#### Tom Bishop

• Zetetic Council Member
• 6236
• Flat Earth Believer
##### Re: Three flights forming a triangle with interior angles much more than 180 degrees
« Reply #20 on: December 05, 2018, 10:30:08 PM »
Quote
"UTM NAD83 is a projected coordinate system that represents physical locations abstracted to a flat, cartesian coordinate system."

NAD83 is a State Plane Coordinate System:

https://www.e-education.psu.edu/geog862/book/export/html/1644

Quote
State Plane Coordinates rely on an imaginary flat reference surface with Cartesian axes. They describe measured positions by ordered pairs, expressed in northings and eastings, or x- and y- coordinates. Despite the fact that the assumption of a flat Earth is fundamentally wrong, calculation of areas, angles and lengths using latitude and longitude can be complicated, so plane coordinates persist.

It uses only x- and y- coordinates. Flat. We are told that the State Plane Coordinate maps are used on the inside of the WGS model because they are the most accurate. They are only imagined to be abstracted from a globe. Surveying and mapping uses flat maps. The larger globe models merely temporarily show you the more accurate flat model elements, as explained in the article.

The truth is that there is no spherical model. It's just a mess of flat maps.
« Last Edit: December 05, 2018, 11:16:12 PM by Tom Bishop »

#### stack

• 1038
##### Re: Three flights forming a triangle with interior angles much more than 180 degrees
« Reply #21 on: December 05, 2018, 10:32:26 PM »
Quote
"UTM NAD83 is a projected coordinate system that represents physical locations abstracted to a flat, cartesian coordinate system."

NAD83 is a State Plane Coordinate System:

https://www.e-education.psu.edu/geog862/book/export/html/1644

Quote
State Plane Coordinates rely on an imaginary flat reference surface with Cartesian axes. They describe measured positions by ordered pairs, expressed in northings and eastings, or x- and y- coordinates. Despite the fact that the assumption of a flat Earth is fundamentally wrong, calculation of areas, angles and lengths using latitude and longitude can be complicated, so plane coordinates persist.

It uses only x- and y- coordinates. Flat. We are told that the State Plane Coordinate maps are used on the inside of the WGS model because they are the most accurate. They are only imagined to be abstracted from a globe. Surveying and mapping uses flat maps. The larger globe models just stitch them together and translate them through transformation layers

NAD83:
"The North American Datum of 1983 is based on a newer defined spheroid (GRS 80)"

https://en.wikipedia.org/wiki/North_American_Datum
Not much is known about the celestial bodies and their distances.

#### MCToon

• 153
##### Re: Three flights forming a triangle with interior angles much more than 180 degrees
« Reply #22 on: December 05, 2018, 10:35:46 PM »
Here is a source that says that military aeronautical charts are using the WGS84 model mentioned in the above Earth Not Flat! article:

https://www.degruyter.com/downloadpdf/j/pcr.2018.50.issue-1/pcr-2018-0002/pcr-2018-0002.pdf

What makes you think that your maps are any different? WGS84 is the standard.
Based on the spherical earth.

Here is the article for you again:

The Earth is Not Round! Utah, NAD83 and WebMercator Projections

It says that it is using flat maps underneath because they are more accurate.

"..locations abstracted to a flat, cartesian coordinate system.."

It's abstracted to a flat system, not from a flat system.

The source is a sphere.  Thank you for driving this in.

While very helpful, it's irrelevant to the ONC maps.  They do not come from UTM NAD83.

This is the image they use in the article to note the center of their coordinate system.

« Last Edit: December 05, 2018, 10:38:25 PM by MCToon »
I love this site, it's a fantastic collection of evidence of a spherical earth:
Flight times
Full moon
Horizon eye level drops
Sinking ship effect

#### Bobby Shafto

• 1383
• https://www.youtube.com/channel/UCdv72TaxoaafQr8WD
##### Re: Three flights forming a triangle with interior angles much more than 180 degrees
« Reply #23 on: December 05, 2018, 10:36:16 PM »
Less than 80° north and south, ONCs are based on Lambert Conformal Conic Projection.

North of 80°, they use the Polar Stereographic projection.

Horizontal datum (reference ellipsoid) is current World Geodetic System (WGS) standard.

#### Tom Bishop

• Zetetic Council Member
• 6236
• Flat Earth Believer
##### Re: Three flights forming a triangle with interior angles much more than 180 degrees
« Reply #24 on: December 05, 2018, 10:37:17 PM »
https://en.wikipedia.org/wiki/State_Plane_Coordinate_System

Quote
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.

Lower down in that article:

Quote
Originally, the state plane coordinate systems were based on the North American Datum of 1927 (NAD27). Later, the more accurate North American Datum of 1983 (NAD83) became the standard (a geodetic datum is the way a coordinate system is linked to the physical Earth). More recently there has been an effort to increase the accuracy of the NAD83 datum using technology that was not available in 1983.

The government says so as well:

https://catalog.data.gov/dataset/united-states-stateplane-zones-nad83

Quote
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.

NAD83 is a flat coordinate system.

You can call it "abstracted from a globe" if you imagine the earth to be so. However, they are flat coordinate systems, and are used because these flat coordinate systems are more accurate.
« Last Edit: December 05, 2018, 10:42:19 PM by Tom Bishop »

#### MCToon

• 153
##### Re: Three flights forming a triangle with interior angles much more than 180 degrees
« Reply #25 on: December 05, 2018, 10:40:48 PM »
https://en.wikipedia.org/wiki/State_Plane_Coordinate_System

Quote
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.

Lower down in that article:

Quote
Originally, the state plane coordinate systems were based on the North American Datum of 1927 (NAD27). Later, the more accurate North American Datum of 1983 (NAD83) became the standard (a geodetic datum is the way a coordinate system is linked to the physical Earth). More recently there has been an effort to increase the accuracy of the NAD83 datum using technology that was not available in 1983.

The government says so as well:

https://catalog.data.gov/dataset/united-states-stateplane-zones-nad83

Quote
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.

Its flat.

This is all great stuff showing how they mapped the 3D coordinates to a 2D system to make things easier.  Very helpful in understanding how these work.  But still off topic.  ONC maps are Lambert Conformal Conic projections from a different dataset.
I love this site, it's a fantastic collection of evidence of a spherical earth:
Flight times
Full moon
Horizon eye level drops
Sinking ship effect

#### Tom Bishop

• Zetetic Council Member
• 6236
• Flat Earth Believer
##### Re: Three flights forming a triangle with interior angles much more than 180 degrees
« Reply #26 on: December 05, 2018, 10:43:45 PM »
This is all great stuff showing how they mapped the 3D coordinates to a 2D system to make things easier.  Very helpful in understanding how these work.  But still off topic.  ONC maps are Lambert Conformal Conic projections from a different dataset.

Show us. The military says that their aeronautical charts are based on the WGS-84 model in question:

Quote from: Tom Bishop
Here is a source that says that military aeronautical charts are using the WGS84 model mentioned in the above Earth Not Flat! article:

https://www.degruyter.com/downloadpdf/j/pcr.2018.50.issue-1/pcr-2018-0002/pcr-2018-0002.pdf

What makes you think that your maps are any different? WGS84 is the standard.

Why should your model be any different?

#### stack

• 1038
##### Re: Three flights forming a triangle with interior angles much more than 180 degrees
« Reply #27 on: December 05, 2018, 10:45:10 PM »

NAD83 is a flat coordinate system.

You can call it "abstracted from a globe" if you imagine the earth to be so. However, they are flat coordinate systems, and are used because these flat coordinate systems are more accurate.

You apparently missed it the first time:NAD83:

"The North American Datum of 1983 is based on a newer defined spheroid (GRS 80)"

https://en.wikipedia.org/wiki/North_American_Datum

And, according to you logic, NAD83 is based upon the wrong shape so any map based on it must be wrong. Interesting.
Not much is known about the celestial bodies and their distances.

#### MCToon

• 153
##### Re: Three flights forming a triangle with interior angles much more than 180 degrees
« Reply #28 on: December 05, 2018, 10:47:20 PM »
This is all great stuff showing how they mapped the 3D coordinates to a 2D system to make things easier.  Very helpful in understanding how these work.  But still off topic.  ONC maps are Lambert Conformal Conic projections from a different dataset.

Show us. The military says that their aeronautical charts are based on the WGS-84 model in question:

Quote from: Tom Bishop
Here is a source that says that military aeronautical charts are using the WGS84 model mentioned in the above Earth Not Flat! article:

https://www.degruyter.com/downloadpdf/j/pcr.2018.50.issue-1/pcr-2018-0002/pcr-2018-0002.pdf

What makes you think that your maps are any different? WGS84 is the standard.

Why should your model be any different?

Yes, ONC are based on WGS, not UTM NAD83.

Tom, have you changed stripes?  Why are you supporting the globe case so aggressively here?

I love this site, it's a fantastic collection of evidence of a spherical earth:
Flight times
Full moon
Horizon eye level drops
Sinking ship effect

#### Tom Bishop

• Zetetic Council Member
• 6236
• Flat Earth Believer
##### Re: Three flights forming a triangle with interior angles much more than 180 degrees
« Reply #29 on: December 05, 2018, 11:45:48 PM »
Quote from: stack
"..locations abstracted to a flat, cartesian coordinate system.."

It's abstracted to a flat system, not from a flat system.

The source is a sphere.  Thank you for driving this in.

If you believe the earth to be a sphere then it is abstracted to a flat system. The fact remains, however, that these flat systems are used because they are the most accurate. They are state-plane coordinate systems. Feel free to look it up.

WGS relies on these maps to give out accurate data.

Quote from: MCToom
Yes, ONC are based on WGS, not UTM NAD83.

Tom, have you changed stripes?  Why are you supporting the globe case so aggressively here?

Here you go:

https://www.gpsworld.com/data-collection-of-wgs-84-information-or-is-it/

Quote
In the meantime, here are a few of the main differences between WGS 84 and NAD83:

The coordinate system for WGS 84 is geographic, and the NAD83 system is projected.

https://www.gpsworld.com/data-collection-of-wgs-84-information-or-is-it/

Quote
WGS84 doesn't define a projection, so it's up to the GIS software to decide which projection to use for displaying the data on the screen (unless you manually pick a projection, of course).

Take a look at the list of projections for ARCGIS software:

http://desktop.arcgis.com/en/arcmap/latest/map/projections/pdf/geographic_transformations.pdf

NAD83 is one of them. These are all flat coordinate systems. It's taking data from flat systems, because as the "Earth Not Round!" article said, it is these flat systems that are more accurate and give out more accurate figures.
« Last Edit: December 05, 2018, 11:52:33 PM by Tom Bishop »

#### stack

• 1038
##### Re: Three flights forming a triangle with interior angles much more than 180 degrees
« Reply #30 on: December 05, 2018, 11:56:27 PM »
If you believe the earth to be a sphere then it is abstracted to a flat system. The fact remains, however, that these flat systems are used because they are the most accurate. They are state-plane coordinate systems. Feel free to look it up.

WGS relies on these maps to give out accurate data.

World Geodetic System (WGS84)

"The Global Positioning System uses the World Geodetic System (WGS84) as its reference coordinate system. It comprises of a reference ellipsoid, a standard coordinate system, altitude data and a geoid.
Because the Earth is curved – and in GIS we deal with flat map projections – we need to accommodate both the curved and flat views of the world. Surveyors and geodesists have accurately defined locations on Earth.”

https://gisgeography.com/wgs84-world-geodetic-system/

"What are Map Projections?

Earth is a big blue marble that’s the shape of a sphere (or close to it). This is why a globe is the best way to represent the Earth.

But globes are hard to carry in your suitcase and you can only see one side of the globe. On top of that, it’s hard to measure distances and they’re just not as convenient as paper maps.

This is why we use map projections on globes and flatten it out in two-dimensions. But as you’re about to find out, you can’t represent Earth’s surface in two dimensions without distortion. "

https://gisgeography.com/map-projections/
Not much is known about the celestial bodies and their distances.

#### MCToon

• 153
##### Re: Three flights forming a triangle with interior angles much more than 180 degrees
« Reply #31 on: December 06, 2018, 12:08:45 AM »

NAD83 is one of them. These are all flat coordinate systems. It's taking data from flat systems, because as the "Earth Not Round!" article said, it is these flat systems that are more accurate.

Yes, the article says NAD83 is more accurate than Web Mercator, nothing more:
"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)"

So, when you need to calculate distance, reproject from Web Mercator to UTM NAD83 then back to Web Mercator.

According to the article, NAD83 is "...abstracted to a flat, cartesian coordinate system..." from "... the GRS80 ellipsoid and a center-of-the-earth anchor point as its datum..."  The source of the datum is not flat.

All this is off topic.  ONC charts use neither Web Mercator nor UTM NAD83.  They use WGS.  They predate WGS84 by decades.

All the links you posted agree, the source of all this data is an oblate spheroid.

That still changes nothing.  The specific source of ONC data makes little difference.  The charts could have been found petrified in the bottom of a mountain left here by reptilian ancestors.  The charts work.  They have worked for decades.
The charts closely approximate a sphere.  The discrepancies between the conical projection and the spherical source are known and navigators can correct for these when the margin of error must be smaller.

Either the charts are grossly inaccurate or the earth is an oblate spheroid.  The videos validates the accuracy of the charts.

The burden of proof has been met again supporting the globe.

Thank you for this forum to share this truth.
I love this site, it's a fantastic collection of evidence of a spherical earth:
Flight times
Full moon
Horizon eye level drops
Sinking ship effect

#### Tom Bishop

• Zetetic Council Member
• 6236
• Flat Earth Believer
##### Re: Three flights forming a triangle with interior angles much more than 180 degrees
« Reply #32 on: December 06, 2018, 01:46:58 AM »

NAD83 is one of them. These are all flat coordinate systems. It's taking data from flat systems, because as the "Earth Not Round!" article said, it is these flat systems that are more accurate.

Yes, the article says NAD83 is more accurate than Web Mercator, nothing more

The full name of Web Mercator is WGS 84 Web Mercator

https://en.m.wikipedia.org/wiki/Web_Mercator_projection

"While the Web Mercator's formulas are for the spherical form of the Mercator, geographical coordinates are required to be in the WGS 84 ellipsoidal datum."

It's a web-based version of WGS 84. The WGS part is also mentioned in the Earth Not Round! article. You can make your own inferences from there.

#### stack

• 1038
##### Re: Three flights forming a triangle with interior angles much more than 180 degrees
« Reply #33 on: December 06, 2018, 01:55:48 AM »

NAD83 is one of them. These are all flat coordinate systems. It's taking data from flat systems, because as the "Earth Not Round!" article said, it is these flat systems that are more accurate.

Yes, the article says NAD83 is more accurate than Web Mercator, nothing more

The full name of Web Mercator is WGS 84 Web Mercator

https://en.m.wikipedia.org/wiki/Web_Mercator_projection

"While the Web Mercator's formulas are for the spherical form of the Mercator, geographical coordinates are required to be in the WGS 84 ellipsoidal datum."

It's a web-based version of WGS 84. The WGS part is also mentioned in the Earth Not Round! article. You can make your own inferences from there.

Why are you referencing "web mercator"? As MCToon already stated and showed in the video ONC maps are Lambert Conformal Conic projections using the WSG84. In any case, here is how WGS84 is created:

"WGS84 is based on a consistent set of constants and model parameters that describe the Earth's size, shape, and gravity and geomagnetic fields.

WGS84 identifies four defining parameters. These are the semi-major axis of the WGS84 ellipsoid, the flattening factor of the Earth, the nominal mean angular velocity of the Earth, and the geocentric gravitational constant as specified below."

https://confluence.qps.nl/qinsy/en/world-geodetic-system-1984-wgs84-29855173.html

"Numerical values for planets

For the WGS84 ellipsoid to model Earth, the defining values are:

a (equatorial radius): 6 378 137.0 m
1/f (inverse flattening): 298.257 223 563
from which one derives

b (polar radius): 6 356 752.3142 m,
so that the difference of the major and minor semi-axes is 21.385 km (13 mi). (This is only  0.335% of the major axis, so a representation of Earth on a computer screen would be sized as 300px by 299px. Because this would be virtually indistinguishable from a sphere shown as 300px by 300px, illustrations typically greatly exaggerate the flattening in cases where the image needs to represent Earth's oblateness.)"

https://en.wikipedia.org/wiki/Flattening
Not much is known about the celestial bodies and their distances.

#### Pete Svarrior

• e
• Planar Moderator
• 9273
• (◕‿◕✿)
##### Re: Three flights forming a triangle with interior angles much more than 180 degrees
« Reply #34 on: December 06, 2018, 10:35:00 AM »
Interesting that the RE peanut gallery is ignoring the fact that the route presented is not a triangle. It's almost as if you weren't interested in resolving the critical contradiction in your self-proclaimed victory.
Read the FAQ before asking your question - chances are we've already addressed it.
Follow the Flat Earth Society on Facebook and Twitter!

*mic stays stationary and earth accelerates upwards towards it*

#### stack

• 1038
##### Re: Three flights forming a triangle with interior angles much more than 180 degrees
« Reply #35 on: December 06, 2018, 10:45:32 AM »
Interesting that the RE peanut gallery is ignoring the fact that the route presented is not a triangle. It's almost as if you weren't interested in resolving the critical contradiction in your self-proclaimed victory.

You obviously did not watch what the challenge was and how MCToon won the challenge.
Not much is known about the celestial bodies and their distances.

#### MCToon

• 153
##### Re: Three flights forming a triangle with interior angles much more than 180 degrees
« Reply #36 on: December 06, 2018, 08:52:07 PM »
Interesting that the RE peanut gallery is ignoring the fact that the route presented is not a triangle. It's almost as if you weren't interested in resolving the critical contradiction in your self-proclaimed victory.

Sometimes geometry can be hard:
http://mathworld.wolfram.com/SphericalTriangle.html

The flat earther that issued the challenge declared that entry the winner:

I love this site, it's a fantastic collection of evidence of a spherical earth:
Flight times
Full moon
Horizon eye level drops
Sinking ship effect

#### totallackey

• 939
##### Re: Three flights forming a triangle with interior angles much more than 180 degrees
« Reply #37 on: December 07, 2018, 01:53:19 PM »
There can never be an accurate FE map because the map that already works cannot be flattened without distortions.
I believe your sentence would be accurate if it was thus written:
There can never be accurate FE map because the map that already works cannot be flattened because it is already flat, as are all maps.

#### Pinky

• 88
##### Re: Three flights forming a triangle with interior angles much more than 180 degrees
« Reply #38 on: December 07, 2018, 05:09:18 PM »
less than 540 degrees.

That's incorrect. On a 2D-manifold with positive curvature, the inside-angle of a triangle goes from 180° (infintely small area inside triangle) to 3*(360°-60°)=900° (infinitely small area outside triangle).

#### Pinky

• 88
##### Re: Three flights forming a triangle with interior angles much more than 180 degrees
« Reply #39 on: December 07, 2018, 05:13:06 PM »
Interesting that the RE peanut gallery is ignoring the fact that the route presented is not a triangle. It's almost as if you weren't interested in resolving the critical contradiction in your self-proclaimed victory.

It is a triangle. Three points connected by geodesic lines.