# Views of Toronto from Hamilton and Fort Niagara Illustrate Earth's Curvature

Discussion in 'Flat Earth' started by Mick West, Nov 14, 2016.

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1. ### Mick WestAdministratorStaff Member

When people want to practically illustrate the curvature of the Earth, they often give the example of a boat disappearing over the horizon. While the boats example is perfectly valid, it's quite hard to observe and the effects of refraction make it confusing to interpret. It's also hard to repeat as you need a good boat.

Mountains, on the other hand, rise up above the distorting effects of refraction and you can usually get a very good fit to the peaks using Google Earth which allows you to show exactly how much is obscured by the horizon.

They are also very repeatable, weather permitting the distant mountain is generally visible in the same way many days of the year. For example observing the partial hiding of Catalina Island is an easy experiment anyone in Los Angeles can do with a quick ride to the beach.

I thought perhaps I'll start a thread collecting these examples, with locations, so that people can replicate them if they are having doubts about the rotundity of Earth, or just for a fun science experiment.

What you need is a tall island, preferably a mountain or volcano, that's between 30 and 60 miles off the coast. (It does not need to be an island specifically, but does need a mountain near its coast) You then need to take a photo of the island from near the waterline so that a significant portion of it is obscured by the horizon.

Then you need to demonstrate how much is hidden, you can do this by measuring it based on the camera field of view. Or by fitting it to the view in Google Earth from the same distance, but higher viewpoint.

Ideally you would have several photos from different altitudes, showing more if the land is visible from high ground, and a lot less down at 2 feet above the water.

You don't have to take the photos yourself, you can use photos on the Internet of common places (like Hawaii). So long as you can identify the camera location, and the mounting being viewed, then you can apply the process and figure out how much is being hidden.

Surprisingly a great source of these photos is the people who believe the Earth is flat. Generally they miscalculate how much of a distant peak or skyscraper should be visible. They will forget to factor in the view height, or they will ignore refraction, or perhaps misidentify the peak. Then they will post the results on YouTube as proof that the Earth is Flat.

Here's a video discussing how to do the view matching for a group of buildings

Source: https://www.youtube.com/watch?v=ogzAufGmBNM

Last edited: May 15, 2017
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2. ### AbishuaMember

[unnecessary, off topic chit chat removed]

This video of Toronto was taken by Jenna Fredo. It was taken across Lake Ontario from a place called Niagara on the Lake. Viewer elevation is 37 feet, distance to target Rogers Center Dome is 30.86 miles.Humidity was 50%.

Elevation of ground where Dome is built is 262 feet, dome is 282 feet tall. According to this dome should have been hidden 50 feet below the curvature. Yet it can be clearly seen. Refraction was included into calculations because calculator used for curvature was by Mick West from metabunk.

Check it out guys and let me know what you think!

Last edited by a moderator: Mar 11, 2017
3. ### Mick WestAdministratorStaff Member

Not really very good images there:

There's lots of far better photos of the skyline from that location

https://www.google.com/search?q=toronto+skyline+from+fort+niagara&num=50&tbm=isch

It's a mistake to focus on the images close to the horizon, as they are by far the most affected by "looming", which can be quite significant based on the weather. It's better to fit the highest (least distorted) points of the image, and then see where the horizon is:

If we align based on the CN tower we get:

But even if we align with the tops of the lower buildings we get:

So it's just looming of the lowest structures.

Last edited: May 15, 2017
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4. ### Mick WestAdministratorStaff Member

Incidentally, this would be an ideal location for the "stand-up" demonstration of the Earth's curvature. On a clear day with limited refraction there would be a very distinct difference with what is visible - especially with the large varity in height of building, and the easy identification of the skyline features.
https://www.metabunk.org/stand-up-to-detect-the-curve-of-the-earth.t8364/

Last edited: Mar 11, 2017
5. ### AbishuaMember

does not seem like looming to me.. because the tallest building left of the tower should also be looming then.. and it's height differential from the building partially covering up the dome matches with the height difference from other photo.. yet in your comparison dome should be hovering above the taller building left of the tower.. and this is clearly not the case..

Could these effects looming, refraction, mirrage work both ways? In a way to make things look like they are behind the curve when they are not, and make things look like they are not behind the curve when in actuallity they should be, or is it a one way streat and these effects always work "against the curvature"? Sorry for a messy question I hope you understand what I am asking? So could they work "with the curvature" and "against it"?

6. ### Mick WestAdministratorStaff Member

Here's the expected view with no refraction and flat earth:

But what we are seeing here is a compression of things close to the horizon. Here I've simulated this on the left, transitioning to the "correct" view on the right:

Or with the full image:

The actual degree of compression varies. Unfortunately the video images are quite hard to make out, but there's nothing really out of line as far as I can see.

7. ### Mick WestAdministratorStaff Member

You seem to be asking in, on a flat Earth, refraction effects could make it look like the Earth is round.

No. Because the less refraction there is, the more what we see approaches the ideal view of a globe earth. i.e. when there is little refraction you get a very sharp horizon at about the right distance, and obscuring about the right amount of distant objects with very little distortion.

This can be seen very clearly with my Venice/Santa Monica photos. You have a very clear horizon in focus with detail of the water surface all the way up to the horizon and the buildings (and boats) that are behind the horizon exhibit near zero vertical distortion.

This cannot be explained by "refraction" on a flat earth. If there was refraction hiding the distant shore then there would be distortion at the horizon. There is no distortion, so it's not refraction.

8. ### AbishuaMember

Ok.. makes sense. I just can't shake off the feeling its a rather convenient way to explain one situation over the other. Not saying its not true.. I am no expert on atmospheric distortions. I just had a feeling refraction can go both ways.. diff temps, humidity etc. could cause light to bend in a way to compliment the curve, or counter it. These are just my amateur thoughts tho.. so won't go further into it or try to debate you because truth is I don't know enough about it to do so.

I think it's bad if we learned in detail about refraction by observing long stretches of distance on earth, since we need to assume things about earth before we "nail" the refraction, and that makes it pointless to use that same refraction as a reverse engineer tool to prove what we assumed about earth in the first place. That would make it sort of like dating how old something is, but first u need to assume how old it is. Circular reasoning.

On the other hand I think it's good if we learned about refraction in controlled lab conditions. So we can use that precise knowledge and apply it to real life conditions that are always more complex but at least we have a good solid base to work with. We can take temperature and humidity readings at various altitudes, sun position, etc to get a more precise result.

9. ### Mick WestAdministratorStaff Member

Well that's basically what happens. The science of how light travels through a medium is very well understood. The factors that alter refractive index are very well understood. The problem to those who refuse to accept any science is that you've got to derive that from observations and first principles, and most people are not capable of that.

Think about the general situation.

We've got many verifiable situations where buildings and mountains are hidden by a clean horizon with little or no distortion. We can do the math and see that the amount hidden is generally just a bit less than the expected amount for a globe Earth with no atmosphere - based on inarguable geometry. These are things you can verify personally.

We know that the air gets thinner as we go higher, and we know how much on average, and can verify it personally by walking up a mountain with a barometer.

We know light bends towards a more dense medium, towards the medium with a higher refractive index. (which we can verify with a variety of simple experiments) , so we know that looking towards the horizon will bend the light down very slightly.

Now as we are on a globe these observations all fit. We'd expect the horizon to obscure buildings. We'd expect to see a bit more than if there were no atmosphere. We can even explain the times when we can see even further or less past the horizon than normal, when the temperature gradient of the air is more, or less, or inverted.

The problems only start when you introduce the idea of a flat earth. Now you could theoretically explain away in the distorted images and mirages as the effect of refraction - after all we see heat mirages on roads, and they sometimes create a false horizon.

But how does refraction and a flat Earth explain the case of a sharp horizon, and an undistorted background?

How does refraction and a Flat earth explain how more and more of a mountain is gradually visible as you get higher - exactly simulating the expected figures from a round Earth? How does it explain these three photos I took (all unaltered other than lining them up)?

This is explained quite simply by the world being round. The island is just behind the curve of the ocean.

How can you explain these photos by the world being flat? How is refraction so closely simulating exactly what we expect from a round world?

Last edited: May 15, 2017
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10. ### AbishuaMember

True.. I got shocked when I saw some flat earth videos.. so I just had to buy p900 and test things myself. At start I was 90% convinced earth was flat.. but I made some mistakes. Now as things are I have to be honest and say I lean towards globe earth.. but I still think
[off topic 'broader theory' text removed]

Thx Mick for your time.

Last edited by a moderator: Mar 13, 2017
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11. ### jenna1789New Member

Actually it was taken from Fort Niagara, NY...and remember the view depends on the elevation...there may be better photos...but do they state what height above the lake they were when they took them? It's not that easy to look through 30+ miles of atmosphere over a lake...

12. ### jenna1789New Member

And I did just recently take another one from the same location but closed to the water...the tripod was only at 5 feet but I put six feet in the calculator just because...

Source: https://youtu.be/__liPsAYnJs

Oh and you can find the sign in the vid on Google earth for coordinates

Last edited by a moderator: Apr 12, 2017
13. ### TrailblazerModeratorStaff Member

That's a good demonstration of how refraction can make more visible than you "should" be able to see. But that's all it is. If you look at other photos and videos taken on different days from the same place you can see how variable the view is:

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14. ### Mick WestAdministratorStaff Member

Great example! As I noted above the best way of removing the refraction effects is to focus on the TOPs of the buildings. Take an undistorted rendering of the actual expected image where the yellow line represents the lake horizon

And overlay that on the real-world image viewed though the atmosphere:
(drag slider to compare)

Here I've used the observation deck of the CN Tower as the reference point. Again we see this huge compression of things near the horizon. Compare with Post #6.

Last edited: May 16, 2017
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15. ### deirdreModeratorStaff Member

huh. I ran across @jenna1789 's video on another video. Then found this thread. That is actually amazing how the buildings in the back (red circle) completely shrink up. Wild.

16. ### Mick WestAdministratorStaff Member

Just another comparison from @jenna1789's video. Showing how it's obviously a mirage.

17. ### Mick WestAdministratorStaff Member

Playing around with the new mirage simulator.
https://www.metabunk.org/mirage/

Here's what you would expect to see if the Earth was flat, with no atmosphere, from five feet, 30.85 miles away.

Here's the globe earth view, no atmosphere, the Rodgers center is hidden

Here's the globe earth view with the standard atmosphere, more building are visible, but not the Rodger's center. The rays are bent downwards a little, so you can see over the horizon a bit more. They bend down because light bends towards more dense air. The lower air has a higher pressure, so it denser. The decrease in temperature as you get higher counteracts this a bit, but overall still bending down.

Here it is with a slight temperature inversion, just an increase of about 1°C over 100 feet, with a steeper increase near the lake surface. The Rodger's center is now in view, and distorted in a similar way to the video. The light is bending down more because the cooler air near the lake surface is denser. this is still from 5 feet above the water surface.

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18. ### Mick WestAdministratorStaff Member

Added a laser dot at the shoreline. Visible from 30 miles away, viewer height of 6 feet.

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19. ### Z.W. WolfSenior Member

Here's my go at reproducing the image in this YT video...

I used this shape for the inversion, from this description of a ducted mock mirage.
https://www.atoptics.co.uk/atoptics/gfmmform.htm

Looking at Dr. Andrew Young's site, it just seemed to me to be the best match.

https://aty.sdsu.edu/mirages/mirsims/mock/ductMM.html

I'm afraid that if you look at this page you'll find that there's still another variable - the distance to the target.

Last edited: Apr 3, 2018
20. ### Z.W. WolfSenior Member

Another mock mirage...

I'm sure the sun is actually well below the horizon at this point. I wonder how far?

Last edited: Apr 3, 2018
21. ### Mick WestAdministratorStaff Member

There's several more variables, which are currently hard coded. The distance to the target and the height of the target are in the code, as is the initial viewer height, and the initial temperature gradiant

Note the height of the gradient graph has an effect on what you can do - the one you used is goes up to 200 feet, making it harder to edit the values closer to the ground.

One thing I should fix is the current lack of temperature lapse above the top of the graph - the current RI gradient is just from pressure, so a bit bigger than it should be.

22. ### Mick WestAdministratorStaff Member

Fixed!
https://www.metabunk.org/mirage/
Just a minor smoothing thing really. Not significant in terms of visibility.

23. ### Mick WestAdministratorStaff Member

The new version has much better smoothing, more accurate overall, and get a closer match

The shape you were using was actually more like mine, you had some of yours below zero, which would have been ignored.

24. ### Z.W. WolfSenior Member

I didn't even notice until later that the scale went below zero.

But I think it's pretty solid that the original YT video is showing the effects of ducted rays. Whether we should call this a superior mirage, a mock mirage, or a late mirage I don't know.

Last edited: Apr 4, 2018
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25. ### Z.W. WolfSenior Member

From Dr. Young's site: https://aty.sdsu.edu/explain/atmos_refr/duct.html

Last edited: Apr 4, 2018
26. ### Z.W. WolfSenior Member

More info from Dr. Young's site:

Another kind of “pseudo-mirage."

"The observer within a duct" does not necessarily equal "the observer within the inversion." It's possible to be below the inversion but within the duct.

This is complicated stuff and I'm a naive reader, but it seems to me that the camera in the YT video may have either been below the inversion and within the duct, or below the inversion and just below the bottom of the duct; as explained on this page: https://aty.sdsu.edu/explain/simulations/ducting/duct_intro.html#at100m

This page talks about the sun - an astronomical body - so we need to be careful when using this info when we are talking about even a distant terrestrial object.

Last edited: Apr 4, 2018
27. ### Z.W. WolfSenior Member

The best I can say is that we appear to be seeing an inverted image of the Rogers Centre Dome above an erect image. The erect image is only the upper part of the dome, which itself would normally be hidden. The inverted image has a flat top because the erect image is cut off in a straight line by the horizon and the inverted image also has this straight line, but at the top. In this case it's a true superior mirage.

Alternatively it might be an erect image over the lower erect image - with a very compressed inverted image between. A 3-image mirage. The top erect image is flat topped because it is "squashed." Notice that the top image is not completely flat topped. There does seem to be a hint of a curved dome shape.

In that case, this info would be apropos:

(Mock mirages and late mirages don't necessarily produce a 3-image mirage.)

I think we can rule out the late mirage because the dome is too low. It's tempting to rule out the mock mirage because the camera is so low above the water. But this site says: https://www.atoptics.co.uk/atoptics/mmirsun.htm

Also, Dr. Young seems to be saying,here, that the observer may be below, or within, the inversion layer: https://aty.sdsu.edu/mirages/mirsims/mock/mock.html

I'm confused by this. Wouldn't this now just be a late mirage?

Last edited: Apr 4, 2018
28. ### Mick WestAdministratorStaff Member

My temp gradient editor currently uses the possibly confusing feet and celsius. So -0.11°C/m is 0.033528 °C/feet, or 1°C in 30 feet, we can do this in, like:

That quite nicely brings things into view with minimal distortion.

Ducting tends to hit the target at a similar height to the observer - i.e it requires the observer to be IN the duct.So when we see ducting in the Toronto image it looks dark, as it's the shoreline

So I think we are seeing something just short of that.

29. ### NthMember

It may be beating the proverbial dead horse at this point, but somebody bringing up Jenna Fredo's heavily distorted view of Toronto (not her fault, of course) as "flat earth proof" prompted me to look up shots of Toronto from across Lake Ontario. Anyway, I found this incredibly clear shot posted by a Reddit user:

Source: https://www.reddit.com/r/CityPorn/comments/5gx6b4/the_toronto_skyline_from_across_lake_ontario/

Creating a feet/pixel scale based off the distance between the tip of the spire and the skypod, I came away with about 423 feet hidden. Without knowing exact height and distance, it's hard to peg down perfect predictions, but on another thread, he references taking the shot from Winona, which puts a minimum value of 31 miles and a maximum value of 32 miles. If we take the minimum value to be accurate and have an 8-foot observer height, refracted hidden's prediction is dead on.

Either way, there is 423 feet of missing city without any signs of severe atmospheric distortion that may be hiding it.

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30. ### TrailblazerModeratorStaff Member

On that thread he says Stoney Creek. Which is right next door anyway.

31. ### NthMember

Yeah, it almost looks like Winona is effectively a suburb of Stoney Creek, or something similar. For reference, here is where he cites Winona as the location:
Source: https://www.reddit.com/r/pics/comments/5gysof/my_view_of_toronto_from_across_lake_ontario/dawl50b/?context=3

I might try to contact him through Reddit at some point, but his last activity is almost a year and a half ago, so it's hard to know if he even monitors the account regularly.

32. ### AntithesisNew Member

Despite the precise date and location of the picture being unknown, I can't resist testing the formula

(temperature gradient) = ((air temperature) - (water temperature)) / (visible height of target)​

Let's guess it was taken the previous day. Shadows indicate late afternoon.

Source: https://www.wunderground.com/history/daily/ca/toronto/CYTZ/date/2016-12-5

Source: https://www.seatemperature.org/north-america/canada/toronto-december.htm:

Temperature gradient is (43 - 40.8)/(1815 - 423) ≈ 0.00158045977.

Source: https://metabunk.org/curve

411.37; expected 423. It may be just be luck, of course. I suppose the point is that such pictures don't warrant revising our understanding of the universe.

33. ### NthMember

Good analysis, but I want to seize on this particular point. Seeing "further than we should" by an amount that could tilt the scales in favor a flat earth is a pretty rare occurrence. In particular, there is a flat earther who observes oil rigs off the coast of California, and posted a video showing a view of, apparently, zero earth curvature. The problem is, by his own admission, it took him a long time of observing to get that photograph, with other shots showing the oil rigs hidden to varying degrees. It was trying to use the exception to prove the rule.

This is kind of branching off into editorializing, so I'll leave it here.

34. ### Amber RobotMember

Seeing the curvature is not the only evidence of a globe Earth though. The flat earthers focus on this particular one because it can be difficult to measure. If we lived on a planet the size of Jupiter we could still figure out it was a globe for many other reasons. All the reasons why the flat earth model fails.

35. ### Z.W. WolfSenior Member

A common misconception among FE Believers: We Globeheads are saying that there's a wall of water or a hump of water that obscures distant objects.

This is an example of the misunderstanding. Mr. Thrive & Survive is objecting to Soundly's photos of Lake Pontchartrain.

He presents this argument about the depth of Lake Pontchartrain.

He's referring to the depth of the lake, which he reports as 15 feet.

He's saying the lake would have to be much deeper to account for the "bulge" - the big hump of water - we are insisting is there. So 15 feet of depth PLUS the 88 feet of the bulge would apparently mean the lake would have to be 103 feet deep in the center. (Or would it only be 88 feet in depth? I'm not sure. Or 176 feet with the bulge plus the curved bottom?)

In this second illustration he's also showing what the lake would have to look like on a curved Earth, because water "seeks its own level."

The first illustration is apparently his solution to the depth, with the hump, problem we are presenting him with. The curve plus the bulge of water. He presents this as an absurdity.

How do you get past a misunderstanding this basic?

Last edited: Sep 29, 2019
36. ### Amber RobotMember

I’m not sure you can. It’s like finding a bug in a code so deeply embedded that you’d basically have to rewrite the code to fix it.

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37. ### NthMember

And I have to concur with @Amber Robot. T&S is formulating his conclusion based off the premise that water, even on a spherical earth, must be geometrically flat, which is not and never has been claimed to be the case. In reality, water seeks its lowest potential energy, which leads to it "curving". Basically, the surface layer of a given static body of water will all be at the same elevation relative to earth's core, meaning that the lake doesn't need to be extra deep to account for "the bulge".

What's hard to figure out is how to communicate this. I've always been pretty decent at math and physics, so it's easy for me to understand, but I'm growing increasingly cognizant of the fact that a lot of people just don't have that sort of background knowledge, so my above explanation for "why water curves" might as well be voodoo to the average flat earth believer. Heck, even just to the general member of the public.

Then again, some people are actively opposed to earth being spherical and will not even attempt to understand explanations for why their claimed "globe earth debunks" are wrong, but that's a different can of worms entirely.

38. ### PriyadiMember

To my experience, most flat Earthers are smart enough to understand the concept of curved water & equipotential. It is just that after knowing the fact, suddenly everything makes sense. It debunks a large part of their belief and it is too big for them to swallow.

My go-to explanation for that:

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39. ### Amber RobotMember

From my interactions with flat earthers on Facebook and watching their videos it is not clear to me that they understand that we already knew the Earth was round when Newton invented gravity. The way they argue suggests that somehow they think we believe that gravity explains the round earth rather than describes it. There isn’t anything intrinsically wrong with Newton’s laws but they want to throw them all out along with gravity. Something causes things to fall down and their explanations for that are always incomplete.

Last edited: Oct 1, 2019
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40. ### NthMember

If I had to guess, I'd probably say that most of this comes from a video on the YouTube channel Vsauce that answered the question of "is earth really flat?" by pointing out that a flat earth of large size would be rounded out into a spherical shape due to gravity. So, in essence, the video's producer is saying that because gravity is a thing, it wouldn't be possible for earth to be flat which, while technically correct, is getting ahead of the issue a bit and probably unduly confusing a lot of FEs.

Besides that, it is admittedly quite difficult to satisfactorily demonstrate gravitational attraction outside of a relatively advanced and well-equipped laboratory, just because the forces involved on a human scale are so small, which in turn makes it easy for FEs to just call it fake and move on.

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