Earth's Curve Calculator

They are all close (depending on what you are viewing, distance and size). The closer they are, the less accurate it is. The problem is, it's quite complicated, so you can't really give a simple explanation.

Where's the debate?
 
The above point is being discussed right now on a YouTube panel debate. From listening to them, it seems that it would really benefit to define "close" more specifically. One person thinks "close" means six inches but not six feet; another thinks six feet is "close". And there may be others who think twenty feet is "close".

How close is "too close" depends on how thick the increased density gradient is above the water, and how much of your line of sight goes through the region of increased density gradient.

For example, in my location, at least during the cooler months, standard refraction seems to nearly always hold true. In one case I measured the dip of the horizon with a theodolite from 56 feet up - and I measured 0.124 degrees - which very close to the standard atmospheric refraction globe model figure of 0.123 degrees.

However, we know that Joshua Nowicki in his Chicago Skyline time lapse videos shows sometimes a drastic refraction even from a high vantage point of nearly 200 feet as I recall -- and while looking at a target that is a thousand feet tall.

Now it doesn't mean that the region of increased density gradient is all that thick over the water (Although it could be) - but the view of the distant skyline fits into a pretty narrow space at the point in the middle of the lake, so the rays of light between the target and the observer pass pretty close to the water in the middle.

And if the density gradient is enough, the light path can spend quite a bit more time in that region close to the water.

In my region, I don't see much in the way of strong refraction, but one time shooting a theodolite 6 ft above the water, the horizon was slightly above eye-level - which means I was actually getting a pretty strong refraction within 6ft of the water.
 
The above point is being discussed right now on a YouTube panel debate. From listening to them, it seems that it would really benefit to define "close" more specifically. One person thinks "close" means six inches but not six feet; another thinks six feet is "close". And there may be others who think twenty feet is "close".

I think it's not just how close the observer/camera is to the water, but also how many degrees the distant object is above the horizon. Nearly all the FE claims about seeing farther than the calculator predicts, are showing distant objects (islands, mountains, ships, buildings, etc..) that appear less than half a degree above the water. That's the region where the sun distorts and flattens out right before sunset. This produces photographic "proof", like the grainy Loch Ness Monster photo, that can be debated ad nauseam.
 
The point has come up that labeling one set of results as "geometric" allows the inference that the refracted results are not geometric, although they are.
 
Would it be possible to add a knob to your curve calculator to adjust the number of significant digits in the answers?
I ask because I would like to be able to challenge flat earthers if they think they could tell if one end of a 100m track is higher than the other by looking from either end.

Currently in your calculator if I calculate for a 6ft man viewing 100m I get a (surface level) Geometric Drop = 0 meters (I'd like more precision)

I presume it would be such a small number that it would be ridiculous to suggest you could see it with the naked eye.
I think this would be a decent answer to "why does the horizon look flat?"

Perhaps this a better scenario but is a bit harder to explain...

Place a person off to the side of the middle of a 100m track, 100m from each end, and ask which end is higher.
Then have an item to imagine which is equivalent to the calculated "drop" and/or "saggita" and ask if they can tell which end of the track has a "human hair" height difference (if that's the equivalent "drop"). or a paint layer. or a tin foil layer, or... ???
(or ask how much higher is the middle of the track than the ends)
This would illustrate how slowly the earth's surface curves, and how unreasonable it is to suggest you could see that with the naked eye.
 
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