# Curvature Experiment showing relation between x-axis and z-axis

Discussion in 'Flat Earth' started by Bass In Your Face, Aug 6, 2016.

1. ### Bass In Your FaceActive Member

Hey guys, I decided to whip up this experiment at my shop when somebody questioned a graphic of mine that I created to help demonstrate the horizon of a sphere the size of the earth, by zooming in it and showing the FOV. This was the graphic:

(Yes I wrote in the wrong FOV for the last pic :/, should be 35 miles, but it's irrelevant anyways.)

So I received a long response to this claiming I am wrong, and that I am misleading with this comparison.
I completely disagree with him. Here is an example of an argument against "seeing curvature", as well as
the long response to the graphic above.
and..

I knew there would come a time when I would need to do this setup without a computer, so this weekend I did. I don't know if it's necessary to post every original photo from my experiment as a whole, so I also made 1 graphic to represent my experiment. My hope is that the result of this can easily be shared on social media as 1 simple graphic instead of having to have long discussions on such simple topics.

I am open to sharing all the photos in their original size, so if that seems important than I will do that. For now, here is my experiment:

(This was created only to demonstrate the relation of the x-axis arc and z-axis arc, mimicking a sphere)

Image is 3163x2034. I took the photos with my Samsung Galaxy S3 (I know I need a new phone) Took me about an hour and a half to set it up and get things measured.

There are a few variables I did not bother to record, as they were not relevant to the purpose of the experiment, so again, the only purpose was to show that the arc on the x-axis, being the same size arc as the z-axis, can look flat, while still seeing curvature in the distance. Its clearly a simple concept, but I have received a few conflicting answers trying to tell me how I am wrong..zoomed in photos of spherical objects, and graphed circles are somehow discounted.

I'd like to reproduce this in the future to possibly answer more than just one question, but I would need more control. I am aware of most things I could do to better this experiment, but for the sake of discussion and open ideas, I'd like to hear any suggestions of how to improve this, or how it could be modified to answer or settle any other questions. (example: camera focus on distant object too blurry, hence my added redline to mark the top of my 1 inch marker)

Thanks guys!

Last edited: Aug 6, 2016
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2. ### deirdreModeratorStaff Member

How do i know that cardboard of yours is a sphere?

3. ### Bass In Your FaceActive Member

Yea I should have included the picture of making the arc in the graphic. I want to update it but for some reason the edit button is not showing on my thread anymore, so here is my updated large graphic, and ill add some other photos that didnt fit on the graphic

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4. ### Bass In Your FaceActive Member

I'm going to add another update to this to help clarify what's being addressed.

5. ### TrailblazerModeratorStaff Member

While your set-up is useful in showing distant objects disappearing over the horizon in the z-axis direction, it is not analogous to the Earth's horizon in the x-axis direction.

When you're on or above the Earth, the line of the horizon is always a constant distance below your eyeline in all directions, which forms a slice through the Earth (top diagram below). You can basically ignore the portion of the Earth above the slice, because you are looking over it and it is not forming the horizon, so effectively the scenario is the same as if you were hovering above a flat circular disc formed by chopping a slice off the Earth through the tangent points of your eyeline (bottom diagram below).

So, the horizon is not curved in the x direction. It is FLAT in the x-direction, i.e it is always a constant distance below your eyeline, all the way round, and the visible curvature is simply because it describes a circle and you are looking down on it. Imagine a big, flat circular rug. From the perspective of a human standing in the middle of it, the rug is clearly curved. But a spider sitting in the middle of it would see a virtually flat horizon (ignoring the shag pile!). On the scale of the Earth, we are spiders. To get the "human-eye view", you would have to be hundreds of miles up, in a spacecraft.

If the perceived lack of curvature was simply due to the narrower field of view, then you wouldn't be able to stand on a ship in the middle of the ocean, turn 360 degrees and see the horizon as a constant flat line. This seems to be a common misconception when discussing the flat Earth idea. In truth, the horizon on a globe is just as flat as the horizon would be on a disc-shaped Earth. The difference is that things can disappear over the horizon in the z-direction, as demonstrated by the coloured markers in your photographs.

Also, while it is true that the horizon line is flat on both a globe and a flat Earth, the size of the horizon is very different in both models.

On a flat Earth, the visible horizon would always be the same size, at any height above the surface: it would always be equal to the circumference of the disc-shaped Earth.

On a globe, the circumference of the horizon depends on your height above the Earth: the higher you get, the lower, and therefore larger, the "slice" becomes in my diagram above. As you get higher, the size of the horizon approaches (but never quite reaches) the circumference of the Earth, until when you are extremely distant, say a million miles away like the DSCOVR satellite, you can see almost, but not quite, half the Earth:

This is also why not all "Blue Marble" photos show the same proportions, of course, as described in this post: https://www.metabunk.org/debunked-blue-marble-photos-show-a-changing-earth.t6616/

Even if you are far enough away to see the full circle of the horizon, that doesn't mean you are seeing the whole of the near side of the Earth.

Last edited: Aug 10, 2016
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6. ### Bass In Your FaceActive Member

I complete agree with you, thank you for the reply. I knew this going in to the experiment but I was trying to design something that could combat the specific claim I kept hearing over and over (if we can see a boat curve after 5 miles, where's the curve left and right?: the "you cant have it both ways" argument).

I was trying to figure out a way to best demonstrate this without a computer model of a sphere, and coming across a spherical-like object to use that could be used as an accurate scale for cheap, takes a little more work/money.
I would love to expand this experiment to be more accurate, its just the scale of it that holds it back. I can see how this could be misleading, so anything I can do to change that conception is appreciated!

7. ### Bass In Your FaceActive Member

Correct, I have even started asking FEers:

"So if you claim is that the horizon must be curved if we are standing on a sphere, then what should it look like? Should it look like this? Or less exaggerated?."

Then clearly when you pan left and right, that argument falls apart.
Arguing the "horizon looks flat" claim backwards seems like a good way to get someone to answer without some irrelevant deflective argument .

8. ### TrailblazerModeratorStaff Member

I think the best way to demonstrate what the horizon looks like would be with a large globe and a small camera with a macro setting. It would need to be a very big globe, of course, so making one might not be practical.

Maybe a giant beach ball? Amazon has some up to 12 feet across, but they are not cheap. This one is 42 inches (107cm) in diameter:
Source: https://www.amazon.co.uk/Intex-42-Jumbo-Beach-Ball/dp/B004EIZRZ2/ref=pd_vtph_21_bs_t_1?ie=UTF8&psc=1&refRID=EQF6THP4KMWHV3WZ5SJC

If you could get the lens axis 1cm above the surface on that ball, that would still be equivalent to a height of about 75 miles above the Earth, so bigger would certainly be better!

The 12ft ball I found is apparently only about 10ft across when inflated, or roughly three metres. Scaling up to Earth size, a photo from 1cm above the surface would still be equivalent to over 25 miles, or 130,000 feet. From that height the curve should be visible, but not especially pronounced.

9. ### TrailblazerModeratorStaff Member

I think the key thing is that the camera should be above the centre of the "Earth", so that the horizon is even all the way round. One thing you could do, although it would be more work, is to make lots of copies of your arc, and arrange them in a star fashion so that they form "lines of longitude" around a section of a sphere. You could cover this framework with a sheet stretched to approximate the spherical surface. Then you mount the camera on top of the intersection point, and observe your horizon, looking down over the sphere, from different heights. I don't know if you'd be able to get the camera low enough though.

10. ### Bass In Your FaceActive Member

I actually thought of doing several arcs in a star fashion but I decided to simplify to 2 for my first ex, just to make sure I didn't make too much work for myself if it didn't work out how I wanted.

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11. ### Z.W. WolfSenior Member

I've been thinking about giant spherical storage tanks, but there aren't any near me. And you'd have to get permission and all that.

There are also giant globes here and there. http://www.roadarch.com/mim/globes.html

Heathrow has a 3 meter globe in each terminal.

12. ### TrailblazerModeratorStaff Member

Somebody in another thread here used a giant stone ball on a fountain or statue for some photos, but I can't find it now.

13. ### Z.W. WolfSenior Member

You might be thinking of this video by dazzathecameraman

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14. ### TrailblazerModeratorStaff Member

Not that: I was thinking of a series of photos of a similar ball from different distances. Those, and this video, have the same flaw, though. They are zooming in on a photo of an extremely distant "horizon", rather than showing the horizon from close to the sphere itself. It's equivalent to zooming in on a tiny portion of an Apollo "Blue Marble" picture, which is not much use when you are trying to demonstrate the lack of curvature as viewed from a relatively small distance above sea level.

What you need is a great big globe, and a tiny camera placed as close to the surface as possible. You could then show that yes, the horizon on a globe appears flat from near the surface. You could pan around 360 degrees to show that it's the same all the way around. Then move the camera a bit higher and show that the curvature becomes a bit more pronounced, and so on. At some stage the perception "flips" and instead of looking at a slightly curved horizon, you are looking at a ball.

Google Maps shows the effect reasonably well. You have to get really really high before the curvature is obvious. This is centred over Kansas, and those are the Great Lakes showing up in the top right by the end:

As a ballpark figure, if you wanted to replicate the view from a plane at 40,000 feet, that's roughly one thousandth of the diameter of the Earth. If you could get the camera to within half an inch of the surface, the globe would have to be 500 inches across, or over 40 feet. Giant storage tanks may be the only answer.

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Last edited: Aug 11, 2016
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15. ### TrailblazerModeratorStaff Member

Maybe something like this?

Good luck getting permission to take photos that close, though!

There's also the Ericsson Globe, in Sweden, which has a diameter of 361 feet. It is open to the public, but it looks like it is composed of lots of flat panels rather than being a curved surface.

Last edited: Aug 11, 2016
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