[Stagiri]

Is there any formula for calculating the radius of a certain circle of latitude?
I've read that each latitude degree is 69.5 miles further from the North Pole. Is it correct?

[Tumeni]

"Each degree of latitude is approximately 69 miles (111 kilometers) apart. The range varies (due to the earth's slightly ellipsoid shape) from 68.703 miles (110.567 km) at the equator to 69.407 (111.699 km) at the poles."

The radius of the Earth is pretty much constant, given the variance (oblateness) described above.

Are you looking to draw a 'horizontal' at each latitude line, and calculate the radius of each, like the base of a spherical cap, where the cap height moves closer and closer to the North Pole?

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

[douglips]

I think Stagiri wants the radius of the circle, not the radius of the earth.

In the mono-polar north-centric flat earth model, the radius of the circle is just 60 nautical miles (approximately 69 statute or "normal" miles) times the the difference in degrees between 90 degrees north and the latitude in question. So, here are some approximate radii:
Arctic circle: 1617 miles
tropic of cancer: 4590 miles
equator: 6210 miles
tropic of capricorn: 7830 miles
antarctic circle: 10800 miles.

In the round earth theory, the distance from the north pole as measured along the surface of the earth is the same as the radius from flat earth model. But, because of the curve, the radius of the actual planar circle is smaller.

The radius of the circle (ignoring the oblateness of the earth) is the radius of the earth times the cosine of the latitude. Here are the same latitude circle radii:
Arctic circle: 1578 miles
tropic of cancer: 3630 miles
equator: 3959 miles
tropic of capricorn: 3630 miles
antarctic circle: 1578 miles.

[Stagiri]

I think Stagiri wants the radius of the circle, not the radius of the earth.

In the mono-polar north-centric flat earth model, the radius of the circle is just 60 nautical miles (approximately 69 statute or "normal" miles) times the the difference in degrees between 90 degrees north and the latitude in question. So, here are some approximate radii:
Arctic circle: 1617 miles
tropic of cancer: 4590 miles
equator: 6210 miles
tropic of capricorn: 7830 miles
antarctic circle: 10800 miles.

In the round earth theory, the distance from the north pole as measured along the surface of the earth is the same as the radius from flat earth model. But, because of the curve, the radius of the actual planar circle is smaller.

The radius of the circle (ignoring the oblateness of the earth) is the radius of the earth times the cosine of the latitude. Here are the same latitude circle radii:
Arctic circle: 1578 miles
tropic of cancer: 3630 miles
equator: 3959 miles
tropic of capricorn: 3630 miles
antarctic circle: 1578 miles.

Thank you very much, this is exactly what I was looking for.
By the way, is it FE approved?

[douglips]

I don't know what that means.

I'm not an FE believer, and the FE case I described is one model. People like Tom Bishop say that that model is not official.

If you are looking for an official flat Earth model I think you'll be disappointed.

[Macarios]

Is there any formula for calculating the radius of a certain circle of latitude?
I've read that each latitude degree is 69.5 miles further from the North Pole. Is it correct?

Yes, it is correct along same longitude.
It is like that in both models, Flat and Globe (see Gleason's map and its legend in the corners).

Along meridians, and along great circles, one degree is 60 nautical miles (69.0468 statute miles, 111.12 kilometers).
Nautical mile was defined as 1852 meters because that is the distance of one arc minute. One degree is 60 arc minutes / 60 nautical miles.
Along parallels it  works only on Equator, becuse other latitude lines get smaller and smaller the closer to pole they are.

Another thing that is the same in both models is longitudes of places.
Along the same meridian solar noon comes at the same exact moment, whether it is flat or globe model.
Solar noon comes regardless of the Earth's shape.
Knowing that, we can use the speed of solar noon to measure circumference of any latitude circle we want.

Let's take latitude of 45 degrees north as an example:

First, we find two places at 45 degrees north, some reasonable distance apart.
We find public records of the distance.
Those public records are under public scrutiny.
Public records are used by military, inustry, infrastructure, transportation times and fuel consumption and so on...

Two convenient places will be Ruma and Saint-Flour.
Ruma, Serbia: 45 degrees north, 19.826 degrees east.
Saint-Flour, France: 45 degrees north, 3.087 degrees east.
Distance: 1312.02 km.
Longitude difference: 19.826 - 3.087 = 16.739 degrees.

Sun (and solar noon) always travel 15 degrees per hour.
It doesn't change with the change of model.
It is seen when you go outside and measure for yourself, any time of day, any time of year.
Between these two places will have ground speed of (1312.02 / 16.739) * 15 = 1175.72 km/h.
The full circle will take 24 hours, and it is 1175.72 * 24 = 28 217.28 km.

So, circumference of the latitude 45 degrees north is 28 217 kilometers.
Radius of that latitude is 28 217 / 2Pi = 4491 km.

But it is not measured from Earth's center.
It was measured from the Earth's axis.
From the Earth's center radius will be ab / SQRT(a²sin²(45) + b²cos²(45) ) where a = 6378 km (equatorial radius) and b = 6357 km (polar radius).
So, radius from Earth's center at 45 degrees north will be 6367.5 km.

Now, let's check it out.
At 45 degrees of latitude radius from Earth's axis will now be 6367.5 km * cos(45) = 4502 km.
Our calculated radius is 4491 km.
Error is (Val_measured - Val_correct) / Val_correct = (4491 - 4502) / 4502 = -0.0024 = -0.24%.

Pretty low error, don't you think?

[Tumeni]

The 'formula', surely, is simply pythagoras for right-angled triangles?

http://www.cleavebooks.co.uk/scol/calrtri.htm

The axis of the Earth is a vertical from point A. The radius at any point of latitude will equal side b, as it will be a line parallel to side b, connecting C with a point on the vertical above A. 

For 10 degrees N or S, imagine the Earth viewed from the side. Hypotenuse is Earth radius of 6,371km (side c), angle A = 10 degrees, put these into the calculator, and side b results at 6,270km

For 20 degrees, b = 5,990 km

Repeat, repeat for 30 to 80 degrees

[Macarios]

The 'formula', surely, is simply pythagoras for right-angled triangles?

http://www.cleavebooks.co.uk/scol/calrtri.htm

The axis of the Earth is a vertical from point A. The radius at any point of latitude will equal side b, as it will be a line parallel to side b, connecting C with a point on the vertical above A. 

For 10 degrees N or S, imagine the Earth viewed from the side. Hypotenuse is Earth radius of 6,371km (side c), angle A = 10 degrees, put these into the calculator, and side b results at 6,270km

For 20 degrees, b = 5,990 km

Repeat, repeat for 30 to 80 degrees

This will work for ideal sphere, where vertical intersection is circle.
Hypotenuse will always be 6371 km.
Local radius from axis would be 6371 * cos(latitude).
At 45 degrees north (or south) it is 6371 * cos(45) = 4505 km
Circumference at 45 degrees latitude will be 2 * Pi * 4505 = 28 306 km
We will have pretty accurate result.

-------------------------------------------------------------

If we want more accuracy, we do more work, like this:

Polar radius of Earth is smaller, so vertical intersection is ellipse with semi-major axis a = 6378 km and semi-minor axis b = 6357 km.
In that case we don't have 6371 km at all angles.
As latitude grows hypotenuse will decrease from 6378 km to 6357 km.
At 45 degrees we will have hypotenuse to be 6378 * 6357 / SQRT(6378²sin²(45) + 6357²cos²(45) ) = 6367.5 km
(That is not 6371.)

From there we can use 6367.5 km as hypotenuse of the triangle to get local radius as 6367.5 * cos(45) = 4502.5 km
Circumference at 45 degrees latitude will be 2 * Pi * 4502.5 = 28 290 km

We are now more accurate by 16 km which is 0.000565 (or 0.0565% , or 565 ppm - parts per million).

[Tom Bishop]

I don't know what that means.

I'm not an FE believer, and the FE case I described is one model. People like Tom Bishop say that that model is not official.

If you are looking for an official flat Earth model I think you'll be disappointed.

If you are looking for a well funded and organized organization that studies the shape of the earth you will be disapointed. I think you do not realize that this entire thing is based on a few people who individually contribute their time to think about it on what little free time they have away from their work.

[Frocious]

I don't know what that means.

I'm not an FE believer, and the FE case I described is one model. People like Tom Bishop say that that model is not official.

If you are looking for an official flat Earth model I think you'll be disappointed.

If you are looking for a well funded and organized organization that studies the shape of the earth you will be disapointed. I think you do not realize that this entire thing is based on a few people who individually contribute their time to think about it on what little free time they have away from their work.

Buddy you've got to stop bringing this funding excuse up.

[Tumeni]

If you are looking for a well funded and organized organization that studies the shape of the earth you will be disapointed. I think you do not realize that this entire thing is based on a few people who individually contribute their time to think about it on what little free time they have away from their work.

Why would your contributions be held to have any value, then, when you devote so little time and effort to them?

[inquisitive]

I don't know what that means.

I'm not an FE believer, and the FE case I described is one model. People like Tom Bishop say that that model is not official.

If you are looking for an official flat Earth model I think you'll be disappointed.

If you are looking for a well funded and organized organization that studies the shape of the earth you will be disapointed. I think you do not realize that this entire thing is based on a few people who individually contribute their time to think about it on what little free time they have away from their work.

Is something as simple as measuring the angle of the sun from different locations at different times to start producing a model of the shape of the earth beyond your ability?

[AATW]

If you are looking for a well funded and organized organization that studies the shape of the earth you will be disapointed. I think you do not realize that this entire thing is based on a few people who individually contribute their time to think about it on what little free time they have away from their work.

But even when you're shown simple experiments which would cost you do virtually nothing to do you refuse to do them.
Stop making excuses. There's plenty you could be doing. What ARE you doing to test your models and theories?

[Devils Advocate]

If you are looking for a well funded and organized organization that studies the shape of the earth you will be disapointed. I think you do not realize that this entire thing is based on a few people who individually contribute their time to think about it on what little free time they have away from their work.

Whilst thousands of professional scientists from a wide range if disciplines dedicate their full attention to their area of expertise and all refer to earth as a globe. But yeah, the world should listen to Tom Bishop and his one experiment......

[Tom Bishop]

Is something as simple as measuring the angle of the sun from different locations at different times to start producing a model of the shape of the earth beyond your ability?

We dispute your ideas about how perspective works.

But even when you're shown simple experiments which would cost you do virtually nothing to do you refuse to do them.
Stop making excuses. There's plenty you could be doing. What ARE you doing to test your models and theories?

I'm talking about it. I'm bringing you up to speed by talking about the Earth Not a Globe conclusions about perspective under the Flat Earth model. Once we have a full understanding, a test may be derived.

The problem I am finding is that you guys are not listening. The conclusions on how perspective works in FET is quite different than the continuous version of perspective under the theories of the Ancient Greeks.

You are not helping when you keep coming up with tests that depend on those Ancient Greek assumptions. You are not working with me, you are working against me. That's where the problem is.

[AATW]

Is something as simple as measuring the angle of the sun from different locations at different times to start producing a model of the shape of the earth beyond your ability?

We dispute your ideas about how perspective works.

Really? But in this diagram from your Wiki you take no account of perspective.
Correctly, as it happens, so when it suits your argument you do understand how perspective works in the real world:



If you're going to use that argument and that diagram explaining that argument then you can do the experiment which has been suggested to you.

You are not helping when you keep coming up with tests that depend on those Ancient Greek assumptions. You are not working with me, you are working against me. That's where the problem is.

You made a claim the other day about the horizon always being at eye level. A claim which is not true.
The best you could come up with as evidence was a video from a drone which you admitted was not stabilised and thus useless to testing that claim.
You were shown a video of an experiment which clearly showed your claim to be incorrect, an experiment you could repeat at minimal cost.
That test is nothing to do with perspective. It's a simple thing you could do to test part of your theory.

You are making all kinds of assertions based on Rowbotham's writings.
You claim to be an empiricist but you have taken no empirical measurements on anything.

[Tom Bishop]

No. What happened is that I provided evidence that the horizon rose upwards when the altitude increased. When the drone increased its altitude, the horizon rose upwards in reference to the buildings. That is evidence that your prediction that the horizon would drop is false.

Rather than addressing this, you guys posted an entirely different experiment involving a device filled with water and eyeballing its comparison to the horizon. A total distraction, and basically an admission that you don't want to talk about rising horizons anymore because the video clearly shows that you are wrong and the traditional theory of perspective is false.

[Tumeni]

No. What happened is that I provided evidence that the horizon rose upwards when the altitude increased. When the drone increased its altitude, the horizon rose upwards in reference to the buildings.

... but didn't someone point out to you that the horizon stayed pretty much in place in the frame, and the building merely moved in the foreground as the drone rose?

[Tom Bishop]

No. What happened is that I provided evidence that the horizon rose upwards when the altitude increased. When the drone increased its altitude, the horizon rose upwards in reference to the buildings.

... but didn't someone point out to you that the horizon stayed pretty much in place in the frame, and the building merely moved in the foreground as the drone rose?

Yes, the horizon pretty much stayed in the same place while the buildings fell beneath it. The horizon line was keeping level with the rising observer. It rose with the observer.

Under the Ancient Greek continuous perspective model the horizon should have dropped along with everything else.

AllAroundTheWorld predicted that it would fall rather than rise, and he was wrong. The entire premise of his thread was shown to be fallacious. Rather than addressing this failing he and others started harping on some other Youtube video about a water device and eyeballing its position with the horizon. The premise in the OP was busted. The traditional theory of perspective shown to be untrue, and all he can do is distract.

[HorstFue]

What I saw in the video provided by Tom:
The only reference line I see, is the line from the drone to the roof of the building.
At the beginning this line is pointing towards the sky. Then, as the drone goes higher, this line is tilted/dipped downwards.
It's no surprise, that anything that's farther away than the building, now appears to be rising relative to the building's roof.