I want to be clear that I’m not 100% certain of what I’m arguing here and so I welcome the truth even if it contradicts my understanding but I believe I’m right. One thing to keep in mind is that these angular size corrections are not applicable in any other circumstance; it only applies to calculating the “hidden” amount. The point of this video was to create a ratio that will translate a distant apparent size of an object into a measurement in feet, because the angular size (degrees) is inversely proportional to the distance in feet.
Plane surveyors wouldn’t learn the angular size reduction as no one calculates blockage from a visual perspective; it has no on-the-spot ground application. Mathematicians probably would never have learned the angular size reduction as well; we are essentially combining curvature drop, visual angles, the Pythagorean Theorem, perspective, and angular size into one formula. I believe this is all new territory but relies on common sense.
If you are at 6 feet and zoom in with the camera, the horizon will be 3 miles away from you under the dimensions of the globe. http://www.ringbell.co.uk/info/hdist.htm. That 3-mile mark constitutes the top of the alleged bulge from the observer’s perspective. That’s an unquestionable fact of the globe model. I can zoom in all I want with a telescope or ultra-zoom camera but I will not see anything flat (like water) beyond the 3-mile mark as it would be obscured by the purported bulge of the earth. I think everyone must agree with this first assertion (maybe some might claim standard refraction would put the refracted horizon at 3.2 miles instead of 3 miles but that’s really irrelevant for this discussion).
Just like the picture of the man at 0:26 the video above. This is perspective we witness on a daily basis but we rarely ponder what’s happening. I can take an ultra-zoom camera and zoom in all I want on the man’s head, but because he has a larger respective angular size being closer, he will block the more distant wall even though the wall is actually much taller. There is the actual size of the distant object and the angular or apparent size of the object based on distance. Again, I think everyone can agree so far as this is all common sense.
I think it’s easier to think of Denali and the alleged bulge as 2D cutout pictures but at the same actual height but no depth. The supposed bulge height would, at 135 miles and a 6-foot observer, would be 3,038 feet high. If you instead imagine the bulge as a wall and place the 20,310-foot Denali cutout just a foot beyond the bulge wall, the wall would understandably block 3,038 feet.
That’s how the curvature calculators work but the hidden becomes 11,616 feet based on the angle from the observer.
Now, presuming the world is flat, move the Denali cutout 5 miles, 10 miles, 100 miles, and 132 miles beyond the wall. The wall remained stationary but Denali just shrunk to 2% the size it was at the beginning. Do you see how the wall would quickly block Denali?
Look at the picture of Denali again and see how the trees block roughly 1/3 of Denali. You can see from the closer pictures that the rest of Denali is hidden behind the trees.
Remember at 135 miles, Denali would have an apparent size of only 500 feet. Now, the trees blocking 1/3 of Denali makes perfect sense. There’s no difference between those trees and the claimed bulge of the earth’s curvature. You can zoom in on the trees and increase their angular size (along with Denali) but the ratio blocked by the trees will remain exactly the same. The only time the bulge wouldn’t have a different effect is if the bulge wall was moved with Denali at the same distance. Then they would shrink together but that wouldn’t happen with the globe.
Maybe it’s easier if you imagine the wall as 500 feet tall and unrelated to any bulge height to separate it from curvature. Can you see how Denali will shrink behind that 500-foot wall until it disappears (135 miles later) and it has nothing to do with curvature?
The angular size reduction is a globe killer as the oft-repeated claim that refraction levels the globe visually is 100% impossible to the extent to make Denali disappear after only 50 miles distance.