The tray seam, shown as an arc in the screen capture, dips 3 pixels below the long straight blue line. Were it the same width as the image, 1117 pixels, it would dip (1117/715) x 3 = 4.6 pixels. This is still sustantially less than the estimated 23 pixels the horizon rises above the straight red line, in fact about a fifth of the rise.
This continues not to be how geometry works. I'm sorry, but there's nothing more I can do to help you with this. The ratio between the "line" and "dip" have nothing to do with the eccentricity of these two arcs. I can keep pointing out that you're wrong and explaining why you're wrong, but in the end of the day you won't accept it, because you're not interested in being correct - you just want to confirm your preconceptions.
But hey, let's keep on keeping on. Let's illustrate the issue with my previous example:
The span of the white frame is 590 pixels, and the "dip" (sagitta) of the first arc is 14 pixels.
The second arc has a span of 195 pixels and a sagitta of 1.5 pixels.
You assert that I can make these comparable through a simple ratio. Let's do that.
1.5*590/195 = 4.53
As you can see, by your logic, I should expect that the arc towards the bottom of the image is much less curved than the one closer to the middle. However, even a cursory visual comparison will reveal that not to be the case. In reality, when measured correctly, the sagitta of the second arc is 23 pixels. Your logic fails.
The physical reason behind your error is that (as you astutely pointed out) the effect is more pronounced the further away from the centre of the frame you are. By sampling the curvature from just the (horizontal) middle of the frame, you fail to account for the significant increase in effect towards the edges.
You also entirely ignored the many issues with your "23 pixels" estimate - the line you're using as your reference point does not touch the horizon on either edge of the frame (or, indeed, at all). When adjusted appropriately, the correct sagitta is more akin to 10 pixels.
You already know how to correctly verify your claim. If you choose to "deliberately refrain" from proving your position, then I don't think we have much left to discuss.
I repeat the general point about barrel distortion being important near the edges of an image, whereas it's very slight near the middle of the same image.
Terms like "very slight" and "important" continue to be meaningless. The supposed curvature of the horizon in the image you're focusing on is "very slight" and "not important" and yet here you are fixating on it.
The lens was an 18-135mm zoom
Do you realise how extremely wide this range is, and how useless that statement is as a result? An 18mm focal would be bordering on a fisheye lens, which this obviously isn't. A 135mm focal wouldn't capture anything remotely close to this wide an area. Before you can perform your experiment, you need to know the actual focal of the lens at the time of filming, not what the particular device is capable of.
I deliberately do not intend to process the image for distortion in Lightroom or any other program, because we have both seen many claims over the years that this, that or another image can't be trusted as it's been "Photoshopped" and we both know the pointlessness of such arguments.
Yes, as I pointed out many times, there are more severe issues at play here than you trying to circumvent simple optics and geometry. Nonetheless, my focus for now is on pointing out these two failures, and altering the photograph to more accurately represent what you
should see from an altitude of 27km would be beneficial to you.
Yours must be a thankless task, moderating forums populated mostly by people who doubt or outright reject the flat earth hypothesis.
Oi now, governor. There is absolutely no need to get personal, innit.
Another week and another sceptic with experience and real-world knowledge asks difficult questions
Yes, with insight and expertise like referring to a lens as an "18mm-135mm zoom" when trying to determine its barrel distortion, claiming that the Earth is round but 5 times smaller than in RET, or demonstrating your excellent knowledge of geometry as you did above, you're guaranteed to blow me away.
EDIT: I note that I've been referring to these curves as "arcs" which may be a bit hasty - they could be arcs, but they might not be depending on the specific situation. I'll leave the phrasing as-is since it doesn't particularly affect any of the underlying reasoning, but it's only fair that I highlight that inaccuracy.