[Bobby Shafto]

First step (if possible) is to fill out this table:



We all know how to calculate (or how to use online calculators) to come up with how much of a target height will be hidden on a sphere of earth's claimed radius, not accounting for surface irregularities or atmospheric effects on optics.  I used a popular calculator found on GitHub to fill out the table for a spherical earth.

What I don't know for sure is how to fill out the flat earth column. I would be inclined to put 0 all the way down, but I don't want to presume and potentially skew the challenge. So I ask any willing flat earth advocate (not "globetards" playing devil's advocate) to step forward and propose values for the flat earth column.

We are to ignore atmospheric effects like refraction, which has been disparaged as a "magic wand" used to salvage spherical calculations.

Step 2 will be to examine a series of images taken of a target at these ranges/heights and see if we can assess actual hidden/not hidden values. I can promise up front that the values in the spherical earth column above will not match what we will deduce from the images. Since I have no values for the flat earth column, I can't yet make the same declaration for that camp, but I predict that whatever values flat earth calculation might produce will likely be "ballpark" and not perfectly match what we find in the images either. That's okay.

Step 3 will likely and unavoidably occur coincident with the process of Step 2 since it is human nature to want to analyze with an eye on the desired conclusion. But, if we can, the step will be to assess whether the evidence is more supportive of a flat earth of FET (flat earth theory) or a spherical earth of the size that is the consensus in RET (round earth theory). 

Finally -- and since I predict the measured/derived values will be less than Step 1 calculated values of RET's but greater than FET's, we can then debate using "magic wands" to argue for adjustments that could swing the raw values closer to your supported model and away from the opposing model.  That is if we actually get that far.

This might not even get out of the blocks.  To do that, we need some flat earth numbers to fill in the table.  Anyone?

[Bobby Shafto]

This might not even get out of the blocks.  To do that, we need some flat earth numbers to fill in the table.  Anyone?

Here's a proposal for the flat earth hidden height column, based on a simple formula derived from the explanation for flat earth horizon and "bottom-first" disappearing found in Earth Not a Globe.

[Bobby Shafto]

No takers?

TFES.org has a Wiki page dedicated to round earth calculation of hidden heights, but nothing on how to calculate the "sunken ship" phenomenon of how much can appear hidden on a flat earth?

Isn't that a rather significant gap in the knowledge base of Flat Earth Theory (FET)? I've posted many times my interpretation of Earth Not a Globe and how to calculate distance to the horizon, and I've tried to find a way to apply that to quantifying how much of ship's hulls, or the bottom of distant islands or mountains will be lost to view on a flat earth while their tops remain visible.

I know I read elsewhere Tom Bishop say this community could make round earthers do the work, but come on. What can I do to goad someone on the flat earth side of the aisle to step up and provide something quantifiable? Something comparable to the curve earth calculator to predict hidden heights on a flat earth that we can compare, alongside the round earth predictions, with observation? Is this an unreasonable request? 

[Tom Bishop]

It's not a simple distance-feet chart. There are several phenomena going on with the Sinking Ship Effect.

Firstly, there is a limit to resolution of the eye, which is less than 1/60th of a degree. Rowbotham describes the matter in the Sinking Ship Chapter. This limitation may make it appear if some bodies merge in the distance. Those bodies can, however, be restored with a telescope, which is the cause of the accounts of restored hulls in the book Zetetic Cosmogony and Cellular Cosmogony, and why several Youtube authors claim to be able to restore hulls.

Secondly, in the chapter Perspective at Sea Rowbotham describes that often times on the environment of the sea bodies can be hidden by waves, swells, or bulges of the water (perhaps tidal?). Sometimes bodies are obscured, and at other times they are visible. Examples are given of the Nab Light ship and the Eddystone Lighthouse, which were at various time visible and invisible. During these times a telescope cannot restore the hull.

The affect of the water may be associated with the winds. In the chapter On The Dimension of Ocean Waves Rowbotham states the following:

It is well known that even on lakes of small dimensions and also on canals, when high winds prevail for some time in the same direction, the ordinary ripple is converted into comparatively large waves. On the "Bedford Canal," during the windy season, the water is raised into undulations so high, that through a powerful telescope at an elevation of 8 inches, a boat two or three miles away will be invisible; but at other times, through the same telescope the same kind of boat may be seen at a distance of six or eight miles.

During very fine weather when the water has been calm for some days and become as it were settled down, persons are often able to see with the naked eye from Dover the coast of France, and a steamer has been traced all the way across the channel. At other times when the winds are very high, and a heavy swell prevails, the coast is invisible, and the steamers cannot be traced the whole distance from the same altitude, even with a good telescope.

Instances could be greatly multiplied, but already more evidence has been given than the subject really requires, to prove that when a telescope does not restore the hull of a distant vessel it is owing to a purely special and local cause

Rowbotham generally recommends that the experiment is conducted on calm days, on the most calm body of water that can be found. I would say that the amount hidden has more to do with that than than "this is how much is hidden at this distance."

[Bobby Shafto]

I apprehend all that, but what i'm asking for is akin to the pure geometry of the earth curve calculator that doesn't included variables like atmospheric effects or surface irregularities (hills, ocean swells, structures. etc.)

Is it fair to say that on a flat earth, there should be no hidden elevation other than what is caused by such obstructions as you mentioned. If there is no dense air, no fog/smoke/particulates/vapor, no waves (or what not)...all hidden values would be 0 feet.

In the 2nd table above I tried to interpret Rowbotham's perspective and limits of visual acuity to provide a value for what might be hidden even if all obstacles to geometric perfect flatness were removed. I don't know if it's right, and I certainly don't believe it to be true, but I don't want to invoke my own stance onto what flat earth ascribes to.

If values are 0, I'll put 0. If values need to account for some Natural Law of Perspective formula, I'll plug them in. But I need you (or someone) to tell me what they are. I'd love to know how they are derived if they are non-0, but that's not the point of this exercise. I just want to apply baseline numbers. We can apply waves or atmosphere or other adjustments to those base numbers during the assessment, but you have to start out with a baseline, I should think.

Here's my gripe. Every flat earth demonstration or video I come across uses the earth curve calculator to put a round earth on the carpet, and if that calculated result isn't observed, flat earth is declared proven and round earth debunked. But what if you flip the script? If flat earth 'calculator' says 0' should be hidden and yet we see that some elevation is hidden, does it debunk a flat earth and prove the earth surface is convex? I

I'm sure you'll say "no." But you won't allow for deviations from the earth curve calculator,  which is a strict geometric calculation, because you say it's all "magic wand" stuff. Why is what's good for the Rowbotham goose not good for the Globe gander?

So, what I was hoping for was to set a no-magic-wand baseline of hidden/visible calculations. We've got that for the globe. We don't have that for flat earth, unless you're implicitly saying that a flat earth geometric value should be 0' at any distance. I'm fine with that. It's during the later step(s) when we're looking at observations/recorded evidence and analyzing how much is hidden and why that might be so that you can apply "waves" or "perspective" or "convergence layer" effects to explain deviation from that baseline. And round earth defenders will do that too. The challenge is to see which camp can explain those deviations better and make reasoned adjustment from the baseline to get closer to the observation.

Doesn't this make more sense than both sides just shouting at each other and broadly asserting claims of proving their side and debunking the other?

[MCToon]

Bobby, I love this idea.  Start with predictions for interested models.  Perform a test, for each set of predictions see if the predictions match the observations.  Use that data to draw conclusions.  This is science.

I hope we can get some consensus on the predicted flat earth predictions.  Maybe JRow could include a dual earth prediction to add in a third set?

[Bobby Shafto]

Firstly, there is a limit to resolution of the eye, which is less than 1/60th of a degree. Rowbotham describes the matter in the Sinking Ship Chapter. This limitation may make it appear if some bodies merge in the distance. Those bodies can, however, be restored with a telescope, which is the cause of the accounts of restored hulls in the book Zetetic Cosmogony and Cellular Cosmogony, and why several Youtube authors claim to be able to restore hulls.

I derived values in the flat earth column in this table from that description, calculating based on this naked eye resolution. Telescopic photo lenses and telescopes would necessarily reduce these numbers, and the images I'd like to present are from a camera with a zoom lens. But I'd like to move forward and so rather than trim them to 0, let's go with them and make this the flat earth baseline. If this should later prove to be objectionable, we can revisit:




So the next step is to look at some observation and evaluate what we are seeing. I hadn't seen this video until this weekend when someone pointed me to an old discussion topic (from before I poked my head in) that discussed this video, published by YouTuber Mathias Kp about 2 and a half years ago:



I think it's obviously pro-spherical earth, but there is no narration. Just images and data from which we might be able to draw some conclusions or test our theories.

One of the difficulties of analyzing photos at or near the horizon is judging vertical distance/elevation, which usually involves some guesswork and best guess estimation to work out the trigonometry or making indices or finding reference points. What I thought was unique about this was the feature of the structure itself, which is segmented, providing a potential gauge that reduces the estimating error. The videographer refers to the sections as "blocks" and with a documented height and 9 of these "blocks" along with the roof structure and the ground-level floor, we have a pretty good means of knowing how much of the structure is visible and how much is hidden. Why hidden is the ultimate objective, but both flat and convex earth can make their strongest cases for explaining what is recorded in the images.

Neither should claim "victory" simply because the geometric prediction of the other isn't exhibited. If we agree on what we're seeing, then we can argue over why we are seeing it and which earth topography (and it's assorted "magic wand" explanations for why the values might deviate from baseline) is the better fit.

[Bobby Shafto]

This is a graphic the video author constructed:


And here is something I've made to offer a first suggestion as to elevation heights where each image appears to be "cut-off."

(updated to correct significant errors)


 If anything looks out of whack, please chime in.

[Bobby Shafto]

Here as a set of data sheets based off of my tower estimates: one for curved earth and one for flat, using the baseline values in the earlier table:

(updated to correspond with fixed tower graphic above)


I'll let this percolate. The idea is to refine these before moving on to explain the deltas. Of course, flat earth proponents will naturally look to reduce the estimates to bring them closer to the baseline so that the remaining amount that appears hidden will be easier to explain. Similarly, round earth proponents will likely want to push the height estimates up to make the shortfall from the baseline numbers explicable by its own factors for adjustment. That's all understandable, but remember that the idea isn't to preserve a belief but to try to determine a truth as best we can.

The observed values fall between the lower flat earth values and the higher round earth values. Before we try to argue for why they are more or less than a baseline prediction, try to look objectively and see if these observed estimates are at least correct so that the real contest isn't over what we're seeing but why. 

[QED]

It's not a simple distance-feet chart. There are several phenomena going on with the Sinking Ship Effect.

Firstly, there is a limit to resolution of the eye, which is less than 1/60th of a degree. Rowbotham describes the matter in the Sinking Ship Chapter. This limitation may make it appear if some bodies merge in the distance. Those bodies can, however, be restored with a telescope, which is the cause of the accounts of restored hulls in the book Zetetic Cosmogony and Cellular Cosmogony, and why several Youtube authors claim to be able to restore hulls.

Secondly, in the chapter Perspective at Sea Rowbotham describes that often times on the environment of the sea bodies can be hidden by waves, swells, or bulges of the water (perhaps tidal?). Sometimes bodies are obscured, and at other times they are visible. Examples are given of the Nab Light ship and the Eddystone Lighthouse, which were at various time visible and invisible. During these times a telescope cannot restore the hull.

The affect of the water may be associated with the winds. In the chapter On The Dimension of Ocean Waves Rowbotham states the following:

It is well known that even on lakes of small dimensions and also on canals, when high winds prevail for some time in the same direction, the ordinary ripple is converted into comparatively large waves. On the "Bedford Canal," during the windy season, the water is raised into undulations so high, that through a powerful telescope at an elevation of 8 inches, a boat two or three miles away will be invisible; but at other times, through the same telescope the same kind of boat may be seen at a distance of six or eight miles.

During very fine weather when the water has been calm for some days and become as it were settled down, persons are often able to see with the naked eye from Dover the coast of France, and a steamer has been traced all the way across the channel. At other times when the winds are very high, and a heavy swell prevails, the coast is invisible, and the steamers cannot be traced the whole distance from the same altitude, even with a good telescope.

Instances could be greatly multiplied, but already more evidence has been given than the subject really requires, to prove that when a telescope does not restore the hull of a distant vessel it is owing to a purely special and local cause

Rowbotham generally recommends that the experiment is conducted on calm days, on the most calm body of water that can be found. I would say that the amount hidden has more to do with that than than "this is how much is hidden at this distance."

Unfortunately, these claims are easily proven mistaken by using your own telescope. On the calmest days, one can easily see that the ship bows remain below the horizon when viewed from a distance. This is in contrast to Rowbotham's claim that the entire ship should manifest upon magnification if FET was viable.

[Bobby Shafto]

Tom Bishop (for flat earth) and I (for globe earth) may be the only two spending any time on this.

But on the off chance that someone else is out there (preferably another flat earther) digging in, here's a video I found by the same YouTuber (Mathias KP) in which he details how he analyzed the vertical dimensions of the Turning Tower in Malmö, Sweden. (Starting at the 3:55 mark)



It's more laborious than I would ever attempt, but he does seem to be exacting.
I captured the portion of his spreadsheet that shows his elevation figures by floor or vertical element (in meters):

 

He starts his elevation count with height above mean sea level (1.98m or 6.5'), something I had overlooked.

[stack]

The observed values fall between the lower flat earth values and the higher round earth values. Before we try to argue for why they are more or less than a baseline prediction, try to look objectively and see if these observed estimates are at least correct so that the real contest isn't over what we're seeing but why.

Great stuff Bobby. The data estimates look about as accurate as you can get for a baseline. I'd say we should start examining the why. Seemingly RE would start to factor in refraction to close the delta gap. I'm not sure what an FE factor would be. 

[Bobby Shafto]

I'd like to give Tom more time. I know he's working on his own approach to height estimates. He had a post up for a bit but deleted it due to a small error. I did see it and it alerted me to some more significant errors I had made, which prompted me to correct and and edit my posts. So the dialogue is good. I don't really want this to be a soliloquy.

But I do think we are "good enough for government work" (as the saying goes). It doesn't have to be gnat's arse accurate. I think within +/- 5' is fine for what I was proposing. The trickier part is, once we reach consensus on ballpark floor tower heights, estimating where the sight line in each of the observations is to determine the value for how much of the structure is missing from view. That's the number we really want, and something within 10' is about as good as I would probably hope for.

I do think the estimates above are good, but Tom or someone might see something or think of some consideration that I'm missing, so I'd like to wait a bit.

[stack]

Just trying some things out:

Using F2 in the illustration above, we have an RE delta of calculated hidden versus measured hidden of -75 ft.

If refraction were calculated, according to the Walter Bislins earth curvature calc, we would need to factor in approximately 0.189 of a refraction value to erase the -75 foot delta.

http://walter.bislins.ch/bloge/index.asp?page=Advanced+Earth+Curvature+Calculator

What I’m missing are the values that would comprise a 0.189 refraction value.

_______________

Using F2 in the illustration above, we have an FE delta of calculated hidden versus measured hidden of 205 ft.

If refraction were calculated, according to the Walter Bislins earth curvature calc, we would need to factor in approximately 0.90 of a refraction value to erase the 205 foot delta.

What I’m missing are the values that would comprise a 0.90 refraction value.

_______________

I could be doing this all wrong, let me know.

[Bobby Shafto]

Just trying some things out:

Using F2 in the illustration above, we have an RE delta of calculated hidden versus measured hidden of -75 ft.

If refraction were calculated, according to the Walter Bislins earth curvature calc, we would need to factor in approximately 0.189 of a refraction value to erase the -75 foot delta.

http://walter.bislins.ch/bloge/index.asp?page=Advanced+Earth+Curvature+Calculator

What I’m missing are the values that would comprise a 0.189 refraction value.

If atmospheric refraction is all that is involved in accounting for the deviation from a geometric "hidden-by-curve" calculation, then yes. The challenge for a globe earth advocate is to make a case for how atmospheric refraction can make the earth seem a little flatter, enough to account for 75' of target elevation being visible that would otherwise be hidden in that particular case.

A refraction value of 0.189 is greater than the standard value of 0.17 so that means light would have to have been a little super-refracted, meaning the bending toward earth of the light a little more extreme.

Using F2 in the illustration above, we have an FE delta of calculated hidden versus measured hidden of 205 ft.

If refraction were calculated, according to the Walter Bislins earth curvature calc, we would need to factor in approximately 0.90 of a refraction value to erase the 205 foot delta.

What I’m missing are the values that would comprise a 0.90 refraction value.

I could be doing this all wrong, let me know.

For FE the challenge is different because I don't know how you account for atmospheric refraction over a flat plane. Bilsin's tool doesn't apply refraction to its FE model. Light propagation can certainly be affected by changing air (atmolayer) conditions across the line of sight, but since there is no curve on a flat plane, the air doesn't curve according to a "standard" that follows the curvature of the earth, so there's no standard index as such. There is thus 0' hidden target for all distances and observer elevations for a FE model, no matter the refractive index in a GE model. You need some other tool or set of explanations to work out the delta in predicted vs observed hidden heights for FE.

I chose not to start FE out at 0' hidden for all ranges and observer altitudes. It's not much, and it may not be right, but I worked out a simple formula from Earth Not a Globe's perspective and visual acuity explanations to derive baseline hidden values that are not found in the Bilsin tool. These may be exaggerations for FE since the observations came from using a telephoto lens and not the naked eye, but I included them anyway; but they are relatively small values.


I put forth this challenge, because I don't know how the FE model reasons to account for the hidden value. The predominant FE approach I've seen to these hidden target height observations is to critique globe earth based on its geometric calculations not matching what is observed. Little attention is paid to why geometric calculations for a flat earth don't match what is observed.

I'm a globe defender, so I can argue for the globe. I can't do that for a flat earth, thus I hope Tom or someone will accept that challenge.

[stack]

A refraction value of 0.189 is greater than the standard value of 0.17 so that means light would have to have been a little super-refracted, meaning the bending toward earth of the light a little more extreme.

Using the std 0.17 would put F2 at 212 with a -68 delta

For FE the challenge is different because I don't know how you account for atmospheric refraction over a flat plane. Bilsin's tool doesn't apply refraction to its FE model. Light propagation can certainly be affected by changing air (atmolayer) conditions across the line of sight, but since there is no curve on a flat plane, the air doesn't curve according to a "standard" that follows the curvature of the earth, so there's no standard index as such. There is thus 0' hidden target for all distances and observer elevations for a FE model, no matter the refractive index in a GE model. You need some other tool or set of explanations to work out the delta in predicted vs observed hidden heights for FE.

Got it.


I guess a next step might be to compare the Turning Torso height calculations in the theodolite video to yours and then maybe factor in the atmospheric values he gathered to derive a refraction value. Though those values were most likely from a different day as the first video. I can take a look at the height calcs.

[Bobby Shafto]

I guess a next step might be to compare the Turning Torso height calculations in the theodolite video to yours and then maybe factor in the atmospheric values he gathered to derive a refraction value. Though those values were most likely from a different day as the first video. I can take a look at the height calcs.

I suppose we've given enough time for review. Here's what I derive from Mathias' measurements:



His numbers include ground elevation height, which I forgot; and all of his measurements come out a little higher than mine.

But that favors the GE case, so I'll take the handicap and stick with the lower estimates, which I've depicted with the red arrows on these graphs;



The GE straight geometric curve calculator hidden footage is indicated by the green arrows, and the FE baseline hidden footage by the blue arrows.

If the observed (red) arrow needs to be adjusted up or down, we can talk it through. Obviously, up helps GE's argument; down helps FE's argument.

The debate can then begin with GE making the case for adjustments to the green arrows downward for whatever reasons are cogent while FE makes the case for adjustments upward of the blue arrows with whatever reasons (such as the ones Tom made a few days ago in this topic).

[iamcpc]

I apprehend all that, but what i'm asking for is akin to the pure geometry of the earth curve calculator that doesn't included variables like atmospheric effects or surface irregularities (hills, ocean swells, structures. etc.)

Well you are using images, observations, and measurements which are affected by all of those things.  You can't compare Apples (calculations which outright ignore all of these variables) to oranges (observations which are heavily influenced by all of these variables)

Is it fair to say that on a flat earth, there should be no hidden elevation other than what is caused by such obstructions as you mentioned. If there is no dense air, no fog/smoke/particulates/vapor, no waves (or what not)...all hidden values would be 0 feet.

I don't think that this is because the observed earthly horizon does exist on a perfectly flat/spherical line, does not exist in a vacuum, and is limited by the ability of the tool/person to perceive.

So the next step is to look at some observation and evaluate what we are seeing. I hadn't seen this video until this weekend when someone pointed me to an old discussion topic (from before I poked my head in) that discussed this video, published by YouTuber Mathias Kp about 2 and a half years ago:


I think it's obviously pro-spherical earth, but there is no narration. Just images and data from which we might be able to draw some conclusions or test our theories.

You can't claim these are pro spherical without first identifying (or attempting to identify) variables between each image like
-Elevation of the camera
-Wind speed
-Humidity
-Time/date of image
-Barometric pressure
-Atmospheric composition
-amount of cloud cover
-type of camera
-type of lens
-camera and lens condition
-average wave height on the water


furthermore the camera appears to be held in a hand vs on something like a tripod which also calls into question if any sort of human movements could (or could not) possibly create different results.

[Bobby Shafto]

You can't claim these are pro spherical...

The video is pro-spherical. I'm not saying (yet) that the images are pro-spherical.

 

...without first identifying (or attempting to identify) variables between each image like

Haven't gotten to the sphere/flat debate yet. Still just resolving what we're seeing. Not why we're seeing it.

But if these matter, they matter for both pro-spherical AND pro-flat claims. Flatness isn't the default.


-Elevation of the camera: that's what the elevation figures are. Tripod not specified.
-Wind speed: westerly 8-12 knots
-Humidity: 67%
-Time/date of image: included in table above
-Barometric pressure: 29.78" Hg
-Atmospheric composition: up to flat or globe earth defender to estimate
-amount of cloud cover: passing clouds
-type of camera: Canon Powershot SX60 HS
-type of lens: integrated 21 - 1365mm
-camera and lens condition: unspecified

...furthermore the camera appears to be held in a hand vs on something like a tripod which also calls into question if any sort of human movements could (or could not) possibly create different results.

Make that argument then, if it helps whatever side (flat or sphere) case you wish to argue. But if you do so, explain why and how it figures into the analysis.

[iamcpc]

It's not a simple distance-feet chart. There are several phenomena going on with the Sinking Ship Effect.

Firstly, there is a limit to resolution of the eye, which is less than 1/60th of a degree. Rowbotham describes the matter in the Sinking Ship Chapter. This limitation may make it appear if some bodies merge in the distance. Those bodies can, however, be restored with a telescope, which is the cause of the accounts of restored hulls in the book Zetetic Cosmogony and Cellular Cosmogony, and why several Youtube authors claim to be able to restore hulls.

Secondly, in the chapter Perspective at Sea Rowbotham describes that often times on the environment of the sea bodies can be hidden by waves, swells, or bulges of the water (perhaps tidal?). Sometimes bodies are obscured, and at other times they are visible. Examples are given of the Nab Light ship and the Eddystone Lighthouse, which were at various time visible and invisible. During these times a telescope cannot restore the hull.

The affect of the water may be associated with the winds. In the chapter On The Dimension of Ocean Waves Rowbotham states the following:


Rowbotham generally recommends that the experiment is conducted on calm days, on the most calm body of water that can be found. I would say that the amount hidden has more to do with that than than "this is how much is hidden at this distance."

When all images are taken at a similar time of day, during similar wind conditions, similar water conditions, similar atmospheric pressure and through a telescope/camera which negates perceptive abilities of the human eye (which Bobby has already addressed) etc many of these things are moot. The round earth model predicts observations and measurements patterns based on a mathematical calculation.

where can we find some examples of flat earth viewing distance calculators/formulas to compare the predictions of a flat earth model to the predictions of a round earth model?