I think that's an admirable pursuit, to try to bring credibility to the flat earth side of things. I've generally reached a stage where I don't mind people believing something incorrect - but I do like it if they at least try to use the correct calculations.

I actually think most flat earthers do believe there is mathematics to describe a sphere, but just that many of them don't know how to apply it properly, or which equation they should use for which measurement.

That's probably why I describe "8 inches per mile squared" as, for all intents and purposes, as far as the flat earth discussion is concerned, "useless".

I mean, when would you actually use that?

"8 inches per mile squared" can be used for any situation where you can use C^2=A^2+B^2 if exact accuracy doesn't matter and it's a sight distance under 1000 miles.

It's simpler as it removes a bunch of constants and still gives surprising accuracy.

By way of comparison, the dip at 1000 miles according to C^2=A^2+B^2 and 8 inches per mile squared is as follows:

656,525ft for C^2=A^2+B^2, and

666,667ft for 8"/mi^2

That is an error of only 1.5%. And that's at a thousand miles which of course is usually too far to clearly see objects unless they are super bright.

For more reasonable distances, like 100 miles:

6667.287ft for P's T, and

6666.667ft for 8"/mi^2

The error there is less than 0.01%!

So for near distances, like a hundred miles, it's very accurate -- its error is much less than other errors like leveling errors or atmospheric refraction etc.

So yeah, a simple easy accurate shortcut can be real handy when a glober and I are standing on a hill looking at another hill 100 miles away, and we're talking about whether the far hill appears where it should appear, or if it's about 6700 feet too low or not.

It's important to be able to keep things simple so nobody gets lost in the math. Right?