI*R = C applies here, where PI = 3.14, C is the Circumference of the Equatorial Circle and R is the Radius from 90 Degrees North to 0 Degrees Latitude.  R by definition then, Equals 3439.49 Nautical Miles.
One Degree of Latitude consistently with some variation Equals approximately 38.216 Nautical Miles

bdh

bdhfe wrote:Nautical Mile definitions

There is only one Latitude where One minute of Longitude  equals One minute of Latitude.  And where would that be?

Somewhere between the 30th and 45th Northern Latitudes.  See Gleason:



The virtual square formed between the 30th and 45th N  Latitudes and Longitudes provides us this fact as the Longitude and Latitude are virtually the same length.
So that magic Latitude Longitude matchup lies somewhere in that virtual square.

bdh

Interestingly enough..... and I did not use the word "magically" intentionally..... the one point on Earth where the distance between degrees Latitude and distance between degrees Longitude match is the 33rd degree North Latitude.

Funny that.  

bdh