# Is the Earth flat? Experiment

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#### Villi

• 2
##### Is the Earth flat? Experiment
« on: September 04, 2016, 10:52:29 AM »
Hi everyone,
I performed an experiment to test the flat earth theory and got some interesting results. I was wondering what you all think.

Thank you.

#### Definitely Not Swedish

• rutabaga
• 8309
• Flat Earth Inspector General of High Fashion Crime
##### Re: Is the Earth flat? Experiment
« Reply #1 on: September 04, 2016, 11:22:07 AM »
It is not clear what you calculated.
Have you considered your own altitude?
Quote from: croutons, the s.o.w.
You have received a warning for breaking the laws of mathematics.

Member of the BOTD

#### TotesReptilian

• 2210
##### Re: Is the Earth flat? Experiment
« Reply #2 on: September 04, 2016, 12:38:18 PM »
First of all, thanks for making a very clear and concise video. It's a breath of fresh air around these parts. Here is my analysis using the Hilton Towers. I decided to use the Hilton Towers rather than the Skylon Tower because their proximity to each other allows us to get a good estimate of how much of the tower is visible.

Round Earth Hypothesis:
Unfortunately, as User324 stated, you forgot to take into account the telescope's altitude. Based on the video, I am guessing you were about 3 meters above the lake. Assuming absolutely no refraction gives us 253 m obscured from 63 km away. From what I've read, a common way to estimate refraction is to increase the radius of the earth by 15% in our calculations. So assuming standard refraction, 218 m should be obscured.

Flat Earth Hypothesis:
None of the building should be obscured, except what is blocked by other buildings. 0 m obscured.

Observation:
Height of Hilton Tower 2 = 183 m
Elevation of base of tower = 205 m
Elevation of Lake Ontario = 75 m

I used this website to find the elevations. This gives us a total height for Hilton Tower 2 above the lake of 313 m.

Hilton Tower 2 is 60 m taller than Hilton Tower 1. In your picture, Hilton Tower 2 is about twice as tall as Hilton Tower 1. Therefore, about 120 m of Hilton Tower 2 is visible.

313 m total - 120 m visible = 193 m obscured

Conclusion:
Round Earth (no refraction): 253 m obscured
Round Earth (standard refraction): 218 m obscured
Flat Earth: 0 m obscured
Observation: 193 m obscured

None of them were perfectly correct. The Flat Earth hypothesis was obviously the most wrong. The Round Earth estimate with standard refraction was the closest (surprise, surprise). It was only off by 25 meters.

Possible Sources of Error:
1. Height of observer was only a guess.
2. Actual amount of refraction was unknown. Local weather conditions are unknown.
3. Elevation data might not be 100% correct.
« Last Edit: September 04, 2016, 12:42:36 PM by TotesReptilian »

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#### Villi

• 2
##### Re: Is the Earth flat? Experiment
« Reply #3 on: October 05, 2016, 04:08:06 PM »
Thank you so much TotesReptilian. I was wondering where you got the 15% increase in radius for the refraction value. Can you provide a reference?

To any one else: I do not understand light travelling over long distance but one of the ideas proposed by FE is that light bends. Is it possible that the "curvature" in my data can be a function of light bending due to gravity for example?

#### rabinoz

• 26528
• Real Earth Believer
##### Re: Is the Earth flat? Experiment
« Reply #4 on: October 05, 2016, 05:15:11 PM »
Thank you so much TotesReptilian. I was wondering where you got the 15% increase in radius for the refraction value. Can you provide a reference?

To any one else: I do not understand light travelling over long distance but one of the ideas proposed by FE is that light bends. Is it possible that the "curvature" in my data can be a function of light bending due to gravity for example?

Yes, gravitation bends light, but the (Globe earth's) massive Sun only bends light by 0.4 seconds of arc and
the mass of the (Globe) earth is estimated to bend light by about 0.0002 arc seconds - far too small to be measurable.

The only significant cause of light bending in this situation is refraction due to the different densities of the layers of the atmosphere.
That refraction can be in either direction but usually makes objects seem higher than they actually are.
There is quite a good paper by Rohan Academic Computing, San Diego State University

#### Ski

• Planar Moderator
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• Homines, dum docent, dispenguin.
##### Re: Is the Earth flat? Experiment
« Reply #5 on: October 05, 2016, 09:57:55 PM »
Flat Earth Hypothesis:
None of the building should be obscured, except what is blocked by other buildings. 0 m obscured.

This is very misleading,  because Dr. Rowbotham, for example, clearly predicts that less of the building will be discernible (though strictly speaking not "obscured").

Overall, congratulations to all participants so far, first to the OP who has both attempted and documented his own search for truth, and to TR for a rational response.

If you are soliciting options for furthering your study, Villi, I would be quite interested in the amount of restoration we would see see using higher magnification, for example, in addition to the boat observations.
"Never think you can turn over any old falsehood without a terrible squirming of the horrid little population that dwells under it." -O.W. Holmes "Truth forever on the scaffold, Wrong forever on the throne.."

#### RocksEverywhere

• 1041
• Literally everywhere.
##### Re: Is the Earth flat? Experiment
« Reply #6 on: October 06, 2016, 02:28:21 AM »
I'm amazed to find a quality post here. Keep it up, guys.
AMA: https://www.theflatearthsociety.org/forum/index.php?topic=68045.0

Just because you don't understand something, doesn't mean it's not real.

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#### southern hemispherer

• 287
##### Re: Is the Earth flat? Experiment
« Reply #7 on: October 07, 2016, 12:25:04 AM »
Agreed, for once a positive post explained without any arguments like fake, CGI or your proofs are wrong. Quick, close the thread.

#### 29silhouette

• 3324
##### Re: Is the Earth flat? Experiment
« Reply #8 on: October 07, 2016, 09:44:30 AM »
I would be quite interested in the amount of restoration we would see see using higher magnification, for example,
Depending on the weather, I need to stop by the landing on my way home from work and try out my high powered lens on some distant objects again.  If things are 'sunken' at low elevation shots compared to higher elevation shots, I'll get some pictures from 18mm up to 1300mm and see if anything 'raises' up at all.

#### johnnyorbital

• 867
##### Re: Is the Earth flat? Experiment
« Reply #9 on: October 07, 2016, 12:24:39 PM »
this, once again, is a void experiment.. camera has to be at ground level, a small change in elevation of vantage point makes a huge difference with distances viewable

end point, all these similar experiments show some part of the landmark below the horizon, always proving curvature

Dr. Rowbotham? haha, check my signature, he couldn't even do the Bedford level experiment correctly

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#### southern hemispherer

• 287
##### Re: Is the Earth flat? Experiment
« Reply #10 on: October 10, 2016, 07:06:52 AM »
The best way to do an experiment like this is in a long flat piece of desert, where the altitude of all the points can be confirmed by an altimeter. There will be extremely little water vapor to cause refraction, and if it is repeated over a number of days early in the morning before there is any heat haze. There are many dried up salt pans which are pretty flat around the earth. All we need now is a group of FE'ers to set up a line of poles about 1 meter high and 1 km apart for 8 kms, with special poles at 4.70 km and 7.14 km and see when they disappear from a camera at: a) at 0.1 meters above ground level and b) from 1 meter above ground level at the first pole. The special poles are there at the points when they should not become visible from each of the test heights. My guess is there is not a new Bedford out there who wants to join the hall of shame, so the answer will be let a round earther prove it, then we can say it is fake, and revert to Bedford again.

#### Ski

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• Homines, dum docent, dispenguin.
##### Re: Is the Earth flat? Experiment
« Reply #11 on: October 10, 2016, 12:06:54 PM »
As someone who has spent a lot of time in deserts, I would think that would be the last place I'd go if I was looking to rid myself of refraction as a source of error.
I don't think your altimeter wojld be sensitive enough for this experiment either,  but it would probably be better than "it looks flat enough."
"Never think you can turn over any old falsehood without a terrible squirming of the horrid little population that dwells under it." -O.W. Holmes "Truth forever on the scaffold, Wrong forever on the throne.."

#### TotesReptilian

• 2210
##### Re: Is the Earth flat? Experiment
« Reply #12 on: October 10, 2016, 03:09:24 PM »
Thank you so much TotesReptilian. I was wondering where you got the 15% increase in radius for the refraction value. Can you provide a reference?

Sure. I was actually using a factor of 7/6 8/7 in my calculations. I'm not sure why I wrote 15% instead of the more accurate 17%. Realistically though, the precision of these approximations isn't high enough for it to matter. Sources:

http://aty.sdsu.edu/explain/atmos_refr/horizon.html (Not a scientific publication, but this is where I got my 7/6 approximation. I originally found the 7/6 approximation in an actual scientific publication, but I didn't save it, and I can't for the life of me find it.)

http://articles.adsabs.harvard.edu/cgi-bin/nph-iarticle_query?letter=.&classic=YES&bibcode=2006Obs...126...82Y&page=&type=SCREEN_VIEW&data_type=PDF_HIGH&send=GET&filetype=.pdf, page 6. (Recommends a k=1/6 for a simple approximation, which results in a 20% increase in effective radius.)

http://prod.sandia.gov/techlib/access-control.cgi/2012/1210690.pdf (Recommends a 4/3 approximation for radar. I mistakenly used a 4/3 approximation for visible light in the past on the "other" site. If you stumble on them, feel free to point out the error to me and I'll correct it.)

Keep in mind, these are not particularly reliable approximations. Wikipedia lists quite a few more complicated approximations, but they require knowing the temperature, temperature gradient, pressure, etc.

Here are some choice words of warning from my first source (emphasis mine):

Quote
Unfortunately, the refraction varies considerably from day to day, and from one place to another. It is particularly variable over water: because of the high heat capacity of water, the air is nearly always at a different temperature from that of the water, so there is a thermal boundary layer, in which the temperature gradient is far from uniform.
...
So the nice-looking formulae for calculating “the distance to the horizon” are really only rough approximations to the truth. You can consider them accurate to a few per cent, most of the time. But, occasionally, they will be wildly off, particularly if mirages are visible. Then it's common to see much farther than usual — a condition known as looming.

The "thermal boundary layer" is what causes those weird distortions right at the edge of the horizon.

Edit: Correction:

Actually I used an 8/7 factor in my approximation, which is a 14.3% increase. I'm not sure where I got that from. Always triple check your work, people! Regardless, the difference is rather minimal considering the error margin we are working with.

8/7 factor gives 218 m obscured.
7/6 factor (from the first source I listed) gives 213 m obscured.
6/5 factor (from the second source I listed) gives 207 m obscured.

In the picture we observe 193 m obscured.
« Last Edit: October 10, 2016, 04:37:11 PM by TotesReptilian »

#### rabinoz

• 26528
• Real Earth Believer
##### Re: Is the Earth flat? Experiment
« Reply #13 on: October 10, 2016, 03:12:16 PM »
As someone who has spent a lot of time in deserts, I would think that would be the last place I'd go if I was looking to rid myself of refraction as a source of error.
I don't think your altimeter wojld be sensitive enough for this experiment either,  but it would probably be better than "it looks flat enough."
I agree. The problem with refraction is why I don't like to see "curvature" pushed as evidence - either way. The numerous photos of Toronto and Chicago attest to this problem.

In line of sight radio transmission the radius of the earth is usually taken as 4/3 times the physical radius, but when you read papers on refraction, this figure is no more than a "rule-of-thumb" and the actual value is quite variable.

#### TotesReptilian

• 2210
##### Re: Is the Earth flat? Experiment
« Reply #14 on: October 10, 2016, 03:23:42 PM »
Flat Earth Hypothesis:
None of the building should be obscured, except what is blocked by other buildings. 0 m obscured.

This is very misleading,  because Dr. Rowbotham, for example, clearly predicts that less of the building will be discernible (though strictly speaking not "obscured").

He doesn't predict that part of the building will be obscured/indiscernible. He explains why it is obscured using vaguely plausible sounding reasoning. I can show why his reasoning is utterly wrong if you want, but we should do that in another thread.

More importantly, Rowbotham does not offer a way to calculate the amount that should be obscured based on height and distance. Therefore, there is no way to make a prediction based on his explanation. If you know of a way to come up with an actual number based on Rowbotham's explanation, feel free to let me know and we can test it out.

#### TotesReptilian

• 2210
##### Re: Is the Earth flat? Experiment
« Reply #15 on: October 10, 2016, 04:12:24 PM »
this, once again, is a void experiment.. camera has to be at ground level, a small change in elevation of vantage point makes a huge difference with distances viewable

If you take into account the height of the camera, it's much better to have the camera NOT at ground level, to prevent small obstructions/imperfections from obscuring your view, which is one of the excuses Rowbotham gives for why stuff is obscured. Here is the math to take into account the height of the camera:

h_1 = height of the camera
h_2 = amount of object being obscured
a = distance to horizon from camera
b = remaining distance to object being obscured
a+b = total distance to the object being obscured

We already know the height of the camera (h_1), the total distance to the object (a+b), and R.

1. Calculate distance to horizon from the camera

a = R * arccos(R/(h_1+R))

2. Subtract that from the total distance to find b.

b = (a+b) - a

3. Find the amount obscured based on a camera resting on the horizon from the distance b.

h_2 = R/cos(b/R) - R

* Make sure you are using radians, not degrees
* This only works for objects behind the horizon, obviously. If the object is too close, b will be negative.
* I recommend saving this to a spreadsheet, rather than trying to plug it into a calculator over and over.
* To use the approximation for refraction from above, simply scale R by your chosen factor. I use 7/6.

Here it is in one doozy of an equation:

d = distance to object (a+b)

height obscured = R/cos((d - R*arccos(R/(h_1+R))) / R) - R
« Last Edit: October 10, 2016, 04:17:18 PM by TotesReptilian »

#### Ski

• Planar Moderator
• 8730
• Homines, dum docent, dispenguin.
##### Re: Is the Earth flat? Experiment
« Reply #16 on: October 10, 2016, 10:44:14 PM »
More importantly, Rowbotham does not offer a way to calculate the amount that should be obscured based on height and distance. Therefore, there is no way to make a prediction based on his explanation. If you know of a way to come up with an actual number based on Rowbotham's explanation, feel free to let me know and we can test it out.

I think it would be fantastic to try. Observation suggests it would occur asymptotically in the vertical axis. The main difficulty remains refraction which would make observations inconsistent even with a proper formula. I would think working backward toward a formula would be frightfully difficult.
"Never think you can turn over any old falsehood without a terrible squirming of the horrid little population that dwells under it." -O.W. Holmes "Truth forever on the scaffold, Wrong forever on the throne.."

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#### southern hemispherer

• 287
##### Re: Is the Earth flat? Experiment
« Reply #17 on: October 11, 2016, 12:44:20 AM »
As someone who has spent a lot of time in deserts, I would think that would be the last place I'd go if I was looking to rid myself of refraction as a source of error.
I don't think your altimeter wojld be sensitive enough for this experiment either,  but it would probably be better than "it looks flat enough."

...which is why I said it needs to be done just after sunrise, preferably with the sun at right angles to the line of poles, and it can be done with time lapse pictures taken seconds or minutes apart to see what distortion, if any, occurs.
There are plenty of sensitive instruments that will give extremely accurate altitude readings and the pole heights could be adjusted for any minor changes in height to make each one subsequent to the first one exactly the same height above sea level, but obviously these altitude readings must not differ by more than a small fraction of a meter, or the experiment would be invalid.

#### rabinoz

• 26528
• Real Earth Believer
##### Re: Is the Earth flat? Experiment
« Reply #18 on: October 11, 2016, 05:11:01 AM »
The experiment I would like to see done is measuring the "dip angle to the horizon".

Flat Earthers (from Rowbotham to John Davis?) claim that "the horizon always rises to eye level" as in
Quote from: the Wiki
Basic Perspective
A fact of basic perspective is that the line of the horizon is always at eye level with the observer. This will help us understand how viewing distance works, in addition to the sinking ship effect.

Have you ever noticed that as you climb a mountain the line of the horizon seems to rise with you?

This is because the vanishing point is always at eye level with the observer. This is a very basic property of perspective. From a plane or a mountain, however high you ascend - the horizon will rise to your eye level. The next time you climb in altitude study the horizon closely and observe as it rises with your eye level.

The horizon will continue to rise with altitude, at eye level with the observer, until there is no more land to see.

It is certainly true that the horizon appears to rise to eye-level, at least for moderate elevations. This is simply because the distance down to the horizon is so small compared to the distance to the horizon.

If this "dip angle to the horizon" is measured and found to be always zero, then the assertion that "the line of the horizon is always at eye level with the observer" will be proved.

but if we find that the "dip angle to the horizon" is close to that expected on the globe, then we have good evidence that the earth indeed is a globe.

 So what is expected on the Globe?Neglecting any refraction we get these horizon distances and dip angle to the horizon  1.5 m above sea-level, the horizon is about 4.4 km away and 3 m below eye level. This makes the horizon only 0.04°  below eye-level - quite imperceptible!100 m above sea-level, the horizon is about 36 km away and 200 m below eye level. This makes the horizon 0.32° below eye-level - measurable with good instruments!1000 m above sea-level, the horizon is about 113 km away and 2000 m below eye level. This makes the horizon 1.0° below eye-level - easily measurable.10,000 m above sea-level, the horizon is about 357 km away and 20,000 m below eye level. The horizon is now 3.2° below eye-level - barely detectable to the unaided eye, but easily measurable!So, while the horizon does not quite rise to eye-level, as "the Wiki" claims, it does appear to nearly rise to that level, certainly up to 1,000 m or so. This because the 2,000 m drop to the (Globe) horizon is over a distance of 113 km - or only 1 part in 56, quite close to level. dg is the "dip angle to the horizon:

I have a photo and video showing some measurements that have been done, but measurements from more people would be highly desirable.

There is this a photo showing this "dip angle to the horizon" from an aircraft's instruments superimposed on the outside horizon.

The angle down to the visible horizon (a line is added at the estimated horizon) looks to be about 2.8°. This is a bit less than the 3.2° I gave above, but I made no allowance for refraction in that.

I had not given a thought that flight instruments prove this horizon dip on every high altitude flight!

Then there is this video, which is aimed at "debunking" the idea that "The horizon always rises to eye-level", so it is certainly biased that way:
The altitude readout on the iPhone is certainly not the true altitude of the aircraft - I presume it is from the iPhone's pressure sensor.

None of these are really aimed at showing "curvature", but at showing the "dip angle to the horizon", which is much easier to measure and much more definitive, besides being one way that the radius (of curvature) of the earth has been measured even from ancient times.

You could look at:
Al Biruni measured the radius of the earth by measuring the dip angle to the horizon as in Al-Biruni's Classic Experiment: How to Calculate the Radius of the Earth?

The ideal test for this would be for someone with access to surveying equipment to measure the dip from elevayed points to an ocean horizon.

#### TotesReptilian

• 2210
##### Re: Is the Earth flat? Experiment
« Reply #19 on: October 11, 2016, 06:18:06 AM »
More importantly, Rowbotham does not offer a way to calculate the amount that should be obscured based on height and distance. Therefore, there is no way to make a prediction based on his explanation. If you know of a way to come up with an actual number based on Rowbotham's explanation, feel free to let me know and we can test it out.

I think it would be fantastic to try. Observation suggests it would occur asymptotically in the vertical axis. The main difficulty remains refraction which would make observations inconsistent even with a proper formula. I would think working backward toward a formula would be frightfully difficult.

First of all, it appears that I was wrong. Rowbotham does seem to offer a relatively specific way to calculate the amount obscured. In my defense, I was going from memory, and I don't think the specifics were included in the extract I read. However, there is one major flaw in that he doesn't seem to offer an obvious way to take into account the height of the observer.

I made a separate thread for this! For now, I'll hang back and let the flat earthers have a go at it first. It's your theory, after all! If you want my earnest input, feel free to ask.

#### narcberry

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• Official Flat Earth Society Spokesman/min
##### Re: Is the Earth flat? Experiment
« Reply #20 on: October 12, 2016, 02:07:58 PM »
ANOTHER VICTORY FOR FE!!!!

#### TotesReptilian

• 2210
##### Re: Is the Earth flat? Experiment
« Reply #21 on: October 12, 2016, 02:12:11 PM »
ANOTHER VICTORY FOR FE!!!!

I realize you are probably just trolling, but under the slim chance that you actually believe anything you say, I'd like to highlight the following...

However, there is one major flaw in that he doesn't seem to offer an obvious way to take into account the height of the observer.

Which means that 0 meters is still the best prediction I can make for a flat earth. If you know of a way to make a better prediction, feel free to let us know in either this thread or the one I made specifically dedicated to it.

#### narcberry

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• Official Flat Earth Society Spokesman/min
##### Re: Is the Earth flat? Experiment
« Reply #22 on: October 12, 2016, 02:14:03 PM »